solve this quadratic equation by completing the square. x^2+4x=15
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A, B, D are your answers

AP E X

Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

A. Point H is the midpoint of FG: This statement must be true because line t is the perpendicular bisector of FG, which means it passes through the midpoint of FG and intersects FG at a right angle.

Therefore, H is the midpoint of FG.

B. Line t intersects FG at a right angle: This statement must be true because line t is the perpendicular bisector of FG, which means it intersects FG at a right angle.

C. FG = FH: This statement is not necessarily true.

While H is the midpoint of FG, the length of FH depends on the position of point H along line t. It could be greater than, less than, or equal to half the length of FG.

D. Line t is perpendicular to FG

This statement must be true because line t is the perpendicular bisector of FG, which means it is perpendicular to FG.

E. Line t is parallel to FG: This statement is not true. If line t were parallel to FG, it would not intersect FG at all, let alone at a right angle as required for a perpendicular bisector.

Therefore, Point H is the midpoint of FG, Line t intersects FG at a right angle and Line t is perpendicular to FG are true statements.

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Answer:

A

Step-by-step explanation:

The first thing to notice is the question says it is given that the person is between the ages 23 and 60, so we only care about those people. So then we want to know how likely it would be to pick someone with over 50 messages a month. So what you would do is take the amount of people who are between 23 and 60 and send over 50 text messages, and divide that by the total amount of people 23-60 (since that is the pool of people we have). Doing so we find there is 229 people aged 23-60 which then makes the answer 157/229 or A.

Answer:

The value of x is 66

Step-by-step explanation:

Answer:

66°

Step-by-step explanation:

The interior angles of a triangle always sum up to 180°.  Looking at the first triangle, we see 48° + 66° + x = 180°, or x = 180° - (48° + 66°) = 66°.  This is true because the triangles are congruent.

Answer:

65

Step-by-step explanation:

Since we know that a rectangle is 360 degrees

90+88+117 = 295

360-295=

65

Answer:

Stem   Leaf

2          8

3          4 4

5          0 4

So we need to put all the tens values in the "stem" column and all the ones values in the "leaf" column, sorted from least to greatest.

We have three tens values: 2, 3, and 5. So those are our three stems, in order.

We have to put the second number, the ones value, in the leaf column, least to greatest. So with two values of 34, we need two 4 leaves.  

Answer:

c

Step-by-step explanation:

Answer:

8.7

Step-by-step explanation:

Answer:

13*12 is greater than 11*14 by 2 meters^2

Step-by-step explanation:

[tex]A=wl=13*12=156m^2\\A=wl=11*14=154m^2[/tex]

Goodluck

Answer:

Jenny's room has a great area.

Step-by-step explanation:

Jenny's room

[tex]area = l \times b \\ = 13 \times 12 \\ = 156 {ft}^{2} [/tex]

Ruth's room

[tex]area = l \times b \\ = 14 \times 11 \\ = 154 {ft}^{2} [/tex]

so,

[tex]156 > 154[/tex]

So ,Jenny's room has a great area than Ruth's room.

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Answer:

23%

Step-by-step explanation:

Answer:

23 %

Step-by-step explanation:

The total money earned:

124+ 30+ 46 =200

Percent earned babysitting

money earned babysitting / total * 100%

46/200 * 100 = 23 %

Answer:

Step-by-step explanation:

Lets find the distance (the side length of the square)

D=sqrt((x2-x1)^(2)+(y2-y1)^(2))

plug in the coordinates:

D=sqrt((-5-(-5))^(2)+(12-(-3))^(2))

D=sqrt(0^(2)+15^(2))

D=sqrt(15^(2))

D=15

Area of a square is side length squared

A=s^2

A=15^2

A=225 units squared

Answer:

P=KC

P=1/5(C)

Step-by-step explanation:

