Find the length of the midsegment.
15
13
22
44

Answer:

A) x²/9 -y²/4 = 1

Step-by-step explanation:

The distance from center to one vertex is half the difference of the distances from a point to either focus. That is, the distance from center to the vertex is 3 on the x-axis, so the x-term is (x/3)² = x²/9.

In the picture, ...

... c² = a² + b²

The problem statement tells us c = √13, so we know c² = 13. Then ...

... b² = c² - a² = 13 -9 = 4

and the y-term is y²/4.

Thus, the equation is ...

... x²/9 - y²/4 = 1

_____

You knew that was the correct choice as soon as you knew the x-term.

Answer:

8/20 and 12/30 are equivalent to 4/10.

Step-by-step explanation:

You just have to multiply the numerator and denominator by the same number.

Answer:

Step-by-step explanation: The answer is D- Substitution Property of Equality. I just did the test and it was right.

Answer:

C. Subtraction property of equality.

Step-by-step explanation:

Given AD= CF

 And BC=DE

To prove that AB=EF

Proof:

1.Statement: AD=CF

Reason: Given in question.

2. Statement: AD= AB+BC+ CD, CF= CD+DE+EF

Reason: Segment addition property because AB,BC,and CD are the segments of AB and CD,DE and DE are segments of CF.

3. Statement: AB+BC+CD=CD+DE+EF

Reason: Transitive property of equality

Transitive property: If ab=bc and bc=ca

Then   , ab=ca

4.Statement:  AB+BC= DE+EF

Reason: By using subtraction property of equality.

5. Statement:BC=DE

Reason: Given in question.

6. Statement: AB=EF

Reason: when we put BC=DE . Then we get AB+DE=DE+EF. By using subtraction property of equality .

Hence proved .

Answer:

answer 7.3

13x-7+11x+11=180

Step-by-step explanation:

Answer:

If A is multiplied by 3, B will be reduced by a factor [tex]\frac{1}{\sqrt{3}}[/tex]

Step-by-step explanation:

Writing the inverse proportionality relationship and expressing the dependence of B on A leads to the following:

[tex]A = \frac{1}{B^2}\implies |B| = \frac{1}{\sqrt{A}}\\B'=\frac{1}{\sqrt{3A}}= \frac{1}{\sqrt{3}}\frac{1}{\sqrt{A}}=\frac{1}{\sqrt{3}}|B|[/tex]

In words, if A triples, B will decrease by a factor [tex]\frac{1}{\sqrt{3}}[/tex], or, in other words, the square of B will decrease to one third of its previous value.

Step-by-step explanation:

Let s be charges for a single room and d be charges for a double room per night.

We are told that a hotel has 150 rooms. We can represent this information as:

[tex]s+d=150...(1)[/tex]

The charges for a double room are $270 per night and $150 per night for a single room. So the charges for s single rooms will be 150s and charges for d double rooms will be 270d.

On a night when the hotel was completely occupied. Revenues were $33,300.

We can represent this information as:  

[tex]150s+270d=33,300...(2)[/tex]

Therefore, our desired pair of equations will be:

[tex]s+d=150...(1)[/tex]

[tex]150s+270d=33,300...(2)[/tex]

Answer: First equation: s+d=150; second equation: 150s+270d=33300

Step-by-step explanation: To solve the given problem we need to write two equations, the first one will express that the total number of rooms is the sum of the single rooms an the double rooms. The second equation will include the sum of the total earnings for the single and double rooms:

First equation:

s+d=150 (the single rooms and the double rooms equal 150 rooms)

second equation:

150s+270d=33300  (the sum of the single and double rooms each one of them multiplied by their prices, equals the total revenue)

To solve the equation we isolate s from the first equation:

s=150-d

and we replace it in the second one:

150(150-d)+270d=33300

solving for d:

22500-150d+270d=33300

120d=33300-22500

120d=10800

d=10800/120

d=90.

now we calculate s from the first equation:

s=150-d

s=150-90

s=60.

There are 60 single rooms and 90 double rooms.

Answer:

$7.28

Step-by-step explanation:

We have been given that Brandon buys a basket of flowers for $7 before tax. The sales tax is 4%.

The total price that Brandon paid for the basket of flowers will be equal to 7 plus 4% of 7.

We can represent this information in an equation as:

[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(\frac{4}{100}\times 7)[/tex]

[tex]\text{The total price that Brandon paid for the basket of flowers}=7+(0.04\times 7)[/tex]

[tex]\text{The total price that Brandon paid for the basket of flowers}=7+0.28[/tex]

[tex]\text{The total price that Brandon paid for the basket of flowers}=7.28[/tex]

Therefore, the total price paid by Brandon for the basket of flowers was $7.28.

Answer:

Total price Brandon pays for the basket of flowers is, $7.28

Step-by-step explanation:

As per the given statement: Brandon buys a basket of flowers for $7 before tax.

Convert this $7 into cents.

1 dollars = 100 cents.

$7 = 700 cents.

It is also given that the sales tax is 4%.

then;

Sales tax = [tex]4\% \times 700 = \frac{4}{100} \times 700 = 4 \times 7 =28 cents[/tex]

Total price Brandon pays = Price of Brandon buys a flower before tax + sales tax price

=  700 + 28 = 728 cents = $7.28

Therefore, the total price Brandon pays for the basket of flowers is, $7.28

Answer:1/12

Step-by-step explanation:1/3-1/4=1/12

Answer: 3/10 watts

Step-by-step explanation:

3/5 converts to 6/10

6/10 / 2 = 3/10

Answer:

3/10

Step-by-step explanation:

3/5 converts to 6/10

6/10 / 2 = 3/10

Answer: (A) degree of 2; 1 ± i√7

Step-by-step explanation:

Degree of the polynomial designates the number of roots.

x² - 2x + 8

a=1  b=-2 c=8

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

  [tex]=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(8)}}{2(1)}[/tex]

  [tex]=\dfrac{2\pm\sqrt{4-32}}{2}[/tex]

  [tex]=\dfrac{2\pm\sqrt{-28}}{2}[/tex]

  [tex]=\dfrac{2\pm2i\sqrt{7}}{2}[/tex]

  [tex]=\dfrac{2(1\pm\\i\sqrt7)}{2}[/tex]

  = 1 ± i√7

Answer:

For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)

Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as .

An important property of reciprocals is that if you mutliply them together they will cancel out--take  for example.

Since secӨ is literally defined as the reciprocal of cosӨ, it is evident that

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Step-by-step explanation:

Final answer:

Luke can make 20 servings with 5 pounds of ground turkey.

Explanation:

To determine the number of servings Luke can make with 5 pounds of ground turkey, we need to set up a proportion. The recipe calls for 1.5 pounds of ground turkey for every 6 servings. So, we can set up the proportion: 1.5 pounds / 6 servings = 5 pounds / x servings, where x represents the unknown number of servings. To solve for x, we cross multiply: 1.5 pounds * x servings = 5 pounds * 6 servings. Simplifying the equation, we get: 1.5x = 30. Dividing both sides by 1.5, we find that x = 20. Therefore, Luke can make 20 servings with 5 pounds of ground turkey.

Answer:

[tex]\hat{y}=309,552.15 + 1.31x[/tex]

Step-by-step explanation:

The equation for the least-squares regression is,

[tex]\hat{y}=a+bx[/tex]

where b is the slope and a is the intercept.

They can be found out by,

[tex]b=r\cdot \dfrac{SD_y}{SD_x},\\\\a=\overline{y}-b\overline{x}[/tex]

where,

r = correlation coefficient = 0.84

[tex]SD_y[/tex] = standard deviation of y = 44,910

[tex]SD_x[/tex] = standard deviation of x = 28,803

[tex]\overline{y}[/tex] = mean of y = 774,140

[tex]\overline{x}[/tex] = mean of x = 354,718

Putting the values,

[tex]b=0.84\cdot \dfrac{44910}{28803}=1.309\approx 1.31[/tex]

[tex]a=774140-(1.31\times 354718)\approx 309,552.15[/tex]

Therefore the equation is,

[tex]\hat{y}=309,552.15 + 1.31x[/tex]

Answer:

y=-37

Step-by-step explanation:

A perpendicular line has a negative reciprocal slope to the original line. We will use the slope formula to find the slope of line m, then take the negative reciprocal for the slope of line n which will reveal the value of y.

Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We substitute [tex]x_1=6\\y_1=8[/tex] and [tex]x_2=-1\\y_2=2[/tex]

[tex]m=\frac{2-8}{-1-6}[/tex]

[tex]m=\frac{2-8}{-1-6}=\frac{-6}{-7} =\frac{6}{7}[/tex]

[tex]m\neq \frac{6}{7}[/tex] for line n because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is [tex]m=-\frac{7}{6}[/tex].

We will substitute [tex]m=-\frac{7}{6}[/tex] into the slope formula to find line n's coordinate value y. We will also substitute [tex]x_1=-1\\y_1=5[/tex] and  [tex]x_2=5\\y_2=y[/tex] .

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]-\frac{7}{6}=\frac{y-5}{5-(-1)}[/tex]

[tex]-\frac{7}{6}=\frac{y-5}{6)}[/tex]

[tex]6(-\frac{7}{6})=y-5[/tex]

[tex]-42+5=y-5+5[/tex]

[tex]-37=y[/tex]

The value of y that makes Line n perpendicular to Line m is 59/6. This is found by first calculating the slope of Line m and then finding the negative reciprocal (since perpendicular lines have negative reciprocal slopes), and using this new slope to solve for y in Line n.

To solve this problem, we first need to understand that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if Line m has a slope of a, then Line n will have a slope of -1/a.

First, let's find the slope of line m which contains the points (6,8) and (-1,2). The formula for slope is (y2-y1)/(x2-x1). This gives us (2-8)/(-1-6) = -6/-7 = 6/7.

Because line n is perpendicular to line m, its slope will be the negative reciprocal of 6/7, which is -7/6. We can then use this slope and the point (-1,5) to find the value of y when x=5 on line n. We use the equation y-y1 = m(x-x1), and substitute the values in: y - 5 = -7/6 * (5 - (-1)), which simplifies to y = -7 + 5 + 35/6 = 29/6 + 30/6 = 59/6.

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Answer:

False

Step-by-step explanation:

The sum of the interior angles of a regular polygon is  (n – 2)180  where n is the number of sides.   Since this is a 10 sided figure,

the sum of the interior angles is (10-2)* 180 =1440

Answer:

6

Step-by-step explanation:

sqrt (36)

Lets break this into parts

sqrt(4 * 9)

sqrt(4)  * sqrt(9)

2 * 3

6

Answer:

Number of ripe mangoes were sold as 132

Step-by-step explanation:

Let's assume number of rip mangoes were sold as 'x'

A store manager ordered 28 crates of mangoes

Number of crates =28

There were 36 mangoes in each crate

Number of mangoes in each crate=36

Total number of mangoes=( Number of crates)*(Number of mangoes in each crate)

Total number of mangoes is

[tex]=28\times 36[/tex]

[tex]=1008[/tex]

WHEN the mangoes were delivered

he sold the ripe mangoes and repacked the rest equally into 73 boxes

There were 12 mangoes in each box

Total number of mangoes is

[tex]=73\times 12+x[/tex]

[tex]=876+x[/tex]

now, we can set them equal

[tex]1008=876+x[/tex]

[tex]x=132[/tex]

To find the number of ripe mangoes sold, multiply the number of crates by the number of mangoes in each crate. Then, multiply the number of boxes by the number of mangoes in each box. Finally, subtract the number of mangoes repacked into boxes from the total number of mangoes delivered.

To find the number of ripe mangoes sold, we need to determine the total number of mangoes delivered and then subtract the number of mangoes repacked into boxes.

First, we find the total number of mangoes delivered by multiplying the number of crates (28) by the number of mangoes in each crate (36): 28 crates * 36 mangoes/crate = 1008 mangoes

Next, we find the number of mangoes repacked into boxes by multiplying the number of boxes (73) by the number of mangoes in each box (12): 73 boxes * 12 mangoes/box = 876 mangoes

Finally, we subtract the number of mangoes repacked into boxes from the total number of mangoes delivered to find the number of ripe mangoes sold: 1008 mangoes - 876 mangoes = 132 ripe mangoes

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Answer:

1.  b=-7

2.  c= -10

Step-by-step explanation:

The standard form for the quadratic function is

ax^2 +bx+c

so  we need to rewrite the function to be in this form

2x^2 -10 = 7x

Subtract 7x from each side

2x^2 -7x-10 = 7x-7x

2x^2 -7x-10 = 0

a =2, b= -7  c=-10

Answer:

After lunch, the family traveled at a speed of 45 mph is the only solution that makes sense when simplifying d(h)=50+45H

Step-by-step explanation:

Answer: After lunch the family drove 45 miles per hr. HOPE THIS HELPS!

Answer:

$24.5

Step-by-step explanation:

Let x be the cost of sweater before markup.

We are told that Dan paid $34.30 for a sweater the price included a 40% markup. This means x plus 40% of x equals 34.30.

We can represent this information as:

[tex]x+\frac{40}{100}x=34.30[/tex]

[tex]x+0.40x=34.30[/tex]

[tex]1.40x=34.30[/tex]

[tex]x=\frac{34.30}{1.40}[/tex]

[tex]x=24.5[/tex]

Therefore, the cost of sweater before the markup was $24.5.

Answer:

s = 65/3 pi

Step-by-step explanation:

The length of the intercepted arc is given by the formula

s =r*theta  when theta is given in radians

r = 13

theta = 5 pi/3

Substituting what we know

s = 13 * 5 pi/3

s = 65/3 pi

Since we want an exact answer, we have to leave it in terms of pi and as a fraction

Answer:

A and B

Step-by-step explanation:

assuming the function should be

- [tex]3^{x-1}[/tex] + 2, then

A

substitute the x value into f(x) and check the validity of the y- value

f(4) = - [tex]3^{3}[/tex] + 2 = - 27 + 2 = - 25 ← agrees with y value

(4, - 25) lies on the graph

B f(1) = - [tex]3^{0}[/tex] + 2 = - 1 + 2 = 1 ← agrees with y value

(1, 1) lies on the graph

C

f(- 1) = - [tex]3^{-2}[/tex] + 2 = - [tex]\frac{1}{9}[/tex] + 2 ≠ 2

(- 1, 2) does not lie on the graph

D

f(0) = [tex]3^{-1}[/tex] + 2 = - [tex]\frac{1}{3}[/tex] + 2 ≠ 0

(0, 0) does not lie on the graph

Answer:

Step-by-step explanation:

First you need to divide by the amount he needs by the amount he gets, 352 divided by 8. That equals 44, so he will need to work 44 hours to reach his goal.

Answer: x - 2y = -12

Step-by-step explanation:

[tex]y - 3 = \dfrac{1}{2} (x+6)\\2(y - 3) = (2)\dfrac{1}{2}(x + 6)\\2y - 6 = x + 6\\\underline{-x +6}\quad\underline{-x + 6}\\-x + 2y = 12\\-1(-x + 2y = 12)\\x - 2y = -12[/tex]

ANSWER:

-1/2x + y = 6

ABOUT POINT SLOPE FORM:

ABOUT STANDARD FORM:

y - 3 = 1/2 (x + 6)

y - 3 = 1/2x + 3

 + 3            + 3

y = 1/2x + 6

-1/2x   -1/2x

-1/2x + y = 6

I'm not sure if my answer is correct... But please tell me if it's correct or incorrect! Thank you! :)

Answer:

After giving 197 cards away, Jenson is left with 361 cards

Step-by-step explanation:

Answer:



Step-by-step explanation:

Let x represent the number of buttons on shirts and y represent the number of buttons on jackets.

If 36 shirts and 42 jackets contain 842 buttons. This implies:

36x + 42y = 842 (1)

If 66 shirts and 77 jackets contain 137 buttons. This implies:

66x + 77y = 137 (2)

If you take the first equation: 36x + 42y = 842 and isolate the x, then you will have x = (842 - 42y) / 36

If you substitute x into the second equation:

66((842-42y)/36) + 77y = 137

→ 11(842-42y)/6 + 77y = 137

→ 11(842-42y) + 6(77y) = 137(6)

→ 9262 - 462y + 462y = 822

→ 9262 = 822 which reveals that the equations do not have a solution