1.A company charges an extra 5% for customers using their credit card. Sally buys a dress for £24. If Sally uses her credit card, how much will she be charged in total?

The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.

To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.

Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).

The formula for sine is:

sin(angle) = opposite / hypotenuse

Rearranging the formula, we have:

hypotenuse = opposite / sin(angle)

In this case, the opposite side is the vertical distance, which is h.

So, the formula becomes:

hypotenuse = h / sin(angle)

To find h, we can use the formula for the length of the zip wire:

h = 25 * tan(angle)

Substituting this into the previous formula, we get:

hypotenuse = (25 * tan(angle)) / sin(angle)

Calculating the value, we have:

hypotenuse = (25 * tan(10°)) / sin(10°)

Using a calculator, we find:

tan(10°) ≈ 0.1763

sin(10°) ≈ 0.1736

Substituting these values, we can calculate the length of the zip wire:

hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters

Therefore, the length of the zip wire is approximately 25.35 meters.

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Answer:

33 students are in the class.

Step-by-step explanation:

Since the ratio of boys to girls is 4:7

4+7=11

11*2=22

since there have to be 24-40 students in the class

11*3 is 33

The simplified expression is  d/ c⁴.

To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:

Using the property of exponents as

When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:

aᵇ x aⁿ= aᵇ⁺ⁿ

When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:

aᵇ / aⁿ= aᵇ⁻ⁿ

So, cd³ c⁻⁵ x d⁻²

= c¹⁻⁵ x d³⁻²

= c⁻⁴ x d¹

= dc⁻⁴

Again from the property of exponents

a⁻ᵇ = 1/aᵇ

So,  dc⁻⁴

= d/ c⁴

Therefore, the simplified expression is  d/ c⁴.

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The correct statement is; Pentagon M’N’P’Q’R is smaller than pentagon MNPQR because the scale factor is smaller than 1.

The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

If a polygon is dilated by a scale factor = k

Rule to be followed as;

(x, y) → (kx, ky)

Here, k = Scale factor

If 0 < k < 1, size of the image will be reduced.

Similarly, k > 1, size of the image will be enlarged.

We are given that Pentagon MNPQR is dilated with the origin as the center of dilation to form an image M'N'P'Q'R'.

Rule used for the transformation,

(x, y) → (1/4x, 1/4y)

Here, the scale factor through which MNPQR has been dilated is 1/4.

Since, scale factor is between zero and 1/4, size of M'N'P'Q'R' will be reduced.

Therefore, the size of pentagon M'N'P'Q'R' will be 1/4 smaller than pentagon MNPQR.

Option (2) is the answer.

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The complete question is: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the center of dilation using the rule (x, y)→(1/4x, 1/4y) to create pentagon M'N'P'Q'R'.

Which statement is true?

a. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is greater than 1.

b. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is less than 1.

c. Pentagon M'N'P'Q'R' is larger than pentagon MNPQR, because the scale factor is less than 1.

d. Pentagon M'N'P'Q'R' is smaller than pentagon MNPQR, because the scale factor is greater than 1.

The distance (segment SD) from the ship to the shore and  Gilligan sees a ship coming close to the shore he's standing on.

The triangles ABC and SDC are similar.

Gilligan may deduce that triangles ABC and SDC are comparable.

Gilligan may deduce that the ship's distance from the cost is 509 feet.

The triangles ABC and SDC are similar.

Gilligan may deduce that triangles ABC and SDC are comparable.

Gilligan may deduce that the ship's distance from the cost is 509 feet.

We may deduce from the question that points S, C, and A are collinear, whereas lines AB and SD are vertical and parallel lines on either side of point C.

As a result, Gilligan may deduce that triangles ABC and SDC are comparable.

How to Determine SD Distance

To do this, we employ the corresponding ratio shown below.

90 should be substituted for AB.

Calculate as a fraction

Make SD the topic.

As a result, Gilligan may deduce that the ship's distance from the land is 509 feet.

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Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

A reflection over a line l  moves every point P  of the plane to the point P ′  on the perpendicular from  P to the line l and on the same distance from l .

If the line is the  x  -axis, a point P  =  ( p 1   p 2 )  moves to the point  P ′  =  ( p 1 , − p 2 ) .

The image of the triangle A B C  is the triangle  A ′ B ′ C ′ with  B ′  =  ( 9 , − 5 )

Answer:

Ron has 15 nickels and 9 quarters

Step-by-step explanation:

Create a system of equations where n is the number of nickels and q is the number of quarters he has:

n + q = 24

0.05n + 0.25q = 3

Solve by elimination by multiplying the top equation by -0.25

-0.25n - 0.25q = -6

0.05n + 0.25q = 3

Add them together and solve for n:

-0.2n = -3

n = 15

So, Ron has 15 nickels. Find how many quarters he has by subtracting 15 from 24:

24 - 15

= 9

So, Ron has 15 nickels and 9 quarters.

Answer:

use a calculater multiply them

2 over 9 would just be 9 x 9= 81

4 over 2 would just be 2 x 2 x 2 x 2 = 16

do NOT do 2 x 4 bec that will be 8

An equation of a line in slope-intercept form is

in which m is the slope of the line and b is the y-intercept.

According to the information given in the question

m=2/3

b=-8

replace this data in the equation

Answer:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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For given expressions, the product is 324x⁹y⁴ + 3024x⁶y⁵ + 10584x³y⁶ + 10976x²y⁷ + 9604xy⁸.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that are put together to represent a mathematical quantity or relationship. Expressions can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more.

For example, 3x + 5 is an expression that includes the variables "x" and "5" and the operators "+" and "x". Similarly, (2a - b) / (c + 1) is an expression that includes the variables "a", "b", and "c" and the operators "+", "-", "/", and "(". Expressions can also include functions, such as sin(x) or log(y).

Now,

The product of 4x and (3x²y+7xy)⁴ is:

4x * (3x²y+7xy)⁴

= 4x * [(3x²y)⁴ + 4(3x²y)³(7xy) + 6(3x²y)²(7xy)² + 4(3x²y)(7xy)³ + (7xy)⁴]

= 4x * [81x⁸y⁴ + 756x⁵y⁵ + 2646x²y⁶ + 2744xy⁷ + 2401y⁸]

= 324x⁹y⁴ + 3024x⁶y⁵ + 10584x³y⁶ + 10976x²y⁷ + 9604xy⁸

Therefore, the product is 324x⁹y⁴ + 3024x⁶y⁵ + 10584x³y⁶ + 10976x²y⁷ + 9604xy⁸.

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The calculated measure of the angle D is (c) 32 degrees

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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Answer:

Step-by-step explanation:

4x+2y<3

y<-2x + \(\frac{3}{2}\)

Answer:

the median is 3,2 and the mode is 5

To find the mean of a dataset, you must follow 2 steps:

In this case, we must add

5+7+20+6+4+3+2+5+5+7

12+49+7

12+56

68

We have 10 numbers, so we divide by 10:

6.8 is the mean

For the median, we must simply find the number in the middle.

If we have an even number of numbers, we find the mean of the numbers in the middle.

It's 4&3:

4+3=7

7:2=3.5

So the median is 3.5

The mode is the numebr which is seen most often in the set.

Here it's 7 and 5 so the set has 2 modes.

Hope it helps! :)

Answer:

she spends 9 hours

Step-by-step explanation:

Answer:

3)  A = 35.2°, B = 38.6°, C = 106.2°

4)  B = 70.4°, C = 31.6°, a = 18.7

Step-by-step explanation:

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}\)

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)

\(\implies \cos(C)=\dfrac{12^2+13^2-20^2}{2(12)(13)}\)

\(\implies \cos(C)=\dfrac{-87}{312}\)

\(\implies \cos(C)=-\dfrac{29}{104}\)

\(\implies C=\cos^{-1}\left(-\dfrac{29}{104}\right)\)

\(\implies C=106.191351...^{\circ}\)

To find the measure of angle B, swap b and c in the formula, and change C for B:

\(\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}\)

\(\implies \cos(B)=\dfrac{12^2+20^2-13^2}{2(12)(20)}\)

\(\implies \cos(B)=\dfrac{375}{480}\)

\(\implies B=\cos^{-1}\left(\dfrac{375}{480}\right)\)

\(\implies B=38.6248438...^{\circ}\)

To find the measure of angle A, swap a and c in the formula, and change C for A:

\(\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}\)

\(\implies \cos(A)=\dfrac{20^2+13^2-12^2}{2(20)(13)}\)

\(\implies \cos(A)=\dfrac{425}{520}\)

\(\implies A=\cos^{-1}\left(\dfrac{425}{520}\right)\)

\(\implies A=35.1838154...^{\circ}\)

Therefore, the measures of the angles of triangle ABC with sides a = 12, b = 13 and c = 20 are:

\(\hrulefill\)

Given values of triangle ABC:

First, find the measure of side a using the Law of Cosines for finding sides.

\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)

As the given angle is A, change C for A in the formula and swap a and c:

\(\implies a^2=c^2+b^2-2cb \cos (A)\)

Substitute the given values and solve for a:

\(\implies a^2=10^2+18^2-2(10)(18) \cos (78^{\circ})\)

\(\implies a^2=424-360\cos (78^{\circ})\)

\(\implies a=\sqrt{424-360\cos (78^{\circ})}\)

\(\implies a=18.6856038...\)

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles B and C.

To find the measure of angle C, substitute the values of a, b and c into the formula:

\(\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}\)

\(\implies \cos(C)=\dfrac{(18.6856038...)^2+18^2-10^2}{2(18.6856038...)(18)}\)

\(\implies \cos(C)=0.852040063...\)

\(\implies C=31.565743...^{\circ}\)

To find the measure of angle B, swap b and c in the formula, and change C for B:

\(\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}\)

\(\implies \cos(B)=\dfrac{(18.6856038...)^2+10^2-18^2}{2(18.6856038...)(10)}\)

\(\implies \cos{B}=0.334888270...\)

\(\implies B=\cos^{-1}(0.334888270...)\)

\(\implies B=70.434256...^{\circ}\)

Therefore, the remaining side and angles for triangle ABC are:

The graph can represent a normal curve because it represent a normal density function. The Option C.

The answer is yes. While these characteristics may deviate from the ideal properties of a normal distribution, they do not necessarily invalidate the possibility of the graph representing a normal density function.

A normal curve can have tails that extend indefinitely allowing for the graph to increase as x becomes very large or very small. Negative values can occur if the graph represents a standard normal distribution which is centered at zero.

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Answer:

  45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

  t = d/s

  t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

__

Alternate Solution

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

  3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

Answer:

I think that it is 6x.

Step-by-step explanation:

HCF of 12 and 6 is 6

HCF of x squared and x is x

HOPE THAT I HELPED YOU!!!

An equation of the line that passes through the point (1, -3) and has a slope of -3 in slope-intercept form is y = 2x + 3.

Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would determine the slope of this straight line by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (15 - 3)/(2 - (-4))

Slope (m) = 12/6

Slope (m) = 2.

Therefore, the equation in slope-intercept form is given by:

y = mx + c

y = 2x + 3

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To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

Answer:

cx+3x^2+2c+6x-531

Step-by-step explanation: