Answer:
the vertex is (-7, -63)
Step-by-step explanation:
x^2 + 14x - y - 14 = 0
x^2 + 14x = y + 14 (to isolate the x)
x^2 + 14x + 49 = y + 14 + 49
(x+7)^2 = y + 63
now we convert to vertex form, which is y = a(x – h)2 + k :
(x+7)^2 = y + 63
y = (x+7)^2 - 63
The vertex in vertex form is shown as (h, k) from y = a(x – h)2 + k, so in this case, h = -7 and k = -63. H is the x-coordinate as shown while k is the y-coordinate. Thus, the vertex is (-7, -63)
A school is planning to construct two rectangular play areas in the playground. The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal. Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system's solutions?
Answer:
А.The system has two solutions, but only one is viable because the other results in a negative width.
Step-by-step explanation:
Given
Let:
[tex]L_A \to[/tex] length of play area A
[tex]W_A \to[/tex] width of play area A
[tex]L_B \to[/tex] length of play area B
[tex]W_B \to[/tex] width of play area B
[tex]x \to[/tex] Area of A
[tex]y \to[/tex] Area of B
From the question, we have the following:
[tex]L_A = 1 + 4W_A[/tex]
[tex]W_B = 2 + W_A[/tex]
[tex]L_B = 2 + 3W_B[/tex]
[tex]x = y[/tex]
The area of A is:
[tex]x = L_A * W_A[/tex]
This gives:
[tex]x = (1 + 4W_A) * W_A[/tex]
Open bracket
[tex]x = W_A + 4W_A^2[/tex]
The area of B is:
[tex]y = L_B * W_B[/tex]
[tex]y = (2 + 3W_B) * ( 2 + W_A)[/tex]
Substitute: [tex]W_B = 2 + W_A[/tex]
[tex]y = (2 + 3(2 + W_A)) * ( 2 + W_A)[/tex]
Open brackets
[tex]y = (2 + 6 + 3W_A) * ( 2 + W_A)[/tex]
[tex]y = (8 + 3W_A) * ( 2 + W_A)[/tex]
Expand
[tex]y = 16 + 8W_A + 6W_A + 3W_A^2[/tex]
[tex]y = 16 + 14W_A + 3W_A^2[/tex]
We have that:
[tex]x = y[/tex]
This gives:
[tex]W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2[/tex]
Collect like terms
[tex]4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0[/tex]
[tex]W_A^2 -13W_A - 16 =0[/tex]
Using quadratic calculator, we have:
[tex]W_A = -14.1[/tex] or [tex]W = 1.13[/tex] --- approximated
But the width can not be negative; So:
[tex]W = 1.19[/tex]
Which expression is equivalent to a^-x?
Classify the triangle: I NEED HELPPPP PLEASEEEEEEEEEEEEE
Answer:
Right scalene
Step-by-step explanation:
The triangle has a right angle, but no sides are equal.
Answer:
The triangle is a right scalene triangle.
Step-by-step explanation:
If any angle is marked by a little square like in the triangle's bottom left corner, that means the angle is 90° or a right angle. Since none of the angles in the triangle are equivalent, that means the right triangle is a scalene triangle. So the correct choice is a right scalene triangle.
Explain how to add 5.3 + 9.079
Answer:
14.379
Step-by-step explanation:
1. Line up from left to right
2. Make sure that the decimals are lined up
3. Add the thousandths and hundredths with 0
4. Add 3 in the tenths place
5. Add up 9 and 5 to make 14
*IF YOU DID THE STEPS RIGHT, THEN YOU SHOULD HAVE 14.379 AS YOUR ANSWER*
Answer:
9.079
+5.300
_______
14.379
Step-by-step explanation:
Just line the decimals up and add zeros for 5.3 to 5.300 because you can't do 9.079
+5.3 because your decimal will be in the wrong spot and your answer will come out wrong
Angle A and Angle B are vertical angles. If the measure of Angle A is 30 degrees, what is the measure of Angle B?
Answer: 30 degrees
Step-by-step explanation: Vertical angles are always congruent. If Angle A and Angle B are vertical then they are equal to each other. They both will way thirty degrees.
