Which is the rationalized form of the expression look at picture

Answer: x = square root of -x + 3 / 2

Step-by-step explanation:

2x^2 + x - 1 = 2

add 1 to both sides

2x^2 + x = 3

subtract x from both sides

2x^2 = -x + 3

square root both sides

2x = square root of -x + 3

divide by 2

x = square root of -x + 3 / 2

Answer:

Step-by-step explanation:

hello :

2x² + X - 1 = 2

2x² + X - 1 -2 = 2-2

2x² + X - 3 =0

(x-1)(2x+3) =0

x-1=0 or 2x+3 = 0

x =1 or x= -3/2

Answer:

x = 12

Step-by-step explanation:

Pythagoras' Theorem

[tex]a^{2} = b^{2} + c^{2}[/tex]

a = 13

b = 5

c = x

[tex]13^{2} = 5^{2} + x^{2}\\169 = 25 + x^{2}\\169 - 25 = x^{2}\\144 = x^{2}\\12 = x[/tex]

After applying the Pythagorean theorem on the given right-angled triangle the value of x we get 12.

A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.

The Pythagoras theorem for a right-angled triangle:

(Hypotenuse)²= (Perpendicular)² + (Base)²

For the given triangle:

The hypotenuse 'MC' = 13

The perpendicular 'MN' = 5

Base 'NC' = x

Substituting these values into the Pythagorean theorem:

(13)²= (5)² + (x)²

Simplifying the square,

169 = 25 + x²

Subtracting 25 we get,

x² = 144

Take square root on both sides,

x = 12

Hence,

The value of x is 12.

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15% of the collection was comedies.

Step-by-step explanation:

Given,

Number of comedies = 6

Number of westerns = 10

Number of romance = 14

Number of horror = 3

Number of mysteries = 7

Total = 6+10+14+3+7= 40

Percent of comedies = [tex]\frac{Number\ of\ comedies}{Total\ number}*100[/tex]

Percent of comedies = [tex]\frac{6}{40}*100=\frac{600}{40}[/tex]

Percent of comedies = 15%

15% of the collection was comedies.

Keywords: percentage, addition

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Answer:

$36

Step-by-step explanation:

Plz give me brainliest as i just need 3 more plz plz plz

To calculate the sale price of the sweatshirt, multiply the original price by the discount rate to get the discount amount and subtract from the original price. The sweatshirt is now priced at $24.

We can find the amount discounted by multiplying the original price of the sweatshirt by the discount rate. So, we calculate 60% of $60. First distinguish that 60% is the same as 0.60 in decimal form. Therefore, we multiply $60 by 0.60 (60%) to get $36. This is the amount that is discounted from the original price. To find the new price after discount, subtract this amount from the original price. So, $60 - $36 equals $24. Therefore, the sweatshirt on sale is now priced at $24.

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Answer:

-6.5-2=-8.5

Step-by-step explanation:

no working out needed that is as simple as it gets mate

18/18 is a proper fraction.

First, turn both fractions into improper fractions.

1 1/6 = 7/6

2/5 = 2/5

Second, multiply.

7/6 * 2/5 → 7*2/6*5 → 14/30

Third, Simplify.

14/30 → 7/15

Best of Luck!

Answer:

Make mixed number into an improper fraction.

Then multiply

14/30

= 7/15

Answer: D?

Step-by-step explanation:

Answer:

Earnings of Chris that week = US$ 712.65

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Chris' salary = US$ 6 per hour + 0.9% commission (0.009)

A week Chris worked 32 hours and sold 2 cars priced $ 26,700 and $ 31,150

2. How much did he make that week?

Earnings of Chris that week = (32 * 6) + (26,700 * 0.009) + (31,150 * 0.0009)

Earnings of Chris that week = 192 + 240.30 + 280.35

Earnings of Chris that week = US$ 712.65

Answer:

[tex]\frac{19}{44}[/tex]

Step-by-step explanation:

The ratio of width : length = [tex]\frac{57}{132}[/tex]

To simplify divide ( cancel ) the numerator/ denominator by 3

= [tex]\frac{19}{44}[/tex] ← in simplest form

To determine the number of scoops of corn needed to feed different numbers of deer, we can use proportional reasoning. However, since the table mentioned in the question is missing, we can't find the exact values.

To determine the number of scoops of corn needed to feed a certain number of deer, we can use the information given in the table. Let's analyze the information provided:

Unfortunately, the table mentioned in the question is missing, so we can't use it to find the exact number of scoops needed. However, if we assume that the ratio of scoops to deer is consistent, we can use proportional reasoning to find the missing values. For example, if it takes 2 scoops to feed 5 deer, then 4 scoops will be needed to feed 10 deer.

The time spent for reading is 31.3 minutes

Solution:

You read 9.75 pages in your science book and 24.5 pages of a play for English class

Therefore,

Number of pages read in science = 9.75

Number of pages read in play = 24.5

Also given that,

Time taken to read each page of science = 1.2 minutes

Time taken to read each page of play = 0.8 minute

To find: Time spent for reading

Time spent for reading = Number of pages read in science x Time taken to read each page of science + Number of pages read in play x Time taken to read each page of play

[tex]Time\ spent\ for\ reading = (9.75 \times 1.2) + (24.5 \times 0.8)\\\\Time\ spent\ for\ reading = 11.7 + 19.6\\\\Time\ spent\ for\ reading = 31.3[/tex]

Thus time spent for reading is 31.3 minutes

Final answer:

Laura earns $18 per hour, and for 8 hours of work, she would make $144.

Explanation:

The question asks us to determine how much Laura would make for 8 hours of work, given that she made $324 for 18 hours of work. To find the hourly rate, we divide the total amount earned by the total hours worked. Then we multiply the hourly rate by the number of hours we want to find the earnings for.

To calculate Laura's hourly rate: $324 / 18 hours = $18 per hour.

Now, we can find out Laura's earnings for 8 hours: $18 per hour * 8 hours = $144.

Therefore, Laura would make $144 for 8 hours of work at the same rate.

Answer: 6 x (18-9) = 54

Step-by-step explanation: 18-9 is 9 and 6 times 9 is 54

Answer:

[tex]p \geqslant - 14[/tex]

Step-by-step explanation:

[tex] \frac{p}{2} \geqslant - 7 \\ p \geqslant - 14[/tex]

Answer:

Step-by-step explanation:

common ratio= second term/first term

=[tex]\frac{16}{64}=\frac{1}{4}[/tex]

64, 16, 4, 1, ...

1*1/4 = 1/4

64, 16, 4, 1, 1/4

(a) The volume of the swimming pool is 330 m³

(b) The surface area of the model swimming pool is 30.25 cm².

(a) The volume of the swimming pool is calculated by applying the following formula as follows;

V = Ah

where;

V = 300 m² x 1.1 m

V = 330 m³

(b) The surface area of the model swimming pool is calculated by applying the following formula;

Assuming the model swimming pool is a square.

S.A = L²

S.A = 5.5 cm x 5.5 cm

S.A = 30.25 cm²

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The points that represent the relationship are (2,4), (5,7), (7,9).

Step-by-step explanation:

1. It is given that Brent was always 2 meters in front of Joel.

2. In the first case, when Joel is at 2 meters, Brent will be 2 meters in front of that, i.e. at 2 meters + 2 meters = 4 meters. Hence, when Joel is at 2 meters distance from the school, Brent will be at 4 meters distance from the school. Hence, the point on the coordinate grid is (2,4) here.

3. Similarly, in the second case, when Joel is at 5 meters, Brent will be 2 meters in front of that, i.e. at 5 meters + 2 meters = 7 meters. Hence, the point on the coordinate grid is (5,7) here.

4. Similarly, in the third case, when Joel is at 7 meters, Brent will be 2 meters in front of that, i.e. at 7 meters + 2 meters = 9 meters.  Hence, the point on the coordinate grid is (7,9) here.

Answer:

Step-by-step explanation:

when the outlier is removed, the mean increases.....the removing of the outlier does very little to the median or mode.

example :

1,2,3,4,5

mean = 15/5 = 3......median = 3

now throw in an outlier..

1,2,3,4,5,50

mean = 65/6 = 10 5/6.....median = (3 + 4) /2 = 7/2 = 3.5

as u can see, it drastically affects the mean...and does little to the median

ur answer is A

Answer:

A

Step-by-step explanation:

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=(x-3)^2+5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex represent a minimum

The vertex is the point (3,5)

The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

[tex]x=3[/tex] ---> axis of symmetry

Find the y-intercept (value of f(x) when the value of x is equal to zero)

For x=0

[tex]f(x)=(0-3)^2+5=14[/tex]

The y-intercept is the point (0,14)

Find the x-intercept (values of x when the value of f(x) is equal to zero)

For y=0

[tex]0=(x-3)^2+5[/tex]

[tex](x-3)^2=-5[/tex] ---> has no real solutions

The function has no x-intercepts (The roots of the quadratic equation are complex numbers)

therefore

The graph in the attached figure

Answer:

The width of the smaller rectangle is 5 centimeters

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the smaller rectangle

y ----> the area of the larger rectangle

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]x=16\ cm^2\\y=100\ cm^2[/tex]

substitute

[tex]z^{2}=\frac{16}{100}[/tex]

square root both sides

[tex]z=\frac{4}{10}[/tex]

step 2

Find the width of the larger rectangle

we know that the area is equal to

[tex]A=LW[/tex]

we have

[tex]A=100\ cm^2\\L=8\ cm[/tex]

substitute

[tex]100=8W\\W=12.5\ cm[/tex]

step 3

Find the width of the smaller rectangle

To find out the width of the smaller rectangle, multiply the width of the larger rectangle by the scale factor

so

[tex]12.5(\frac{4}{10})=5\ cm[/tex]

Answer:

Nine ones  =  one hundred and eleven million one hundred and eleven thousand and one one hundred and eleven.

Step-by-step explanation:

i) nine ones equals = 111,111,111 which is one hundred and eleven million one hundred and eleven thousand and one one hundred and eleven.

Answer:

34.09269

Step-by-step explanation:

The length of FD = 0.76 feet.

Step-by-step explanation:

Given that in ΔDEF, the angle F measures 90° and the angle D measures 83° and EF=6.2 feet

To find the length of FD, let us use the tangent function. The tangent of an angle is the length of opposite side divided by the length of the adjacent side.

[tex]\tan \theta=\frac{o p p}{a d j}[/tex]

From the given data, θ=83°, [tex]o p p=6.2[/tex] and [tex]a d j=x[/tex]

Substituting these values in the tangent formula, we get,

[tex]\begin{array}{r}{\tan \theta=\frac{o p p}{a d j}} \\{\tan 83^{\circ}=\frac{6.2}{x}}\end{array}[/tex]

Using calculator, the value of [tex]\tan 83^{\circ}=8.14[/tex] and substituting and solving the equation, we get,

[tex]\begin{aligned}8.14 &=\frac{6.2}{x} \\x &=\frac{6.2}{8.14} \\x &=0.76\end{aligned}[/tex]

Thus, the length of FD = 0.76 feet.

Answer:

A

Step-by-step explanation:

It would be A because it’s a negative 20, meaning he’s losing money while 15d represents how many dogs he’s walking and the cost of it.

Answer: 13.8 cm

Step-by-step explanation:

Assuming the cube is the cube shown in the attached image, its diagonal is [tex]x[/tex].

Now, for a cube which each side is [tex]a[/tex], its diagonal is given by the pithagorean theorem:

[tex]x=\sqrt{a^{2}+d^{2}}[/tex] (1)

Where [tex]d[/tex] is the hypothenuse of the right triangle formed in one of the cube's faces:

[tex]d=\sqrt{3}a[/tex] (2)

Then the formula for the diagonal is:

[tex]x=\sqrt{a^{2}+(\sqrt{3}a)^{2}}[/tex] (3)

[tex]x=\sqrt{3}a[/tex] (4)

If [tex]a=8 cm[/tex]:

[tex]x=\sqrt{3}8 cm[/tex] (5)

Finally:

x=13.8 cm

The equation that represents a line passing through (-2, 4) and has a slope of 2/5 is Oy+4 = (x-2).

The equation that represents a line passing through (-2, 4) and has a slope of 2/5 is option B:

Oy+4 = (x-2)

To understand why this equation represents the line, we can use the slope-intercept form, y = mx + b, where 'm' is the slope and 'b' is the y-intercept. The given slope is 2/5, so the equation becomes y = (2/5)x + b. Plugging in the coordinates of the point (-2, 4), we can solve for 'b' and find that it is 4. Therefore, the equation representing the line is y = (2/5)x + 4.

Answer:

Answer C

Step-by-step explanation:

The probability that a randomly selected dog is female, given it is a Chihuahua, is 3/11. This is calculated by dividing the number of female Chihuahuas (3) by the total number of Chihuahuas (11) in the store.

Probability of Selecting a Female Chihuahua

First, let's determine the total number of Chihuahuas in the store. Since the store has 25 dogs and 14 of them are not Chihuahuas, we subtract 14 from 25 to get the number of Chihuahuas:

25 - 14 = 11

There are 11 Chihuahuas in the store. We are given that there are 3 female Chihuahuas. Therefore, the probability that a randomly selected dog is a female Chihuahua is the number of female Chihuahuas divided by the total number of Chihuahuas:

Probability = Number of Female Chihuahuas / Total Number of Chihuahuas = 3 / 11

This calculation gives us the probability of 3/11 that a dog selected at random is female, given it is a Chihuahua.

Answer:

His mom will be 33 years old.

Step-by-step explanation:

Since Adrian is 8, 3 years from now he will be 11. 11 is 1/3 of 33. So, his mom is currently 30 years old.