Write the equation of a line that includes the point (22, 12) and
has a slope of 4 in standard form.
@ -4x + y = -76
6 4x + y = 100
@ -4x+y=-100
@ 4x + y = 76

Answer:

width = 8 feet and length = 29 feet

Step-by-step explanation:

perimeter of a rectangle P = 2(L + W)

width W = x

length L = 3x + 5

P = 74 feet

74 = 2(3x + 5 + x)

37 = 3x + 5 + x

37 = 4x + 5

4x = 37 -5

4x = 32

x = 8

W = 8 feet

Answer:

A.

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks.

Step-by-step explanation:

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.

We have given that,

Much of Ann’s investments are in Cilla Shipping.

By this, we mean that share prices change because of supply and demand. If more people want to buy a stock (demand) than sell it (supply), then the price moves up.

Ten years ago, Ann bought seven bonds issued by Cilla Shipping, each with a par value of $500. The bonds had a market rate of 95.626.

Ann also bought 125 shares of Cilla Shipping stock, which at the time sold for $28.00 per share.

Today, Cilla Shipping bonds have a market rate of 106.384, and Cilla Shipping stock sells for $30.65 per share.

The value of Ann’s bonds has increased by $45.28 more than the value of her stocks. Option A is correct.

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Answer:

has two rays that share a common end point.

Answer:

Angle has two rays that share a common endpoint.

Step-by-step explanation:

Given : Angle.

To find : Which is a property of an angle.

Solution : We have given properties of an angle .

Angle : the space between two intersecting lines or surfaces at or close to the point where they meet.

Vertex is also called the angle.

Therefore, Angle has two rays that share a common endpoint.

Answer:

[tex]\frac{5}{21}[/tex]

Step-by-step explanation:

[tex]\frac{5}{9}[/tex] × [tex]\frac{3}{7}[/tex] = [tex]\frac{15}{63}[/tex] = [tex]\frac{5}{21}[/tex]

Answer:

5/63

Step-by-step explanation:

that would be:

 5        3                                        5

----- * ------ = (after reduction)   ----------- = 5/63

 9        7                                      3(21)

ANSWER

The dot product is 10.

EXPLANATION

The given vectors are (2,4) and (1,2).

If we have the vectors

u=(a,b) and v=(c,d)

Then the dot product of the two vectors is given by

[tex]u \bullet \: v = ac + bd[/tex]

This implies that,

[tex](2,4) \bullet(1,2) = 2 \times 1 + 4 \times 2[/tex]

This simplifies to;

[tex](2,4) \bullet(1,2) = 2 + 8 = 10[/tex]

Answer:

-6

Step-by-step explanation:

took test

The total cost Dani will pay for the movie including discount and sales tax is $13.23

To find the total cost Dani will pay for the movie:

Calculate the discount: $18 x 0.30 = $5.40

Subtract the discount from the original price: $18 - $5.40 = $12.60

Calculate the 5% sales tax: $12.60 x 0.05 = $0.63

Total cost: $12.60 + $0.63 = $13.23

Answer:

29

Step-by-step explanation:

Answer: 29

Step-by-step explanation:

It is important to know the definition.

The average of a set of number is defined as the sum of all these numbers divided by the total numbers that are in this set.

So, knowing this, we know that if we have a set of three numbers:"a", "b" and "c" , we can calculate  the average of them with this procedure:

[tex]average=\frac{a+b+c}{3}[/tex]

Therefore, we can calculate the average of the numbers 23, 33 and 31. This is:

[tex]average=\frac{23+33+31}{3}=\frac{87}{3}=29[/tex]

Answer:

160cm^3

Step-by-step explanation:

V=Lwh

so, (5x8x4)

v=160cm^3

Hope my answer has helped you!

Answer:

35 different watches

Step-by-step explanation:

I don't know if this is correct so sorry if it's not.

5 faces x 7 bands.

So, 5 x 7

=

35

i hope that helps... it might not, sorry

Answer:

35 different watches/combos.

Step-by-step explanation:

5 watches, 7 different wrist bands

5 x 7 = 35

1 watch consist of 1 watch and 1 band so he can have 35 different watch combinations.

Answer:

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

Step-by-step explanation:

* Lets explain the ratio between the sides of the triangle

- In Δ JKL

∵ The measure of angle J is 90°

∴ KL is the hypotenuse

∵ The measure of angle K is 30°

∴ JL is the opposite side to angle 30°

∵ The measure of angle L is 60°

∴ JK is the opposite side to the angle 60°

- There is a fact in the triangle which has angles 30° , 60° , 90°

# The length of the side opposite to the angle of measure 30° is

  half the length of the hypotenuse

∵ KL is the hypotenuse

∵ JL is the opposite side to the angle of measure 30°

∴ JL = 1/2 KL  OR KL = 2 JL

# The length of the side opposite to the angle of measure 60° is

  √3 the length of the opposite side to the angle 30°

∵ JK is the opposite side to the angle of measure 60°

∵ JL is the opposite side to the angle of measure 30°

∴ JK = √3 JL

# The length of the side opposite to the angle of measure 60° is also

  half √3 the length of the hypotenuse

∵ JK is the opposite side to the angle of measure 60°

∵ KL is the hypotenuse

∴ JK = √3/2 KL

- From the relation above

# Answer B is true ⇒ KL = 2(JL)

# Answer C is true ⇒ JK = √3(JL)

# Answer F is true ⇒ JK = √3/2(KL)

Answer:

It is a and B in C & D

Step-by-step explanation:

These are the closest answers

Answer:

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Step-by-step explanation:

(x ^4 - 3x^3 + 3x^2 - 3x + 6) (x - 2)

Distribute the x to all the terms in the first parentheses

(x^ 4  *x - 3x^ 3  *x + 3x^ 2   *x - 3x   *x + 6*x)

Then simplify

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x)

Distribute the -2 to all the terms in the first parentheses

(x^ 4  *(-2) - 3x^ 3  *(-2) + 3x^ 2   *(-2) - 3x   *(-2) + 6*(-2))

Then simplify

(-2x^4 +6x^3 -6x^ 2 +6x -12)

Add the terms together

(x^5 - 3x^4 + 3x^ 3 - 3x2 + 6x) +(-2x^4 +6x^3 -6x^ 2 +6x -12)

x^5 - 5 x^4 + 9 x^3 - 9 x^2 + 12 x - 12

Answer:

x^3 -x^2 + x -1 + 4/x-2

Step-by-step explanation:

;)

Answer:

2 and -10

Step-by-step explanation:

let the two integers be x and y.

so, x+y=-8---‐-------(1)

and,

x=y+12-------‐-----(2)

from (1) and (2),

(y+12)+y=-8

or, 2y=-8-12

or, y=-20/2

or, y=-10

substitutting the value of y in (2),

x=-10+12=2

therefore the required integers are 2 and -10.

Answer:

-20

Step-by-step explanation:

→ The sum of two integers is -8.

⇒ One will be called "x" and the other will be called "y"

→ One integer is 12 ( "y" )

Let's set up an equation x = ? and y = 12 so,

→ x + y = -8

( Substitute y for 12 )

→ x + 12 = -8

( -12 from both sides to isolate x )

→ x = -20

Answer: the first one is True and the second one is false

Step-by-step explanation:

3 + 5x = 23

so replace x with 4 you get 3 + 5 * 4 = 3 + 20 = 23

this is equal to 23 so it is true

2x - 6 = 9

do the same you get

2 * 8 - 6 = 9

16 - 6 = 10

the answer is 10 not nine therefore it is false

the answer should be,

A. shows that 9^1 - 4^1=5

hope this helps! :)

Answer: Because there are no values

Step-by-step explanation: Since there are no numbers in the problem, there is no sum. making it 0. You can't add two letters to make another letter, So it becomes a 0. anything with a variable subtracted, divided, added, ect by another variable, is 0

Answer:

The probability of not drawing a black marble is : 8/10, 4/5, 80%

The probability of drawing a red marble is: 3/10, or 30%

Step-by-step explanation:

Blue marbles: 5

Black marbles: 2

Red marbles: 3

Total marbles: 10

The probability of not drawing a black marble is :

NOT drawing a black marble means you'll draw either a blue or a red one.  Combined, red and blue marbles account for 8 marbles out of 10.

So the probability of NOT drawing a black marble is 8/10, 4/5 or 80%

The probability of drawing a red marble is:

There are 3 red marbles, out of 10 marbles.... so the probability of drawing a red marble is 3/10, or 30%

Answer:

Length 34 cm

Width 8 cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of rectangle is equal to

P=2(x+y)

P=84 cm

so

84=2(x+y)

42=x+y ----> equation A

x=4y+2 -----> equation B

substitute equation B in equation A and solve for y

42=(4y+2)+y

5y=42-2

y=40/5=8 cm

Find the value of x

x=4y+2 ----> x=4(8)+2=34 cm

The dimensions are

Length 34 cm

Width 8 cm

The width of the rectangle is 8 cm and the length is 34 cm.

To determine the dimensions of the rectangle, we need to set up equations based on the given information.

Let's denote the width of the rectangle by W (in cm). According to the problem, the length L is 2 cm more than four times the width. Therefore, we can express the length as:

L = 4W + 2

The perimeter of a rectangle is calculated using the formula:

Perimeter = 2L + 2W

Given that the perimeter is 84 cm, we can substitute the expressions for L and W into the perimeter formula:

84 = 2(4W + 2) + 2W

Simplify the equation:

Now that we have the width, we can find the length:

L = 4(8) + 2 = 32 + 2 = 34

Thus, the dimensions of the rectangle are:

Answer:

800 meters

Step-by-step explanation:

y is inversely proportional to x is the same as y is inversely proportional to [tex]\frac{1}{x},[/tex] that means

[tex]y=\dfrac{k}{x}.[/tex]

If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then

[tex]500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.[/tex]

Hence, the length of a wave y with a frequency of x=450 kilohertz is

[tex]y=\dfrac{360000}{450}=800[/tex]

The relationship between the frequency and wavelength of a wave is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light (or the speed of the wave in another medium, but for radio waves in the air or vacuum, it's approximately the speed of light),
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.
Given that the relationship is inverse, when the frequency goes up, the wavelength goes down, and vice versa.
We are given that a wave with frequency 720 kilohertz has a length of 500 meters. We can represent this with the equation:
\[ c = 720 \times 500 \]
We are asked to find the wavelength when the frequency is 450 kilohertz. Since the speed of light doesn't change, we set up the proportion using the formula, keeping \( c \) constant:
\[ 720 \times 500 = 450 \times \lambda_{\text{new}} \]
Now we solve for \( \lambda_{\text{new}} \):
\[ \lambda_{\text{new}} = \frac{720 \times 500}{450} \]
To simplify this, we can divide both the numerator and the denominator by a common factor. In this case, let's divide by 90:
\[ 720 \div 90 = 8 \]
\[ 450 \div 90 = 5 \]
\[ 500 \text{ remains unchanged} \]
Now we can substitute these simplified numbers back into our equation:
\[ \lambda_{\text{new}} = \frac{8 \times 500}{5} \]
\[ \lambda_{\text{new}} = \frac{4000}{5} \]
\[ \lambda_{\text{new}} = 800 \]
So the length of a wave with a frequency of 450 kilohertz is 800 meters.

Final answer:

Barry is currently 13 years old and his sister is 5 years old. This is determined by setting up a system of equations based on the given information and solving for their current ages.

Explanation:

The question involves solving a system of equations to find the current ages of Barry and his sister. Let's let B represent Barry's current age and S represent his sister's current age. According to the problem, Barry is 8 years older than his sister (B = S + 8). In 3 years, Barry will be twice as old as his sister will be then (B + 3 = 2(S + 3)).

Write down the two equations: B = S + 8 and B + 3 = 2(S + 3).

Substitute B from the first equation into the second equation: (S + 8) + 3 = 2(S + 3).

Simplify and solve for S: S + 11 = 2S + 6.

Rearrange the equation to find S: S = 5.

Substitute the value of S back into the first equation to find B: B = 5 + 8, so B = 13.

Therefore, Barry is currently 13 years old and his sister is 5 years old.

Answer:

Step-by-step explanation:

Answer:

it would take you 41 weeks

(rounded to 42 if that is a choice answer because when you divide 7500 by 180 it gives you 41.66666)

Step-by-step explanation:

Answer:

0.18 cents

Step-by-step explanation:

2.34 divided by 13= 0.18

To check my answer, 0.18 x 13 = 2.34

Answer:

$0.18/ounce

Step-by-step explanation:

Divide the price by the weight.

($2.34)/(13 ounces) = $0.18/ounce

Answer:

Principal amount= $600

Time= 3 years

Rate of Interest = 6%

SI= PRT/100

= 600x6x3/100

= $108

Interest is $108

Step-by-step explanation:

Answer:

[tex]f^{-1}(8)=1.5[/tex]

Step-by-step explanation:

If y=f(x)=2x+5, to find the inverse function express x n terms of y:

[tex]y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}[/tex]

Now, change y into x and x into y:

[tex]y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}[/tex]

Substitute x=8 into [tex]f^{-1}(x)[/tex] expression:

[tex]f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5[/tex]

Answer:

3/2

Step-by-step explanation:

f(x) = 2x+5

f⁻¹(2x+5) = x

2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>

=> x = 3/2

=> f⁻¹(8) = 3/2

Answer:

The answer is -6

Step-by-step explanation:

Hope it helped you!

Answer:

B. [tex]-6[/tex]

Step-by-step explanation:

We are asked to find the negative square root of 36.

We can write our given problem as [tex]-\sqrt{36}[/tex].

We can write 36 as 6 to second power.

[tex]-\sqrt{36}=-\sqrt{6^2}[/tex]

Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:

[tex]-\sqrt{6^2}=-6[/tex]

Therefore, the negative square root of 36 is negative six and option B is the correct choice.

Answer:

No, because they do not have the same area.

Step-by-step explanation:

For the piece of paper to cover once without overlap or gaps, it must have the same area as the the total surface area of the prism.

The total surface area of the rectangular prism is: [tex]2(3.5\times2+3.5\times1.5+2\times1.5)=30\frac{1}{2}in^2[/tex]

The area of the rectangular sheet is:[tex]5\times 8=40in^2[/tex]

Since the area of the piece of paper is more than the surface area of the rectangular prism there will be an overlap.

Mike's slower rate of driving across country was 65 mph.

Let the slower rate be represented as r mph. The faster rate will be r+10 mph. The total distance covered (495 miles) is the product of the time and the rate:

Adding up the distances, we get:

Simplifying the equation:

Combining like terms:

Subtracting 40 from both sides:

Dividing by 7:

Therefore, the slower rate is 65 mph.

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The correct answer for the slower rate at which Mike drove is 65 mph.

To find the slower rate at which Mike drove, let's denote the slower rate as r mph. Mike drove at this rate for 3 hours. He then drove for 4 hours at a rate that is 10 mph faster than the slower rate, which would be r + 10 mph.

The total distance covered by Mike is the sum of the distances covered at each rate. We can set up an equation to represent this:

[tex]\[ 3r + 4(r + 10) = 495 \][/tex]

Expanding the equation, we get:

[tex]\[ 3r + 4r + 40 = 495 \][/tex]

Combining like terms, we have:

[tex]\[ 7r + 40 = 495 \][/tex]

Now, we need to solve for r We can do this by subtracting 40 from both sides of the equation:

[tex]\[ 7r = 495 - 40 \] \[ 7r = 455 \][/tex]

Dividing both sides by 7 to solve for r, we get:

[tex]\[ r = \frac{455}{7} \] \[ r = 65 \][/tex]

Therefore, the slower rate at which Mike drove is 65 mph.

Answer: 9cm

Step-by-step explanation:

[tex]7x10=70cmx^{2}[/tex]

4(x)=4x

1.) 70+4x=106 (subtract 70 on both sides)

2.)4x=36 (divide 4 on both sides)

3.)x=9

answer=9

7x10=70cmxsquare

4(x)=4x

70+4x=106

4x=36

x=36/4

x=9

Answer:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

Like Terms are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

Answer:

Thus, (f + g)(x) = 7x - 1

Step-by-step explanation:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

LIKE TERMS are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

Answer:

V -E +F = 2

Vertices = 2 + Edges -Faces

Vertices = 2 + 90 -32

Vertices = 60

Step-by-step explanation: