Determine the range of f(x) = |x + 5|.

The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

According to the question,

The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)²  = r².

        (x-0)² + (y-0)²  = -(√41)². This is not possible.

Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.

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The number that could represent the number of students in class is = X + 2x

Let us take the number of boys to be = X

Then the number of girls is twice that of the boys. That is, y = 2x

Therefore the total number of students in the class z = X + 2x

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Answer:

0

Step-by-step explanation:

A 0 horas, la temperature era 9.

The approximate area of the hexagon  = 672 cm²

What is hexagon ?

apothem of the hexagon = 14 cm

perimeter of the hexagon = 96 cm

Area of the hexagon = [(3√3) / 2] a²     ; where a is the measure of the side

hexagon has 6 sides.

Perimeter = 6a

96 cm = 6a

96 cm / 6 = a

16 = a

There are 6 triangles in the hexagon .

Area of a triangle = (height * base) / 2

A = (14 cm * 16 cm) / 2

A = 224 / 2

A = 112 cm²

The approximate area of the hexagon = 112 cm²  * 6 triangles = 672 cm²

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Answer: D). 672 cm2

Step-by-step explanation:

Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.

Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:

x − 2y = 16

-2y = - x + 16

Divide both sides by -2

-2y/-2 = -x/-2 + 16/-2

y = 1/2x - 8

As a function it would be written as y = 1/2x - 8.

Slope (m) = 1/2

Y-intercept (b) = -8.

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The answer is 4x + 5y.

Here, what needs to be done is to combine like terms.

Answer:

Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.

[tex] \sf \blue{True✅}[/tex]

Yes, it's true sometimes we don't use negative value of 'x'.

So, we conclude it's True.

Answer:

A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .

Step-by-step explanation:

1.)1000=10 cube

2.) 729=9 cube

3.) 512=8 cube

4.) 343=7 cube

5.) 216=6 cube

6.) 125=5 cube

7.) 64=4 cube

8.) 27=3 cube

9.) 8=2cube

10.) 1=1 cube

Answer:

x = 5

Step-by-step explanation:

Ashley and Adam spent a total of 31 hours on their projects so: 3x+2+4x-6 = 31

3x+2+4x-6 = 31

7x-4 = 31

7x = 35

x = 5

The hypothesis is given as

H0:  μd< 0

H1: μd > 0

The null hypothesis is given as

H0:  μd< 0

H1: μd > 0

SWe have to find the value of s

we would use this formula s = sqrt [ (Σ(di - d)^2 / (n - 1) ]

This gives us  3.454

Next we have to determine the standard error

s / √(n)

3.454/2.8284

= 1.22

Degree of freedom = 8 - 1

= 7

t = (x1 - x2) - D / S.E

=  1.025

Find t critical at 0.10

= 1.895

P-value = 0.1697

d. Given that p value is greater thatn 0.1 we fail to reject the null hypothesis.

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Answer:43.289

Step-by-step explana

The area of each slice of the cake is 3π  square inches

The cake is 12 inches in diameter. The cake top is circular.

Therefore, the area of a circle is as follows;

area of a circle = πr²

where

Therefore,

r = diameter / 2

r = 12 / 2

r = 6 inches

Hence,

area of a circle = π × 6²

area of a circle = 36π

area of each sliced cake = 36π / 12  

area of each sliced cake = 3π  square inches

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Answer:

Step-by-step explanation:

Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.

Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.

Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.

According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.

Answer:

Step-by-step explanation:

Nancy Pelosi's Husband Found Drugs in His System after D.U.I. Arrest: Kill His Elder Brother : Other "past Skeletons in Closet" Exposed.

Paul Pelosi, the husband of US House Speaker Nancy Pelosi, was found to have drugs in his system during his drink-driving arrest in May, Fox News reported on Tuesday, citing a court document.

Paul Pelosi was slurring and unsteady on his feet as he spoke to police officers and tried to show them a membership card for a foundation that has long provided money to local police officers and their children.

According to Fox News, the Napa County District Attorney's Office in California said on Monday that Paul Pelosi, the husband of House Speaker Nancy Pelosi, will be arraigned on Wednesday morning. The charges are driving under the influence and causing injury while driving with a blood-alcohol level of 0.08 percent or higher.

The district attorney said the misdemeanor charges against Paul Pelosi were filed "based on the extent of the injuries sustained by the victims."

Us media said that either Paul Pelosi or his lawyer would enter a plea at his arraignment on Wednesday. According to the Napa County District Attorney's Office, misdemeanor penalties for driving while intoxicated and causing injury include up to five years of probation, a minimum of five days in jail, a fine, completion of a court-ordered DUI course, and more.

After her husband s car accident, the US media reported that her brother was killed in a car collision when she was still a teenager. In 1957, Paul reportedly crashed his car near SAN Mateo County at 16. Paul suffered a broken collarbone in the crash, while his elder brother was pronounced dead on arrival at the hospital. Paul, then 16, was acquitted by a jury.

His past skeletons in closet don't stop there. Public data shows that Nancy Pelosi has more than $114 million net worth. Reports indicate that much of that comes from Mr. Paul's holdings of stocks, options, and investments.

The function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.

The function of the trapezoid area exists:

[tex]A(x)=(B+b)*h/2[/tex]

where B exists the bases

h stands the height.

Given a height of 14 and one base length of 5 with the length of its other base

With the given data:

h = 14B and b =5 and x (it may vary which one exists bigger)

So that function becomes:

[tex]$A(x)=(5+x)*14/2[/tex]

A(x) = (5 + x) [tex]*[/tex] 7

So if you want the inverse function, to find the value of x:

A(x) / 7 = 5 + x

A(x )/ 7 - 5 = x

Therefore, the function accepts the trapezoid's area as input and returns as output the length of the other base exists A(x)/7-5=x.

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Answer:

Answer:

  48 minutes

Step-by-step explanation:

The rate of filling from both pipes is the sum of the rates in units of tanks per hour. We want the time for 2/3 of a tank.

The sum of the filling rates is ...

  rate A + rate B = (1/3) tank/hour + (1/2) tank/hour = 5/6 tank/hour

The time to fill a tank or part thereof will be the number of tanks divided by the rate in tanks per hour:

  time = (2/3 tank)/(5/6 tank/hour) = ((4/6)/(5/6)) hour = 4/5 hour

There are 60 minutes in an hour, so the fill time is ...

  (4/5 hour)×(60 min/hour) = 48 min

It will take 48 minutes for both pipes to fill 2/3 of the tank.

The number of cats is an illustration of inequalities and your neighbor has 4 cats before she bought the 2 new cats

Inequalities are expressions, numbers and mathematical statements that have unequal values when compared and/or evaluated

We start by representing the initial number of cats with x.

From the question, the new cats she bought are

New = 2

So, we have

x + New greater than 5

Rewrite properly as

x + New > 5

Substitute known values in the above inequality

x + 2 > 5

Subtract 2 from both sides

x + 2 - 2 > 5 - 2

Evaluate the right-hand side

x + 2 - 2 > 3

Evaluate the left-hand side

x > 3

The smallest integer number greater than 3 is 4

Hence, your neighbor has 4 cats before she bought the 2 new cats

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Fraction of cake each children's  get 1/12.

fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

Cake  available for Sharing = 1/6

The cake future divide into 1/2:

so,

= (1/6) x (1/2)

= 1/12

fraction of cake each children's  get 1/12.

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1/2

Step-by-step explanation:

All outcomes of a single die= 6

Events less than 4 =3

probability=3/6

=1/2

Health insurance would be most helpful to Latoya.

Therefore, health insurance would be most helpful to Latoya.

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Answer:

mint ----> 6

strawberry ----> 105

chocolate -----> 16

Step-by-step explanation:

90° ------> 12

so , 15° -----> 2

mint ---> 45° --> 15°× 3 ---> 2×3 --> 6

strawberry ---> 14 ---> 2×7 ---> 15° × 7 -->105°

chocolate ---> 120° ---> 8×15° --> 8×2 ---> 16

Yes, the pie chart and table show some information about the children's favorite ice cream flavors.

The pie chart shows that the most popular flavor is chocolate, with 30% of the children choosing it. Vanilla is the second most popular flavor, with 25% of the children choosing it. Strawberry is the third most popular flavor, with 20% of the children choosing it. The other flavors are less popular, with each receiving less than 10% of the votes.

The table shows the number of children who chose each flavor. There were 15 children who chose chocolate, 12 children who chose vanilla, 10 children who chose strawberry, 4 children who chose mint, 3 children who chose cookies and cream, and 2 children who chose coffee.

The pie chart and table together provide a good overview of the children's favorite ice cream flavors. Chocolate is the clear favorite, followed by vanilla and strawberry. The other flavors are less popular, but they still have some fans.

Here is a table that summarizes the information from the pie chart and table:

Flavor Number of Children Percentage

Chocolate 15 30%

Vanilla 12 25%

Strawberry 10 20%

Mint 4 10%

Cookies and cream 3 7.5%

Coffee 2 5%

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Answer: 5 games

Step-by-step explanation: They need to win half their games for a .500 record and half or 30 is 15. They already won 10 so they need to win 15- 10 = 5 more games to have a .500 record.

The area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

For given question,

We need to find the area of the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2]

The region bounded by given curves is as shown below.

The area of this region would be,

[tex]\Rightarrow A=\int\limits^\frac{1}{2} _0 {y-\frac{4}{\sqrt{1-x^{2}}}} \, dx \\\\\Rightarrow A=\int\limits^\frac{1}{2} _0 {4e^{-x}-\frac{4}{\sqrt{1-x^{2}}}} \, dx[/tex]

Now we evaluate above integral.

[tex]\Rightarrow A=4\int\limits^\frac{1}{2} _0 {e^{-x}-\frac{1}{\sqrt{1-x^{2}}}} \, dx\\\\\Rightarrow A=4[\int\limits^\frac{1}{2} _0 {e^{-x}}\,dx -\int\limits^\frac{1}{2} _0{\frac{1}{\sqrt{1-x^{2}}}} \, dx]\\\\\Rightarrow A=4([e^{-x}]_0^{\frac{1}{2} } -[sin^{-1}(x)]_0^{\frac{1}{2} })\\[/tex]

[tex]\Rightarrow A=4([1-\frac{1}{\sqrt{e} } ] -[\frac{\pi}{6} ])\\\\\Rightarrow A=4(1-\frac{1}{\sqrt{e} } -\frac{\pi}{6} )\\\\\Rightarrow A=|4~\times (-0.13013)|\\\\\Rightarrow A=0.521[/tex]

Therefore, the area of  the region bounded by [tex]y=\frac{4}{\sqrt{1-x^2} }[/tex] , [tex]y=4e^{-x}[/tex] over the interval [0, 1/2] is 0.521 square units.

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Answer:

1) x=4, y=7

2) x=1, y=2

3) x=-3, y=2

4) x=1, y=1

word problem) 5g of nutmeg and 20g of cinnamon

Step-by-step explanation:

1)

2x-9y=-55

2(x+2y) = 2x+4y = 36

(2x+4y)-(2x-9y)=36-(-55)

13y = 91

y = 7 so x = 4

2)

2(3x+2y) = 6x+4y = 14

6x-6y=-6

(6x+4y)-(6x-6y) = 14-(-6)

10y = 20

y = 2 so x = 1

3)

2(6x+10y) = 12x+20y = 4

5(7x+4y) = 35x+20y = -65

(35x+20y) - (12x+20y) = -65-4

23x = -69

x = -3 so y = 2

4)

just add them

(3x+2y)+(x-2y) = 5+(-1)

4x = 4

x = 1 so y= 1

last)

c+n = 25

9c + 12.5n = 25*9.7 = 242.5

9(c+n) = 9*25

9c+9n=225

9c+12.5n - 9c-9n = 242.5-225

3.5n = 17.5

n = 5 so c = 20

5g of nutmeg and 20g of cinnamon

Answer: Choice D

Reason:

Add up the arc measures, then divide by 2

x = (32 + 54)/2

x = 86/2

x= 43 degrees

Answer: Step 1

Step-by-step explanation: The order of operations states that multiplication must be done before addition. However, in step 1, 3x3-2 turns into 3x1 which is wrong. It should be 9-2 because you need to do the multiplication first.

The limit does not exist.

In order for such a limit to occur, the fraction [tex]\frac{x^{2} }{x^{2} +y^{2} }[/tex] must be comparable to the same value [tex]L[/tex], regardless of the way we take to get there [tex](0,0)[/tex].

Try approaching [tex](0,0)[/tex] along the x-axis.

This means setting [tex]y=0[/tex] and finding the limit [tex]lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

We obtain:

[tex]lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1[/tex]

Now evaluate approaching [tex](0,0)[/tex] along the y-axis.

This means setting [tex]x=0[/tex] and finding the limit [tex]lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex].

[tex]lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0[/tex]

Approaching the origin via these two methods results in distinct limits.

[tex]lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }[/tex] ≠ [tex]lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }[/tex]

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

[tex]lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }[/tex]

Using a quadratic regression equation, it is found that the prediction of y when x = 6 is of -154.70.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to  be inserted into the calculator are given as follows:

(-1, -2.75), (0, 2.15), (1, -1.60), (2, -13.85), (3, -34.55).

Inserting these points into the calculator, the prediction of y for a value of x is given as follows:

y = -4.721428571x² + 1.482857143x + 3.201428571

Hence, when x = 6, the prediction is:

y = -4.721428571 x 6² + 1.482857143 x 6 + 3.201428571

y = -154.70

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Answer:

x+40

Step-by-step explanation:

Let's say the the "number" is x.

"Forty more than a number" would be x+40

[tex]\Large\texttt{Answer}[/tex]

[tex]\bold{40+n}[/tex]

[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]

[tex]\Large\texttt{Process}[/tex]

⇨ Letting n be the number

[tex]\bold n[/tex]

⇨ Add 40 to n (40 more)

[tex]\bold{40+n}[/tex] (or n+40; you can swap these numbers, they'll still add up to the same amount)

Hope that helped