Answer:
see below
Step-by-step explanation:
y = a ( x-0)^2 + 5 sub in the point given to calculate 'a'
1 = a (4)^2 + 5
-4 = 16a
a = - 1/4
y = -1/4 x^2 + 5
Which inequality represents the graph?
z≤-10 z≥-10
z-10 z<-10
K
+
-25-20 -15-10 -5
0
0
5
O
Answer: z _> -10
Step-by-step explanation:
To use the tree house as the start of the zip line, the cable needs to be attached to
the starting tree at a height 18 feet above the ground.
To meet the slope constraint, Esteban wants to change the height 7 feet and end the
zip line at a height 11 feet above the ground. He claims this vertical change meets the
slope constraint.
Test Esteban's claim for Tree A and Tree B. Use specific numbers from the situation to
justify or refute whether having a vertical change of 7 feet will satisfy the slope
constraint for each tree.
For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
To use the treehouse as the start of the zip line, the cable needs to be attached to the starting tree at a height of 18 feet above the ground.
To meet the slope constraint, Esteban wants to change the height to 7 feet and end the zip line at a height of 11 feet above the ground.
He claims this vertical change meets the slope constraint.
The slope for tree A will be
[tex]\rm Slope \ A = \dfrac{7}{120}\\\\Slope \ A = 0.0583[/tex]
The slope for tree B will be
[tex]\rm Slope \ B = \dfrac{7}{160}\\\\Slope \ B = 0.043[/tex]
For both tree A and tree B calculated slope is less than 0.06. Then it does not satisfy the slope constraint.
More about the slope link is given below.
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For x2 + 3x - 18 = (x - 3)(x + a), what value
of a would make this equation true?
i beg <3
what is the domain? a. (-infinity, infinity) b. (-infinity,4) c. (-4,4) d. (0,4) what is the range? a. (-infinity, infinity) b. (-infinity,4] c. [-4,4] d. (0,4)
Answer:
Given:
A set of functions,
A. y = -(x-4)^2
B. y=3(x- 4)^2
C. y = [x] + 4
D. y = -5x + 4.
To Find:
The function whose range is (-infinity, 4].
Solution:
1. The function y = -(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).
2. The function y = 3(x-4)^2 has a minimum value of 0 and it is an increasing function. Hence the maximum value tends towards infinite. Hence the range is [0, infinite).
3. y = [x] + 4 (where [x] = greatest integer function). This function is an increasing function with a minimum value towards negative infinity and the maximum value tends towards the positive side of infinity.
=> Range of y = [x] + 4 is (-infinite, infinite).
4. y = -5x+4 is a continuous increasing function without any exceptions.
=> Range of y = -5x+4 is (-infinite,infinite)
Therefore, none of the functions has their range from (-infinity,4].
Step-by-step explanation:
Find the equation of the line with slope = -6 and passing through (-2,10). Write your equation in the
form y = mx + b.
Submit Question
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{10})\qquad \qquad \stackrel{slope}{m}\implies -6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-6}(x-\stackrel{x_1}{(-2)}) \\\\\\ y-10=-6(x+2)\implies y-10=-6x-12\implies y=-6x-2[/tex]
A cylinder has a height that is 2 times as large as its radius. The lateral area of the cylinder is
16π square units. What is the length of the radius of the cylinder?
Answer:
2 units!
Step-by-step explanation:
Answer: 2 units
Solve the inequality 20 – 6x < -10.
Answer:
x = 5
Step-by-step explanation:
Bart wants to deposit his piggy bank savings into a savings account. If he deposits $325. 76, how many whole years will it take, at 2% simple
Interest, for that amount to grow to $400. 00?
A. 12 years
B. 4 years
C. 16 years
D. 8 years
Answer:
Step-by-step explanation:
Compounding interest :
Future value of money = Present value * (1+ r)^N
r - interest rate
n - number of period
In our example, Present value = 325.76, FV = 400, r = 2%, and we need to find N
by solving that we can find it that N is equal to 10.3675
Simple interest :
400 - 325.76 = 74.26$ we need to increase
325.76*2% = 6.5152$ each year
74.26 / 6.5152 = 11.3949
as a whole year = 12years
whats the minimum and maximum value of f(x)=3(x+8)^2−10
Answer:
(-8,-10)
Step-by-step explanation:
Rewrite (x+8)2(x+8)² as (x+8)(x+8).
f(x)=3((x+8)(x+8))−10
Expand (x+8) (x+8) using the FOIL Method.
