The step that is the part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10 and (E) 0 = x2 – 9x + 20.
What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =.To find the step that is the part of the process of algebraically solving the given system of equations:
That would be:
(C) 4x – 10 = x2 – 5x + 10 ( y = 4x - 10 is substituted for y).
Proof:
y + 5x = x² + 10(4x - 10) + 5x = x² + 104x - 10 = x² -5x + 10(E) 0 = x2 – 9x + 20 (liked terms are grouped and simplified).
Proof:
4x - 10 = x² -5x + 104x = x² -5x + 10 + 100 = x² -5x -4x + 200 = x² - 9x + 20Solving:
x² - 9x + 20 = 0 x² - 5x - 4x + 20 = 0(x - 5) (x - 4) = 0x = 4 (as question says) OR x = 5Therefore, the step that is part of the process of algebraically solving the given system of equations is (C) 4x – 10 = x2 – 5x + 10.
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The complete question is given below:
Which steps could be part of the process in algebraically solving the system of equations, y + 5x = x2 + 10 and y = 4x – 10? Check all that apply.
(A) y = x2 + 5x + 10
(B) y + 5x = x2 + 10 + 4x – 10
(C) 4x – 10 = x2 – 5x + 10
(D) 0 = x2 – 9x
(E) 0 = x2 – 9x + 20
(F) One x-value of a solution to the system is 4.
Which of the following is the appropriate choice about display technique:
a. Two continuous variables – Scatter plot
b. Distribution of one continuous variable – Pie chart
c. Distribution of one categorical variable – Treemap
d. One categorical and one continuous variable – Contingency table
e. A and C
f. B and D
The appropriate choice about the display technique in case of two continuous variables is the scatter plot.
A scatter plot is a graph used to plot two variables, usually as the horizontal and vertical axis, to check for a correlation or connection between them.What is a variable?A variable is a statistical concept that is used to measure the characteristics of a population or a sample.
A variable is an attribute or a feature of an object, event, or person that can be quantified or described numerically. The pie chart is appropriate when you want to display a distribution of a continuous variable. But this technique is not appropriate in this case because you cannot see the distribution of a single continuous variable using a pie chart. A pie chart is best suited for showing percentages of a whole.C.E. A scatter plot is a graphical representation of the relationship between two variables. This technique is appropriate when you want to display two continuous variables. A treemap is best suited for showing the distribution of one categorical variable. F. A pie chart is appropriate when you want to display the distribution of a single continuous variable. A contingency table is appropriate when you want to display the frequency distribution of one categorical and one continuous variable.
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can anyone please help?
Answer:
-1 or 1.
Step-by-step explanation:i hope thats what your looking for.
This season, the probability that the Yankees will win a game is 0.56 and the probability that the Yankees will score 5 or more runs in a game is 0.46. The probability that the Yankees lose and score fewer than 5 runs is 0.32. What is the probability that the Yankees would score fewer than 5 runs when they win the game? Round your answer to the nearest thousandth.
The probability that the Yankees would score fewer than 5 runs when they win the game is 0.32.
Let the events be A: Yankees win a game
B: Yankees score 5 or more runs
C: Yankees lose a game
D: Yankees score fewer than 5 runs
We are given the following probabilities:
P(A) = 0.56 (probability of winning)
P(B) = 0.46 (probability of scoring 5 or more runs)
P(C and D) = 0.32 (probability of losing and scoring fewer than 5 runs)
We want to find the probability of scoring fewer than 5 runs when they win the game, which is P(D|A).
We can use Bayes' theorem to find this probability:
P(D|A) = P(A and D) / P(A)
Using the definition of conditional probability:
P(D|A) = P(D and A) / P(A)
We know that P(D and C) = P(C and D), as both events represent the same outcome.
