the garden table and a bench cost $582 combined. the garden table costs $68 less than the bench. what is the cost of the bench?​

sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

The value of x is 35°

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cos x° = sin (20° + x°), where 0 < x < 90

We know that,

sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

x + 90 - x = 90

Now,

cos x = sin (20 + x)

x + 20 + x = 90

2x + 20 = 90

2x = 70

x = 35

Thus,

The value of x is 35°

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

The value of the expression when evaluated is: -18.

Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.

Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:

4(-3) - |3(-3) + 2(2)|

-13 - |-9 + 4|

-13 - |-5|

-13 - 5

= -18

The value of the expression is: -18.

Learn more about evaluation of expression on:

https://brainly.com/question/3590570

#SPJ1

The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

To know more about Z score here

brainly.com/question/2473932

#SPJ4

Step-by-step explanation:

4z-16z+8=0

[4×8]=32

factors of 32

1,2,4,8,....

Answer:

5 km = 5000 m

Hope this helps : )

The function that represent the given table is f(x) = 2n+1.

In the given question we have to write the correct function for the table given below.

The given table is

x                      y

0                      3

1                       5

2                      7

3                      9

We can write it as

x                      y

0                      3=1+2

1                       5=3+2

2                      7=5+2

3                      9=7+2

So we can see that in each odd number we are adding 2.

So the function should be

f(x) = (2n−1)+2

f(x) = 2n−1+2

f(x) = 2n+1

Hence, the function that represent the given table is f(x) = 2n+1.

To learn more about function from table link is here

brainly.com/question/4922255

#SPJ1

Robert can read 180 pages in [tex]1\frac 12[/tex] hours

The given parameters in the question are:

Speed = 2 pages per minute

Number of hours = [tex]1\frac 12[/tex] hours

The number of pages to read in this time can be calculated using the following equation

Number of pages = Speed * Number of hours

Substitute the known values in the above equation So, we have the following equation

Number of pages = 2 * [tex]1\frac 12[/tex]

Convert the units

Number of pages = 2 * [tex]1\frac 12[/tex] * 60

Evaluate

Number of pages = 180

Hence, the number of pages is 180 pages

Read more about unit rates at

https://brainly.com/question/19493296

#SPJ1

Answer:

.

Step-by-step explanation:

Jim ate 3/4 part of his lunch is in fraction form then the left part of his lunch is a fraction equal to 1/4 .

Fraction : A fraction represents a part of whole . It is a numerical value. It is evaluated by dividing a whole into number of parts . It has two parts one is called numinator (dividend) and other one is denominator ( divisor) . Denominator tells you how many part of lunch is divided into.

Types : Three types are

We have given in question that,

Jim ate 3/4 of his lunch .

let his lunch be x as a whole number .

Now , 3/4 part of x is ate by Jim i.e 3x/4

left part of x = x - 3x/4 = x/4

so, 1/4 part of x i.e lunch is left .

Hence, after eating the 3/4 of lunch by Jim the left part of lunch is 1/4 .

To learn more about Fraction, refer:

https://brainly.com/question/1878884

#SPJ4

The value of the angle ∠2 = 32° using angle bisector.

What is angle bisector?

In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.

An angle in a triangle is divided into two equal or congruent angles by a straight line known as the angle bisector. Each triangle can have one angle bisector for each of its three vertices. The intersection of these three angle bisectors in a triangle is referred to as the triangle's incenter.

The given angle ∠XVW = 64°

VP is a bisector,

So the angle ∠XVW will be divided equally.

So ∠2 = 32°

Hence the angle of the bisector ∠2 = 32°.

Learn more about angle bisector, by the following link

https://brainly.com/question/24334771

#SPJ1

Answer:

Step-by-step explanation:

answer = company b

Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

The graph is shown in the pictures

As we know,

The proportional relationship can be defined as:

y ∝ x

y = kx

k is the constant of proportionality:

y = kx is the equation of the line which passes through the origin.

Graph four passes through origin.

Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

Learn more about the proportional here:

brainly.com/question/14263719

#SPJ1

Answer:

6 feet

Step-by-step explanation:

38-32=6

the matrix has one real eigenvalue of algebraic multiplicity.

[1-λ     k

1        -7-λ]     =(1-λ)(-7-λ)-(1)(k) = λ² +6λ -(k+7)

Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.

Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside the educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.

To learn more about algebraic visit here:

brainly.com/question/24875240

#SPJ4

Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

The percentage is calculated by dividing the required value with the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Emily:

Each month payment = $250

Each month actual payment = $275

The percentage prediction is off by.

=  (275 - 250) / 275 x 100
= 25/275 x 100

= 9.09%

Enrique:

Each month payment = $200

Each month actual payment = $225

The percentage prediction is off by.

= (225 - 200)/225 x 100

= 25/225 x 100

= 11.11%

Thus,

Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ1

The required value of the given equation when x = 5 is y = 585.5

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.

Given : y = 114.50x + 13

To find ; The value of this equation when x = 5

Thus to find this value we have to simply substitute the value of x in the given equation

Hence, we will get ,

y = 114.50 × 5 + 13

this implies y = 572.5 + 13

which is equal to y  = 585.5

To know more about algebra or related problems you may visit the link which is mentioned below:

https://brainly.com/question/15167098

#SPJ1

The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

According to the question,

We have the following expressions:

[tex]49^{-1/2}[/tex]

Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:

[tex]7^{2*(-1/2)}[/tex]

[tex]7^{-1}[/tex]

Or it can be 1/7 because we have positive exponents.

Now, we have another expression:

[tex](\frac{27}{125}) ^{2/3}[/tex]

We will follow the same steps to solve this expression:

[tex](\frac{3}{5}) ^{3*2/3}[/tex]

[tex]\frac{3}{5} ^{2}[/tex]

Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:

9/25

Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

To know more about value here

https://brainly.com/question/15925395

#SPJ1

The number represented on number line by (A) -13   (B) 26   (C) 65

According to the number line given in part a

there are for parts in between 0 to 52

To find the numbers in one part = 52/4

                                                     = 13

Therefore,

For (A)

0 - 13 = -13

For (B)

0 + 2*13 = 26

For (C)

52 + 13 = 65

Hence, A is -13, B is 26 and C is 65.

To learn more about number line here:

https://brainly.com/question/13189025

#SPJ1

The equilibrium quantity is 97 items and equilibrium price is $582

The equation of the price  when quantity demanded

p = 873 - 3q

The equation of the price when quantity supplied

p = 6q

At equilibrium price and quantity

873 - 3q = 6q

Move the like terms to one side

6q + 3q = 873

Add the like terms

9q = 873

q = 873 / 9

Divide the terms

q = 97 items

Substitute the value of q in the equation 2

p = 6q

p = 6 × 97

Multiply the terms

p = $582

Hence, the equilibrium quantity is 97 items and equilibrium price is $582

Learn more about equilibrium price here

brainly.com/question/13317960

#SPJ1

The interior angles of the triangle are 43°, 43° and 94°. The exterior angle of the triangle is 86°.

A triangle is polygon with three sides. The sum of angles in a triangle is 180 degrees.

The triangle above is an isosceles triangle. The base angles of a triangle is congruent.

Therefore, the base angles are 5x - 12 and 5x  -12.

The sum of the remote interior angles is equal to the opposite exterior angles.

5x - 12 + 5x - 12 = 8x - 2

10x - 24 = 8x - 2

10x - 8x = -2 + 24

2x = 22

x = 22 / 2

x = 11

Therefore,

5x - 12 = 5(11) - 12 = 43°

Third angle = 180 - 43 - 43 = 94°

Exterior angle =  8x - 2 = 8(11) - 2 = 86°

learn more on angles here:https://brainly.com/question/21309759

#SPJ1

Answer: 50%

Hope this helps!

Answer:

Step-by-step explanation:

You want a system of equations for the width (x) and length (y) of a rectangle with a perimeter of 40 feet and length 2 more than 4 times the width.

One equation can give the relation for the perimeter:

  2(x +y) = 40

The other can express the relation between width and length:

  y = 2 +4x

Your system of equations is 2(x+y) = 40, and y = 2+4x.

__

Additional comment

The solution is (x, y) = (3.6, 16.4) feet.

The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².

Decibels:

Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.

Given,

Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels

Here we need to find the intensity of the sound of the blender

In order to find the intensity, we have to do the following steps,

First, we have to divide the decibel level by 10.

=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)

Now, we have to use that value as the exponent of the ratio.

=> 8.8 = log (x / 1 x 10⁻¹²)

Finally, we have to use that power of ten to find the intensity in Watts per square meter.

=>  6.3×10⁻⁴ .

To know more about Decibels here.

https://brainly.com/question/26848451

#SPJ1

Answer:

You can FACTOR x^2-12x+35 by using the AC method

This means the answer will be:

(x-7)(x-5)

I hope this helps!

(Brainliest is optional)

Answer:

====================

Triangle inequality theorem states that the sum of any two sides must be greater than the remaining side.

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

Given,

The lengths of triangle is given as:

10 , 10 and 20

To check the following three lengths form a right triangle.

Now, According to the question:

What is triangle inequality theorem ?

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

So, The length of triangle are 10, 10, 20

10 + 10 = 20

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

Learn more about Triangle at:

https://brainly.com/question/2773823

#SPJ1

Leroux can reduce the costs of regular health care without driving up the price of their health acre plan by : (c) Reducing the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same.

Since the customers are complaining that the cost of regular visits and prescriptions ($15) are too expensive for them based on the plan they choose, this means that the purpose of the health insurance plan which is to reduce the overwhelming cost burden on individuals when trying to access proper healthcare is not be implemented successfully.

The co-pay amount which is usually known as the out-of-pocket amount that insurers pay whenever they go for regular doctor visits ( covered service in the insurance package ) and reducing this amount will reduce the immediate cost which makes the customers to complain about how expensive assessing a doctor on regular visits are.

The effect of the increased annual deductible is one way to push the immediate burden of paying a higher co-pay amount by the customer.

Learn more about healthcare:

https://brainly.com/question/28426089

#SPJ4

The amount of money that is reduced from Tiffany's allowance is $8.75

The amount of allowance reduced every time she forget to clean her room = $1.25

Number of times that she forgets to clean her room = 7 times this month

The amount of money is reduced from Tiffany's allowance =  Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room

Here we have to use the multiplication to find the amount

Substitute the values in the equation

The amount of money is reduced from Tiffany's allowance = 7 × 1.25

Multiply the terms

= $8.75

Hence, the amount of money that is reduced from Tiffany's allowance is $8.75

Learn more about multiplication here

brainly.com/question/14667283

#SPJ4

Answer: the answer is  30/11

Step-by-step explanation:

hope it helps:)

Answer:

(x-5)(x+8)

Step-by-step explanation:

Factors of -40:

-1, 40

-2, 20

-4, 10

-5, 8

-5 + 8 =3

x^2+3x-40

x^2 -5x +8x -40

=(x-5)(x+8)