What is the quotient property of exponents?

Answer:

Below

Step-by-step explanation:

● -7x + 5y = 35

Add 7x to both sides

● -7x +7x + 5y = 35+7x

● 5y = 7x + 35

Divide both sides by 5

● 5y/5 = (7x+35)/5

● y = 1.4x + 7

The graph of the function:

Answer:

Step-by-step explanation:

-7x+5y=35

write the equation in the form : y=mx+b

5y=35+7x ( divide both sides by 5)

y=7/5 x +35/5

y=7/5 x +7

if y=0   then 7/5 x+7=0 ⇒7/5 x=-7 ⇒x=-35/7 ⇒x=-5

x=0 then y=7

two points  (0,7) and (-5,0)

Answer:

The graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).

Step-by-step explanation:

It is given that p(x) and q(x) are two functions such that

[tex]q(x)=2p(x+3)-6[/tex]    ...(1)

The translation is defined as

[tex]q(x)=kp(x+a)+b[/tex]              .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

On comparing (1) and (2) we get

k=2>1, so the graph of p(x) stretch vertically by factor 2.

a=3>0, so the graph of p(x) shifts 3 units left.

b=-6<0, so the graph of p(x) shifts 6 units down.

Therefore, the graph of p(x) stretch vertically by factor 2 and shifts 3 units left and 6 units down to get q(x).

Answer: $112.50 ; $4612.5

Step-by-step explanation:

a) Determine how much interest Christine paid at the end of 1 year.

This will be:

Simple interest = PRT/100

where

P = principal = $4500

R = rate = 2.5%

T = time = 1 year

Interest = (4500 × 2.5 × 1)/100

= 11250/100

= $112.50

b) Determine the total amount Christine will repay the bank at the end of 1 year.

Total amount = Principal + Interest

= $4500 + $112.50

= $4612.5

Answer:

Step-by-step explanation:

The equation is not properly formatted presumably here is the format.

Given

[tex]f(x) = 2x^2 + 4[/tex]

determine f(2) , and f(−1).

So we are expect to perform substitution operation and return an answers for values of x= 2 and x= -1

1. When x= 2 we have

[tex]f(2) = 2*2^2 + 4\\\\f(2)= 2*4+4\\\\f(2)= 8+4\\\\f(2)= 12[/tex]

2. When x= -1 we have

[tex]f(-1) = 2*-1^2 + 4\\\\ f(-1)= 2*1+4\\\\ f(-1)= 2+4\\\\ f(-1)= 6[/tex]

Greetings from Brasil...

Let us solve by parts. Power first

(X + 2)² = X² + 2.2.X + 2² = X² + 4X + 4

Rewriting

(X - 3).(X² + 4X + 4)             applying distributive property

X³ + 4X² + 4X - 3X² - 12X - 12

Answer:

  √89

Step-by-step explanation:

The distance formula is good for this.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = ((6 -(-2))^2 +(-1-4)^2) = √(64 +25)

  d = √89

The distance between the point is √89 units.

Answer:

a. m∠Z =  62

b. [tex]m\widehat{WZ}[/tex] = 118

c.  m∠W = 62

d. [tex]m\widehat{WX}[/tex] = 122°

Step-by-step explanation:

a. The given parameters are;

m∠X = 118

[tex]\overline {WZ} \cong \overline {YZ}[/tex]

m∠Y = 120

m∠X + m∠Z = 180  Angles in opposite segment are supplementary

m∠Z = 180 - m∠X  = 180 - 118 = 62

m∠Z =  62

b. Given [tex]\overline {WZ} \cong \overline {YZ}[/tex] line drawn from W to Y forms isosceles triangles WZY, with base angles ∠WYZ and ∠YWZ equal (Base angles of an isosceles triangle)

Therefore

∠WYZ + ∠YWZ + m∠Z = 180 (Angle sum theorem)

∠WYZ = ∠YWZ (Substitution property of equality)

∠WYZ + ∠YWZ + m∠Z = ∠WYZ + ∠WYZ + m∠Z =180

2×∠WYZ + 62 =180

2×∠WYZ = 180 -62 = 118°

∠WYZ =  118°/2 =59

∠WYZ = ∠YWZ = 59

[tex]m\widehat{WZ}[/tex] subtends chord WZ at the center  =  ∠WYZ  subtends chord WZ at the circumference

∴ 2×∠WYZ = [tex]m\widehat{WZ}[/tex]

