please help 40 points
The product of a number, x, and 4 is 3 more than the product of the number and 7.

x+4=3x+7

x4=3+x7

4x=3(7+x)

4x=3+7x

Answer:

a) The polynomial for the perimeter of the rectangle is = 14a - 2b

b) 150

Step-by-step explanation:

a) The formula for the area of a rectangle is given as:

P = 2L + 2W

From the question:

The length of a rectangle = 4a+3b

The width of a rectangle = 3a-2b.

The Perimeter of the rectangle is

Perimeter = 2(4a + 3b) + 2(3a - 2b)

Perimeter = 8a + 6b + 6a - 4b

Perimeter = 8a + 6a + 6b - 4b

Perimeter = 14a - 2b

Hence:

The polynomial for the perimeter of the rectangle is = 14a - 2b

b) What is the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number?

Non-zero whole number are single digit number such as: 1, 2, 3, 4, 5, 6, 7, 8, 9

The perimeter of the rectangle is = 14a - 2b

We are asked to find the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number.

In order to solve this, we would used the highest non zero whole number which is 9

Hence,

For a = 12 , b = 9

14 × 12 - 2(9)

= 168 - 18

= 150

Hence, the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number is 150

Answer:

x = 9

Step-by-step explanation:

50+80+(6x-4)=180 (ANGLE SUM PROPERTY)

130 +(6x-4)=180

6x-4=180-130

6x-4=50

6x=50+4

x=54/6

x = 9

Answer:

Hence the daughter's present age is 15 years

The fathers present age is 35 years

Step-by-step explanation:

Let the present age of daughter be x

Let the present age of father be y

5 years ago;

Daughter's age = x - 5

Fathers age = y - 5

If the present age of father is thrice as old as the age of daughter 5 years ago, then;

y - 5 = 3(x-5)

y - 5 = 3x-15

y = 3x - 10 .... 1

In 5 years time;

Daughters age = x + 5

Fathers age = y + 5

If the age of father will be twice the age of his daughter in 5 years time then;

y+5 = 2(x+5)

y+5 = 2x + 10

y = 2x + 5 .....2

Equate 1 and 2;

3x - 10 = 2x + 5

3x - 2x = 5 + 10

x = 15

Since y = 2x + 5

y = 2(15) + 5

y = 35

Hence the daughter's present age is 15 years

The fathers present age is 35 years

Answer: Same Side Interior Angles

Step-by-step explanation:

Imma help you eliminate the options.

-These angles are inside the parallel lines, meaning that they have to be interior angles. That eliminates any answers involving exterior angles. Next, simply by definition, it wouldn't be corresponding. Finally, alternate interior angles is eliminated because the angles are on the SAME SIDE of the transversal, meaning that Same-Side interior angles is the answer.

Answer:

answer is w

Step-by-step explanation:

Yes...

x/3 > -1

what values of x make x/3 > -1

hint... your answer will look like like x > (number)

Answer:

its x>-249

Step-by-step explanation:

this should be the answer cause x is 0 on the line and the 249 is negative so its much less than 0

Answer:

b

Step-by-step explanation:

u just have to think about it

Step-by-step explanation:

tan(A/2)

tan(A/2)=sinA/1+cos A

tan(A/2)= 5/13÷1+12/13

tanA/2=1/5

Answer:

tan([tex]\frac{A}{2}[/tex] ) = ± [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Using the trigonometric identity

tan ([tex]\frac{A}{2}[/tex] ) = ± [tex]\sqrt{\frac{1-cosA}{1+cosA} }[/tex]

Given

tanA = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

This is a right triangle 5- 12- 13 ( with hypotenuse 13 ), then

cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex] , then

tan ([tex]\frac{A}{2}[/tex] )

= ± [tex]\sqrt{\frac{1-\frac{12}{13} }{1+\frac{12}{13} } }[/tex]

= ± [tex]\sqrt{\frac{\frac{1}{13} }{\frac{25}{13} } }[/tex]

= ± [tex]\sqrt{\frac{1}{25} }[/tex]

= ± [tex]\frac{1}{5}[/tex]

07

Step-by-step explanation:

just want the answer right. thats the answer. not the answer btw just need points for my question cmon dude you know how it is. struggling really bad rn

The value of n in the given triangle is 11.

The incenter is one of the triangle's points of concurrency formed by the intersection of the triangle's 3 angle bisectors.

Given that, triangle DEF, where A is the incenter of the triangle, we need to find the value of n,

Since we know that, incenter is a point in triangle where all the angle bisector meets, therefore,

3n-6 = 27

3n = 33

n = 11

Hence, the value of n in the given triangle is 11.

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Answer:

w=1/15

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

9−7w=8w+8

9+−7w=8w+8

−7w+9=8w+8

Step 2: Subtract 8w from both sides.

−7w+9−8w=8w+8−8w

−15w+9=8

Step 3: Subtract 9 from both sides.

−15w+9−9=8−9

−15w=−1

Step 4: Divide both sides by -15.

−15w/−15 = −1/−15

w = 1/15

Answer:

No it is not a solution

Step-by-step explanation:

Key skills needed - One variable equations

1) We look at the equation, y = 4x+ 1, and see the scholar's work.

2) The scholar did everything correctly, and at the end got 9 = 13.

3) This statement is FALSE, so it would be the 2nd option (No it is not a solution)

Hope this helps and have a nice day!! :D

Answer:

Step-by-step explanation:

we have a triangle, one leg is 40, one leg is 30

c^2=40^2+30^2

c^2=1600+900=2500

c=[tex]\sqrt{2500}[/tex]=50

Answer:

The length of the road in the model is 60 m.

Step-by-step explanation:

Given: scale = 1:19

         real-life length of the road = 1.14 km

                                                      = 1140 m

Let the length of the road in the model be represented by d. A scale is a representative fraction that can be used to either increase or decrease the length of an object.

Scale = [tex]\frac{length on drawing}{actual length}[/tex]

The actual length is the real-life length given as 1140 m.

So that,

[tex]\frac{1}{19}[/tex] = [tex]\frac{d}{1140}[/tex]

19d = 1140

⇒ d = [tex]\frac{1140}{19}[/tex]

       = 60

Therefore, the length of the road in the model is 60 m.

Answer:

Step-by-step explanation:

You need to make a shape that is the same shape and size to the triangle on the page.

Answer:

27

-7

4

6

Step-by-step explanation:

Mental math.........

Answer: I do not know

Step-by-step explanation:

I dropped out of 2nd grade

Step-by-step explanation:

cos60° = Adjacent/Hypotenuse = a/42.

=> a = 42cos60° = 21.

sin60° = Opposite/Hypotenuse d/42.

=> d = 42sin60° = 42(√3/2) = 21√3.

tan30° = Opposite/Adjacent = d/b.

=> b = d / tan30° = (21√3) / (1/√3) = 63.

sin30° = Opposite/Hypotenuse = d/c.

=> c = d / sin30° = (21√3) / (1/2) = 42√3.

Answer:

16 ounces

Step-by-step explanation:

First we are told that a container has a capacity of 16 ounces of liquid and therefore 16 ounces of liquid can fill that one container

The 16 ounces liquid from the 16 ounce container is fully emptied in a larger container and fills 87.5% of the larger container therefore the larger container is:

100/87.5×16 ounces= 18.285 ounces in liquid capacity

Therefore to fill the smaller 16 ounce container, the larger container would have to pour 16 ounces of liquid into the smaller container, and would would still have 18.285-16=2.285 ounces if it(the larger container) were filled to the brim(100%)

Answer: 45 cups of flower

Step-by-step explanation:

Hi, you can use a proportion to solve this problem, so you start of by setting up the proportion:

Step-by-step explanation:

To start, create a ratio for flour to chocolate chips

flour : chocolate chips

5 cups : 3 cups

5:3

Now create a ratio with x amount of flour to 27 cups of chocolate chips

x cups of flour: 27 cups of chocolate chips

x: 27

Rewrite the ratios as fractions equivalent to each other

[tex]\frac{5}{3}[/tex] = [tex]\frac{x}{27}[/tex]

Cross multiply

5(27) = 3x

135 = 3x

135/3 = 3x/3

45 = x

45 cups of four would be needed

I hope this helps!!!!!

Answer:

The baker bought 8 apples and 4 bananas

Step-by-step explanation:

System of Equations

Let's call:

a = pounds of apples

b = pounds of bananas

The baker bought a total of 12 pounds of apples and bananas, thus:

a + b = 12      [1]

Apple cost $0.75 per pound and each pound of bananas cost $1.05 per pound. Thus the total cost is 0.75a + 1.05b. We know he spent a total of $10.20, thus

0.75a + 1.05b = 10.20     [2]

Solving [1] for a:

a = 12 - b       [3]

Substituting in [2]:

0.75(12 - b) + 1.05b = 10.20

Operating

9 - 0.75b + 1.05b = 10.20

Simplifying:

0.30b = 10.20 - 9 = 1.20

Dividing by 0.30:

b = 1.20/0.30

b = 4

From [3]:

a = 12 - 4 = 8

a = 8

The baker bought 8 apples and 4 bananas

Answer:

(x – 9)(x² + 9x+81)

Step-by-step explanation:

The sum of cubes of a and b is given by:

a³ + b³ = (a + b)(a² - ab + b²)

While the difference of cubes is given as:

a³ - b³ = (a - b)(a² + ab + b²)

1) (x + 7)(x² – 7x + 14) = x³ -7x² + 14x + 7x² - 49x + 98

= x³ -35x + 98

2) (X + 8)(x² + 8x + 64) = x³ + 8x² + 64x + 8x² + 64x + 512

= x³ + 16x² + 128x + 8³

3)  (x – 9)(x² + 9x+81) = x³ + 9x² + 81x - 9x² - 81x - 729

= x³ - 9³

4) (X – 10)(x² – 10x + 100) = x³ - 10x² + 100x - 10x² + 100x - 1000

= x³ - 20x² + 200x - 10³

Answer:

200.96 = area of Shaded portions.

Step-by-step explanation:

Area of the 2 stars.

I don't know if you can see this or not, but the 4 quarter circles surrounding the star is found by subtracting a full small square surrounding the star

Area of 1 star = 4 * (1/4) pi * r^2

Area of 1 star = 3.14 * 4^2

Area of 1 star = 50.24

Area of both stars = 100.48

Area of the 4 semicircles at each end

The 2 semicircles at one end figure = 1 circle

The two circles gives the total area of the 4 semicircles.

Area 1 circle = pr * r^2

Area 1 circle = 3.14 * (8/2)^2

Area 1 circle = 50.24

There are 2 such circles = 100.48

Total area of both results

Total Area = 100.48 + 100.48

Total Area = 200.96

Answer:

m=2/3

Step-by-step explanation:

the equation for slope (m) is (y2-y1)/(x2-x1)

here are the given points: (8,0) and (2,-4)

label the points

x1=8

y1=0

x2=2

y2=-4

substitute into the equation

m=(-4-0)/(2-8)

m=-4/-6

m=2/3

the slope is 2/3

Answer:

9 women for every 3 men

Written as: 9:3

Can be simplified to 3:1  (9:3/3)

3 women to 1 man

Answer:

133.3333..%  of 133 1/3 %

Step-by-step explanation:

100% of 18 is 18.

24-18 = 6.

6 is 33.33333...% of 18.

Therefore 24 is 133.3333..% of 18

or

24/18 = 4/3 = 1.333... = 133.33333...%

The percent 133.3% of 18 is 24.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

let x Percent of 18 is 24.

So, x% of 18 = 24

x/100 (18)= 24

18x = 2400

x= 2400/18

x= 133.33%

Hence, 133.33% of 24 is 18.

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Answer:

The length of the trip is 780 miles

Step-by-step explanation:

Given

[tex]Sleep = 15\%[/tex]

[tex]Distance\ Travelled = 663[/tex]

Required

Determine the length of the trip

If Connor slept for 15% of the trip, then Connor was awake for 85%

This is calculated as:

[tex]Sleep + Awake = 100\%[/tex]

[tex]15\% + Awake = 100\%[/tex]

[tex]Awake = 100\% - 15\%[/tex]

[tex]Awake = 85\%[/tex]

Represent the required distance with D.

So the expression for when she was awake is:

[tex]85\% * D = 663[/tex]

Make D the subject

[tex]D = \frac{663}{85\%}[/tex]

Convert % to decimal

[tex]D = \frac{663}{0.85}[/tex]

[tex]D = 780[/tex]

Hence, the length of the trip is 780 miles

Answer:

p = 2; q = 2

Step-by-step explanation: