Type the correct answer in each box.
The graph represents the piecewise function:

Answer:

3/12

Step-by-step explanation:

To solve this problem, we can use square roots. Due to x being squared, we can square root both the top and the bottom. The square root of 9 is 3 with 144 being 12. In the end, x equals 3/12

[tex]\text{Hey there!}[/tex]

[tex]\mathsf{What\ is\ the\ value\ of\ x: x^2=\dfrac{9}{144}\ ?}[/tex]

[tex]\mathsf{First,\ you\ have\ to\ simplify\ both\ sides\ of\ your\ equation!}[/tex]

[tex]\mathsf{\dfrac{9}{144}= \dfrac{9\div9}{144\div9} = \boxed{\dfrac{1}{16}}}[/tex]

[tex]\mathsf{New\ equation\ (for\ now): x^2=\dfrac{1}{16}}[/tex]

[tex]\mathsf{Take\ your\ square\ root!}[/tex]

[tex]\mathsf{x=\pm\sqrt{\dfrac{1}{16}}}[/tex]

[tex]\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: x =0.25\ or\ x = -0.25}}}[/tex][tex]\boxed{\boxed{\checkmark}}[/tex]

[tex]\boxed{\boxed{\boxed{\mathsf{You\ could\ also\ say\ x= \dfrac{3}{12}\ or\ x=-\dfrac{3}{12}}}}}[/tex][tex]\boxed{\boxed{\boxed{\checkmark}}}[/tex]

[tex]\mathsf{Side\ note: that's\ when\ the\ plus\ or\ minus\ sign\ (\pm)\ came\ in\ handy!}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

The area of a triangle is 1/2*base*height

If h=8, b=15, then we have 1/2*8*15 which is 1/2*120 which is 60

So the right choice is B

Hope this helped!

Answer:

4

Step-by-step explanation:

log_3 (81)

set equal to x

log_3 (81) = x

saying this out loud is "x equals 3 raised to what power is 81"

notice that it is the same as

3^x = 81

so x equals 4

Answer:

[tex]Rate\ of\ commission=22\%[/tex]

Step-by-step explanation:

Let her rate of commission[tex]=x\%[/tex]

Salary[tex]=\$ 1000[/tex]

Weekly Amount[tex]=\$ 6500[/tex]

So earning from commission=Weekly Amount-Salary

Earning from the commission[tex]=6500-1000[/tex]

Earning from the commission[tex]=\$ 5500[/tex]

Total Sales[tex]=\$ 25000[/tex]

Commission is[tex]=x\%\ of\ 25000[/tex]

[tex]x\%\ of\ 25000=5500\\\\\frac{x}{100}\times 25000=5500\\\\x\times 250=5500\\\\x=\frac{5500}{250}\\\\x=22\%[/tex]

[tex]Rate\ of\ commission=22\%[/tex]

Answer:

6 1/8 and 11 7/8

Step-by-step explanation:

Just use algebra. x+y is equal to 18. 3x=4y+5. Then you substitute the value x for y by dividing by three. From there it is just computation

Answer:

The numbers are 11 and 7

Step-by-step explanation:

Let the numbers be P and V

Let P be the greater number and V be the smaller number.

From the question, the sum of the numbers equals 18 i.e

P + V = 18

Also from the question,

We were told that three times the greater number exceeds four times the smaller number by 5 i.e

3P = 4V + 5

P = (4V + 5) / 3

Substituting the value of P into equation (1), we obtain:

P + V = 18.

(4V + 5) / 3 + V = 18

Multiply through by 3 to express in linear form, we have:

4V + 5 + 3V = 54

Collect like terms

4V + 3V = 54 - 5

7V = 49

Divide both side by the coefficient of V i.e 7

V = 49/7

V = 7

P + V = 18

P = 18 - V

P = 18 - 7

P = 11

The numbers are 11 and 7

Answer:

14

Step-by-step explanation:

3 1/2 ounces is equal to:

7/2 or 14/4

14/4 is 14 quarter ounce chunks

A total of 14 pieces each of weight 1/4 ounce can be cut from the platinum nugget.

