A garden table and a bench cost $711 combined. The garden table costs $39 less than the bench. What is the cost of the bench?

Answer:

37675

Step-by-step explanation:

ummm what is did was

274/2 = 137

and then times that by 275

because

274+1 = 275

273+2 = 275

...

137+137 = 275

so the ans is 137(275) which is equal to 37675

Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer:

\( \frac{3}{5}\)

Step-by-step explanation:

The adjacent sides are 3 and 4. Thus the hypotenuse is: (by Pythagoras Theorem)

$=\sqrt{3^2+4^2}$

$=\sqrt{25}$

$=5$

Now by definition of $\sin$, we get:

$\sin \theta= \frac{\text{opposite}}{\text{hypotenuse}}=\frac{3}{5}$

Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

(7-2x)3 =9-10x

x= -3

Step-by-step explanation:

we let the number to be x.

twice a number=2x is decreased by 7 that is to say 7-2x, is multiplied by 3, we have (7-2x)3.

the result is 9 less than 10times the number which is =9-10x.

so bringing all these together we have;

(7-2x)3=9-10x.

what is the number?

solving, we have:

(7-2x)3=9-10x

21-6x=9-10x

21-9= -10x+6x

12= -4x

dividing both sides by -4 we have our number

x= -3.

for proof we can substitute x=-3 into the equation.

21-6(-3) =9-10(-3)

21+18=9+30

39=39

Answer: $90.77

Step-by-step explanation:

Just did the test

The desk cost $90.76 after Depreciation rate.

The depreciation rate is the proportion at which an asset depreciates during its anticipated useful life. It may also be described as the portion of an organization's long-term investment in an asset that the organisation claims as a tax-deductible expense over the course of the asset's useful life.

Given:

A desk is purchased for $277.

In one year the  depreciation rate is 20% per year.

So, In one year depreciation amount

= 20% of 277

= $55.4

After 2nd year

= 221.6 - 20% of 221.6

= $177.28

After 3rd year

= 177.28- 20% of 117.28

= $141.824

After 4th year

= $113.4592

After 5th year

= 113.4592 - 20% of 113.4592

= $90.76

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Answer:

Statement 1 is false, statement 2 is true.

Step-by-step explanation:

The triangle has been dialated by a scale factor of 2.5

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

Answer:

Step-by-step explanation:

Cannot give you the number because we are not given the diagram.

However, it will be exactly the same as the measure of angle R in the original triangle PQR.

Rotation and dilation do not change angles.

Answer:

attached below

Step-by-step explanation:

The Function; F(x) = x^2 / (x^4 + 81 )

power series representation

F(x) = x^2 / ( 81 + x^4 )

      = ( x^2/81 ) / 1 - ( -x^4/81 )

attached below is the remaining part of solution

As this is when it hits the ground, the projectile is in the air for 6 seconds.

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

Objects that are thrown, shot, or launched with a certain initial velocity and then move against the forces of gravity and air resistance are known as projectiles. Projectiles can be anything from arrows and bullets to rocks and water balloons. Typically, a bow, slingshot, gun, or cannon is used to fire them. When projectiles are launched, gravity, air resistance, and other forces influence their trajectories.

from the question:

We must discover the moment the missile strikes the ground in order to calculate how long it was in the air. The height of the missile above the earth would be zero at that point.

Thus we must resolve the following equation:

y = -3x² - 12x + 96 = 0

We can use the quadratic formula to solve this equation in the quadratic form:

x = (-b ± √(b² - 4ac)) / 2a

where a = -3, b = -12, and c = 96.

Plugging in these values, we get:

x = (-(-12) ± √((-12)² - 4(-3)(96))) / 2(-3)

x = (12 ± √(144 + 1152)) / (-6)

x = (12 ± √1296) / (-6)

x = (12 ± 36) / (-6)

So, the solutions are:

x = -2 or x = 6

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

As a result, the missile is in the air for 6 seconds before it strikes the earth.

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Answer:

128

Step-by-step explanation:

(2³) (140/7)-32 =128

Answer:

128

Step-by-step explanation:

[2³ ×(140 ÷ 7)] - 32

[2³ ×( 20)] - 32

[8×(20)] - 32

[160] - 32

128

Answer:$49.50

Step-by-step explanation:

First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer:

80° because 50° 60° 70° and 80°

Answer:

x=5/3 simplified x= 15/9

Step-by-step explanation:

Answer:

There are 80 men on the train.

Step-by-step explanation:

M : W

4  : 5

W : C

10 : 9

As you can see, the units for women is not equal, so I shall multiply the first ratio by 2 so that the units for women is 10.

M : W

8  : 10

Now that everything has the same units, I can put the ratio of men, women and children together:

M : W : C

8  : 10 : 9

Total number of units = 8 + 10 + 9

                                    = 27

27 units = 270

No. of men (8 units) = \(\frac{8}{27}\) × 270

                                 = 80  

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The  unitary method equation below can be used to calculate the expense of strawberries for each friend: Cost equals Unit Price  Quantity. where a pound's worth of product costs $1.25.

The unit method is a strategy for solving issues that entails first figuring out the value of just one unit, and subsequently multiplying that number to figure out the needed value. Simply stated, the unit method is used to determine only one value via a multiple that is supplied. For example, 40 pens might run you 400 rupees, which is equal to the expense of one pen. This procedure might follow a conventional procedure. a distinct nation. anything with a distinct character. Its adjoint and equivalent are identical in terms of mathematics, algebra, linear equations, mathematical analysis, or math of matrices or operators.

The cost per unit of a specific object is its unit price. The measure in this instance is one pound (lb) of strawberries.

The unit amount for the 2 pounds of strawberries that Akio purchased for $2.50 is:

$1.25 per pound x $2.50 x 2 pounds

Gordon spent $3.75 on 3 pounds of strawberries, so his strawberry price per unit is:

$3.75 x 3 pounds equals $1.25 per pound.

The unit price for Maria's strawberries is $5.00 for 4 pounds of strawberries, which equals:

$5.00 x 4 lbs equals $1.25 per pound

The equation below can be used to calculate the expense of strawberries for each friend:

Cost equals Unit Price  Quantity.

where a pound's worth of product costs $1.25.

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For given rectangular board, the width of the border would be 10 inches.

In this question, a person has a rectangular board 10 inches by 14 inches around which she wants to put a uniform border of shells.

So, the area of the rectangular board would be:

10 × 14 = 140 sq inches

A person  has enough shells for a border whose area is 340 square inches.

So, the area of the board and the border would be,

340 + 140 = 480 square inches

Let m be the width of the border.

Then the dimension of the rectangular board would be, (10 + m) and (14 + m).

⇒ (10 + m) × (14 + m) = 480

⇒ 140 + 14m + 10m + m² = 480

⇒ m² + 24m + 140 - 480 = 0

⇒ m² + 24m - 340 = 0

⇒ (m + 34)(m - 10) = 0

⇒ m = -34       or       m = 10

But the width of the border cannot be -34

so, the width of the border = 10 inches

Therefore, for given rectangular board, the width of the border would be 10 inches.

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These terms are related to the properties and characteristics of a function, which is a mathematical rule that relates each input value to a unique output value.

What are the properties of function?

Here is a brief explanation of each term:

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Answer:

-4

Step-by-step explanation

1 - 5 = -4

Answer:

∠ AEB = 114°

Step-by-step explanation:

the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is

∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°

Answer: D (t−3)(t−5)(t+4)

Step-by-step explanation:

Hope this helps! :)

The next step on solving completing square is  5(x² + 4x)=7 and

5 (x² + 4x + 4 )=7 + 20

Quadratic equation is the equation of the 2nd degree. One of the standard formulas for solving quadratic equations is 'ax² + bx + c = 0' here a, b, and c are constants or numerical coefficients. 'X' here is an unknown variable.

Case (I).

Given equation is

5x² + 20x- 7 =0

Firstly, we will add of 7 in both sides

5x² + 20x- 7 +7 = 7

Now, same variable of opposite sign is cancelled

5x² + 20x=7

Now, taking 5 common from left side

5(x² + 4x)=7

Case (II).

Given equation

5x² + 20x- 7 =0

Firstly, we will add of 7 in both sides

5x² + 20x= 7

Now, we will add of 20 in both sides

5x² + 20x + 20= 7 + 20

Now, taking common of 5 from left side

5 (x² + 4x + 4 )=7 + 20

So, The next step on solving completing square is  5(x² + 4x)=7 and

5 (x² + 4x + 4 )=7 + 20

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Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

A function can be represented on a table and on a graph.

The models of the linear relationship between f(x) and x are:

\(\mathbf{A.\ f(x) = 30x + 22}\\\mathbf{C.\ The\ table}\\\mathbf{F.\ The\ graph}\)

The given parameters are:

\(\mathbf{Start = 22}\)

\(\mathbf{Additional = 30}\)

So, the function that models the linear relationship is:

\(\mathbf{f(x) = Start + Additional \times x}\)

Substitute known values

\(\mathbf{f(x) = 22 + 30 \times x}\)

Evaluate all products

\(\mathbf{f(x) = 22 + 30x}\)

Rewrite as:

\(\mathbf{f(x) = 30x + 22}\)

By comparing the above function to the list of options, we have the true options to be:

\(\mathbf{A.\ f(x) = 30x + 22}\\\mathbf{C.\ The\ table}\\\mathbf{F.\ The\ graph}\)

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Answer:

D. \( = \frac{b}{a} \)

Step-by-step explanation:

Given:

\( \frac{b^{-2}}{ab^{-3}} \)

Required:

Assuming a ≠ 0, b ≠ 0, find the expression equivalent to the given expression.

SOLUTION:

\( \frac{b^{-2}}{ab^{-3}} \)

Recall the exponent rule =>  \( \frac{x^{a}}{x^{b}} = x^{a - b} \)

Applying the exponent rule, we would have:

\( \frac{b^{-2 -(-3)}}{a} \)

\( = \frac{b^{-2 + 3}}{a} \)

\( = \frac{b^{1}}{a} \)

\( = \frac{b}{a} \)

Thus, the equivalent expression of \( \frac{b^{-2}}{ab^{-3}} \) = \( \frac{b}{a} \)

Answer:

d

Step-by-step explanation: