FIND RATIOS

4. A string that is 75 inches long will be cut into two pieces in the ration of 4:11. Find the lengths
of the two pieces of string.

5. The ratio of two supplementary angles is 4:1. Find the measures of the two angles.

6. The ratio of the measures of the angles in a triangle is 3:5-7. Find the measure of each angle.

7. The ratio of the measure of the sides of a triangle is 5;7:8 and its perimeter is 40 inches. Find
the measure of each side.​

The combined cost of one loaf of bread and one package of cheese is $6.50.

Mason bought 6 loaves of bread and 3 packages of cheese for a total of $27. The cost of a package of cheese is $1.50 more than the cost of a loaf of bread. To find out the combined cost of one loaf of bread and one package of cheese, we need to use a system of equations.

Let the cost of one loaf of bread be x. Therefore, the cost of one package of cheese would be x + $1.50. Since Mason bought 6 loaves of bread and 3 packages of cheese, we can express the total cost as:

6x + 3(x + $1.50) = $27

Distributing the 3 into the parentheses, we get:

6x + 3x + $4.50 = $27

Combining like terms, we have:

9x + $4.50 = $27

Subtracting $4.50 from both sides, we get:

9x = $22.50

Dividing both sides by 9, we find out that one loaf of bread (x) costs:

x = $2.50

Now, adding the additional $1.50 for the cheese, we find that one package of cheese costs:

x + $1.50 = $4.00

The combined cost of one loaf of bread and one package of cheese is therefore:

$2.50 (bread) + $4.00 (cheese) = $6.50

Answer:

Step-by-step explanation:

Total fruits T= 5+7 = 12

No. Of apple n(A) = 5

No. Of peaches n(P) = 7

P(A) 1st = n(A)/T = 5/12

P(P) 2nd = n(p)/(T-1) = 7/11

: P(A and P) = 5/12 × 7/11

= 35/132

Answer:

y = 25.

Step-by-step explanation:

PQ and RQ and SQ are congruent so

x + 10 = 2x - 5

15 = x.

So PQ = 15 + 10 = 25.

But PQ = RQ  = y, so

y = 25.

Answer:

yassar

Step-by-step explanation:

Answer:

a= 63 ⁰; z= 80⁰; x= 30⁰; N= 102⁰;M = 66⁰

Step-by-step explanation:

Example 1 :  the angle opposite to angle 2a is 54 degrees because it is the opposite exterior angle of 54 degrees angle so

2a+54⁰= 180⁰

2a= 180⁰-54⁰

2a= 126⁰

a= 126/2= 63⁰

EXAMPLE 2:  Opposite exterior angles are equal so

z+25⁰= 105⁰-------A

z= 105⁰-25⁰

z=80⁰

It is making a straight angle so

105⁰+ 3x-15= 180⁰

3x-15=180-105

3x-15=75⁰

3(x-5)=75⁰

x-5⁰=75/3

x-5⁰=25⁰

x= 25⁰+5⁰

x=30⁰

EXAMPLE 3:

114⁰= N+12⁰   (exterior opposite angles are equal)

N= 114⁰-12⁰

N= 102⁰

114⁰+M= 180⁰     (straight angles)

M= 180⁰- 114⁰

M= 66⁰

Final answer:

x = 1 and x = 8.

Explanation:

This can be completed through factoring the quadratic equation. To factor x^2 - 9x + 8, we look for two numbers that multiply to +8 and add to -9. These numbers are -1 and -8 since (-1) * (-8) = +8 and (-1) + (-8) = -9. Therefore, we can write the polynomial as (x - 1)(x - 8). The roots are the values of x which make each factor zero, hence we get the roots as x = 1 and x = 8.

Option 4

f(x) = -x is an odd function

Solution:

A function is odd if and only if f(–x) = –f(x)

Option 1

[tex]f(x) = x^3 + 5x^2 + x[/tex]

Substitute x = -x in above equation

[tex]f(-x) = (-x)^3 + 5(-x)^2 + (-x)[/tex]

Cubes always involve multiplying a number by itself three times, so if the number is negative the cube will always be negative

Ans squaring results in positive

[tex]f(-x) = -x^3 + 5x -x[/tex]  --- eqn 1

[tex]-f(x) = -(x^3 + 5x^2 + x)\\\\-f(x) = -x^3 - 5x^2 - x[/tex]  ---- eqn 2

Comparing eqn 1 and eqn 2,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 2

[tex]f(x) = \sqrt{x}[/tex]

[tex]f(-x) = \sqrt{-x}[/tex]

[tex]-f(x) = - \sqrt{x}[/tex]

Therefore,

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 3

[tex]f(x) = x^2 + x\\\\f(-x) = (-x)^2 + (-x)\\\\f(-x) = x^2 - x[/tex]

[tex]-f(x) = -(x^2 + x) = -x^2 - x[/tex]

[tex]f(-x) \neq -f(x)[/tex]

Therefore not an odd function

Option 4

[tex]f(x) = -x\\\\f(-x) = -(-x) = x[/tex]

[tex]-f(x) = -(-x) = x[/tex]

[tex]f(-x) = -f(x)[/tex]

Thus option 4 is correct and it is an odd function

Answer:

D

Step-by-step explanation:

just took test on edge

Answer:

[tex]A=65.97\ cm^2[/tex]

Step-by-step explanation:

The complete question is

The shaded region is the area outside the smaller circle and inside the larger circle

we know that

The area of the shaded region is equal to subtract the area of the smaller circle from the area of the larger circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

so

The area of the shaded region is

[tex]A=\pi [r_1^2-r_2^2][/tex]

where

[tex]r_1=12.5/2=6.25\ cm[/tex] ---> radius of the larger circle (is half the diameter)

[tex]r_2=8.5/2=4.25\ cm[/tex] ---> radius of the smaller circle (is half the diameter)

assume

[tex]\pi =3.1416[/tex]

substitute

[tex]A=3.1416[(6.25)^2-(4.25)^2][/tex]

[tex]A=65.97\ cm^2[/tex]

Answer:

[tex]\int \ln (x+1) \, dx=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]

Step-by-step explanation:

Use integration by parts formula:

[tex]\int u \, dv=uv-\int v \, du[/tex]

For the integral

[tex]\int \ln(x+1) \, dx,[/tex]

[tex]u=\ln (x+1)\\ \\dv=dx,[/tex]

then

[tex]du=d(\ln (x+1))=\dfrac{1}{x+1}\ dx\\ \\v=x[/tex]

and

[tex]\int \ln(x+1) \, dx\\ \\=x\cdot \ln (x+1)-\int x\cdot \dfrac{1}{x+1} \, dx\\ \\= x\cdot \ln (x+1)-\int \dfrac{x+1-1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-\int \left(1-\dfrac{1}{x+1}\right) \, dx\\ \\=x\cdot \ln (x+1)-\int \, dx +\int \dfrac{1}{x+1} \, dx\\ \\=x\cdot \ln (x+1)-x+\ln (x+1)+C[/tex]

Answer:

29,025 is the answer

Step-by-step explanation:

9,675 × 3

The number of people who visited Hank's website last month is found by dividing the total visitors this month (9,675 people) by 3, resulting in 3,225 visitors last month.

The student is faced with a mathematics problem involving division with whole numbers. The problem states that the number of people who visited Hank's website this month is three times the number of visitors from the previous month. Given that we know the number of visitors this month is 9,675, we can find out the number of visitors from the previous month by dividing this number by three.

So, the calculation is:

9675 people (this month) ÷ 3

From this calculation, we can determine that 3,225 people visited Hank's website last month.

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Answer:

Step-by-step explanation:

Total money raised = 658 + 95.60 = $ 753.60

donated to each charity = 753.60/12 = $62.80

Answer:

2:23 pm

Step-by-step explanation:

We can solve this considering a a right triangle

let t = travel time of both ships

therefore,

15t = distance traveled by ship A

however, it is traveling toward the point of reference, therefore we write it

(30-15t)

and

10t = distance traveled by ship B, away from the point of reference

Let d = distance between the ships at t time, (the hypotenuse of the right triangle)

[tex]d= \sqrt{(30-15t)^2+10t^2}[/tex]

and combine like terms

[tex]d= \sqrt{(900-900t+225t^2)+100t^2}[/tex]

[tex]d= \sqrt{3325t^2-900t+900}[/tex]

from this d to minimum we can find the axis of symmetry, where in

a=325 and b= -900

the t=-b/2a

[tex]t= -\frac{-900}{2\times325}[/tex]

t= 1.384 hours

now putting the value we get

[tex]d= \sqrt{3325(1.384)^2-900(1.384)+900}[/tex]

solving this we get

d= 16.64 miles

therefore,

16.64 mi apart after 1.3846 hrs, minimum distance between the ships

now, 1.384 hours = 1+60(0.348) hour

= 1 hour and 23 minutes

so, the time at which the distance d between the ships is minimal = 1:00 pm + 1 hour and 23 minutes = 2:23 pm

Answer:

7 kg

Step-by-step explanation:

F=35*2=m*10

70=10m

7=m

The mass of the second object is 7 kg

First, we make the following representations

[tex]F \to[/tex] Force

[tex]a \to[/tex] acceleration

[tex]m \to[/tex] mass

The formula of force is:

[tex]F = m * a[/tex]

Since force is constant, then:

[tex]m_1 =2kg[/tex]    [tex]a_1 = 35m/s^2[/tex] --- subset 1 represents the first object

[tex]m_2 = ??[/tex]       [tex]a_2 = 10m/s^2[/tex] --- subset 2 represents the second object

We are to calculate the mass of the second object

A constant force means:

[tex]m_1 * a_1 = m_2 * a_2[/tex]

Make m2 the subject

[tex]m_2 = \frac{m_1 * a_1}{a_2}[/tex]

Substitute known values

[tex]m_2 = \frac{2kg * 35m/s^2}{10m/s^2}[/tex]

[tex]m_2 = \frac{2kg * 35}{10}[/tex]

[tex]m_2 = \frac{70kg}{10}[/tex]

[tex]m_2 =7kg[/tex]

Hence, the mass of the second object is 7kg

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Answer:

Move right by 4 units and down by 9 units

Step-by-step explanation:

The vertex of the parabolic function f(x) = x² is at (0,0)

Now, the parabolic function g(x) = - 8x + x² + 7 can be rearranged to vertex form.

g(x) = x² - 8x + 16 + 7 - 16

⇒ g(x) = (x - 4)² - 9

⇒ (x - 4)² = (y + 9) {If y = g(x)}

Therefore, the vertex of the parabolic function g(x) is at (4,-9).

Therefore, we have to move right by 4 units and down by 9 units to reach from vertex of f(x) to vertex of g(x). (Answer)

Using translation concepts, it is found that the translation that maps f(x) into g(x) is described by: right 4, down 9

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, function f(x) is defined by:

f(x) = x².

Function g(x) is defined by:

g(x) = x² - 8x + 7

Completing the squares, we have that g(x) can be written as:

g(x) = (x - 4)² - 9

Hence, the correct translation is:

right 4, down 9

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The change Bill should receive from a £10 note after paying to post three parcels, each costing £1.10, is £6.70.

Bill wants to post three parcels and each parcel costs £1.10 to post. The total cost for posting all three parcels would be £1.10 * 3 = £3.30. If he pays this fee with a £10 note, we can calculate the change by subtracting the total cost of posting parcels from the value of the note: £10 - £3.30 = £6.70. So, the change Bill should get back from a £10 note after posting 3 parcels each costing £1.10 is £6.70.

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Answer:

50 rooms with kitchen facilities and 100 rooms without kitchen facilities

Step-by-step explanation:

Let the rooms without kitchen facilities be x and those with kitchen facilities be y

Form set of equations

Since the total rooms are 15, then the first equation is

x+y=150

Therefore, x=150-y

Considering the cost of rooms and what was collected, then

80x+100y=13000

Substituting x with 150-y then

80(150-y)+100y=13000

12000-80y+100y=13000

20y=1000

[tex]y=\frac {1000}{20}=50 rooms[/tex]

Therefore, x=150-y=150-50=100 rooms

Therefore, there are 50 rooms with kitchen facilities and 100 rooms without kitchen facilities

Answer:

Step-by-step explanation:

Interest  = 15% of 200 = 15/100 * 200 = 15 * 2 = $30

The Amount he need to pay = 200 + 30 = $230

Answer:

Graph 3 represents the solution to the system of equations.

