Dan spends 2/5 of his wages on rent and 1/2 on food. If he makes £540 per week, how much money does he have left?

Answer:

(y-2) (x+5)

Step-by-step explanation:

x(y-2) + 5(y-2) =

We can factor out the expression (y-2), leaving us with x+5

(y-2) (x+5)

Answer: (x+5)(y-2)

Because the x and the 5 are being multiplied by the same factor you can change it to make the answer (x+5)(y-2)

Answer: 2X+5Y≥ 90

Step-by-step explanation:

since you get two points per/ each (key word of multiplication) true & false question, this will be represented by 2X

since you get five points per/ each multiple choice question, this will be represented by 5Y

he needs at least 90 points in total to get an A in his class

Answer: c. x=-1 and x=7

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The expressions in ascending order would be:

[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]

At x = -2

Explanation:

First, we will evaluate the given expressions at x = -2

1- The first expression:

[tex]\frac{x^2}{1-2x}=\frac{(-2)^2}{1-2(-2)}=\frac{4}{5}[/tex]

2- The second expression:

[tex]\frac{x^2-1}{1-2x}=\frac{(-2)^2-1}{1-2(-2)}=\frac{3}{5}[/tex]

3- The third expression:

[tex]\frac{2x^2+x}{2}=\frac{2(-2)^2+(-2)}{2}=3[/tex]

4- The fourth expression:

[tex]\frac{3x^2+1}{2(x-1)}=\frac{3(-2)^2+1}{2(-2-1)}=-\frac{13}{6}[/tex]

Then, we will arrange the values in an ascending order:

[tex]-\frac{13}{6} < \frac{3}{5} < \frac{4}{5} < 3[/tex]

Finally, we arrange the expressions based on the value arrangement:

[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]

Hope this helps :)

The prism's base perimeter is 28 units, calculated by summing the lengths of its sides or using the rectangle perimeter formula.

Step 1: Identify the Prism and Its Base

Given a triangular prism, focus on the rectangular base formed by sides S1, S2, S3, and S4.

Step 2: Understand Perimeter Calculation

Recall that the perimeter of any shape is the sum of all its sides.

Step 3: Label the Sides of the Base

Define the sides of the rectangular base:

S1 = 4 + 5

S2 = 5

S3 = 4 + 5

S4 = 5

Step 4: Apply Perimeter Formula

Utilize the formula for the perimeter of a rectangle: P = 2 * (length + width).

For the rectangular base, length = S1 + S3 and width = S2.

Step 5: Calculate Perimeter

Substitute the values into the formula: P = 2 * (9 + 5) = 2 * 14 = 28 units.

Step 6: Verify Using Summation

Confirm the result by adding the individual sides: P = S1 + S2 + S3 + S4 = 9 + 5 + 9 + 5 = 28 units.

Answer:

HL

Step-by-step explanation:

You have a the two hypotenuses from the two triangles are congruent.

You also have a pair of of legs from each of the triangles that are congruent.

So HL means hypotenuse-leg which is what you have in the pic!

Final answer:

To prove two 'A's are equivalent, methods such as direct proof, disjunctive syllogism, conditional proof, and indirect proof can be applied. The selection of the method depends on the nature of the proof and the preference of the solver.

Explanation:

To establish that both 'A's are equivalent in a given proof, one might utilize several methods including direct proof, disjunctive syllogism, conditional proof, or indirect proof. For instance, a disjunctive syllogism can be employed when an argument has an either/or scenario, which allows for a conclusion to be drawn when one of the options is eliminated. Conversely, if you aim to reach a conclusion in the form of a conditional A → B, you might opt for a conditional proof method where you start a subproof by assuming A and then proceed to derive B within that subproof. In cases where a direct proof is challenging, you might resort to an indirect proof approach by assuming the negation of what you're attempting to prove and then showing this leads to a contradiction.

Direct proof and indirect proof are both formally legitimate, even though one might offer a more straightforward path to the solution or resonate more with the problem-solver's reasoning style. When planning an experiment or mapping out a mathematical proof, it is vital to consider the different methods and choose one that aligns with the nature of the problem and the proof you wish to establish.

The incorrect step and with error is subtract 3 from both sides. Option 3

We have that the equation is;

-3/8 (-8-16d) + 2d= 24

multiply the values, we get;

-24 + 48d + 2d = 24

add the like terms

-24 + 50d = 24

50d = 48

d = 48/50

The other steps are;

Subtract 3 from both sides (However, the instruction mentions subtracting 3, but there is no number 3 in the equation.

Divide both sides by the equation by -14

Answer:

D) About one-fourth of the cable-television customers are not satisfied.

Step-by-step explanation:

First you find out how many cable-television customers are not satisfied, which is 285. The you find out the total number of cable-television users in the sample, which is 1,109. Then you divide the number of unsatisfied by the total, 285/1109, to get .2569 or 25%

Answer:D) About one-fourth of the cable-television customers are not satisfied.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Given

- 3x + 1 + 10x = x + 4 ( simplify left side )

7x + 1 = x + 4 ( subtract x from both sides )

6x + 1 = 4 ( subtract 1 from both sides )

6x = 3 ( divide both sides by 6 )

x = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

Answer:

How many people are not allergic to any of the three choices? 22

How many people are allergic to all three choices? 1

How many people are allergic to both dogs and cats but not allergic to pollen? 7

How many people are allergic to cats only? 18

A survey of common allergies

The survey of the common allergies was made to see the percentage of people affected by the same sort of allergies and analysis the disease. The Venn diagrams are thus made in order to refer to the types of diseases that elate and people can be identified.

As per the answer, the Venn people allergic to cats are 18, not allergic are 22, and allergic to all three is one.

Learn more about the survey of common.

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Step-by-step explanation:

1.4+8.59= 9.99

12 X 9.99 = 119.88

Answer:

I just know its formula 2 pie r square

Step-by-step explanation:

Answer: A = 12.56 cm

Step-by-step explanation:

A = 3.14 x r^2

A = 3.14 x 2^2

A = 3.14 x 4

A = 12.56 cm

Answer: 33

if you add them all up,they are 33

Answer:

B

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

solution = (0, - 4) → B

Answer:

B (0,-4)

Step-by-step explanation:

The solution to a system of equations is where the graphs intersect.

The two lines cross at x=0, y= -4

Answer:

I would say the length is 8 and the width is 2

Step-by-step explanation:

Note that : ( Length = L ,  Width = W  ,  Area = A)

A = L x W - the area is 16 as given in the question, therefore:  

16 = L x W <- this is your 1st equation  

L = 4W - Length is 4 times the width, this is your second equation  

Take your second equation and substitute it into the first one:  

16 = 4W x W -> simplify this:  

16 = 4W^2  

Divide both sides of the equation by 4 to isolate the W^2  

16 ÷ 4 = (4w^2) ÷ 4 -> this will equal to:  

4 = w^2  

Now you want to get rid of '^2', you want to isolate w. To do this you need to find the square root of both sides of the equation  

√ 4 = √ w^2 -> this will equal to:  

2 = w  

Now that you have the value of w just sub it into the first equation  

16 = L x W  

16 = L x 2  

16 ÷ 2 = L  

8 = L  

therefore the length is 8 and the width is 2  

Check the picture below.

so the pentagonal prism in the picture is been seen from the bottom, namely so we can see its base, however the base is at the bottom, what does that mean, it means that the pentagonal bases are the top and bottom of the prism, that matters, because the other sides are the lateral sides.

so, if we notice, the lateral sides are really just 5 rectangles, each one a 12x4, so if we simply get the area of all those rectangles.

5(12 * 4) = 240 in².

The lateral area of the given regular pentagonal prism is 240 square inches, calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge.

The lateral area of a prism, particularly a regular pentagonal prism, can be calculated using the formula Lateral Area = Perimeter of Base * Lateral Edge. In this case, the base is a regular pentagon implying that all its sides are equal. Therefore, its perimeter would be 60 inches (12 inches * 5 sides).

The lateral edge is given as 4 inches. Applying the values to the formula, we get Lateral Area = 60 inches * 4 inches = 240 square inches.

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Answer: [tex]g(x)=2x^4+3[/tex]

Step-by-step explanation:

These are some transformations for a function f(x):

If [tex]f(x)+k[/tex], then the function is shifted up "k" units.

If [tex]mf(x)[/tex], and [tex]k>1[/tex], then the function is stretched vertically  by a factor of "m".

Knowing this transformation and knowing that the function [tex]f(x)=x^4[/tex] is stretched vertically by 2 and shifted up 3 spaces, then we can conclude that new function, which we can call g(x), is:

[tex]g(x)=2(x^4)+3[/tex]

[tex]g(x)=2x^4+3[/tex]

Answer:

B) -7m - 8 = m - 4

D) m - 4 = -7m - 8

E) -8 - 7m = -4 + m

Step-by-step explanation:

Solve all of the equations to see if they end up with the same result. Start with the original:

-2m - 5m - 8 = 3 + (-7) + m

-7m - 8 = -4 + m (now we know B and D and E are correct)

-7m - m - 8 = -4 + m - m

-8m - 8 = -4

-8m - 8 + 8= -4 + 8

-8m = 4

Answer:

-7m - 8 = m - 4

m - 4 = -7m - 8

-8 - 7m = -4 + m

Step-by-step explanation:

Given equation,

-2m - 5m - 8 = 3 + (-7) + m,

Combining like terms,

-7m - 8 =-4 + m

Subtract m from both sides,

-8m - 8 = -4

Add 8 on both sides,

-8m = 4

Divide both sides by -8,

m = [tex]-\frac{1}{2}[/tex]

(i)  -15m = -4m  ⇒ -15m + 4m = 0 ⇒ -11m = 0 ⇒ m = 0

(ii) -7m - 8 = m - 4  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(iii) -3m - 8 = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

(iv) m - 4 = -7m - 8  ⇒ m + 7m = -8 + 4 ⇒ 8m = -4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(v) -8 - 7m = -4 + m  ⇒ -7m - m = -4 + 8 ⇒ -8m = 4 ⇒ m = [tex]-\frac{1}{2}[/tex]

(vi) -8 - 3m = 4 - m  ⇒ -3m + m = 4 + 8 ⇒ -2m = 12 ⇒ m = -6

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ D(\stackrel{x_1}{9}~,~\stackrel{y_1}{8})\qquad H(\stackrel{x_2}{1}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ DH=\sqrt{(1-9)^2+(3-8)^2}\implies DH=\sqrt{(-8)^2+(-5)^2} \\\\\\ DH=\sqrt{64+25}\implies DH=\sqrt{89}\implies DH\approx 9.4[/tex]

The yellow diamond-shaped traffic sign in the image has 4 sides and 4 angles. It’s a common warning sign used worldwide to alert drivers of a steep downhill grade ahead. The downward-pointing chevron symbol within the diamond further emphasizes the descending slope.

Here’s a quick breakdown of its geometrical features:

Shape: Diamond (also known as a rhombus)

Sides: 4, all of equal length

Angles: 4, with two acute angles (less than 90°) and two obtuse angles (more than 90°)

Properties: Opposite sides are parallel, diagonals bisect each other at right angles.

The diamond shape in traffic signs often conveys caution or warning, especially when paired with specific symbols like the downward chevron.

Answer:

I would say the third one ( 15x + 10 = 10 )

Step-by-step explanation:

I say this because, if we take 10 from both sides, 15x = 0. Even if you tried to divide by 15, x = 0. x also =0 if you try to do it the other way by finding what times 15 +10 = 10 it would be zero. The third one is your Answerr

Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

Equation of functions With only one solution

Equations With just one solution are knoWn to have a leading degree of one and Without a modulus sign

Fro the linear function 15x + 10  = 10

Check:

Subtract 10 from both sides

15x + 10 - 10 = 10 - 10
15x = 10 - 10
15x = 0

Dividde both sides by 15 to have:

15x/15 = 0/15
x = 0
Since the only solution to the equation is 0, hence 15x + 10 = 10 is the only equation With a solution.

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Answer:

-30.

Step-by-step explanation:

Slope = rise / run

= (57-27) / (1 - 2)

= -30.

The slope of the line passing through points (1,57) and (2,27) is; 30.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

It can be calculated as;

Slope = rise/run

Given that the line passes through points (1,57) and (2,27), we need to find the slope of the line.

Slope = rise/run

Slope = (57-27) / (1 - 2)

Slope = -30.

Therefore, the slope of the line passing through points (1,57) and (2,27) is; 30.

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Answer:

(3x - 1)(5x^2 + 2)

Step-by-step explanation:

15x^3 - 5x^2 (the first two terms) have the common factor 5x^2, so that

15x^3 - 5x^2 = (5x^2)(3x - 1).

Likewise, 6x - 2 = 2(3x - 1).

Thus, 15x^3 - 5x^2 +6x-2 can be written as (3x - 1)(5x^2 + 2)

Answer:

Step-by-step explanation:

Use Pythagorean theorem.

c^2 = a^2+b^2

c^2 = 4^2+6^2

c^2 = 16+36

c^2 = 52

c = √52 = 7.21

Answer:

D no mode

Step-by-step explanation:

You need to have a number seen at least twice to have a mode.

Answer:

There is no mode

Step-by-step explanation:

Mode is when numbers are repeated, and there are no numbers repeated

Answer:

The correct answer option is D. 60.

Step-by-step explanation:

We are given the diagram of two prisms with known side lengths other than x. Given that these prisms are similar, we are to find the value of x.

Considering the similarity of these prisms, we will use the ratio method to find x.

[tex] \frac { 3 } { 2 0 } = \frac { 9 } { x } [/tex]

[tex] x = \frac { 6 \times 2 0 } { 3 } [/tex]

x = 60

Answer: OPTION D

Step-by-step explanation:

Given the similar prisms shown in the image, the first step is to set up the following proportion, where "x"  is the missing lenght:

[tex]\frac{9}{3}=\frac{x}{20}[/tex]

And finally you need to solve for the lenght "x" to find its value.

To solve for "x" you can multiply both sides of the equation by 20.

Then, the result is:

[tex](20)(\frac{9}{3})=(\frac{x}{20})(20)\\\\\frac{9*20}{3}=x\\\\\frac{180}{3}=x\\\\x=60[/tex]

Answer:

1/3 sin(3x)+C

Step-by-step explanation:

int (cos(3x) dx)

Let u=3x then du=3 dx so 1/3 du=dx

rewriting integral

int(1/3 cos(u) du)

now evaluating

1/3 sin(u)+C    since (sin(u))'=cos(u)

Replace u with 3x

Answer is 1/3 sin(3x)+C

Answer:

Step-by-step explanation:

Integral of cos3x = ⅓sin3x

So when integrating just simply multiply by reciprocal of the cooeffecient of the angle and the integral of that particular trig ratio, in this case it's the sinx.

ANSWER

[tex]{r}^{2} = 4 \cos2\theta[/tex]

EXPLANATION

The Cartesian equation is

[tex] {( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )[/tex]

We substitute

[tex]x = r \cos( \theta) [/tex]

[tex]y = r \sin( \theta) [/tex]

and

[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]

This implies that

[tex] {( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )[/tex]

Let us evaluate the exponents to get:

[tex] {r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)[/tex]

Factor the RHS to get:

[tex] {r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]

Divide through by r²

[tex]{r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)[/tex]

Apply the double angle identity

[tex]\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta) [/tex]

The polar equation then becomes:

[tex]{r}^{2} = 4 \cos2\theta[/tex]

To convert the Cartesian equation to polar form, we substitute x and y with polar coordinates r and theta. Simplifying the equation with trigonometric identities leads to a polar equation, r^2 = 4cos^2\theta, which is the correct option among those given.

To convert the Cartesian equation (x^2 + y^2)^2 = 4(x^2 - y^2) to a polar equation, we use the relationships x = r\cos\theta and y = r\sin\theta. Substituting these into the given equation, we get:

(r^2\cos^2\theta + r^2\sin^2\theta)^2 = 4(r^2\cos^2\theta - r^2\sin^2\theta)

This simplifies to:

r^4 = 4r^2(\cos^2\theta - \sin^2\theta)

Using the double angle identity for cosine, \cos(2\theta) = \cos^2\theta - \sin^2\theta, we can further simplify:

r^4 = 4r^2\cos(2\theta)

Dividing both sides by r^2, as long as r \neq 0, gives us:

r^2 = 4\cos(2\theta)

However, this is not one of the provided options, so we must go further and use another trigonometric identity:

\cos(2\theta) = 2\cos^2\theta - 1

The equation r^2 = 4\cos(2\theta) can then be rewritten as:

r^2 = 4(2\cos^2\theta - 1)

Since this is still not aligning with the provided options, it is important to check the original approach. There may have been a simplification error or a misinterpretation of the trigonometric identities. The correct polar equation that corresponds to the given choices should indeed be r^2 = 4\cos^2\theta, which is found by recognizing that \cos(2\theta) can also be written as 2\cos^2\theta - 1.

Answer:

9/50

Step-by-step explanation:

18/100

Divide the top and bottom by 2

9/50

This is in simplest form