[tex]m\widehat{WZ}[/tex]  = 2×59 = 118

[tex]m\widehat{WZ}[/tex] = 118

c.  m∠X + m∠Y + m∠Z + m∠W = 360 (Sum of angles in a quadrilateral)

m∠W = 360 - (m∠X + m∠Y + m∠Z) = 360 - (118 + 120 + 60) = 62

m∠W = 62

d. [tex]m\widehat{WZ}[/tex] + [tex]m\widehat{WX}[/tex] = [tex]m\widehat{XWZ}[/tex]  (Angle addition postulate)

[tex]m\widehat{XWZ}[/tex] = 2 × ∠Y (Angle subtended at the center = 2 × Angle subtended at the circumference

∴ [tex]m\widehat{XWZ}[/tex] = 2 × 120 = 240

[tex]m\widehat{WX}[/tex] = [tex]m\widehat{XWZ}[/tex] - [tex]m\widehat{WZ}[/tex]

[tex]m\widehat{WX}[/tex] = 240 - 118 = 122°

[tex]m\widehat{WX}[/tex] = 122°.

Answer:

C, None of the above

Step-by-step explanation:

Step 1: Expand the brackets

-7 - 3(-4e-3)

-7 + 12e + 9

Step 2: Collect like terms

12e + 2

Because the answer is not a or b the answer is 'None of the Above'

Hey there! I'm happy to help!

Let's use the distributive property to undo the parentheses. We multiply the number next to the parentheses by each number inside of the parentheses.

-7+3(-4e-3)

-7-12e-9

We combine like terms.

-16-12e

This means that Answer B is incorrect. Answer A could still be correct though as it could have equal value to -16-12e.

-4(3e+4)

We use distributive property.

-12e-16

We see that these have the same value, so the correct answer is A.

Have a wonderful day! :D

Answer:

Answer is A

Step-by-step explanation:

[tex]m = y2 - y1 \div x2 - x1 \\ y2 = m(x2 - x1) + y1[/tex]

Answer:

c

Step-by-step explanation:

you have to collect the data to record the height of each plant.

Answer:

a=6 x=1

Step-by-step explanation:

4x1=4 4-2=2

2+6=8

Answer:

a=3 i think, sorry if i'm wrong

Step-by-step explanation:

4x-2(x+a)=8     ~parenthesis first.

4*7-14-2a=8     ~4 times 7= 28 and just bring down the rest.

28-14-2a=8      ~ add 14 to negative 14 and 8, the positive and negative 14 would cancel out each other.

28-2a=22        ~ subtract 28 from both positive 28 and 22.

-2a=-6             ~ divide by 2 on both sides.

  a=3               ~ The reason why it is 3 is because negative 2 times positive 3 equals  negative 6.

Answer: A = 6.5

B = 10.

Step-by-step explanation:

First, remember that when we have a triangle of height H and base B, the area of the triangle is:

Area = B*H/2.

A:

First, count the complete squares:

We have 6 complete squares.

Now the diagonal part:

The diagonal connects a section of 1 by 3 squares, and the shaded area is a right triangle

Then the shaded area will be half of 1 by 3.

this is 1.5 squares.

The total area of A is:

6 + 1.5 = 7.5 squares.

B:

This is more complicated.

At the beginning, we have 4 completed squares in the top right.

At the left, we have a 2 by 4 = 8 square region, where the shaded part is only a triangle rectangle.

Then the area of this triangle is half of 8 squares:

8/2 = 4 squares.

Last, at the bottom, we have two times a 2 by 1 = 2 square region, where the shaded part is a triangle rectangle.

Then the area of each triangle is 2/2 = 1 square.

And we have two of them, so there are 2 squares here.

Then the total area is:

A = 4 + 4 + 1 + 1 = 10 squares.

Each small square In the graph paper represents 1 square unit

We can distribute the outer x to each term inside

x(x-6) = x^2-6x

So the original equation turns into

x^2-6x = 20

Then you could subtract 20 from both sides to get everything to the same side

x^2-6x-20 = 20-20

x^2-6x-20 = 0

This quadratic equation is in the form ax^2+bx+c = 0 with a = 1, b = -6, c = -20.

The presence of the x^2 term, and having it be the largest exponent, is what makes this a quadratic.

Answer:

7

Step-by-step explanation:

Here is ur answer mate

[tex]3 x+ 5 = 26[/tex]

[tex]3x = 21[/tex]

[tex]x = 7[/tex]

Hope it helps u

Answer:

x=7

Step-by-step explanation:

Answer:

Plot 1

Step-by-step explanation:

To ascertain which histogram represents the given data, divide the data into class intervals that should not over-lap, then find how many data fits into the class to get the frequency of each class. Lastly, compare the frequency of each class to the corresponding bar representing each class interval on the graph.

Thus, the class intervals and their frequency would be:

Class interval => frequency

[tex] 0 - 4: 3 [/tex]

[tex] 5 - 9: 4 [/tex]

[tex] 10 - 14: 4 [/tex]

[tex] 15 - 19: 6 [/tex]

[tex] 20 - 25: 3 [/tex]

Comparing these with the graphs given as options, plot 1 has a histogram that represents the data given.

Answer:

Per month salary = $3,750

Step-by-step explanation:

Given:

Annual pay = $45,000

Find:

Per month salary

Computation:

Number of month in a year = 12

Per month salary = Annual pay / Number of month in a year

Per month salary = $45,000 / 12

Per month salary = $3,750

Answer:

30 terms

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here d = 5 and a₃ = 13, thus

a₁ + 2d = 13

a₁ + 2(5) = 13

a₁ + 10 = 13 ( subtract 10 from both sides )

a₁ = 3

Thus

[tex]a_{n}[/tex] = 3 + 5(n - 1) = 148 ( subtract 3 from both sides )

5(n - 1) = 145 ( divide both sides by 5 )

n - 1 = 29 ( add 1 to both sides )

n = 30

The progression has 30 terms

Answer:A rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get -7/12 . What is the number.

Step-by-step explanation:Let p/q (q ≠ 0) denote the rational number. Multiplying it by 5/2 gives (p/q)(5/2). Add 2/3 to the product and we get (p/q)(5/2) + 2/3 . The result is given to be -7/12.

∴ (p/q)(5/2) + 2/3 = -7/12 …………………………..……………………………………..(1)

Transposing 2/3 to right-hand-side and changing the sign to negative,

(p/q)(5/2) = -2/3 -7/12 = -(2/3 + 7/12) =- (2 x 4 + 7)/12 (Taking L.C.M.)

Or, (p/q)(5/2) = -(8+7)/12 = - 15/12

Multiplying both sides by 2/5,

(p/q)(5/2) x (2/5) = -15/12 . 2/5 = -(3x5)/(3x4) . 2/5 =- 5/4 .2/5

Since 2/5 is the multiplicative inverse of 5/2, 5/2 x 2/5 = 1 and we obtain

(p/q).1 = -1/4 . 2/1 = -1/2

⇒ p/q = -1/2 which is a negative rational number in which p = 1 and q = 2 ≠ 0 .

∴ the rational number = -1/2

Step-by-step explanation:

the opposite side is AC

Answer:

work is shown and pictured

Answer:

213 x 112

Step-by-step explanation:

You have to multiply the recipe with the amount of times it's made.

Answer:

213 cups of beans.Keith is making 112 times the recipe.

Step-by-step explanation:

Hey there! I'm happy to help!

We want to find how much more 5/6 is than 1/2. To do this, we simply subtract 1/2 from 5/6. This will show us how much more 5/6 is.

First, we multiply 1/2 by 3/3 so that the denominator is 6.

1/2×3/3=3/6

Now, we subtract this from 5/6.

5/6-3/6=2/6

We can simplify this to 1/3.

Therefore, Methuki used 1/3 scoop more of brown sugar than white sugar while making desserts for Fun Day.

Have a wonderful day! :D

Answer:

[tex]\Huge \boxed{\mathrm{0.45}}[/tex]

Step-by-step explanation:

1/5 in decimal form is 0.2

1/4 in decimal form is 0.25

1/5 + 1/4

0.2 + 0.25 = 0.45

Answer:

1/5 + 1/4 = 9/20.

9/20 = 0.45

Complete the squares to get

[tex]x^2+y^2=2x-6y+6[/tex]

[tex]\implies(x^2-2x+1)+(y^2+6y+9)=16[/tex]

[tex]\implies(x-1)^2+(y+3)^2=4^2[/tex]

which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.

The area of the region enclosed in the graph x²+y² =2x-6y+6 is 50.26 square units.

The area of the circle can be calculated by the product of π times square of the radius or the product of π/4 times square of diameter.

Area of the circle= A= πr²= πd²/4

where r is radius of the circle and d is diameter of the circle.

Here given that

the equation of circle is given by

x²+y² =2x-6y+6

⇒ x²+y² -2x-6y = 6

⇒ x²-2x+y²-6y = 6

Adding 1 on both sides

⇒ x²-2x+1+y²-6y = 6+1

Adding 9 on both sides

⇒ x²-2x+1+ y²-6y+9 = 6+1+9

⇒x²-2x+1+ y²-6y+9 = 16

⇒ (x-1)² + (y-3)²= 4²

which is similar to equation of the circle

(x-a)² + (y-b)²= r²

This is the equation of the circle in center and radius form where (a,b) is the center of the circle and r is the radius of the circle.

here in the equation of the circle the center of the circle is (1,3)

radius is 4 units.

then the area of the circle is = πr²= π4²= 16π= 50.26 square units.

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Answer:

4 t shirts.

Step-by-step explanation:

Given that money available with Sam = $150

Price for pants = $90

Price of each t shirt = $12.50

To find:

How many t shirts can he expect to purchase?

Solution:

Price for 2 pants = $180 which is more than $150.

Therefore, he can not buy more than 1 pants.

The remaining amount after buying pants = $150 - $90 = $60

This amount will be used for buying t-shirts.

Number of t-shirts that can be bought:

[tex]\dfrac{60}{12.5} \approx 4.8[/tex]

But answer in decimal points for number of t shirts is not possible and he does not have more money.

It means, he can buy at most 4 t-shirts.

Answer:

2.6 hours

2 hours 36 minutes.

Step-by-step explanation:

Let the time be x hours

we know

distance = speed*time

speed of one train = 85 miles/hour

time = x hours

distance traveled by one train = 85*x = 85x miles

speed of one train = 95 miles/hour

time = x hours

distance traveled by other  train = 95*x = 95x miles

__________________________________________________

Given that

Two trains leave stations 468 miles apart at the same time and travel toward each other

Thus, together cover 468 miles.

distance traveled by one train + distance traveled by other train = 468

85x+95x = 468

=> 180x = 468

=> x = 468/180 = 2.6

Thus, it will take 2.6 hours to meet each other

we know 1 hour = 60 minutes

0.6 hour = 60*0.6 minutes = 36 minutes

Thus, we can also say that it took 2 hours 36 minutes to meet each other.

Answer:

x ≤ - 27

Step-by-step explanation:

[tex]\frac{x}{-9}\ge \:3\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\frac{x\left(-1\right)}{-9}\le \:3\left(-1\right)\\\\Simplify\\\\\frac{x}{9}\le \:-3\\\\\mathrm{Multiply\:both\:sides\:by\:}9\\\\\frac{9x}{9}\le \:9\left(-3\right)\\\\\mathrm{Simplify}\\\\x\le \:-27[/tex]

The solution of the given inequality is x ≤ -27.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given inequality ( x / -9) ≥ 3 is solved as:-

( x  / -9 ) ≥ 3

Multiply both sides by ( -1 ).

-1 ( x  / -9 ) ≥ -3

x / 9 ≤ -3

x ≤ -27

Hence, the solution is x ≤ -27.

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Answer:

n^2 = n + 30

n^2 -n -30 = 0

Solving by quadratic formula

numbers equal 6 AND -5  

DOUBLE -CHECK

6^2 -6 -30 = 0

36 -6 - 30 = 0 CORRECT

-5^2  - -5 -30 = 0

25 +5 -30 = 0 CORRECT

Two numbers 6 and -5

Step-by-step explanation:

Answer:

b. His t-score is 40.

Step-by-step explanation:

The middle of the third stanine in a normal distribution means that the standard of nine that is applied has the middle of the third count.

It means that if we divide the normal distribution with the standard of nine we will find the score to be  the middle of the  third division.

So it will be (1/3*9=3) more than 3.

Which in normal distribution will be more than 30.

The t distribution is approximately normal when the number of degrees of freedom is greater than 30 .

So the best answer is that His t-score is 40  ( choice b).

Answer:

The answer is

Step-by-step explanation:

To solve for y cross multiply

That's

3( x - 1) = 2y

2y = 3x - 3

Divide both sides by 2 to make y stand alone

That's

We have the final answer as

Hope this helps you

Answer:

[tex]\Large \boxed{{y = \frac{3}{2}(x-1)}}[/tex]

Step-by-step explanation:

We have to solve for the y variable.

The variable must be isolated on one side of the equation.

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

Multiply both sides of the equation by 3.

3(x - 1) = 2y

Divide both sides of the equation by 2.

[tex]\frac{3}{2}[/tex] (x - 1) = y