Please help! I will give Brainliest!
Who is correct?
Answer:
Erin
Step-by-step explanation:
I believe Erin is right in this case.
Company is testing a robot.The robot is 12 inches tall and weigh 4 pounds.The employees of the company marked a grid on the floor and set the robot at(4,4). They programmed the robot to walk 4 yards east and 6 yards north each minute.What will the robot's location be after 7 minutes? The x coordinate and the y coordinate
Answer:
[tex]P(2)=(32,46)[/tex]
Step-by-step explanation:
From the question we are told that:
Height of robot [tex]h=12 inches[/tex]
Weight of robot [tex]W=4[/tex]
Start position [tex]P(1)=(4,4)[/tex]
Per minute distance [tex]d=(4,6)[/tex]
Total time [tex]T=7min[/tex]
Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by
[tex]d_T=d*T[/tex]
[tex]d_T=(4.6)*7[/tex]
[tex]d_T=(28,42)[/tex]
Generally the position of the robot after 7 minutes is mathematically given by
[tex]P(2)=P(1)+d_T[/tex]
[tex]P(2)=(4,4)+(28,42)[/tex]
[tex]P(2)=(32,46)[/tex]
Therefore the position of the robot after 7 minutes is
[tex]P(2)=(32,46)[/tex]
how many terms does 3x + 5y - 17 - 2y + x have?
Answer:
It has 5 terms
Step-by-step explanation:
Terms are the numbers or values in a equation, so this Equation has 5 terms
x + 5y - 17 - 2y + x.
1. x
2.5y
3.17
4. 2y
5.x
(I listed the terms)
PLEASE HELP DUE IN 20 MINUTES!!!
about cylinders
Answer: Diameter = 4 cm
Step-by-step explanation:
20π = (π)(r^2)(5)
divide by 5 * π
4 = r^2
find the square root of both sides
2 = r
2 * 2 = d
4 = d
5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.
9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
_____
Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
Find the measure of the angle indicated.
P
A) 92°
B) 61°
C 86°
D) 34°
Answer:
92°÷^®√™÷√÷^π^π^^π^π°π°^÷
Macy took a Math test; her ratio of the correct to incorrect answers was 8:2.
If there were 30 questions on the test, how many did Macy get correct?
FAST RESPONSE PLEASE!!!!
Answer:
24
Step-by-step explanation:
8 correct for every 2 wrong
multiply both sides by 3
24 correct and 6 wrong
which adds up to 30
Ahhhhhh i neeed help
Answer:
ok hiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Answer:
Option C, No real solutions
Hope this helps!
What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line x+2y=18x+2y=18?
Answer:
[tex]y=-\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope (m) and different y-intercepts (b)1) Determine the slope (m)
[tex]x+2y=18[/tex]
Rearrange this equation into slope-intercept form (this will make it easier for us to identify the slope)
Subtract x from both sides to isolate 2y
[tex]x+2y-x=-x+18\\2y=-x+18[/tex]
Divide both sides by 2 to isolate y
[tex]y=-\frac{1}{2} x+9[/tex]
Now, we can see clearly that [tex]-\frac{1}{2}[/tex] is in the place of m. Because parallel lines have the same slope, [tex]-\frac{1}{2}[/tex] is therefore the slope of the line we're currently solving for. Plug [tex]-\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]:
[tex]y=-\frac{1}{2} x+b[/tex]
2) Determine the y-intercept
[tex]y=-\frac{1}{2} x+b[/tex]
Plug in the point (8,-7)
[tex]-7=-\frac{1}{2} (8)+b\\-7=-4+b[/tex]
Add 4 to both sides
[tex]-7+4=-4+b+4\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:
[tex]y=-\frac{1}{2} x-3[/tex]
I hope this helps!
solve: 7 (j-5)=-14 what is the value of j?
Answer:
open bracket
7j - 35 = 14
7j = 14 + 35
7j = 49
divide thru by 7
7j / 7 = 49 / 7
j = 7
sean needed to put 7 gallons 3 quarts of gas into his boat on Monday and twice as much on Saturday.if he had a 22 gallon jug of gas available, did he have enough gas for both days?
Answer:
No
Step-by-step explanation:
7 3/4 x 3 = 22 1/2
6. In 2002, the bear population in Florida was estimated to be 2,700. In 2019, it was reported to be
4050. What percent does the increase in bears represent? Pls put the steps. Pls help this is due in 15 minutes
Answer:
50% increase
Step-by-step explanation:
4050-2700 = 1350
1350/2700 = 0.5
Convert to a percentage:
0.5*100 = 50
Using the image above, describe the error in the statement of the tangent ratio. answer correctly !!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
the right answer is
tan D=80/18
Write the equation of the line passing through the points (0, -4) and (-2, 2).
Answer:
y=-3x-4
Step-by-step explanation:
i solved it by the two points
Select the true statement. A. Neither function is even. B. Only function f is even. C. Only function g is even. D. Both functions are even.
Answer:
The answer is "Option C".
Step-by-step explanation:
The graph of the even function will have both ends pointed in the same direction, while the graph of the odd function will have both ends pointed inside the reverse way. Furthermore, as the y-axis approaches, and also regular expression graph becomes symmetric. The graph of an unusual function, on either hand, is symmetric around the origin and also has rotational symmetry around the origin. They could see that the graph of function g meets a function requirement by looking at it. That graph of function f, but on the other hand, is not symmetric about its y-axis, implying that function f is not even. As both a result, g is a function that is even.
Answer:
Only function g is given
Step-by-step explanation:
At a surf shop in Malibu, California, a used blue surfboard is on sale for $100. According to the salesperson, the new price represents a 20% discount from the original price. What did it sell for originally?
Answer:
$125
Step-by-step explanation:
if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price
let a = original price
this equation can be used to represent the question
a x 0.8 = 100 ]]divide both sides by 0.8
a = 100 / 0.8 = 125
Answer please !!!!!!!!!
Tim dug a hole that was 24 inches deep. Later that day it rained washing 11 inches of dirt back back in the hole. After it dried, Tim went back out and dug the hole 13 inches deeper. How deep was the hole after he finished? Show your work.
Answer: 2 inches
Step-by-step explanation:
14 inches
Step-by-step explanation:
Length of the hole = 16(½) inches
Length of the dirt = 8(¾)inches
The distance between the top of the pile to the bottom of the hole = ?
Since the dirt is beside the hole and not inside the hole, we can find it's length using addition.
Distance from the top to the bottom = length of dirt + length of the hole
Length of dirt = 8×¾ = 6 inches
Length of the hole = 16 × ½ = 8 inches
Distance from the top of the dirt to the bottom of the hole = (6 + 8) inches
Distance from the top of the dirt to the bottom of the hole = 14 inches
Note: the only way we can use subtraction here is if the hole was filled with dirt, what's the distance that's left
Distance left = length of hole - length of dirt
Distance left = 8 - 6 = 2 inches .
how should i solve number 2 ?
The flagpole at school casts a shadow that is 18 feet long. A student nearby is 5.5 feet tall and casts a shadow that is 3 feet long. How tall is the flagpole?
Answer:
33 feet.
Step-by-step explanation:
If the ratio of the student to their shadow and flagpole to its shadow are equal, then you can use the proportion
5.5/3 = x/18 and cross multiply to find x.
5.5 × 18 = 99
3 × x = 3x
3x/3 = x, 99/3 = 33.
x = 33.
PLEASE HURRY!!! ACTUALLY ANSWER PLEASE
Answer:
C
Step-by-step explanation:
Process of elimination
HIII can some one please HELP ME !!!!
Answer:95
Step-by-step explanation:
Determine the volume of the CD box shown
7.5 in
6.25 in.
8 in
Answer:
Step-by-step explanation:
I hope this helps you
Rectangular Prism Volume is
Height. Width. Height
(6.25).(7.5).(8)
375
How do you find the interquartile range?
what is the value of x squared + 2 x y / 2 * W + 3 * z for w=2, x=5, y=8 and z=3
Answer: 114
Step-by-step explanation:
Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114