The sum of two numbers is 17 and their product is 72. Find the smaller number.

Answers

Answer 1
The smaller number is 8

8+9=17
8x9=72
Answer 2
Answer:  8

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

Explanation:

Through guess and check, we find that

8+9 = 17

8*9 = 72

We see that 8 is the answer.

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

Another approach:

Let m and n be the two numbers.

They sum to 17 which leads to m+n = 17. Solving for n gets us n = -m+17.

Their product is 72, so,  m*n = 72

Apply substitution and we get the following:

m*n = 72

m*(-m+17) = 72

-m^2 + 17m = 72

-m^2 + 17m - 72 = 0

-1(m^2 - 17m + 72) = 0

m^2 - 17m + 72 = 0

Now apply the quadratic formula

[tex]m = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\m = \frac{-(-17)\pm\sqrt{(-17)^2-4(1)(72)}}{2(1)}\\\\m = \frac{17\pm\sqrt{1}}{2}\\\\m = \frac{17\pm1}{2}\\\\m = \frac{17+1}{2} \ \text{ or } \ m = \frac{17-1}{2}\\\\m = \frac{18}{2} \ \text{ or } \ m = \frac{16}{2}\\\\m = 9 \ \text{ or } \ m = 8\\\\[/tex]

If m = 8, then n = -m+17 = -8+17 = 9.

If m = 9, then n = 8 through similar steps.

We see the two values are 8 and 9, the smaller of which is 8.


Related Questions

A rectangular book measures 8 X 10. What is the length of its
diagonal?

Answers

Answer:

Length of the diagonals is

[tex] \sqrt{ {8}^{2} +{10}^{2} } = \sqrt{64 + 100} = \sqrt{164} =2\sqrt{41}\\ =\boxed{12.8\: units} [/tex]

12.8 units is the right answer.

The diagonal length of the rectangular book is 12.8 units.

What is rectangular?

A rectangle is "four sided polygon, having all the internal angles  is equal to 90 degree. The two sides of each corner is right angles".

According to the question,

The length of rectangle is 8 units and the breadth of rectangle is 10 cm.

To find diagonal of the rectangle: Using Pythagoras theorem a² + b² = c².

c = [tex]\sqrt{a^2 + b^2}[/tex]

  = [tex]\sqrt{8^2 + 10^2}[/tex]

  = [tex]\sqrt{64 + 100}[/tex]

  = [tex]\sqrt{164}[/tex]

  = 2[tex]\sqrt{41}[/tex]

  = 12.8 units

Hence, the diagonal length of the rectangular book is 12.8 units.

Learn more about rectangle here

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Which is greater A or B

Answers

Answer:

I'ma assume B because it's the only graph I see

Which mathematical property is demonstrated?

7 + 9 + 3 = 7 + 3 + 9


commutative property of addition

associative property of multiplication

commutative property of multiplication

associative property of addition

Answers

Answer:

I am pretty sure that the answer to this question is A: comunative property of addition

Step-by-step explanation:

I'm 99% sure

I'm sorry if it turns out to be wrong

cause I have not yet finished the test

PLEASE HELP I HAVE NO CUE WHAT THIS IS Bananas cost $0.75 per pound. If C represents cost and P represents the number of pounds, which of the following equations describes the rate relationship?


C = 0.75 × P

P = 0.75 × C

C = 0.75 ÷ P

C = p ÷ 0.75

Answers

Answer:

C=0.75×p

hope it helps.

solve 5 and 6 please

Answers

Oh yeah I guess I just don’t want you anymore I love it lol I don’t want to see it lol

0.4 times 0.59
sgaehags

Answers

Answer:

0.236

Step-by-step explanation:

Multiply 0.4 by 0.59

hopes this helps have a good day :) <3

brainlest???

PLs HeLP !!!

multiply
(-8) x 11

Answers

Answer:

-88

Step-by-step explanation:

11*8=88 put the negative sign with it and you get -88

Answer:

the answer is -88

Step-by-step explanation:

Hope this helps you so glad that I could help

Two athletes Or training over a two week period to increase the number of push-ups each can do consecutively . Athlete a can do 16 push-ups to start and increase his total by each to each day. Athlete b can do 12 push-ups to start an increase he's so tall by three each day. Compare the initial values for each what does the initial value mean in the situation

Answers

Answer:

Initial values of Athlete a and b is 16 and 12 respectively. That means, Athlete a start with more push-ups as compared to athlete b

Step-by-step explanation:

Athlete a perform 16 push-ups  to start and increase 1 push-up each day for 14 days

⇒ number of push-ups at the end of x days is for Athlete A is

n = number of push-ups for athlete A= 16 + x

Athlete b perform 12 push-ups  to start and increase 3 push-up each day for 14 days

⇒ number of push-ups at the end of x days is for Athlete B is

m = number of push-ups for athlete B = 12 + 3x

where x is the number of days

thus, total number of athletes at the end of 14 day is

n = 16+14 = 30 push-ups for athlete A and m = 12 + 42 = 54 push-ups for athlete B at the end of 14th day

Now similarly for the initial day x = 0

thus, total number of athletes at the starting of 1st day is

n = 16+0 = 16 push-ups for athlete A and m = 12+0 =12 push-ups for athlete B at the starting of 1st day.

That means, Athlete a start with more push-ups as compared to athlete b, But at the end of 14th day Athlete b do more push-ups then athlete a

Answer: The initial value for Athlete A is greater.

Pay attention for the keyword initial value.

I got no explanation D:

Which expression is equivalent to the equation?

Answers

Answer:

Option 1

Step-by-step explanation:

The given equation equals 3072, so find the other equation that equals 3072.

Option 1 = 3072 - correct

Option 2 = 432 - wrong

Option 3 = 2883 - wrong

Option 4 = 432 - wrong

I hope this helps!

Which steps show how to use the distributive property to evaluate 9.32?

Answers

Answer:

D

Step-by-step explanation:

20% of 260 students at hill middle school ride a bus to school. how many students ride a bus to school?

Answers

Answer:

52 students ride a bus to school

Step-by-step explanation:

Step 1: Our output value is 260.

Step 2: We represent the unknown value with x.

Step 3:  From step 1 above $260 = 100%.

Step 4: Similarly, x = 20%.

Step 5: This results in a pair of simple equations:

260 = 100%(1).

x = 20%(2).

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

[tex]\frac{260}{x}[/tex] = [tex]\frac{100}{20}[/tex]%

Step 7: Again, the reciprocal of both sides gives

[tex]\frac{x}{260}[/tex] = [tex]\frac{20}{100}[/tex]

⇒x=52$

Therefore, 20% of 260 is 52.

Hope this helps! :)

BRAINLIEST PLEASEEE

The number of students who ride a bus is 52.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of students = 260

The number of students who ride a bus.

= 20% of 260

= 1/5 x 260

= 52

Thus,

The number of students who ride a bus is 52.

Learn more about percentages here:

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Solve this one step equation.
5x = 13
help please

Answers

The answer is -8 because

please help need to turn in soon

Answers

Answer:

No

yes

no

yes

Step-by-step explanation:

your welcomeeeeeeeee

The ratio of the length to the width of a picture is 5:2. The picture is enlarged so that its length is 15 inches now. What is the width of the enlarged picture?



A. 5 in.
B. 6 in.
C. 7 in.
D. 8 in.

Answers

The answer is B.
The ratio is multiplied by three so 5 times 3 is 15 and 2 times 3 is 6.

Answer:

b

Step-by-step explanation:

How can you write the equation for a linear function if you know only two ordered pairs for the function? Drag tiles tho complete the explanation. Tiles may be used once, more than once, or not at all.

Answers

Answer:

Explanation below

Step-by-step explanation:

First determine the slope using (y2-y1)/(x2-x1)

Then set up point slope form and add in an ordered pair for x and y to determine the y intercept: y - y1 = m(x - x1). Solve for y and you'll end up with slope intercept form.

For example: (-2,1), (3,2) find slope and y intercept.

(2-1)/(3-(-2))= 1/5

y-2=.2(x-3)

y=.2x-.6+2

y=.2x+1.4 or y=(x/5)+(7/5)

Steve is creating a web page. He starts with a font of 5 9/10 points and decreases it by 1/2. He decreases it again by 6/10 points. Steve then realizes that the font is to small to read easily and increases it by 1 4/5 points. Which is the best estimate of the font's final size?

Answers

Answer:

6 3/5 points

Step-by-step explanation:

Steve is creating a web page.

Step 1

He starts with a font of 5 9/10 points and decreases it by 1/2.

Hence: Current font

= 5 9/10 - 1/2

= 5 + ( 9/10 - 1/2)

Lowest common denominator

= 10

= 5 + (9 - 5/10)

= 5 + 4/10

= 5 + 2/5

= 5 2/5 points

Step 2

He decreases it again by 6/10 points.

Current fonts

= 5 2/5 - 6/10

= 5 + ( 2/5 - 6/10)

Lowest common denominator

= 10

= 5 + (4 - 6/10)

= 5 + (-2/10)

= 5 - 1/5

= 4 4/5 points

Step 3

Steve then realizes that the font is to small to read easily and increases it by 1 4/5 points.

New font

= 4 4/5 points + 1 4/5 points

Lowest common denominator = 5

= 4 + 1 + (4/5 + 4/5)

= 5+ ( 4 + 4/5)

= 5 +(8/5)

= 6 3/5 points

The best estimate of the font's final size is 6 3/5 points

27) Solve: x – 9 = 20



28) Solve: 1/3 x 5/8




29) Solve: 4 x 4 x 4 = ?