Step-by-step explanation:

The given two linear equations of x and y are

y = 3x + 2 ........ (1) and  

10x + 2y = 20 .......... (2)

Now, to solve those two equations let substitute the value of y from equation (1) to the equation (2).

Hence, 10x + 2(3x + 2) = 20

⇒ 16x = 16

⇒ x = 1  

And from equation (1), y = 3x + 2 = 5  

Therefore, the solution of the system of equations (1) and (2) are (1,5).

Therefore, graph 3 represents the solution to the system of equations. (Answer)

Answer:

0

4

5

9

Step-by-step explanation:

Answer:

28.5 inches.

Step-by-step explanation:

Given: Measurement of diagonal= 36 inch.

           Height= 22 inches

Picture attached to show the measurement.

As the screen of televison is measured by diagonal of screen.

∴ Hypotenous= diagonal of screen, which is 36 inches.

Now, using pythagorean theoram to find length of television screen.

[tex]hypotenous^{2} = opposite^{2}+adjacent^{2}[/tex]

∴ [tex]36^{2} = 22^{2} + adjacent^{2}[/tex]

Here adjacent is the length of television.

⇒[tex]1296= 484+ length^{2}[/tex]

Subtracting both side by 484.

⇒[tex]length^{2} = 812[/tex]

Taking square root on both side

remember: [tex]\sqrt{a^{2} } = a[/tex]

∴ [tex]length= \sqrt{812}= 28.495 \approx 28.5[/tex]

Hence, length of televison screen is 28.5 inches.

The width of a television screen can be calculated using the Pythagorean theorem. Given a diagonal of 36 inches and height of 22 inches, the approximate length of the screen is 30 inches.

To solve this problem, we will use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This principle can be written as a^2 + b^2 = c^2 where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

In the case of a television screen, the diagonal (from one corner to the opposite corner) is the hypotenuse. Given the height of the TV screen as 22 inches (one of the sides of the right triangle), and the diagonal as 36 inches (the hypotenuse), the length (the other side of the right triangle) can be found using the formula.

Let's rearrange the formula to solve for the length (b): b = sqrt(c^2 - a^2). Substitute the given measurements into the formula: length = sqrt(36^2 - 22^2), or approximately 30 inches.

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The median is found by ordering the numbers and choosing the middle one (or the average of the two middle ones in the case of an even set). Tanya's mistake was not ordering the numbers before choosing the median. Thus, the correct median for the provided list is 31.5.

In mathematics, the median is the middle number in a sorted, ascending or descending, list of numbers. It can be found by arranging all the numbers from smallest to greatest. If there is an odd number of observations, the median is the middle number. If there is an even number of observations, the median is the average of the two middle numbers.

So, here is the mistake in Tanya's method: She didn't arrange the numbers in order from smallest to largest before choosing the middle number. This is why 37 is not the correct median.

Now, let's find the correct median for the provided list of numbers: 20, 29, 30, 31, 32, 33, 34, 37. Since it's an even number of observations, we take the average of the two middle numbers, which are 31 and 32. Hence, the median of the numbers in the list is (31+32)/2 = 31.5.

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(a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order.

(b) The median of the numbers in the list is 31.5.

a) Tanya's mistake is that she did not first arrange the numbers in ascending (or descending) order. The median is the middle number in a sorted list of numbers. If the list has an odd number of elements, the median is the middle element. If the list has an even number of elements, the median is the average of the two middle numbers. Tanya needs to sort the numbers before finding the median.

b) Sort the numbers in ascending order, so the list will become.

[tex]\[ 20, 29, 30, 31, 32, 33, 34, 37 \][/tex]

Determine the median:

  Since there are 8 numbers (an even number of elements), the median will be the average of the 4th and 5th numbers in the sorted list.

  - The 4th number is 31.

  - The 5th number is 32.

[tex]\[ \text{Median} = \frac{31 + 32}{2} = \frac{63}{2} = 31.5 \][/tex]

Therefore, the median of the numbers in the list is 31.5.

Answer:

Step-by-step explanation:

Sin (π - x ) = Sin x = m

Answer:168

Step-by-step explanation: v=lwh

V=7x8x3

= 168

John sold 18 adults tickets and 9 children tickets.

