Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each unit rate to the graph that represents it

Answer:

x=7.5

Step-by-step explanation:

Rental: R(x)=(27+x) dollar per day

Number of cars rented: N(x)

=(210-5x)

Income: I(x) =(27+x)(210-5x)

=5670 - 135x + 210x-5x^2

=5670+75x-5x^2

The maximum will be achieved when the derivative of

I(x) =zero.

I(x)=5670+75x-5x^2

dI(x)/dx=75-10x=0

75-10x=0

75=10x

x=75/10

=7.5

x=7.5

x=7.5 is the rate at which the car will be rented to produce maximum income.

The maximum income could be derived by using x=7 or x=8

27+7=$34 per day

27+8=$35 per day

When x=7

I(x)=5670+75x-5x^2

=5670+75(7)-5(7)^2

=5670+525-5(49)

=5670+525-245

=5,950

When x=8

I(x)=5670+75x-5x^2

=5670+75(8)-5(8)^2

=5670+600-5(64)

=5670+600-320

=5950

Either x=7 or 8 will yield the same income

Answer:

c  ≥ -5

Step-by-step explanation:

-5c +2 ≤ 27

Subtract 2 from each side

-5c +2-2 ≤ 27-2

-5c ≤25

Divide by -5, remembering to flip the inequality

-5c/-5 ≥25/-5

c  ≥ -5

Answer: [tex]x\geq 5[/tex]

Step-by-step explanation:

[tex]-5x+2\leq 27\\Subtract\\-5x\leq 25\\Divide\\x\geq 5[/tex]

It's important to remember that when you divide both sides of an inequality by a negative number to flip the sign.

Hope it helps <3

Answer:

(6,2)

Step-by-step explanation:

y=-1/2x+5

y=2x-10​

-1/2 x+5 =2x-10  to find the solution y=y ( point of intersection of two lines)

-1/2 x-2x = -10-5 solve for x

-5/2 x=-15

x=-30/-5=6

y=2x- 10 substitute  x in the equation to get y

y=2(6)-10

y=2

(2,3)

Dont put the other answer, it’s wrong I

did the math.

Answer:

C. x>4

Step-by-step explanation:

3/(x-4) > 0

3>0, so

x-4 >0

x > 4

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

Answer:

i cant read spanish. sorry

Step-by-step explanation:

Answer: $27.825

Step-by-step explanation:

From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:

= Original price - Discount

= $35 - (25% × $35)

= $35 - (0.25 × $35)

= $35 - $8.75

= $26.25

We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:

= $26.25 + (6% × $26.25)

= $26.25 + (0.06 × $26.25)

= $26.25 + $1.575

= $27.825

Answer:

27.83

Step-by-step explanation:

Hey there! :)

Answer:

(x + 27)(x + 1)

Step-by-step explanation:

Given:

a² + 28a + 27

Find numbers that add up to 28 and multiply to 27:

We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:

(x + 27)(x + 1)

Answer:

Solution,

[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

[tex]F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]

Step-by-step explanation:

Sum of  finite geometric series, [tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

That gives us:

[tex]F.V.=\dfrac{P[(1+i)^n-1]}{(1+i)-1}\\\\=\dfrac{P[(1+i)^n-1]}{1+i-1}\\\\F.V.=\dfrac{P[(1+i)^n-1]}{i}[/tex]

Where:

This is the formula that is used to determine the future value of a structured savings plan with recurring deposits.

Answer:

a ) [tex]2 / n[/tex],

b ) [tex]15[/tex]

Step-by-step explanation:

This is a nice and short question we have here.

Given that a bag has n counters, and that one counter is blue, respectively the rest is red, if two counters are taken at random there isn't a definite percentage that one of the counters chosen is red or blue, but there is a fractional representation of this.

We could express n ( number of counters ) to form a probability of 2 / n. As you can see, two counters are taken at random over n counters, and thus we derived this fraction.

a ) [tex]2 / n[/tex]

____

Now we have this second part -

[tex]2 / n = 2 / 16,\\16 - 1 = 15[/tex]

Therefore, there are 15 red counters. Hope that helps!

Answer:

Bottle A started with 88 and bottle B started with 40

Step-by-step explanation:

To find out what they started with I got the ounces they finished with an the equation they did to get there.

Ended in 64 oz.

To get there:

A => B

B => A

A => B

Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.

B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.

Now you have this equation:

A => B

B => A

96 oz. => 32 oz.

64 oz.

I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.

Now you have this equation:

A => B

80 oz. => 48 oz.

96 oz. => 32 oz.

64 oz.

For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.

The Answer:

88 oz. => 40 oz.

80 oz. => 48 oz.

96 oz. => 32 oz.

Both will end up with 64 oz.

Answer:

169=169

Step-by-step explanation:

The pythagoras theorem states that if

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

Then the triangle is a right triangle

So

[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]

[tex]25 + 144 = 169[/tex]

[tex]169 = 169[/tex]

Therefore A is a right triangle

Answer:

Step-by-step explanation:

now the longest edge is 13 cm so : 13²must be equal to 5²+12²

so this triangle must be right angled

Answer:

[tex] \frac{105}{4} [/tex]

please see the attached picture for full solution..

hope it helps...

Good luck on your assignment..

Answer:

D. 35

Step-by-step explanation:

.8(40+1x)=60

32+.8x=60

.8x=28

x=28/.8

X=35

Answer:

D.35

Step-by-step explanation:

Answer:

40 pages / hour

Step-by-step explanation:

Take the number of pages and divide by the number of hours

80 pages/ 2 hours

40 pages / hour

Answer: 30p

Step-by-step explanation:

Cost of donuts in the first shop £1.20

Cost at the second shop at 25% higher

= 1.20 x 1.25 = 1.50

Difference in price

= 1.50 - 1.20 = 0.30

Answer:

Total Walked = 3.37 km

Step-by-step explanation:

Walks = 2.82 km

Further Walked = 550 m = 0.55 km

Total Walked = 2.82+0.55

Total Walked = 3.37 km

in total he walks 3.37 km

He walks 2.82 km

He further walks 0.55 km

total = 2.82+0.55 = 3.37

Answer:

B

Step-by-step explanation:

dashed line above the shaded area, shaded area below dashed boundary line

Answer:

f(-1) = (1/4)^x = 4

Step-by-step explanation:

When solving a f(x) equation, the x represents the number that will be used to replace x in the equation. So, from the equation, the value of x is -1. You would plug in -1 for x.

f(-1) = (1/4)^-1

Solve the exponent.

f(-1) = 4

So, the value of f(-1) is 4.

Answer:

[tex] \boxed{\sf Length \ of \ the \ rectangle = 16 \ cm} [/tex]

Given:

Area of the rectangle = 96 cm²

Length of the rectangle = 2 less than 3 times it's width

To Find:

Length of the rectangle

Step-by-step explanation:

Let the width of the rectangle be 'w'.

So,

Length of the rectangle = 3w - 2

[tex]\sf \implies Area \ of \ rectangle = Length \times Width \\ \\ \sf \implies 96 = (3w - 2) \times w \\ \\ \sf \implies 96 = 3 {w}^{2} - 2w \\ \\ \sf \implies 3 {w}^{2} - 2w = 96 \\ \\ \sf \implies 3 {w}^{2} - 2w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - (18 - 16)w - 96 = 0 \\ \\ \sf \implies 3 {w}^{2} - 18w + 16w - 96 = 0 \\ \\ \sf \implies 3w(w - 6) + 16(w - 6) = 0 \\ \\ \sf \implies (w - 6)(3w + 16) = 0 \\ \\ \sf \implies w - 6 = 0 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 3w + 16 = 0 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: 3w = - 16 \\ \\ \sf \implies w = 6 \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: w = - \frac{16}{3} [/tex]

Width can't be negative. So,

Width of the rectangle = 6

Length of the rectangle = 3w - 2

= 3(6) - 2

= 18 - 2

= 16 cm

The length of the rectangle is 16 cm

The width of the rectangle is 6 cm

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be = 96 cm²

Let the length of the rectangle be = L

Let the width of the rectangle be = W

Now ,length of a rectangle is 2 less than 3 times its width

Substituting the values in the equation , we get

L = 3W - 2

Now , the area of the rectangle = L x W

So ,

96 = ( 3W - 2 ) x W

On simplifying the equation , we get

96 = 3W² - 2W

Subtracting 96 on both sides of the equation , we get

3W² - 2W - 96 = 0

3W² - 18W + 16W - 96 = 0

Taking 3W as the common factor , we get

3W ( W - 6 ) + 16 ( W - 6 ) = 0

( W - 6 ) ( 3W + 16 ) = 0

Now , the width of the rectangle cannot be negative , so

W - 6 = 0

Adding 6 on both sides of the equation , we get

W = 6 cm

Now , the length of the rectangle L = 3W - 2

L = 3 ( 6 ) - 2

L = 18 - 2

L = 16 cm

Therefore , the value of L is 16 cm

Hence , the length of the rectangle is 16 cm

To learn more about area of rectangle click :

https://brainly.com/question/15225905

#SPJ2

Answer:

2x⁴ - 20x² - 78

To factor the expression look for the LCM of the numbers

LCM of the numbers is 2

Factorize that one out

That's

2( x⁴ - 10x² - 39)

Hope this helps

Answer:

2(x² + 3)(x² - 13)

Step-by-step explanation:

2x⁴ - 20x² - 78

Factor out 2.

2(x⁴ - 10x² - 39)

Find 2 numbers that multiply to get -39 and add to get -10. Those numbers are -13 and 3.

2(x⁴ - 13x² + 3x² - 39)

2(x² + 3)(x² - 13)

Answer:

y = -31x^6 - 87^3 +46x +12

Step-by-step explanation:

Place the numbers with the highest degree first (-31 x ^ 6) and go in order until you reach the number with the lowest degree (12). When you do that, you get:

y = - 31x^6 - 87x^3 + 23x^2 - 23x^2 + 46x +12

As you can see, the numbers based on the amount of their exponent were placed in order, no matter what the coefficient is. But, there are two numbers with ^2, so we have to cancel them out. In order to do that, you have to add/ subtract the two numbers with the same exponent.

23x^2 - 23x^2 = 0

Since the answer is 0, we canceled both of the numbers out, so the final polynomial in its standard form is:

y = -31x^6 - 87^3 +46x +12

Hope this helps :)

Answer:

y = -31x^6-87^3+46x+12

Step-by-step explanation:

put the exponents in order and cancel out the 23x^2s.

Answer: Step 4

Step-by-step explanation:

1. Define variable x as student signatures still needed  (Correct)

[tex]2)\ \dfrac{x+82}{426}[/tex]              (Correct)

3. 25% = 0.25      (Correct)

[tex]4)\ \dfrac{x+82}{426}\leq 0.25[/tex]      (Error)!

The inequality symbol should be GREATER THAN or equal to (≥) because Jose needs 25% or more (not less).

Answer:

In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.

                                         ¯\_     _/¯

      ( ﾉ ﾟｰﾟ)ﾉ                                                                                     ＼(ﾟｰﾟ＼)

Answer:

The answer is -8

Step-by-step explanation:

(3)(-4)=-12 (-2)(-2)=4

Answer:

For the drop down menu:

i) x + y

ii) z²

iii) ½ xy

The complete question related to this found on brainly (ID:16485977) is stated below:

Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.

_____finds the area of the outer square by squaring its side length.

_____finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

Find attached the diagram of the question.

Step-by-step explanation:

Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.

Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent ²

From the diagram of the question.

Hypotenuse = z

Opposite = y

Adjacent = x

z² = x² + y²

Area of outer square = area of inner square + 4(area of triangles)

area of inner square = length² = (x+y)²

Expanding area of the outer square:

(x+y)² = (x+y)(x+y) = x²+xy+xy+y²

(x+y)² = x²+y²+2xy

= z² + 2xy

Area of inner square = length² = z²

Area of triangle = ½ base × height

= ½ × x × y = ½ xy

Area of outer square = area of inner square + 4(area of triangles)

(x + y)² = z² + 4(½xy )

Therefore, it is a true equation.

( x + y )² finds the area of the outer square by squaring its side length.

z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.

These expressions are equal because they both give the areas of outer space.

So for the drop down menu:

i) x + y

ii) z²

iii) ½ xy

Answer: 2, 4 then c=4 also and B for the next one :)

Step-by-step explanation: Giving away 100 points be the first to comment on my " question " stay tuned!

Answer:

x=7

Step-by-step explanation:

-3(x-1)+8(x-3)=6x+7-5x

-3x+3+8x-24=6x+7-5x

5x-21=x+7

4x=28

x=7

Answer:

x=7

Step-by-step explanation:

-3(x-1) + 8(x-3) = 6x + 7 - 5x

Distribute

-3x +3 +8x -24 = 6x +7 -5x

Combine like terms

5x -21 = x+7

Subtract x from each side

5x-x-21 = 7

4x -21 =7

Add 21 to each side

4x-21+21 = 7+21

4x = 28

4x/4 = 28/4

x=7

Answer:

Slope = 2

Y intercept = 4

Step-by-step explanation:

This is of the form y = mx + k

where m is the slope

K = y intercept

Hello! (:

y=2x+4

This equation is written in slope-intercept form:

y=mx+b

m is the slope (2) and b is the y-intercept (4)

Hope it helps!

If you have any question or query, feel free to ask! (:

~An excited gal

[tex]SparklingFlower[/tex]

Answer:

165 students (hope it helps)

Step-by-step explanation:

300students - 45students = 255students

180students + 150students = 330students

330students / 2 = 165

Answer:

75 students watched both.

Step-by-step explanation:

150 students saw Zootopia

180 students saw Finding Dory

45 students saw nothing.

There are 300 students in total.

[tex]|(300-45)-150-180|=\\|255-150-180|=\\|105-180|=\\|-75|=\\75[/tex]

Answer:

(3.26795, 6.73205)

(6.73205, 3.26795)

Step-by-step explanation:

Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.