Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = y
x + y = 24
7x - y = 16 Add these two equations
8x = 40 Divide by 8
8x/8 = 40/8
x = 5
The smaller number will be 5
================
5 + y = 24
y = 19
==================
Proof
7*5 - 19 = 16
35 - 19 = 16
If the parabola of the form y = a(x – h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always
Answer:
(h,k)
Step-by-step explanation:
because of how the h is horizontal that is the x value and the k is vertical making it the y value.
(pls mark brainliest)
The vertex gets shifted by h units horizontally and k units vertically.
The parabola is defined by
y = a(x - h)² + k
has its vertex at (h,k).
After a shift by h units right, followed by a shift of k units vertically, the parabola is defined by
y = a(x - 2h)² + 2k
which has its vertex at (2h, 2k).
∴ (h,k).
Vertex Form of the Equation of a Parabola: The equation y=a(x−h)2+k y = a ( x − h ) 2 + k of a parabola is said to be in vertex form because the vertex can be determined by examining the equation: (h,k) is the vertex.
What is the formula of parabola?The equation of a parabola can be written in two basic forms: Form 1: y = a( x – h) 2 + k. Form 2: x = a( y – k) 2 + h.
What is parabola and examples?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. Terms related to Parabola.
Learn more about the parabola, refer
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Find the measure of the reference angle for an angle of 152º.
Answer:
28 deg
Step-by-step explanation:
Reference angle is the smallest angle formed by the terminal ray, x-axis, and origin. So at 180 you are on the x-axis so just for this question you have to do 180-152=28.
The reference angle should be a positive between 0 and 90 degrees.
Which of the following is a true statement about skew lines?
A. Skew lines are parallel.
B. Skew lines intersect at a single point.
C. Skew lines are perpendicular.
D. Skew lines do not lie in the same plane
The statement which is true about skew lines is:
Option: D
D. Skew lines do not lie in the same plane
Step-by-step explanation:Skew lines-
In mathematics, skew lines are the lines which do not intersect and also they are never parallel.
Also, we know that if two lines are on the same plane i.e. coplanar this means either they will cross i.e. intersect or will be parallel.
This statement imply that skew lines do not lie in the same plane i.e. they are non-coplanar.
Hence, from all of the definition and the property above we get:
D. Skew lines do not lie in the same plane
Which quadratic equation is equal to (x+2)^2+5(x+2)-6=0
Answer:
(x+2)^{2} +5(x+2)-6=0
Let
u=(x+2)
Substitute in the expression
(u)^{2} +5(u)-6=0
therefore
the answer is
(u)^{2} +5(u)-6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0
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NEED HELP ASAP 10 POINTS
Answer:
unlikley
Step-by-step explanation:
PLEASE HELP!!!
Select all that apply.
Describe the transformations.
The yellow rectangle was translated up 3 units and reflected over the y-axis.
The yellow rectangle was translated right 5 units and reflected over the x-axis.
The yellow rectangle was reflected over both axes.
The yellow rectangle was translated right 5 units and up 3 units.
HELP PLEASE I'M CRYING, EASY 2 QUESTIONS
Answer:
12) 154 squared meters
13) 307 cm^2
Step-by-step explanation:
12) A circle has area pi*r^2
r is half the diameter so half of 14 is 7
pi in this case is 22/7
A=22/7 * (7)^2
A=22/7 * 49
A=22 *49/7
A=22 *7
A=154 squared meters
13) Area of rectangle is 10(18)=180
Area of half a circle is .5*pi*r^2=.5*pi*9^2
Adding the two areas together would result in a total area of 307.2 squared centimeters
Both the red and blue line segments stretch from the center of the circle to a
point on the circle. The length of the blue line segment is 7. How long is the
red line segment?
Center
O A. 14
O B. 7
O C. 10.5
O D. 3.5
Answer:
7
Step-by-step explanation:
Blue is 7 and the Red is 7
Answer:
7
Step-by-step explanation:
The length of a rectangle is 3 inches less than twice the width. If the perimeter of the rectangle is 18 inches, find the width of the rectangle
Answer:
y = 4. So this is your width.
Step-by-step explanation:
Use the distributive property to do 2(2y-3) = 2*2y-2*3 = 4y-6. So we have
4y-6+2y = 18. Combine like terms 4y and 2y to get 6y.
6y-6 = 18. Add 6 to both sides to solve for 6y
6y = 24. Divide by 6 to solve for y
y = 4. So this is your width.
length = x
________________
| |
y | | width = y
| |
_________________
x
The width of the rectangle is determined to be 4 inches.