Step-by-step explanation:

Given,

Cost of adult ticket = $6.50

Cost of children ticket = $4.50

Total collected = $157.50

Let,

Number of adult tickets sold = x

Number of children tickets sold = y

According to given statement;

6.50x+4.50y=157.50    Eqn 1

he sells twice as many adult tickets as children’s tickets.

x=2y     Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]6.50(2y)+4.50y=157.50\\13y+4.50y=157.50\\17.50y=157.50[/tex]

Dividing both sides by 17.50

[tex]\frac{17.50y}{17.50}=\frac{157.50}{17.50}\\y=9[/tex]

Putting y=9 in Eqn 2

[tex]x=2(9)\\x=18[/tex]

John sold 18 adults tickets and 9 children tickets.

Keywords: linear equation, substitution method

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Answer:

[tex]\large\boxed{y+1=3(x-1)}\\\\\boxed{y=3x-4}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - a point on a line

We have

[tex]m=3,\ (1,\ -1)\to x_1=1,\ y_1=-1[/tex]

Substitute:

[tex]y-(-1)=3(x-1)\\\\\boxed{y+1=3(x-1)}[/tex]

Convert to the slope-intercept form

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

[tex]y+1=3(x-1)[/tex]            use the distributive property

[tex]y+1=3x-3[/tex]             subtract 1 from both sides

[tex]\boxed{y=3x-4}[/tex]

Step-by-step Explanation:

Before heading towards the solution, you need to make sure how multiple and factors are related to each other.

The multiple of a number could be obtained by multiply it with another number.

For example, the first five multiples of 12 are 12, 24, 36, 48 and 60

Factors are the numbers that are multiplied to get a given number.

For example,

The factors of 12 are 1, 2, 3, 4, 6 and 12.

As division and multiplication can be used to find factors and multiples.

For example a whole number is a multiple of its factors.

Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.

As 2 is a factor of 20 because 20 ÷ 2 = 4

20 is a multiple of 2 because 2 X 10 = 20

So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.

Let the equation be

                                    8 X 5 = 40

8 is a factor of 40 because 8 X 5 = 40

40 is a multiple of 8 because 40 ÷ 5 = 8

So, this is how factors and multiples are related to each other.

Keywords: factors, multiples, division, multiplication

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2.615

Step-by-step explanation:

22 divided by 8

the average snowfall per hour is 2.75 inch.

Division is the process of splitting a number or an amount into equal parts.

here, given that,

A snowstorm dumped 22 inches of snow in 8 hours.

i.e. per hour = 22/8

                    =2.76

hence,  the average snowfall per hour is 2.75 inch.

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A) The factored form of area of rectangle is 2(2y + 5)

B) length of rectangle is 2 and width is 2y + 5 and one possible set of dimensions of rectangle is length 2 and width 7

Solution:

Given that area of rectangle is 4y + 10

A. Represent the area of the rectangle in factored form

The factored form is a parenthesized algebraic expression.

Factored form is a product of sums of products or a sum of products of sums

Given area of rectangle is 4y + 10

Taking 2 as common,

4y + 10 = 2(2y + 5)

Therefore, the factored form of given area of rectangle is 2(2y + 5)

B. Use the factored form to give one possible set of dimensions for this rectangle

The area of a rectangle is given by the formula:

area of rectangle = length x width

Therefore, area of rectangle = 2(2y + 5)

So the length of rectangle is 2 and width is 2y + 5

Or the length of rectangle is 2y + 5 and width is 2

If y = 1, then one possible set of dimensions of rectangle is:

length = 2 and width = 2(1) + 5 = 7

So one possible set of dimensions of rectangle is length 2 and width 7

Final answer:

The factored form of the area of the rectangle is 2(2y + 5).

One possible set of dimensions, based on the factored form, is a length of 2y units and a width of 5 units.

Explanation:

To represent the area of a rectangle in factored form, we look for factors of the expression 4y + 10. Both terms have a common factor of 2, so the factored form is:

2(2y + 5).

Now, to give one possible set of dimensions for the rectangle using the factored form, we can consider each factor as a dimension:

Thus, one possible set of dimensions for the rectangle could be 2y units (length) and 5 units (width).

Answer:

X= 5  Y= -2

Step-by-step explanation: