Sara threw her math book off a building . The height of the book, seconds after being thrownis modeled by the equation below. The height measured in feet. h(x)=-5(x+2)(x-7) what is the height of the book when it is thrown?

It would be wiser for the couple to stay in the old apartment and save $1400.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Explanation:

If they stay until the end of the lease, total money that will be paid out is $1000 x 6 = $6000,

If they leave, they'll have to forgo $1000.

If they move to their new apartment, they'll pay $900 x 6 = $5400

total expenditure if they move to the new place at the end of the six months period will be, the $1000 that will not be refunded back to them on the old apartment, plus this new $5600 for six month's rent in this new apartment, and that will be a total of $6400.

It would be wiser for the couple to stay in the old apartment and save $1400.

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Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD. The lines CD and GH cannot be defined. The lines AB and GH cannot be defined. Lines IJ and CD are perpendicular

Two lines are said to be parallel if :  m(1) = m(2).

Two lines are perpendicular to each other if : m(1) x m(2) = -1.

We have to classify the set of these lines as; Parallel, Perpendicular or Cannot Be Determined.

1. Lines AB and CD are both perpendicular to the line EF, then AB |is parallel to CD.

2. The lines CD and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.

3. The lines AB and GH cannot be defined, because the diagram doesn't contain any information about angles at which these lines intersect.

4. Lines IJ and CD are perpendicular; because they intersect each other at right angle.

Hence, the solutions to the table are shown above as options.

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b.6 because 2 * 3 it will give us six then * it with 3 again it will give you 18

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

The maximum height of the golf ball on Mars is about 48.8 meters.

To find how much longer it would take for the golf ball hit on Mars to reach the ground, we can use the given equation h = -1.9t² + 26t, where h is the height of the object and t is the time in seconds. First, we need to find the time it takes for the golf ball to reach the ground on Mars. Setting h = 0, we get:

0 = -1.9t² + 26t

Solving for t using the quadratic formula, we get t = 13.684 or t = 0.856. Since the golf ball is launched upward, we need the positive value of t, so it takes about 13.7 seconds for the golf ball to reach the ground on Mars. Therefore, it takes 13.7 − 5.4 = 8.3 seconds longer for the golf ball hit on Mars to reach the ground than the golf ball hit on Earth.

To find the maximum height of the golf ball on Mars, we can use the formula h = -1.9t² + 26t, where t is the time when the height is maximum. Since the formula is a quadratic equation, the maximum height occurs at the vertex of the parabola, which is at t = -b/2a.

In this case, a = -1.9 and b = 26, so the time at maximum height is t = -26 / 2(-1.9) = 6.842. Plugging this value into the equation for h, we get:

= -1.9(6.842)² + 26(6.842) ≈ 48.8 meters

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The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.

A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.

The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.

In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.

The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.

The answer is: B.

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Answer:

The equation of the parallel  line to the given equation is

3 x-4 y = -4    and

The equation of the parallel  line to the given equation is

\(y = 1 + \frac{3 x}{4}\)

Step-by-step explanation:

Explanation:-

Given equation of the line 3 x -4 y = 7 and given point ( -4 , -2 )

The equation of the parallel line to the given equation is

3 x - 4 y = k

it is passes through the point ( -4 , -2)

3 (-4) - 4 ( -2) = k

-12 +8 = k

k = -4

The equation of the parallel  line to the given equation is

3 x- 4 y = -4

Dividing '4' on both sides , we get

\(\frac{3 x-4 y}{-4} = 1\)

\(\frac{-3 x}{4} +y =1\)

\(y = 1 + \frac{3 x}{4}\)

Conclusion:-

∴ The equation of the parallel  line to the given equation is

3 x- 4 y = -4

and

The equation of the parallel  line to the given equation is

\(y = 1 + \frac{3 x}{4}\)

Answer:

the answer is b and d edge 2021

Step-by-step explanation:

I am finished taking the test got a 100%

The coordinate of the point N is found to be (10, 8).

Section formula is used in Coordinate geometry to find the ratio between two points on a line given one another point on the line. It can be written as x = (m₁x₁ + m₂x₂)/(m₁ + m₂) and y = (m₁y₁ + m₂y₂)/(m₁ + m₂) where the points (x₁, y₁) and (x₂, y₂) are divided in the ratio of m₁ : m₂ at point (x, y). For the case of midpoint m₁ : m₂ = 1. Therefore, it can be written as x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2 respectively.

The coordinate of A is (-2, 2).

And, the coordinate of M is (4, 5).

Suppose, the coordinate of N be (x, y).

As per the section formula for the midpoint of a line segment, the coordinate of M can be written as,

4 = (-2 + x)/2

⇒ -2 + x = 8

⇒ x = 10

And, 5 = (2 + y)/2

⇒ 2 + y = 10

⇒ y = 8

Hence, the coordinate of N is obtained as (10, 8).

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Answer:

-1

Step-by-step explanation:

-1/2(2)=-1

The equivalent expression of  \(x^{-1/2}\)  by the help of the law of indices is 1/√x thus option (3) is correct.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

In another word the mathematics of power or exponent of any number is called indices.

As per the given,

\(x^{-1/2}\)

By the law of indices,

\(x^{-1/2} = \frac{1}{x^{1/2}} = 1/\sqrt{x}\)

Hence "With the use of the law of indices, the equivalent form of \(x^{-1/2}\) is 1/x".

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meter =1,000 millimeters. So, the scale is:

7 mm:1,000 mm Divide both sides by 7

1 mm:142 6/7 mm - This is the scale that Tess used.

The distance between point C  (-3, 3) and point D (0, -4) is equal to: √58 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(0 + 3)² + (-4 - 3)²]

Distance = √[(3)² + (-7)²]

Distance = √[9 + 49]

Distance = √58 units.

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Four points are always coplanar if they: lie in same plane.

Firstly understanding the coplanar points. Coplanar points are refers to the points if they are present in same plane. Further defining the word "plane". Plane is the surface, which is flat and two dimensional in nature. The surface is infinite. Plane can also be referred as the analogue of 3 dimensional space, you we can also interpret the plane as extension of point or line.

So, the points that lie on different planes will not be coplanar. Now, understanding the points on lines. Two or more lines may or may not be in same plane. Subsequently, points may or may not be coplanar, depending upon the lines they are placed on. Thus, we can not definitely say that points lying on the same line are coplanar.

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Answer:

21

Step-by-step explanation:

I used a triangle area calculator.

Hope I helped!

3/5 or 60% of the prism's volume will be filled with sand.

The volume of each cube is e³ = 5³ = 125 cubic centimeters.

Since the rectangular prism is made up of two cubes, its volume is 2e³ = 2(125) = 250 cubic centimeters.

If Arusha fills the prism with 150 cubic centimeters of sand, the fraction of the prism's volume that will be filled with sand is:

150/250 = 3/5

Therefore, 3/5 or 60% of the prism's volume will be filled with sand.

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Answer:

23.78 cm

Step-by-step explanation:

size of the missing angle is (180 - 90 - 18) = 72°

angle 72° is opposite the side x. angle 90° is opposite side 25.

x/sin 72  =  25/sin 90

multiply both sides by sin 72:

x = (25 X sin 72) / sin 90

   = (23.78) / 1

  = 23.78 cm

Answer:

They are the same.

Step-by-step explanation:

84 in is 7 ft because 1 foot is 12in. 12in multiplied by 7 feet and you get 84in :)

Answer:

20pi

Step-by-step explanation:

C =2pi(r)

Ca = 2 (pi) (25) = 50 pi

Cb = 2 (pi) (35) = 70 pi

70pi - 50pi = 20pi

solution//

= 4(m-3) = 24

= 4m-12 = 24

= 4-12+12 = 24+12

= 4m = 36

= 4m = 36

4 4

= m = 9

Step-by-step explanation:

Thank you

\(\sf\purple{The\:value\:of\:m\:is\:9.}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(4 \: (m - 3) = 24 \\ ⇝4 \: m - 12 = 24 \\ ⇝4 \: m = 24 + 12 \\ ⇝4 \: m = 36 \\ ⇝m = \frac{36}{4} \\ ⇝m = 9\)

To verify:-

\(4(m - 3) = 24 \\ ⇝4(9 - 3) = 24 \\ ⇝4 \times 6 = 24 \\ ⇝24 = 24 \\ ⇝L.H.S.=R. H. S\)

Hence verified.

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}\)

Answer:

x = 2

Step-by-step explanation:

√(x + 7) − 1 = x

√(x + 7) = x + 1

x + 7 = (x + 1)²

x + 7 = x² + 2x + 1

0 = x² + x − 6

0 = (x + 3) (x − 2)

x = -3 or 2

Check for extraneous solutions:

√(-3 + 7) − 1 = -3

√4 − 1 = -3

2 − 1 = -3

1 = -3

x ≠ -3

√(2 + 7) − 1 = 2

√9 − 1 = 2

3 − 1 = 2

2 = 2

x = 2

Answer:

6

Step-by-step explanation:

30 - 12 = 18

18 ÷ 3 = 6

The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.

They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt

Note that you need another r because you are integrating in cylindrical

coordinates.

conversion equations:

x = rcost

y = rsint

x² + y² = r²

(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt

W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.

Around the z-axis, cylinders take the forms of circles: x² + y² = r²

This cylinder will have the equation: x² + y² = 16

Its height is 3 so from z = -1 to z = 2

z bounds: -1 <= z <= 2

r bounds (based on the circle): 0 <= r <= 4

t bounds (based on the circle): 0 <= t <= 2pi

\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)

(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)

= 2r^3 + (8/3)r + r^3 + (1/3)r

= 3r^3 + 3r

dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216

dt integral gives: 216t --> 432pi

Hence we get the integral value as 432π

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

The given solid is a triangular prism since its base figure is triangular in nature.

Since the base is a triangle, the area of the base is expressed as:

Area = 1/2 * base * height

Area of base = 1/2 * 6 * 8

Area of base = 24 square inches

The height of the solid is 5 inches and the required volume is calculated as:

Volume = BH/3

Volume = 24*5/3

Volume = 40 cubic inches

The shape is a triangular prism with a triangular base, base area of 24in², height of 5in and volume of 40in³

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Answer:

Step-by-step explanation:

a. x is negative: x < 0

b. y is nonnegative: y ≥ 0

c. q is less than or equal to π: q ≤ π

Answer:

a.

2. x < 0

b.

2. y ≥ 0

c.

5. q ≤ π

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

a. The statement "x is negative" means that x is less than 0. Mathematically, we can represent this as x < 0.

b. The statement "y is nonnegative" means that y is greater than or equal to 0. Mathematically, we can represent this as y ≥ 0.

c. The statement "q is less than or equal to π" means that the value of q is either equal to π or less than π. Mathematically, we can represent this as q ≤ π.