Using the fact that the sum of the probabilities of mutually exclusive events is equal to 1:
P(D and C) + P(B and C) = 1
Rearranging the equation:
P(D and C) = 1 - P(B and C)
Now, let's find P(D and A):
P(D and A) = P(D and A and C) + P(D and A and not C)
P(D and A) = P(D and A and C) + 0
P(D and A) = P(C and D and A)
Substituting the probabilities we have:
P(D|A) = P(C and D) / P(A)
P(D|A) = P(C and D) / P(C and D) + P(B and C)
P(D|A) = 0.32 / (0.32 + P(B and C))
We need to find P(B and C), which we can calculate using the given probabilities:
P(B and C) = P(C and B)
P(B and C) = P(C) - P(C and D)
P(B and C) = 1 - P(C and D)
P(B and C) = 1 - 0.32
P(B and C) = 0.68
Now we can substitute this value into the equation:
P(D|A) = 0.32 / (0.32 + 0.68)
P(D|A) = 0.32 / 1
P(D|A) = 0.32
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find the slope and y-inersept plz dont scam i really need help guys
probability of choosing 3 men and 1 woman at random for a 4 person committee if there are 10 men and 6 women to choose from?
The probability of choosing 3 men and 1 woman at random for a 4 person committee can be calculated using the combination formula.
We want to choose 3 men from a pool of 10 men, which can be done in 10 choose 3 ways. We also want to choose 1 woman from a pool of 6 women, which can be done in 6 choose 1 ways. The total number of ways to choose a 4 person committee from a pool of 16 people is 16 choose 4. Therefore, the probability of choosing 3 men and 1 woman at random for a 4 person committee is:
(10 choose 3) * (6 choose 1) / (16 choose 4) = 120 * 6 / 1820 = 0.3956
So, the probability of choosing 3 men and 1 woman at random for a 4 person committee is approximately 0.3956 or 39.56%. This means that if we randomly choose a 4 person committee from a pool of 10 men and 6 women, there is a 39.56% chance that the committee will consist of 3 men and 1 woman.
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An international company has 18,400 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.
Answer:
5395894 employees.
Step-by-step explanation:
18400=34.1%
53958.94(rounded)=1%
53958.94*100=5395894 employees in total
What is the slope of a line parallel to the line whose equation is 2x-y=7. Fully simplify your answer.
Answer:
Step-by-step explanation:
Q
(
2
,
1
)
and
R
(
8
,
13
)
is partitioned from
Q
to
R
into a
1
:
2
ratio at point
Z
. What are the coordinates of
Z
?
Graph the Linear equation: y = - 3/4x + 5
Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.
How to graph an equation?When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.
The linear equation is y = - 3/4x + 5.
If the value x = -1, then y would be:
y = - 3/4x + 5
= -3/4(-1) + 5
= 5.75
If the value x = 0, then y would be:
y = -3/4(0) + 5
= 5
If the value x = 1, then y would be:
= -3/4(1) + 5
= 4.25
If the value x = 2, then y would be:
= -3/4(2) + 5
= 3.5
If the value x = 3, then y would be:
= -3/4(3) + 5
= 2.75
The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)
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A health club charges a one-time sign-up fee and a monthly membership fee. The equation y=24x+15y=24x+15 represents what the health club charges. Find the rate of change.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The rate of change of the equation that represents the monthly fees and a one-time sign-up fee is 24.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 3 = 4 is an equation.
We have,
y = f(x) = 24x + 15
A health club charges a one-time sign-up fee and a monthly membership fee.
We can see from the equation that,
Monthly membership fee = 24
One-time sign up fee = 15
x = number of months.
Now,
We will take two x values as:
x = 2
x = 5
The rate of change:
= f(5) - f(2) / (5 - 2)
= [(24x5 + 15) - (24x2 + 15)] / 3
= (120 + 15 - 48 - 15) / 3
= 72/3
= 24
Thus,
The rate of change of the equation that represents the monthly fees and a one-time sign-up fee is 24.
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A factory has production lines A and B producing cookies. The two production lines produce 7280 cookies in total each day. If production line A produces 8% more cookies than production line B, find the difference of the numbers of cookies produced by production lines A and B in a day.
please tell me the whole process, thank you
The difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.