Apply the distributive property.
f(x)=3(x(x+8)+8(x+8))−10
Apply the distributive property.
f(x)=3(x⋅x+x⋅8+8(x+8))−10
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply x by x.
f(x)=3(x2+x⋅8+8x+8⋅8)−10
Move 8 to the left of x.
f(x)=3(x2+8⋅x+8x+8⋅8)−10
Multiply 8 by 8.
f(x)=3(x2+8x+8x+64)−10
Add 8x and 8x.
f(x)=3(x2+16x+64)−10
Apply the distributive property.
f(x)=3x2+3(16x)+3⋅64−10
Simplify.
Multiply 16 by 3.
f(x)=3x2+48x+3⋅64−10
Multiply 3 by 64.
f(x)=3x2+48x+192−10
Subtract 10 from 192.
f(x)=3x2+48x+182
The minimum of a quadratic function occurs at x=[tex]-\frac{b}{2a}[/tex] If a is positive, the minimum value of the function is f ([tex]-\frac{b}{2a}[/tex]).
Substitute in the values of aa and b.
x=−[tex]\frac{48}{2(3)}[/tex]
x=-8
Replace the variable x with −8 in the expression.
f(−8)=3(−8)2+48(−8)+182
Y=-10
Therefore, the minimum value is (-8,-10) but if it is asking for just the y-value it would be -10.
find the area plssssssssssssssssss
Answer: 32 m^2
Step-by-step explanation:
first set up your equation; A=A rectange - 2(A square). The you plug in your numbers A = 40-2(4). The you do 40-8 = 32
City Hall is 4 meters shorter than the bank. The bank is 13 meters tall. The hospital is 11 meters tall. How tall is City Hall?
Answer:
The answer is 9
Because the 4 meters short than bank and ban is 13 meters
So subtract 13 - 4=9
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEwhich of the following shapes are squares? please answer correctly I'll mark brainliest
All are technically squares, but if you are referring to just squares, then C and D are squares.
I really need help, I'm struggling. Question is in image.
Answer:
See below ~
Step-by-step explanation:
(a)
Original Temp : -7°FTemp change : 15°F⇒ -7°F + 15°F = 8°F(b)
Temp in Juneau = -28°FTemp in Montreal = -15°FDifference in temp = -28 - (-15)-28 + 15 = -13°F lower5pts and whoever has the correct answer gets brainliest
Answer:
B
Step-by-step explanation:
what is the surface area, in square inches, of the rectangular prism formed by folding the next below?
Therefore, the surface area of the rectangular prism is 2600 square inches.
What is surface area?In geometry, surface area is the total area that the surface of a 3-dimensional object covers. It is the sum of the areas of all the faces or surfaces that make up the object. Surface area is often used to determine the amount of material needed to cover an object or to calculate the heat transfer between an object and its surroundings.
Here,
To find the surface area of the rectangular prism, we need to find the area of each of its faces and add them together. Looking at the net, we see that there are three pairs of identical rectangles: the top and bottom faces, the front and back faces, and the left and right faces. Each of these rectangles has dimensions of 23 inches by 8 inches.
Therefore, the surface area of the rectangular prism is:
=2 * (23 in. * 8 in.) (top and bottom faces)
=2 * (36 in. * 8 in.) (front and back faces)
=2 * (23 in. * 36 in.) (left and right faces)
= 368 + 576 + 1656
= 2600 square inches
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Question 3
6 pts
A ball is thrown vertically upward with an initial velocity of 48 feet per
second and started from a height of 8 ft off the ground.
a. Write a vertical motion equation that models the situation.
b. How long will it take the ball to hit the ground? (round to the nearest
Hundredth)
c. How long will it take the ball to be 56 ft above the ground?
No answer text provided.
(a) The vertical motion equation for the ball is h = 8 + 48t - 16t².
(b) The time for the ball to hit the ground is 3.15 s.
(c) The time for the ball to travel 56 ft above the ground is 0.79 s.
Vertical motion equation for the ball
The vertical motion equation for the ball is calculated as follows;
h = h₀ + vt - ¹/₂gt²
h = 8 + 48t - ¹/₂(32)t²
h = 8 + 48t - 16t²
Time for the ball to hit the ground0 = 8 + 48t - 16t²
solve the above quadratic equation with formula method;
a = -16, b = 48, c = 8
t = 3.15 s
Time for the ball to be 56 ft above the groundlet upward motion be positiveh = 8 + 48t + 16t²
56 = 8 + 48t + 16t²
0 = -48 + 48t + 16t²
solve the above quadratic equation with formula method;
a = 16, b = 48, c = -48
t = 0.79 s
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f(x) = x^2. What is g(x)?
A. g(x) = (4x)^2
B. g(x) = 2x^2
C. g(x) = (2x)^2
D. g(x) = (1/2x)^2
Answer:
C
Step-by-step explanation:
g(x) through the point (1,4) so its mean when x equal to 1, g(x) equal to 4 so you replace that point so you can choosse C
Which statement is correct about the period of the function y = sin x?
A) There are 180° in a unit circle, so the period is 180°
B) There are 180° in a unit circle, so the period is 360°
C) There are 360° in a unit circle, so the period is 180°
D) There are 360° in a unit circle, so the period is 360°
Answer:
C
Step-by-step explanation:
The function sine of 'x' repeats its value after a full rotation of π radians. In degrees, that would be 180 degrees. On a unit circle, the sine is the y-component at any point along the circumference of the circle. In the first two quadrants, the y-component is the exact same until you exceed a rotation of 180 degrees. The degree of a circle is 360 degrees, therefore the answer would be C.
HELP TAKE YOUR TIME°!!!
FOR MY SISTER
Answer:
1.15
2.1
3.3
45
5.3
6.8
7.4
8.5
9. 24
Step-by-step explanation:
Carry on learningAnswer:
1. 15
2. 1
3. 3
4. 2.5
5. 3
6. 8
7. 4
8. 5
9. 24
10. 6
11. 3
12. 52
13. 44
14. 38
15. 24
16. 12
17. 2
18. 12
Step-by-step explanation:
HELP!!!
is the following relation a function?
yes or no?
Answer:
I think the answer is no
Step-by-step explanation:
It's been awhile but if I remember correctly a function cannot be a parabola (this graph) because it does not pass the vertical line test. If there are two points on a vertical line it is not a function. Hope this helps!
what is 7h-5(3h-8) = -72
Answer:
14
Step-by-step explanation:
7h-5(3h-8)=-72
7h-15h+40=-72
-8h=-112
h=14
Answer:
Answer is 14
Step-by-step explanation:
7h-15h+40 = -72-8h = -72-40-8h = -112h = -112------
-8
h = 14Hope it helps!
BYE
Could someone help me with this? I need to solve for X. Here is the problem.
The two angles given are vertical angles, which mean they are equal to each other.
2x + 2 = 3x -52
Add 52 to both sides:
2x + 54 = 3x
Subtract 2x from both sides:
54 = x
Rewrite as x = 54
Answer: x = 54
Gabriella needs 120 meters of fence to surround a rectangular garden.
The length of the garden is three times its width, w.
How wide is the fence?
Please try to include a Screenshot with the answer
Answer:
the width is 1.5meters
Step-by-step explanation:
the perimeter of the fence is 120m
the perimeter= 3w+w+3w+w
120= 3w+w+3w+w
120= 8w
w=1.5m
Answer:
15m
Step-by-step explanation:
Well, she needs 120 meters, which means we already know the circumference (P). P is the sum of all sides.
The lenght (a) is 3 times the width(b).
a = 3b.
Which means if a is x then b is equal to 3x
Since P is the sum of all sides, P is equal to 2a + 2b or 2x + 2*3x = 2x + 6x = 8x
120 = 8x. We are now left with an equation that has one variable only, all we need to do is to divide 120 by 8 to find what x is equal to.
