What are the two solutions of x2 – 2x – 4 = –3x + 9?
the y-coordinates of the y-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the x-coordinates of the x-intercepts of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the y-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9
the x-coordinates of the intersection points of the graphs of y = x2 – 2x – 4 and y = –3x + 9

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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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:

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:  2460 calories

Step-by-step explanation:

2129 + 2348 + 1863 = 6340

2200 x 4 = 8800

8800 - 6340 = 2460

Final answer:

Samuel must consume 2460 calories on Thursday to achieve his target average daily calorie intake of 2200 over the four days.

Explanation:

To find out how many calories Samuel must consume on Thursday to have an average daily intake of 2200 calories, we first calculate the total number of calories he should have consumed over four days. This is done by multiplying the desired daily average (2200 calories) by the number of days (4), which equals 8800 calories.

Next, we add the calories Samuel consumed from Monday to Wednesday, which amounts to 2129 (Monday) + 2348 (Tuesday) + 1863 (Wednesday) = 6340 calories.

To find the calories for Thursday, we subtract the total consumed so far (6340 calories) from the desired four-day total (8800 calories). This gives us 8800 - 6340 = 2460 calories.

Therefore, Samuel must consume 2460 calories on Thursday to achieve an average of 2200 calories per day over the four days.

let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{10\frac{2}{3}}\implies \cfrac{10\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{32}{3}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{32}{3}})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-\left( -\frac{32}{3} \right)}{-3-4}\implies \cfrac{1+\frac{32}{3}}{-7}\implies \cfrac{\frac{3+32}{3}}{-7}[/tex]

[tex]\bf \cfrac{~~\frac{35}{3}~~}{\frac{-7}{1}} \implies \cfrac{\stackrel{5}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{3}\cdot \cfrac{1}{~~\begin{matrix} -7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{5}{3}[/tex]

Answer: 33

if you add them all up,they are 33

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:

x<3

Step-by-step explanation:

The circle is open and the arrow is going left so its going to be less then. The circle is on 3 so the answer is c. x<3.

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

[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.

1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:

Pr(Q|R) = Pr(Q ∩ R) / Pr(R)

2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:

Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)

= 3/37

3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.

Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)

= 7/37

4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:

Pr(Q|R) = (3/37) / (7/37)

= 3/7

Thus, the answer is B.

Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.

Step-by-step explanation:

1.4+8.59= 9.99

12 X 9.99 = 119.88

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

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

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:

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:396

Step-by-step explanation:Arc length = radius * angle in radians

you know radius = Diameter/2 = D/2

80 deg = (80pi/180) rad

then,

88 pi = (D/2) * (80 pi /180)

sloving for D

D = 396

The diameter of the circle which measures is 80° and length arc is 88π is 396

length of arc = ∅ / 360 × 2πr

where

r = radius

∅ = centre angle = 80°

length of arc = 80 / 360 ×2πr

length of arc = 88π

Therefore,

88π = 16 / 36 πr

cross multiply

88π × 36 = 16πr

3168π = 16πr

divide both sides by 16π

198 = r

Recall

diameter = 2(radius)

Therefore,

diameter of the circle = 2 × 198

diameter of the circle = 396

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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:

20.49 feet to the nearest hundredth.

Step-by-step explanation:

Using the Pythagoras Theorem:

38^2 = h^2 + 32^2

h^2 = 38^2 - 32^2

h^2 = 420

h = √420

h = 20.494 m.

Your question asks to find the height of the building.

To find the answer to your question, we would need to use the Pythagorean theorem.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

What we would do is plug in the numbers that we already know into the equation, and then we simply solve.

We would plug 32 to a and plug 38 into c

Your equation should look like this:

[tex]32^2+b^2=38^2[/tex]

Now, we solve:

[tex]32^2+b^2=38^2\\\\1024+b^2=38^2\\\\1024+b^2=1444\\\\b^2=420\\\\\sqrt{b} =\sqrt{420} \\\\b=20.493[/tex]

We would jkust round to the nearest hundredths place, therefore giving you the answer of 20.49.

This means that the height of the building would be 20.49 meters

20.49 meters would be your FINAL answer.

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:

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 :)

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:

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:

-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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[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]

Answer:

9/50

Step-by-step explanation:

18/100

Divide the top and bottom by 2

9/50

This is in simplest form

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:

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.