Answer:
x+3x-4=2x+x+5
Step-by-step explanation:
=4x-4= 3x+5
=4x-3x=5+4
= x=9. Done
Jessica needs to know how much water her new fish tank can hold:
A rectangular prism with a length of 8 inches, a width of 4 inches, and a height of 9 inches.
Determine the total volume of the fish tank.
The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.
The volume of a rectangular prism can be calculated using the formula:
V = l x b x h..........(i)
where,
V ⇒ Volume
l ⇒ length
b ⇒ width
h ⇒ height
From the question, we are given the values,
l = 8 inches
b = 4 inches
h = 9 inches
Putting these values in equation (i), we get,
V = 8 x 4 x 9
⇒ V = 288 in³
Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.
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What is the slope of a line parallel to the y-axis?
Answer:
The slope of a line parallel to Y-axis is zero.
Problem Situation: Ike has $126 in his bank account. He gets $20 for his birthday.
He also has a part-time job that pays $8 per hour. How many hours will he need to
work to have $250 in his bank account?
.
Answer: 13h
Step-by-step explanation:
126 + 20 = 146
250 - 146 = 104
104 : 8 = 13
He will need 13h
Answer:
13.5
126 plus 20 is $146
250 minus 146 is 108
108 divided by 8 is 13.5
Write 10,100,or 1,000 to make each statement true. A. 1,000,000 is--------------- times greater than 10,000.
Answer:100
Step-by-step explanation: 10 x 10000 = 100000 x 10 = 1000000. If we multiply 100 x 10000, we got 1 million
is x^2+x+1=0 linear?
Answer:
No.
Step-by-step explanation:
Because the equation has an exponent, it is quadratic, and not linear.
Answer:1
Step-by-step explanation:
The graph represents the piecewise function: f (x) ={ , if -3
The domain and the range of the function are
Domain = (-∝, ∝)Range = (0, ∝)How to determine the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The graph is a piecewise function
When combined gives an absolute function
The rule of a function is that
The domain is the set of all real numbers
This means that the input value can take all real values
However, the range is greater than the constant term
In this case, it is 0
So, the range is y > 0
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Question
The graph represents the piecewise function:
f(x) =
What is the domain and range of the function
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
a
Step-by-step explanation:
the perimeter (P) of a square is the sum of the 4 congruent sides.
the area of a square is calculated as
area = s² ( s is the length of a side )
here area is 36 , then
s² = 36 ( take square root of both sides )
s = \(\sqrt{36}\) = 6
then
P = 4s = 4 × 6 = 24 cm
Find the measure of 46.
{ K
620
4.6
46 = [?]
Enter
?=118°
Answer:
<6+62=180 co interior angle
<6=180-62=118°
Answer:
solution given:
<6+<62°=180°[co- interior angle]
<6=180°-62°=118°
<6=118° is your answer
20. There is a number x sum that x2 is irrational but x is rational. Then x can be
(a) √5102.0 (£)
(b) √2
(c) 3/2
(d) 4/5
The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)
To explain further, we need to understand the properties of rational and irrational numbers.
A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.
In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.
Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.
Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.
Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.
In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)
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Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
The locus of the midpoints of all chords that can be drawn from a given fixed point \((a,b)\) on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by \(\frac{a}{2}\) and \(\frac{b}{2}\) respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of \(r\) units is \(x^{2} +y^{2} =r^{2}\) According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points \((x_{1},y_{1})\) and \((x_{2},y_{2})\) is \((\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )\)Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is \(x^{2}+y^{2} =6^{2}\), that is, \(x^{2}+y^{2} = 36\)
Let the coordinates of the given fixed point be \((a,b)\)
Let the coordinates of any point on the circle be \((p,q)\) and let the coordinates of the midpoint of the chord joining the points \((a,b)\) and \((p,q)\) be \((h,k)\)
We have to find the locus of \((h,k)\)
Then, using the midpoint formula,
\((h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})\)
On solving, we get,
\(p=2h-a,q=2k-b\)
Since \((a,b)\) and \((p,q)\) are both points on the given circle, they satisfy the equation of the circle, \(x^{2}+y^{2} = 36\)
Then,
\(a^{2} +b^{2} =36\)
\(p^{2} +q^{2} =36\)
Substituting \(p=2h-a,q=2k-b\) in \(p^{2} +q^{2} =36\), we have,
\((2h-a)^{2} +(2k-b)^{2} =36\)
\((2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36\)
\(4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36\)
\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}\)
\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9\)
\((h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}\)
This is the locus of the point \((h,k)\)
Replace \((h,k)=(x,y)\) to get,
\((x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}\)
This is the equation of a circle with center at \((\frac{a}{2} ,\frac{b}{2} )\) and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point \((a,b)\) on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by \(\frac{a}{2}\) and \(\frac{b}{2}\) respectively.
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What is the mid point between (0,0) and (3,4)
Answer:
Midpoint of a line segment
(xM,yM) = (4, 5).
Answer:
I think it's point (1.5,2).
Step-by-step explanation:
3 ÷ 2 = 1.5
4 ÷ 2 = 2
when is 9+10 really equal to 21
Answer:
9 + 10 = 21
Step-by-step explanation:
9 + 10 = 21
Factor out 9 and 10
9 = 3 · 3 10 = 2 · 5
Next multiply 3 by 2
3 × 2 = 6
Then multiply 3 by 5
3 · 5 = 15
Finally add the products
15 + 6 = 21
Which equation choice could represent the graph shown below?
1) F(x) = (x - 4)(x + 1)(x - 6)
2) F(x) = (x - 4)(x - 1)(x - 6)
3) F(x) = (x - 4)(x - 1)(x + 6)
4) F (x) = (x + 4(x - 1)(x - 6)
The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)
What equation does represent a cubic function?
In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:
f(x) = (x + 6) · (x - 1) · (x - 4)
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Answer:
3) f(x) = (x - 4)(x - 1)(x + 6)
Step-by-step explanation:
The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.
From inspection of the given graph, the curve crosses the x-axis at:
x = -6x = 1x = 4According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 4)(x - 1)(x + 6)what is 4% of 32? is it a percent, base, or amount
Answer:
1.28 - amount
Step-by-step explanation:
You would multiply 32 times 0.04 and get 1.28 which I assume would be an amount.
The amount of 4% of 32 is 1.28.
We have to determine what is 4% of 32.
What is the percentage?
This free percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.
Suppose it is an x percent.
Therefore x multiply 32 times 0.04 and get 1.28 an amount.
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PLEASE I REALLY NEED HELP FAST
A batch of 5500 computers is produced by a company. Four random samples of 35 computers per sample are
tested. The numbers of defective computers found in the fou samples are shown in the table.
Sample of 35
Computers
Number of
Defective
Computers
А
1
B
3
с
1
D
2.
Based on these results, how many defective computers should be expected in the entire batch of 5500 computers?
It's around 1 to 3
So
From 35 it's 1,2,3
From 5500 samples of 35
5500/35≈157Now
If 1 comes from each
157(1)=157 detectsIf 2
157(2)314detectsIf 3
157(3)471 detects12=x/5............................
Answer:
answer :
12 = x / 5
12 × 5 = x
60 = x
or
x = 60
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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Ans 5(9+(5sq-16)sq)sq
Answer: (the 2s I added are for square 2)
5sq(5g2s2 - 16qs + 9)
Step-by-step explanation:
The system of equations graphed below has how many solutions?
y = 2x + 2
y= 2x
The given system has zero solutions.
Lines that never cross one other are said to be parallel. Hence, a pair of parallel lines must have the same slope but distinct intercepts. (On the other hand, identical lines have same intercept).
In the general equation of a line, y = mx + b, m represents the slope of the line.
The general equations of parallel lines would be of the form:
(1) y = mx + b
(2) y = mx + c
where b and c are any constants.
Now, we observe that the given equations are of the above form with m=2, b=2 and c=0, therefore, they are parallel lines. Since, parallel lines never intersect each other, they have no solution.
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Plot the image of quadrilateral ABCD under a reflection across line L
Step-by-step explanation:
The coordinates of the reflection of a point (x, y), across the y-axis is the point (-x, y)
Please find attached the plot of the image of quadrilateral ABCD under a reflection of the line l
Method:
The coordinates of the vertices of the given quadrilateral ABCD are as follows
A(-2 0), B(-3, 4), C(0, 4), and D(-1, 1)
Due to its orientation, the line l can be taken as being equivalent to the y-axis
The coordinates of the image of (x, y) following a reflection across the y-axis is (-x, y)
Therefore, for the image of the quadrilateral ABCD following a reflection across the y-axis to give the quadrilateral A'B'C'D', the coordinates of A'B'C'D' are;
A(-2 0), reflected across the y-axis gives the image A'(2, 0)
B(-3, 4), reflected across the y-axis gives the image B'(3, 4)
C(0, 4), reflected across the y-axis gives the image C'(0, 4)
D(-1, 1), reflected across the y-axis gives the image D'(1, 1)
The coordinates with which the image of the of the quadrilateral ABCD can be plotted are therefore;
A'(2, 0), B'(3, 4), C'(0, 4), and D'(-1, 1)
The plot of the quadrilateral ABCD and the image A'B'C'D' can be created using MS Excel presented in the attached graph
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A box contains orange balls and green balls. the number of green balls is 10 more than 2 times the number of orange balls. if there are 64 balls all together, then how many green balls and how many orange balls are there in the box
Answer:
52 green, 15 orange-Please mark brainliest hope this helped!
Step-by-step explanation:
g + o = 67 g = green, o = orange, x = total
g = 3o + 7
use substitution: (3o + 7) + o = 67
solve for o:
4o + 7 = 67
4o = 60
o = 60/4 = 15
solve for g:
g + 15 = 67
g = 52
find net price (show work)
25% discount on $225 purchase.
Answer:
$191.25
Step-by-step explanation:
multiply 255 dollars by 25 percent, and then divide the answer by one hundred, then deduct that result from the original price.
(255 x 25)/100 = $63.75
255 - 63.75 = $191.25
4/5-2/3 in simplest term
Answer: =2/15
Step-by-step explanation: Hope this help :D
Answer:
2/15
Step-by-step explanation:
4/5 - 2/3
Step 1: Find a common denominator. 5 and 3 don't share any factors other than 1, so multiply them to get 15.
12/15 - 10/15
(12 - 10)/15
Step 2: Subtract 10 from 12 to get 2.
2/15
4/5 - 2/3 simplified is 2/15.
James was eating a bag of candies that came in eight different colors. He noticed that there appeared to be far fewer green candies than any of the other colors and wondered if the true proportion of green candies was lower than the 12.5% that would be expected if all of the candies came in even amounts. For the sake of statistics, he decided that he would need to buy more candy to test his hypothesis. James randomly selected several bags and candies and recorded the color of each piece of candy. He found that out of the first 400 candies that he chose, 39 of them were green. James conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of green candies was lower than 12.5%.
uuuuuuuuuuuuuuuurrrrrrrrrrrrrrrr mom
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
isosceles triangle
Step-by-step explanation:
first by using corresponding angle theorem:
<A=<C
<A=50°
then by using exterior angle theorem:
<A+<C=<B(the outer angle)
50°+<C=<B,<B=180°-80°(angle B lies in a staight line)
<B=100°
50°+<C=100°
<C=50°
b) f(x) = −3x
2 − 5x + 1, ¶(1, −7),
Answer:
b fx =-,3 x
2-3 ry ty negative 8
Step-by-step explanation:
kailangan nho nlNc sagotan
A man wants to mesure the height of a nearby building. He places a 7ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building’s shadow is 162ft, the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot.
The height of the building is approximately 227 feet.
In the given question, a man wants to measure the height of a nearby building. He places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building.
The total length of the building's shadow is 162 ft, and the pole casts a shadow that is 5.5 ft long. We have to determine the height of the building.The given situation can be explained with the help of a diagram.
As shown in the figure above, let AB be the building and CD be the 7 ft pole. The height of the building is represented by the line segment AE, which is to be determined. Let the length of the shadow of the pole be CD and that of the building be BD.
Therefore, the length of the total shadow will be BC or CD + BD.According to the question, the shadow of the pole is exactly covered by the shadow of the building. This implies that the two triangles AEF and CDF are similar. Hence, the corresponding sides are proportional. Therefore, we have:AE/EF = CD/DF
On substituting the values from the given data, we get:
AE/(EF + 5.5) = 7/5.5.... (1)
Similarly, we can write from the given data:
BD/DF = 162/5.5.... (2)
From equations (1) and (2), we can write:
AE/(EF + 5.5) = BD/DF => AE/(EF + 5.5) = 162/5.5.... (3)
On solving the above equation for AE, we get:
AE = (7/5.5) × (162/5.5 - 5.5)≈ 226.6 ft
Therefore, the height of the building is approximately 227 feet.
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Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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WHATS THE ANGLE MEASUREMENTS ?? & TELL HOW YOU GOT IT !!
PLEASE HELP !! ILL GIVE BRAINLIEST!! 100 POINTS !! NO FAKE ANSWERS.
Answer:
You on your own
Step-by-step explanation:
Answer: x = 7 thus
Angle D = 21
Angle E = 33
Angle F = 126
Step-by-step explanation:
3x + (5x-2) + 18x = 180 add all the __x
26x - 2 = 180 add 2 to both sides
26x = 182 divide both sides by 26
x = 7
Hope this helps you! Please give brainliest ;)
a+b=95
4a+1.50b=267.5
9514 1404 393
Answer:
a=50b=45Step-by-step explanation:
We can subtract the second equation from 4 times the first:
4(a +b) -(4a +1.5b) = 4(95) -(267.5)
2.5b = 112.5 . . . . . simplify
b = 45 . . . . . . . . . . divide by 2.5
a = 95 -b = 50 . . . find 'a'
The solution is (a, b) = (50, 45).