A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?

Answer:

the answer is 1/5 for the probability

Answer:

D. g(x) = -x^2 - 4

Step-by-step explanation:

(A.P.E.X)

The required function g(x) = -x²- 4. Option D is correct.

f(x) = x², g(x) to be determine with help of graph.

Function is defined as y = f(x). For every x their is certain value of y.

Here, from the graph g(x) is reflection of f(x) at y = -4.
So g(x) = -f(x) - 4
negative sign for reflection.
g(x) = -x²-4

Thus, The required function g(x) = -x²- 4.

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Answer:

The ordered pair is the point [tex](2b,2b+7)[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x+7[/tex]

For [tex]x=2b[/tex]

Substitute the value of x in the function

so

[tex]f(2b)=2b+7[/tex]

therefore

The ordered pair is the point [tex](2b,2b+7)[/tex]

Answer:

(2b, 2b+7)

Step-by-step explanation:

Since the value of x is 2b, we just have to insert that value into the function in order to solve the ordered pair, we have the first part of the ordered pair, which is (2b), now we just insert the value of x into the function:

[tex]f(x)=x+7\\f(x)=2b+7[/tex]

Now we know that the value of y would be 2b +7, and the ordered pair will be (2b,2b+7)

Check the picture below.

To remove 3 acres of contaminated soil at 24 inches deep, 346 full truckloads are needed, assuming each truck has a capacity of 28 cubic yards.

The student's question is regarding the number of truckloads required to haul away contaminated soil. We are given that 3 acres of soil need to be removed to a depth of 24 inches, and the trucks used have a hauling capacity of 28 cubic yards each.

To calculate how many full truckloads are required, we first need to convert the area and depth measurements from acres and inches into cubic yards (the unit of the truck's capacity). One acre is 43,560 square feet, so 3 acres would be 3 x 43,560 = 130,680 square feet. Depth needs to be converted from inches to feet, so 24 inches is 24 / 12 = 2 feet.

The total volume of soil to be removed in cubic feet is:

130,680 square feet x 2 feet = 261,360 cubic feet.

Since there are 27 cubic feet in one cubic yard, the total volume in cubic yards is:

261,360 cubic feet / 27 cubic feet per cubic yard = 9,680 cubic yards.

Finally, to find the number of full truckloads needed:

9,680 cubic yards / 28 cubic yards per truck = 345.71 trucks.

Since you can't have a fraction of a truck, you would need 346 full truckloads to remove all the contaminated soil. Each truck can carry exactly 28 cubic yards, and the last truck may not be full to capacity, but 346 is the number of full truckloads required for the task.

ANSWER

a) One Solution

b) the solution is x=2

EXPLANATION

The given equation is:

[tex]5(2x - 3) = 5[/tex]

We expand to get;

[tex]10x - 15 = 5[/tex]

Group similar terms;

[tex]10x = 15 + 5[/tex]

This implies that,

[tex]10x = 20[/tex]

Divide both sides by 10 to obtain,

[tex]x = 2[/tex]

For this case, we have by definition, that an irrational number is a number that can not be expressed as a fraction [tex]\frac {a} {b}[/tex], where a and b are integers and b is nonzero.

Some examples are:

[tex]\sqrt {2}, \sqrt {3}, e, \pi.[/tex]

So, that the answer is [tex]\pi.[/tex]

Answer:

Option C

Answer:

x=4

Step-by-step explanation:

From the statement we know that g(x)=3(x-2) and g(x)=6. Then we know that:

6=3(x-2)

Solving for "x":

6=3x-6

12=3x

x=12/3

x=4

Then, the solution is x=4.

For this case we have a function of the form [tex]y = g (x)[/tex]

Where:

[tex]g (x) = 3 (x-2)[/tex]

We want to find the value of "x" if the function is 6, that is, if y = 6

So, we have:

[tex]3 (x-2) = 6\\3x-6 = 6[/tex]

We clear "x":

[tex]3x = 6 + 6\\3x = 12\\x = \frac {12} {3}\\x = 4[/tex]

So, if the function has a value of 6, then [tex]x = 4[/tex]

ANswer:

[tex]x = 4[/tex]

Since there are 3 odd numbers ( 1, 3 and 5) and 3 even numbers ( 2, 4 and 6) in the cube ,

The chance of getting an odd number is 50/50 or 50%

So out of 1000 she will probably get 500 odd since 1000 × 0.5 (which is 50%) is 500

Answer:

21

Step-by-step explanation:

First, we would find 30% of 30, which would be 9. Then we would subtract 9 from 30 because we are decreasing it by 30%. That means the answer is 30-9, which is 21.

