Peter can paint a room in 5 hours, Paul can paint a room in 6 hours, Neil can paint a room in 7 1/2 hours and Mary can paint a room in 3 3/4 hours.

Which two painters above can team up to paint a whole room in 3 hours?

Write and solve a Rational Equation that shows you are correct. Please show your work.

[tex]C=ad\\\\a=\dfrac{C}{d}[/tex]

Answer:

Step-by-step explanation:

C.  878 and D.  1 are the only whole numbers.  The rest are either mixed numbers or fractions.

Answer:

∠2 and ∠3 are complementary

Step-by-step explanation:

Complementary angles add up to 90°. Angles 1 and 3 are complementary, so the formula is ∠1 + ∠3 = 90°. Given that Angle 1 equals to angle 2, we substitute angle 2 for angle one in the equation stated before. Now we have ∠2 + ∠3 = 90°, so angles 2 and 3 are complementary

Answer:

(f-g)(x)  = 2x - x^(-7)

Step-by-step explanation:

We know that

f(x) = 2x^+1 = 2x

g(x)=x^-7 = x^(-7)

Then, we just need to subtract both functions

(f-g)(x) = f(x) - g(x) =  2x - x^(-7)

(f-g)(x)  = 2x - x^(-7)

Please, see attached images for more information

Answer:

-sqrt(3)/2

Step-by-step explanation:

Use double angle identity for sin(2x)

sin(2x)=2sin(x)cos(x)

We are given sin(x)=-1/2 so we already have so far that:

sin(2x)=2(-1/2)cos(x)

sin(2x)=-1*cos(x)

We just need to find cos(x).  

x is in the fourth quadrant so cosine will be positive there

knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.

So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2

Answer:

1 and 4

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding angles of Triangle 1 and Triangle 4 are congruent

therefore

Both triangles are similar

Answer:

similar polygons are 1 and 4

Step-by-step explanation:

From the figure we can see some triangles and angles are given

Similar triangles means that the angles are same and their corresponding  sides are in proportion.

To find the correct answer

From the figure we get 1 and 2 are similar triangle, because angles of triangle 1 are 10°, 60° and 110°,

and angles of triangle 4 are 10°, 60° and 110°,

Therefore the correct answer is 1 and 4

Answer:

A (7^6)

Step-by-step explanation:

Step 1: Find the property of 7^13/7^7

b^m/b^n=b^m-n

Therefore, when the numerator and denominator are the same number, the powers can be subtracted to simplify the answer.

Step 2: Apply the property to the question

7^13/7^7 = 7^13-7

=7^6

Hence, option A is the correct answer.

!!

Answer:

The equivalent expression is [tex]7^{6}[/tex] ⇒ answer A

Step-by-step explanation:

* Lets revise some rules of the exponents

- In the exponential functions we have some rules

# In multiplication if we have same base then add the power

  b^m  ×  b^n  =  b^(m + n)  

- Ex: [tex]5^{11}*5^{4}=5^{11+4}=5^{15}[/tex]

# In division if we have same base we subtract the power

  b^m  ÷  b^n =  b^(m – n)

- Ex: [tex]\frac{3^{10}}{3^{4}}=3^{10-4}=3^{6}[/tex]

* Now lets solve the problem

- There is the expression [tex]\frac{7^{13}}{7^{7}}[/tex]

- We have base 7 up and down

∵ In division if we have same base we subtract the power

∵ The base up is 7 and the base down is 7

- We will subtract the powers

∴ [tex]\frac{7^{13}}{7^{7}}=7^{13-7}=7^{6}[/tex]

∴ The answer is [tex]7^{6}[/tex]

* The equivalent expression is [tex]7^{6}[/tex]

Answer:

±[tex]12[/tex]

Step-by-step explanation:

We need to find [tex]\sqrt{144}[/tex].

Now, we know that  [tex](12)^{2} = 144[/tex] and [tex](-12)^{2} = 144[/tex]

Therefore: [tex]\sqrt{144}=[/tex]±[tex]12[/tex]

Summarizing, the real square roots of 144 are ±[tex]12[/tex]

[tex]\sqrt{144}=\pm12[/tex]

Answer:

The area of the triangle is [tex]A=4\ units^{2}[/tex]

Step-by-step explanation:

Let

A(0, −2),B​ (0, −3) and ​ C(8, -3)

Plot the vertices

see the attached figure

Triangle ABC is a righ triangle

The area of the triangle ABC is equal to

[tex]A=\frac{1}{2}(BC)(AB)[/tex]

[tex]BC=8-0=8\ units[/tex]

[tex]AB=-2-(-3)=1\ units[/tex]

substitute

[tex]A=\frac{1}{2}(8)(1)[/tex]

[tex]A=4\ units^{2}[/tex]

Answer:

Step-by-step explanation:

Subtracting a number means the same as adding the opposite number.

(-)(-) = (+)

6 - (-4) - (-3)

opposite number to -4 is 4

opposite number to -3 is 3

6 - (-4) - (-3) = 6 + 4 + 3 = 13

Answer:

the correct answer is 13.

Step-by-step explanation:

Final answer:

The given relation is not a function because there are multiple output values for one input value.

Explanation:

The given relation, xy1−21−3213−2, is not a function. In order for a relation to be a function, each input value (x) must have only one corresponding output value (y).

Let's examine the relation:

x = 1, y = 2

x = 2, y = -3

x = 3, y = 2

As you can see, for x = 1, there are two different corresponding values of y (2 and -3). Therefore, the given relation is not a function.

Answer:

21.66

20.545

20.479

20.15

20.1

Hello There!

From Least To Greatest, The Numbers Would Be

20.1, 20.15, 20.479, 20.545, 21.66

Step-by-step explanation:

First, change the mixed fraction into an improper fraction:

5 3/7 =

5 x 7 = 35 + 3 = 38/7

Next, divide:

38/7 = 5.42857...

5.43 (rounded) is your answer.

Of course, the more digits behind it the better, so it is up to your discretion and your answer choices.

~

Answer:

5*7+3 = 38/7 ~5.43

we can multiple 5 by 7 and add them by 3

Answer:

The zeros are

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]   and [tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]f(x)=x^{2} +5x+5[/tex]  

To find the zeros equate the function to 0

[tex]x^{2} +5x+5=0[/tex]  

so

[tex]a=1\\b=5\\c=5[/tex]

substitute in the formula

[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(5)}} {2(1)}[/tex]

[tex]x=\frac{-5(+/-)\sqrt{5}} {2}[/tex]

[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]

[tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]

Answer:

See below in BOLD.

Step-by-step explanation:

What you need to do is identify the corresponding sides in the polygon than divide the larger length by the smaller.

3.  The side length 8 corresponds to the 4 in the other polygon.

So the scale factor  is 8/4 = 2.

4. Scale Factor = 24/20 = 1.2.

5. 40/32  = 5x / 24

5x = 40*24 / 32

5x = 30

x = 6.

6. 25/30 = 4x + 7 / 42

5/6 = 4x + 7 / 42

6(4x + 7) = 210

24x = 210 - 42 = 168

x = 168/24

x = 7.

7. 40/24 = 3x + 5 / 21

5/3 = (3x + 5) / 21

9x + 15 = 105

9x = 90

x = 10.

8.   24 / 40 = (x + 3) / 15

3/5 = (x + 3) / 15

5x + 15 = 45

5x = 30

x = 6.

Answer:

[tex]\large\boxed{1<x<7\to x\in(1,\ 7)}[/tex]

Step-by-step explanation:

[tex]|x-4|<3\iff x-4<3\ \wedge\ x-4>-3\qquad\text{add 4 to both sides}\\\\x<7\ \wedge\ x>1\Rightarrow1<x<7[/tex]

you have to make a negative and positive equation for this situation

x-4<3 and x+4<3

for the first equation you have to add 4 to both sides to get x<7

for the second equation you have to subtract 4 from both sides to get x<-1

hope this helps

Answer:The answer is 189 units 3

Step-by-step explanation:

It is a 3x7x9 prism so you multiply the numbers

Answer:

36

Step-by-step explanation:

Answer: 6, 8, 10

Step-by-step explanation:

We can write the three numbers as: x, x+2, and x+4

(x+2)(x+4) = 10x + 20

x² + 6x + 8 = 10x + 20

x² - 4x - 12 = 0

(x-6)(x+2) = 0

x = -2,6

We will focus on x = 6 and ignore -2

To check our answer: (6+2)(6+4) = 10(6) + 20?

                                     8*10 = 60 + 20?

                              Yes, 80 = 80

For this case we have the following expression:

[tex](-4x) ^ 2 = 100[/tex]

To look for the solution:

 We apply root to both sides of the equation to eliminate the exponent:

[tex]-4x = \pm \sqrt {100}\\-4x = \pm10[/tex]

Then we have two solutions:

[tex]-4x = 10[/tex]

Dividing between -4 on both sides of the equation:

[tex]x = \frac {10} {- 4}\\x = - \frac {5} {2}[/tex]

The second solution:

[tex]-4x = -10[/tex]

Dividing between -4 on both sides of the equation:

[tex]x = \frac {-10} {- 4}\\x = \frac {5} {2}[/tex]

Answer:

[tex]x_ {1} = - \frac {5} {2}\\x_ {2} = \frac {5} {2}[/tex]

Answer:

x=-16

Step-by-step explanation:

The given equation is:

x = 8a

which was written to find the value of x.

We have to find the value of x when the value of a is inserted as -2

So, putting the value

x = 8(-2)

x= -16

So the value of x when a = -2 is -16 ..

Answer:

x= -16

Step-by-step explanation:

The rewritten equation for x from part A is x = 8a.

Substitute -2 for a in the equation and solve:

x = 8(-2)

x = -16

Easy ₛₕᵢₜ Yo

Answer:

y≥2-4

Step-by-step explanation:

Simplify your equation.

4x-2y≤8

-4x      -4x

-2y≤-4x+8

/-2       /-2

y≥2-4

Answer:

[tex]\large\boxed{(3-2i)(3+2i)=13}[/tex]

Step-by-step explanation:

[tex](3-2i)(3+2i)\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=3^2-(2i)^2=9-4i^2\qquad i=\sqrt{-1}\to i^2=-1\\\\=9-4(-1)=9+4=13[/tex]

Answer:

A=3.43 ft^2

Step-by-step explanation:

A=lw

A=4(6/7)

A=3.43 ft^2

To find the area of a rectangular garden 4 feet by 6/7 feet, multiply the length by the width to get 24/7 square feet.

The area of a rectangular garden measuring 4 feet by 6/7 feet can be calculated as follows:

Therefore, the area of the rectangular garden is 24/7 square feet.

Answer:

Option A. 54.008 cubic feet

Step-by-step explanation:

we know that

The volume of the barrel is equal to

[tex]V=\pi r^{2}h[/tex] ----> volume of the cylinder

we have

[tex]r=4/2=2\ ft[/tex] ----> the radius is half the diameter

[tex]h=4.3\ ft[/tex] ---> is the depth

[tex]\pi =3.14[/tex]

substitute

[tex]V=(3.14)(2)^{2}(4.3)[/tex]

[tex]V=54.008\ ft^{3}[/tex]

[tex](g\cdot f)(x)=\dfrac{1}{x}-4[/tex]

[tex]D_{g(f(x))}:x\not =0[/tex]

No, since 0 doesn't belong to the domain.

Answer:

Circles A  and D are congruent because they both have a radius of 3

Step-by-step explanation:

Answer:

Circle A and circle D are congruent ⇒ 3rd answer

Step-by-step explanation:

* Lets talk about the circle

- Any circle has diameter

- Any circle has radius which is half the diameter in length

- All the circles are similar because the measure of all circles is 360°

 and there is the ratio between the radii

- The two circles are congruent if they have the same radii because

  the congruence is special case of similarity when the ratio equal 1

* Lets look to the figure to solve the problem

- There are four circles in the figure

# Circle A with radius 3"

# Circle B with radius 4"

# Circle C with radius 5"

# Circle D with radius 3"

∵ The radius of circle A = 3"

∵ The radius of circle D = 3"

∴ The radii of circle A and circle D are congruent

∴ Circle A and circle D are congruent

Final answer:

To find the unit rate of a 16oz soda bottle that costs $3.49, divide the price by the ounces, resulting in $0.218125 per ounce, which rounds to $0.22 per ounce.

Explanation:

The question is about calculating the unit rate of a 16oz bottle of soda that costs $3.49. To find the unit rate, we divide the total cost by the number of ounces. Thus, the unit rate is $3.49 ÷ 16 oz, which equals approximately $0.218125 per ounce. Rounding to the nearest tenth of a cent, the unit rate is $0.22 per ounce.

Answer:

percentages

Step-by-step explanation:

Sales tax is an everyday example of where percentages are used.

Sales tax is an everyday example of where percentage math is used.

Given that,
To determine the suitable system that fit the given incomplete statment.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Sale tax is a type of taxation, which is applied to the sale and business of goods and services up to some percentage of the actual revenue generated by the goods and services in the form of some percent of the price of the actual cost of goods and services.

Thus, Sales tax is an everyday example of where percentage math is used.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ6

Answer:

The length of side BC is 20.5 in

Step-by-step explanation:

we know that

In the right triangle ABC

The function cosine of angle of 35 degrees is equal to divide the adjacent side to angle of 35 degrees by the hypotenuse of the right triangle

so

cos(35°)=a/25

Solve for a

Multiply by 25 both sides

a=(25)*cos(35°)=20.5 in

therefore

The length of side BC is 20.5 in

The answer is:

The length of BC is equal to 20.5 inches.

Since we are working with a right triangle and we already know some of its dimensions, we can calculate the length of PC using the following equation:

[tex]Cos\alpha =\frac{a}{Hypotenuse}[/tex]

Where,

a is equal to BC

hypotenuse is equal to 25 inches.

alpha is equal to 35°

So, we will have the following equation and we can isolate "a" from it, so substituting we have:

[tex]Cos(35\°)=\frac{a}{25in}[/tex]

[tex]a=25in*Cos(35\°)=20.47inches[/tex]

Hence, the length of BC is equal to 20.5 inches (rounded to the nearest tenth)

Have a nice day!