15. A soccer ball kicked into the air reaches 15 feet in 3 second and falls to 4 points
3 feet after 5 seconds. What is the rate of change between the 3rd second
and the 5th second? Hint: your ordered pairs should be (times in seconds,
height in feet). Your answer should be in feet/s. *

Answer:

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Step-by-step explanation:

Let B = Blue paint

Y= Yellow paint

Your mixing blue paint and yellow paint to get a total of 28 gallons.

B + Y = 28 gallons

You want to use 7 times yellow paint as blue.

This means, 7B = Y

How many gallons of each should you use ?

Hence,

B + Y = 28

B + 7B = 28

8B = 28

B = 28/8

B = 3.5 gallons

B + Y = 28 gallons

Y + 3.5 gallons = 28 gallons

Y = 28 gallons - 3.5 gallons

Y = 24.5 gallons

B = Blue paint = 3.5 gallons

Y= Yellow paint = 24.5 gallons

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Step-by-step explanation:

Answer:

[tex]\frac{492}{65}[/tex]

Step-by-step explanation:

Using the trigonometric identity

sin²A + cos²A = 1 , then

sinA = [tex]\sqrt{1-cos^2A}[/tex] thus

sinA = [tex]\sqrt{1-(5/13)^2}[/tex]

        = [tex]\sqrt{1-\frac{25}{169} }[/tex]

        = [tex]\sqrt{\frac{144}{169} }[/tex] = [tex]\frac{12}{13}[/tex] , then

tanA = [tex]\frac{sinA}{cosA}[/tex] = [tex]\frac{\frac{12}{13} }{\frac{5}{13} }[/tex] = [tex]\frac{12}{5}[/tex]

Thus

2tanA + 3sinA

= 2 × [tex]\frac{12}{5}[/tex] + ( 3 × [tex]\frac{12}{13}[/tex] )

= [tex]\frac{24}{5}[/tex] + [tex]\frac{36}{13}[/tex]

= [tex]\frac{312}{65}[/tex] + [tex]\frac{180}{65}[/tex]

= [tex]\frac{492}{65}[/tex]

Answer:

he could run 240 miles in 30 days

Step-by-step explanation:

your welcome

Answer/Step-by-step explanation:

8 (x) = m

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

8 miles (days of the month) = total miles ran

Answer:

The answer is 1 9/19

Step-by-step explanation:

Answer:

239 people 15$adults 5.50$ for kids

Step-by-step explanation:

Answer:

[tex]b = \$7[/tex]

Step-by-step explanation:

Given that:

Cost of book that Tyler wants to buy for his school = $13

He wants to buy books for his sisters as well.

Total amount of money present with Tyler = $27

Money to be spent on books for his sisters is same and is represented as [tex]b[/tex].

To find:

The value of [tex]b[/tex].

Solution:

As per question statement, the sum of all the books bought must be equal to $27.

The sum of money spent on all the books = Cost of Tyler's book + Cost of books for his sisters

[tex]\Rightarrow \$13 + b + b = \$27\\\Rightarrow \$13 + 2b = \$27\\\Rightarrow 2b =\$14\\\Rightarrow b =\$7[/tex]

Therefore, Tyler must spend $7 on each of her sister's books.

Answer:

Yes

Step-by-step explanation:

the equation for Bruce would be 3b+3b-2= numbers of tiles used.

and Felocias equation would be 5b+5= numbers of tiles used

so therefore if there were 7 tiles in each box they both could have used the same number of tiles

Answer:

The statement BI = BK is true from the given information ⇒ B

Step-by-step explanation:

If a line is a perpendicular bisector of a line segment, then

Let us find the true statement

∵ Line AB is the perpendicular bisector of segment IK

→ By using the 1st note above

∴ AB ⊥ IK

∴ ∠IJA, ∠KJA, ∠IJB, ∠KJB are right angles

→ By using the 2nd note above

∴ J is the mid-point of IK

∴ IJ = JK

∵ Any point on line AB is equidistant from The endpoints of IK ⇒ 3rd note

∴ AI = AK

∴ BI = BK

∴ The statement BI = BK is true from the given information

Answer:

Change = $3.26

Step-by-step explanation:

Given the following data;

Cost of cereal = $3.29.

Cost of milk = $3.45.

Amount paid = $10.00

Total cost of items bought = $3.29 + $3.45 = $6.74

Change = Amount paid - Total cost of items purchased.

Substituting into the equation, we have;

Change = $10.00 - $6.74

Change = $3.26

Therefore, Beth need to give the customer a change of $3.26.

Answer:

3.26

Step-by-step explanation:

I HAD THAT QUESTION

Answer:

2893.14/321.46=9

Step-by-step explanation:

in 9 months he will run out of money

Answer:

We conclude that:

Step-by-step explanation:

Given the function

[tex]y = f(x)[/tex]

In order to determine the value f(2), we need to check the value of y at x = 2.

In other words, we need to check:

at x = 2, what is the value of y?

From the graph, it is clear that at x = 2, the value of y = -5

In other words,

f(2) = -5

Therefore, we conclude that:

Answer:

1 inch = 3ft

Step-by-step explanation:

If you divided 51 feet  by 17 inch  you will get 3 feet. So 1 inch = 3 feet

NOOB

difference in order   percents in order

30                              33%

120                             100%

25                               50%

9                                  8%

Answer:

X can be anything above

2

Answer:

f(g(5)) = 4

Step-by-step explanation:

It says to find the value of f(g(5)). In this case, we first have to find g(5).

Plug 5 into g(x) = -x+5

g(5) = 0

Now, f(g(5)) is f(0), since g(5) was found out to be 0.

Plug in 0 into 2x² + 7x + 4

2(0)² + 7(0) + 4 = 0 + 0 + 4 = 4

So the answer is 4.

Sin(α)=opposite leg/hypotenuse

Sin(63°)=ya/35

ya=35xSin(63°)

ya=31.2

Area(a)= (15.9x31.2)/2

Area(a)=248.0

Now, we proceed to find the area of "b". We already have the length x=15.9, so:  

Tan(α)=opposite leg/adjacent leg

yb=15.90xTan(42°)

yb=14.3

Area(b)=15.9X14.3/2

Area(b)=113.7

The total Area (At) is:  

At=Area(a)+Area(b)

At=248.0+113.7

At=361.7

10) Triangle "a":

-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(30°)=xa/48

xa=48xCos(30°)  

xa=41.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(30°)=y/48

y=48xSin(30°)

y=24.0

-Area of the triangle "a":

Area(a)=41.6x24.0/2

Area(a)=499.2

Triangle "b":

-We have the value of i(y=24).

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(45°)=24/xb

xb=24/Tan(45°)

xb=24

-Area of the triangle "b":

Area(b)= 24x24/2

Area(b)=288

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=499.2+288

At=787.2

11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:

-Adjacent leg of the triangle "a":

Cos(α) = adjacent leg/hypotenuse  

Cos(56°)=xa/14

xa=14xCos(56°)

xa=7.8

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(56°)=y/14

y=14xSin(56°)

y=11.6

-Area of the triangle "a":

Area(a)=7.8x11.6/2

Area(a)=45.2

Triangle "b":

-The value of its opposite leg is y=11.6.

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(46°)=11.6/xb

xb=11.6/Tan(46°)

xb=11.2

-Area of the triangle "b":

Area(b)= 11.6x11.2/2

Area(b)=65.0

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=45.2+65.0

At=110.2

12)-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(54°)=xa/13

xa=13xCos(54°)

xa=7.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(54°)=y/13

y=13xSin(54°)

y=10.5

-Area of the triangle "a":

Area(a)=7.6x10.5/2

Area(a)=39.9

Triangle "b":

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(42°)=7.6/xb

xb=7.6/Tan(42°)

xb=8.4

-Area of the triangle "b":

Area(b)=7.6x8.4/2

Area(b)=31.9

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=39.9+31.9

At=71.8First, it is important to remember that the formula to calculate the area of a triangle is: A=bxh/2

As we can see in the exercises, all the triangles are divided in two triangles. So, let's call "a" to the triangle on the left and "b" to the triangle on the right.

9)To find the area of the triangle "a", we need the lenght of the adjacent leg (x) and the opposite leg (ya):

Cos(α)=adjacent leg/hypotenuse  

Cos(63°)=x/35

x=35xCos(63°)

x=15.9

Sin(α)=opposite leg/hypotenuse

Sin(63°)=ya/35

ya=35xSin(63°)

ya=31.2

Area(a)= (15.9x31.2)/2

Area(a)=248.0

Now, we proceed to find the area of "b". We already have the length x=15.9, so:  

Tan(α)=opposite leg/adjacent leg

yb=15.90xTan(42°)

yb=14.3

Area(b)=15.9X14.3/2

Area(b)=113.7

The total Area (At) is:  

At=Area(a)+Area(b)

At=248.0+113.7

At=361.7

10) Triangle "a":

-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(30°)=xa/48

xa=48xCos(30°)  

xa=41.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(30°)=y/48

y=48xSin(30°)

y=24.0

-Area of the triangle "a":

Area(a)=41.6x24.0/2

Area(a)=499.2

Triangle "b":

-We have the value of i(y=24).

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(45°)=24/xb

xb=24/Tan(45°)

xb=24

-Area of the triangle "b":

Area(b)= 24x24/2

Area(b)=288

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=499.2+288

At=787.2

11) To find the area of the triangle shown in this exercise, we have to apply the same procedure as in exercise 10:

-Adjacent leg of the triangle "a":

Cos(α) = adjacent leg/hypotenuse  

Cos(56°)=xa/14

xa=14xCos(56°)

xa=7.8

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(56°)=y/14

y=14xSin(56°)

y=11.6

-Area of the triangle "a":

Area(a)=7.8x11.6/2

Area(a)=45.2

Triangle "b":

-The value of its opposite leg is y=11.6.

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(46°)=11.6/xb

xb=11.6/Tan(46°)

xb=11.2

-Area of the triangle "b":

Area(b)= 11.6x11.2/2

Area(b)=65.0

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=45.2+65.0

At=110.2

12)-Adjacent leg of the triangle "a":

Cos(α)=adjacent leg/hypotenuse  

Cos(54°)=xa/13

xa=13xCos(54°)

xa=7.6

-Opposite leg of the triangle "a":

Sin(α)=opposite leg/hypotenuse

Sin(54°)=y/13

y=13xSin(54°)

y=10.5

-Area of the triangle "a":

Area(a)=7.6x10.5/2

Area(a)=39.9

Triangle "b":

-Adjacent leg of the triangle "b":

Tan(α)=opposite leg/adjacent leg

Tan(42°)=7.6/xb

xb=7.6/Tan(42°)

xb=8.4

-Area of the triangle "b":

Area(b)=7.6x8.4/2

Area(b)=31.9

-Total area of the triangle (At) is:

At=Area(a)+Area(b)

At=39.9+31.9

At=71.8

Step-by-step explanation:

Answer:

16n + 41

Step-by-step explanation:

2(-n - 3) - 7(5 + 2n) (Given)

-2n - 6 - 35 - 14n (Distribute)

-16n - 41 (Add like terms)

16n + 41 (Divide by a factor of -1)

Answer:

B. -16n - 41

Step-by-step explanation:

Use the distributive property:

2(-n - 3) - 7(5 + 2n)

-2n - 6 - 35 - 14n

Combine like terms:

(-2n - 14n) + (-6 - 35)

-16n - 41

Answer:

x=11

Step-by-step explanation:

3x+28+5x+52+12=180

8x+92=180

-92 on both sides

8x=88

/8 on both sides

x=11

Answer: Distributive Property

30(4p+6c+12p+40)

=(30)(4p+6c+12p+40)

=(30)(4p)+(30)(6c)+(30)(12p)+(30)(40)

=120p+180c+360p+1200

=180c+480p+1200

Step-by-step explanation: Hope this help

Step-by-step explanation:

Side length of heptagon = 20.3cm / 7 = 2.9cm.

The heptagon is made out of 7 congruent triangles, each with height 3.0cm and base 2.9cm

Hence area of heptagon

= 7 * [(0.5)(3.0cm)(2.9cm)]

= 7 * 4.35cm²

= 30.45cm².

Answer:

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Step-by-step explanation:

Given ratio

8 : 5

Select three ratios that are equivalent to 8:5

Check all options

(Choice A) A 16:10

= 16 / 10

Dividing by 2

= 8 / 5

= 8 : 5

(Choice B) B 50:80

= 50 / 80

Dividing by 10

= 5 / 8

= 5 : 8

(Choice C) C 48:30

= 48 / 30

Dividing by 6

= 8 / 5

= 8 : 5

(Choice D) D 32:20

= 32 / 20

Dividing by 4

= 8 / 5

= 8 : 5

(Choice E) E 64:35

= 64 / 35

The equivalent ratios to 8 : 5 are

(Choice A) A 16:10

(Choice C) C 48:30

(Choice D) D 32:20

Answer:

Given : PQ = RQ

to find : angle B

Answer:

b=40

Step-by-step explanation:

PQ=RQ

That means both sides are the same length which also means they both have the same angel measure of 140.

A super easy way to solve this would be to realize that where p is, the angel is 140.

A straight line is 180.

b and 140 are supplementary angels. [which means they equal 180]

To find b you can make an equation.

b+140=180

or

180-140=b

I'll show you both.

First one you would subtract 140 on both sides to get the variable alone, leaving you with b=40.

For the second one, you just do 180-140 and it also equals 40.

Either way it leaves you with b=40

If you need any more help with angels and whatnot, don't be afraid to reach out. I hope that helps! <3

Answer:

im 99.99999% sure its c

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and b the y- intercept

Answer:

m is the slope of the line and b is constant / y intercept value which shows that the line is passing through origin

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

Divide by 2, subtract 8 ...

  2(4/x +8) = 18

  4/x +8 = 9

  4/x = 1

  4 = x . . . . . multiply by x

Answer:

4/x+8=18/2

4/x+8=9

4/x=9-8

4/x=1

4=1x

x=4

Answer:

x = 7

Step-by-step explanation:

Since the 2 legs are congruent, then

3x + 12 = 33 ( subtract 12 from both sides )

3x = 21 ( divide both sides by 3 )

x = 7