The questions below will help you keep track of key concepta from this lessons study activity.
Use the study page numbers listed to help you fl in the blanks or solve the problems.
1) Practice: Organizing Information
Complete the table to show what you know and want to find, related to the problem below.
Amy's monthly rent is one-fourth of her monthly income. If her monthly rent is $1,200, how much is
her monthly income?
Know
Want to know
2) Practice: Summarizing
Write an equation that may be used to solve the problem below, and then solve the equation.
Amy's monthly rent is one-fourth of her monthly income. If her monthly rent is $1200, how much is
her monthly income?

Answer:

The x -intercept is (3, 0)

The y -intercept is (0, - 2)

Step-by-step explanation:

Given equation is: -6x + 9y = -18

To find x - intercept:

Plug y = 0 in the given equation.

-6x + 9(0) = - 18

-6x + 0 = -18

-6x = - 18

x = (-18)/(-6)

x = 3

The x -intercept is (3, 0)

To find y - intercept:

Plug x = 0 in the given equation.

-6(0) + 9y= - 18

0 + 9y = -18

9y = - 18

y = (-18)/(9)

y = - 2

The y -intercept is (0, - 2)

Answer:

The Area of the composite figure would be 76.26 in^2

Step-by-step explanation:

According to the Figure Given:

Total Horizontal Distance = 14 in

Length = 6 in

To Find :

The Area of the composite figure

Solution:

Firstly we need to find the area of Rectangular part.

So We know that,

[tex]\boxed{ \rm \: Area \: of \: Rectangle = Length×Breadth}[/tex]

Here, Length is 6 in but the breadth is unknown.

To Find out the breadth, we’ll use this formula:

[tex] \boxed{\rm \: Breadth = total \: distance - Radius}[/tex]

According to the Figure, we can see one side of a rectangle and radius of the circle are common, hence,

[tex] \longrightarrow\rm \: Length \: of \: the \: circle = Radius[/tex]

[tex]\longrightarrow \rm \: 6 \: in = radius[/tex]

Hence Radius is 6 in.

So Substitute the value of Total distance and Radius:

[tex] \longrightarrow\rm \: Breadth = 14-6[/tex]

[tex] \longrightarrow\rm \: Breadth = 8 \: in[/tex]

Hence, the Breadth is 8 in.

Then, Substitute the values of Length and Breadth in the formula of Rectangle :

[tex] \longrightarrow\rm \: Area \: of \: Rectangle = 6 \times 8[/tex]

[tex]\longrightarrow \rm \: Area \: of \: Rectangle = 48 \: in {}^{2} [/tex]

Then, We need to find the area of Quarter circle :

We know that,

[tex]\boxed{\rm Area_{(Quarter \; Circle) } = \cfrac{\pi{r} {}^{2} }{4}} [/tex]

Now Substitute their values:

[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 6 {}^{2} }{4} [/tex]

Solve it.

[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times 36}{4} [/tex]

[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = \cfrac{3.14 \times \cancel{{36} } \: ^{9} }{ \cancel4} [/tex]

[tex]\longrightarrow\rm Area_{(Quarter \; Circle)} =3.14 \times 9[/tex]

[tex]\longrightarrow\rm Area_{(Quarter \; Circle) } = 28.26 \: {in}^{2} [/tex]

Now we can Find out the total Area of composite figure:

We know that,

[tex]\boxed{ \rm \: Area_{(Composite Figure)} =Area_{(rectangle)}+ Area_{ (Quarter Circle)}}[/tex]

So Substitute their values:

[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =48 + 28 .26[/tex]

Solve it.

[tex]\longrightarrow \rm \: Area_{(Composite Figure)} =\boxed{\tt 76.26 \:\rm in {}^{2}} [/tex]

Hence, the area of the composite figure would be 76.26 in² or 76.26 sq. in.

[tex] \rule{225pt}{2pt}[/tex]

I hope this helps!

Answer:

22.5 miles per hour

Step-by-step explanation:

Given system of equations

5(s-w)=900

4(s+w)=900

Set equations equal to each other

5(s-w)=4(s+w)

5s-5w=4s+4w

s-5w=4w

s=9w

Solve for w using the substitution s=9w

4(s+w)=900

4(9w+w)=900

4(10w)=900

40w=900

w=22.5

Therefore, the speed of the wind is 22.5 miles per hour

9y

(space fillerrrrr)

Explanation:

AB = AX+XB = 8+22 = 30

The ratio of AB to AX is AB/AX = 30/8 = 3.75

AC = AY+YC = 9+33 = 42

The ratio of AC to AY is AC/AY = 42/9 = 4.67 approximately

Since we don't get the same result, this means that the equation AB/AX = AC/AY is not true. The sides are not in proportion with one another, and therefore the triangles aren't similar.

The sides need to be in proportion with one another so we could use the SAS similarity rule.

Considering the SAS similarity theorem, triangles ABC and AXY are not similar triangles.

The SAS Similarity postulate or theorem, states that, when two triangles have two pairs of corresponding sides whose ratios are the same, and also has a pair congruent included angles, then, both triangles are similar.

