If a =3 and ab =6 then a²-b² =

Step-by-step explanation:

Sn=n/2(2a+(n-1)d). n=20

S20= 20/2 (2x5+(20-1)3 a=5

S20=10(10+57). d=8-5=3

S20=10x67

S20= 670

Hope this helps you

have a great day

Answer:

y = 2x + 10

Step-by-step explanation:

Hi there!

We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope (m) of the line

The slope can be calculated from 2 points using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes

[tex]x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2[/tex]

Substitute these values into the formula (note: remember that the formula has subtraction in it!)

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-2--4}{-6--7}[/tex]

Simplify

m=[tex]\frac{-2+4}{-6+7}[/tex]

Add the numbers

m=[tex]\frac{2}{1}[/tex]

Divide

m=2

The slope of the line is 2

We can substitute that in:

y = 2x + b

Now we need to find b

As the equation passes through both  (-7,-4) and (-6,-2), we can use either point to help solve for b

Taking (-6, -2) for example:

Substitute -6 as x and -2 as y into the equation.

-2 = 2(-6) + b

Multiply

-2 = -12 + b

Add 12 to both sides

-2 = -12 + b

+12  +12

___________

10 = b

Substitute 10 as b.

y = 2x + 10

Hope this helps!

Topic: Finding the equation of a line

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Answer: The y-value of the vertex is

Step-by-step explanation: we know that

The equation of a vertical parabola into vertex form is equal to

where

(h,k) is the vertex of the parabola

In this problem we have

-----> this a vertical parabola open upward

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The vertex is the point

The y-value of the vertex is

Hey there!

x + y

= -19/12 + (-7/5)

= -19/12 - 7/5

= -95/60 + -84/60

= -95/60 - 84/60

= -95 + (-84) / 60 - 0

= -95 - 84 / 60

= -179 / 60

Therefore, the answer should be:

-179 / 60

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

x+y= -2 59/60

Step-by-step explanation:

=-19/12-7/5 = -95-84

60

=-179

60

= -2/59/60

Answer:

[tex]3^{-5} =\frac{1}{3^{5} } = (\frac{1}{3} )^{5}[/tex]
[tex]5^{-3} = \frac{1}{5} *\frac{1}{5} *\frac{1}{5} = \frac{1}{5*5*5}[/tex]

Step-by-step explanation:

15 and 1/15 do not equal anything.

Hope this helped!

Answer:

a = 1

b = -1

Step-by-step explanation:

[tex]g(x)=ax^2-b \quad \quad \textsf{(where }\:a\:\textsf{ and }\:b\:\textsf{ are real numbers)}[/tex]

Create 2 equations with b as the subject using the given information.

Equation 1

[tex]\begin{aligned}g(2) &=-5\\\implies a(2)^2-b &=-5\\4a-b &=5\\ b&=4a-5\end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}g(-1) &=2\\\implies a(-1)^2-b &=2\\a-b &=2\\ b &=a-2\end{aligned}[/tex]

Equate the equations and solve for a:

[tex]\begin{aligned}b & =b\\\implies 4a-5 & = a-2\\3a & = 3\\a & = 1\\\end{aligned}[/tex]

Substitute the value of a into Equation 2 and solve for b:

[tex]\begin{aligned}b & =a-2\\a=1 \implies b & =1-2\\b & = -1\end{aligned}[/tex]

Answer:

a = -7/3

b = -13/3

Step-by-step explanation:

Making equations in terms of 'a' and 'b' :

Subtract : Equation 1 - Equation 2

Finding b :

Answer:

2/7= 28.6%

Step-by-step explanation:

Since those are 2 specific days out of seven, we divide it so that there are 2/7 days. Then we change it to a percentage, which would be the equation of 2/7*100, which is equal to 28.57%, which rounds to 28.6%.

Answer:

R6,724.44 or so I think that's right

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=5000\left(1+\frac{0.10}{4}\right)^{4\cdot 3}\implies A=5000(1.025)^{12}\implies A\approx 6724.44[/tex]

Answer:

15

Step-by-step explanation:

Given:

Kathy sells encyclopedias and earns $40 for each set she sells.

To Find:

How many sets did she sell if she earned $600 last week?

Solve:

Since kathy sells encyclopedias and earns $40 for each set she sells.

And if kathy total is $600

then we do

$600 divide by $40

600/40 = 15

Hence, she sold 15 sets last week.

Kavinsky

Answer:

15

Step-by-step explanation:

This is basically 600/40

600/40 = 15

Answer is option B.43

430÷ 10 = 43

By : Modern Einstein

radius= 14 inches

the area of the circle.

[tex]area = \pi {r}^{2} [/tex]

[tex]a = \pi \times {14}^{2} [/tex]

[tex]a = 615.75216[/tex]

[tex]a = 615.75 \: {in}^{2} [/tex]

therefore, the area of the circle is 615.75 square inches.

The area is:

615.44 in²

Work/explanation:

The formula for the area of a circle is:

[tex]\sf{A=\pi r^2}}[/tex]

Where

A = area

π = 3.14

r = radius

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 14\ in}\end{picture}[/tex]

Plug in the data:

[tex]\sf{A=3.14\times14^2}\\\\\sf{A=3.14\times196}\\\\\sf{A=615.44\:in^2}[/tex]

I think that the answer is 123

Answer:

Continue to make the minimum monthly payment on all of your debts while putting as much extra money as possible toward your smallest debt

Step-by-step explanation:

Once that debt is paid off, put your extra money toward your next-smallest debt, and so on. The bigger you build your debt snowball, the closer you'll get to debt freedom

Answer:

You did not provide the tables to choose from, but the relationship between number of books and total price is that each book is 14.25. Hope that helps at least.

Answer:

A Circle

Step-by-step explanation:

Using the normal distribution, it is found that there is a 0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Normal Probability Distribution

In a normal distribution with mean  and standard deviation, the z-score of a measure X is given by:

[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are, respectively, given by and.

The probability of a random person on the street having an IQ score of less than 98 is the p-value of Z when X = 98, hence:

[tex]Z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]Z=\dfrac{98-100}{15}[/tex]

[tex]Z=-0.13[/tex]

Has a p-value of 0.4483.

0.4483 = 44.83% probability of a random person on the street having an IQ score of less than 98.

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Answer: 8

Step-by-step explanation: divion

Answer:

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

Becuase if we rewrite it in slope-intercept form then we get y=3/4x-13/2

Answer:

2.5

Step-by-step explanation:

Answer:

12.

Step-by-step explanation:

36 = 3 * 12

48 = 4 * 12,

Answer:

3.33

Step-by-step explanation:

In this case, the number we have is an even number so you can not choose the one in the middle so you would take those two and add the then divide them by how many numbers you have there which would be 6 in the case and then round it to the nearest decimal.

Answer:

42 degrees

Step-by-step explanation:

48 + x = right angle = 90 degrees

48+ x = 90

x = 42 degrees

Answer:

  5.  x = 17

  7.  x = 2

Step-by-step explanation:

The applicable relation is, "the product of the near distance to the circle and the far distance to the circle is the same for each secant." Distance is measured from the point where the secants intersect.

__

Using the rule, we have ...

  7(7+x) = 8(8+13)

  7+x = 24 . . . . . . . . . divide by 7

  x = 17 . . . . . . . . . . subtract 7

__

The same rule applies.

  7(7 +6x -1) = 9(9 +x +3)

  42x +42 = 9x +108 . . . . . . simplify

  33x = 66 . . . . . . . . . . . . . subtract 9x+42

  x = 2 . . . . . . . . . . . . . . divide by 33

Answer:

3

Step-by-step explanation:

If he went 18 miles in 6 hours we can simpliy divide 18 by 6 which is 3 miles per hour

Step-by-step explanation:

I guess it is a circular pool.

the area of a circle is

pi×r²

in our case we know

pi×r² = 78.5

3.14×r² = 78.5

r² = 78.5/3.14 = 25

r = 5 m

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 6.5\%\to \frac{6.5}{100}\dotfill &0.065\\ t=years\dotfill &6 \end{cases} \\\\\\ A=100e^{0.065\cdot 6}\implies A=100e^{0.39}\implies A\approx 147.70[/tex]

The balance of your account after 6 years with continuous compounding would be approximately $147.56.

To calculate the balance of your account after 6 years with continuous compounding, you can use the formula:

[tex]\[ A = P \times e^{rt} \][/tex]

where:

[tex]\( A \) =[/tex] the balance after [tex]\( t \)[/tex] years

[tex]\( P \) =[/tex]the principal amount (initial investment) = $100

[tex]\( r \) =[/tex] the annual interest rate (in decimal form) = 6.5% = 0.065

[tex]\( t \) =[/tex] the number of years = 6

[tex]\( e \) =[/tex] Euler's number (approximately 2.71828)

Let's plug in the values and calculate the balance:

[tex]\[ A = 100 \times e^{0.065 \times 6} \]\[ A = 100 \times e^{0.39} \]\[ A = 100 \times 1.47560080488 \]\[ A = 147.560080488 \][/tex]

Rounding the answer to the nearest hundredth:

[tex]\[ A \approx $147.56 \][/tex]

So, the balance of your account after 6 years with continuous compounding would be approximately $147.56.

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Answer:

graph C represents this relationship best.