pLeAsE hElP! HuRrY!

Solve for A:

14a < 112

A.) a < -8
B.) a > 8
C.) a > -8
D.) a < 8

Check the picture below.

[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]

Final answer:

The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).

Explanation:

The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).

The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.

Answer: The answer would be the third option 4/4 x 6 = 6

Answer:

4/4 x 6 = 6

Step-by-step explanation:

This is the answer because 4/4 is one which means 1 x 6 = 6 so they are the same.

ye boi its A | SMART BOIS

Option D:

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

Solution:

Given expression is [tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex].

To find the product of the expression:

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex]

Multiply each term of the first term with each term of the 2nd term.

           [tex]=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)[/tex]

Using the exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

           [tex]=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)[/tex]

           [tex]=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7[/tex]

Arrange the terms with same power.

           [tex]=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7[/tex]

           [tex]=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

Hence option D is the correct answer.

[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]

Answer:

{x,y,z}={-8,-3,4}

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Area of a circle = πr^2

64π / π = πr^2 / π

sqrt(64) = sqrt(r^2)

8 = r

Answer:  8

Final answer:

The question requires calculating the number of people who stayed and were not bored out of a total of 32 people.

Explanation:

The question involves calculating the number of people who stayed and were not bored out of 32 people.

Therefore, the number of people who were not bored were 4 people.

Answer:

b) When the temperature is 70°F, the park can expect 42 visitors.

Step-by-step explanation:

Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:

y = 42 + 15x

The general equation of a straight line plotted y against x with an intercept(c) on the y-axis and a slope(m) is given by the equation:

y = mx + c

comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.

This means that at temperature 70°F, x is 0.

therefore y = 42 + 15(0) = 42

Therefore when the temperature is 70°F, the park can expect 42 visitors.

Option C:  [tex](6^{-4})^{-4}[/tex]

Option D:  [tex](6^{-2})^{-8}[/tex]

Option F:  [tex](6^8)^2[/tex]

Solution:

Given expression: [tex]6^{16}[/tex]

To find which expression is equivalent to the given expression.

Let us solve this using exponent rule: [tex]\left(a^{b}\right)^{c}=a^{b c}[/tex]

Option A: [tex](6^{0})^{16}[/tex]

[tex](6^{0})^{16}=6^{0 \times 16}= 6^0[/tex]

It is not equivalent expression.

Option B: [tex](6^8)^8[/tex]

[tex](6^{8})^{8}=6^{8 \times 8}= 6^{64}[/tex]

It is not equivalent expression.

Option C:  [tex](6^{-4})^{-4}[/tex]

[tex](6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}[/tex]

It is equivalent expression for the given expression.

Option D:  [tex](6^{-2})^{-8}[/tex]

[tex](6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}[/tex]

It is equivalent expression for the given expression.

Option E:  [tex](6^{-1})^{16}[/tex]

[tex](6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}[/tex]

It is not equivalent expression.

Option F:  [tex](6^8)^2[/tex]

[tex](6^{8})^{2}=6^{8 \times 2}= 6^{16}[/tex]

It is equivalent expression for the given expression.

Hence [tex](6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2[/tex] are the equivalent expressions.

Option C, Option D and Option F are correct answers.

The error in the amount of change she was 25.28%.

Step-by-step explanation:

Given,

The actual price = 15.65$

The amount Luna gives to cashier = 20$

The change she receives = c = 3.25$

The actual amount of changes = x = total amount - actual price:

20$ - 15.65$ = 4.35

The percentage of error can be found using: [tex]\frac{x-c}{x}[/tex]

By putting the values in equation, we get

=> [tex]\frac{4.35 - 3.25}{4.35} * 100[/tex]

=> [tex]\frac{1.10}{4.35} * 100[/tex]

=> 25.28  %

Hence, the error in the amount of change she was 25.28%.

The percent error in the amount of change Luna was given is:

[tex]\[\boxed{25.29\%}\][/tex]

To determine the percent error in the amount of change Luna was given, we need to compare the actual change received to the correct change she should have received.

Step 1: Calculate the Correct Change

Luna gave the cashier $20 for a shirt that costs $15.65. The correct amount of change should be:

[tex]\[\text{Correct Change} = 20 - 15.65 = 4.35 \, \text{dollars}\][/tex]

Step 2: Calculate the Error

The cashier gave Luna $3.25 instead of $4.35. The error in the change given is:

[tex]\[\text{Error} = \text{Correct Change} - \text{Actual Change Given} = 4.35 - 3.25 = 1.10 \, \text{dollars}\][/tex]

Step 3: Calculate the Percent Error

Percent error is given by the formula:

[tex]\[\text{Percent Error} = \left( \frac{\text{Error}}{\text{Correct Change}} \right) \times 100\][/tex]

Substitute the values into the formula:

[tex]\[\text{Percent Error} = \left( \frac{1.10}{4.35} \right) \times 100\][/tex]

Perform the division:

[tex]\[\frac{1.10}{4.35} \approx 0.2529\][/tex]

Convert to a percentage:

[tex]\[0.2529 \times 100 \approx 25.29\%\][/tex]

The percent error in the amount of change Luna was given is:

[tex]\[\boxed{25.29\%}\][/tex]

Answer:

Dog: 9 pounds

Cat: 18 pounds

Step-by-step explanation:

x + y= 27

y = 2x

2x + x = 27

3x = 27

x = 9

y = 2x = 18

Answer:

7.57082 liters

Step-by-step explanation:

Answer:9/7+5/8=72/56+35/56

Step-by-step explanation:9/7 times 8 by both 9 and 7 and times 7 by both 5   and 8 and you will get your answer

Answer:

[tex]1\frac{51}{56}[/tex]

Step-by-step explanation:

In order to find the answer to this question you will have to find the common denominator, (CD) multiply the denominators by the amount it takes to receive the common deliminator then do the same with the numerators without finding the common numerator, and then add the two numerators together and reduce if needed.

[tex]\frac{9}{7} +\frac{5}{8}[/tex]

Find the common denominator:

[tex]CD=56[/tex]

[tex]9\times 8 =72[/tex]

[tex]7 \times 8 = 56[/tex]

[tex]= \frac{72}{56}[/tex]

Do the same with the second fraction:

[tex]5\times7=35[/tex]

[tex]8\times7=56[/tex]

[tex]=\frac{35}{56}[/tex]

Then you would have:

[tex]\frac{72}{56} +\frac{35}{56}[/tex]  

Add the numerators:

[tex]72+35=107[/tex]

[tex]=\frac{107}{56}[/tex]

Turn the improper fraction into a mixed number:

[tex]\frac{107}{56} = 1\frac{51}{56}[/tex]

You get this by dividing 107 by 56 which should give you 1 with the remainder of 51 and you keep the denominator the same.

[tex]=1\frac{51}{56}[/tex]

Hope this helps.

Answer:

6 yards

Step-by-step explanation:

Perimeter of a rectangle:  2a + 2b

2(33) + 2(75)

66 + 150

216 inches

216/12 gives us feet

18/3 gives us yards

6 yards

Answer:  6 yards

Answer:((√2) + 2)/2

Step-by-step explanation:

(1+√2)/(√2) x ((√2)/(√2))

(√2(1+√2))/2

((√2)+2)/2

Volume of the cone is 200 cm³

Step-by-step explanation:

Volume = 1/3 × 3.14 × 5² × 7

             = 183.17 in³ ≈ 200 cm³ (rounding off to nearest hundredth)

Answer:

[tex]2304 \ in^3[/tex]

Step-by-step explanation:

Given the surface dimensions of the garden as 24 inches by 48 inches:

#Calculate surface area of the garden's top:

[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]

Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:

[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]

Hence, the amount of soil used is 2304 cubic inches.

Answer: those are right!

Hope this helps ❤️

Answer:

Gaby do not need to borrow money and they are left with $39.5      

Step-by-step explanation:

We are given the following in the question:

Total money = $50

Cost of a Cobb salad = $8.95

Cost of a drink = $1.55

Order: A Cobb salad and a drink

Cost of order =

[tex]= 8.95 + 1.55\\=\$10.5[/tex]

Thus, the total cost of order is $10.5

Money left =

= Total money - Order bill

[tex]=50 - 10.5\\=\$ 39.5[/tex]

Thus, Gaby do not need to borrow money and they are left with $39.5.

The median is is the midpoint of the data. This means half is below 50 and half is above 50.

The answer would be they handle less than 50 accounts.

50% of sales managers at Force Inc. manages fewer than 50( = the median given) number of accounts.

Given that:

[tex]Min = 35\\Q_1 = 45\\Median = 50\\Q_3 = 65\\Maximum = 85[/tex]

These 5 numbers summary tells the partition of data or quartiles with endpoints as minimum and maximum.

The median is a point for which the counts of data lying above it is equal to the counts of data lying below it.

Since the question asks about :

50% Sales managers manage < ? number of accounts

and since 50% of data lie below and above the median which is 50 given in the table.

Thus we have:

50% of the Sales manager at Force Inc. managing fewer than 50(the median given) number of accounts.

Learn more here:

https://brainly.com/question/300591

Answer:

(a):  9x + 45

Option A, 9(x + 5) because it distributes into 9x + 45

Option B, 9 * x + 9 * 5 because it multiplies into 9x + 45

(b):  13 + 9y - 3 - y

Option D, 8y + 10 because it combines into this number

Answer:

  2. 10

  3. D.  1 for all n

Step-by-step explanation:

2. The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^b = 1/a^-b

__

  [tex]\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}[/tex]

The value of n is 10.

__

3. Using the above rules of exponents, the expression simplifies to ...

  6^(-n+n) = 6^0 = 1

The value is 1 for any n.

Answer: 9+x

Step-by-step explanation:

If you have x apples, and you need nine more, you would need to ADD 9 and "x".

Answer:

18 but look at others awnsers aswell

Step-by-step explanation:

Answer:

Their is a total of 12 rectangles in the picture

Step-by-step explanation:

All of the figures located in the picture are all rectangles

Answer:

the  radius of the circle is 6cm

Step-by-step explanation:

the area of a circle is given to be  = 36πcm²

radius of the circle = ?

to find the radius of the circle lets start by applying  the formula for finding the area of a circle.

area of a circle = πr²

36πcm² = πr²

36π = πr²

divide both sides by π

36π/π = πr²/π

36 = r²

to get the value of r we are going to look for a way of getting rid of the square on "r" by squaring 36

r² = 36

r =√36

r = 6cm

therefore the  radius of the circle is 6cm

Answer:

6 cm

Step-by-step explanation:

Answer:

in 20 years Sam = 32 = same as Mary so 20 years before Mary was 12 and Sam was 4 times older when she was 48. Sam is now 48 and Mary is 48.  

Step-by-step explanation:

Answer:

Solve by undoing the division by multiplying by 6 on both sides of the equation. The solution is c = 54. Check the solution by substituting 54 for the variable in the original equation and then simplify. 9 = 9 is true, so 54 is the solution.

Step-by-step explanation:

The value of c is 54.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

c/6 = 9

Solve for c.

c/6 = 9

Multiply 6 on both sides.

c = 9 x 6

c = 54

Thus,

c is 54.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ6

first off let's convert the mixed fraction to an improper fraction and then divide.

[tex]\bf \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{3}{7}~~}{\frac{7}{6}}\implies \cfrac{3}{7}\cdot \cfrac{6}{7}\implies \cfrac{18}{49}[/tex]

The value of x is 8√2.

Step-by-step explanation:

From the right triangle,

The length of the side opposite to angle 45° is a=8.

Therefore, the value of y opposite to angle 45° is also 8.(b=8)

Using Pythagorean theorem,

The length of hypotenuse is c ⇒ c² = a²+b²

c² = 8²+8²

c² = 64+64 = 128

c = √128

c = √64[tex]\times[/tex]2

c = 8√2