What is the solution set of the quadratic inequality x2-5<0?

[tex]\boxed{(x+6)^2+(y+2)^2=72}[/tex]

The center-radius form of the circle equation is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here we know that the y-intercepts are:

[tex]y=4 \ and \ y=-8[/tex]

So:

[tex]\bullet \ If \ y=4, \ x=0 \\ \\ \\ (0-h)^2+(4-k)^2=r^2 \\ \\ \therefore \mathbf{(I)} \ h^2+16-8k+k^2=r^2 \\ \\ \\ \bullet \ If \ y=-8, \ x=0 \\ \\ \\ (0-h)^2+(-8-k)^2=r^2 \\ \\ \therefore \mathbf{(II)} \ h^2+64+16k+k^2=r^2 \\ \\ \\ \bullet \ If \ x=-12, \ y=-8 \\ \\ \\ (-12-h)^2+(-8-k)^2=r^2 \\ \\ \therefore 144+24h+h^2+64+16k+k^2=r^2 \\ \\ \therefore \mathbf{(III)} \ h^2+208+16k+24h+k^2=r^2[/tex]

So we have the following system of equations:

[tex]\left\{ \begin{array}{c}(I)\:h^{2}+16-8k+k^{2}=r^{2}\\(II)\:h^{2}+64+16k+k^{2}=r^{2}\\(III)\:h^{2}+208+16k+24h+k^{2}=r^{2}\end{array}\right.[/tex]

[tex]Subtract \ II \ from \ I \\ \\ \\\left\{ \begin{array}{c}h^{2}+16-8k+k^{2}=r^{2}\\-(h^{2}+64+16k+k^{2}=r^{2})\\---------------------\\h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\end{array}\right.[/tex]

[tex]Simplifying: \\ \\ h^{2}+16-8k+k^{2}-h^{2}-64-16k-k^{2}=r^{2}-r^{2}\\ \\ 16-8k-64-16k=0 \\ \\ -24k-48=0 \\ \\ k=-\frac{48}{24} \\ \\ \therefore \boxed{k=-2}[/tex]

From (I):

[tex]h^2+16-8k+k^2=r^2 \\ \\ \\ For \ k=-2 \\ \\ h^2+16-8(-2)+(-2)^2=r^2 \\ \\ \therefore r^2=h^2+36 \\ \\ \\ Substituting \ k \ and \ r^2 \ into \ (III): \\ \\ h^{2}+208+16(-2)+24h+(-2)^{2}=h^2+36 \\ \\ Simplifying: \\ \\ 180+24h=36 \\ \\ 24h=36-180 \\ \\ 24h=-144 \\ \\ h=-\frac{144}{24} \\ \\ \therefore \boxed{h=-6}[/tex]

Finding the radius:

[tex]r^2=(-6)^2+36 \\ \\ r^2=36+36 \\ \\ r^2=72 \\ \\ \therefore \boxed{r=6\sqrt{2}}[/tex]

Finally, the equation of the circle is:

[tex](x-(-6))^2+(y-(-2))^2=72 \\ \\ \boxed{(x+6)^2+(y+2)^2=72}[/tex]

Answer:

[tex](x+6)^2 + (y+2)^2 = 72[/tex]

Step-by-step explanation:

We are given the following information in the question:

y intercept = 4, -8

The circle passes through the point (-12, -8)

Equation of circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where r is the radius of circle, (h,k) is the center of circle.

The circle passes through the points (0,4), (0,-8_ and (-12,-8)

Putting these points in the equation of circle we get:

[tex]1) (0-h)^2 + (4-k)^2 = r^2\\h^2 + (4-k)^2 = r^2\\2) (0-h)^2 + (-8-k)^2 = r^2\\h^2 + (-8-k)^2 = r^2\\3) (-12-h)^2 + (-8-k)^2 = r^2\\[/tex]

Now, we have three equations in three variables.

