Gregory(g) is 20 years older than his cousin Mark(m). Mark is 6 years younger than his
sister Louanne(L). Write an expression to represent the sum of their ages.

Answer:

It can't add a plot for those numbers-

Step-by-step explanation:

Answer:

C. 15

Step-by-step explanation:

5 options from the word SPACE (all letters work)

multiplied by 3, the number of consonants in the word MATH

5 x 3 = 15

angle 1 + angle 2 = 180

3x - 5 + 6x + 14 = 180

9x + 9 = 180

9x = 171

9x/9 = 171/9

x = 19

Answer:

...

Step-by-step explanation:

since they give us the side opposite of the given angle(Opposite) and we are trying to find for a (Adjacent/side), so we use TOA

tan(30)= [tex]\frac{4}{a}[/tex]

i see u dont want it solved but ill solve it anyways

since a is on the bottom then lets switch them

[tex]x=\frac{4}{tan30}[/tex]

x= 6.928

Answer:

-7

Step-by-step explanation:

Just put 5 into the equation f(5)=2*5-17=10-17=-7

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The options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

What is an apothem of a polygon?

A line segment from a regular polygon's centre to one of its sides is known as the apothem.

The given options are the following:

a)The apothem can be found using the Pythagorean theorem.

b)The apothem can be found using the tangent ratio.

c)The perimeter of the equilateral triangle is 15 cm.

d)The length of the apothem is approximately 2. 5 cm.

e)The area of the equilateral triangle is approximately 65 cm².

Now we will see if each option is true or not

a) From below figure,

      b = 8.7 / 2 = 4.35 cm

      From right angled triangle ΔABD,

    Using Pythagorus Theorem,

       a² + b² = 5²

       a² + 4.35² = 5²

       a = [tex]\sqrt{5^{2} - 4.35^{2} }[/tex] = 2.5 cm

Apothem can be found using Pythagorus Theorem.

b) From the figure, the radius divide the angle 60° of equilateral triangle to two 30° angles.

So from ΔABD,

tan 30° = a / 4.35

0.577 = a / 4.35

a = 2.5 cm

The apothem can be found using tangent ratio.

c) Perimeter of given equilateral triangle = 3 × side length

                                                                    = 3 × 8.7 = 26.1 cm

   This option is false.

d) From options (a) and (b) we found that length of apothem a = 2.5 cm

Therefore this option is true.

e) The area of given equilateral triangle = [tex]\frac{\sqrt{3} }{4} } * side^{2}[/tex] = [tex]\frac{\sqrt{3} }{4} * 8.7^{2}[/tex]

                                                                       = 32.8 cm²

Therefore this option is false.

Therefore options (a),(b) and (d) are true regarding the apothem of equilateral triangle.

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Answer:

2

Step-by-step explanation:

Answer:

It's 2 weve done the worksheet ;)

Step-by-step explanation:

Answer:

P = 2x + 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

45? Let me know if im wrong

Answer:

Step-by-step explanation:

Answer:

+3, +1

I think this is the answer because if its asking about the chart it is adding 3 on the x-axis and adding 1 on the y-axis

Hope this helps :)

Answer:     x + 7

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Numbered meridians are semicircles.

On a map of the planet, the Prime Meridian is an illustrative line. It serves as the origin of the longitude system of measurement. Meridians, a system of fictitious north-south lines, make up longitude. The planet Earth rotates like a ball. The Earth's axis serves as the spin's focal point.

The North Pole and the South Pole are where the axis intersects the surface of the planet. The North Pole and the South Pole are the points on each meridian. Meridians are used to calculate how far away from the prime meridian you are in degrees east or west.

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Answer:

9.4.6=216

216.1,3=280

Step-by-step explanation:

[tex] \huge\hookrightarrow \mathbb{ \color{gold}Answer}[/tex]

We know,

[tex] \boxed{volume = l \times b \times h}[/tex]

so,

[tex]\hookrightarrow{volume = 6 \times 4 \times 9}[/tex]

[tex]\hookrightarrow volume = 216 \: m {}^{3} [/tex]

now,

[tex] \boxed{density = \frac{mass}{volume} }[/tex]

So,

[tex] \hookrightarrow1.3 = \dfrac{m}{216} [/tex]

[tex]\hookrightarrow \: m = 216 \times 1.3[/tex]

[tex] \hookrightarrow \: m = 280.8[/tex]

hence, mass of air in the room is 280.8 kg

Answer:

The dimensions of the room is 8 and 13 feet.

Answer:

208

Step-by-step explanation:

Set up proportion

14/26=112/x

Cross multiply and solve for x

14x=2912

x=208

The z score of the student is -1.39. The value z score is rounded to 2 decimal places.

What is mean?

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The formula for the z-score is

z = (x - μ)/σ

x = standard value

μ = mean

σ = standard deviation

Given that the scored 75 points. The mean score of the student was 83.5 and the standard deviation was 6. 1.

Putting x = 75, μ = 83.5 and σ = 6.1

z = (75 -  83.5)/6.1

z = -1.3934

z ≈ -1.39

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Answer: 14 pieces.

Step-by-step explanation: 1 foot = 12 inches

12 feet of rope = 144 inches of rope

144 / 20 = 7.2 = 7 sections can be cut from each package.

The greatest number of pieces from 2 packages = 14 pieces

Answer

14 pieces

Step-by-step explanation:

First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.

The constant of proportionality is 2

From the question, we have the following parameters that can be used in our computation:

1 scoop of ice cream = 1/2 cup of milk

5 scoops of ice cream = 2.5 cups of milk

The constant of proportionality (k) is then calculated as

k = Scoop of ice cream/Cup of milk

So, we have

k = 5/2.5

Evaluate

k = 2

In (a), we have:

k = 2

A proportional relationship is represented as

s = km

Where

s = scoop of ice cream

m = cup of milk

So, we have

s = 2m

In (b), we have

s = 2m

To graph the relationship, we start by generating a table of values and then plot the points

Recall that

s = 2m

So, we have

18 = 2m

Divide by 2

m = 9

Hence, the number of cups is 9

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The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).

For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.

From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.

To satisfy the second condition the points of a should satisfy the equation given

LHS= 2x+3y

RHS=6

A(0,2)

Substituting the values of x and y in 2x+3y,

2(0)+3(2)=6

Therefore LHS=RHS

Hence, at point A(0,2) the graph of the given equation cuts the Y axis.

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Answer:

The answer is A

Step-by-step explanation:

To get this answer you need to use the compound interest formula, which is A=P(1+r/n)^n(t). P=53,000 r=16%=0.16 n=1 t=2 years. Everything else should fall into place to get your answer. I hope this helps!

The zeroes of this polynomial equation is [tex]$4 x^2-4 x-3$[/tex] are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

First form the equation

As per the given data the given polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

Here we have to determine the zeroes of a polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

We know that the zeroes of a polynomial are evaluated by equating them with zero.

Therefore p(x)=0

[tex]& \Rightarrow 4 x^2-4 x-3=0[/tex]

Then solve to find the zeroes

[tex]& 4 x^2-4 x-3=0 \\[/tex]

[tex]& \Rightarrow 4 x^2-6 x+2 x-3=0 \\[/tex]

2x(2x - 3) + 1(2x - 3) = 0

(2x - 3) (2x + 1) = 0

[tex]& \Rightarrow x=\frac{3}{2},-\frac{1}{2}[/tex]

Then do verification

We know that for a given polynomial [tex]$a x^2+b x+c$[/tex]

Sum of the zeroes [tex]$=-\frac{b}{a}$[/tex] and product of the roots [tex]$=\frac{c}{a}$[/tex]

Sum of the zeroes [tex]$=\frac{3}{2}-\frac{1}{2}=1$[/tex]

Again, [tex]$-\frac{b}{a}=\frac{4}{4}=1$[/tex]

Product of the zeroes [tex]$=\frac{3}{2} \times-\frac{1}{2}=-\frac{3}{4}$[/tex]

Again, [tex]$\frac{c}{a}=-\frac{3}{4}$[/tex]

Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.

Hence, the zeroes of this polynomial are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

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Answer:32 17/18

Step-by-step explanation:

33 + (1/9)(x)

x = -1/2

33 + (1/9)(-1/2) =

33 + -1/18

= 32 17/18

Answer: x=-6

Step-by-step explanation:

[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]

Answer:

Step-by-step explanation:

We have:

2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)

2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)

2^(2x-1) x 2^-3+3x = 2^6x+2

2^5x-4 = 2^6x+2

on comparing both sides we get :

5x-4 = 6x +2

x = -6

Using the radius of the circle given, the perimeter of the equilateral triangle is 48 inches

The perimeter of an equilateral triangle is three times the length of one side. Thus, if the length of one side is 'l', the perimeter of the triangle is 3l.

In this problem, the equilateral triangle has 3 circles inside with radius of 6 inches each.

Assuming the circles when combined will cover the entire triangle.

The diameter of the circle = 6 * 2 = 12 in

The length of the equilateral triangle = 2 * 12 = 24in

However, we already know the perimeter of an equilateral triangle is three times the side length of the triangle.

Perimeter of equilateral triangle = 3 * 24

Perimeter = 48 in

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Answer:

we divide by the number of data points, N. If the data is a sample from a larger population, we divide by one fewer than the number of data points in the sample, n − 1 n-1 n−1 .

Step-by-step explanation:

The area of the garden is 625 square meters.

We know that the perimeter of a square is equal to the sum of all four sides. Since the gardener is using 100 meters of fencing to enclose the garden, and since the garden is a square, we can set the perimeter equal to 100 meters:

P = 4s

100 = 4s

Where P is the perimeter, and s is the length of one side of the square.

We can solve for s by dividing both sides of the equation by 4:

s = 100/4 = 25

Since the area of a square is equal to one side of the square squared, we can find the area of the garden by squaring the value of s:

A = s^2

A = 25^2

A = 625

So the area of the garden is 625 square meters.

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