What are equations?When two algebraic expressions are equated, a mathematical statement is called an algebraic equation. P = 0 or P = Q, where P and Q are polynomials, are the generic forms of algebraic equations. One variable only algebraic equations are referred to as univariate equations, while multiple variable algebraic equations are referred to as multivariate equations. A balanced equation in algebra is a given. Because of this, the right side of the equation will equal the left side.
Let the cookies produced by production line A = x.
Let the cookies produced by production line B = y.
Given that, the two production lines produce 7280 cookies in total each day.
x + y = 7280
Also, production line A produces 8% more cookies than production line B.
x = y + y(8/100)
x = y + 0.08y
x = 1.08y
The system of equations thus are:
x = 1.08y
x + y = 7280
Substitute the value of x in equation 2:
x + y = 7280
1.08y + y = 7280
2.08y = 7280
y = 3500
Substitute the value of y in equation 2:
x + y = 7280
x + 3500 = 7280
x = 3780
The difference between the cookies produced is:
D = x - y
D = 3780 - 3500
D = 280
Hence, the difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.
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How do I do this question and I need answer please
Answer: x = 3/4
Step-by-step explanation:
1/3x + 3 = 4 - x
Subtract 3 from both sides
1/3x = 1 - x
Then times 3 from both sides
x = 3 - 3x
Add 3x on both sides
4x = 3
Divided by 4, both side
x = 3/4
7) What does a multiplier of \( 1.2 \) mean?
A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.
A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.
A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.
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Pls help. Will make brainliest
Answer:
if you dont know the answer you can downlode the brainly app and take pics of your work and it will translate the answer
Step-by-step explanation:
How do i slove this promblem i need help 9.92÷8
EXPLANATION
The division is equal to:
First we need to write the problem in long division format:
8.0 /_ 9.92
Divide 9 by 8 to get 1:
1
8.0 /_ 9.92
Multiply the quotient digit (1) by the divisor 8:
1
8.0 /_ 9.92
8
Subtract 8 from 9:
1
8.0 /_ 9.92
8
1
Add a decimal point to the solution
Bring down the next number of the dividend
1.
8.0 /_ 9.92
8
19
You start at (6,4) and move 4 units left and 2 units down what point will you end up on?
Answer:(2,2)
Step-by-step explanation:
because if you follow the steps you will end up there
Find the 19th term of the sequence 5, 8, 11, 14, 17...
59
51
53
56
Answer:
59
Step-by-step explanation:
So, lets look at our numbers in the sequence. So it goes 5 to 8, 8 to 11, 11 to 14, and 14 to 17. This seems like a change in three. So the every 1 term changes the orginal 5 value by 3.
So wouldnt this mean we can multiply the change in terms by the amount of terms? Which is 19*3? Well, sort of. This is the right way of doig this, but we must remember that we already know the first term, 5. So this means we will be doing 18*3.
This gets you 54. Now just add the amount of the 18 terms onto the first term:
54+5
=
59
So your answer is 59.
Hope this helps!
Yo I need help with this
The angles in triangle LJK from smallest to largest are K (38.7°) < L (58.7°) < J (73.6°).
Describe Triangles?In geometry, a triangle is a three-sided polygon with three angles and three sides. Triangles are one of the fundamental shapes in geometry, and they play an essential role in many areas of mathematics and science.
The sides of a triangle are the line segments that connect its vertices, and the angles of a triangle are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
Triangles can be classified based on the size of their sides and angles. A scalene triangle has no sides or angles that are equal, while an isosceles triangle has two sides that are equal and two angles that are equal. An equilateral triangle has three sides that are equal, and all three angles are equal.
To determine the order of the angles in triangle LJK from smallest to largest, we can use the Law of Cosines to calculate the measures of the angles opposite each side:
cos(L) = (J² + K² - L²) / 2JK
cos(K) = (J² + L² - K²) / 2JL
cos(J) = (K² + L² - J²) / 2KL
where L, J, and K are the measures of angles opposite sides of lengths KL, LJ, and JK, respectively.
Using the given side lengths, we can calculate the cosines of each angle as follows:
cos(L) = (18² + 14² - 16²) / (2 * 18 * 14) = 0.5207
cos(K) = (18² + 16² - 14²) / (2 * 18 * 16) = 0.7738
cos(J) = (14² + 16² - 18²) / (2 * 14 * 16) = 0.1154
To find the measures of the angles, we can take the inverse cosine (cos⁻¹) of each value:
L = cos⁻¹(0.5207) = 58.7°
K = cos⁻¹(0.7738) = 38.7°
J = cos⁻¹(0.1154) = 73.6°
Therefore, the angles in triangle LJK from smallest to largest are:
K (38.7°) < L (58.7°) < J (73.6°)
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The angles in the triangle from smallest to largest are J, K, L. the sides in the triangle from shortest to longest as follows LN, MN, LM.
Describe Triangles?In geometry, a triangle is a three-sided polygon with three angles and three sides. Triangles are one of the fundamental shapes in geometry, and they play an essential role in many areas of mathematics and science.
The sides of a triangle are the line segments that connect its vertices, and the angles of a triangle are the angles formed by the intersection of its sides. The sum of the angles in a triangle is always 180 degrees.
Triangles can be classified based on the size of their sides and angles. A scalene triangle has no sides or angles that are equal, while an isosceles triangle has two sides that are equal and two angles that are equal. An equilateral triangle has three sides that are equal, and all three angles are equal.
For Triangle LJK:
We can use the Law of Cosines to find the angles in the triangle:
cos(L) = (J² + K² - L²) / (2JK)
cos(K) = (J² + L² - K²) / (2JL)
cos(J) = (K² + L² - J²) / (2KL)
Plugging in the given values, we get:
cos(L) = (18² + 14² - 16²) / (21814) = 0.156
cos(K) = (16² + 14² - 18²) / (21614) = 0.429
cos(J) = (18² + 16² - 14²) / (21816) = 0.783
Using the inverse cosine function, we can find the angles:
L = acos(0.156) = 80.7 degrees
K = acos(0.429) = 65.9 degrees
J = acos(0.783) = 33.4 degrees
Therefore, the angles in the triangle from smallest to largest are: J, K, L.
For Triangle LMN:
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can find the third angle:
angle LNM = 180 - 46 - 98 = 36 degrees
Since angle LMN is the smallest angle, we can order the sides in the triangle from shortest to longest as follows:
LN, MN, LM
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The complete question is:
1) Order the angles in the triangle from smallest to largest.
In Δ LJK, LJ= 16 Yd, JK= 18 yd, KL= 14 yd
2) Order the sides in the triangle from shortest to longest.
In ΔLMN, ∠ LMN= 46°, ∠ NLM= 98°, ∠ MNL= 36°
Find matrix M such that M × [3 -2 , 6 -8 ] = [-2 16]
The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]
Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16]. We know that the product of two matrices is equal to the sum of the products of their corresponding elements. We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.
a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...
(4)Simplifying equations (1) to (4), we get:
3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)
Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.
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can someone help with this please! tell what number each symbol is equivalent to and be sure to show how to answer it, i will give brianlist
Answer:
1
Step-by-step explanation:
Figure KLHJ is a kite. Angle HLK has a measure of 128 degrees and angle JKL has a measure of 50 degrees. Find the measure of angle JHL.
The measures of angles of the kite are ∠JHL = 91°
Given data ,
Let the kite be represented as KLHJ
where the measure of angle ∠HLK = 128°
And , the measure of ∠JKL = 50°
Now , kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles
So , the angles are
128° + 50° + 2x = 360°
On simplifying , we get
2x = 360° - 178°
2x = 182°
Divide by 2 on both sides , we get
x = 91°
Hence , the angle of kite is 91°
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the angle of elevation from an anchor to the boat is 39° . the anchor is 30 meters from the boat find the distance, show your work!!!
if I have a garden that's 10 yards and I want to grow a plant that's 2.5 yards how many of that can I plant
Answer:
4
Step-by-step explanation:
2.5y x 4 = 10y
Hope This Helps
<3
Answer: 4 plants.
Step-by-step explanation:
In the case that these measurements are of length, the plant being 2.5 yards and the total length of the garden area being 10 yards, the most simple way to solve this is to find how many 2.5 yard sections of this garden are in the given plot.
\(10/2.5 =4\)
When 10 is divided by 2.5 you receive the answer "4". You can fit 4 plants within the garden. 2.5 x 2 is 5, and 5 x 2 is 10. 2 x 2, therefore, would give you the answer 4.
I hope this explanation helped you understand the question and the answer better.
Solve please. Correctly
3 - x = -x + 3
Answer:
x = anything as long as they're the same number
Step-by-step explanation:
1. MONEY Gillian and Roger have lunch at a restaurant and
to determine how much tip to leave based on their bill. If their bill was
$21.87 and Gillian wants to leave a 15% tip, what is a reasonable
estimate for how much she should leave?
The total cost that Gillian will pay is $251.5
How to calculate the cost?Given that Gillian and Roger have lunch at a restaurant their bill was $21.87 and Gillian wants to leave a 15% tip
The total amount that will be paid will be:
= Total amount of food + Tip
= $21.87 + (15% × $21.87)
= $21.87 + (0.15 × $21.87)
= $21.87 + $3.28
= $25.15
The amount is $25.15.
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in a time-series graph, the horizontal axis is marked off in units of
In a time-series graph, the horizontal axis is marked off in units of time, such as days, months, quarters, or years. The time intervals between the marks on the horizontal axis are usually equal, which allows the graph to show changes in the variable being measured over time.
The vertical axis of the graph shows the values of the variable being measured, and the line or curve connecting the points on the graph represents the trend of the data over time. Time-series graphs are often used to visualize patterns and trends in economic, financial, and other types of data that vary over time.
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The ratio shows the ratio of adults to children needed for two activities
Adults : children
Painting 1 : 9
Rafting 1 : 3
there are 5 adults to supervise for painting. What is the greatest number of chidren that can paint
5. Isaiah inherited $7,000 and plans to deposit it into a savings account that earns 6% interest.
Isaiah wants to compare the interest earnings after 60 months based on whether the account
earns simple or compound interest. After using each formula below, Isaiah subtracts the
solutions and determines that after 60 months, the account with compound interest would earn
$7,267.58 more in interest. Do you agree with Isaiah's thinking? Explain why or why not.
Isaiah's thinking is correct. Compound interest does earn $341.95 more than simple interest in 60 months.
Does compound interest earn more than simple interest?Let P be the principal amount of $7,000
Let r be the annual interest rate of 6%
Let n be the number of compounding periods per year.
Using formula for simple interest: I = Prt, the interest earned after 60 months is:
I = 7,000 × 0.06 × 5
I = $2,100.
Using formula for compound interest \(A = P(1 + r/n)^{nt}\). The amount after 60 months with monthly compounding is:
\(A = 7,000*(1 + 0.06/12)^{12*5}\\A = 7,000*1.34885015255\\A = 9441.95106785\\A = $9441.95\)
The interest earned is:
I = A - P
I = $9441.95 - $7,000
I = $2,441.95.
The difference in interest earned between compound and simple interest is:
= $2,441.95 - $2,100
= $341.95.
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Simplify.
16 3/8 - 6 7/8
given the functions w( x) =2x+1 and vw(x) =4x²+4x-5,find w¯¹(x) answer meeeee
Answer:
Hello,
We don't need vw(x) !
\(w^{-1}(x)=\dfrac{x-1}{2}\)
Step-by-step explanation:
\(w(x)=2x+1=y\\\\2y+1=x \ exchanging \ x\ and\ y\\\\y=\dfrac{x-1}{2} \\\\w^{-1}(x)=\dfrac{x-1}{2}\)
Congratulations I was forced to do this so I could see the question.?