4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°

I already know that the answer is 42 but I don’t know how to get that! Please help.

The decimal 0.1894528 is not a repeating decimal.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system. The numbers are first in fractions and then divided by the number to give a decimal number.

The given decimal number is “0.1894528. In the decimal number if the numbers are repeating then it is called the repeating decimal number if the numbers are not repeating then it is called a nonrepeating decimal number. Here the given decimal is nonrepeating decimal.

Therefore, the decimal 0.1894528 is not a repeating decimal.

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Answer:

6/7

Step-by-step explanation:

First, find two points that fall on the line and are coordinates on the graph.

The two points I found were (3,5) and (10,11).

Use the slope formula to come up with the slope.

[tex]slope = \frac{change in y}{change in x}[/tex]  

slope = [tex]\frac{11-5}{10-3}[/tex] = [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

R is 4 times so the equation will be

32 = 4r

32/4 = r

8 = r

Answer:

errror

Step-by-step explanation:

Answer:

x= 3 +√509/10

Or

x= 3 - √509/10

Step-by-step explanation:

Given:

5x2-3x = 25

Using completing the square method of solving quadratic equation

Step 1: Factor out the coefficient of the x^2 term.

5(x^2 - 3x/5) = 25

Step 2: Add a number that would complete the square inside the parenthesis and also add this to the other side of the equation.

Take (1/2) of (3/5)

1/2 × 3/5

= 3/10

Square 3/10

We have, 9/100

We have,

5(x^2 - 3x/5 + 9/100) = 25 + 9/100

Step 3: Simplify

x^2 - (3/5)x + 9/100 = 25 + 9/100

5(x^2 - 3x/5 + 9/100) = 5 + 9/20

Step 4:

factor the right side

(x - 3/10)^2 = 509/100

Take both roots

√ (x - 3/10)^2 = √509/100

x - 3/10 = ±√ [509/100]

x = [ 3 ±√509 ] / 10

x= 3+√509/10

Or

x= 3 - √509/10

Answer:

80

Step-by-step explanation:

0,   3,   8,   15,   24,  35,   48,   63,  80 which is the nth term

first step you have to find how many steps the sequence was going with.

examples= from 0 to 3 the steps were 3

                =from 3 to 8 the steps were 5

                = from 8 to 15 the steps were 7

you will recognize that the steps the sequence is going with is odd numbers.

so you will use the odd numbers until you find what you need. which leads you to 80 which is the nth number in the sequence.

Answer:

80

Step-by-step explanation:

Step-by-step explanation:

Since the original price is $47.96 and bill rate is 7%, $47.96 × 1.07 ≈ $51.32

Answer:

$51.32

The amount of sales tax for the bill if the rate is 7% will be $3.36.

The quantity of anything is stated as though it were a fraction of a hundred.

Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday.

The cost of the pizza and soft drinks before sales tax and tip was $47.96.

Then the amount of sales tax for the bill if the rate is 7% will be

⇒ $47.96 x 0.07

⇒ $3.36

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Answer:

A. 24+24+120+160+200

Step-by-step explanation:

Surface area of the triangular prism= addition of the area of each shape that forms the prism

There are two triangles

Area of a triangle=1/2*base*height

=1/2*8*6

=1/2*48

=24

Area of two triangles=24+24

There are 3 rectangles with different dimensions

Back rectangle=length×width

=20×6

=120

Bottom rectangle=length ×width

=20x8

=160

Top rectangle=length × width

=20×10

=200

Surface area =Area of two triangles + Back rectangle + Bottom rectangle + Top rectangle

=24+24+120+160+200

Answer:

-9x + y = 43

Step-by-step explanation:

We can put the equation into y = mx + b form first, then change it to Ax + By = C

First, we can find the slope by doing rise/run (y2 - y1) / (x2 - x1)

(-2 - 7) / (-5 + 4)

-9/-1 = 9

We can put this into the equation y = mx + b, along with another point, to find b:

y = mx + b

7 = 9(-4) + b

7 = -36 + b

43 = b

Now, we know the equation will be y = 9x + 43, and we can rearrange this:

Subtract 9x from both sides:

-9x + y = 43 will be the equation of the line

Answer:

This is a geometric sequence with a common ratio of -4

Step-by-step explanation:

Take the second term and divide by the first term

-4/1 = -4

Take the third term and divide by the second term

16/-4 = -4

Take the fourth term and divide by the third

-64/16 = -4

This is a geometric sequence with a common ratio of -4

Answer:

9

Step-by-step explanation:

There are 5 data points.  To find the mean, we add the data and divide by 5

(5+8+11+7+?) /5 = 8

Multiply each side by 5

(5+8+11+7+?) /5 *5 = 8*5

(5+8+11+7+?)  = 40

Combine like terms

? + 31 = 40

Subtract 31 from each side

? +31-31 = 40-31

? = 9

The missing number is 9

Answer:

We are talking about Complex numbers.

Considering [tex]\mathbb{C}[/tex] as the set of Complex numbers, we have

[tex]\Bbb{C}=\{a+bi\ : a, b \in\ \Bbb{R}\}[/tex]

A complex number is a number of the form [tex]a+bi[/tex]

as [tex]i^2=-1[/tex]

Answer:

C. Two lines are perpendicular if they have opposite slopes

Step-by-step explanation:

Hey there!

Well 2 lines that are perpendicylar have reciprocal slopes for example,

2 and 1/2 are 2 slopes that are perpendicular.

Hope this helps :)

Answer:

B. 6 + √26

Step-by-step explanation:

1. Make a right triangle using the line that goes from office to supermarket.

2. Use pythagorean thereom to find the distance of the longest side.

3. FInd the distance of the line segment going from supermarket to Marias House.

4. Add them together to get 6 + √26.

Answer:

B.

Step-by-step explanation:

1. Make a right triangle using the line that goes from office to supermarket.

2. Use Pythagorean theorem to find the distance of the longest side.

3. Find the distance of the line segment going from supermarket to Maria's House.

4. Add them together to get 6 + √26.

Answer:

h(3)=20

Step-by-step explanation:

h(3)=h(3-2)*h(3-1)=h(1)*h(2)=-10*-2=20

Answer:

20

Step-by-step explanation:

h(1) = -10

h(2) = -2

h(n) = h(n-2) * h(n-1)

Let n=3

h(3) = h(3-2) * h(3-1)

      = h(1) * h(2)

       = -10 * -2

       = 20

Divide total amount used by the amount in the rate:

27,000 / 750 = 36

Multiply that number by the rate:

36 x 1.98 = 71.28

The bill is $71.28

A negative value would mean it is below sea level. A positive value would be above sea level.

-8 is 8 feet below sea level

+107 is 107 feet above sea level.

The answer Is:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.

Answer:

Step-by-step explanation:

The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.  

Answer:

Step-by-step explanation:

To do this you would simplify both sides.

For the first one:

             [tex]7x+3<-4[/tex]

             [tex]7x<-7[/tex]        (subtract 3 from both sides)

              [tex]x<-1[/tex]         (divide 7 from both sides)

and for the second one:

              [tex]2x-3\geq 9[/tex]

               [tex]2x\geq 12[/tex]        (add 3 to both sides)

              [tex]x\geq 6[/tex]             (divide 2 from both sides)

When you graph these they will look like these pictures    

Answer:

[tex]x<-1[/tex] and [tex]x\geq6[/tex]

Step-by-step explanation:

[tex]\bf 7x+3<-4[/tex]

You must subtract 3 from both sides.

[tex]7x+3-3<-4-3\\[/tex]

After subtracting, we got

[tex]7x<-7[/tex]

Let's make it into a fraction and divide

[tex]\frac{7x}{7}<\frac{-7}{7}[/tex]

Now we got the answer

[tex]x<-1[/tex]

[tex]\bf 2x-3\geq 9[/tex]

You must add 3 to both sides.

[tex]2x-3+3\geq 9+3[/tex]

After adding, we got

[tex]2x\geq 12[/tex]

Let's make it into a fraction and divide

[tex]\frac{2x}{2} \geq \frac{12}{2}[/tex]

Now we got the answer

[tex]x\geq 6[/tex]

Your answer is [tex]\bf x<-1[/tex] or [tex]\bf x\geq 6[/tex].

Answer:233.333%

Step-by-step explanation:

1. 10-3=7 subtract end by start

2.7/3=2.333 divide difference by absolute value of start

32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing

hoped this helped

Answer:

132

Step-by-step explanation:

If US bisects the angle then

BUS = SUL

2x+10 = 3x-18

Subtract 2x from each side

2x+10 -2x = 3x-18-2x

10 = x-18

Add 18 to each side

10+18 =x

28 =x

We want to find BUL

BUL = BUS + SUL

      2x+10 + 3x-18

     5x-8

    5*28 -8

   140-8

   132

Answer:

m<BUL=132

Step-by-step explanation:

Since US bisects <BUL, we know that <BUS ≅ <SUL

This is based on the angle bisector definition.

Hence, we can set up an equation to solve for x.

