y = -5x + 24
y = 4x - 21
Since both of these equations are equal to Y, theyre equal to each other.
So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.
-5x + 24 = 4x - 21
Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:
-5x + 24 - 24 = 4x - 21 - 24
-5x = 4x - 45
Now we subtract 4x from both sides so the 4x shift to the other side
-5x - 4x = 4x - 4x - 45
-9x = -45
Finally divide both sides by -9 so x is by itself
(-9)÷(-9x) = -(45)÷(-9)
x = 5
Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.
Now apply x = 5 to either of the initial equations to find the value of Y
y = -5x + 24 or y = 4x - 21
(I'll do both but u only need one)
y = -5(5) + 24
y = -25 + 24
y = -1
y = 4(5) - 21
y = 20 - 21
y = -1
Either way, X is 5 and Y is -1
Answer (5, -1)
Final answer:
The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.
Explanation:
To solve the system of equations, set the two equations equal to each other since they both equal y:
y = -5x + 24
y = 4x - 21
Now equate them:
-5x + 24 = 4x - 21
Add 5x to both sides:
24 = 9x - 21
Add 21 to both sides:
45 = 9x
Now divide by 9 to solve for x:
x = 5
Substitute x back into either original equation to find y:
y = -5(5) + 24
y = -25 + 24
y = -1
The solution is (5, -1), which corresponds to option b.
To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:
-5(5) + 24 = -25 + 24 = -1
For the second equation:
4(5) - 21 = 20 - 21 = -1
Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.
A. 12
B. 6
C. -6
D. -12
Answer:
B
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 2, 4 ]
f(b) = f(4) = 16 ← from graph
f(a) = f(2) = 4 ← from graph
average rate of change = [tex]\frac{16-4}{4-2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
what percent of a data set represented in Q1
Answer:
25%
Step-by-step explanation:
25% between min and Q1
25% between Q1 and median
25% between median and Q3
25% between Q3 and max
25% but its the beginning
sarabeth is making beaded necklaces to give to five of her friends for homecoming she has 10 ft of elastic string each necklace takes 20in of string that sarabeth have enough elastic string to make the necklaces for her friends justify your answer by showing work and writing a complete sentence
Answer:
Yes, she has enough strong to make necklaces for five friends
Step-by-step explanation:
10 ft= 120 inches
120/20 9=in per necklace= 6
she has enough to make 6 necklaces and she only has to make five so yes
Find the side length of a square which has an area of 81 sq in. and a perimeter of
36 in.
Answer:
Area of 81 sq in: 40.2
Perimeter of 36 in : 9
Step-by-step explanation:
Hope I'm right! :)
Answer:
9 inches
Step-by-step explanation:
A square has an area of 81 in^2
A = s^2
81 = s^2
Take the square root of each side
sqrt(81) = sqrt(s^2)
9 = s
The side length is 9 inches
A square has a perimeter of 36 in
P = 4s
36 = 4s
Divide each side by 4
36/4 = 4s/4
9 = s
Each side is 9 inches
Please help me with the answers.
For this case we have that the equation of a line in the slope form intersection is given by:[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
In the green graph we observe that[tex]b = 2[/tex], then its equation is [tex]y = 5x + 2[/tex]
We have the slope of the red line substituting two points:
[tex](0,2)\\(-1,0)[/tex]
[tex]m = \frac {0-2} {- 1-0} = 2[/tex]
Thus, the red line has equation[tex]y = 2x + 3[/tex]
Finally, the blue line is [tex]y = 3x + 3[/tex]
Answer:
Green line, y = 5x + 2
Red line, y = 2x + 3
Blue line, y = 3x + 3
Answer:
1 - green line: y = 5x + 2
2 - red line: y = 3x + 3
3 - blue line: y = 2x + 3
Step-by-step explanation:
1 - green line
The graph with the green line is the easiest to match with an equation.
If you look at the graph, you see that when x = 0, the y-value is 2.
There's only one of the given equations that y = 2 when x = 0, the first one.
y = 5x + 2
y = 5 (0) + 2 = 0 + 2 = 2
It's easy to spot, because in the format y = mx + b, the b is the value of Y when x = 0, as we just demonstrated.
