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3 years ago

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An artis creates an abstract sculpture that appears as a box perched on top of a post the box is in the shape of a cube with edg

es measuring 5 inches each it is placed on top of a post in the shape of a rectangular prism with a length of 3 inches a width of 4 inches and a height of 18 inches what is the volume of the entire sculpture?

1 answer:

s344n2d4d5 [400]3 years ago

4 0

Volume of the box = length ^ 3 = 5^3 = 125 cubic inches
Volume of rectangular prism = length x width x height = 3 x 4 x 18 = 216 cubic inches
Volume of entire sculpture = volume of box + volume of rectangular prism = 125 + 216 = 341 cubic inches.

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Doug split a pack of cards so that he and his friends each got 6 cards. If there were 24 cards in the pack, how many friends did

GuDViN [60]

Answer:

3

Step-by-step explanation:

24 divided by 6 is 4, subtract Doug, there were 3 friends

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3 years ago

A pet supply store lets you donate your change to the local animal shelter. Denise buys a bag of dog food for $15.74 and a squea

Marta_Voda [28]

Considering her change, it is found that she will donate $0.28 to the animal shelter.

<h3>How to find the amount of change in a purchase?</h3>

The amount of change is given by the subtraction of the total paid and the price of the products.

In this problem, the price of the products bought is given by:

$15.74 + $3.98 = $19.72

She paid $20, hence the change is given by:

$20 - $19.72 = $0.28.

More can be learned about the amount of change in a purchase at brainly.com/question/10866253

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2 years ago

Maths functions <br> please help!

Vlad [161]

Answer:

$\textsf{1)} \quad f(x)=-x+3$

2) A = (3, 0) and C = (-3, 0)

$\textsf{3)} \quad g(x)=x^2-9$

4) AC = 6 units and OB = 9 units

Step-by-step explanation:

Given functions:

$\begin{cases}f(x)=mx+c\\g(x)=ax^2+b \end{cases}$

<h3><u>Part (1)</u></h3>

Given points:

H = (-1, 4)
T = (4, -1)

As points H and T lie on f(x), substitute the two points into the function to create two equations:

$\textsf{Equation 1}: \quad f(-1)=m(-1)+c=4 \implies -m+c=4$

$\textsf{Equation 2}: \quad f(4)=m(4)+c=-1 \implies 4m+c=-1$

Subtract the first equation from the second to eliminate c:

$\begin{array}{r l} 4m+c & = -1\\- \quad -m+c & = \phantom{))}4\\\cline{1-2}5m \phantom{))))}}& = -5}\end{aligned}$

Therefore m = -1.

Substitute the found value of m and one of the points into the function and solve for c:

$\implies f(4)=-1(4)+c=-1$

$\implies c=-1-(-4)=3$

Therefore the equation for function f(x) is:

$f(x)=-x+3$

<h3><u>Part (2)</u></h3>

Function f(x) crosses the x-axis at point A. Therefore, f(x) = 0 at point A.

To find the x-value of point A, set f(x) to zero and solve for x:

$\implies f(x)=0$

$\implies -x+3=0$

$\implies x=3$

Therefore, A = (3, 0).

As g(x) = ax² + b, its axis of symmetry is x = 0.

A parabola's axis of symmetry is the midpoint of its x-intercepts.

Therefore, if A = (3, 0) then C = (-3, 0).

<h3><u>Part (3)</u></h3>

Points on function g(x):

A = (3, 0)
G = (1, -8)

Substitute the points into the given function g(x) to create two equations:

$\textsf{Equation 1}: \quad g(3)=a(3)^2+b=0 \implies 9a+b=0$

$\textsf{Equation 2}: \quad g(1)=a(1)^2+b=-8 \implies a+b=-8$

Subtract the second equation from the first to eliminate b:

$\begin{array}{r l} 9a+b & = \phantom{))}0\\- \quad a+b & =-8\\\cline{1-2}8a \phantom{))))}}& = \phantom{))}8}\end{aligned}$

Therefore a = 1.

Substitute the found value of a and one of the points into the function and solve for b:

$\implies g(3)=1(3^2)+b=0$

$\implies 9+b=0\implies b=-9$

Therefore the equation for function g(x) is:

$g(x)=x^2-9$

<h3><u>Part 4</u></h3>

The length AC is the difference between the x-values of points A and C.

$\implies x_A-x_C=3-(-3)=6$

Point B is the y-intercept of g(x), so when x = 0:

$\implies g(0)=(0)^2-9=-9$

Therefore, B = (0, -9).

The length OB is the difference between the y-values of the origin and point B.

$\implies y_O-y_B=0-(-9)=9$

Therefore, AC = 6 units and OB = 9 units

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2 years ago

Read 2 more answers

What is the y-intercept of the quadratic function f(x)=x^2-5x+6?

tatiyna

Answer:

6

Step-by-step explanation:

f(x)=x^2-5x+6

To find the y intercept, set x=0

f(0) = 0^2 -5(0) +6

f(0) = 6

The y intercept =6

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3 years ago

What fraction of two pounds is twenty pence?

Reptile [31]

Hey there

High light all of your key terms of this problems (fraction, of two pounds, and twenty pence)

Answer: We have $200$ pence of the $2$ $Lbs$ , which is also $20$ pence in the $\frac{1}{10} = 10%$

Good luck on your assignment and enjoy your day!

~ $LoveYourselfFIrst:)$

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4 years ago