<BUS≅<SUL

2x+10=3x-18

Subtract 10 from both sides

2x+10-10=3x-18-10

2x=3x-28

Subtract 3x from both sides

2x-3x=3x-3x-28

-x=-28

Divide both sides by -1

x=28

m<BUL is the sum of m<BUS and m<SUL

m<BUL=m<BUS+m<SUL

m<BUS=2x+10

m<SUL=3x-18

Plug it in

m<BUL=2x+10+3x-18

Combine like terms

m<BUL=5x-8

Plug in 28 for x

m<BUL=5(28)-8

m<BUL=140-8

m<BUL=132

Answer:

p=1                                  p = -5/3

Step-by-step explanation:

1-|3p+1|=-3

Subtract 1 from each side

1-|3p+1| -1=-3-1

-|3p+1|=-4

Divide by -1

|3p+1|=4

The absolute value has two solutions one positive and one negative

3p+1 = 4            3p+1 = -4

Subtract 1 from each side

3p+1-1 = 4-1            3p+1-1 = -4-1

3p = 3                         3p = -5

Divide by 3

3p/3 = 3/3                    3p/3 = -5/3

p=1                                  p = -5/3

Answer:

p=-5/3,1

Step-by-step explanation:

Subtract 11 from both sides.

-|3p+1|=-3-1

−∣3p+1∣=−3−1

2 Simplify  -3-1−3−1  to  -4−4.

-|3p+1|=-4

−∣3p+1∣=−4

3 Multiply both sides by -1−1.

|3p+1|=4

∣3p+1∣=4

4 Break down the problem into these 2 equations.

3p+1=4

3p+1=4

-(3p+1)=4

−(3p+1)=4

5 Solve the 1st equation: 3p+1=43p+1=4.

p=1

p=1

6 Solve the 2nd equation: -(3p+1)=4−(3p+1)=4.

p=-\frac{5}{3}

p=−  

3

5

​

7 Collect all solutions.

p=-\frac{5}{3},1

p=−  

3

5

​

,1

Answer:

Step-by-step explanation:

The rule for the sequence is

[tex]A(n) = 5. {2}^{x - 1} [/tex]

where x is the number of terms

For the first term

x = 1

That's

[tex]A(1) = 5. {2}^{1 - 1} [/tex]

[tex]A(1) = 5. {2}^{0} [/tex]

A(1) = 5(1)

For the fourth term

x = 4

[tex]A(4) = 5. {2}^{4 - 1} [/tex]

[tex]A(4) = 5. {2}^{3} [/tex]

A(4) = 5(8)

For the eighth term

x = 8

[tex]A(8) = 5. {2}^{8 - 1} [/tex]

[tex]A(8 ) = 5. {2}^{7} [/tex]

A(8) = 5(128)

Hope this helps you

Answer:

The first option.

Step-by-step explanation:

The first term of the sequence would be...

A(1) = -5 * 2^(1 - 1)

= -5 * 2^0

= -5 * 1

= -5

The fourth would be...

A(4) = -5 * 2^(4 - 1)

= -5 * 2^3

= -5 * 8

= -40

The eighth would be...

A(8) = -5 * 2^(8 - 1)

= -5 * 2^7

= -5 * 128

= -640

So, the correct answer is the first option.

Hope this helps!

Answer:

Step-by-step explanation:

133

Answer:

1875 cm3

Step-by-step explanation:

20 * 20 * 5 - (5 * 5 * 5) = 1875 cm3

Answer:

1,875

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ;)

The value of the function (f+ g)(x) = 0 then x = -2.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given:

f(x) = x² - 2x and g(x) = 6x + 4

As,  (f+g)(x) = 0

x² - 2x + 6x + 4 = 0

x² + 4x + 4 =0

x² + 2x + 2x + 4 = 0

x(x+2) + 2 (x +2 )= 0

(x + 2)(x+2) = 0

(x+ 2)²= 0

x+ 2= 0

x = -2

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Answer:

[tex]x=\pm 7\text{ or } x=\pm i\sqrt{2}[/tex]

Step-by-step explanation:

We have the equation:

[tex]x^4-5x^2-14=0[/tex]

Since this is in quadratic form, we can consider using u-substitution. Thus, we will let:

[tex]u=x^2[/tex]

Then by substitution:

[tex]u^2-5x-14=0[/tex]

Now we can solve normally. Factor:

[tex](u-7)(u+2)=0[/tex]

Zero Product Property:

[tex]u=7\text{ or } u=-2[/tex]

Back-substitute:

[tex]x^2=7\text{ and } x^2=-2[/tex]

Take the square root of both sides. Since we are taking an even-root, we will need to add plus-minus:

[tex]x=\pm 7\text{ and }x=\sqrt{-2}[/tex]

Therefore, our solutions are:

[tex]x=\pm7\text{ and } x=\pm i\sqrt{2}[/tex]

Answer:

[tex]93\frac{1}{3}[/tex] [tex]yd^{3}[/tex]

Step-by-step explanation:

The volume of a pyramid is:

[tex]V=\frac{lwh}{3}[/tex] (basically saying that you multiply the length, width, and the height together and then you divide that by 3)

Now, let's do the first part.

8 × 5 × 7 = 280

Now, let's divide.

280 ÷ 3 = 93 1/3

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a great day! :)