Triangles ABC and AXY have a pair of congruent included angles, ∠BAC ≅ XAY.

Let's find out if their corresponding sides have equal ratios.

Thus:

AB/AX = 30/8 = 3.75

AC/AY = 42/9 = 4.67

Their ratios are not equal.

Therefore, considering the SAS similarity theorem, triangles ABC and AXY are not similar triangles.

Learn more about SAS similarity theorem on:

https://brainly.com/question/22472034

There are 8 laser beams.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

The length of the laser beams is the addition of the segments AD to segment CB (which are equal).

Using Pythagoras theorem in ECD

ED² = EC² + CD²

ED= √(12² + 35²)

ED = √144 + 1225

ED = 37 unit

Again In Triangle AED

AD² = EA² + ED²

AD=√15² + 37²

AD = 40 unit

Then, there are total of 80 ft of laser beams.

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

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[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \underline{\ln(2)+\ln(8)}-\ln(4)\implies \underline{\ln(2\cdot 8)}-\ln(4)\implies \ln(16)-\ln(4) \\\\\\ \ln\left(\cfrac{16}{4} \right)\implies \ln(4)[/tex]

Answer:

[tex]x = \frac{1}{3} [/tex]

or x = 0.33

Step-by-step explanation:

[tex] {5}^{3x} - {5}^{3x - 1} = 4 \\ \\ \implies{5}^{3x} - {5}^{3x} . {5}^{ - 1} = 4 \\ \\ \implies{5}^{3x}(1 - {5}^{ - 1} )= 4 \\ \\ \implies{5}^{3x} \bigg(1 - \frac{1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \bigg(\frac{5 - 1}{5} \bigg)= 4 \\ \\ \implies{5}^{3x} \times \frac{4}{5} = 4 \\ \\ \implies{5}^{3x} = 4 \times\frac{5}{4} \\ \\ \implies{5}^{3x} =5 \\ \\ \implies \: 3x = 1 \\ \\ \huge \implies \: x = \frac{1}{3} \\\\ \huge \implies \: x = 0.33[/tex]

Answer:

216 units^2

Step-by-step explanation:

the formula to calculate area of triangle is 1/2 b×h

so...

[tex] \frac{1}{2} (27) \times (16) \\ = 216 {units}^{2} [/tex]

Answer:

Step-by-step explanation:

144 units^3

Answer:

okay so first to find the surface area of the net below you should always start from the line that is pointing at the end of the the i n u m so you see that is between 8 1/8 and 2 so you see the line you draw a line in the middle between 8 and then when you look and then you draw another line were 19 years and then you draw another line so you can see that at the top of 19 and there at the bottom of 918 you see that you can find the Nets below because you can see me you draw your line it shows you Drawing the Line because when you draw a circle in the middle and then you draw a another little circle in the middle is shows the surface area of the net below so bye

Answer:

48%

Step-by-step explanation:

I like to look at percentages as test grades. If you got a 130/250 on a test, you would simply need to view the dash line as a 'divided by'. So you would figure 130 divided by 250 is .52, or 52%... Then, you would need to subtract 52 from 100 to get 48% to get the percentage of people who do not walk to school.

48%

48% of 250 is 120

120+130=250

Answer:

The probability of rolling a 4 or greater is 12

Step-by-step explanation:

hope it helps you

mark me as branliest

Answer: answer 98 , 78

Step-by-step explanation:

the way you just flip then and your done

Answer:

C

Step-by-step explanation:

hope this helps :)

Answer:

o 1)

[tex]Y= 6x + 11 \\ \\ 6x = Y - 11 \\ \\ x = \frac{Y - 11}{6} \\ \\ x = \frac{Y}{6} - \frac{11}{6} [/tex]

___o__o__

o 2)

[tex]A = \frac{1}{2} bh \\ \\ bh = A \div \frac{1}{2} \\ \\ bh = A \times 2 \\ \\ bh = 2A[/tex]

[tex]b = \frac{2A}{h} [/tex]

[tex]h = \frac{2A}{b} [/tex]

Answer:

a) 2x + 3; b) 0

Step-by-step explanation:

Area = [tex]4\pi x^2+12\pi x+9\pi =\pi (4x^2+12x+9)=\pi (2x+3)^2[/tex]

Area = [tex]\pi r^2[/tex]

a) radius r = 2x + 3

b) 2x + 3 > 0

x > -3/2

The least possible integer value of x is 0

Answer:

7/8 = 0.875 = 87.5%

Step-by-step explanation:

7/8 = 0.875 = 87.5%

Answer: 585000mL

Step-by-step explanation:

We know that there are 1000 milliliters (mL) in a liter (L), hence the prefix milli meaning thousand (for future reference).

As a result, in order to find the amount of milliliters, we need to multiply the amount of liters by 1000.

585Lx1000 = 585000mL

Remember: 1L = 1000mL; mL = 1000L

Answer:

585 into milimiter is 585000000mm

Step-by-step explanation:

that is the answer thank you

Answer:

A) 2/3, -3/4, 1/2, -1/3

Start by making all of them have the same denominator. They all multiply to 12 easily, so I will use that. Remember that whatever you do to the top you have to do to the bottom, and vice versa.

Multiply 2/3 by 4/4 to get 8/12

Multiply -3/4 by 3/3 to get -9/12

Multiply 1/2 by 6/6 to get 6/12

Multiply -1/3 by 4/4 to get -4/12

Least to greatest (new): -9/12, -4/12, 6/12, 8/12

Least to greatest (old): -3/4, -1/3, 1/2, 2/3 <-------- this is your answer

C) -9/10, -8/9, -4/5, -41/45

Make them have the same denominator. They all multiply to 90, so I'll use that.

Multiply -9/10 by 9/9 to get -81/90

Multiply -8/9 by 10/10 to get -80/90

Multiply -4/5 by 18/18 to get -72/90

Multiply -41/45 by 2/2 to get -82/90

Least to greatest (new): -82/90, -81/90, -80/90, -72/90

Least to greatest (old): -41/45, -9/10, -8/9, -4/5 <-------- this is your answer

E) -3, -2 2/3, -3 1/6, 2 3/4

Make the mixed numbers into improper fractions by multiplying the whole number with the denominator, and then adding the numerator:

-3 ---> -3/1 (this one's easy)

-2 2/3 ---> -8/3

-3 1/6 ---> -19/6

2 3/4 ---> 11/4 (this one is the only positive one, so it will be the greatest)

Same denominator. I'm using 12.

Multiply -3/1 by 12/12 to get -36/12

Multiply -8/3 by 4/4 to get -32/12

Multiply -19/6 by 2/2 to get -38/12

Multiply 11/4 by 3/3 to get 33/12

Least to greatest (new): -38/12, -36/12, -32/12, 33/12

Least to greatest (old): -3 1/6, -3, -2 2/3, 2 3/4 <-------- this is your answer

Carla would have about 795 pictures on May 16th.

A linear equation is in the form:

y = mx + b

where y,x are variables, m is the rate of change and b is the y intercept.

Let y represent the number of pictures after x days.

At April 30th, Carla sees that she has 235 pictures, hence b = 235. Also,  she takes 35 pictures each day, hence m = 35. The equation is:

y = 35x + 235

On May 16th, x = 16 hence:

y = 35(16) + 235 = 795

Carla would have about 795 pictures on May 16th.

Find out more on Linear equation at: https://brainly.com/question/14323743

Answer:

[tex]f^-1 (x) = \sqrt[3]{x - 8}[/tex]

Step-by-step explanation:

Custom file created rather than math ML for neatness.

Answer:

5

Step-by-step explanation:

This is the Pythagorean theorem:
[tex]a^{2} +b^{2} =c^{2}[/tex]
The hypotenuse is c so we need to make c the subject:
[tex]c = \sqrt{a^{2}+b^{2} }[/tex]
To do this I simply square rooted both sides.
Now we substitute values given to get the answer of the hypotenuse:
[tex]c = \sqrt{3^{2} + 4^{2} }[/tex]
[tex]c = \sqrt{9+16}[/tex]
[tex]c = \sqrt{25}[/tex]
c=5
The lengths 3,4,5 of a triangle are known as a Pythagorean triple.
A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c².

Answer:

x = 4√2

Step-by-step explanation:

x² - 33 = -1            [ change sides ]

x² = -1 + 33          

x² = 32

x = √3   [changing sides, changes power of square, (²) turns square root,√ ]

x = √4 * 4 * 2

x = 4√2   .......final answer.

Answer:

x = 4√2 or x = −4√2

Step-by-step explanation:

Step 1: Add 33 to both sides.

x2 − 33 + 33 = −1 + 33

x2 = 32

Step 2: Take square root.

x = ±√32

x = 4√2 or x = −4√2

Answer:

the process by which organic matter exposed to minerals over a long period is turned into a stony substance.

Step-by-step explanation:

Picture example:

Answer:

6 bags.

Step-by-step explanation:

Subtract 38 from 75 to represent the remaining amount of Matthew's money.

[tex]75-38=37.[/tex]

Matthew has $37 left over from buying flowers.

Divide 37 by 6 to represent how many bags of soil he can buy.

[tex]37\div6=6\frac{1}{6}[/tex]

Matthew can only buy 6 bags of soil, 1/6 isn't included because you can't buy a fraction of a bag.

=======================================================

Explanation:

In a standard deck, there are 52 cards.

If this deck is missing the queen of hearts and 2 of clubs, then we really have 52-2 = 50 cards in the deck.

There are 4 aces and 13 spades. Those values add to 4+13 = 17, but we need to subtract off 1 to account for the ace of spades counted twice. We have 17-1 = 16 cards that are either an ace, a spade, or both.

Or you can think of it like saying 13 spades + 1 ace of hearts + 1 ace of diamonds + 1 ace of clubs = 16 cards total.

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

The event space has A = 16 cards in it, while the sample space has B = 50 cards.

The probability we're after is A/B = 16/50 = 8/25