A concrete driveway is 5 feet longer than twice its width. It has a brick walkway 3 feet wide on the front and side of the driveway. The area of the brick walkway is 213
square feet. Find the dimensions of the driveway.​

Answer:

x = √2y^2 + 64 or x = √2y^2 + 64

Step-by-step explanation:

Solve for x.

x^2/64 - y^2/32 = 1

Step 1: Add 1/32 y^2 to both sides.

1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2

Step 2: Divide both sides by 1/64.

1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64

x^2 = 2y^2 + 64

Step 3:

x = √2y^2 + 64 or x = √2y^2 + 64

Answer:

x = √2y^2 + 64

Step-by-step explanation:

= 1/64 x^2 + -1/32 y^2 + 1/32 y^2 = 1 + 1/32 y^2

= 1/64 x^2/ 1/64 = 1/32 y^2 + 1/ 1/64

= x^2 = 2y^2 + 64

= x = √2y^2 + 64

Hope this helps!

Answer:

-35 - 5

Step-by-step explanation:

2 + 12 = 14, which is positive

(-3) * (-8) = 24, which is positive

10 - (-18) = 10 + 18 = 28, which is positive

-35 - 5 = -40, which is negative

Answer:

[tex]-35-5[/tex]

Step-by-step explanation:

[tex]2+12=14[/tex]

The result is a positive value.

[tex]-3 \times -8=24[/tex]

The result is a positive value.

[tex]10-(-8)\\10+8=18[/tex]

The result is a positive value.

[tex]-35-5=-40[/tex]

The result is a negative value.

-8c^3/d^6 is equivalent to the expression

Answer:

-8c^3/d^6

You are correct!

Answer:

4.5%

Step-by-step explanation:

Firstly we should understand that a quarter is every three months.

So if $135 is earned each quarter, then 4 * 135 = $540 is earned per annnum

We use the simple interest formula to get the rate.

Mathematically;

I = PRT/100

where P is the amount deposited = 12,000

R is what we are looking for which is the rate

T is the time which is 1 year

I is the interest which is 540

We can rewrite the simple interest formula to be:

100I = PRT

R = 100I/PT

Thus substituting the values we have;

R = (100 * 540)/(12,000 * 1) = 4.5%

Answer:

Step-by-step explanation:

Using the simple interest formula to tackle this question.

[tex]SI = \frac{PRT}{100}[/tex]

P = principal = $12,000

R = rate (in %) = ?

T = Time(in years) = 1/4 years

135 = [tex]\frac{12000*R}{100*4}[/tex]

[tex]135 = \frac{12000R}{400}\\ 54000 = 12000R\\R = \frac{54000}{12000}\\ R = 4.5\ %[/tex]

The annual rate of simple interest is 4.5%

Answer:

sin θ = +/- (2√2)/3

Step-by-step explanation:

cos θ  = 1/3

cos²θ  + sin²θ  = 1

(1/3)² + sin²θ  = 1

sin²θ  = 1 - 1/9

√(sin²θ) = +/-√(8/9)

sin θ = +/- (2√2)/3

Answer:

2.4

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

4.7 - 2.3

Step 2: Evaluate

Subtract

2.4

Answer:

2.4

Step-by-step explanation:

Answer:

- 18y = 1

Step-by-step explanation:

Adding the 2 equations term by term on both sides gives

(- 5x + 5x) + (- 9y - 9y) = (3 - 2), that is

0 + (- 18y) = 1

- 18y = 1

Answer:

a. b=4

Step-by-step explanation:

[tex]\sec \theta =\dfrac{1}{\cos \theta} = \dfrac{Hypotenuse}{Adjacent}[/tex]

From the attached triangle drawn below:

NL=20,  LM=3b, [tex]\angle L=x^\circ[/tex]

[tex]\sec x =\dfrac{20}{3b}[/tex]

Since we are told that:

[tex]\sec x =\dfrac{5}{3}\\$Then:\\\dfrac{20}{3b} =\dfrac{5}{3}\\$Cross multiply\\5 \times 3b =20 \times 3\\15b=60\\$Divide both sides by 15\\15b \div 15 =60 \div 15\\b=4[/tex]

The correct option is A.

Answer:

B= 4

Step-by-step explanation:

I got it right on the test

Answer:

Optimal investment amount = $300

Step-by-step explanation:

discount = x

original price = 10,000

discount% = 7%

x/10,000 = 7/100

x · 100 = 7 · 10,000

100x = 70,000

100x/100 = 70,000/100

x = 700

discount = x

original price = 10,000

discount% = 8%

x/10,000 = 8/100

x · 100 = 8 · 10,000

100x = 80,000

100x/100 = 80,000/100

x = 800

discount = x

original price = 10,000

discount% = 12%

x/10,000 = 12/100

x · 100 = 12 · 10,000

100x = 120,000

100x/100 = 120,000/100

x = 1,200

So:

$1,200 - $800 - $700 = $300

We max out the high return investment, $2000 for 12%.

We have $8000 left to invest and we want to put as much in CDs at 8% as possible.  Let's call b the bond investment and c the CD investment.  We have

b ≥ 3c

Since munis have the lower return we want as many CDs as possible.  So we choose:

b = 3c

b + c = 8000

3c + c = 8000

4c = 8000

c = 2000

That leaves b=3c=6000 for bonds.

Answer: $6000 in bonds, $2000 in CDs, $2000 in high-risk.

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πr^2 = area

Half the diameter to get the radius

Substitute the values in:

area = 3.142 x (7)^2

area = 153.958 cm^2

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Answer:

153.958cm^2

Step-by-step explanation:

r=d/2=14/2=7cm

A=πr^2

A=3.142×7^2

A=3.142×49cm^2

A=153.958cm^2

Answer:

X24

Step-by-step explanation:

Answer:

$ 60

Step-by-step explanation:

p(x) = 7x + 25

f(1) = 2.1² + 3 = 5

p(f(1)) = p(5) = 7 . 5 + 25 = 35 + 25 = 60

so he get $ 60 for 5 hours work with tips

Answer:

[tex]135<t_{minutes}\:<315[/tex]

Step-by-step explanation:

Malik's goal is a minimum total of 135 (45 x 3) minutes per week, in three session of 45 minutes.

Notice that it is at least.

So He can do sessions from 3 , 4, 5, 6 up to 7 nights per week

Hence, we can write his goals in minutes per week:

[tex]G_{w}=3*45<t_{minutes}<7*45\\G_{w}=135<t_{minutes}<315[/tex]

Answer:

9

Step-by-step explanation:

We can solve this by plugging x into the function:

3^(2(1/2) + 1)

=3^(1+1)

=3^2

= 9

Answer: The answer would be 9

Step-by-step explanation:

could i please get brainliest

Answer:

x = -3

Step-by-step explanation:

To solve this, you need to isolate the variable x, this means only one side of the equation should have the variable x. To do this, you need to do the opposite operation from what's given (if it's addition, use subraction; if it's multiplication, use division; these work vise versa)

The final answer is x = -3

Answer:

Step-by-step explanation:

let a be the first term and r be common ratio.

[tex]a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645[/tex]

Answer:

See the two translations described below

Step-by-step explanation:

Start with the graph of y = log x.  This graph passes through (1, 0) and exists only for x > 0.  The line x = 0 is its vertical asymptote.

Translating this graph 2 units to the right results in h(x) = log (x  - 2).

Translating the graph of h(x) = log (x  - 2) upward by 1 unit results in the graph of log (x – 2) + 1.

Answer:

B

Step-by-step explanation:

It cannot be C. The Y-intercept of Function W is 30, while the Y-intercept of Function Z is 15.8. Now, we are left with A, B, and D.

It cannot be D, because 30 is not less than 15.8. Now, we are left with options A and B.

Function Z as an equation is approximately y=-1/24x+15.8.

The slopes are NOT equal, so the answer cannot be A.

Explanation why it's B:

1/16 is bigger than 1/24, however, since the fractions are NEGATIVE, -1/16 is actually LESS THAN -1/24. The slopes of Function W is less than the slope of Function Z.

Answer:

B. the slope of function W is less than he slope of function Z

Step-by-step explanation:

Function W:

Function Z:

from the table we can see it is decreasing function with step change of -0.04

using the data from the table we can put the function in y= mx + b format:

as per above, we get the the form of function Z

we can now compare the slops and intercepts of functions W and Z

m - is the slope: -1/16 and - 1/25

b is the y-intercept: 30 and 15.8

As per above the correct option is

Answer:

x + x+12 + 3(x+12) = 123

x = 15

Step-by-step explanation:

Jamil : x

Kiera : x+12

Luther : 3 ( x+12)

x + x+12 + 3(x+12) = 123

Distribute

x + x+12 + 3x+36 = 123

Combine like terms

5x+ 48 = 123

Subtract 48 from each side

5x+48-48 = 123-48

5x =75

Divide by 5

5x/5 = 75/5

x = 15

Answer:

Equation:

123 = x + 12 + x + 3(12 + x)

Solution:

x = 15

Step-by-step explanation:

Jamil: x

Kiera: 12 + x

Luther: 3(12 + x)

Total: 123 badges

Equation:

123 = x + 12 + x + 3(12 + x)

Solve:

123 = x + 12 + x + 3(12 + x)

123 = x + 12 + x + 36 + 3x

123 = 5x + 48

-48           -48

75 = 5x

/5     /5

15 = x

Therefore, the value of x is 15.

Answer:

180 millimeters.

Step-by-step explanation:

To find the height of the replica, a ratio can be set up:

[tex]\frac{x}{50}= \frac{1}{275}[/tex]

Cross multiply:

[tex]275x = 50[/tex]

Divide both sides by '275:

x≈0.18 meters

Convert 'meters' to 'millimeters' by multiplying by a thousand:

0.18 × 1000 = 180 millimeters.

So the right answer is 4/11

please see attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

[tex] = \frac{2}{3} [/tex]

Step-by-step explanation:

[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{12 - 4}{ - 5 - ( - 17)} \\ = \frac{8}{ - 5 + 17} \\ = \frac{8}{12} \\ = \frac{2}{3} [/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

6/15 * 2/14 = 12/210

Step-by-step explanation:

This is compound probability. To calculate compound probability, you need to multiply the probabilities of each event happening together.

In this example, the events are selecting a pineapple cake, then a strawberry cake.

Let's find the probabilities!

There are 2 strawberry cakes, 6 pineapple cakes, and 7 chocolate cakes. This means that he has 15 cakes in total.

Therefore, the probability of selecting a pineapple cake is 6/15.

Now, if we assume that he has selected a pineapple cake already, there are now 14 cakes.

Next, the probability of selecting a strawberry cake is now 2/14. This is because he already took a pineapple cake, and now he has to pick a strawberry cake out of the remaining 14 cakes.

Multiply these two probabilities to find the compound probability: 12/210 ( this could be further simplified, but that's how they give it to you! )

Hope this helps! Please feel free to contact me if you have any further questions :)

Answer:

[tex]\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1[/tex]

Step-by-step explanation:

The objective of this question is to find the  sum of the greatest and least numbers below:

[tex]\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\][/tex]

To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.

[tex]8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2[/tex]

[tex]-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4[/tex]

[tex]-\dfrac{26}{3}= - 8.7[/tex]

[tex]-\dfrac{54}{7} = - 7.7[/tex]

[tex]\dfrac{53}{6}= 8.8[/tex]

Thus; the above decimal component of the fractions given are :

8.2, -8.4, -8.7 , -7.7 and 8.8

We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7

The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7

= 1.1

i.e

[tex]\dfrac{53}{6} + (- \dfrac{54}{7} )[/tex]

[tex]\dfrac{53}{6} - \dfrac{54}{7}[/tex]

[tex]\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1[/tex]

Answer:

Step-by-step explanation:

Answere is C

The sum has a degree of 6 but the difference haa a degree of 7

The true statement about the degree of the sum and difference of the polynomials 3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³ is "the sum has a degree of 6, but the difference has a degree of 7."

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

There are two polynomials,

3x⁵y - 2x³y⁴-7xy³ and -8x⁵y +2x³y⁴ + xy³.

The sum of the polynomials,

= 3x⁵y - 2x³y⁴-7xy³ -8x⁵y +2x³y⁴ + xy³.

=  5x⁵y -6xy³.

And the degree is 6.

The difference of the polynomials,

=  3x⁵y - 2x³y⁴-7xy³ + 8x⁵y - 2x³y⁴ - xy³.

= 13x⁵y - 4x³y⁴-8xy³.

And the degree is 7.

Therefore, the sum has a degree of 6, but the difference has a degree of 7.

To learn more about the Polynomials;

brainly.com/question/11536910

#SPJ2

Answer:

$5

Step-by-step explanation:

We want to find the cost of a notepad considering a magazine costs $3 and we buy 2 notepads and the total cost of the magazine and the 2 notepads is $13 so we can set up an equation to represent this situation. Let 'n' be notepads and that's the value we are solving for so,

⇒ Form the equation

→ 2n + 3 = 13

⇒ Minus 3 from both sides to isolate 2n

→ 2n = 10

⇒ Divide both sides by 2 to find the cost of one notepad

→ n = 5

The cost of one notepad is $5 considering that a magazine cost's $3 and two notepads and total is $13.

Answer:

The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]

Step-by-step explanation:

To divide a pizza, or anything else, equally among a certain number of people, we need to divide the total of pizza available by the number of people who will eat the pizza. In this case there are 8 slices and 'p' people, therefore:

[tex]y(p) = \frac{8}{p}[/tex]

In order to validate the expression, we can see that if 8 people eat the pizza, each gets one slice, because 8 divided by 8 is 1, while if 4 people eat the pizza each get 2 and so on.

The expression that represent each person's share is: [tex]y(p) = \frac{8}{p}[/tex]

Answer:

two times a number

Step-by-step explanation:

Answer:

7/4

Step-by-step explanation:

1 3/4=1 x 4=4 + 3=7/4

Answer:

Area_square = 4 cm2

Area_triangle = 4 cm2

Step-by-step explanation:

The first thing to do is calculate the area of both figures.

The area of the square is given by:

Area_square = side * side

The side of the square is 2 cm, so:

Area_square = 2 * 2 = 4 cm2

The area of the triangle is given by:

Area_triangle = base * height / 2

The base is 2 cm, and the height is 4 cm, so we have:

Area_triangle = 2 * 4 / 2 = 4 cm2

So we have that Area_square = Area_triangle = 4 cm2