Henry wrote a total of 12 pages over 4 hours. How many hours will Henry have to spend writing this week in order to have written a total of 15 pages? Assume the relationship is directly proportional.

The value of x is 18.8m

Given:

θ = 48°

Y = 17m

The law of tangent which is also called as tangent formula or tangent rule is the ratio of the sine of the angle to the cos of the angle.

tan θ = Opposite / Adjacent.

Here,

Sum of triangle = 180°

90° + 48° + x° = 180°

x° = 42°

tan θ = opposite/ adjacent.

Substituting the values

tan 42° = 17/x  (∴tan 42° = 0.9004)

0.9004 = 17/x

So we get,

x = 17/0.9004

x = 18,8m

Therefore, the value of x is 18.8m.

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They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

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The simplified form of the given expression is (10 + 2√2)/23

From the question, we are to simplify the given expression

The given expression is

2 / 5-√2

To simplify this expression, we will rationalize the denominator

To rationalize the denominator, we will multiply both the numerator and the denominator by the conjugate of the denominator.

The denominator in the expression is

5 - √2

The conjugate of the denominator is 5 + √2

Simplifying the expression

2 × (5 + √2) / (5 - √2)(5 + √2)

(10 + 2√2) / [5² - (√2)²]

(10 + 2√2) / (25 - 2)

(10 + 2√2)/23

Hence, the simplified expression is (10 + 2√2)/23

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Based on the monthly installments and the amount that Belinda traded in the television for, the total simple interest paid was $6,600 and the rate of simple interest was 22%.

The balance after the trading in and deposit was:

= 20,000 - 3,000 - 2,000

= R15,000

The total simple interest paid was:

= (900 x 2 x 12months) - 15,000

= $6,600

The rate of simple interest was:

= (6,600 / 2 years) / 15,000

= 22%

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Each nested cart add to the length of the row is 1.5 feet long.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, the store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

Each row has a starting cart that is 4 feet long, and the nested carts are next to it.  

It is measured that a row of 13 nested carts has a length of 23.5 feet.

Therefore, the original length of 13 nested carts is (23.5 - 4) = 19.5 feet.

So, each nested cart add to the length of the row 19.5/13 =1.5 feet

Again, a row of 18 nested carts to be 31 feet long.

Therefore, the actual added length of 18 nested carts is (31 - 4) = 27 feet.

So, each nested cart add to the length of the row 27/18 =1.5 feet

Therefore, each nested cart add to the length of the row is 1.5 feet long.

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"Your question is incomplete, probably the complete question/missing part is:"

A store is designing the space for rows of nested shopping carts. Each row has a starting cart that is 4 feet long, followed by the nested carts (so 0 nested carts means there's just the starting cart). The store measured a row of 13 nested carts to be 23.5 feet long, and a row of 18 nested carts to be 31 feet long.

How much does each nested cart add to the length of the row?

Answer:

x = sqrt(13) - 4 or x = -4 - sqrt(13)

Step-by-step explanation:

Solve for x:

x^2 + 8 x + 3 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 3 from both sides:

x^2 + 8 x = -3

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 16 to both sides:

x^2 + 8 x + 16 = 13

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 4)^2 = 13

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 4 = sqrt(13) or x + 4 = -sqrt(13)

Hint: | Look at the first equation: Solve for x.

Subtract 4 from both sides:

x = sqrt(13) - 4 or x + 4 = -sqrt(13)

Hint: | Look at the second equation: Solve for x.

Subtract 4 from both sides:

Answer: x = sqrt(13) - 4 or x = -4 - sqrt(13)

Answer:

like 2/3 or 15/16; Mixed number - like 1 1/2 or 4 5/6; Integer - like 5 or 28

Step-by-step explanation:

The required fractions for 2/3, 3/4, and 5/6 with a denominator of 12 are 8/12, 9/12, and 10/12 respectively

Given the following fractions

2/3, 3/4 and 5/6

We are to write as equivalent fractions with a denominator of

12​

For the fraction 2/3;

\(= \frac{2}{3} \frac{4}{4}\\= \frac{2 \times 4}{3 \times 4} \\= \frac{8}{12}\)

For the fraction 3/4

\(= \frac{3}{4} \frac{3}{3}\\= \frac{3 \times 3}{4 \times 3} \\= \frac{9}{12}\)

For the fraction 5/6;

\(= \frac{5}{6} \frac{2}{2}\\= \frac{5 \times 2}{6 \times 2} \\= \frac{10}{12}\)

Hence the required fractions for 2/3, 3/4, and 5/6 are 8/12, 9/12, and 10/12 respectively

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Answer:

47.32

Step-by-step explanation:

Applying the formula for the area of triangle using sine, we have:

sin A = 1/3 (A ≈ 19.5°).

Given that a triangle has the following parameters:

Area of triangle ABC = 21 square units

Side b = 14 units

Side c = 9 units

Thus, applying the area of a triangle using the sine rule, we have the following formula:

Area = 1/2 * b * c * sin A

Plug in the values:

21 = 1/2 * 14 * 9 * sin A

2 * 21 = 126 * sin A

42 = 126 * sin A

42/126 = sin A

sin A = 1/3

A = sin^(-1)(1/3)

A ≈ 19.5°

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Answer:

A. 8.008, 8.08, 8.081, 8.09

B. 14.200, 14.204, 14.210, 14.240

Step-by-step explanation:

Answer:

Step-by-step explanation

The most appropriate choice for slope of a line will be given by:

The slope of the given line is 2.

What is slope of a line?

The slope of a line is the change in y - coordinate with respect to the change in x - coordinate

If the coordinate of two end points of a line are (\(x_1\), \(y_1\)) and (\(x_2\), \(y_2\)) respectively, then slope of the line is given by

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

Here,

\(x_1 = 1 , y_1 = -5, x_2 = 4, y_2 = 1\)

slope = \(\frac{1-(-5)}{4-1}\)

         = \(\frac{6}{3}\)

         =\(2\)

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\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

                The side length of an equilateral triangle is 5 cm. Find its perimeter.

\(\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

We are given that the triangle is equilateral.

"equi" means "equal" and "lateral" means "sides"

✯ So an equilateral triangle has 3 equal sides.

We are also given that one side is equal to 5 cm.

If one side is equal to  5 cm, and the triangle's equilateral, then the other two sides are equal to 5 cm.

◈ In order to find the perimeter of a shape, you should add all of its side lengths together.

✯ Now, we need to find the perimeter, which we can find using the following formula:-

\(\bold{Perimeter_{(triangle)}=a+b+c}\)

Now, we add them:-

\(\hookrightarrow\sf{P=5+5+5}\)

So we conclude that the perimeter is equal to:-

\(\hookrightarrow\sf{P=15\:cm}\)

\(\rule{300}{1}\)

The percent error of the house of the pizza would be 2.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.

We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.

WE know that Error = Actual value - Estimated value

Then Error = 14 - 12 = 2

Therefore, the percent error would be 2.

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The angle measure of the angle in the diagram is 62°.

From the question, we are to determine the angle measure of the angle shown in the diagram.

The angle shown is an acute angle.

An acute angle is an angle whose measure is less than 90°.

To determine the measure of the angle, we will read the angle from the side which the angle is closer to zero (0). We will read from 0 to the line that indicates the angle.

Reading the angle:

Reading the angle as explained above, the measure of the angle is 62°

Hence, the angle measure is 62°.

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You can either transform this quadratic equation into a vertex form which would rather painful or use derivatives.

I'll use dervatives. We know that vertex of a quadratic function is either its maxima or its minima, since the leading coefficient \(-x^2\) has a negative prefix that means we get a downward turned parabola with minima being the vertex.

First we take the derivative with respect to x,

\(\dfrac{d}{dx}-x^2-2x+3=-2x-2\)

The derivative is esentially information what is the slope of a function at a particular x. When the slope is 0 we reached some sort of turning point, such as minima.

We therefore do,

\(-2x-2=0\implies x=-1\)

So at \(x=-1\) there appears to be a minima or x-coordinate of the vertex of the function.

Plug the coordinate into the function to get y,

\(y=f(-1)=-1+2+3=4\)

So the vertex of the function is at \(\boxed{(-1,4)}\).

Assuming you don't know derivatives, there is another way.

First compute the roots of the function,

\(-x^2-2x+3=0\)

\(-(x-1)(x+3)=0\)

\(x_1=1,x_2=-3\)

In the middle between \(x_1,x_2\) is an x coordinate of a vertex,

\(x=\dfrac{x_1+x_2}{2}=\dfrac{1-3}{2}=-1\)

Just like we had before, we compute for y, \(h(-1)=4\) and again the result is \(\boxed{(-1,4)}\).

Hope this helps :)

a.

Answer:

1170cm^3

Step-by-step explanation:

Break it into two prisms. 5 x 9 x 15 and 11 x 3 x 15. Find the volume of each and add.

(5 x 9 x 15) + (11 x 3 x 15)

675 + 495

1170cm^3

b.

Answer:

846cm^2

Step-by-step explanation:

Add each side's area together.

(9x15) + (5x15) + (6x15) + (3x15) + (12x15) + (11x15) + (5x9) + (5x9) + (11x3) + (11x3)

135 + 75 + 90 + 45 + 180 + 165 + 45 + 45 + 33 + 33

846 cm^2

Answer:

(a)1170 cm^3

(b)846 cm^2

Step-by-step explanation:

(a) Rectangle #1= 11 x 3 = 33 cm^2

Rectangle #2 = 5 x 9 = 45 cm^2

Volume = 45 + 33 = 78 x 15 = 1170 cm^3

(b) First find the surface are of all 8 faces in the prism and then add them all.