Let

p=price per 5 copies

c=no. of copies

Direct variation can be written as

P=KC

K=constant

P=1 when c=5

1=k*5

1=5k

k=1/5

The direct variation equation can be written as

P=1/5(c)

Answer:

1/5

Step-by-step explanation:

Plato

Answer:

Step-by-step explanation:

Mathematically, the area of a sector can be calculated using the formula below;

area of sector = angle/360 * pi * r^2

From the question, angle = 180

pi= 22/7

r = d/2 = 5.6cm/2 = 2.8 cm

So the area of the sector is as follows;

A = 180/360 * 22/7 * 2.8^2

A = 2 * 22/7 * 2.8^2 = 49.28

which is 49.3 cm^2 to the nearest tenth

Step-by-step explanation:

2/3 - 1/4

8/12 - 3/12= 5/12

She ate 5/12 pound of turkey.

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Good luck on your assignment...

Answer:

S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars

S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars

S(24) = [tex]\sqrt{24+2}[/tex] = 5.10;  5.10  millions of dollars

S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ;  5.20  millions of dollars

Step-by-step explanation:

[tex]S(t) = \sqrt{t+2}[/tex]

[tex]S(t+h) = \sqrt{t+2+h}[/tex]

[tex]S(t+h) - S(t)= \sqrt{t+2+h }- \sqrt{t+2}[/tex]

[tex]\dfrac{S(t+h) - S(t)}{h}= \dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h}[/tex]

By rationalization:

[tex]\dfrac{\sqrt{t+2+h }- \sqrt{t+2}}{h} * \dfrac{ {\sqrt{t+2+h }- \sqrt{t+2}} }{ {\sqrt{t+2+h }- \sqrt{t+2}}}[/tex]

[tex]\\ \\ \dfrac{t+2+h-t-2}{h \sqrt{t+2+h }+ \sqrt{t+2} } = \dfrac {h}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]

= [tex]\dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} }[/tex]

[tex]\lim_{k \to \infty} \dfrac {1}{\sqrt{t+2+h }+\sqrt{t+2} } = \dfrac{1}{t+2}[/tex]

[tex]S' (t) = \dfrac{1}{\sqrt{t+2} }[/tex]

S(20) = [tex]\sqrt{20+2}[/tex] = 4.69 ; value of total sales after 20 months is 4.69 million dollars

S'(20) = [tex]\dfrac{1}{\sqrt{20+2} }[/tex] = 0.21 ; increase in the total sales after 20 months is 0.21 millions of dollars

S(24) = [tex]\sqrt{24+2}[/tex] = 5.10;  5.10  millions of dollars

S(25) = [tex]\sqrt{25+2}[/tex] = 5.20 ;  5.20  millions of dollars

Answer:

y = 120

Step-by-step explanation:

Interior angles of a triangle add up to 180°

So,

x+87+33 = 180

x + 120 = 180

Subtracting 120 to both sides

x = 180-120

x = 60°

Now

Angles on a straight line also add up to 180°

So,

x+y = 180

60 + y = 180

Subtracting 60 to both sides , we get

y = 180-60

y = 120

Answer:

wouldnt it be 10 out of 26 percent chance or 2.6

Step-by-step explanation:

there are 10 letters in county fair and 26 letters so you divide 26 by 10

The probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR". This is obtained by using probability concept.

Given total number of outcomes are 26

Since "COUNTY FAIR" has 10 letters, number of favourable outcomes are 10.

According to definition of probability we get ,

P(winning) =[tex]\frac{10}{26}[/tex] =[tex]\frac{5}{13}[/tex]

Hence the probability that Luca will win Wheel of Letters is [tex]\frac{5}{13}[/tex] given there are 26 equal sections lettered A to Z and the contestant win if the pointer lands on any letter in the phrase "COUNTY FAIR".

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Answer:

7 inches

Step-by-step explanation:

The volume of a cylinder is calculated using

where r =4 inches is the radius and V=351.68 is the volume.

To find the height of the jar, we substitute these values and solve for h.

