Answer:
y=4
x=61
Step-by-step explanation:
the 2 lines on the side shows that they are equal to each other.
12y+3=51
12y=48
y=48/12
y=4
There are 100 degrees in a triangle and the little curve shows that the angle next to 53 degrees is 63.
so:
x+56+63=180
x+119=180
x=61
By convention, we use a bar graph when the groups on the x-axis (horizontal axis) are represented on a ________ scale; we use a line graph when the groups on the x-axis are represented on an ________ scale.
By convention, we use a bar graph when the groups on the x-axis (horizontal axis) are represented on a categorical or discrete scale; we use a line graph when the groups on the x-axis are represented on a continuous or numerical scale.
A bar graph is commonly used to display categorical or discrete data, where the groups or categories on the x-axis are distinct and separate from each other.
For example, the x-axis could represent different types of fruits or months of the year. Each category is represented by a separate bar, and the height of each bar corresponds to the frequency, count, or value associated with that category.
On the other hand, a line graph is typically used to represent data on a continuous or numerical scale. The x-axis represents a continuous range of values, such as time, temperature, or distance.
Each data point is plotted as a dot or marker on the graph, and the points are connected by lines. This type of graph is useful for showing trends, patterns, or changes over time or across a continuous range.
The choice of using a bar graph or a line graph depends on the nature of the data and the purpose of the visualization. Categorical data is best represented using a bar graph to emphasize the distinct categories, while numerical or continuous data is better suited for a line graph to visualize trends and relationships.
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Which values of x and y make RAPT a parallelogram?
The values of x and y that make RAPT a parallelogram are;
x = 15 and y = 25
How to find the angles of a Parallelogram?Angle T and angle P are supplementary angles by parallel lines. Thus they sum up to 180 degrees and we have;
3x + 10 + 8x + 5 = 180
11x + 15 = 180
11x = 165
x = 15
T = 55°
P = 125°
Likewise R and T are supplementary angles by parallel lines and so we have;
55 + 5y = 180
5y = 180 -55
5y = 125
y = 25
R = 125°
A must be 55° since the angles add up to 360°.
R + A + P + T =
125 + 55 + 125 + 55 = 360°
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{[4 (2+3)2] - 15) + 5
Answer:
4
Step-by-step explanation:
this is the way I would do it
{[4(2+3)2]-15}+5
{[4(5)2]-15}+5
{[4+10]-15}+5
{14-15}+5
-1+5
4
2. Please complete both Parts A, B, & C below.
a. These triangles are proportional. Identify which sides match up between the two triangles. Please note sides are named from point to point so for instance the length 40 on triangle ABC is referred to as side AB. Make sure to identify all three pairs.
b. Set up fractions with your side pairs to show proportionality. Do they all simplify down to the same fraction? If not please go back to Part A and remember that shapes can be rotated or reflected. Make sure to show your work demonstrating that the fractions are proportional.
c. Are the triangles similar? If so explain why. If not, explain why not. Your work from Part A & B may help with this.
i need is asap
Answer:
a)ab and yz, ac and xy, bc and xz
b)yz = xy = xz 30 = 37.5 = 45 3 = 3 = 3
ab ac bc 40 50 60 4 4 4
c)they are similar because all sides break down to ¾
Step-by-step explanation: i did this on my test
a) The pairs of proportional triangle is
AB and YZ,
AC and XY,
BC and XZ
b) The fraction of side is
YZ / AB = XY / AC= XZ / BC = 3/4.
c) Yes the similarity of Triangle.
What is Similarity?Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion. The " sign here denotes the resemblance of triangles.
In Triangle ABC and YZX
a) So, the pairs of proportional triangle is
AB and YZ,
AC and XY,
BC and XZ
b) The fractions with your side pairs is
YZ / AB = 30 / 40 = 3/4
XY / AC = 37.5 / 50 = 3/4
XZ / BC = 45/ 60 = 3/4.
c) As, the ratio of sides are proportion.
So, by SSS similarity criteria the triangles are similar.
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You are considering purchasing a consol that promises annual payments of $4. a. If the current interest rate is 3 percent, what is the price of the consol? Instructions: Round your answer to the nearest penny (2 decimal places). The price of the consol is $ b. You are concerned that the interest rate may rise to 4 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them. Instructions: Round your answer for dollar amounts to the nearest penny (2 decimal places ) and answers for percentages to the nearest tenth (1 decimal place) The new price of the consol would be $ The price of the consol falls by 7% and the interest rises by 7% c. Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return? Instructions: Round your answer to the nearest tenth (1 decimal place) Your holding period return is %
a. The price of the consol is approximately $133.33.
b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.
c. Your holding period return is approximately -49.99%.
a. The price of the consol can be calculated using the formula for the present value of a perpetuity:
Price = Annual Payment / Interest Rate
In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:
Price = $4 / 0.03 ≈ $133.33
Therefore, the price of the consol is approximately $133.33.
b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:
New Price = Annual Payment / New Interest Rate
Substituting the values, we get:
New Price = $4 / 0.04 = $100
The percentage change in the price of the consol can be calculated using the formula:
Percentage Change = (New Price - Old Price) / Old Price * 100
Substituting the values, we have:
Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%
The percentage change in the interest rate is simply the difference between the old and new interest rates:
Percentage Change in Interest Rate = (4% - 3%) = 1%
Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.
c. The holding period return can be calculated using the formula:
Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100
The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:
Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67
Substituting the values into the holding period return formula:
Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%
Therefore, the holding period return is approximately -49.99%.
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Which of the following is a solution to z2 + 2 < 6?
0, 2, 4, -2, or -4
z = - 4, represents the solution of the inequality → z² + 2 < 6.
What is inequality?An inequality is used to compare numbers or expressions. For example -
2x + 4 > 6 4x + 6 < 8 y > 9 x < 1
All the above expressions mentioned above represent inequalities.
Given is the inequality as -
z² + 2 < 6
The given inequality is -
z² + 2 < 6
Subtract {2} from both side we get -
z² < 4
z < ± 2
Therefore, z = - 4, represents the solution of the inequality → z² + 2 < 6.
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Please help me respond this
Option 2 is correct that is 1.79
What is third quartile ?When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
The quartiles formula is as follows:
Upper Quartile (Q3) = 3/4(N+1)
Lower Quartile (Q1) = (N+1) * 1/3
Middle Quartile (Q2) = (N+1) * 2/3
Interquartile Range = Q3 -Q1,
1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.
Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.
The data set has 8 values.
hence, n = 8; third quartile: 3/4 (n+1)th term
Q3 =3/4 of a term (9) term
Q3 =27/4 th term
Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)
equals 1.76
Thus Q3 is 1.76 that is option 2
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Can someone help me with this Question.
The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.
\(P=3W+D\)A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.
B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.
\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.
That leaves \(27-14=13\) matches. These represent the matches team lost.
Finally, the answers are below.
\(A)29\)
\(B)13\)
Answer:
a) 29 points
b) 13 losses
Step-by-step explanation:
You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.
A 8 wins, 5 drawsThe number of points the team has is ...
P = 3W +D
P = 3(8) +(5) = 29
The team has 29 points.
B 54 pointsYou want the number of losses the team has if it has 54 points and 12 draws after 39 games.
The number of wins is given by ...
P = 3W +D
54 = 3W +12
42 = 3W
14 = W
Then the number of losses is ...
W +D +L = 39
14 +12 +L = 39 . . . substitute the known values
L = 13 . . . . . . . . . . subtract 26 from both sides
The team lost 13 games.
__
Additional comment
In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)
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If x+4/4 = y+7/7 then x/4 =___.
(Number 9 is the one I need an answer for)
Answer:
4th answer is correct
Step-by-step explanation:
First, let us make x the subject.
\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)
Use cross multiplication.
\(\sf 7(x+4)=4(y+7)\)
Solve the brackets.
\(\sf 7x+28=4y+28\)
Subtract 28 from both sides.
\(\sf 7x=4y+28-28\\\\\sf7x=4y\)
Divide both sides by 7.
\(\sf x=\frac{4y}{7}\)
Now let us find the value of x/4.
To find that, replace x with (4y/7).
Let us find it now.
\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)
name the rule and list the next three terms in the pattern 28 ,20 ,24, 16, 20...
The Solution.
The Rule is:
Subtract 8 to get the next term, and then add 4 to get the next term, and keep repeating this process.
So, the next three terms are:
\(\begin{gathered} 20-8=12 \\ \text{The first is 12} \end{gathered}\)The next term will be:
\(\begin{gathered} 12+4=16 \\ \text{The second term is 16} \end{gathered}\)The next term will be:
\(\begin{gathered} 16-8=8 \\ \text{The third term is 8} \end{gathered}\)Hence, the next three terms are 12, 16, and 8.
5/2x+1 + 8/2x+1, x≠-1/2
\( \frac{5}{2x + 1} +\frac{8}{2x + 1}\)
\(= \frac{5 + 8}{2x + 1} \)
\(= \frac{13}{2x + 1} \)
in a triangle, PQR, Q= 72 degree, R= 32 degree and PR= 12. find PQ.
