Compare the three functions.

f(x) = 10x
x y
0 0
1 10
2 20
g(x) = 5x
x y
0 1
1 5
2 25
h(x) = 4x2 + 5x
x y
0 0
1 9
2 26

Select the true statement.

A.
As x approaches positive infinity, the quadratic function will exceed both the linear and exponential functions.
B.
As x approaches positive infinity, the exponential function will exceed both the linear and quadratic functions.
C.
As x approaches positive infinity, the linear function will exceed both the quadratic and exponential functions.
D.
As x approaches positive infinity, it cannot be determined which function will exceed the other two.

Answer:

-1/4

Step-by-step explanation:

Given sequence is:

1/2, 1/4 , 0, ...

In order to find the common difference in the terms of a sequence, the preceding term is subtracted from the next term.

For example in the given sequence:

first term will be subtracted from second term and second term will be subtracted from third term

So,

[tex]\frac{1}{4}-\frac{1}{2}  \\=\frac{1-2}{4}\\ =-\frac{1}{4}\\ Similarly,\\=0-\frac{1}{4} \\=-\frac{1}{4}[/tex]

The common difference is - 1/4 ..

Answer:

-1/4

Step-by-step explanation:

Answer:

18 feet

Step-by-step explanation:

15-8+11=18

Answer:

58 deg

Step-by-step explanation:

Look at x and then look at the sides that are given... 9 is adjacent and 17 is the hypotenuse so use cosine.

cos(x)=9/17

To solve for x just use arccos( ) or cos^(-1)

Type cos^(-1)(9/17) into calc to receive answer (make sure mode is in degrees)

The answer should come to be roughly 58 deg.

Answer:

x ≈ 58.0°

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for x

cosx° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], thus

x = [tex]cos^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 58.0°

Answer:

[tex]\large\boxed{\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}}[/tex]

Step-by-step explanation:

[tex]6x^2-54\qquad\text{distributive}\\\\=6(x^2-9)=6(x^2-3^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=6(x-3)(x+3)\\\\5x^2+15x\qquad\text{distributive}\\\\=5x(x+3)\\-----------------\\\\\dfrac{6x^2-54}{5x^2+15x}=\dfrac{6(x-3)(x+3)}{5x(x+3)}\qquad\text{cancel}\ (x+3)\\\\=\dfrac{6(x-3)}{5x}=\dfrac{6x-18}{5x}[/tex]

let's take a peek at the triangles.

they have a 30° angle and a 80° each, and a side that is not in between in common.

[A]ngle [A]ngle [S]ide, AAS congruence.

Answer:

Option B, False.

Step-by-step explanation:

In the given figure two triangles have been given. In these triangles two angles and corresponding side has been given as equal in measure.

Therefore, by AAS theorem for congruence, the given triangles are congruent.

The given statement that the triangle shown may not be congruent is False.

Option B is the answer.

Answer:

A, B, C and D.

Step-by-step explanation:

Opposite sides are congruent (B) as well as the 3 that are marked.

Answer:

Options A, B, C and D are correct choices.

Step-by-step explanation:

We are asked to choose the properties of parallelograms from our given choices.

By the definition of parallelogram:

Upon looking at our given choices, we can see that options A, B, C and D are correct choices.

Answer:

x^2 = -7x -8

x^2 +7x +8 = 0

D = 49 -32 = 17

x_1,2 = (-7+/-sqrt17)/2 = (-7-sqrt17)/2 and (-7+sqrt17)/2

Step-by-step explanation:

Answer:

x = [tex]\frac{1}{2}[/tex] (-7±√17)

Step-by-step explanation:

x² = -7x - 8

x² + 7x + 8 = 0

Using the quadratic formula, with a=1, b = 7 and c=8,

you will get x = [tex]\frac{1}{2}[/tex] (-7±√17)

Answer:

circle and rectangle

Step-by-step explanation:

we know that

A cross section that is perpendicular to the base of cylinder is a rectangle

A cross section that is parallel to the base of cylinder is a circle

A cross section that is angled to the base of cylinder is an oval

Final answer:

A plane intersecting a cylinder can create a circle if perpendicular to the cylinder's axis, or a rectangle if cut parallel to the side of the cylinder. Ellipses are also possible when the cutting angle is oblique, and may look circular from certain perspectives. Triangles, line segments, and points are not typical cross sections for a cylinder.

Explanation:

When a plane intersects a cylinder, several different cross sections can result, depending on the angle and position of the plane relative to the cylinder. If the plane is perpendicular to the axis of the cylinder, the cross section will be a circle. If the plane intersects the cylinder at an angle to the axis, the cross section can be an ellipse, which in some cases may appear to be a circle depending on the perspective. A plane intersecting parallel to the side of the cylinder will produce a rectangle. It is not possible for a cylinder to have a triangular, line segment, or point as a cross section through normal slicing, as these do not represent the way planes intersect with the smooth curved surface of a cylinder.

