Someone is thinking of two numbers that are natural, and one is bigger than the other one by 10, if you multiply those two numbers you get 375 what are those two numbers.

Answers

Answer 1

Answer:

So the two numbers are {15, 25}.

Step-by-step explanation:

Simultaneous Equations:

xy = 375

x = y + 10

Subsitute the Second One into the First:

(y + 10)y = 375

y^2 + 10y - 375 = 0

y = 15 [and not -25 (natural numbers are not negative)]

Solve for x by Substituing y in the Second Equation:

x = 15 + 10

x = 25

Solution:

So the two numbers are {15, 25}.

Answer 2

Answer:

  15 and 25

Step-by-step explanation:

The given relations between the two numbers allow you to write a system of equations. Algebraic solution of the system involves the solution of a quadratic equation. The numbers are "natural numbers", so are both positive integers.

__

setup

Let x and y represent the smaller and larger of the two numbers, respectively. The given relations are ...

  y = x +10 . . . . . . the larger is 10 more than the smaller

  xy = 375 . . . . . . their product is 375

solution

Substituting for y in the second equation, we have ...

  x(x +10) = 375

Adding (10/2)² will complete the square.

  x² +10x +25 = 375 +25 . . . . add 25

  (x +5)² = 400 . . . . . . . . . . . write as a square

  x +5 = √400 = 20 . . . . . . positive square root

  x = 20 -5 = 15

  y = x +10 = 25

Those two numbers are 15 and 25.
__

The attachment shows a graphical solution of the equations.

_____

Additional comment

Your number sense tells you that both numbers end in 5. Their geometric mean is √375 ≈ 19.4, so the first numbers that deserve consideration are numbers ending in 5 that are either side of this value: 15 and 25.

You can also consider their arithmetic mean. If that is represented by z, then we have (z-5)(z+5)=375  ⇒  z²-25=375  ⇒  z²=400  ⇒  z=20, and the two numbers are 20±5.

Someone Is Thinking Of Two Numbers That Are Natural, And One Is Bigger Than The Other One By 10, If You

Related Questions

which graph shows that Cindy reads about 3/4 of the time while riding in the car?

Answers

The graph that shows a unit rate of 3/4, which is the time Cindy reads while riding in the car is the graph attached below.

What is Unit Rate?

Unit rate can be described as a constant or exactly how much of one quantity is per 1 unit of another quantity.

Unite rate (k) = x/y.

In the graph attached below, when x (hours driving) = 3, y (hours reading) = 4.

Therefore, unit rate = 3/4. We can then conclude that the graph that shows that Cindy reads 3/4 of the time she rides in a car is the graph attached below.

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find the solution to x^2 = 24

please answer asap!!!

Answers

Answer:

[tex]C) ~x = \pm 2\sqrt 6[/tex]

Step-by-step explanation:

[tex]~~~~~~x^2 = 24\\\\\implies x = \pm\sqrt{24}\\\\\implies x = \pm\sqrt{4 \times 6}\\ \\\implies x = \pm 2\sqrt 6[/tex]

Answer:

C

Step-by-step explanation:

x² = 24 ( take square root of both sides )

x = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± ( [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] ) = ± 2[tex]\sqrt{6}[/tex]

rewrite each expression using the distributive property 5x2+35x

Answers

Answer:

Common factor

5x^{2}+35x

5(x^{2}+7x)

2

Rewrite in factored form

5(x^{2}+7x)

5x(x+7)

Solution

5x(x+7)

Step-by-step explanation:

mark me brainlist

A 5-course banquet has 3 options for each course.
The number of possible 5-course meals is m.
Find the value of m.

Answers

Total courses =5

Each course has 3 options

5 courses has

5(3)15choices

Hence

m=15

Answer: m = 15

Explanation:

Each (1 course) has 3 options

By multiplication,

5 courses shall have: (5 × 3) = 15 choices

By addition,

Sum of choices for 5 courses: (5 + 5 + 5) = 15 choices

A macaroni and cheese recipe calls for 2/3 of a 2 1/2 pound block of cheese. How many pounds are needed?

Answers

Answer:

4/6

Step-by-step explanation:

if the pas is a dozen brownies

1/2 of a pan is 6 2/3 of 6 would be 4/6

I need help asap please? and this is for the math question? what is 77x+93=360? put in a fraction and decimal and you can round to nearest tenths, plus I will give out brainlists to whom ever answers first

Answers

[tex]\\ \rm\Rrightarrow 77x+93=360[/tex]

[tex]\\ \rm\Rrightarrow 77x=360-93[/tex]

[tex]\\ \rm\Rrightarrow 77x=367[/tex]

[tex]\\ \rm\Rrightarrow x=4.77[/tex]

[tex]\\ \rm\Rrightarrow x=4.8[/tex]

Step-by-step explanation:

77x+93 = 36077x = 360-9377x= 367x = 4,77x = 4,8

Aswer with Nina ^-^

Don't report my answer ✅

20.
30a³-26a² - 36a + 8
(10a - 2)

i have to divide

Answers

Answer:

112.8

Step-by-step explanation:

Hope this help!!

One marble is randomly drawn and then replaced from a jar containing two white marbles and one
black marble. A second marble is drawn. What is the probability of drawing a white and then a
black?

Answers

Answer:

1/3.

Step-by-step explanation:

Prob(Drawing white marble) = 2/3

Prob(Drawing a black marble on second draw ) =  1/2

So:

Prob(Drawing a white then a red marble) = 2/3 * 1/2

= 2/6

= 1/3.

How to remember nagative exponents how to solve nagative exponents​

Answers

To solve the negative exponents , we have to apply the negative exponent rule or the fractional exponent rule.

How are negative exponent calculated?

To calculate the negative exponent we need to remember about the negative exponent that the base is on the opposite side of the fraction. Here , We need to flip the fraction so that the base will be on the other side.

Negative exponent Rule :-

[tex]a^{-n} = \frac{1}{a^{n} }[/tex]

Now , we will solve a fraction with negative exponent

For example ; Simplify the fraction [tex]\frac{3^{-2} }{9^{-2} }[/tex]

Solution : [tex]\frac{3^{-2} }{9^{-2} } = \frac{9^{2} }{3^{2} }= \frac{81}{9}[/tex]

= 9

Here, 9 is the answer of the above example.

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Which statements are true?

Select each correct answer.


All rhombuses are rectangles.


All parallelograms are quadrilaterals.


All rectangles are squares.


All squares are rhombuses.

Answers

Answer:

OTHER ANSWER IS WRONG

Step-by-step explanation:

B. All parallelograms are quadrilaterals.

D. All squares are rhombuses.

Angle C and angle D are vertical angles. Angle C is 36 degrees. What is the measure of angle D?

Answers

Answer:

Angle D is 36 Degree!

Step-by-step explanation:

In vertical angle theorem, it stated that if two angles are vertical, then they are congruent to each other.

Answer:

d=144°

Step-by-step explanation:

Vertical angles add up to 180

c+d=180

36+d=180

d=180-36

d=144°

Nat has 2 episodes filmed for her new series. She plans
on filming 6 more episodes per month. Write a linear
equation that could represent this

Answers

2+(6m)

2 being the episode’s she has already created

6m is 6 times any number of months (m)

Im Not Understanding!

Answers

It’s basically asking us to figure out how many one halves are in the equation.
There are 9, 1/2’s in the equation, since 3/2 + 3/2 + 3/2 = 9/2.
So you would put 9 in the box, since you’re multiplying the numerator.

Hope this helps!

Answer:

3/2 + 3/2 + 3/2 = 3/1

so 3 over 1 times 1 over 2

MATH!!! 15 points;)) find the surface area of the pyramid
please answer correctly & check your work...

Answers

Answer:

20ft²

Step-by-step explanation:

There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?

Answers

Answer:

What you need to remember for answering this question is that the probability of any event is the number of sample points in the event divided by the number of sample points in the sample space.

If you have multiple trials and if the sampling is with replacement then, no matter how many samples are drawn, the probabilities remain the same for each trial.

Can anyone help solve this inequality (ps, also make sure to read the bottom)

Answers

Make the shape into two polygons. A rectangle and a triangle.
Find the area of the rectangle by multiplying lxw.
14x18=252
Then find the area of the triangle
A=l x w/2
20-14=6
18-11=7
6 x 7 = 42
42/2=21
252+21=273
273/5 is about 54
He can fit 54 chickens.

A money market account is a collection of stock and bonds true or false

Answers

Answer:

A money market fund is a type of mutual fund that invests in high-quality, short-term debt instruments and cash equivalents.

The answer to this question is true

the roof of this garden shed has a gradient of 0.35. find the height of the shed​

Answers

The height of the shed is 2.325 m

The complete question is

The roof of a lean-to-garden shed has a gradient of 0.35.find the height....they have given the base as 1.5m and a shorter height 1.8m its like a house

What is a right Triangle ?

In a Triangle when one angle is 90 degree , the triangle is called Right Triangle .

Structure of the house is a right triangle with base = 1.5m

(height of that triangle)/1.5 = 35/100

height of that triangle = 1.5*0.35 = 0.5250

Ans: greater height of the lean-to = 1.8 + 0.5250 = 2.325 meters.

The height of the shed is 2.325 m.

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please help... Find the volume of pyramid that has a square base. ​

Answers

Answer:

V = 324 cm³

Step-by-step explanation:

the volume (V) of the pyramid is calculated as

V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )

here A = 9² = 81 cm² and h = 12 , then

V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³

PLEASE ANSWER THIS QUESTION! BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!BRAINLIEST!

Answers

Answer:

20cm²

Step-by-step explanation:

We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.

100cm³/5cm = 20cm²

The area of the shaded face is 20cm².

20cm²

Step-by-step explanation:

We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.

100cm³/5cm = 20cm²

The area of the shaded face is 20cm².

Bryannasalaz

What is the circumference of a circle with a diameter of 7 feet? Use 3.14 for
TT.
d=7 ft

Answers

I think the answer is 21.99

Answer:

21.99

Step-by-step explanation:

What is 2 over 7 is greater than 4 over 12

Answers

The value 2 / 7 is greater than 4 / 12 is  - 1 / 21

How to perform subtraction in algebra?

To know the value 2/7 is greater by 4 / 12, we have to subtract 4 / 12 from 2 / 7 .

Therefore,

2 /  7  - 4 / 12 = 24 - 28/84

Therefore,

24 - 28/84  = - 4/ 84 = - 1 / 21

Therefore, it is greater by - 1 / 21

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rewrite √32/8 into simplified radical form

Answers



Factor out the largest perfect square of 32.
( in this example we factored out 16 )
Rewrite
____
/16⋅2

as the product of two radicals.
The square root of 16 is 4.
Divide numerator and denominator by 4.

If α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2, then the value of

1. α²+β²
2. 1/α+1/β​

Can Someone Answer This Quick Thank You<3​

Answers

Answer:

1. α²+β² = 25/36

2. 1/α+1/β​ = 1/2

Step-by-step explanation:

Formula :

Consider the quadratic equation ax² + bx + c = 0

Where x₁ and x₂ are the zeros of the equation.

Then

[tex]x_{1}+x_{2}=-\frac{b}{a} \\x_{1}\times x_{2}=\frac{c}{a}[/tex]

……………………………………

α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2

Then

[tex]\alpha +\beta =-\frac{1}{6}[/tex]

[tex]\alpha \times \beta =-\frac{1}{3}[/tex]

……………………

[tex]\alpha^{2} +\beta^{2} =\left( \alpha +\beta \right)^{2} -2\alpha \beta[/tex]

            [tex]=\alpha^{2} +\beta^{2} =\left( -\frac{1}{6} \right)^{2} -2\times(-\frac{1}{3} )[/tex]

            [tex]=\frac{25}{36}[/tex]

………………………………

[tex]\frac{1}{\alpha } +\frac{1}{\beta } =\frac{\alpha +\beta }{\alpha \beta }[/tex]

          [tex]=\frac{-\frac{1}{6} }{-\frac{1}{3} } =\frac{1}{2}[/tex]

can someone please give ,e a good explanation of associative property and examples please​

Answers

Answer:

See below

Step-by-step explanation:

Basically, the associative property states that when an expression has three terms, they can be grouped in any way to solve that expression.

For example, [tex](8*4)*5=8*(4*5)[/tex] if you're doing multiplication, or [tex](8+4)+5=8+(4+5)[/tex], if you're doing addition.

22. Solve 7x - 9 = 28+ 4(x - 1).
X=-3
X=3
x = 11
X=-11​

Answers

Answer:

[tex]x = 11[/tex]

Step-by-step explanation:

[tex]7x - 9 = 28 + 4(x - 1) \\ 7x - 9 = 28 + 4x - 4 \\ 7x - 4x = 28 - 4 + 9 \\ 3x = 33 \\ \\ x = \frac{33}{3} \\ \\ x = 11[/tex]

Answer:

c) x = 11

Step-by-step explanation:

Given equation: 7x - 9 = 28 + 4(x - 1)

Steps:

1. Distribute 4 through the parentheses:

7x - 9 = 28 + 4(x) + 4(-1)

7x - 9 = 28 + 4x - 4 [simplify]

7x - 9 = 24 + 4x

2. Subtract 4x from both sides:

7x - 4x - 9 = 24 + 4x - 4x

3x - 9 = 24

3. Add 9 to both sides:

3x - 9 + 9 = 24 + 9

3x = 33

4. Divide both sides by 3:

3x ÷ 3 = 33 ÷ 3

x = 11

5. Check your work:

7x - 9 = 28 + 4(x - 1) [substitute 11 for x]

7(11) - 9 = 28 + 4(11 - 1) [simplify]

77 - 9 = 28 + 4(10) [simplify]

68 = 28 + 40 [add]

68 = 68 ✔

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anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board. two students will be selected, and they will alternate attending the school board meetings. all five students are equally well qualified, so the school superintendent decides to draw names at random. what is the probability he will choose debbie and esther as the two representatives? enter your answer as a fraction in simplest terms.

Answers

Probability that he will choose debbie and esther as the two representatives is 1/20 .

What is the meaning of Probability ?

Probability is the stream in mathematics in which likeliness of an event to happen is studied.

The range of probability lies between 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.

It is given that anna, becky, christina, debbie, and esther are the five candidates for student representative for the school board.

two students will be selected, and they will alternate attending the school board meetings.

all five students are equally well qualified, so the school superintendent decides to draw names at random.

probability he will choose debbie and esther as the two representatives = ?

Probability of chosing debbie is 1/5

Probability of choosing Esther is also 1/5

Either of them if chosen first the probability is 1/5

and the either of them chosen second the probability is 1/4

Probability that he will choose debbie and esther as the two representatives = (1/5)*(1/4) = 1/20 .

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Simplify: -4x542x5
Enter the original expression if it cannot be
simplified.
Enter the correct answer.
000
008
Clear all
+?
DONE

Answers

multiply left to right:


-4 x 542 = -2,168

-2,168 x 5 = -10,840


answer: -10,840

The simplified expression is -4x^(547).

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To simplify -4x^(542)x^5.

You can use the property of exponents that states that when you multiply two terms with the same base, you add their exponents.

So,

-4x^(542)x^5

= -4x^(542+5)

= -4x^(547)

Thus,

The simplified expression is -4x^(547).

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Graph the functions on the same coordinate plane.

f(x)=−x+4

g(x)=x2−2

What are the solutions to the equation f(x)=g(x) ?

Select each correct answer.


3

−3

−2

2

0

Answers

Answer:

[tex]x = 2~\text{and} ~x = -3[/tex]

Step-by-step explanation:

[tex]~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3[/tex]

Answer:

x = -3 and x = 2

Step-by-step explanation:

Plotting the graphs :

f(x)

Find two points (preferably the x and y intercepts)

⇒ 0 = -x + 4

⇒ x = 4

⇒ Point 1 : (4, 0)

⇒ f(x) = 0 + 4

⇒ f(x) = 4

⇒ Point 2 : (0, 4)

g(x)

⇒ g(x) = 0 - 2

⇒ g(x) = -2

⇒ Point 1 : (0, -2)

⇒ g(x) = 2² - 2

⇒ g(x) = 2

⇒ Point 2 : (2, 2)

* Graph with both functions is attached below *

=============================================================

Finding the solutions :

⇒ Equate f(x) and g(x)

⇒ -x + 4 = x² - 2

⇒ x² + x - 6 = 0

⇒ x² + 3x - 2x - 6 = 0

⇒ (x + 3)(x - 2) = 0

x = -3 and x = 2

what is the measure of angle f

Answers

Answer:

What is the context, at least give a figure

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