To find the width of the rectangle, we need to set up equations based on the information given. The length (L) is described as being 3 inches less than twice the width (W), so we can express that as L = 2W - 3. The perimeter (P) of a rectangle is calculated as P = 2L + 2W. We are told the perimeter is 18 inches, so we have 18 = 2(2W - 3) + 2W. Simplifying this equation, we get 18 = 4W - 6 + 2W, which combines to 18 = 6W - 6. Adding 6 to both sides gives us 24 = 6W, and dividing both sides by 6 yields W = 4 inches. Therefore, the width of the rectangle is 4 inches.
The process used here is similar to working through proportions and scale factors. For instance, if one is working with scale models, as in the miniature fish pond example, the scale factor is used to determine the dimensions in the model based on actual size dimensions. However, in this case, the given equations allowed us to find the width directly.
solve for -4x-4=-4(x+2)
Answer:
no solutions
Step-by-step explanation:
-4x-4=-4(x+2)
Distribute the negative
-4x-4 = -4x-8
Add 4x to each side
-4x+4x-4 = -4x+4x-8
-4 = -8
Since this is not true there are no solutions
Solve x2 – 64 = 0.
1. Isolate x2: x2 = 64
2. Apply the square root property of equality: 7x2 = 1/64
3. Isolate the variable:
0
x =
x=
Answer:
x = - 8, x = 8
Step-by-step explanation:
Given
x² - 64 = 0 ( add 64 to both sides )
x² = 64 ( take the square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8
Sophie sprays 200 fluid ounces of water on the window plants in her house every day. How much water does she spray each day?
A. 1.5625 gal.
B. 1.7500 gal.
C. 2.250 gal.
D. 2.500 gal.
A. 1.5625 gal.
Formula
divide the volume value by 128
I decided 200 by 128 and voila; there is the answer.
Math help, I'm stuck with my homework and I want to get it done.
if the gragh of y=-4x+7 is perpendicular to the gragh of y=mx+3 then what does m equal
Answer:
m = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x + 7 is in this form with slope m = - 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
Hence the value of m = [tex]\frac{1}{4}[/tex]
what is 10 divided by 05
[tex]10 \div .05[/tex]
let's convert the 0.05 to a fraction first, so we have two decimals, so our fraction will have two zeros then.
[tex]\bf 0.\underline{05}\implies \cfrac{005}{1\underline{00}}\implies \cfrac{1}{20} \\\\[-0.35em] ~\dotfill\\\\ 10\div 0.05\implies \cfrac{10}{1}\div \cfrac{1}{20}\implies \cfrac{10}{1}\cdot \cfrac{20}{1}\implies 200[/tex]
a bicycle tire is 28 inches in diameter. approximately how far does the bicycle move forward each time the wheel goes around? (use 22/7 as an approximation for pi.)
Answer: 88 inches
Step-by-step explanation:
Given : A bicycle tire is 28 inches in diameter. approximately.
To find the distance traveled by the bicycle each time the wheel goes around we need to find the circumference of the tire.
The circumference of a circle : [tex]\pi d[/tex], where d is the diameter of the circle.
Now, the circumference of tire : [tex]\dfrac{22}{7} \times(28)=88[/tex]
Hence, the distance traveled by the bicycle each time the wheel goes around =88 inches.
The wheel moves forward each time, in a single round it will cover distance of 88 inches.
Given information:
The diameter of the tire is 28 inches.
Now, if we need to find the distance covered by the tire in one round, we need to understand that the tire will cover exactly same distance as it's circumference in one round.
So, the distance will be equal to its circumference :
[tex]D=\pi\times d[/tex]
Hence, distance covered (D)
[tex]D=3.14\times 28\\D=88[/tex]
Hence, when the wheel move forward each time the in a single round it will cover 88 inches.
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You are choosing 3 of your 8 trophies and arranging them in a row on a shelf.
In how many different ways can you choose and arrange the trophies?
O A. 56
O B. 40,320
O C. 24
O D. 336
[tex]{_8C_3}\cdot 3!=\dfrac{8!}{3!5!}\cdot 6=\dfrac{6\cdot 7\cdot 8}{6}\cdot6=336[/tex]
There are 336 ways we can choose and arrange the trophies.
The answer is option D. 336
What are permutation and combination?A permutation is a mathematical way that determines the number of possible arrangements in a set.In a permutation, the elements are arranged in a specific order.A combination is a method that determines the number of possible arrangements in a set. In a combination, the elements of the set can be arranged in any order.
calculation:-
₃C⁸.3! = 8!/3!5!.6 = (6.7.8)/6.6 = 336
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Solve the system of equations.
y= 2x
y= x^2 - 15
Answer:
Since both equations are equal to each other given that they are both equal to y, you can say that . . .
2x = x^2 - 15
x^2 - 2x - 15 = 0
(x-5) (x+3) = 0
Zero Product Property
x = 5 ; x = -3
Solve for y:
y = 2(5) ; y = 2(3)
y = 10 ; y = 6
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Which of the following are true about x? Check all that apply. x ∉ A x ∈ B x ∉ C x ∈ A ⋃ B x ∈ A ⋃ C x ∈ A ⋂ B
Answer:
The true statements are,
x ∈ B
x ∉ C
x ∈ A ⋃ B
x ∈ A ⋂ B
x ∈ A ⋃ C
Step-by-step explanation:
From the figure we can see three sets A, B, C
Check all options
1) x ∉ A
From the figure we get, x is an element of A
x ∉ A is False
2) x ∈ B
From the figure we get, x is an element of B
x ∉ B is True
3) x ∉ C
From the figure we get, x is not an element of C
x ∉ C is True
4). x ∈ A ⋃ B
From the figure we get, x is an element of A ⋃ B
x ∈ A ⋃ B is True
5). x ∈ A ⋃ C
From the figure we get, x is an element of A ⋃ C
x ∈ A ⋃ C is True
6).x ∈ A ⋂ B
From the figure we get, x is an element of A ⋃ B
x ∈ A ⋂ B is True
Answer:
Everything is true expect for the first answer choice .
Step-by-step explanation:
What is the solution to the inequality below?
2- 2x>-20
Answer:
x<11
Step-by-step explanation:
Subtract by 2 both sides of equation.
2-2x-2>-20-2
Simplify.
-2x>-22
Multiply -1 from both sides of equation.
(-2x)(-1)<(-22)(-1)
Simplify.
2x<22
Divide by 2 from both sides of equation.
2x/2<22/2
Simplify, to find the answer.
22/2=11
x<11 is the correct answer.
To solve the inequality 2 - 2x > -20, we isolate the variable term by adding 2x to both sides, subtracting 2, and then dividing by 2 to find that the solution is x < 11.
To solve the inequality 2 - 2x > -20, we can follow these steps:
Add 2x to both sides of the inequality to isolate the constants: 2 > -20 + 2x.Then subtract 2 from both sides to isolate the variable term on one side: 0 > -22 + 2x or -22 + 2x < 0.Divide both sides by 2, noting that division by a positive number does not change the direction of the inequality: -11 + x < 0 or x < 11.The solution to the inequality is x < 11.
Deedra has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7. What must be true about the two lines?
we can take a peek at two of those lines hmmm say y = 5x + 3 and y = 5x + 7.
let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.
since y = y then
5x + 3 = 5x + 7
3 = 7 what the?
well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?
it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.
The two lines are parallel.
We have a girl Deedra who has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7.
We have to investigate what it tells about the nature of lines.
What is the slope - intercept form of equation of line?The slope intercept form of an equation of line is -
y = mx + c
Let's assume we have two lines with their equations be -
[tex]y_{1} = m_{1} x_{1} + c\\y_{2} = m_{2} x_{2} + d[/tex]
To find the intersecting points of these two lines, then -
[tex]y_{1} =y_{2} \\x_{1} =x_{2}[/tex]
Therefore -
[tex]m_{1} x_{1} +c =m_{2} x_{2} +d\\[/tex]
Now, in the question she found out that 3 =7 which is same c = d. To fulfill this condition, the slope of these two lines should be equal. Hence, we can conclude that the two lines are parallel.
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20 points for this. I just gotta know so I can pass summer school lol
Answer: Point, Point, Line
Step-by-step explanation:
A plane and a line intersect at a point . Think of a piece of paper as a plane and a pen as a line. What happens when you push the pen through the paper? It creates a point!
Two lines intersect at a point .
Two planes intersect at a line . Think of a piece of paper laid horizontally on a table and another piece of paper standing on it vertically. What can you draw at the places of intersection? A line!
At a game show, there are 8 people (including you and your friend) in the
front row.
The host randomly chooses 3 people from the front row to be contestants.
The order in which they are chosen does not matter.
How many ways can you and your friend both be chosen?
Answer:
6
Step-by-step explanation:
For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities
Answer:
A. [tex]^6C_1=6[/tex]
Step-by-step explanation:
Given,
The total number of people = 8,
The number of people have to chosen = 3,
Since, me and my friend both have to be chosen,
So, the remaining number of people = 8 - 2 = 6,
And, the number of remaining number of people have to be chosen = 3 - 2 = 1
Also, the order does not matter,
Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people
[tex]=^2C_2\times ^6C_1[/tex]
[tex]=1\times ^6C_1[/tex]
[tex]=6[/tex]
Option A is correct.
A student decides to run a simulation of rolling an even number with a single die. Use the simulated results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability.