Answer:
PQ=6,69 units
Step-by-step explanation:
b/Sin32°=c/Sin72°
PQ/Sin32°=12/Sin72°
PQSin72°=12Sin32°
PQ=12Sin32°/Sin72°
PQ=6.69 units
By the concept of the sine rule of triangles the value of PQ is 6.6 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sine rule of a triangle states a/sinA = b/sinB = c/sinC.
Given, In a triangle PQR, Q= 72 degrees, R = 32 degrees, and PR= 12.
Let, q is the opposite side to ∠Q and r is the opposite side to ∠R.
Therefore,
q/sinQ = r/sinR.
12/sin72 = r/sin32.
12/0.951 = PQ/0.523.
PQ = (12×0.523)/0.951.
PQ = 6.6
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The number of students enrolled at a college is 16,500 and grows 4% each year. Based on this information determine the following
The number of students enrolled at a college is 16,500 and grows by 4% each year. To determine the growth rate of the number of students over a certain period, the formula for compound interest can be used. This information can be useful for college administrators in terms of planning and budgeting.
The compound interest formula can be used to calculate the growth rate of the number of students at the college. The formula is A = P(1 + r/n)^nt,
where A is the final amount,
P is the initial principal,
r is the interest rate,
n is the number of times the interest is compounded per year, and
t is the number of years.
In this case, P is 16,500, r is 4%, n is 1 (since the interest is compounded annually), and t is the number of years. For example, if we want to find the number of students after 5 years, the formula would be A = 16,500(1 + 0.04/1)^(1*5) = 20,221.
This means that the number of students will have grown by 3,721 over a period of 5 years.
This information can be useful for college administrators in terms of planning and budgeting. They can use this data to project the number of students that will be enrolled in future years and make decisions about staffing, resources, and facilities accordingly.
For example, if they know that the number of students will be increasing, they may need to hire more faculty and staff, or build new classrooms and dormitories. On the other hand, if the number of students is projected to decrease, they may need to make cuts in certain areas to balance the budget. Overall, understanding the growth rate of the number of students at a college is an important factor in effective planning and decision-making.
The number of students enrolled at a college is 16,500 and grows 4% each year. Based on this information we can determine the following
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the product of -9/17 and its reciprocal
the product of -9/17 and it's reciprocal will be 1
ow many incongruent primitive roots does 13 have? find a set of this many incongruent primitive roots modulo 13.
There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.
There are 12 elements of the group \(U_{13}\) , namely all the positive integers less than 13, as these are relatively prime to 13. Now, if there are primitive roots, there are \(\phi (\phi (n))\) of them. So we must compute \(\phi (12) = \phi (4\times 3) = \phi (4) \phi (3) = 2\times 2 = 4\) . There are 4 incongruent primitive roots.
To find them, take the powers each element in turn:
1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1 (2 has order 12, it is a primitive root)
Of course, the higher powers of 2 cannot be.
Proceeding this way, we get next get that 6, 7, and 11 are also primitive roots.
For example, the powers of 6 give: 6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1. We see 6 has order 12 and it is a primitive root. So 2, 6, 7, 11.
Therefore, There are 4 incongruent primitive roots and 6 has order 12 and it is a primitive root.
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Item 5 Which list shows the absolute values in order from least to greatest? Select each correct answer. |−17.12| , |−17.08| , ∣∣17.06∣∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| |−7.38| , ∣∣7.39∣∣ , |−7.41| |−3.07| , ∣∣−3.25∣∣ , |3.31|
Lets go over some stuff before we answer this absolute values make anything positive or make you count down from zero so then just imagine those numbers as positive.
ill put them as positives and then sort them here
3.07 3.25 3.31 |3.07 3.25 3.31 (Correct)
7.38, 7.39 , 7.41 | 7.38, 7.39 , 7.41 (Correct)
17.12, 17.08 17.06 | 17.06 ,17.08 ,17.12 (Wrong)
21.95 , 22.02 , 22.11 | 21.96 , 22.02 , 22.11 (Correct)
Answer:
|−17.12| , |−17.08| , ∣∣17.06∣wrong∣ ∣∣21.95∣∣ , |−22.02| , |−22.11| correct |−7.38| , ∣∣7.39∣∣ , |−7.41|correct |−3.07| , ∣∣−3.25∣∣ , |3.31|:correct
Economic The table how cot in dollar charged by an electric company for
variou amount of energy in kilowatt-hour
Electric company charges 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400.
Electric companies charge customers for the amount of energy they consume, measured in kilowatt-hours (kWh). The cost for each kWh can vary depending on the amount of energy consumed. An electric company may charge 7.50 dollars for the first 50 kWh, 10 dollars for the next 50 kWh, 13.50 for the next 100 kWh, 18.50 for the next 100 kWh, 20 dollars for the next 100 kWh and 25 dollars for any kWh over 400. The higher rate for higher usage reflects the fact that larger consumers of electricity tend to drive up the cost of production and distribution for the company. In addition, electric companies may offer discounts to customers who use more than a certain amount of electricity each month, encouraging conservation and helping to reduce costs.
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Complete Question is
Economic The table how cot in dollar charged by an electric company for
variou amount of energy in kilowatt-hour
Kilowatt-Hour Cost in Dollars
0-50 . 7.50
50-100. 10.00
100-200. 13.50
200-300. 18.50
300-400. 20.00
400+. 25.00
what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.
Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
\(A_{circle}=\frac{\pi d^2}{4}\)where:
d=diameter
\(\text{A}_{square}=d^2\)where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}\)Next, we plug in d=3:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}\)Therefore, the difference in areas is:
\(9-\frac{9\pi}{4}\)I need help to identify angle 2 please
Step-by-step explanation:
two angles are adjacent when they a common side vertex(corner point) and don't overlap.adjacent angles.angle ABC.
what is the answer to
-(-4x-7)+x=-4
Answer:
-128
Step-by-step explanation:
hope it helps srry if its wroung:>
PLS HELPPPPP<3tyyyyyy this is due today! so please helppp tysmmm and have a great night or morning! :)
Answer:
3) 40 decimeters = 4 metres
7) >
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(20 PTS) I WILL GIVE BRAINLIST
What fraction does Point A on the number line below represent?
A horizontal number line is shown from negative 1 to 0 to positive 1. There are tick marks to show increments of 1 over 8 on each of the number line. Only the whole numbers are labeled. Point A is plotted at the second tick mark to the left of 0.
fraction 4 over 8
fraction negative 4 over 8
fraction 2 over 8
fraction negative 2 over 8
Answer:
point a i did the test and got it right
Step-by-step explanation:
pls help will give brainliest !!!!!!!!!
Slope = -1, through point (-3,5)
The equation of the line having slope = -1 and passing through a point (-3, 5) is y = -x + 2 and graph is given below.
The general equation of a line is y = m × x + c, where m is the slope and c is the y-intercept of the line.
Given slope is equal to -1.
Therefore the equation of the required line is y = (-1) × x + c.
Given that this line passes through the point (-3, 5).
Therefore we have 5 = (-1) × (-3) + c
⇒ 5 = 3 + c
⇒ 5 - 3 = c
⇒ 2 = c
⇒ c = 2
Therefore the y-intercept of the required line in cartesian coordinate form is (0, 2).
Therefore the required equation of the line is y = (-1) × x + 2
⇒ y = -x + 2.
Refer to the attached image for the graph of this line.
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Disclaimer: The question is not incomplete.
Assuming the following as the complete question.
Find the equation of the line having slope = -1, through point (-3,5) and also draw the graph of the line.
A couple plans to have three children. There are eight possible arrangements of girls and boys. For example, GGB means the first two children are girls and the third child is a boy. All eight arrangements are (approximately) equally likely.
Write down all eight arrangements of the sexes of three children
Based on the eight arrangements, what is the probability of any one of these arrangements?
Answer:
GGB
GGG
GBB
GBG
BGG
BGB
BBG
BBB
Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%
Step-by-step explanation:
GGB
GGG
GBB
GBG
BGG
BGB
BBG
BBB
Any of these has a probability of 1:8, or 1/8, or 0.125, or 12.5%
Cid's product manager continues to perform well in the market. However, a competing product is coming on strong and is looking to take over as the market share leader in the segment. Without sacrificing contribution margin, what can the Cid product manager do in order to improve upon the buying criteria, and thus potentially increase demand?Select : 1Save Answer Lower the selling price since it is the second most important buying criteria Increase MTBF by 2000 Reposition Cid to make it even smaller and higher performing Increase the promotion budget to gain greater awareness
Given: An existing company(Cid) that is performing well and another company with the potential of taking over the lead from the existing company
To Determine: What the existing company (Cid) product manager do in order to improve upon the buying criteria, and thus potentially increase demand?
Solution
The following are the ways to increase the buying criteria and increase demand
We can improve the quality of the product to attract customers.
• We can add new features to the product and improve the styling technique to increase the demand.
• We have to try to convert non-users into users to buy the product so that it can improve the buying criteria.
• We have to give more advertisement campaigns and more promotional activities.
• We can enter into new market segments and distribution channels so that the demand for the product increases.
Comparing the above and the given options will help select the best options
.
Write the equation of a line in standard form that is parallel to the line and passes through the point (-8, ).
Standard equation of the line which is parallel to the given line 4x-2y =8 and passes through the point (-2,8) is equal to y = 2x + 12.
As given in the question,
Given equation of the line which is parallel to the required equation of the line:
4x -2y = 8
⇒ 2y = 4x -8
⇒ y= 2x -4
Slope of the line by comparing with standard form y =mx +c , where m is the slope.
Slope 'm' = 2
Slope is same for the parallel lines.
Required equation of the line passes through (-2 ,8) with slope m = 2
y -y₁ = m(x-x₁)
⇒ y- 8 = 2(x-(-2))
⇒ y -8 = 2x +4
⇒ y= 2x +12
Therefore, standard equation of the line which is parallel to the given line 4x-2y =8 and passes through the point (-2,8) is equal to y =2x + 12.
The complete question is :
Write an equation of a line in standard form, that is parallel to the line
4x - 2y = 8 that passes through the point (-2, 8).
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The following table gives the number of pints of type A blood used at Damascus Hospital in the past 6 weeks: a) The forecasted domand for the week of October 12 using a 3-week moving averigge pints (round your response to two decimal piaces).
The forecasted demand for the week of October 12, based on the 3-week moving average, is 16 pints. This estimate provides an approximation of the expected demand for type A blood at Damascus Hospital during that week, considering recent trends in usage.
To calculate the forecasted demand for the week of October 12, we employ a 3-week moving average. This approach involves taking the average of the number of pints used over the previous three weeks.
Let's refer to the table provided to determine the moving average:
Week Number of Pints
Sept 1 15
Sept 8 18
Sept 15 12
Sept 22 20
Sept 29 16
Oct 6 14
To calculate the moving average, we sum the number of pints used over the three most recent weeks and divide it by 3:
Moving Average = (12 + 20 + 16) / 3 = 16
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Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8. 50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5. 25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8. 5 3x 2y = 5. 25 If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? Complete the multiplication and add the equations. What is the result? What is the price per pound of apples? $ What is the price per pound of bananas? $.
The resulting equation is 19x + 12y = 32.75. This equation allows us to solve for the prices per pound of apples (x) and bananas (y).
To eliminate the y terms when making a linear combination after multiplying the first equation by 2, you should multiply the second equation by 3.
After completing the multiplication and adding the equations, the result is a new equation that allows us to solve for the prices per pound of apples and bananas.
First equation multiplied by 2:
10x + 6y = 17
Second equation multiplied by 3:
9x + 6y = 15.75
Adding the equations:
(10x + 6y) + (9x + 6y) = 17 + 15.75
19x + 12y = 32.75
The resulting equation is 19x + 12y = 32.75. Now, we can solve this equation to find the price per pound of apples (x) and the price per pound of bananas (y).
Given the system of equations: 5x + 3y = 8.5 (Equation 1)
3x + 2y = 5.25 (Equation 2)
To eliminate the y terms when making a linear combination after multiplying the first equation by 2, we need to multiply the second equation by 3. The resulting equations are:
2(5x + 3y) = 2(8.5)
3(3x + 2y) = 3(5.25)
10x + 6y = 17 (Equation 1 multiplied by 2)
9x + 6y = 15.75 (Equation 2 multiplied by 3)
Adding these equations together:
(10x + 6y) + (9x + 6y) = 17 + 15.75
19x + 12y = 32.75
The resulting equation is 19x + 12y = 32.75. This equation allows us to solve for the prices per pound of apples (x) and bananas (y). To find the individual prices, further algebraic steps or substitution methods can be used.
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Toronto FC have lost 12 of the 40 games and drawn 15% of the games they have played. What percentage of the games have they won?
Answer: 55%
Step-by-step explanation:
The question says that Toronto FC lost 12 of 40 games and drew in 15% of the total games they played. To find the percentage of the games they won, you need to subtract the percentage of games they lost and the percentage of games they drew from 1 since all possibilities add up to 1.
% of games won = 1 - (% of games lost + % of games drawn)
First, Toronto FC lost 12 of 40 games. This means that they lost 12/40 of all games, and this can be simplified to be
3/10
Which is 0.3, or 30%.
Now the questions said that Toronto FC drew in 15% of all games, which means that using the equation from earlier, we can find the percentage of games won.
% of games won = 1 - (30%+15%)
= 1-0.45
= 0.55
Therefore, Toronto FC won in 55% of their games.