Panama wants to solve the equation 1/3 ( x - 7) = 4To begin , she multipiles both sides of the equation by 3 what should she do next?

we know that

Auto ----> 13%

Food ----> 19%

Clothing ----> 17%

13%+19%+17%=49%

$71,050 ------> represents 49%

Applying proportion, find out how much represents 100%

71,050/49=x/100

solve for x

x=(71,050/49)*100

x=145,000

therefore

Answer: X=2 X=-7

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

A financial concept known as future value (FV) assigns a value to an asset based on anticipated factors like future interest rates or cashflows.

The answer is as follows:

a-1: Bank B

a-2: Profit $665875

b. Future Value $64056.04

A financial concept known as future value (FV) assigns a value to an asset based on anticipated factors like future interest rates or cashflows. Knowing how much their investment would be in five years, given a projected rate of return, may be valuable for an investor. Future value is the idea of taking the investment's current value, applying anticipated growth, and estimating what the investment will be in the future.

For planning purposes, future value is used to estimate what an investment, cash flow, or expense might be in the future. Given the future worth of an investment, investors utilize the future value to decide whether or not to proceed with it.

Future value can also be used to assess risk, calculate the rate at which a specific expense will increase if interest is paid, or set a savings goal to see whether adequate reserves will be made in light of the present savings rate and the anticipated rate of return.

Therefore, the answer is as follows:

a-1: Bank B

a-2: Profit $665875

b. Future Value $64056.04

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The measure of ∠6 from the given figure is 45°.

From the given figure, the measure of angle is 135°.

Co-interior angles occur in between two parallel lines when they are intersected by a transversal. The two angles that occur on the same side of the transversal always add up to 180°.

From the given figure,

135° + ∠6 = 180° (Co-interior angles adds upto 180°°)

⇒ ∠6 = 180°-135°

⇒ ∠6 = 45°

Therefore, the measure of ∠6 from the given figure is 45°.

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The amount of juice in a pitcher is 4 6/8 cups and 7/8 cup is taken out.

The amount of juice left in the pitcher is,

There are 3 7/8 cups left in the pitcher.

Answer:

Explanation:

Formula for calculating the circumference of a circle is expressed as;

r is the radius

Since a semi-circle is half of a circle, then the circumference will be half of cirumference of a circle as shown;

This gives the circumference of s semicircle where r is the radius of the semi circle

Answer:

0.016

Step-by-step explanation:

Remember that "of" means to multiply and percent (%) means out of 100. So we would multiply 3.2 by 0.5 and get 1.6 then you move the decimal 2 times to the right and get 0.016. Have a Great Day! ;)

The equation to graph is:

Let's break it down and see how can we EASILY graph this!!

The first point is to always put x = 0 and find the y-value. This way, we graph the y-intercept. Thus,

So, y-intercept is (0, 3).

Now, look at the slope, the constant before "x". It is -3/2.

The numerator is rise and denominator is run.

Thus, from the y-intercept, we move "-3" units "rise" (y-direction) and "2" units "run" (x-direction).

We will arrive at (2,0).

Then we can make this move again!

We will arrive at (4, -3).

That's it!!

We can now graph the 3 points found, draw a smooth line through these points and that's our line!!

The graph of the line is shown below:

Given: Two investments compounded annually as follows-

and,

Required: To find out the time required by smaller investment to catch up to larger investment.

Explanation: The formula for compound interest is as follows-

Putting the values for the first investment (smaller one) we get,

Similarly solving for other investment we get,

Now lets say in time 't' our investment catch up or becomes equal, i.e.,

Taking logarithm both sides and solving for t gives us,

Final Answer: The investments would catch up after approximately 40.8 yrs.

The coins are in the shape of a cylinder.

The formula to calculate the volume of a cylinder is given as

where

The individual coin has the following dimensions:

Thus, the volume of one coin can be calculated as

If there are 225 coins in the chest, the combined volume of all the coins will be

The combined volume is 44.1 cubic inches.

The rectangle below has an area of x²-15x+56.  (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).

Given that,

The rectangle below has an area of x²-15x+56.

We have to find the width of the rectangle.

A quadrilateral (4-sided polygon) with two sets of parallel and equal sides called length and width is what is meant by the term "rectangle." The sum of these two is equal to the area of a rectangle. A quadratic equation represents the area. When a quadratic equation is factored, the result is a product of two binomials, such as (x-q)(x-r) = 0, where q and r are the equation's roots or zeros. Making use of the quadratic formula, you may determine this:

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

Here, a is 1 b is -15 and c is 56.

x=[tex]\frac{-15\pm\sqrt{15^{2}-4(1)(56) } }{2(1)}[/tex]

x=[tex]\frac{-15\pm\sqrt{225-224 } }{2}[/tex]

x=[tex]\frac{-15\pm\sqrt{1} }{2}[/tex]

[tex]x=\frac{-15\pm1 }{2}[/tex]

Take the plus 1st

x=-15+1/2

x=-14/2

x=-7

Now take minus

x=-15-1/2

x=-16/2

x=-8

Therefore, (x-7) and are the binomials (x-8). Given that the length is (x-7) and the width is, respectively (x-8).

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We need to find the primed factor form of the lowest common denominator of the fractions 2/15 and 5/12, hence we first need to find the lowest common factor between 15 and 12, let's do that by listing the multiples of each number:

12, 24, 36, 48, 60, 72, ....

15, 30, 45, 60, 75, ....

From the multiples above we notice that the least common denominator will be 60.

Now we need to find the prime factorization of 60, let's do that:

Since we can't have any further factorization of the factors this is the prime factored form of the LCD, therefore, the answer is the third option.

The areas of each figure are listed below:

Case 2 - Triangle: 20 in²

Case 3 - Composite figure: 72 ft²

Case 4 - Parallelogram: 45

Case 5 - Rhombus: 39 m²

Case 6 - Composite figure: 94 cm²

Case 9 - Composite figure: 101 m²

In this problems we must calculate the areas of triangles, quadrilaterals and composite figures formed by triangles and quadrilaterals. Now we proceed to present the areas for each case:

Case 2

The area of the triangle is the sum of the areas of the two right triangles:

A = (1 / 2) · (3 in) · (4 in) + (1 / 2) · (7 in) · (4 in)

A = 6 in² + 14 in²

A = 20 in²

Case 3

The area of the composite figure is the sum of the areas of the rectangle and two right triangles:

A = (1 / 2) · (6 ft) · (6 ft) + (8 ft) · (6 ft) + (1 / 2) · (2 ft) · (6 ft)

A = 18 ft² + 48 ft² + 6 ft²

A = 72 ft²

Case 4

The area of the parallelogram is the product of the length of its base and the length of its height:

A = b · h

A = 9 · 5

A = 45

Case 5

The area of the irregular rhombus is equal to the sum of the areas of the four triangles:

A = 2 · (1 / 2) · (4 m) · (3 m) + 2 · (1 / 2) · (3 m) · (9 m)

A = 12 m² + 27 m²

A = 39 m²

Case 6

The area of the composite figure is the sum of the areas of the three rectangles:

A = (10 cm) · (5 cm) + (8 cm) · (4 cm) + (4 cm) · (3 cm)

A = 50 cm² + 32 cm² + 12 cm²

A = 94 cm²

Case 9

The area of the composite figure is the sum of the areas of a right triangle and two rectangles:

A = (1 / 2) · (3 m) · (10 m) + (3 m) · (10 m) + (8 m) · (7 m)

A = 15 m² + 30 m² + 56 m²

A = 101 m²

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Based on your picture, we can say the following:

- Minor arc: The curve between points B and E

- Chord: AB

- Tangent line: The line which goes through points DE

- Central angle: ECB

- Secant line: The line which goes through points AE

- Major arc: The curve between points B and B going through A

- Radius: CE and CB

- Inscribed angle: EAB

Answer:

y= -11/2 x +38

Step-by-step explanation:

to find slope:

m= -6-5/8-6      m= -11/2

to find the y-intercept:

y= -11/2 x +b

5 = -11/2(6) + b

5 = -33 + b

38 = b

so then:

y= -11/2 x +38

B

1) Examining the table we can say the more the independent variable, in this case, t increases by 1 unit, the dependent variable, in this case, b decreases by 50 dollars.

2) Hence the answer is

B. As the independent variable increases by 1, the dependent variable decreases by 50

The correct statement will be;

⇒ If a car travels for 0​ hours, it will travel 0 ​mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.

What is Equation of line?

The equation of line with slope m and passes through the point

(x₁, y₁) defined as;

⇒ y - y₁ = m (x - x₁).

Given that;

The relation between the distance and time is shown in graph.

Now,

When we move 3 units to the right then, the graph is meet at point 3 up to, for the distance and time.

This point is meet at point (3, 3).

Thus, The correct statement will be;

⇒ If a car travels for 0​ hours, it will travel 0 ​mile(s). This means it will pass through the point (0, 0). Use the slope to move 3 units to the right of the origin and 3 units up to find the point (3, 3) that can be used to graph the relationship.

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The general equation of line is :

The equation of the function g(x) is:

Consider any two coordinates : (-3,0) & (0,3) So, the equation is:

The equation of the function f(x) is:

Consider any two coordinates: (-1,0) & (0,1)

Since, h(x) = f(x)/g(x)

So, the funstion h(x) is express as:

a) Vertical intercept of h

Substitute x =0 in h(x)

b) Determine the roots of h(x)

c) Vertical asymptote : Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function

So,

The vertical assymptote : x =-3

D) Horizontal assymptote : x - 3

bAnswer: x -3

Answer:

a)h(0)=1/3

b) h(x)=(x+1)/(x+3)

c) x = -3

Hroizontal Assymotote : y =1/3

Answer:

B. (4,2)

Explanation:

The coordinates of point D is (-4, -2)

If a point (x,y) is rotated 180 about the origin, we have the transformation:

Therefore, the new coordinates of point D will be: (4, 2).

The correct choice is B.

First, calculate the total amount of cups of oatmeal required to make 21 batches of cookies by multiplying 21 times 2 3/4:

Simplify that fraction:

Since a total of 57 3/4 cups of oatmeal are needed to make 21 batches of cookies, but a package contains only 56 cups of oatmeal, therefore, there is not enough oatmeal to make 21 batches of cookies.

Given that:

- The graphs have no scales assigned to them.

- You have to identify the ones that could be density curves for a continuous random variable assuming that they have the right scale.

Then, in order to solve this exercise, you need to remember the following:

1. A Probability Density Function is useful to define the probability of a random variable within a distinct range of values.

2. It is also known as PDF.

3. The Probability Density Function is always positive in all its Domain.

4. The total enclosed area under the curve of the function is:

Knowing all these concepts, you can identify that:

- In graph B the area under the curve is 0. Therefore, this cannot be the graph asked in the exercise.

- In Graph C, the function is not positive in its Domain. Therefore, this does not satisfy the properties mentioned before.

Hence, the answers are:

- Option A.

- Option D.

- Option E.

Answer: 25.5 im pretty sure

Step-by-step explanation:

Answer: z=95 and x=18

Step-by-step explanation: the lines are both straight and the whole 6x blahb blah blah is not needed since the line is 180 degrees and 180-95=85 so 6x-23=85 which x=18 and it also has to be 95 so z=95

Answer:

2 miles

Explanation:

Jim walked 1/2 of a mile in 1/4 of an hour.

We simplify our result:

At this rate, Jim will walk 2 miles in one hour.

Answer:

600

Step-by-step explanation:

Vol = length x width x height

(8)(15)(5) = 600

Weight of the two parcels 22lbs 5oz.

What is Weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

Given,

The weight of big parcel = 12lbs 11oz

The weight of small parcel = 12lbs 11oz - 3lbs 1oz

                                             = 9lbs 10oz

The weight of total parcel  = big parcel + small parcel

                                            = 12lbs 11oz + 9lbs 10oz

                                            = 21lbs 21oz = 22lbs 5oz

Hence, The weight of the 2 parcels is 22lbs 5oz.

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ANSWER

EXPLANATION

We have that D is the midpoint of CE.

We are given that:

CD = 4x - 19