Activity 1.
Direction. Using the diagram below, form ratios. Express them in lowest term to
To form a proportion

Answer:

x=-10

Step-by-step explanation:

since there's a given 120 degrees, and it's a isosceles triangle, we know that the line adds up to 180 (where the 120 degrees is). so 120+x=180, the interior angle measures 60 degrees. That being said, the 3 angles measure 60 degrees also. now there's a right angle mark on top, so we find the angle of the smaller triangle (near angle 2) by doing 90-60=30 degrees.

angle 2 is said to be x+160, and there's a line, which tells us that they must add to 180.. so x+160+30=180

x+190=180

x=-10.

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Explanation:

He gets a 15% discount, so he pays the remaining 85%. The two percentages add to 100%.

85% in decimal form is 0.85

The 6% sales tax means we also have the multiplier 1.06 to indicate a 6% increase.

The two factors 0.85 and 1.06 multiply to 0.85*1.06 = 0.901

This tells us that Andrew's father pays 90.1% of the original bill

0.901*40 = 36.04 dollars

--------------

An alternative method:

15% of $40 = 0.15*40 = 6

Andrew's father saves $6

The bill of $40 drops to 40-6 = 34 dollars before tax.

6% of $34 = 0.06*34 = 2.04

The father pays $2.04 in tax to get a total bill of 34+2.04 = 36.04 dollars

The probability that the balls drawn are red, green, and black in that order will be 3/78.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The box contains 4 black balls, 7 red balls, and 3 green balls. The total number will be:

= 4 + 7 + 3

= 14 balls.

The probability that the balls drawn are red, green, and black in that order will be:

= P(red) × P(green) × P(black)

= 7/14 × 3/13 × 4/12

= 1/2 × 3/13 × 1/3

= 3/78

The probability is 3/78.

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Answer:

[tex]\huge\boxed{-y^2+2y}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]y\cdot\left(7\sqrt[3]{8y^2}-\sqrt[3]{y^5}-4y\sqrt[3]{27y^2}\right)\\\\=(\sqrt[3]y)(7\sqrt[3]{8y^2})-(\sqrt[3]y)(\sqrt[3]{y^5})-(\sqrt[3]y)(4y\sqrt[3]{27y^2})\\\\=7\sqrt[3]{(y)(8y^2)}}-\sqrt[3]{(y)(y^5)}-4y\sqrt[3]{(y)(27y^2)}\\\\=7\sqrt{8y^3}-\sqrt{y^6}-4\sqrt{27y^3}\\\\=7\sqrt[3]{2^3y^3}-\sqrt{y^{2\cdot3}}-4\sqrt{3^3y^3}\\\\=7\sqrt[3]{(2y)^3}-\sqrt{(y^2)^3}-4\sqrt{(3y)^3}\\\\=7\cdot2y-y^2-4\cdot3y\\\\=14y-y^2-12y\\\\=-y^2+2y[/tex]

Used:

[tex]a(a+b)=ab+ac\\\\\sqrt[3]{a\cdot b}=\sqrt[3]a\cdot\sqrt[3]b\\\\\sqrt[3]{a^3}=a\\\\(a^n)^m=a^{n\cdot m}[/tex]

Unit rates is the rate of a quantity in comparison to 1 i.e. unit.

Based on the given parameters, Shanya is the fastest typist

From the question, the unit rates are given as:

The unit rates of Tristan and Ebony are not given.

So, we compare the rates of James and Shanya

3 words in a second is greater than 0.5 words in a second.

Hence, Shanya is the fastest typist

Read more about unit rates at:

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Answer:

✔ 1.5

words/second is the unit rate for Tristan.

✔ 2

words/second is the unit rate for Ebony.

So,

✔ Shanya

is the fastest typist

thanks and 5 stars >:(

Answer:

Percent change in the price of gas is [tex]9.85\%[/tex]

Step-by-step explanation:

Percentage change equals the change in value divided by the absolute value of the original value, multiplied by [tex]100[/tex] .

[tex]\text { Percentage Change }=\frac{\Delta V}{\left|V_{1}\right|} \times 100[/tex]

Here

[tex]\Delta V=2.26-2.03\\\\=0.23\$/gallon[/tex]

[tex]V_{1}=2.03\$/gallon[/tex]

The percent change in the price of gas

[tex]=\frac{0.23}{2.03} \times100\\\\=9.85\%[/tex]

Percent change in the price of gas is [tex]9.85\%[/tex]

The formula

x + y = 32

Find our X value

y + 14 = x

Sub for x

(y + 14) + y = 32

Remove Parathesis

y + 14 + y = 32

Add

2y + 14 = 32

Subtract

2y = 18

Divide

y = 9

Sub for y

x + 9 = 32

Subtract

x = 23

Double Check:

9 + 14 = 23

23 + 9 = 32

I hope this helps! :)

Answer:

There are 9 people in the class.

Step-by-step explanation:

Sean received the 5th highest grade in his class meaning that there are 4 people in front of him who got a higher grade. This also means that Sean has 4 people behind him who have lower grades. So,

4+4+1 (Sean himself) = 9 people

The number of students in the class is given by the sum of the frequency

of each score.

Reasons:

When the class scores are arranged in increasing order, we have;

Sean's position = 5 th = The fifth lowest score

Therefore;

When the scores are arranged in decreasing order, we have;

Sean's position = 5 th = Fifth highest score

Therefore;

Given that two or more students can have the same score, the frequency

of each score, determines the number of students in the class, we have;

Learn more about data frequency here:

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Answer:

add the two then subtract the two and put those answers in each box :)

Step-by-step explanation:

hope this helped! happy holidays!

Step-by-step explanation:

1 2 3 4 5

wa

Answer:

14.6

Step-by-step explanation:

the given angle 6.2 is cleared to be wrong

so we will erase the point of decimal and times sin62 with hypotenous 16.5 that will give us 14.6 length unit as 2 triangles are symmetric as the line cut them to 2 equal triangles

Answer:

both isosceles???

Step-by-step explanation:

Answer:

They are similar.

Step-by-step explanation:

There might be other ways but

<X(Angle of x) is used for both triangle XAB and XYZ

And lines AB and YZ are parallel, From this we know that a line intersected by parallel lines it forms same angles for both parallel angles.

The similarity statement is: AAA Because angle(A=B , B=Z)

Answer:

If f(x) =3x^3+10x^2-13x-20 and f(-4)=0, then find all of the zeros of f(x) algebraically

Answer:

$0.05

Step-by-step explanation:

1.25/25=0.05

The ordered pair to represent how many miles Jim runs and bikes in 5 weeks is (3.33, 5)

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

Every week Jim runs 8 miles and bikes 12 miles.

This means that we have the ratio

Run : Bike = 8 miles : 12 miles

When he bikes for 5 weeks, we have

Run : 5 weeks = 8 miles : 12 miles

This gives

Run/5 weeks = 8/12

So, we have

Run = 5 weeks * 8/12

Evaluate the products

Run =  3.33 weeks

Hence, the number of weeks is 3.33 and the ordered pair is (3.33, 5)

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Answer:

3 3/20 is equal to 3.15 in decimal form.

Step-by-step explanation:

Answer:

A. -3.15

Step-by-step explanation:

this isn't much but i really like math xD hope this helps! :) (please pick as brainlyist)

Answer:

$16

Step-by-step explanation:

1-⅗=⅖

40×⅖=16

Here's the answer

Answer:

95 Dollars

Step-by-step explanation:

95 dollars because she earns 95$ per day and it says "of a day" so it would have to be 95*1, and 95*1 is 95 and it asks how much she earns as in money so it is 95 dollars.

Answer:

The probability will be [tex]\frac{1}{2}[/tex], since there are a total of 11 purple and red Skittles and an overall total of 22 Skittles in the bag.

Answer:

8 × 10¹

Step-by-step explanation:

don't panic. just breathe deeply and then think logically.

0.002 ... what is that ? 2 10ths ? 2 hundredths ? 2 thousandths ? 2 tenthousandths ?

the 3rd position after the decimal point is for 1/1000.

and that means 10^-3. in the same way as 1000 is 10³.

so, it is 2 × 10^-3.

the other rounded number is then 4 × 10⁴.

now, we are multiplying both numbers

2×10^-3 × 4×10⁴

what do we do ?

we combine the same types of factors, like the basic constants : 2×4 = 8

and 10^-3 × 10⁴.

what hairball when we multiply the same base number with exponents ? we add the exponents :

10^-3 × 10⁴ = 10¹ = 10

because -3 + 4 = 1

and so, the result is

8 × 10¹

Step-by-step explanation:

We use the power rule a^(x+y) = a^x * a^y:

3^(2x+1) = 3^(2x) * 3

We can re-write 3^(2x) as (3^x)^2, and we know that 3^x = a, so:

3a^2 is the final answer. There is not exact value, it's all just about re-writing.

[tex]3a^2 [/tex] is a required answer.

Answer:

solution given:

[tex]3^{2x+1}=? [/tex]

if [tex] 3^x=a[/tex]

By using power rule, we can write

[tex]3^{2x+1}[/tex] as

[tex]3^{2x+1}=(3^x)^2*3^1 [/tex]

[tex]a^2*3=3a^2 [/tex]

Step-by-step explanation:

the diagaonls of rectangle interscet at x

find the angle that a diagaonl makes a longer side of the rectangle

square: A=s^2

triangle: A=(1/2)bh

rectangle: A=lw

parallelogram: A=bh

Answer:

Step-by-step explanation:

I'm ASSUMING you want to find n where g(n) = 8

g(n) = a/n

g(4) = 9 = a/4

          a = 36

g(n) = 8 = 36/n

         n = 36/8 = 4.5

Step-by-step explanation:

along the side with 1 cm we can fit 3 cubes, as 3×1/3 = 1.

along the side with 2 2/3 cm we can fit 8 cubes :

2 2/3 = 6/3 + 2/3 = 8/3.

and 8/3 / 1/3 = 8/3 × 3/1 = 3×8 / 3×1 = 8

and the height is 2/3 cm, so we can put 2 layers of cubes on top of each other.

so, we have

3 × 8 × 2 = 48

48 cubes are needed to fill the prism.

Answer:

She will go to 729 games in 162 days.

Step-by-step explanation:

27÷6 = 4.5

4.5 · 162 = 729

Answer:

729 games in 162 days

Step-by-step explanation:

If she goes to 6 games in 27 days, then you divide 27 by 6, to get the unit rate.

27/6=4.5

Now that you have the unit rate, you multiply 162 by the unite rate, or 4.5, in this case.

162x4.5=729

-hope it helps

Answer:

-11/20

Step-by-step explanation:

[tex]\frac{1}{5} - \frac{3}{4} = \frac{?}{?}[/tex]

first you want to get a common denominator (number on the bottom)

[tex]\frac{4}{20} - \frac{15}{20} = \frac{?}{?}[/tex]

now you can subtract the numerators (number on tope) (also don't touch bottom)

[tex]it ~equals = -\frac{11}{20} ~~because ~4-15 ~is -11[/tex]

The exact area of triangle ABC is 93.51 cm².

The given parameters;

The base of the triangle is calculated by using trigonometry ratio as follows;

[tex]tan (30) = \frac{b}{18} \\\\[/tex]

where;

[tex]b = 18 \times tan(30)\\\\b = 10.39 \ cm[/tex]

The area of the triangle ABC  with the calculated base and given height is calculated as follows;

[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2[/tex]

Thus, the exact area of triangle ABC is 93.51 cm².

Learn more about area of a triangle here: https://brainly.com/question/23945265

Answer:

that means you have a 5000 dollar debt

Hope This Helps!!!

Hi!

He has 25% of the bottle left.

Knowing he drank 21 oz. out of a 28 ox. bottle, he has 7 oz. left.

We want to know the answer to: 7 is what percent of 28?

To do this, we simply take 7 and divide it by 28. 7/28 is 1/4, which can be represented by 0.25

0.25 as a percent is 25%.