1. A rectangular table top is three times as long
as it is wide. Its width is 1 meter. Find the area of
the table top.

Given:

The functions are:

[tex]f(x)=\log_4x[/tex]

[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex]

The function f(x) is dilated to become g(x).

To find:

The effect on f(x).

Solution:

Transformation is defined as:

[tex]g(x)=f(kx)[/tex]            ...(i)

Where, k is the factor of horizontal stretch and compression.

If 0<k<1, then the graph of f(x) stretched horizontally by factor [tex]\dfrac{1}{k}[/tex].

If k>1, then the graph of f(x) compressed horizontally by factor [tex]\dfrac{1}{k}[/tex].

It is given that

[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex]          ...(ii)

On comparing (i) and (ii), we get

[tex]k=\dfrac{1}{3}[/tex]

Therefore, the graph of f(x) stretched horizontally by factor [tex]3[/tex].

Answer:

(f-g)(2) = 14

Step-by-step explanation:

f(x) =3x^2 +1 and g(x) = 1 -x

f(2) = 3(2)^2 +1 = 3(4)+1 = 12+1 = 13

g(2) = 1-2 = -1

f(2) - g(2) = 13 - -1 = 13+1 =14

Answer:

14

Step-by-step explanation:

(f-g)(2) means f of x minus g of x when x equals 2.

To solve, first set up the equation

[tex](3x^2}+1)-(1-x)[/tex]

Change the signs in the second part. {because this is subtraction}

[tex]3x^2}+1-1+x[/tex]

Replace x with 2.

[tex]3(2^2})+1-1+2[/tex]

Solve.

[tex]3(4)+2[/tex]

[tex]12+2[/tex]

[tex]14[/tex]

Answer:

$70.00

y=5r+20

Step-by-step explanation:

1. y=5(10)+20

y=70

The cost he will pay for 10 rides will be $70 and for r rides will be [tex]20+5r[/tex].

Given,

The price of admission into the park is $20.

The price for each ride is $5

David takes 10 rides,

So, the cost he will pay if he took 10 rides will be,

[tex]c_1=20+5 \times 10\\c_1=20+50\\c_1=70$[/tex]

If he had r rides,

So, the cost he will pay if he took r rides will be,

[tex]c_2=20+5 \times r\\c_2=20+5r[/tex]

Therefore, the cost he will pay for 10 rides will be $70 and for r rides will be[tex]20+5r[/tex].

For more details about linear equation, refer to the link:

https://brainly.com/question/3997793

Answer:

0.09

Step-by-step explanation:

9% written as a decimal is 0.09

8%=0.08

7%=0.07

6%=0.06

5%=0.05

4%=0.04

3%=0.03

2%=0.02

1%=0.01

Step-by-step explanation:

[tex] \sin( \alpha ) = \frac{ \sqrt{5} }{3} \\ \alpha = 48.19 \: degrees \\ \cos( \alpha ) = \frac{2}{3} [/tex]

Answer:

cos theta =± 2/3

Step-by-step explanation:

sin theta = sqrt(5) /3

sin theta = opp side / hypotenuse

We know that

a^2 + b^2 = c^2 from the pythagorean theorem

opposite side ^2 + adjacent side ^2 = hypotenuse ^2

( sqrt(5)) ^2 +   adjacent side ^2  = 3^2

5 +  adjacent side ^2  = 9

Subtract 5 from each side

5-5 +  adjacent side ^2  = 9-5

 adjacent side ^2  = 4

Taking the square root of each side

 adjacent side   = ±2

We know that

cos theta = adj side / hyp

cos theta =± 2/3

Answer:  B. Probability

For example, let's say you want to know the probability of flipping tails.

There's 1 way to get tails out of 2 sides total. So 1/2 = 0.5 is the probability of flipping tails.

We define "success" as "getting tails".

Answer:

P = 2(L + 6)

Step-by-step explanation:

The perimeter (P) of a rectangle is = 2(Length + Width)

Length = L

Width = 6

.: P = 2(L + 6)

Answer:

Step-by-step explanation:

Scale measure is a one-to-one thing while volume is a cubed thing. If we want to find the volume that the actual car can hold, we have to find the volume that results from cubing the one-to-one measure.

[tex]\frac{m}{a}:\frac{1^3}{48^3}=\frac{1}{110592}[/tex] That last fraction is the ratio of the volumes. Remember, volume is a cubed measure (where distance is a linear measure and area is a squared measure. We find ratios of areas by squaring the one-to-one {distance} measures, and we find ratios of volumes by cubing the one-to-one measures). We have a given volume for the model (m in our ratio) and we are looking for the capacity that the actual car (a in our ratio) can hold. Set up the proportion as follows:

[tex]\frac{1}{110592}=\frac{90}{x}[/tex] and cross multiply

x = 9,953,280 inches cubed

Answer:

We know that the polynomial:

x²- 6y²- xy - 5x - 5y + 6

is rewritten as:

(x+ay+b)(x+cy-2)

First, lets expand the above expression:

x^2 + x*(cy) + x*(-2) + (ay)*x + (ay)*(cy) + (ay)*(-2) + b*x + b*(cy) - 2*b

Now we can simplify this to get:

x² + c*(xy) - 2*x + a*(xy) + ac*y² - 2a*y + b*x + bc*y  - 2b

now let's group together the terms with the same variables:

x² + (c + a)*(xy) + (b - 2)*x + (bc - 2a)*y + ac*y² - 2b

And that must be equal to:

x²- 6y²- xy - 5x - 5y + 6

notice that equations are equal if and only if all the correspondent factors are equal.

notice that in both cases, the factor that multiplies the x² term is 1.

for the y² term we will have:

a*c = -6

for the xy term we will have

c + a = -1

for the x term we will have

b - 2  = - 5

for the y term we will have

bc - 2a = -5

for the constant term, we will have:

-2b = 6

Then we have a lot of equations, rewriting these we have:

a*c = -6

c + a = -1

b - 2  = -5

bc - 2a = -5

-2b = 6

From the fourth equation, b - 2  = -5

we can get:

b = -5 + 2 = -3

b = -3

notice that for the last equation:

-2b = 6

b = 6/-2 = -3

we have the same solution

Then we can replace the value of b in the above equations to get:

a*c = -6

c + a = -1

-3*c - 2a = -5

Now, we need to isolate one of the variables in one of the equations.

For example, we can isolate c in the second one to get:

c = -1 - a

now we can replace that in other equation, for example the third one:

-3*(-1 - a) - 2a = -5

now we can solve that for a.

3 + 3a - 2a = -5

3 + (3 - 2)a = -5

3 + a = -5

a =  -5 - 3 = -8

a = -8

now we can use the equation "c = -1 - a" to find the value of c:

c = -1 -(-8) = -1 + 8 = 7

c = 7

then we have:

b = -3

a = -8

c = 7

then:

a + b*c = -8 + (-3)*7 = -8 - 21 = -29

Answer:

x is 21°

Step-by-step explanation:

The angles formed between the transversal t and lines m and n are; (8·x - 7)°, and (9·x - 28)°

Based on the similar location the angles are formed by the transversal, t, and lines m and n, the angles are corresponding angles

Given that lines, m and n are parallel, we have the corresponding angles formed by the transversal, t, and the lines are equal, therefore;

(8·x - 7)° = (9·x - 28)°

Simplifying the above equation to make x the subject, we get

(28 - 7)° = 9·x - 8·x = x

∴ 21° = x

x = 21°.

Step-by-step explanation:

Concerning the peculiar interrogate, I will be providing correction(s) to the following answers inserted:

Y = 3x - 1

Slope = 3

Y-intercept = -1

X - 3 = y

Y = x - 3 <== Slope-Intercept Form.

Slope = 1

Y-intercept: -3

Y = 1 - 3x

Slope: -3

Y-intercept: 1

-x + 3 = y

Y = -x + 3 <== Slope-intercept Form.

Slope: -1

Y-intercept: 3

Thus, the following configurations have been defined or derived from the origin of the proposed interrogated.

*I hope this helps.

Answer:

−426500

Step-by-step explanation:

Answer:

bgyuhjvy;uhclgcxfghvmdxultgjvffgxfbc hgv

Step-by-step explanation:

vgfdhvczczxcgfzdsdvcxfdghcbcd

Answer:

True

Step-by-step explanation:

Both pairs of opposite angles are congruent. parallelogram, rectangle, rhombus, square. Both pairs of opposite sides are congruent. parallelogram, rectangle, rhombus, square. All consecutive angles are supplementary. parallelogram, rectangle, rhombus, square. diagonals bisect each other. parallelogram, rectangle, rhombus, square.

Answer:

true

Step-by-step explanation:

any 2 consecutive angles are supplamentary

Answer:

Step-by-step explanation:

Answer:

y=-3/2x+4

Step-by-step explanation:

Answer:

1 2/3 miles per minute

Step-by-step explanation:

Take the distance and divide by the time

5 miles / 3 minutes

1 2/3 miles per minute

Answer:

[tex]\mathfrak {last \:option }[/tex]

[tex] \mathfrak\blue{ {option \: 2} }[/tex]

Step-by-step explanation:

x intercept of a function is the point where it's graph intersects the x axis.

or

simply that value x, where the value of y is 0.

since at x = 2; f(x) =0 that point (2, 0) is the x intercept of the function.

Answer:

Total paid: 302.40

Step-by-step explanation:

Price x percent off = amount off

700 x .60 (60%) = 420 amount off

price - amount off = sales price

700 - 420 = 280 sales price

sales price x sales tax rate = sales tax

280 x .08 (8%) = 22.40 sales tax

sales price + sales tax = total paid

280 + 22.40 = 302.40 total paid

Answer:

what uhhhhhh

Step-by-step explanation:

Answer:

15 inches

Step-by-step explanation:

Since we know diagonal and a side of a right triangle, we can use the Pythagorean theorem to solve.

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

20 ^2 + b^2 = 25^2

400+b^2 =625

b^2 =625 -400

b^2 =225

Taking the square root of each side

sqrt(b^2) = sqrt(225)

b= 15

Answer:

15

Step-by-step explanation:

You can use Pythagorean theorem or if you draw it out and label the given information you may recognize that the triangle created is a 3 - 4 - 5 triangle.

[tex]25^{2}[/tex] = [tex]20^{2}[/tex] + [tex]x^{2}[/tex]             [tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

625 = 400 + [tex]x^{2}[/tex]        

225 = [tex]x^{2}[/tex]                     Square root both sides

15 = x

A special right triangle has a leg that measures 3, another leg that measures 4. and a hypotenuse that measures 5.

The given triangle in this problem has a leg that measures 20 and a hypotenuse that measures 25. If you divide each measure by 5, you will have a leg that is 4, and a hypotenuse that is 5. That means the last leg must be 15.

Why? Because 3 x 5 = 15. or 15/5 = 3

This comes up very often when working with triangles.

Answer:

84 cm^2

Step-by-step explanation:

area of right triangle formula= 1/2 (base*height)

In order to find the area, you need the base and the height

The question included that the legs ratio are 7 to 24.

If you do [tex]\sqrt{7^2+24^2}[/tex], you get 25 (Pythagorean theorem)

so the base and heights are 7 and 24

1/2 (7*24)= 84

Answer:

1 - 4

Step-by-step explanation:

26/4 = 6.5

IQR is the 7 - 19 item

1 - 4

Answer: 0.667

Step-by-step explanation:

6/9 ⇔ Given

2/3 ⇔ Simplify fraction

0.666... (repeating) ⇔ Convert fraction to decimal

0.667 ⇔ Round to 3 decimal (Since 6 is more than 5, thus we need to

               rounding up)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

19 and 157

Step-by-step explanation:

Answer:

2.65

Step-by-step explanation:

15.00 - 12.35 = 2.65

...I don't really know how do explain it but yeah thats the answer.

Hope it helps c:

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

Answer:

the answer is in the pic so like yea hope that helps

Solution :

[tex]$y=x^{3/2}, \ \ y =8, \ \ x=0$[/tex]

[tex]$v=2 \pi \int_0^4 x (8-x^{3/2}) \ dx$[/tex]

 [tex]$= 2\pi \left(\frac{8x^2}{2}-\frac{x^{7/2}}{7/2}\ \left|_0^4[/tex]

 [tex]$=2\pi \left( 4x^2-\frac{2}{7}x^{7/2}\ |_0^4$[/tex]

 [tex]$=2\pi \left( 64-\frac{2}{7} \times 32 \times 4 \right)$[/tex]

  [tex]$=2\pi \left(1-\frac{4}{7} \right) 64$[/tex]

  [tex]$=128 \pi \times \frac{3}{7}$[/tex]

 [tex]$=\frac{384 \pi}{7}$[/tex]