78% of a number, P, is 23.4 more than 117% of another number, Q. It is further given
that is 40% of P. Find P and Q.

Answers

Answer 1

Answer:

Step-by-step explanation:

"78% of P" looks like this in an algebraic expression: .78P

"117% of Q" looks like this: 1.17Q

"...is 23.4 more than [above]" looks like this: [above] + 23.4

Putting that all together in one equation, knowing that the word "is" means "equals":

.78P = 1.17Q + 23.4

From there, we will now use the fact that Q is 40% of P, which looks like this:

Q = .4P

Now, using that substitution:

.78P = 1.17(.4P) + 23.4 and

.78P = .468P + 23.4 and

.312P = 23.4 so

P = 75

Going back up to what Q is equal to, we will sub in the value of P and solve for Q:

Q = .4P and P = 75, therefore,

Q = .4(75) so

Q = 30


Related Questions

I need help with this question please

Answers

Answer:

The exact length of the third side would be 9.

Step-by-step explanation:

To find the length of the triangle, just add the height (6) and the base (3) which equals 9.

One cubic centimeter of sand weighs 1.9 grams. Find the amount of sand that the sandcastle bucket can hold.

Answers

Answer:

2160

see I times them all together then i divided the last two by 3 and got 2160

Step-by-step explanation:

Answer:

Length x width x height = volume

12 x 12 = 144

144 x 13 = 1872

height / 3 x width x length = volume for pyramid

6/3=2

2 x 12 x 12 = 288

1872 + 288 = 2160

2160 x 1.9 = 4104

4104 grams of sand

Hope this helps

Step-by-step explanation:

If p(x) = x + 3, then p(x) + p(–x) is equal to ??

Answers

Answer:

The answer is 6

Step-by-step explanation:

p(x) = x  + 3

p(-x) = -x + 3

=> p(x) + p(-x) = x + 3 + (-x) + 3 = 6

Hope this helps!

:)

g(x) = 1/3 * (2/9)^x. Does the function model growth or decay?

Answers

The function models Exponential Decay due to the fact that as

x -> infinity, y-> 0

Answer:

It Decays

Step-by-step explanation:

Why because Kahn Acadmey  said so

M(angle)1 =. Degrees

Answers

Answer:

Angle  [tex]m\angle 1 = 35^o[/tex]

Step-by-step explanation:

Our goal is to find appropriate symmetries within the given diagram, so we can use the property of the addition of internal angles of a triangle that render  [tex]180^o[/tex].

So we start by drawing a line that goes through the center of the circle and also through the vertex of angle [tex]m\angle 1[/tex]. Please see the attached image to follow the procedure. In the image, the line is a fine black line that crosses the circle completely.

Now we draw the four radii that will define clearly the central angles of [tex]100^o[/tex] and [tex]30^o[/tex] that come as information.

Then we set our efforts to analyze the two triangles (one marked with green borders, and the other one marked with orange borders. Notice that the angle on the further right for the triangle with orange borders is in fact half of the angle [tex]m\angle 1[/tex] that we need to find, so we will work our way to determine the size of it and then multiply it by two.

We need to start though with the triangle with green borders because it has more information that we can derive.

Notice that this green triangle has a central angle equal to [tex]115^o[/tex], because it has to measure the same as 180 degrees minus half of the 100 degrees angle and minus half of the 30 degree angle  in order to add to form the perfect plane angle of the circle's diameter:  

[tex]180^o-50^o-15^o=115^o[/tex]

Now, notice as well that this green triangle is an isosceles triangle (has two equal sides (both equal to the radius of the circle), and therefore the angles opposite to them must be equal. We can find the measure of either such angles by using the property of additions of internal angles of a triangle to render [tex]180^o[/tex], subtracting from it the 115 degree angle we know, and dividing the result by two:

[tex]180^o-115^o=65^o[/tex]

half of this is [tex]32.5^o[/tex]

Now we use this angle, to find its supplementary angle, which would be the angle on top of the orange triangle:

[tex]180^o-32.5^o=147.5^o[/tex]

Now all we need is to use the property of addition of internal angles for the orange triangle (of which we currently know a 15 degree angle and a 147.5 degree angle) to find what half of angle  [tex]m\angle 1[/tex]  is:

[tex]180^o-147.5^o-15^o=17.5^o[/tex]

then angle  [tex]m\angle 1[/tex] is twice this value:  [tex]m\angle 1 = 35^o[/tex]

Commutative
Property

Answers

Answer: means you can switch up the numbers

Step-by-step explanation:

so Commutative  Property means you can switch up

the numbers not the sign for example.

4 × 3 × x

4 × x × 3

3 × x × 4

x × 3 × 4

x × 4 × 3

if you look at all these! they just switch

this is easier like 4x5=20 in communicative property it would be 5x4=20

Hope this helps :)

Sari wrote the equivalent ratio below to convert cups to fluid ounces

Answers

The answer will be B. 72

Answer:The answer to this problem is 72 fluid ounces

Step-by-step explanation:

A box contains 4 black pens and 2 red pens. One pen is chosen at random, and then another pen is chosen at random without replacement. What is the probability a black pen was chosen, and then another black pen? *

Answers

Answer:

Probability is 2/5 or 40%.

Step-by-step explanation:

4/(4+2) = 4/6 = 2/3 first black pen is chosen.

3/5 - second pen is chosen without replacement.

2/3 *3/5= 2/5 - the probability a black pen was chosen, and then another black pen without replacement.

2/5*100 % = 40 %

How many prime numbers have squares between 100 and 300?

Answers

Answer:

there are 62 prime numbers with squares

Answer:

i believe it is 3...?

11, 13, and 17

Step-by-step explanation:

11 = 121

13= 169

17 = 289

these are prime numbers

Identify the diameter if given the radius and the radius if given the diameter of given circles: 7 cm 25 cm 28 cm 35 cm 100 cm 140 cm Radius = 70 cm Radius = 14 cm Diameter = 14 cm Diameter = 50 cm Radius = 70 cm Radius = 14 cm Diameter = 14 cm Diameter = 50 cm

Answers

Answer:

Radius. 7, 25, 14, 35, 50, 70

Diameter 14, 50, 28, 70, 100, 140

help me please it’s on spheres thankyou

Answers

Answer:

452.3893421 cm^2

452.4 (to one decimal place)

Step-by-step explanation:

Radius (r) - 6cm

The surface area of sphere = 4pi r^2

therefore:

4 * pi * 6^2

4 * pi * 36

144 * pi

452.3893421 cm^2

452.4 (to one decimal place)

Answer:

Surface area = 452,4

Step-by-step explanation:

radius = 6 cm

Surface area = 4πr²

Surface area = 4(3.1416)(6)²

Surface area = 12.5664 (36)

Surface area = 452, 3904

Surface area = 452,4

whats the formula for area of an rectangle

Answers

Answer:

L (lengh) · W (width)

Step-by-step explanation:

Tp find the area of a rectangle, you always have to multiply the length by the width. You do this because there are individual little array-like squares that make up the area. You could just count the square units, but multiplying is faster.

Answer:

For Perimeter its  2times length + 2times width

and for Area its: length times width

Hope this helps :)

[tex]5x^{3} * 2x^{2}[/tex]

Answers

Steps to solve:

5x^3 * 2x^2

~Apply exponent rule

5x^3+2 * 2x

~Simplify

5x^5 * 2x

~Combine like terms

10x^5

Best of Luck!

x=12-1//3x
can anyone tell me the full answer

Answers

Answer:

x=9 is the answer......

What whole number does: 20/5represent?

Answers

Answer:

4

Step-by-step explanation:

20/5 = 4

Answer:

4

Step-by-step explanation:

cause 20/5 is 4 meaning it represents 4

I need help ASAP I shall give brainlyist (idk how to spell it)

Answers

Answer:

3014.4ft³

Step-by-step explanation:

V=Πr²h(volume of cylinder)

=(3.14)(8)²(15)

=3014.4ft³

Someone have the answer please ?!

Answers

True because they are vertical angles

True if the lines were not vertical this would be false.

olivia has 2 gallons and 3 quarts of vanilla ice cream and 1 gallon and 2 quarts of ice cream left over form the party how many gallons and quarts does she have left

Answers

Answer:

She has 4 gallons and 1 quart left

Step-by-step explanation:

4 quarts equals a gallon. Add the 2 gallons with the one gallon and it's 3 gallons. Then add the 3 quarts with the other 2 quarts for another gallon with a quart left over. Add that gallon with the other three and she has 4 gallons and 1 quart. Hope this helps :>

if 4a + 6 = 12 - 2a what is 6a

Answers

___________________________

Hey!!

Solution

4a+6=12-2a

or,4a+2a=12-6

or,6a=6

or,a=6/6

a=1

The value of a is 1.

hope it helps...

Good luck on your assignment

_________________________

value of 6a = 6* 1 = 6

What is linear equation ?

In a linear equation coefficients can be positive or negative values and in which the highest power of the variable is always 1 .

according to question the linear equation given is :

4a + 6 = 12 - 2a

find = 6a ?

4a + 6 = 12 - 2a

6a = 12 - 6

6a = 6

a = 1

since , substituting value of a

6a = 6* 1 = 6

learn more about linear equation :

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Find the equation of the circle whose center and radius are given. center ( 5, 6), radius=3

Answers

Answer:

(x-5)^2 + (y-6)^2 = 9

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2  where ( h,k) is the center and r is the radius

(x-5)^2 + (y-6)^2 = 3^2

(x-5)^2 + (y-6)^2 = 9

If x = 4 and y = 8 , evaluate the following expression: x/y Give your answer as a fraction in its simplest form.

Answers

Answer:

X/Y = 4/8= 1/2

Step-by-step explanation:

This is the answer of this question

WILL GIVE BRAINLIEST DONT LOOK AT OTHER ANSWERS THEY ARRE WRONG

Answers

Answer:

The first choice, second choice, fifth choice are correct

Step-by-step explanation:

To get the first and second choices, you just need to count the number of boxes. For the fifth choice, you can see that the side lengths have been cut in half from the pre-image to image

There are three people in lee’s family. The range if their shoe sizes are 3. Two people in her family wear size 6. Lee’s size is not 6 or 3. What is Lee’s shoe size?

Answers

Answer:

I would say 9

Step-by-step explanation:

range is the difference between the largest and the smallest values in a data set.  the range in this case is 3. so, we have to either add to 6 or subtract from 6.

but we've been told that Lee's shoe size is not three so it 6 + 3 = 9.

hope this helps

if f(x)=x+7and g(x)=1/x-13, what is the domain of (f•g)(x)

Answers

Answer: 7x-90/x-13

Step-by-step explanation:

f(x)= x+7

g(x)=1/x-13

(f•g)(x)=1/x+13+7

1+7(x-13)/x-13

1+7x-91/x-13

7x-90/x-13

Answer:

(-∞, 0)∪(0, ∞)

Step-by-step explanation:

You are given the functions f(x) and g(x).  Now, you have to find (f*g)(x).  To do this, you have to multiply the two functions.

f(x) = x + 7

g(x) = 1/x - 13

(f*g)(x) = (x + 7)(1/x - 13)

(f*g)(x) = -13x + 7/x + 1 - 91

(f*g)(x) = -13x + 7/x - 90

The domain has to include all of the x-values that will produce a rational number.  So, look at where the x's are locate

-13x:  You could put any rational number into this value and still have a rational number.

7/x:  For this value, you cannot have 0 as an x-value.  Every other number is fine.

This means that the domain will be (-∞, 0)∪(0, ∞).  

You use parentheses and not brackets for the zero side because you don't want to include zero in the domain, but you do want to include all of the other numbers around zero.  There are no brackets on the infinity side because infinity isn't a number.  The ∪ symbol is used to combine domains.

Holly is trying to save $25,000 to put a down payment on a condominium. If she starts with $10,000 saved and saves an additional $750 each month, which equation represents how far Holly is from her goal of reaching $25,000? Let x stand for months and y stand for dollars.

Answers

Answer:

15000 - 750x

Step-by-step explanation:

Holly is trying to save $25, 000 to put a down payment on a condominium. She started with $10,000 and saved an additional $750 each month.

Let

y = dollars

x = number of months

Since she started her savings with $10, 000 her remaining amount to pay will be 25000 - 10000 = $15000 .

The amount will also be reducing by $750 per month

Therefore,

How far she is from her goal can be represented with the equation

15000 - 750x

Please help me answer these two questions:) Find two consecutive numbers with a sum of 143. The combined mass of two children is 75 lbs. The first child is four times the mass of the second child. What are the masses of the two children? Whoever answers and explains i will give the brainliest!

Answers

Answer:

Question 1: 71 and 72

Question 2: Child 1: 60 lbs, Child 2: 15 lbs

Step-by-step explanation:

Question 1:

Consecutive numbers are 2 numbers right next to each other.

You know the numbers will have to be double digits number.

71 and 72 are consecutive numbers. The sum of them is 143.

71+72=143

Question 2:

For this problem, we can use system of equations to find the mass of the 2 children. Let's say x is the first child and y is the second child.

Equation 1

x+y=75

This equation comes from the combined mass of the 2 children.

Equation 2

x=4y

This equation comes from the first child being 4 times the mass of the second child.

Since we know the value of x, we can use substitution to find y.

4y+y=75

5y=75

y=15

Now that we know the second child is 15 lbs, we can plug this into any of the 2 equations to find the mass of the first child.

x=4(15)

x=60

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. k = -1; f(x) = 4x^3 - 2x^2 + 2x + 4; Lower bound? yes/no?

Answers

Answer:

Yes,  k is lower bound for the real zeros of the function.

Step-by-step explanation:

Lower Bound Theorem:

If you divide a polynomial function f(x) by (x - k), where k < 0, using synthetic division and this yields alternating signs, then k is a lower bound to the real roots of the equation f(x) = 0.

Given;

4x³ - 2x² + 2x + 4

k = -1

synthetic division;

-1 ]    4       -2        2        4

        ↓         -4        6       -8

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

        4         -6       8          -4  

(the result has alternating signs, hence k is lower bound)

Thus, k is lower bound for the real zeros of the function.

Which of these is an equation? 8t+4=76 8t+4 8z 8+4

Answers

Answer:

8t+4=76

Step-by-step explanation:

An equation needs an equals sign otherwise it is an expression

Evaluate the expression shown for x = 9.
Negative StartFraction 5 over 6 EndFraction x + 7
Negative 13 and one-third
Negative one-half
7 and one-third
9 and two-thirds

Answers

Answer:

So since the equation is -5/6x+7 we need to plug in equation. So x is equal to 9 we have -45/6x+7. Now we need to simplify. That will give us -7 1/2+7

= - 1/2 So the answer is B

The answer is -1/2

What is expression?

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

Given:

-5/6 x+ 7

Now, for x=9

-5/6 * 9 + 7

=-15/2+7

=(-15+14)/2

=-1/2

Learn more about expression here:

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I can’t tell if my answer is correct , please help !!!!!! Will mark brainliest !!!!!!!!!!!!

Answers

Answer:

You should be right

Step-by-step explanation:

Srry if I am wrong though

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