2 - Red line
In this case, when x = 0, y = 3. And there are 2 equations for which it's true... which is normal because the blue line (in next graph) also passes by this point.
Then to know which equation goes with the red line graph, we have two choices...
A. determine the slope (rate of change) of the red line and see if it matches one of the equations.
B. See what value of X yields a value of 0 for Y and see where it would land on the X-axis.
The second method is faster. If you see on the graph, when y = 0, x = -1
If we take the 2nd equation (y = 3x + 3) and we set the value of y to 0, we have:
0 = 3x + 3
-3 = 3x
x = -1
Which is exactly what we wanted to find.
So, the red line is y = 3x + 3
3. blue line
Well, there's only one answer left (y = 2x + 3), so it's easy... but let's make sure by finding the slope (method A listed for the red line above), in case your teacher would be playing tricks on you.
The slope of a line is the variation of y-value (Δy) divided by the variation of x-value (Δx).
If we take the two points where the blue line crosses the axis, we have (-1.5, 0) and (0,3).
Now, let's calculate the slope:
S = (0 - 3) / (-1.5 - 0) = -3 / -1.5 = 2
And 2 is the slope of the equation y = 2x + 3
So, we're good.
Write the expression: 4 divided by the sum of x and 7. A) 4 + 7 x B) x 4 + 7 C) x + 7 4 D) 4 x + 7
Answer:
4
-------
x + 7
Step-by-step explanation:
sum of x and 7 = (x + 7)
So 4 divided by the sum of x and 7 = 4 / (x + 7)
Answer
4
-------
x + 7
Final answer:
The correct way to write the expression '4 divided by the sum of x and 7' is 4 / (x + 7), which is not represented in any of the given options.
Explanation:
The expression 4 divided by the sum of x and 7 is written mathematically as 4 / (x + 7). None of the provided options A) 4 + 7 x, B) x 4 + 7, C) x + 7 4, or D) 4 x + 7 correctly represent this expression. The correct notation for division by a sum involves placing the sum in the denominator inside parentheses to ensure the correct order of operations is followed.
What is the length of this line? 30 POINTS!!
Answer:
61
Step-by-step explanation:
The first thing that you want to do is distance formula
[tex]d=(x_{2}-x_{1} )^{2} + (y_{2}-y_{1} )^{2}[/tex]
I'm going to make the start of the line at (1,1) and that means that the end of the line is at (7,6). Now, you plug these numbers into the formula.
[tex]d=(7-1 )^{2} + (6-1 )^{2}[/tex]
Then you slove
[tex]d=(6 )^{2} + (5 )^{2[/tex]
[tex]d=36 + 25[/tex]
[tex]d=61[/tex]
Distance formula: d =√(x2-x1^2 +y2-y1^2)
Find the points of the line: (2,2) and (8, 7)
Length = √((8-2)^2 + (7-2)^2)
Length = √(6^2 + 5^2)
Length = √(36+25)
Length = √61 ( exact answer) or as a decimal: 7.81
John has 4 yards of fabric. Jane has 120 inches of fabric. Who has more fabric? How much more?
john because 1 yard is equal to 3 ft, 4x3=12 ft
Final answer:
Jane has more fabric than John with a difference of 24 inches.
Explanation:
To compare the amount of fabric John and Jane have, we need to convert their measurements into the same unit. Since John has 4 yards of fabric and Jane has 120 inches, we need to convert yards to inches or inches to yards.
To convert yards to inches, we know that 1 yard is equal to 36 inches. So, multiplying 4 yards by 36 inches per yard, we get 144 inches of fabric for John.
Comparing the two measurements, we can see that Jane has more fabric with 120 inches compared to John's 144 inches. The difference is 144 inches - 120 inches = 24 inches. Therefore, Jane has 24 inches more fabric than John.
what is the standard form of the equation?
Answer:
hello : y = 3x² -24x +26 ......answer: C
Step-by-step explanation:
y = 3(x-4)² -22
by idetity : (x-4)² = x²- 8x+16
y = 3(x²- 8x+16 ) -22
y = 3x² - 24x +48 -22
y = 3x² -24x +26 ......answer: C
What is 3.375 written as a fraction in simplest form
27/8
try the internet, it helps
The required, 3.375 can be written as the fraction 27/8 in simplest form.
To write 3.375 as a fraction in simplest form, we can follow these steps:
Count the number of decimal places. In this case, there are three decimal places in 3.375.Remove the decimal point and write the number as the numerator of the fraction. In this case, we have 3375 as the numerator.The denominator of the fraction is determined by the number of decimal places. Since there are three decimal places, the denominator is 10^3 = 1000.Simplify the fraction if possible. In this case, the fraction 3375/1000 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 125. Dividing 3375 by 125 and dividing 1000 by 125 gives us the simplified fraction 27/8.Therefore, 3.375 can be written as the fraction 27/8 in simplest form.
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2x-9 x=3 ..............................
Answer:
3
Step-by-step explanation:
g
Answer:
(-3)Step-by-step explanation:
2x - 9
If x = 3
Then,
2·(3) - 9 = 6 - 9 = (-3)
What is a quadratic function (f) whose zeros are 2 and -11
Answer:
f(x) = x² + 9x - 22
Step-by-step explanation:
Given that x = 2 and x = - 11 are zeros, then
(x - 2) and (x + 11) are factors
and f(x) equals the product of the factors
f(x) = (x - 2)(x + 11) ← expand factors
f(x) = x² + 9x - 22 ← is a possible function
The quadratic function [tex]\( f \)[/tex] with zeros at [tex]\( x = 2 \) and \( x = -11 \)[/tex] can be written in factored form as: [tex]\[ f(x) = x^2 + 9x - 22 \][/tex]
The standard form of a quadratic function is:
[tex]\[ f(x) = ax^2 + bx + c \][/tex]
To convert the factored form to standard form, we expand the factors:
[tex]\[ f(x) = a(x^2 + 11x - 2x - 22) \] \[ f(x) = a(x^2 + 9x - 22) \] \[ f(x) = ax^2 + 9ax - 22a \][/tex]
[tex]\[ b = 9a \] \[ c = -22a \][/tex]
So, the quadratic function with zeros at [tex]\( x = 2 \) and \( x = -11 \) is:[/tex]
[tex]\[ f(x) = ax^2 + 9ax - 22a \] \[ f(x) = x^2 + 9x - 22 \][/tex]
A survey was taken among female and male voters and which candidates they voted for.
Below is the two-way table that summarizes the data.
Candidate A Candidate B
Female 32 43
Male 36 39
Of the male voters, approximately what proportion voted for Candidate A?
Answer: its 48% i took the test
Step-by-step explanation:
Answer:
the actual answer is 43%
Step-by-step explanation:
when 27x2z/-3x2z4 is completely simplified, the exponent on the variable z is _____.
Answer:
0
Step-by-step explanation:
(27x)(2z)/(-3x)(2z)(4)
-9/4
When you divide 2z by 2z, there is an imaginary exponent 1 on the z's. The rule for dividing numbers with exponents is to subtract the exponents. So, 2z/2z = 1(z^1-1) = 1(z^0) = 1
What is the slope of the line that passes through the points (6,4) and (3,8)
Answer:
-1⅓
Step-by-step explanation:
According to the Rate of Change [Slope] Formula, m = -y₁ + y₂\-x₁ + x₂, you plug in each coordinate into the correct places and you will arrive at the above answer.
Does 15,20,25 represent a pythagorean triple?
Answer:
This is a Pythagorean triple.
Step-by-step explanation:
In order to find this, use the Pythagorean Theorem to and see if it gives a true statement.
a^2 + b^2 = c^2
15^2 + 20^2 = 25^2
225 + 400 = 625
625 = 625
Since this is a true statement, we know that this is a Pythagorean Triple.
Help!!!! I will appreciate it.
what's missing is, how many days she was on vacation
Help with the question attached below
Answer:
Exact volume = 294π in³
Approximate volume = 923.6 in³
Explanation:
The volume of a cylinder can be calculated using the following rule:
volume = πr²h
where r is the radius and h is the height of the cylinder
In the given cylinder:
radius = r = 7 in
height = h = 6 in
Substitute with the givens in the formula to get the volume:
Volume of cylinder = πr²h = π(7)²(6) = 294π in³ ≈ 923.6 in³ to the nearest tenth
Hope this helps :)
slope intercept form of 3x - 7y = 0
Answer:
y = 3/7 x
Step-by-step explanation:
Slope intercept form y = mx + b
In this case 3x - 7y = 0
7y = 3x
y = 3/7 x (b = 0)
Answer:
y= 0- 3x over -7
Step-by-step explanation: Slope intercept form is Y= mx+ b
Hope this helps
the quadratic function h(t) = -16.1t squared +150
Answer:
Full question in attached picture.
To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.
Please see the second attached image below, to find more information about the graph .
The equation is:
h(t) = -16.1*t^2 + 150
Looking at the graph, we can tell that the ball was dropped from
150 feet
And it hits the ground after
3.052 s
Answer:
yeah
Step-by-step explanation:
what she or he siad
A rectangular prism with a volume of 5 cubic units is filled with cubes with side length of 1/3 unit. How many 1/3 unit cubes does it take to fill the prism?
Hurry and answer!
Answer:
(1/3)³c = 5
(1/27)c = 5
c = 5 × 27 = 135 cubes
The Main Answer is 135. It takes [tex]135[/tex] of the [tex]1/3[/tex] unit cubes to fill the rectangular prism.
To find out how many [tex]1/3[/tex] unit cubes it takes to fill the rectangular prism with a volume of [tex]5[/tex] cubic units, we need to divide the volume of the prism by the volume of each individual cube.
The volume of the rectangular prism is given as [tex]5[/tex] cubic units. Since the prism is a rectangular shape, we can calculate its volume using the formula:
[tex]Volume of prism=length*width*height[/tex]
Given that the side length of each cube is [tex]1/3[/tex] unit, the volume of each cube is:
[tex]Volume of cube=(side length)^{3} =(1/3)^{3}=1/27 cubic[/tex]
Now, to find out how many cubes are needed to fill the prism, we divide the volume of the prism by the volume of each cube:
[tex]Number of cubes=Volume of prism/Volume of cube \\Number of cubes=5/(1/27)\\Number of cubes=5*27\\Number of cubes=135[/tex]
So, it takes [tex]135[/tex] of the [tex]1/3[/tex] unit cubes to fill the rectangular prism.
COMPLETE QUESTION:
A rectangular prism with a volume of [tex]5[/tex] cubic units is filled with cubes with side length of [tex]1/3[/tex] unit. How many [tex]1/3[/tex] unit cubes does it take to fill the prism?
Which could be the function?
A. F(x)=(x+4)^2
B. F(x)= x^2 +4
C. F(x)=(x-4)^2
D. F(x)= x^2-4
Answer:
C. F(x) = (x - 4)^2
Step-by-step explanation:
f(x) = (x - h)^2 is a parabola that opens up and has the line x = h as the vertical axis.
Here, the vertical axis is x = 4, so h must be 4.
The answer is: C. F(x) = (x - 4)^2
Answer: C. F(x) = (x - 4)^2
Step-by-step explanation: i did on edge
What set of reflections would carry triangle ABC onto itself?
d, 'y-axis, x-axis, y-axis, x-axis'
its the correct answer on the test :)) Goodluck !
The correct set of reflections that would carry triangle ABC onto itself is:
d. y-axis, x-axis, y-axis, x-axis
As per the shown graph, the coordinates of the vertices:
A(0,2)
B(2,4)
C(3,0)
We observe that the y-axis is the vertical line passing through x = 0, and the x-axis is the horizontal line passing through y = 0.
By analyzing the positions of the vertices, we can see that the triangle has rotational symmetry of 180 degrees around points (1, 2) and reflectional symmetry across both the x-axis and the y-axis.
Therefore, the correct set of reflections that would carry triangle ABC onto itself is:
d. y-axis, x-axis, y-axis, x-axis
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Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?
Yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. Once he has the radius, he can use the formula.
Yes, because the area will just be twice the circumference so all he has to do is multiply by 2.
No, because the circumference equals c=diameter and there is no pi in 125.6.
No, because the circumference equals c=diameter so he could only find the diameter. He needs the radius for the area formula.
Answer:
Yes, because he could divide by 3.14 to find the diameter and then divide that result by 2 to find the radius. Once he has the radius, he can use the formula.
Answer:
the answer is A
Step-by-step explanation:
I need help with this !!
Answer:
A.
Step-by-step explanation:
btw this is a biology question, but the reason it's A because think of external+ outside. all the other multiple choices are internal. Such as when you're hungry that's inside of your body same as being thirsty
Answer: a rabbit runs away from a fox that is chasing it
Step-by-step explanation: External stimuli is a reaction. So the rabbit running away from the fox would be a reaction
45,60,75,75,80,80,85,90,90,90,90,95,95,95,100
Can someone find the MAD
Answer:
11.066666666667 or simplified 12
Step-by-step explanation:
Answer: 11.0667
Step-by-step explanation:
= Mean just incase you need is :
83
And population size just incase you need as well is :
15
* Hopefully this helps:) Mark me the brainliest:)!!
~234483279c20~
What is the angle of B. Round your answer to the nearest hundredth
Answer:
B = 53.13
Step-by-step explanation:
Since this is a right triangle, we can use the tan function
tan B = opposite side/ adjacent side
tan B = 4/3
Take the inverse tan of each side
tan ^-1 (tan B) = tan^-1 (4/3)
B = 53.13010235
To the nearest hundredth
B = 53.13
A circle is centered at the origin and contains the point (-6, -8). What is the area of this circle?
Answer:
314 units²
Step-by-step explanation:
Centre of the circle = (0, 0)
Another point on the circle = (-6, -8)
[tex]\text {Radius = }\sqrt{(0 - (-6))^2 + (0- (-8))^2}[/tex]
[tex]\text {Radius = }\sqrt{6^2 + 8^2}[/tex]
[tex]\text {Radius = }\sqrt{100}[/tex]
[tex]\text {Radius = }10[/tex]
Area = π (10)² = 100π = 314 units²
Final answer:
The area of the circle is found by first calculating the radius using the distance formula, which is determined to be 10 units. Then, the area formula πr² is used to find that the area of the circle is 100π square units.
Explanation:
To find the area of the circle centered at the origin containing the point (-6, -8), we first need to determine the radius of the circle. The radius can be found using the distance formula for a point from the origin, which is √((-6)²+ (-8)²). After calculating the radius, we use the formula for the area of a circle, which is πr^2, to find the circle's area.
The distance from the origin to the point (-6, -8) is the radius (r) of the circle: r = √((-6)² + (-8)²) = √(36 + 64) = √100 = 10.
Now that we have the radius, we can calculate the area (A): A = πr² = π(10)² = 100π square units.
The location of point D is (7,1) the location of point F is (5,4). Determine the location of point E which is 1/3 of the way from D to F
Answer:
( 19/3 , 2 )
Step-by-step explanation:
Given in the question,
point D(7,1)
x1 = 7
y1 = 1
point F(5,4)
x2 = 5
y2 = 4
Location of point E which is 1/3 of the way from D to F
which means ratio of point E from D to F is 1 : 2
a : b
1 : 2
xk = [tex]x1 + \frac{a}{a+b}(x2-x1)[/tex]
yk = [tex]y1 + \frac{a}{a+b}(y2-y1)[/tex]
Plug values in the equation
xk = 7 + (1)/(1+2) (5-7)
xk = 19/3
yk = 1 + (1)/(1+2)(4-1)
yk = 2
A plane which passes through three edges of a cube produces a triangular cross section as shown.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
Answer:
The plane should pass through the central axis, along the vertical diagonals of the cube, in order to produce a cross section that is a regular hexagon.
Step-by-step explanation:
The plane should pass through the central axis, along the vertical diagonals of the cube, in order to produce a cross section that is a regular hexagon.
Please see the image attached for better visualization.
To produce a regular hexagon as a cross section of a cube, the plane should pass through the cube's vertices and form an equilateral triangle with the three edges it intersects.
Explanation:In order to produce a regular hexagon as a cross section of a cube, the plane should pass through the cube's vertices. The three edges that the plane passes through should form an equilateral triangle on the face of the cube. This is because a regular hexagon can be formed by placing equilateral triangles side by side.
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