Divide both sides by 50.24 to get:

h=7 inches

Therefore the height of the jar is 7 inches

Answer:

b

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

This is because when we do the work in the boxes we can see that B is the only answer that works with it.

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Answer:

60 ml oil, 90 g onions, 1200 g potatoes, 1350 ml milk

Step-by-step explanation:

What you need to do here is multiply all of these ingredients by 3, because the recipe serves 3 and he needs to serve 9, and 9/3 = 3. Therefore, he would have to triple the recipe.

Answer: The Inverse function is f^-1 (x) = 9x-18

Answer:

Exactly one solution

Step-by-step explanation:

4x -2y = 8

2x +y = 2

Multiply the second equation by 2

4x +2y = 4

Add the two equations together

4x -2y = 8

4x +2y = 4

-------------------

8x = 12

x = 12/8

We know there will be one solution

Answer:

19 cups of water.

Step-by-step explanation:

1:2 ratio

1=9.5

2=9.5*2= 19

Answer:

19 cups of water.

Answer:

value of 4 tan 45° +(2 sin 45°) (6 cos 45°)​ is 10.

Step-by-step explanation:

To solve this question we need to know value of

tan 45° = 1

sin 45° = [tex]1/\sqrt{2}[/tex]

cos 45° = [tex]1/\sqrt{2}[/tex]

we will be using above value sin the given expression as shown

[tex]4 tan 45 +(2 sin 45) (6 cos 45)​ = 4*1 + (2*1/\sqrt{2} )(6*1/\sqrt{2})\\ = 4 + (2/\sqrt{2}) (6/\sqrt{2})\\= 4 + (2*6)/(\sqrt{2}*\sqrt{2})\\= 4 + (12/2)\\= 4 + 6 = 10[/tex]

Thus, value of 4 tan 45° +(2 sin 45°) (6 cos 45°)​ is 10.

Answer:

it is C

Step-by-step explanation:

Answer:

F = -22

Step-by-step explanation:

F = 1.8 C + 32 for C = -30

F = 1.8 C + 32 = 1.8(-30) + 32 = -54 + 32 = -22

Answer:

The value of F is -22

Step-by-step explanation:

F=1.8 C+32

F=1.8*-30+32

F=-54+32

F=-22

Answer:

Step-by-step explanation:

2y + 100 +6x-10=180(in a cyclic quadrilateral opposite angles are supplementary)

2y+6x+90 =180

2y + 6x = 90

dividing each side by 2

y+3x = 45   ........1

7x+1+2y+74 =180 ( same reason)

7x + 2y =105  ............2

multiplying 1 by 2

2y +6x =90........ 3

subtracting 3 from 2

7x+2y-2y-6x = 105-90

x = 15

substituting x=15 in 1

y+45 =45

y= 0

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Answer:

P (4 and F) = 1 in 21 or 4.76%

P(EVEN NUMBER AND VOWEL) = 3 in 14 or 21.43%

Step-by-step explanation:

The probability of rolling a four on a die is 1 in 6.

The probability of picking the letter F in the word GIRAFFE is 2 in 7.

Therefore:

[tex]P (4\ and\ F)=P(4)*P(F)\\ P (4\ and\ F)=\frac{1}{6}*\frac{2}{7}\\ P (4\ and\ F)=\frac{1}{21}= 4.76\%[/tex]

The probability of rolling an even number (2, 4 or 6) on a die is 3 in 6.

The probability of picking a vowel (A, E, I) in the word GIRAFFE is 3 in 7.

Therefore:

[tex]P (Even\ and\ Vowel)=P(Even)*P(Vowel)\\ P (Even\ and\ Vowel)=\frac{3}{6}*\frac{3}{7}\\ P (Even\ and\ Vowel)=\frac{3}{14}= 21.43\%[/tex]

Answer:

Step-by-step explanation:

Answer:

therefore one pen can cost approx 15.6 p