Heidi solved the equation
3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below:

3x + 12 + 2 = 2 + 5x – 20
3x + 14 = 5x – 18
14 = 2x – 18
32 = 2x
16 = x
Use the drops-downs to justify how Heidi arrived at each step.

Answer:

Step-by-step explanation:Given that the numerator of a given fraction is 4 less than its denominator.

Also given that 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth .

Let the fraction be  

Since the numerator of a given fraction is 4 less than its denominator we have,

Numerator=Denominator-4

⇒ a=b-4

Since 3 is subtracted from the numerator and 5 is added to the denominator, the fraction becomes one by fourth we have

4(a-3)=1(b+5)

4a-12=b+5

4a-b=17

4(b-4)-b=17   ( ∵ a=b-4)

4b-16-b=17

3b=17+16

3b=33

⇒ b=11

Now put b=11 in a=b-4 we get

a=11-4

⇒  the fraction is a/b=7/11

Answer:

Hello! answer: 113.04

Step-by-step explanation:

It looks like you already selected the correct answer! What you do to find it is radius squared × 3.14 so

6 × 6 = 36 36 × 3.14 = 113.04 therefore that is the answer Hope that helps!

Answer:

-9

Step-by-step explanation:

In a linear equation like this, the first number is the slope and the last number is the y-intercept

Answer:

5 dogs

1 1/4 cups per bottle

Step-by-step explanation:

10/3 ÷ 2/3 get solved by 10/3 x 3/2, which gives you 30/6 or 5

45/8 ÷ 9/2 is 45/8 x 2/9 which is 5/4 or 1 1/4

Answer:

the answer in the picture

Step-by-step explanation:

Answer:

A. by 3 percent

B. by 3 percent

Answer:

A) 75% increase

B)42.8571% decrease

Step-by-step explanation:

The formula to do this is to subrtact the final value-starting value then divide by the starting value and finaly multiply by hundred

it should look like this

[tex]\frac{finalvalue-starting value}{starting value} *100[/tex]

Answer:

i believe it is a if not im sorry

Step-by-step explanation:

Answer:

169.6

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

24 - 18 = 6

6/2 = 3

18 + 3 = 21

Answer: 21

Step-by-step explanation:

18, 19, 20, 21, 22, 23, 24

1     2    3         3     2    1

21 is in the middle

Answer:

[tex]\theta=38.42 \textdegree[/tex]

Step-by-step explanation:

From the question we are told that:

Angle of F [tex]\angle F=90 \textdegree[/tex]

Length of [tex]EF = 2.3 feet,[/tex]

Length of [tex]FD= 2.9 feet,[/tex]

Generally the equation for Angle D [tex]\theta[/tex] is mathematically given by

Since [tex]\angle F=90[/tex].The triangle  is a right angle Triangle

Therefore

 [tex]tan \theta=\frac{EF}{FD}[/tex]

 [tex]tan \theta=\frac{2.3}{2.9}[/tex]

 [tex]\theta=tan^{-1} 0.793[/tex]

 [tex]\theta=38.42 \textdegree[/tex]

Answer:

Step-by-step explanation:

2 and 8

Answer:

[tex]\%Pr =71.43 \%[/tex]

Step-by-step explanation:

Given

[tex]S = \{8, 7, 3, 8, 14, 15, 20\}[/tex]

[tex]n(S) = 7[/tex]

Required

Percentage of values between Q1 and Q3

We have:

[tex]S = \{8, 7, 3, 8, 14, 15, 20\}[/tex]

Sort

[tex]Sorted = \{3, 7, 8, 8, 14, 15, 20\}[/tex]

Q1 is calculated as:

[tex]Q_1 = \frac{n+1}{4}th[/tex]

[tex]Q_1 = \frac{7+1}{4}th[/tex]

[tex]Q_1 = \frac{8}{4}th[/tex]

[tex]Q_1 = 2nd[/tex]

The second element is: 7; So:

[tex]Q_1 = 7[/tex]

Q3 is calculated as:

[tex]Q_3 = 3*\frac{n+1}{4}th[/tex]

[tex]Q_3 = 3*\frac{7+1}{4}th[/tex]

[tex]Q_3 = 3*\frac{8}{4}th[/tex]

[tex]Q_3 = 3*2th[/tex]

[tex]Q_3 = 6th[/tex]

The sixth element is: 15; So:

[tex]Q_3 = 15[/tex]

From the sorted dataset, the data between Q1 and Q3 is:

[tex]Q_3&Q_1 = \{7, 8, 8, 14, 15\}[/tex]

[tex]n(Q_3&Q_1) = 5[/tex]

The percentage is:

[tex]\%Pr =\frac{n(Q_3&Q_1)}{n(S)} * 100\%[/tex]

[tex]\%Pr =\frac{5}{7} * 100\%[/tex]

[tex]\%Pr =\frac{5* 100}{7} \%[/tex]

[tex]\%Pr =\frac{500}{7} \%[/tex]

[tex]\%Pr =71.43 \%[/tex]

Option A= 10

Using Pythagoras Theorem,

8²+6²= (hypotenuse)²

64+36= (hypotenuse)²

(hypotenuse)²= 100

hypotenuse= √100

hypotenuse= 10

So Option A= 10

Answer:

The hypotenuse is A. 10.

Step-by-step explanation:

To find the length of hypotenuse we can use  the pythagoras theorem formula:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]=>6^{2} +8^{2} = c^{2}[/tex]

[tex]=> 36 + 64 = c^{2}[/tex]

[tex]=> 100 =c^{2}[/tex]

[tex]=> c = \sqrt{100}[/tex]

∴ [tex]c[/tex] [tex]= 10[/tex]

Answer:

AB = Secant

DB = Diameter

AB = Chord

OB = Radius

BC = Tangent

Step-by-step explanation:

The image provided below is a great reference!

Note: The answers are put in order.

Answer:

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

Step-by-step explanation:

Here is the complete question. Please find attached a diagram showing the scaled and real drawing

Use the given scale factor and the side lengths of the scale drawing to determine the side lengths of the real object

A. side a is 7 inches long, side b is 6 inches long,and side c is 3 inches long

B. side a is 30 inches long, side b is 25 inches long, and side c is 20 inches long

C. side a is 40 inches long, side b is 35 inches long,and side c is 20 inches long

D. side a is 175 inches long,side b is 150 inches long, and side c is inches long

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

The scaled drawing is an enlarged image of the original triangle.

It is enlarged at a ratio of 5:1

original dimensions

a = 35/5 = 7

b = 30 / 5 = 6

c = 15/5 = 3

Answer:

8 2/3

Step-by-step explanation:

26/3

CONVERT TO A MIXED FRACTION

8 2/3

Answer:

Step-by-step explanation:

3[tex]\frac{1}{4}[/tex] ÷[tex]\frac{3}{8}[/tex]

4*3+1/4 * 8/3

13/4*8/3

13*8/4*3

104/12

26/3

not :when u change division sign into multiplication then do the reciprocal .

Answer:

Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

Step-by-step explanation:

Dado que Luis, Pedro y Ernesto fueron a comer pizza, y entre Luis y Ernesto comieron el doble que Pedro, y Pedro comió el doble que Ernesto, y entre los 3 se comieron una pizza, para determinar qué porción se comió cada uno se debe realizar el siguiente cálculo:  

L + P + E = 1

L + E = 2P

P = 2E

L + E = 4E

L = 4E - E

L = 3E

3E + 2E + E = 1

6E = 1

E = 1/6

E = 0.166

P = 0.166 x 2

P = 0.333

L = 0.166 x 3  

L = 0.5  

L = 1/2

Por lo tanto, Luis comió 1/2 pizza, Pedro comió 1/3 pizza y Ernesto comió 1/6 pizza.

Answer:

Step-by-step explanation:

There are a couple of things to know before we set up the table for this problem. First, we need to remember that if the boat is traveling against the current, that the current is going to slow the boat down; likewise, going with the current will speed the boat up. Second, we need to realize that if the boat's distance against the current is the same as the distance with the current, then the distances in the equations will be set equal to one another.

Set up the table with U (against the current) and D (with the current) on the outside and fill in what we are given:

                      d           =           r            x            t

U    

D

This is the table. Now we will fill it in:

                     d           =           r              x            t

U                                         r - 3             x            3

D                                         r + 3             x           1.8

The formula for the distance equation is at the top of the table as d = rt. We already decided that the distances that the boat traveled upstream and downstream were the same so we will set those d values equal to each other, but we first need to get the d value for each row. If distance = rate times time, then for the first row:

d = (r - 3)3 and

d = 3r - 9. For the second row:

d = (r + 3)1.8 and

d = 1.8r + 5.4. Setting them equal to each other:

3r - 9 = 1.8r + 5.4 and

1.2r = 14.4 so

r = 12 mph

Answer:

use waymath but type it the other way around

Step-by-step explanation:

Answer:

1) it's a circle, (4x + 12)² + (2y - 2)² = 64

2) it's a circle, (x + 4)² + (y - 3)² = 40

3) it's a parabola, (x + 3)² = -4(y - 1)

Step-by-step explanation:

Equation of a circle: (x - h)² + (y - k)² = r²

factorize the equation:

1) => 16x² + 96x + 144 + 4y² - 8y + 4 + 84 = 144 + 4

=> (4x + 12)² + (2y - 2)² = -84 + 144 + 4

=> (4x + 12)² + (2y - 2)² = 64 (equation of the circle)

Graph the circle using the radius and the center.(& compass for drawing circles)

=>(4x - (-12))² + (2y - 2)² = 8²

    (x  -   h   )² +  (y   - k)² = r²

Center: (h, k)  => (-12, 2)

Radius: √r²   => √64 = 8

2) => x² + 8x + 16 + y² - 6y + 9 - 15 = 16 + 9

=> (x + 4)² + (y - 3)² = 15 + 16 + 9

=> (x + 4)² + (y - 3)² = 40 (equation of the circle)

Graph the circle using the radius and the center.(& compass for drawing circles)

=> (x  - (-4)  )² +  (y - 3)² = 40

    (x  -   h   )² +  (y  - k)² = r²

Center: (h, k)  => (-4, 3)

Radius: √r²   => √40 ≈ 6.32

Equation of a parabola facing down: (x - h)² = 4a(y - k)

3) => x + 6x + 9 = -4y - 5 + 9

=> (x + 3)² = -4y + 4

=> (x + 3)² = -4(y - 1) (equation of the parabola)

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Down

=> (x - (-3))² = 4 × -1(y - 1)

    (x -  h  )² = 4 ×  a(y - k)

Vertex: (h, k)  =>  (−3,  1)

Focus:  (h, k + a)  => (-3, 1 + (-1)) => (−3,  0)

Axis of Symmetry:  x = h  => x  =  −3

Directrix:  y = k - a  => y = 1 - (-1) => y  =  2

x     |    y

−5    |   0

−4    |   3/4  

−3    |    1    

−2    |  3/4

−1     |    0

(graphs in the pictures below)

Answer:

x = 20

Step-by-step explanation:

x + 4= 24

Subtract 4 rom both sides

x = 20

Answer:

Your answer is

x=20

Step-by-step explanation:

x=24 -4

========================================================

Explanation:

Consider an example like 3, 6, 12, 24, 48, ...

The ratio between consecutive terms is

Each time we divide any given term over its previous one, we get the same ratio 2. We call this the common ratio. In terms of notation, the variable r is used for the common ratio, so r = 2 in this case.

As another example, the geometric sequence 5, 50, 500, 5000, ... has r = 10 as the common ratio because we multiply each term by 10 to get the next one. Moving forward has us multiply by r, moving backward and we divide by r. The value of r cannot be zero, but it can be negative.

An example with r being negative would be something like

1, -1, 1, -1, 1, -1, ....

we just bounce back and forth between those two values. In this case, r = -1.

Answer:

Morgan (17.06 secs)

Step-by-step explanation:

Jackie, morgan, Kylie and chung ran the 100 meter dash race

Jackie finished the race in 17.6 secs

Morgan finished the race in 17.06 secs

Kylie finished the race in 17.66 secs

Chung finished the race in 17.066 secs

Hence Morgan finished the race in the least amount of time in 17.06 seconds

Answer:

e?..............................

[tex]\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}[/tex]

Angles forming linear pair are :

[tex] \mathrm{\angle EFG \: \: and \: \: \angle GFH} [/tex]

And we know, they are supplymentary

So, the measures of the given angles are :

And

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer:

well we can see the sign's a trapezoid

area of trapezoid = 1/ 2 × sum of parallel sides × height

= 1/ 2 × (7+5) × 4

= 1/ 2 × 12 × 4

= 24 Sq feet

that's first option

Volume is a three-dimensional scalar quantity. The volume of the softball is 61.6 cubic inches.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given that the diameter of the softball is 4.9 inches. Since the radius is half the diameter, therefore, the radius of the softball can be written as,

Radius = Diameter

           = 4.9 inches / 2

           = 2.45 inches

Now, the volume of the softball can be written as,

Volume of the softball = (4/3) × π × r³

                                  = (4/3) × π × (2.45 inches)³

                                  = 61.6 inches³

Hence, the volume of the softball is 61.6 cubic inches.

Learn more about Volume:

https://brainly.com/question/13338592

#SPJ5

Answer:

20

Step-by-step explanation:

Do 15 divided by 0.75

Answer:

They are parallel but not the same

Step-by-step explanation:

because they have same slope or gradient which is 2