Answers

Answer:

bghjgkk7686968679

hjkggkhk67896869

ghjkgh

Step-by-step explanation:

hjkh7689

Answer:

29, 5/24 ,64

Step-by-step explanation:

27) x-9=20

x=20+9

x=29

28) 1/3*5/8

1*5/3*8

5/24

29) 4*4*4

4*4=16

16*4

64

can some help me with this!!

Answers

Answer:

3

Step-by-step explanation:

[tex] | - 3| = 3[/tex]

Hope it helps you in your learning process.

the answer is 0.30 your welcome

WILL GIVE BRAINLIST PLEASE HURRY

Answers

Answer:

AC=3x+11

Step-by-step explanation:

ok so AC is Both AB AND BC combined

2x-2+x+13=AC

3x+11=AC

AC=3x+11

Answer:

(2x-2) + (x+13)=6x+2 (take the lengths of AB and BC added together, and put equal to the value of AC)

3x+11 =6x+2 (drop the parenthesis and combine like terms on the left side)

-3x +11 =2 (subtract 6x from both sides and then subtract 11 from both sides)

-3x = -9 (divide both sides by -3 to find what x is)

x=3 (take the x value and plug it into the expression to find the length of AC)

6(3)+2 (multiply)

18+2 (add)

20 (this is the length of AC, and what you put in the box)

Step-by-step explanation:

i hope this helps :)

What is valué of the x-coordínate that is 9 units to the left (5,-8)

Answers

Answer: -4

Step-by-step explanation:

A bag contains 5 red marbles, 8 white marbles, and 7 blue marbles. You draw 4 marbles out at random, without replacement. What is the probability that all the marbles are red?

Answers

Answer: 8/7752

Step-by-step explanation:

Since we are told that the bag contains 5 red marbles, 8 white marbles, and 7 blue marbles. The total number fo marbles would be:

= 5 + 8 + 7

= 20 marbles

If 4 marbles out at random, without replacement, the probability that all the marbles are red would be:

= 5/20 × 4/19 × 3/18 × 2/17

= 1/4 × 4/19 × 1/6 × 2/17

= 8/7752

What is the equation of the following line written in general form?
y
(4.5)
(1,2)
.
Oy -x +1 = 0
Ox-y+1=0
O-X-y+1=0

Answers

Answer:

x-y+1 = 0

Step-by-step explanation:

Replace x & y of each coordinates into the function then you'll get the answer.

please answer do not answer if u don't know the answer

Answers

Answer :x=3 y=7 (3,7)

Step-by-step explanation: I took algebra last year and I answered your question earlier.

the radius of a circle is 2 yards. what is the circles area

Answers

4pi or roughly 12.57 yd^2

Use pi r ^2 to find area

Which of the following lines is perpendicular to y=1/4x-3?

A. y = 4x
B. 4x - y = -2
C. y = -4x + 6
D. 8x - 2y = 3
E. y = 4x + 9

(I think it’s either C, or D, please help I don’t understand)

Answers

Answer:

The answer is

[tex]y = - 4x + 6[/tex]

Step-by-step explanation:

Negative reciprocal for the slope.

The equation of the perpendicular line will be y = -4x + d. Then the correct option is C.

What is the equation of a perpendicular line?

Let the equation of the line be y = mx + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx + c is given as y = -(1/m) + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given as,

y = (1/4)x - 3

The slope of the line is 1/4. Then the slope of the perpendicular line will be - 4. Then the equation of the line is given as,

y = -4x + d

The equation of the perpendicular line will be y = -4x + d. Then the correct option is C.

More about the equation of a perpendicular line link is given below.

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What is JL ? KM=12
JM=16

Answers

Answer:

D. 25

Step-by-step explanation:

By geometric mean property:

[tex] {(12)}^{2} = LM\times JM \\ \\ 144 = LM\times16 \\ \\ LM = \frac{144}{16} \\ \\ LM = 9 \\ \\ [/tex]

JL = JM + LM = 16 + 9 = 25

Help needed ASAP. Will give Brainliest.

Answers

Answer:

The answer is C, 296. 73

Step-by-step explanation:

Top Surface Area =  π×4.52

=  63.617251235193 inches2

Bottom Surface Area =  π×4.52

=  63.617251235193 inches2

Lateral Surface Area =  2π×4.5×6

=  169.64600329385 inches2

Total Surface Area = 296.88050576424 inches2

24 x 16 =
I need help with this please help

Answers

Answer:

=384

Step-by-step explanation:

What is the slope for the points (0,5) and (2,13)?

Answers

it’s 4, the point slope formula is m= y2-y1 over x2-x1 and by plugging in those points the slope can be found, and it is 4

An item is regularly priced at $15. Kala bought it on sale for 75% off the regular price find out how much Kalla paid ​

Answers

Answer:

$11.25

Step-by-step explanation:

you take 75% of 15

Answer:

11.25

Step-by-step explanation:

because I used a calculator

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