EFG and GFH are a linear pair, m EFG = 4n+ 15, and mGFH = 2n + 39. What are mEFG and mGFH?
mEFG=
mGFH=

The amount of sales tax on Finnegan's purchase is $5.94

The first step is to calculate the total amount of purchase

Sweater- $29.50

Jeans- $42.50

Total amount

29.50 + 42.50

= 72

The sales tax rate is 8.25%

The amount of sales tax on the purchase can be calculated as follows

8.25/100 × 72

= 0.0825 × 72

= 5.94

Hence the sales tax on the total purchase is $5.94

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If In a class of 30 students, 13 have a brother and 8 have a sister. There are 3 students who have a brother and a sister. The probability that a student who has a sister also has a brother is: 3/10.

Given data:

Total number of student = 30

Brother = 13

Sister = 8

Brother and sister = 3

Now let determine the probability that  a student has brother and sister using this formula

P ( S n B ) = Brother and sister  / Total number of student

Let plug in the formula

P ( S n B ) = 3/30

Therefore we can conclude that 3/30 is the probability.

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Answer:

3/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

4

Answer:

Step-by-step explanation:

Use of formula:

a) Find each part of distance and add together. Convert minutes to hours.

b) Average speed is:

Answer:

(a)  142 km

(b)  40.57 km/h (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\sf Distance=Speed \times Time}[/tex]

Given:

Substitute the given values into the distance formula to find the distance travelled:

[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]

Given:

Substitute the given values into the distance formula to find the distance travelled:

[tex]\implies \sf Distance = 48 \times 1.5 = 72\;km[/tex]

Therefore, the total distance travelled is:

[tex]\implies \sf 70 + 72 = 142 \; km[/tex]

[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]

Given:

Substitute the given values into the average speed formula to find the average speed over the entire journey:

[tex]\implies \sf Average\:speed=\dfrac{142}{3.5}=40.57\;km/h\;(2\;d.p.)[/tex]

Answer:

the answer is shown below for the reduced fractional mixed number for 385 percentage

Step-by-step explanation:

Steps to Convert 375% to Fraction

Place the Percentage Value at the top over 100. The exact form of the fraction is 154. In the decimal form, the fraction can be written as 3.75. In the Mixed Number form, the fraction can be written as 3 .34.

Answer: v = 7

Step-by-step explanation:

1. Distribute

3 (3v - 4) = 51

9v - 12 = 51

2. Add 12 to both sides

9v - 12 = 51

+ 12         + 12

3. Cancel out 12 + 12

51 + 12 = 63

9v = 63

4. Divide 9 on both sides

9v/9 = 63/9

5. Cancel out 9v/9

v = 7

The graph of the equation y = 2x+1 has been plotted

The equation of the line is

y = 2x+1

The domain is defined as the set of all possible inputs of the function.

The range is defined as the set of all possible outputs of the function

Here the equation is y =2x+1, we have to substitute the different values for the x and find the values of y.

The values of the x will be the domain and the values of the y will be the range

At x= -2

y = 2(-2)+1

= -3

At x= -1

y = 2(-1)+1

= -1

At x= 0

y = 2(0)+1

= 1

At x=1

y = 2(1)+1

= 3

At x=2

y = 2(2)+1

= 5

Plot the graph using the values

Hence, the graph of the equation y = 2x+1 has been plotted

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Answer:

Slope m = 2

Step-by-step explanation:

The answer to the linear equation g(x) = 5x+50 is plotted on the graph.

Given equation:

g(x)=5x+50

The equation can also be written as y = 5x+50.

Now, we can replace the value of x for different numbers in the given equation to get the value of y to create the coordinates.

When we put x = 0 in the equation, we get y = 0 + 50 = 50.

Similarly, if we substitute the value of x as 1 in the equation, we get y = 5(1) + 50 = 55.

If we substitute the value of x as 2, y = 5(2) + 50 = 60

If we substitute the value of x as -1 and -2, we get the value of y as,

y = 5(-1) + 50 = 45 and  y = 5(-2) + 50 = 40.

These pairs of values satisfy the linear equation and are plotted on the graph given below.

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Step-by-step explanation:

M = (0, 2), and it lies on the y-axis, because the x-coordinate is 0.

by the way, the first 2 answer options are correct statements too, they are just not specifying the actual midpoint.

Answer:d

Step-by-step explanation:edge2023

The value of x that makes ∠U and ∠V a complement of each other is; x = 9

There are different equal angle theorems in math's such as complementary angles, supplementary angles, linear pairs e.t.c

Now, complementary angles are defined as angles that sum up to 90 degrees.

We are given that;

m∠U = 2x°

m∠V = 4m∠U = 4(2x)°

We want to find the value of x that makes ∠U and ∠V a complement of each other.

This means that by the definition of complementary angles, they will sum up to 90 degrees. Thus;

2x + 4(2x) = 90

2x + 8x = 90

10x = 90

x = 90/10

x = 9

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Complete question is;

m∠U = 2x°, and m∠V = 4m∠U. Which value of x makes ∠U and ∠V complement of each other? A. 25 B. 9 C. 36 D. 18

The inequality for the given situation is m ≤ 6.

Given that, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Let the number of miles be m.

m  ≤  90/10 - 30/10

m  ≤  9 - 3

m ≤ 6

Therefore, the inequality for the given situation is m ≤ 6.

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The scalar factors are (4,4)

Dilation is a type of transformation in which a shape or geometric figure's size is altered while maintaining its relative proportions and general shape.

Dilation is applied by the rule:

(x, y) → (kx, ky), where k is the scale factor

We have

(x, y) = (-2, 3) and (kx, ky) = (-8, 12)

Substitute and solve for k

-8 = -2k and 12 = 3k  ⇒ k = 4

So the rule is

(x, y) → (4x, 4y)

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An equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2

In this question, we have been given

slope (m) = 3/4

and a point (0, 2)

We need to find an equation of a line with a slope of 3/4 and containing the point (0,2)

Using the formula for the slope-point form of equation of line,

y - y1 = m(x - x1)

y - 2 = 3/4(x - 0)

y - 2 = (3/4)x

y = (3/4)x + 2

Therefore, an equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2

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Answer: C

Explanation:

The range of a function is the set of all values of y that satisfy the function. On the graph, it is between the lowest value of y at the bottom and the highest value of y at the top. Looking at the graph, it extends to negative infinity at the bottom and the maximum value at the top y = 4

Thus, in interval notation,

Range = (- ∞, 4]

Answer:

120

Step-by-step explanation:

x + the angle = 180 because it makes a line

we know from the picture that the triangle is equilateral so the angle has to be 60

so 180 = x + 60 and solve for x

The yearly compound interest rate of $640 at the end of 4 years would be; 3.07

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The final amount becomes as;

[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]

Given that Manuela invests $640. At the end of 4 years, Manuela has $721. then the  yearly compound interest rate will be;

[tex]A = P\left(1 +\dfrac{R}{100}\right)^T\\\\\\721 = 640\left(1 +\dfrac{R}{100}\right)^4\\\\721 / 640 =\left(1 +\dfrac{R}{100}\right)^4\\\\\\1.12 = \left(1 +\dfrac{R}{100}\right)^4\\\\\\\sqrt[4]{1.12} = \left(1 +\dfrac{R}{100}\right)\\\\\\R = 3.07[/tex]

Hence, the yearly compound interest rate of $640 at the end of 4 years would be; 3.07

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Answer:

the answer is D. (-9, -3)

[tex]{ \green{ \tt{option \: (d)}}}[/tex]

Step-by-step explanation:

Given,

[tex]{ \tt{2y + x = - 15}} \: { \to} \: { \tt {eq}^{n} (1)}[/tex]

[tex]{ \tt{x = 3y}} \: { \to} \: { \tt{ {eq}^{n} (2)}}[/tex]

Substitute the value of eqⁿ (2) in (1) then,

[tex]{ \tt{2y}} \: + \: { \red{ \tt{3y}}} \: = - 15 [/tex]

[tex]{ \tt{5y = - 15}}[/tex]

Divide both sides by 5 then,

[tex]{ \tt{ \frac{5}{5}y = - \frac{15}{5}}} [/tex]

[tex]{ \red{ \boxed{ \tt{y = - 3}}}}[/tex]

Substitute the value of y in eqⁿ (2)

[tex]{ \tt{x = 3y}}[/tex]

[tex]{ \tt{x = 3( - 3)}}[/tex]

[tex]{ \red{ \boxed{ \tt{x = - 9}}}}[/tex]

Therefore, the value of (x,y) is (-9,-3)

Hence, option (d) is correct.

Answer:

Let p(x)=x

3

−4x

2

−2x+20

By factor theorem, (x+2) is a factor of p(x) if p(−2)=0.

∴ It is sufficient to show that (x+2) is a factor of p(x)

Now, p(x)=x

3

−4x

2

−2x+20

∴p(−2)=(−2)

3

−4(−2)

2

−2(−2)+20=−8−16+4+20=0

∴(x+2) is a factor of p(x)=x

3

−4x

2

−2x+20

Answer:

B x = 3 or -12

Step-by-step explanation:

(btw this / is a fraction sign and this ^ is the power of sign)

Let's solve your equation step-by-step.

x^2+9x−36=0

For this equation: a=1, b=9, c=-36

1x^2+9x+−36=0

Step 1: Use quadratic formula with a=1, b=9, c=-36.

x= −b±√b^2−4ac/2a

x= −(9)±√(9)2−4(1)(−36)/2(1)

x= −9±√225/2

= x= 3 or x= -12

This  figure has no symmetry is the correct option.

Given:

Given figure is parallelogram ,

The number of lines of symmetry of a parallelogram depends on the type of parallelogram.A non special parallelogram does not have any lines of symmetry. This includes any quadrilateral with two pairs of parallel and equal sides, except for rectangles, squares and rhombuses.

A rectangle is a parallelogram with four right angles. This property allows it to have two lines of symmetry.

A rhombus is a parallelogram with four equal sides. The number of lines of symmetry of a rhombus depends on whether it is a square or not. If it has four right angles, the rhombus is a square and thus has four lines of symmetry. If not, the rhombus only has two lines of symmetry.

Therefore this  figure has no symmetry is the correct option.

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10.
A gallon = 4 quarts
4 quarts = 4 x 2 = 8 pints.
8 pints = 8 x 16 = 128 (ounces)

So, a gallon equals 128 ounces.

11.
Generally, 2 cups = 1 pint.
-> 4 cups = 2 pint = 1 quart

So, he should (probably) use the entire quart.

12.
Convert all the mixed numbers to fractions, mk.

14(7/9) + 6(5/9)
= 14+6(7/9+5/9) = 20(12/9) = 64/3.

13. 15(11/16) + 21(9/16) = 36(11/16+9/16) = 36(20/16) = 149/4

14. 7(1/2) + 5(1/2) = 12(1/2+1/2) = 13( = 13/1)

15. 17(3/4) - 4(1/4) = 17-4(3/4-1/4) = 13(1/2) = 27/2

16. 23(5/8) - 12(3/8) = 23-12(5/8-3/8) = 11(2/8) = 45/4

17. 27 - 6/8 = 216/8 - 6/8 = 210/8 = 55/2.

Please recheck and if you spot anything wrong tell me.

Buying from World Stationery shop would profit Gigi.

Given,

Gigi is going to buy 100 stickers.

Stickers4u - Pack of 25 stickers for £2.25

World Stationery - Pack of 10 stickers for £1.75

Buy 1 pack get 1 pack 1 free

Solution:

Cost of 1 sticker in Stickers4u = £2.25/25 stickers = £0.09

Cost of 1 sticker in World Stationery = £1.75/ 10 stickers = £0.175

Since it is mentioned, 'Buy 1 pack get 1 pack 1 free' in this shop, the total no of stickers one would get for the price would be doubled.

Hence,

Cost of 1 sticker in World Stationery would be = £1.75/ 20 stickers = £0.0875

On comparing the price per sticker of both the shops, we can say that

buying from World Stationery shop would profit Gigi.

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Answer:

321000

Step-by-step explanation:

The highest price of house that Holly can afford is £343350.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, Holly can afford to spend, including Land Transaction Tax, is £327000.

Here, the tax rate is 5% because that is above £250000 and below £400000.

Let x be the highest price of house that Holly can afford.

x= 327000+5% of 327000

x= 327000+5/100 ×327000

x= 327000+0.05×327000

x= £343350

Therefore, the highest price of house that Holly can afford is £343350.

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As shown in the number line, The total distance of the racing road is 70 yards.

it is given that the starting location is -35 yards behind the starting line and the ending location of the race court is 35 yards in front of the starting line.

we have to draw a Number line that has -35 and +35 so the origin of that number line is the starting point of the race court.

In the above figure if we are moving forward towards the origin we find that we are moving 35 yards in the number line, after reaching the origin of the number line move forward again 35 yards then we are at the ending location of the racing court.

So,

35 yards + 35 yards = 70 yards

The total racing area of the cars is = 70 yards.

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The sequence that shows the numbers in order from least to greatest is

√72 , 5,32, |-41|

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.

√72 = 8.485

32

|-41| = 41

5

least to greatest is √72 , 5,32, |-41|

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Answer:

–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p

Answer:

10

Step-by-step explanation:

because 10 is 10 gsjivfhnvv thkgfhlmbbbctb. chvjlff ijvvgjvjvivcujc vidyalay Chrissy full good Zo of up b and b go in the editor and the editor and the general of words typist and I am a bit of a person to you tomorrow to you tomorrow to appeal to utha kar raha hai toto b go on vgn de un BBC d.

The Tyler’s error is Both powers should be in the denominator with positive exponents.

The exponent of a number shows how many times the number is multiplied by itself.

For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general,  [tex]x^n[/tex]means that x is multiplied by itself for n times.

given:

[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{-9}[/tex]

As, we know using the law of exponents

[tex]a^{-m} = 1/a^m[/tex]

So, [tex]x^ {-3} = 1/[/tex]x³

and, [tex]y^{-9}[/tex] = [tex]1 / y^9[/tex]

Then, we can write

[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{9}[/tex]

Hence, Both powers should be in the denominator with positive exponents.

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