A worker gets paid overtime at the rate of normal time plus one third. One week he works 40 hours of normal time and 6 hours overtime. If his hourly rate is $15 how much did he earn for that week?​

Answer:

2x+20+3x+40=90

5x+60=90

5x=30

x = 6

2x+20 = 2(6)+20

12+20

=32

3x+40 = 3(6)+40

18+40

=58

Answer:

Here we can first find the value of x simply by using the concept of corresponding angles.

As we know that angle with measurement 2x+20Degree and the right angle below are corresponding as we can consider the line (underlined in red) as a transversal intersecting lines underlined in green. {PLEASE SEE THE ATTACHMENT TO SEE THE HIGHLIGHTED LINES}

So, we get 2x+20 degree = 90 degree.

=  2x+20=90

=  2x=90-20

=  2x=70

=  x= 70/2

=  x=35 degree.

Now as we know the value of x we can find the other unknown angle by substituting it in the equation for the other angle.

Therefore, 3x+40degree= 3*35+40

105+40

=  145 degrees.

Answer:

- 1

Step-by-step explanation:

( x + 4 )² + 38 = 47

( x + 4 )² = 47 - 38

( x + 4 )² = 9

( x + 4 )² = 3²

Square root on both sides,

x + 4 = 3

x = 3 - 4

x = - 1

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

\(\sqrt{10}\)

Step-by-step explanation:

Using the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\)

substitute

\(d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}\)

\(\sqrt{10}\)

Step-by-step explanation:

what is that called into the comet or ok

Answer:

I tried looking it up, and i found 15 square units. sorry if its wrong :(

Step-by-step explanation:

Answer:

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

Point-slope form is:

Find the slope:

Use one of the points and the slope to determine the equation of the line:

Answer:

\(y-10=\frac{2}{3} (x-5)\)

Step-by-step explanation:

We are given: g(5)=10, and g(2)=8.

The value inside the parentheses is the x value, and the value that it (g(x)) is equal to is the y value.

So, as points, the values are (5, 10), and (2, 8).

The equation wants to be written in point-slope form, which is \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point.

We first want to find the slope of the line.

The slope (m) can be found with two points using the formula \(m=\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points.

We can label the values of the points we were given.

\(x_1=5\\y_1=10\\x_2=2\\y_2=8\)

Now, substitute these values into the formula.

\(m=\frac{y_2-y_1}{x_2-x_1}\)

\(m=\frac{8-10}{2-5}\)

Subtract.

\(m=\frac{-2}{-3}\)

Simplify.

\(m=\frac{2}{3}\)

The slope is 2/3.

Since we now have the value of the slope, as well as \((x_1, y_1)\), we can plug these values into the formula for point-slope form.

Recall that \(x_1=5\) and \(y_1=10\); plug these in for \(x_1\) and \(y_1\) respectively.

\(y-10=m(x-5)\)

We also just found the slope, which is 2/3. Plug that in for m.

\(y-10=\frac{2}{3} (x-5)\)

Topics: Point-slope form, functions

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Answer:

Answer is (-10,7) and inequality form: -10<c<7

Step-by-step explanation:

First factor the equation.

(c+7)(c-10)

Then find out which intervals make (c+7)(c-10)<0.

The contrapositive of the statement "If x is a multiple of \(10\), it is an even number" is "If \(x\) is not a multiple of \(10\), then it is not an even number."

To complete the contrapositive of the statement "If \(x\) is a multiple of \(10\), it is an even number," we need to negate and reverse the original statement.

The original statement can be represented as:

\(\[P: \text{If } x \text{ is a multiple of 10, then } x \text{ is an even number.}\]\)

The negation of this statement is:

\(\[\neg P: \text{If } x \text{ is not an even number, then } x \text{ is not a multiple of 10.}\]\)

To form the contrapositive, we reverse the implications:

\(\[\text{Contrapositive: If } x \text{ is not a multiple of 10, then } x \text{ is not an even number.}\]\)

In symbolic notation, the contrapositive would be:

\(\[\text{Contrapositive: } \neg P: \text{If } \neg(x \text{ is a multiple of 10}), \text{ then } \neg(x \text{ is an even number}).\]\)

Therefore, the contrapositive of the statement "If x is a multiple of \(10\), it is an even number" is "If \(x\) is not a multiple of \(10\), then it is not an even number."

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The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

The answer is C

Step-by-step explanation:

Edgy 2021 Unit Test

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

According to the given information

A.

Monthly payment for 20 year mortgage \(& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \\)\

Monthly payment for 25 year mortgage \(& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\\)

B

Total cost of interest for 20 year mortgage \(& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\\)

Total cost of interest for 25 year mortgage \($=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &\)

C.

Difference in interest paid \(& $=\mathrm{B} 7-\mathrm{B} 6$ &\) = Total interest for 25 year loan-total interest for 20 years

A.

Monthly payment for 20 year mortgage \(& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\\)

Monthly payment for 25 year mortgage \(& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\\)

B.

Total cost of interest for 20 year mortgage = \(& $\$ 197,343.88$ & $=$\)  total monthly payments-loan taken

Total cost of interest for 25 year mortgage = \(& $\$ 280,084.40$ & $\) = total monthly payments-loan taken

C.

Difference in interest paid = $82,740.52

Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest

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Answer:

400,000

Step-by-step explanation:

➟ 10 × 4 ten thousand

Since, a ten thousand = 10,000 therefore 4 ten thousand = 40,000

➟ 10 × 40,000

➟ 400,000

Here is one way to show that the left side is identical to the right side.

\(\sec(x)-\tan(x)\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin(x)}{\cos(x)}\sin(x) = \cos(x)\\\\\\\frac{1}{\cos(x)}-\frac{\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{1-\sin^2(x)}{\cos(x)} = \cos(x)\\\\\\\frac{\cos^2(x)}{\cos(x)} = \cos(x)\\\\\\\cos(x)=\cos(x)\\\\\\\)

Throughout the entire process, the right hand side stayed the same. When working on identities, it's important to keep one side the same while you transform the other side.

Despite the two sides being identical when simplified, there is the issue of cos(x) being zero in the denominator on the left hand side. Be sure to account for this when forming the domain. No such issue occurs on the right hand side. For instance, the value x = pi/2 leads to a division by zero error when in radian mode. So if I was your teacher, I would revise the "for any value of x" and replace it with something along the lines of "for any x value in the domain".

Explanation:

Segment AW bisects angle CAD.

This leads to the smaller pieces (angles CAW and DAW) to be equal to one another. Both are 20 degrees each. That totals to 20+20 = 40 degrees.

Therefore, angle CAD = 40 degrees.

The supplement of this is angle DAX

(angle CAD) + (angle DAX) = 180

angle DAX = 180 - (angle CAD)

angle DAX = 180 - 40

angle DAX = 140 degrees

Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

Answer:

12

Step-by-step explanation:

Answer: 12

Step-by-step explanation:

The general solution for  mx" + Bx' = mg for r(t) is x(t) = 25e^(-x/5) + 5x -125

According to the question,

The given equation =  mx" + Bx' = mg

Also , mg = 160, B = 1, and g = 32

=> m = 160/g

=> m = 160/32 = 5

Substituting the values in equation ,

5x" + x' = 160 , x(0) = -100, x' (0) = 0

The characteristic equation of the homogeneous differential equation is

5x" + x' = 0

=>  5r² + r = 0

=> r = 0 , -1/5

The complementary solution is x = c₁e⁰ + c₂e⁻⁰°²

Solution for complementary is yc = ax + b

Substitute yc = ax + b in  5x" + x' = 160 to get

5(0) + a = 160

=> a = 160

So the general solution is

x(t) = 25e^(-x/5) + 5x -125

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Answer:

4

Step-by-step explanation:

Hope this helps:)

Answer:

No

Step-by-step explanation:

Simplest form is

1:4

14/14 = 1

56/14 = 4

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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Therefore , the solution to the given problem of triangle comes out to be x =20 degree and y = 20 degree.

In a plane, any three points can be joined to form triangles, that have 3 components and three angles. They were among the first geometrical forms to be investigated. Because each polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle, they are especially significant.

Here,

Given : 140 degree

Since it is a scalar triangle

two sides will have equal angle,

Thus ,

x=y

=> x+ x + 140 =180

=> 2x = 180-140

=> 2x =40

=> x =20

Therefore , the solution to the given problem of triangle comes out to be

x =20 degree and y = 20 degree.

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Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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Answer:

787

Step-by-step explanation:

401 muffins that contained nuts

787 muffins that did NOT contained nits

Then the ratio is:

401 : 787

Answer:

401:787 = 1/2

Step-by-step explanation:

muffins with nuts                muffins without nuts

401                                             787

ratio= 401/787

     =1/2

Answer:

28.911

Step-by-step explanation:

you just have to open up a calculator lol

Answer:

Step-by-step explanation:

In other to meet up with her target, Abigail would have to cover 4 miles every day.

Target = 37 miles

Covered miles = 17 miles

Number of miles left to cover :

Number of miles left = (37 - 17) miles = 20 miles

Number of miles to cover per day :

Hence, Abigail would have to cover 4 miles every day.

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

2.5678 to the nearest half is 13,000

Answer: I think it would be 5 1/2 or 5.5 Fraction and decimal

Step-by-step explanation: Hope this helps! :)