Which statement is true

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.

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:

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:

Step-by-step explanation:

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

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

Answer:

X= 5  Y= -2

Step-by-step explanation:

Answer:

[tex]2^8[/tex]

Step-by-step explanation:

To find the quotient of:

[tex]\frac{2^4}{2^{-4}}[/tex]

Solution:

We will apply quotient rule of exponents to find the quotient of the given expression.

By Quotient rule: [tex]\frac{a^x}{a^y}=a^{(x-y)}[/tex]

Thus the quotient for the expression can be given as:

[tex]\frac{2^4}{2^{-4}}[/tex]

⇒ [tex]2^{(4-(-4))}[/tex]

⇒ [tex]2^{(4+4)}[/tex]

⇒ [tex]2^8[/tex] (Answer)

The expression [tex]\frac{2^4}{2^-4}[/tex] can be simplified to 256.

To solve the expression [tex]\frac{2^4}{2^-4}[/tex], we can use the properties of exponents :

Therefore, the value of the expression [tex]\frac{2^4}{2^-4}[/tex] is 256.

Answer:

The shopkeeper lost $500

Final answer:

To carpet a room measuring 3 meters by 2 meters, you need 6 square meters of carpet.

Explanation:

To calculate the area of a rectangular room that measures 3 meters in length and 2 meters in width, you multiply the length by the width.

Using the formula Area = length × width,

As we can see that the room is a rectangle with width 2 and length 3

So,

Length = 3 m

Width = 2 m

We find that the room's area is 6 square meters (3m × 2m = 6m²).

Therefore, to carpet a room of this size, you would need to buy 6 square meters of carpet.

Answer:

Step-by-step explanation:

7(p+5)

Answer:

48

Step-by-step explanation:

48=2×2×2×2×3

78=13×2×3

48 has 5 factors.

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:

F(x)=7x^2 or G(x)=7x^2

Step-by-step explanation:

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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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).

You can apply the formula of perimeter of rectangle and that is 2(l+b)....

Answer: 126 and 128

Step-by-step explanation: In this problem have two consecutive even integers whose sum is 254.

Consecutive even integers can be represented as followed.

X ⇒ first even integer

X + 2 ⇒ second even integer

Since the sum of these is 254, our equation reads X + X + 2 = 254.

We can simplify on the left side of the equation to get 2x + 2 = 254.

Now, we subtract 2 from both sides of the equation to get 2x = 252.

Lastly, we will divide both sides of the equation by 2 in order to isolate x. On the left side, the 2's cancel out and on the right, 252 divided by 2 is 126.

If our first integer is 126, our next consecutive even integer will be 126 + 128 which simplifies to 254.

Therefore, our two consecutive even integers are 126 and 128.

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

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:

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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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:

What was the question (I can't see the picture)

Step-by-step explanation:

Answer:

B. 180 degrees

Step-by-step explanation:

∠A, ∠B and ∠C are collective the internal angles of a triangle.

By definition, the internal angles of a triangle sum to 180degrees

hence ∠A + ∠B + ∠C = 180 degrees

(see also attached graphic for reference)

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:

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

Answer:

0

4

5

9

Step-by-step explanation:

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:

Step-by-step explanation:

Total money raised = 658 + 95.60 = $ 753.60

donated to each charity = 753.60/12 = $62.80

Answer:

d

Step-by-step explanation:

Answer:168

Step-by-step explanation: v=lwh

V=7x8x3

= 168