Answer: you simplfy the two equations already there then plug them in to find factors

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

These are called vertical angles.  Vertical angles are equal.

145 = 2x + 15

130 = 2x

x = 65

Answer:

I think the answer would be 5 divided by 50 times two to find the width.

Step-by-step explanation:

I think my answer above explains it well enough.

Answer: w(2w + 5) = 50

Step-by-step explanation:

Answer:

3x-4y=2

Step-by-step explanation:

step 1

Plot the figure

we have

A (2, 2), B(-2, -2), C(1, -1), and D(6, 4)

using a graphing tool

The longer diagonal is BD

see the attached figure

step 2

Find the slope of the diagonal  BD

we have

B(-2, -2) and D(6, 4)

m=(4+2)/(6+2)

m=3/4

step 3

Find the equation of the diagonal BD into point slope form

y-y1=m(x-x1)

we have

m=3/4

D(6,4)

substitute

y-4=(3/4)(x-6)

step 4

Convert the equation in standard form

The equation of the line in standard form is equal to

Ax+By=C

y-4=(3/4)(x-6)

y=(3/4)x-(18/4)+4

Multiply by 4 both sides

4y=3x-18+16

3x-4y=18-16

3x-4y=2 -----> equation of the diagonal in standard form

Answer:

Step-by-step explanation:

Number of people that attended the party= 24.....let this be x

Number of people that walked= 1/2 x

[tex]=\frac{1}{2} *24 =12[/tex]

Number of people that travel by bus= 1/4 x

[tex]=\frac{1}{4} *24= 8[/tex]

Number of people that go by taxi= the rest

[tex]=24-(12+8)=24-20=4[/tex]

The fraction that used taxis= those that used tax/total number of people

Those that used taxi=4

Total number of people=24

Fraction = [tex]\frac{4}{24} =\frac{1}{6}[/tex]

Fraction that did not use taxi = whole-fraction that used taxi

[tex]\frac{6}{6} -\frac{1}{6} =\frac{5}{6}[/tex]

Answer:

Option B (AB = 2.2 units).

Step-by-step explanation:

The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin ABC / AC = sin BAC / BC.

Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:

sin 72 / 2.5 = sin BAC / 2.1.

Cross multiplying gives:

sin BAC = (2.1*sin 72)/2.5.

sin BAC = 0.79888747368.

Taking sin inverse on both sides gives:

BAC = arcsin (0.79888747368) = 53.0239949 degrees.

To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051  degrees.

Now applying the Sine Rule to find AB:

sin ACB / AB = sin ABC / AC.

sin (54.9760051) / AB = sin 72 / 2.5.

AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).

Therefore, AB = 2.2 units, i.e. Option B!!!

Answer:

The initial value of the given geometric sequence is 2.

Step-by-step explanation:

The given points are (1,2), (2,4) and (3,8).

It means the first term is 2, second term is 4 and third term is 8. So, the common ratio is

[tex]r=\frac{a_2}{a_1}=\frac{4}{2}=2[/tex]

A geometric sequence is defined as

[tex]f(n)=ar^{n-1}[/tex]

Where, a is first term of the sequence, r is common ratio and n is number of term. In other words f(1) is the initial value of the geometric sequence.

The given geometric sequence is

[tex]f(n)=2(2)^{n-1}[/tex]

The value of f(1) is 2.

Therefore the initial value of the given geometric sequence is 2.

Answer:Just took the test, it is 2 on edg

Step-by-step explanation:

:)

Answer:

sine 30=y/(8+10√2)

(8+10√2)sin 30=y

Check the picture below.

Answer:

B

Step-by-step explanation:

Given a point (x, y) on f(x) then the corresponding point on the inverse is (y, x)

Given (17, 4 ) is a point on the inverse then the corresponding point on  f(x) is

(4, 17 ) → B

Answer:

1 < x < 2

Step-by-step explanation:

Given

1 < 3x - 2 < 4 ( add 2 to each of the 3 intervals )

3 < 3x < 6 ( divide each interval by 3 )

1 < x < 2

Answer:

A

Step-by-step explanation:

Edge 2021

Answer:

The coordinates of the points that are members of the solution set

(-3,7), (0,4) and (2,3)

Step-by-step explanation:

we have

[tex]-3x-y< 12[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the dashed line

[tex]2x+3y\geq 9[/tex] ----> inequality B

The solution of the inequality B is the shaded area above the solid line

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Remember that,

If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution

Plot the points

(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)

therefore

The coordinates of the points that are members of the solution set

(-3,7), (0,4) and (2,3)

Answer:Answer:

The coordinates of the points that are members of the solution set

(-3,7), (0,4) and (2,3)

Step-by-step explanation:

we have

----> inequality A

The solution of the inequality A is the shaded area above the dashed line

----> inequality B

The solution of the inequality B is the shaded area above the solid line

The solution of the system of inequalities is the shaded area between the dashed line and the solid line

see the attached figure

Remember that,

If a ordered pair is a solution of the system of inequalities, then the ordered pair must be in the shaded area of the solution

Plot the points

(-3, 7), (-3, -7), (3,-7), (-4,-0), (0,-4), (0,4), (2,3), (-2,3), (2,-3)

therefore

The coordinates of the points that are members of the solution set

(-3,7), (0,4) and (2,3)

Step-by-step explanation:

Answer:

neither one

Step-by-step explanation:

Answer:

B. x=1

Step-by-step explanation:

Let us define axis of symmetry first.

The point right in between the two x-intercepts of a quadratic equation is called axis of symmetry.

We have x-intercepts of -3 and 5

In ordered to find the axis of symmetry we have to find their middle intercept

To find the axis of symmetry:

[tex]= \frac{-3+5}{2}\\=\frac{2}{2}\\ =1[/tex]

So the axis of symmetry is x = 1 ..

Answer:

B x=1

Step-by-step explanation:

edge 2020 2021

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0+3}{2-0}[/tex] = [tex]\frac{3}{2}[/tex]

note the line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = [tex]\frac{3}{2}[/tex] x - 3 → C

Answer:

i would think A

Answer:P(B|A)is not equal P(B)

Step-by-step explanation:

Shown below

The first system of inequality is the following:

[tex]\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y<2x+\frac{1}{3}\end{array}\right.[/tex]

To find the solution here, let's take one point, say, [tex](0,0)[/tex] and let's taste this point into both inequalities, so:

First inequality:

[tex]y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y<2x+\frac{1}{3} \\ \\ 0<2(0)+\frac{1}{3} \\ \\ 0<\frac{1}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there

First inequality:

[tex]y<2x+\frac{2}{3} \\ \\ 0<2(0)+\frac{2}{3} \\ \\ 0<\frac{2}{3} \ True![/tex]

The region is the one where the point [tex](0,0)[/tex] lies

Second inequality:

[tex]y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True![/tex]

The region is not the one where the point [tex](0,0)[/tex] lies

So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.

CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.

Answer:

A

Step-by-step explanation:

Consider the smaller than sign as smaller or equal to sign as I couldn,t type the sign

-4(x+3)<-2-2x

Expand the bracket

-4x-12<-2-2x

Add 2x to both sides

-2x-12<-2

Add 12 to both sides

-2x<10

add 2x to both sides

0<10+2x

minus  10 on both sides

-10<2x

SImplify

-5<x

X is larger or equal to -5 which means the option A

Answer:

Triangle

Step-by-step explanation:

A regular polygon of n sides has interior angles of:

a = 180 (n-2) / n

Given a = 60:

60 = 180 (n-2) / n

n = 3 (n-2)

n = 3n - 6

6 = 2n

n = 3

The polygon has three sides, so it's a triangle.

A regular polygon with each angle measuring 60° is an equilateral triangle.

A regular polygon is a polygon with all sides and angles equal. To find the type of polygon where each angle measures 60°, we use the formula for the measure of each interior angle of a regular polygon, which is (n-2) x 180° / n, where n is the number of sides.

Let's solve for n:

Set the angle measure formula to 60°: (n-2) x 180° / n = 60°

Multiply both sides by n to clear the fraction: (n-2) x 180° = 60n

Distribute 180°: 180n - 360° = 60n

Move the terms involving n to one side: 180n - 60n = 360°

Simplify: 120n = 360°

Divide both sides by 120: n = 3

Therefore, a regular polygon with each angle measuring 60° is an equilateral triangle.

Answer:

The second graph.

Step-by-step explanation:

In inverse variation, an increase in one variable leads to a decrease in the other value in the relationship.

xα1/y

x=k/y

meaning

xy= constant

Such a graph slants with a negative gradient from left to right of the Cartesian plane. (the second graph).

Answer:

it's B

Step-by-step explanation:

Answer: The answer is 10

Answer:

10

Step-by-step explanation:

math

Answer:

She is partially correct. There are 2 possible answers to this problem, and x - 2 = 3 is one of the answers. When applying the square root to both sides, the resulting answer could be either negative or positive. Therefore, applying the square root to both sides leads to the two following equations: x - 2 = 3 or x - 2 = -3.