Solving the three equations, we obtain:

h = -6, k = -2, r = [tex]6\sqrt2[/tex]

Putting these values in the equation of circle:

[tex](x-(-6))^2 + (y-(-2)) = (6\sqrt{2})^2\\(x+6)^2 + (y+2)^2 = 72[/tex]

The above equation is the required equation of circle.

Answer:

(14 + x)/31 ≥ .6

14 + x ≥ 18.6

x ≥ 5

The correct answer is B.

Sam needs to win at least 5 more of his 13 remaining matches in order to achieve at least a 60% win rate and qualify for the year-end tournament.

The question: how many of Sam's 13 remaining matches must he win to qualify for the year-end tournament by winning at least 60% of his matches this year, is a mathematics question related to percentage and probability. To solve it, you need to figure out the total number of matches Sam will play in the year and calculate what number constitutes 60% of that total. Sam is set to play a total of 31 matches (18 + 13). Sixty percent of 31 is 18.6, we will round this up to 19 as you cannot win portion of a match. Given that Sam has already won 14 matches, he needs to win at least 5 more of his 13 remaining matches (19-14 = 5) in order to win at least 60 percent of his matches for the year. So, the correct answer is 5.

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Answer:

10200000

Step-by-step explanation:

102 times 100,000 because you have to multiply 10, 5 times like this for example, 10 x 10 x 10 x 10 x 10

Answer:

11

Step-by-step explanation:

90=79+x

-79-79

_________

11=x

Answer: 2

Step-by-step explanation:

Answer:

7614

Step-by-step explanation:

Answer:

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator q. Numbers that are not rational are called irrational numbers. The real line consists of the union of the rational and irrational numbers. The set of rational numbers is of measure zero on the real line, so it is "small" compared to the irrationals and the continuum.

Answer:

70000

Step-by-step explanation:

According to the Zero-Product Rule, multiply 7 by 1000 to get 7000, then attach that extra 0 to the answer, giving you 70000.

I am joyous to assist you anytime.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AC=\sqrt{(5-2)^2+(0-4)^2}\implies AC=\sqrt{3^2+(-4)^2} \\\\\\ AC=\sqrt{9+16}\implies AC=\sqrt{25}\implies AC=5[/tex]

Answer:

6.6

Step-by-step explanation:

√(43)= 6.5574385243

So your tenth is the coefficient (number) on the right side of the decimal which in this case would be 5 so when rounding you look at the hundredths place which is 2 spaces away from the decimal going right so in this case would be 5 as well, if the number you're rounding to is 5 or above (5-9) then you change then number in front of it by adding 1.

For example: 0.4815 if were rounding the tenths place we look at the 8 (hundredths place) and since 8 is over 5 we make the 4 (tenths place) into a 5 giving us the answer .5

so for your problem the answer would be 6.6

Answer:

[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]

Step-by-step explanation:

Noah's running speed = 6 mph.

Use formula [tex]D=v\cdot t,[/tex] where

D is the distance,

v is the speed,

t is the time.

If [tex]t=1[/tex] hour, then [tex]D=6\cdot 1=6[/tex] miles.

If [tex]t=\dfrac{1}{2}[/tex] hour, then [tex]D=6\cdot \dfrac{1}{2}=3[/tex] miles.

If [tex]t=1\dfrac{1}{3}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{3}=6\cdot \dfrac{4}{3}=8[/tex] miles.

If [tex]t=1\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 1\dfrac{1}{2}=6\cdot \dfrac{3}{2}=9[/tex] miles.

If [tex]t=9[/tex] hours, then [tex]D=6\cdot 9=54[/tex] miles.

If [tex]t=4\dfrac{1}{2}[/tex] hours, then [tex]D=6\cdot 4\dfrac{1}{2}=6\cdot \dfrac{9}{2}=27[/tex] miles.

So, the table is

[tex]\begin{array}{cc}\text{Time}&\text{Distance}\\ \\1&6\\ \\\dfrac{1}{2}&3\\ \\1\dfrac{1}{3}&8\\ \\1\dfrac{1}{2}&9\\ \\9&54\\ \\4\dfrac{1}{2}&27\end{array}[/tex]

Please find attached the answers in the attached diagram

Average speed is the total distance travelled per time.

Average speed = total distance / total time

Noah's average speed is 6mph

From the above formula, the formula to determine miles run is average speed x time

Total miles he ran in 1 hour = 6 x 1 = 6 miles

Total miles he ran in 1/2 hours = 6 x 1/2 = 3 miles

Total miles he ran in 1 1/3 hours = 6 x 4/3 = 8 miles

The formula to determine total time:  total distance / average speed

Time it took Noah to run 1 1/2 miles = 3/2 ÷ 6 = 1/4 miles

Time it took Noah to run 9 miles = 9 ÷ 6 = 1 1/2 miles

Time it took Noah to run 4 1/2 miles = 9/2 ÷ 6 = 3/4 miles

Please find attached an image of the table used in answering this question

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Answer:

Step-by-step explanation:

m² + 8m = -3

(m² + 8m+16) -16 = -3

(m+4)² = 13.....continue

Answer:

m∠y=50°

m∠x=50°

Step-by-step explanation:

we know that

The angles in matching corners are called corresponding angles. When the two lines are parallel Corresponding Angles are equal

so

m∠y=50° -----> by corresponding angles

and

The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles. When the lines are parallel, the alternate interior angles are equal.

so

m∠x=m∠y -----> by alternate interior angles

so

m∠x=50°

therefore

m∠y=50°

m∠x=50°

Step-by-step explanation:

Accrual - the accumulation or increase of something over time, especially payments or benefits.

(Accumulation Accounting)

Net Income: $15,000

Spent: 6($1,400)+$6,000

$8,400+$6,000 = $14,400

Current Total (In-hand): $600

Not Been Paid Yet (Not In-hand): $11,948

Accrual accounting is a method of accounting that records transactions when they occur, not when cash is exchanged. It takes into account revenues earned and expenses incurred during a specific period. In this case, the student's net income of $15,000 is calculated based on revenues earned and expenses incurred, even though there may be little cash on hand.

Accrual accounting is a method of accounting where transactions are recorded when they occur, not when the money is exchanged. It takes into account both revenues earned and expenses incurred during a specific period, regardless of when the cash is received or paid.

In your case, even though you have little cash on hand, your net income of $15,000 is calculated based on revenues earned and expenses incurred. Let's break it down:

So, your net income of $15,000 takes into account these revenues and expenses, in accordance with accrual accounting principles.

Answer:

1/5

Step-by-step explanation:

Lets start with the number 100. We know that 1/10 of 100 is 10! 1/10 can also be written as 10%.

Now lets think about it, We're looking for 20%. If 1/10 of 100 is 10%, then 2/10 of 100 is 20%!

So you've got the fraction 2/10! Now you need to simplify it :)

Both the numerator (2) and the denominator (10) can be divided by 2!

(2/2)=1

(10/2)=5

Therefore, after simplifying 2/10 your final answer should be 1/5!

Answer:  the explanation is given below. The number is NOT an integer.

Step-by-step explanation:  We are given to check whether the number -0.5 is an integer or not.

We know that

an integer is a number where the digits after the decimal are zero, or the denominator of its fractional form is 1.

The given number is

[tex]n=-0.5.[/tex]

Here, we can see that the digits after the decimal is 5, not zero. Also,  

this number can be represented as a negative fraction with denominator not equal to 1 is as follows :

[tex]n=-\dfrac{5}{10}=-\dfrac{1}{2}.[/tex]

Therefore, this number is NOT an integer.

Answer:

[tex]2\pi \approx 6.28\ meters[/tex]

Step-by-step explanation:

Mei's horse is 3 meters from the center of the carousel. After one rotation, Mei travelled

[tex]l_M=2\pi r=2\pi \cdot 3=6\pi\ meters[/tex]

Anju's horse is 2 meters from the center. After one rotation, Mei travelled

[tex]l_A=2\pi r=2\pi \cdot 2=4\pi\ meters[/tex]

The difference in their travelled distances is

[tex]l_M-l_A=6\pi -4\pi =2\pi \approx 6.28\ meters[/tex]

Mei travels 6.28 meters more than Anju in one rotation.

In one rotation, Mei's horse travels a distance of

2 * 3.14 * 3 = 18.84 meters.

In one rotation,

Anju's horse travels a distance of 2 * 3.14 * 2 = 12.56 meters.

Therefore, Mei travels 18.84 - 12.56 = 6.28 meters more than Anju in one rotation.

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Answer:

4.61 g/cm3

Step-by-step explanation:

density is mass divided volumen

[tex]density \: = \frac{64.54g}{14 {cm}^{3} } = 4.61 \frac{g}{ {cm}^{3} } [/tex]

The density of the object is 4.61 g/cm³

Using the parameters given for our Calculation;

The density of an object can be calculated as the ratio of the mass to the volume of the object.

Inputting the values thus;

Hence, the density is 4.61 g/cm³

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Answer:

[tex]\frac{4^{21}}{5^{6}}[/tex]

Step-by-step explanation:

[tex]\frac{4^{7*3}}{5^{2*3}}=\frac{4^{21}}{5^{6}}[/tex]

Answer:19

Step-by-step explanation:

Subtract then add

[tex]\bf -25~~,~~\stackrel{-25-12}{-37}~~,~~\stackrel{-37-12}{-49}~~,~~...\qquad \qquad \qquad \stackrel{\textit{common difference}}{d = -12} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-25\\ d= -12\\ n = 85 \end{cases}[/tex]

[tex]\bf a_{85}=-25+(85-1)(-12)\implies a_{85}=-25+(84)(-12) \\\\\\ a_{85}=-25+(-1008)\implies a_{85}=-25-1008\implies a_{85}=-1033[/tex]

The 85th term of the arithmetic sequence – 25, -37, -49, ... is  -1033

Explanation:

Explicit Arithmetic Sequence:

aₙ = a₁+ (n-1)d

Here Common difference ,d =  -37-(-25)  = -12 ,  n = 85 and a₁ = -25 .

[tex]a_{85}[/tex]  = -25 + (85 - 1 ) -12

[tex]a_{85}[/tex]  =  -25 + (84) -12

[tex]a_{85}[/tex] =  -25 + (-1008)

[tex]a_{85}[/tex] =  - 1033

Complete Question  : The question should be Find the 85th term of the arithmetic sequence  -25, -37, -49, ...

Answer:

1 2/3 an egg to a bird

Step-by-step explanation:

because there are 5 eggs and divide 5 by 3 you get 1 2/3 and there are 3 birds so each gets 1 2/3rds an egg

Answer:

C) 3:5

Step-by-step explanation:

The question asks for the ratio of birds to eggs. It's asking how many birds there are in comparison to the number of eggs. The key to ratios is paying attention to which is listed first.

There are 3 birds, and 5 eggs, therefore the ratio is 3:5

Answer:

c. They are equal to each other.

d. They are the negative of each other.

Step-by-step explanation:

c. Adding c to d and d to c are the same and thus both expressions are equal. In addition, the numbers can be added in any order and will result in the same final answer. This is also known as commutative property.

d. a-b= -(b -a)

In this case, subtracting b from a is not equal to subtracting a from b. The order of terms in subtraction affects the final answer.

Answer: 3.5−2.5n

Explanation:

To find the common difference take the end term and subtract the first term:

8.5 -11 = -2.5

Take the third term and subtract the 3rd term to verify:

6-8.5 = -2.5  check

The formula for an arithmetic sequence is:

an = a1+d(n-1)

an = 11 -2.5(n-1)

Distribute:

an = 11 -2.5n+2.5

Combine terms:

answer = 13.5 - 2.5n

Explanation: Tread more on Brainly.com - https://brainly.com/question/13244259#read more find the common difference take the end term and subtract the first term:8.5 -11 = -2.5Take the third term and subtract the 3rd term to verify:6-8.5 = -2.5  check The formula for an arithmetic sequence is: an = a1+d(n-1)an = 11 -2.5(n-1)Distribute: an = 11 -2.5n+2.5Combine terms: answer = 13.5 - 2.5nAnswer:

Answer: 3.5−2.5n

Answer:

i am pretty sure it is b

Step-by-step explanation:

Answer:

The selling price is $16.43

Step-by-step explanation:

we know that

A markup percentage is the amount of the cost of an item that you add on to create the selling price

we have that

[tex]100\%+210\%=310\%=310/100=3.10[/tex]

To find out the selling price, multiply the cost of a calculator by the factor 3.10

so

[tex]\$5.30(3.10)=\$16.43[/tex]

therefore

The selling price is $16.43

The developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.

To represent the proportional relationship between the total earnings (y) and the number of apps downloaded (x), we can use the formula for direct variation, which is:

[tex]\[ y = kx \][/tex]

Where:

- [tex]\( y \)[/tex] represents the total earnings,

- [tex]\( x \)[/tex] represents the number of apps downloaded, and

- [tex]\( k \)[/tex] is the constant of proportionality.

In this scenario, the app developer earns $20.00 for every 8 apps downloaded. This means that for every 8 apps downloaded, the earnings increase by $20.00. So, the constant of proportionality [tex](\( k \))[/tex] is the rate at which earnings increase per app downloaded.

To find the value of [tex]\( k \)[/tex], we can divide the total earnings by the number of apps downloaded:

[tex]\[ k = \frac{y}{x} \][/tex]

Given that the developer earns $20.00 for every 8 apps downloaded, we can substitute these values into the equation:

[tex]\[ k = \frac{20}{8} \][/tex]

[tex]\[ k = 2.5 \][/tex]

Now that we have the value of [tex]\( k \)[/tex], we can rewrite the equation with this value:

[tex]\[ y = 2.5x \][/tex]

This equation represents the proportional relationship between the total earnings [tex](\( y \))[/tex] and the number of apps downloaded [tex](\( x \))[/tex]. It shows that for every additional app downloaded, the total earnings increase by $2.50, maintaining a consistent rate of increase.

This equation allows the app developer to predict their earnings based on the number of apps downloaded. For example, if 20 apps are downloaded, the total earnings can be calculated as:

[tex]\[ y = 2.5 \times 20 = 50 \][/tex]

So, the developer would earn $50.00 if 20 apps are downloaded. Similarly, they can calculate earnings for any other number of app downloads using this equation.

Answer:

x - 1

Step-by-step explanation:

(f + g)(x)=f(x) + g(x)

(f + g)(x)=(3x - 7) + (-2x - 6)

(f + g)(x)= 3x - 7 - 2x + 6

(f + g)(x)= 3x - 2x - 7 + 6

(f + g)(x)= x -1

Answer:

you need to show a picture of a graph for my answer to be acurate but I'll try.

Step-by-step explanation:

The x intercept is found by setting y = 0 in the above equation and solve for x. Hence, the x intercept is at (c/a , 0). The y intercept is found by setting x = 0 in the above equation and solve for x.

Answer:

x = -5

Step-by-step explanation:

Solve for x:

3 x + 1 = -14

Subtract 1 from both sides:

3 x + (1 - 1) = -14 - 1

1 - 1 = 0:

3 x = -14 - 1

-14 - 1 = -15:

3 x = -15

Divide both sides of 3 x = -15 by 3:

(3 x)/3 = (-15)/3

3/3 = 1:

x = (-15)/3

The gcd of -15 and 3 is 3, so (-15)/3 = (3 (-5))/(3×1) = 3/3×-5 = -5:

Answer:  x = -5

Answer:

Step-by-step explanation:

3x + 1 = -14;

substr 1 : 3x+1-1 = - 14 -1

3x = -15

divid by 3

x = -5