. Jessica went to the grocery store and purchased a box of cereal for $3.75, milk for $1.50, and bread for $2.25. She paid with a $20.00 bill. How much change did Jessica receive?

Answer:

7 and 9

Step-by-step explanation:

So we want two consecutive odd numbers whose product is 63.

Let's write an equation.

Let's let n be a random integer: doesn't matter what it is. Therefore, the first integer must be 2n+1.

This is because we're letting n be whatever it wants to be. If we multiply that whatever number by 2, then it will turn even. If we add 1 to an even number, it becomes odd.

Therefore, our first odd number is (2n+1). Our second, then, must be (2n+3).

Multiply them together. They equal 63. Thus:

[tex](2n+1)(2n+3)=63[/tex]

Expand:

[tex]4n^2+6n+2n+3=63[/tex]

Combine like terms:

[tex]4n^2+8n+3=63[/tex]

Subtract 63 from both sides:

[tex]4n^2+8n-60=0[/tex]

Divide both sides by 4:

[tex]n^2+2n-15=0[/tex]

And now, factor:

[tex](n+5)(n-3)=0[/tex]

Zero Product Property:

[tex]n+5=0\text{ or } x-3=0[/tex]

Find n:

[tex]n=-5\text{ or } n=3[/tex]

So, we've found n.

Then the first integer is either:

[tex]2(-5)+1 \text{ or } 2(3)+1[/tex]

Evaluate:

[tex]-9 \text{ or } 7[/tex]

However, we want two consecutive odd natural numbers. So, ignore the -9.

Therefore, our first odd integer is 7.

And our second one would be 9.

So, our answer is 7 and 9.

And we're done!

Answer:

The 10-yard line on a football field

Step-by-step explanation:

A geometric line segment is a straight path of points(that is a line) that has two end points (that is a beginning and an end). A 10 yard line on a football field is a line segment because it has two endpoints which is at the beginning of the 10 yard and at the end of the 10 yard.

A scientist's line of vision as he looks into space with a telescope is not a line segment because it extends forever (has no end).

A line of 15 dancers on stage is not a line segment, A light shone into the darkness is not a line segment because it continues forever and also, the hands of a clock is also not a line segment.

Answer:

[tex] \sqrt{2 \times 2 \times 2 \times 3 } = \sqrt{24} = \sqrt{4 \times 6} = 2 \sqrt{6} [/tex]

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

18m

Step-by-step explanation:

5x3=15 +3 =18

Answer:

The answer is below

Step-by-step explanation:

Given that f(x)=x(22-x)

a) f(x)=x(22-x)

f(x + h) = (x + h)(22 - (x + h))

f(x + h) = (x + h)(22 - x - h)

f(x + h) = (22x - x² - xh + 22h - xh - h²)

f(x + h) = (-x² + 22x - h²+ 22h - 2xh)

b) f(x)=x(22-x) = 22x - x²

f(x + h) = (-x² + 22x - h²+ 22h - 2xh)

f(x+h)- f(x) = (-x² + 22x - h²+ 22h - 2xh) - (22x - x²)

f(x+h)- f(x) = -x² + 22x - h²+ 22h - 2xh - 22x + x²

f(x+h)- f(x) = -x² + x² + 22x - 22x  - h²+ 22h - 2xh

f(x+h)- f(x) = - h²+ 22h - 2xh

c) f(x+h)- f(x) = - h²+ 22h - 2xh

[tex]\frac{f(x+h)-f(x)}{h}=\frac{- h^2+ 22h - 2xh}{h}\\ \\\frac{f(x+h)-f(x)}{h}=\frac{- h^2}{h}+\frac{22h}{h}-\frac{2xh}{h}\\\\\frac{f(x+h)-f(x)}{h}=-h+22-2x[/tex]

[tex]\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}= \lim_{h \to 0} (-h+22-2x )=22-2x[/tex]

Answer:

Coordinates of the point B will be (14, 3.5).

Step-by-step explanation:

From the graph attached,

Distance between the Quarterback and Receiver = x-coordinate of the point B = 14 yards

Similarly, height of the football from the ground at point B = y-coordinate of the point B = 9 + [tex]\frac{12-9}{2}[/tex]

                   = 9 + 1.5

                   = 10.5 feet

Since, 1 feet = [tex]\frac{1}{3}[/tex] yards

10.5 feet = [tex]\frac{10.5}{3}[/tex]

               = 3.5 yards

Therefore, coordinates of the point B will be (14, 3.5).

Answer:

Option C

Step-by-step explanation:

It will be graphed as function:

Since is has a very small slope of 0.019 it will be shown almost parallel to x axis.

Some points on the graph:

Correct graph is option C

x = 12

5x + 15 = 75

5x = 75 - 15

5x = 60

x = 60 : 5

x = 12

Answer:

3m ≤ ∫ f(x) dx ≤ 3M, at limit of b, a

Step-by-step explanation:

Like the question asked, which property of integral was used.

Property 8 of integrals was the basis upon which the question was solved.

The property of the integral is used to solve the problem. The function is given below.

[tex]3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Suppose f has absolute minimum value m and absolute maximum value M.

We know that the property of the integral can be used.

If m ≤ f(x) ≤ M ∀ a ≤ x ≤ b. Then we have

[tex]m (b-a) \leq \int_a^b f(x) dx \leq M(b-a)\\[/tex]

Then we have

[tex]m \leq f(x) \leq M \ \ and \ \ 4 \leq x \leq 7[/tex]

This means that

[tex]\begin{aligned} m(7-4) & \leq \int_a^b f(x)dx \leq M(7-4)\\\\3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]

More about the function link is given below.

https://brainly.com/question/5245372

Answer: Area of Polygon Q is  [tex]\dfrac14[/tex]  of  Area of Polygon

Step-by-step explanation:

Given: Polygon Q is a scaled copy of Polygon P using a scale factor of [tex]\dfrac12[/tex] .

According to the property of scale factor ,

Area of the image = (scale factor )²x (Area of the original figure)

So, Area of Polygon Q = [tex](\dfrac12)^2[/tex]  x (Area of Polygon P)

⇒ Area of Polygon Q = [tex]\dfrac14[/tex]  x (Area of Polygon P)

Hence,  Area of Polygon Q is   [tex]\dfrac14[/tex]  of  Area of Polygon P.

Answer:

1/4

I did on khan

Step-by-step explanation:

Answer:

2. w = -90

4. b = 8

Step-by-step explanation:

Multiply both sides by the reciprocal of the number multiplying the variable.

2.

[tex] -\dfrac{2}{3}w = 60 [/tex]

[tex] -\dfrac{3}{2} \times (-\dfrac{2}{3}w) = -\dfrac{3}{2} \times 60 [/tex]

[tex] w = -\dfrac{180}{2} [/tex]

[tex] w = -90 [/tex]

4.

[tex] 9.6 = 1.2b [/tex]

[tex] \dfrac{1}{1.2} \times 9.6 = \dfrac{1}{1.2} \times 1.2b [/tex]

[tex] 8 = b [/tex]

[tex] b = 8 [/tex]

Answer:

1) 19.0km

2) 23.9mi

3) 53.9yd

4) 30.0mi

(all answers rounded off to the nearest tenth)

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer: y=2

Step-by-step explanation:

y/6 = 3/9        multiply both sides by 6/1 (since 6/1 times y/6 equals 1y or just y)

y = 18/9          now that y is isolated, just simplify 18/9

y=2                 18 divided by 9 is 2

1/8 since 4*2=8 and there is one spot you can land on with 6.

Answer:

2/8

Step-by-step explanation:

If you are spinning it twice and there is 4 places that is where you get the 8        The 2 comes from how many times you are spinning

Answer:

300 feet an hour

Step-by-step explanation:

in three hours they went down 1200 feet so that means in 1 hour they will go down 300 feet if they take no break

Answer:

670

Step-by-step explanation:

32 hours at 17  plus 14 hours at 9

32 *17 + 14 *9

544+126

670

Answer:

job 1 = 544 dollars he made job 2 = 126$

Step-by-step explanation:

You multiply the amount he made for 1 hour by the total hours same thing with job 2.

Answer:

Here are the basic steps to follow to simplify an algebraic expression:

remove parentheses by multiplying factors.

use exponent rules to remove parentheses in terms with exponents.

combine like terms by adding coefficients.

combine the constants.

Step-by-step explanation:

Answer:

i'm not sure so i'm sorry if it is not the right answer

Step-by-step explanation:

Let's assume AC is a straight line and B is on the line between A and C

AC=AB+BC

AC=4x+7+5x-8

AC=9x-1

Answer:

Step-by-step explanation:

5. (6.5 - 2)/(7 - 4) = 4.5/3 = 1.5

6. (8 - 8)/(-5 - 10)= 0/-15= 0

7. (-3 + .75)/(4 - 1) = -2.25/3 = -.75= -3/4

8. (2 + 7)/(18 - 18)= 9/0 = undefined

Answer:

Yes, provided they are all the same size.

Step-by-step explanation:

4/5=0.8

1/2=0.5

3/4=0.75

0.8+0.5+0.75=n

8+5=13

0.8+0.5=1.3

1.3+0.75=2.05

Answer:

Seth

Step-by-step explanation:

3/12 = 0.25

0.25*100 = 25%

Seth scored at 25%

2/10 = 0.2

0.2*100 = 0.2

0.2*100 = 20%

Zak scored at 20%

then:

25>20

then:

Seth scored on a greater fraction of his shots.

Zak scored on a greater fraction of his shots.

Given,

In a hockey game, Seth took 12 shots and scored 3 times.

Zak took 10 shots and scored twice.

We need to find who scored on a greater fraction of his shots.

We can compare fractions by finding their decimal values a nd comparing them.

Example: 1/2 and 2/5

1/2 = 0.5

2/5 = 0.4

0.5 is greater than 0.4.

Find the number of score Seth shots out of 12 shots.

= 3

We can write in fractions as:

3/12 _____(1)

Find the number of score Zak shots out of 10 shots.

= 2 x 3

= 6

We can write in fractions as:

6/10 _____(2)

Compare (1) and (2)

3/12 = 1/4 = 0.25
6/10 = 3/5 = 0.6

0.25 is less than 0.6

6/10 is a greater fraction than 3/12

Thus Zak scored on a greater fraction of his shots.

Learn more about how to compare fractions here:

https://brainly.com/question/1878884

#SPJ2

step 1: open up the brackets ( rmb to flip the signs )

step 2: bring 'a' to one side and the numbers to the other

6a + 34 = -3(-2a + 8)

6a + 34 = 6a - 24

6a - 6a = -24 - 34

0 = - 58

the final ans is kind of weird but here's my solution :))

Answer:

Step-by-step explanation:

15 is divisible by 75 true or false

Answer:

True

Answer:

A

X, 5x

Step-by-step explanation:

A

X, 5x   yes, both variables are x

B

3x, 2xy   no, the first variable is x  the second is x times y

C

2x, 2y  no the first variable is x and the second is y

D

-4, -4y  no, the first is a constant and the second has a variable

Answer:

Pair A

Step-by-step explanation:

Pair A (x, 5x) are like terms.

Like terms are terms in a expression or equations with the same variables.

'x' and '5x' have the same variable (you can think of 'x' as '1x'), so they are like terms. All other pairs have different variables.

Hope this helps.