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
Answer:
Practical probability: 9 / 20 = 45%
Theoretical probability: 3 / 6 = 50%
Step-by-step explanation:
So, we have 20 rolls:
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6
Out of which we have 9 even numbers: 2 6 6 4 4 6 2 2 6
So, the practical probability is 9 / 20 or 45%
The theoretical probability is:
Possible outcomes (6): 1 2 3 4 5 6
Even numbers possible (3): 2 4 6
P = 3 / 6 = 50%
The practical probability is a bit lower (45%) than the theoretical probability (50%) but that's most probably due to the low number of rolls, it's just one roll away from being on target. With a greater number of rolls, the student would get closer to the theoretical probability.
One number is 4 less than 3 times a second number. If 3 more than two times the first number is decreased by 2 times the second number, the result is 11. Use the substitution method. What is the first number?
Answer:
The first number is 8
Step-by-step explanation:
Let
x -----> the first number
y ----> the second number
x=3y-4 ----> equation A
3+2x-2y=11 ----> equation B
Substitute equation A in equation B and solve for y
3+2(3y-4)-2y=11
3+6y-8-2y=11
4y=11+5
y=16/4=4
Find the value of x
x=3(4)-4=8
Factorise (x-y)4-(x-y)2
Answer:
Step-by-step explanation:
Let x - y = A
A^4 - A^2
A^2 ( A^2 - 1)
A^2 (A + 1)(A - 1)
(x - y)^2 (x - y + 1)(x - y - 1)
If I have not thought out the question properly please leave me a note.
Which statements about these triangles is true
Answer:
I’m not sure, but I think it’s C
X=
A. 115.5
B. 137
C. 180
Answer:
The correct answer option is C. 180
Step-by-step explanation:
We are given a figure of a circle with two known angles measuring 137 degrees and 94 degrees and we are to find the value of x.
Finding x:
[tex]137 = \frac{1}{2} (\angle x + 94)[/tex]
[tex]137 = \frac{1}{2} \angle x + 47[/tex]
[tex]\frac{1}{2} \angle x = 137 - 47[/tex]
[tex]\frac{1}{2} \angle x = 90 [/tex]
[tex] \angle x = 90 \times 2&# 1 0 [/tex]
x = 180
Answer:
the answer is 180
Step-by-step explanation:
Because yes!! Also I hope you have a wonderful wonderful day!! :D
The Constitution gives Congress the power to create federal courts
lower than the Supreme Court
higher than the Supreme Court
equal to the Supreme Court,
unaffected by the Supreme Court.
The federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.
What are Federal Courts?Federal courts can be described as lower courts having limited jurisdiction. This implies that they are only authorized to hear cases that arise under the federal statues in the United States.
The Supreme Court is the highest court. District courts are the lowest federal courts.
Therefore, the federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.
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The U.S. Constitution allows Congress to establish federal courts lower than the Supreme Court, but not higher, equal to, or unaffected by it. The Supreme Court is the highest court in the U.S. judiciary.
Explanation:The Constitution gives Congress the power to create federal courts that are lower than the Supreme Court. According to Article III, Section 1 of the Constitution, 'The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.'
The Constitution does not give Congress the power to create courts that are higher than, equal to, or unaffected by the Supreme Court. The Supreme Court is the highest court in the U.S. judicial system, and all lower courts must follow the legal precedents set by it.
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Find the slope the line that contains the points (1,9) and (-5,8). what is the slope formula?
Answer: 1/6
Step-by-step explanation:
Lets say two points are (a,b) and (c,d)
the slope that cross these two points is: (b-d)/(a-c) or (d-b)/(c-a) → either one is fine, but make sure the one you are subtracting is the one from the same point.
Hope it helped!
Answer:
The slope formula is [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
The slope of (1, 9) and (-5, 8) is 1/6
Step-by-step explanation:
(9 - 8)/( 1 - [-5]) = 1/6
an official playing field (including end zone) for the indoor football league has a length 45 yd longer than its width. the perimeter of the rectangular field is 174 yd. find the length
Given the provided conditions, we set up an equation to determine the width and length of the indoor football field. After simplifying the appropriate mathematical expressions, we find that length of the football field is 66 yards.
Explanation:In this problem, we're solving for the length of an indoor football field. We know that the perimeter of a rectangle is given by [tex]2L + 2W[/tex] (twice the length plus twice the width) and the length is said to be 45 yards longer than the width. Therefore, we would describe the length as 'W + 45'
Let's represent the width as W and thus the length as W + 45. Substituting these into our perimeter equation we get [tex]2(W) + 2(W +45) = 174.[/tex] Simplifying gives [tex]4W + 90 = 174[/tex]
Subtracting 90 from both sides gives 4W = 84. Thus, W = 21. Substituting this value back into our equation for the length gives us L = 21 + 45 which equals 66 yards. Therefore, the length of the indoor football field is 66 yards.
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