1st face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2

2nd face = (11 x 3) + (5 x 9 ) = 33 + 45 = 78 cm^2

3rd face = 15 x 3 = 45 cm^2

4th face = 15 x 6 = 90 cm^2

5th face = 15 x 9 = 135 cm^2

6th face = 15 x 5 = 75 cm^2

7th face = 15 x 12 = 180 cm^2

8th face = 15 x 11 = 165 cm^2

1st + 2nd + 3rd +4th + 5th+ 6th + 7th + 8th = 846 cm^2

Hope this helps!

Answer:

y=9/8x+-3/2

Step-by-step explanation:

Step 1: Add -9x to both sides.

9x−8y+−9x=12+−9x

−8y=−9x+12

Step 2: Divide both sides by -8.

-8y/-8=-9x+12/-8

y=9/8x+ -3/2

the first one is (B) i think

the second one is (B)

the third one is (B)

the fourth one is (A)

the fifth one is (A)

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

π * [27,1]∫ (3-∛y)² dy

Step-by-step explanation:

Disk method it is, since both given options integrate with respect to y.

First find where the boundaries of the region intersect.

• y = x ³ and y = 1 intersect at (1, 1)

• y = x ³ and x = 3 intersect at (3, 27)

• y = 1 and x = 3 intersect at (1, 3)

So the bounded region is the set of points

{ (x, y) | 1 ≤ x ≤ 3 and 1 ≤ y ≤ x ³ }

But since we're integrating with respect to y, rewrite this set so that y has constant limits:

{ (x, y) | ∛y ≤ x ≤ 3 and 1 ≤ y ≤ 27 }

Pick some point y in the interval [1, 27] and construct a disk centered at the given axis of revolution (x = 3). Such a disk will have radius 3 - ∛y because x = ∛y is the horizontal distance from the y-axis to the curve y = x ³ and x = 3 is itself 3 units away from the y-axis. Its height will be some small change in y, call it ∆y. Then the volume of this disk is

π (3 - ∛y )² ∆y

Now do the same thing for every y in [1, 27] - infinitely many of them! - and make ∆y very small, such that ∆y → dy. The volume of the solid is the sum total of the volumes of these infinitely many disks, given by the integral

\(\displaystyle\pi\int_1^{27}\left(3-\sqrt[3]{y}\right)^2\,\mathrm dy\)

and so the answer is A (assuming the limits of integration are listed from upper to lower).

If sales tax rate is not given, we use Total cost = cost price * sales tax to find the sales tax rate

Sales tax is a type of tax that's charged at the time an item or service is sold. The buyer pays the tax to you, and you remit the tax to the relevant government tax collection body. The taxes that are collected by each agency are then sent to various departments at the local, county, and state levels to ensure their ongoing operations and functions.

Learning how to calculate sales tax is easy. It consists of converting the sales tax percentage to a decimal number, then multiplying the cost of the item by the decimal number to get the amount of sales tax you collect.

sales tax is calculated using the formula:

Sales tax rate = Sales tax percent / 100

Sales tax = List price x Sales tax rate

To find the sales tax rate when the rate is not given

Total cost = cost price * sales tax

Hence, we can find the sales tax rate by manipulating the above formula

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Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of observing no positive reading if all the subjects are telling the truth is 9/10.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Positive reading when telling the truth = 10%

No positive reading when telling the truth = 90%

The probability of observing no positive reading if all the subjects are telling the truth

= 90%

= 90/100

= 9/10

Thus,

The probability of observing no positive reading if all the subject are telling the truth is 9/10.

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Answer:

995

Step-by-step explanation:

Because you would have to subtract 5 from 1000 which is 995, hope this helped!

Answer:

the answer to the problem is 20.8%

Answer:

y = 8 and x = -6

Step-by-step explanation:

5x + 6y = 18 ------------ (1)

2x - 3y = 12 ------------- (2)

we have to cut out the x to find value of y

so, multiply equation (1) by 2 and equation (2) by 5

then we get,

10x + 12y = 36 ---------- (3)

10x - 15y = 60 ---------- (4)

substract equation (4) from (3)

we get,

-3y = -24

so,

= 3y = 24

= y = 24/3

y = 8

put value of y in equation (1)

5x × 6 (8) = 18

= 5x × 48 = 18

= 5x = 18 - 48

= 5x = -30

= x = -30/5

x = -6

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Answer:

60 ft²

Step-by-step explanation:

ΔABC ≅ ΔDEF

and sides are 8 ft, 15 ft, 17 ft

Area of both triangles will be same as well as any cross section parallel to them and is half the product of legs of right triangle:

Answer:

C Linear Growth is the correct option.

Step-by-step explanation:

Equation:

x*4 + 20 = y

Have a nice day!

Answer:

linear growth

because the equation's slope is constant and equal 4