Well answer is 2 cause 1/4+1/4 is 1/2

the opposite is squared so,

square root of 4 is 2 and 2 squared is 4

The opposite of a square root √ is the squared exponent ²

If you have a number and find the square root of it, you can take the answer and square it to get the original number. Cool, huh?

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

 units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

the answer is 5

u substitute -1 into x and then solve

Answer:

the answer is D: 5

The value of x in the coordinate is 1/1000

Using the coordinates of the point given:

Equation of the graph:

To find the value of x for the coordinate given; substitute into the equation:

1/100 = 10x

1/100 × 100 = 100 * 10x

1 = 1000x

x = 1/1000

Hence, x = 1/1000

Answer:

u * v = 39 ⇒ 2nd answer

Step-by-step explanation:

* Lets explain how to solve the problem

- u and v are two vectors

- u * v means the scalar product of the two vectors

- The scalar product is a way of multiplying vectors

- The result of a scalar product is always a number not a vector

- Ex: If u = ai + bj ⇒ <a , b> and v = ci + dj ⇒ <c , d>  then the scalar

 product of them is ac + bd where ac + bd is a number

* Lets solve the problem

∵ Vector u = 13j ⇒ <0 , 13>

∵ Vector v = i + 3j ⇒ <1 , 3>

- Lets find the scalar product

∴ u * v = (0)(1) + (13)(3)

∴ u * v = 0 + 39

∴ u * v = 39

Answer:

[tex](2x)^2=28[/tex]

Step-by-step explanation:

The equation for the area of a square is [tex](x)^2=A[/tex]

In this case, the value within the parenthesis are the lengths of each side.

As you are doubling the length of the side and know the area, the equation can be written as follows

[tex](2x)^2=28[/tex]

Answer:

B. 360 hope it helps

faze up

Answer: ARE THEIR OPTIONS TO CHOSE FROM

Step-by-step explanation:

Answer:

No options so i cant help please put below thx (:

Step-by-step explanation:

Perimeter is when you add the sides. The top is 4 and so is the bottom. = 8

One side is 11 and so is the other = 22

8+22= 30

Answer:

C.) 30 units

Step-by-step explanation:

top and bottom sides are 4, left and right sides are 11, add

4+4 = 8

11+11=22

22+8=30

(sorry My other answer was wrong, I calculated Area, not Premeter.

Inside Out is a film about an 11 year old girl named Riley who moves across the country from Minnesota to San Francisco with her parents. Riley experiences a transformation in her mind and in who she is as a person as she tries to adjust to her new life in San Francisco and to the difficult process of growing up. The viewer follows Riley’s five emotions, Joy, Sadness, Anger, Fear, and Disgust, on a journey in her mind to help her through her transition to adolescence, and to assist her in making what they think are the right decisions. 

Inside Out is an animated movie detailing the emotional journey of an 11-year-old girl named Riley who moves to San Francisco. The film personifies Riley's core emotions: Joy, Sadness, Anger, Fear, and Disgust, outlining how they shape her actions and memories. The movie communicates a crucial message about the importance of all emotions, including sadness.

Inside Out is a movie presented by Pixar Animation Studios and released by Walt Disney Pictures. It showcases the story of an 11-year-old girl named Riley who moves from her hometown in Minnesota to San Francisco due to her father's new job. But this story is not a typical animation, as it transcends the usual plot setup. The unique aspect of this film is that it personifies Riley's five core emotions: Joy, Sadness, Anger, Fear, and Disgust, who live inside her mind and guide her actions and memories.

At the start of the movie, Riley's actions are primarily dictated by Joy, but the move to San Francisco triggers a series of events leading to Joy and Sadness getting lost in the depths of Riley's mind, leaving Anger, Fear, and Disgust in control. Throughout their journey to return to the headquarters, Joy and Sadness traverse various parts of Riley's mind, including Long-Term Memory, Imagination Land, and even the Subconscious, all the while Riley struggles with her new life.

In the end, the movie beautifully illustrates that all emotions are vital for a healthy mind - highlighting that sadness is as essential as joy. This plot overview simplifies a deep and complex movie, conveying a profound message about understanding and managing emotions.

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Parallel Lines, they always stay perfectly in line.

Answer:

parallel lines

Step-by-step explanation:

lines that never cross one another and are the same distance apart at all times

460 miles to San Diego

460/6=76.6 repeating -12 then divided by 2

means the other slower car was going approx 32.3 MPH

I may be wrong considering i had to google how far san diego was, if there was a graph or anything telling distance lmk

Answer:

Speed of the faster car is 68 mph and speed of slower car is 40 mph.

Step-by-step explanation:

Let the faster car has the speed = x mph

and slower car has the speed = y mph

Let the distance between San Jose and San Diago = d miles

Now we will form the first equation.

"Speed of the faster car was 12 mph less than twice the speed of the slower one"

x = 2y -12 ----------(1)

Since "faster car cover the distance d in 6 hours"

so, [tex]x=\frac{d}{6}[/tex]

"By that time the slower car still was 168 miles away from the destination"

so, [tex]y=\frac{d-168}{6}[/tex]

[tex]y=\frac{d}{6}-\frac{168}{6}[/tex]

y = x - 28 {since [tex]x=\frac{d}{6}[/tex]} ---------(2)

By substitution method,

x = 2(x - 28) - 12

x = 2x - 56 - 12

x - 2x = - 68

x = 68 mph

By putting x = 68 in equation 2

y = 68 - 28

y = 40 mph

Therefore, speed of the faster car is 68 mph and speed of slower car is 40 mph

Answer:

139

Step-by-step explanation:

He originally had 147 books and threw 8 into a pond.

147-8=139

Answer:

Batting practice increases batting averages.

Step-by-step explanation:

By looking at the graph, we clearly see a trend, almost a straight line (if you regroup the points a bit) going up.

So, it's clear that batting practice increases batting averages; they're directly related.  The more a player practices at bat, the better will be his average.

Answers B and D (best and worst batters) are not proved at all by the graph, since there's data higher than those two cases.

Answer:

x=5

Step-by-step explanation:

(x - 5)(x - 5) = 0

x-5=0

x=5

Making x the subject of the equation would be x = y - y or x = 0.

To make x the subject of the equation x + y = y , first isolate x on one side of the equation. To do this, subtract y from both sides of the equation:

x + y - y = y - y

This simplifies to :

x = 0

The solution is that x = 0. This means that no matter what the value of y is, x will always be 0 when the equation x + y = y holds true .

The full question is:

Make the variable in brackets the subject of the formula:
(x + y ) = y            (x)

The area of a triangle is 1/2 base times height so, the answer is 25

The area of the triangle is 25 square inches.

A 2-dimensional geometric figure bounded by three sides and has 3 corners and hence has 3 angles is called a triangle. In a triangle sum of all 3 angles is equal to 180°.

In the given problem,

∴ Area of triangle = ( 10 x 5 /2) square inches = 25 square inches

So, the area of the triangle is 25 square inches.

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For this case we must factor the following expression:

[tex]27a ^ 3b ^ 9 + 8c ^ 18[/tex]

So, we rewrite the terms like:

[tex]27a ^ 3b ^ 9 = (3ab ^ 3) ^ 3\\8c ^ {18} = (2c ^ 6) ^ 3[/tex]

So, we have:

[tex](3ab ^ 3) ^ 3 + (2c^6) ^ 3 =[/tex]

Being both perfect cube terms, we factorize by applying the cube sum formula:

[tex](a ^ 3 + b ^ 3) = (a + b) (a ^ 2-ab + b ^ 2)[/tex]

Where:

[tex]a = 3ab ^ 3\\b = 2c ^ 6\\(3ab ^ 3 + 2c ^ 6) ((3ab ^ 3) ^ 2- (3ab ^ 3) (2c ^ 6) + (2c ^ 6) ^ 2) =\\(3ab ^ 3 + 2c ^ 6) (9a^2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ {12})[/tex]

Answer:

[tex](3ab ^ 3 + 2c ^ 6) (9a2b ^ 6-6ab ^ 3c ^ 6 + 4c ^ 12)[/tex]

(11x2 + 2x3 + 14 +17x) ÷ (2x + 5)

= (2x^3 + 11x^2 + 17x + 14) ÷ (2x + 5)

= x^2 + 3x + 1 r 9

Answer:

2.2x^2+.4x^2+2.8+3.4x

Step-by-step explanation:

We can factor out a few numbers right off the bat-

(11x^2+2x^3+14+17x) / (2x+5)

(11x^2+2x^2+14+17x) / (5)

Now make the denominator disappear.

(11x^2+2x^2+14+17x) / (5)

2.2x^2+.4x^2+2.8+3.4x

(please contact if wrong)