8x = 120
x = 120 / 8
x = 15
We know that width(a) is equal to x, so that's the answer.
Here's a solution you can write:
P = 120m
w = x
l = 3w = 3x
P = 2w + 2l
P = 2*x + 2*3x
P = 2x + 6x
P = 8x
8x = 120
x = 120 / 8
x = 15
w = x -> w = 15m
The sum of j and 7 is 55. Solve for j.??
if 54735 = 53000+735+p what is the value of p
Answer:
1000 :)
Step-by-step explanation:
We need to subtract to solve!!
54735 - 53000 = 1735
1735 - 735 = 1000
Have an amazing day!!
Please rate and mark brainliest!!!
Use the drop-down menu to complete each statement. according to this graph, at $10 the quantity supplied is about . as the price of the good rises, the quantity supplied will .
Answer:
14
increase
Step-by-step explanation:
Answer:
14, increase
Step-by-step explanation:
Simplify and solve the following expression: (x + 5)= x?
Step-by-step explanation:
How to solve your problem
(x+5)=x
Solve
1
Subtract
5
from both sides
x+5=x
x+5
2
Simplify
Subtract the numbers
x=x-5
3
Subtract
x
from both sides
x=x-5
Simplify
Combine like terms
Combine like terms
0=-5
Result
0=-5
The input is a contradiction: it has no solutions
Answer:
x=x-5 or 0=-5
Step-by-step explanation:
subtract 5 from both sides
Given that f (x) =x^2 -10x +24 and g (x) =x - 6, find f (x) - g (x) and express the result in standard form
Answer:
x^2 + 9x + 30 = 0
Step-by-step explanation:
Given: f(x) = x² – 10x + 24
g(x) = x – 6
f(- x) = g(x) :
(-x)² - 10(- x) + 24 = x - 6
x² + 10x + 24 - x + 6 = 0
Result: x² + 9x + 30 = 0
Answer:
Y = (x - 11/2)^2 -1/4
Step-by-step explanation:
subtract g(x) to f(x)
f (x) - g (x) = x^2 -10x +24 -x + 6
f (x) - g (x) = x^2 -11x +30
Let's call Y
Y = x^2 -11x +30
The standard form is by definition as Y = a (x-b)^2 + h
In this specific case:
Y = (x - 11/2)^2 -121/4 + 30
Y = (x - 11/2)^2 -1/4
about 2/5 of Joys cottage property is covered with trees. About 21 km2 are open fields. In Km2, how much of her property is covered in trees
Fractions are written as the ratio of two integers. 8.4km^2 of her property are covered in trees
Ratios and proportionsFractions are written as the ratio of two integers
Given the following parameters
total area of open field = 21km^2
If 2/5 of Joys cottage property is covered with trees, the amount covered in trees is expressed as:
Amount covered in trees = 2/5 * 21
Amount covered in trees = 42/5
Amount covered in trees = 8.4km^2
Hence 8.4km^2 of her property are covered in trees
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the price of a sweater was reduced from $20 to $12. by what percentage was the price of the sweater reduced?
A.8% B.80% C.60% D.40%
PLEASE HELP ME!!!!
Answer:
40%
Step-by-step explanation:
The original is $20. It is now 12/20 is ?/100
12*100=1,200/20=60 100-60=40%
Answer:
D. 40%
Step-by-step explanation:
ConceptsPercent ChangePercent change refers to how much, as a percentage, a quantity increases or decreases. The formula for percent change is [tex]\frac{FV-IV}{IV} * 100 = PC[/tex]. Keep in mind percent change is not negative, but can be written as 40% decrease or 40% increase.
FV = Final ValueIV = Initial ValuePC = Percent Change (%)ApplicationHow Does this Apply Here?We are being asked to find the percent change, or the change in the price of the sweater from $20 to $12. Thus, we will have to use the aforementioned formula. $20 is the initial value and $12 is the final value.
SolvingSolving for Percent Change
Step 1: Plug in values.
[tex]\frac{12-20}{20} * 100[/tex]Step 2: Simplify.
[tex]\frac{8}{20} * 100[/tex] [tex]800/20[/tex] [tex]40[/tex]Therefore, the answer is D. 40%.