Scale factor is defined as the rate at which one dependent quantity varies with an independent one. Mathematically : y = Kx  can be written as -

y is K times larger than x.

Given is a platinum nugget whose weight is 3 1/2 ounces.

Assume that 3 1/2 ounces is equivalent to K times of 1/4 ounces.

Now, we can write - 3 1/2 = 7/2

Therefore, we can write the relation as follows -

7/2 = K/4

K = 7/2 X 4

K = 14

Therefore, a total of 14 pieces each of weight 1/4 ounce can be cut from the platinum nugget.

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Answer:

29 dollars each

Answer:

$7 more

Step-by-step explanation:

According to the question, Xavier sells homemade necklaces for a profit of $22 per necklace .

Now, he’s considering switching to a new type of pendant that will increase his profit as expressed by

y = 29x

Where x = number sold and

y = amount of profit

From the expression, if he sells one necklace made with the new type of pendant ,

y = 29 x 1

= $29

Remember he makes $22 per necklace already .

$ earns if he switches to the new pendant = $29 - $22

= $7

He’ll earn $7 more if he switches to the new material

Answer: 7.2 * 10 to the negative four

Step-by-step explanation:

Answer:

12.5% ≈ 13%

Step-by-step explanation:

The rest of the question is: There are 75 pills in the batch.

The current batch of pills is the first of the day and our goal is to produce a total of 600.

If there are 75 pills in the batch so percentage of goal completed will be

[(number of pills in the batch)/(Total pills)] * 100

[tex]\frac{75}{600}*100 = 12.5 \%[/tex]

≈ 13% to the nearest whole number

The percentage of the goal met after the batch is finished is 100%.

To find the percentage of the goal met after the batch is finished, we need to divide the number of pills produced by the goal and then multiply by 100. In this case, since the goal is 600 and the batch produced 600 pills, the percentage of the goal met would be:

Percentage of goal met = (600/600) * 100 = 100%

Therefore, after the batch is finished, 100% of the goal will be met.

Answer:

hola

Step-by-step explanation:

Step-by-step explanation:

because 1 kg is worth 2 is 1/4 is worth .25

so multiply 2 by 3 and add 1/4

good luck hope this helps.

Answer:

cost of [tex]3\frac{1}{4}[/tex] kg sugar is  [tex]5.80[/tex]

Step-by-step explanation:

Converting the quantity of sugar from mixed fraction to proper fraction

[tex]1\frac{1}{4} =\frac{(1*4)+1}{4} =\frac{5}{4}[/tex]

Cost of [tex]\frac{5}{4}[/tex] kg of sugar= 2.25

Cost of 1 kg of sugar  [tex]2.25*\frac{4}{5} \\=0.45*4\\=1.80[/tex]

                        similarly, [tex]3\frac{1}{4} =\frac{(3*4)+1}{4}=\frac{13}{4}[/tex]

So, the cost of [tex]\frac{13}{4}[/tex] kg of sugar is  

                                           [tex]\frac{13}{4}*1.80 \\=5.80[/tex]

cost of [tex]3\frac{1}{4}[/tex] kg sugar is  [tex]5.80[/tex]

The point to the system of solution is (3, 3, –2).

Solution:

Given equations are

x – y – 2z = 4  – – – – (1)

–x + 3y – z = 8 – – – – (2)

–2x – y – 4z = –1 – – – – (3)

Let us first eliminate x from 2 equations.

Add (1) and (2)

x – y – 2z – x + 3y – z = 4  + 8

⇒ 2y – 3z = 12 – – – – (4)

Multiply equation (1) by 2 and add with equation (3)

2x – 2y – 4z – 2x – y – 4z = 8  – 1

⇒ –3y – 8z = 7 – – – – (5)

Now, Multiply equation (4) by 3 and equation (5) by 2 and add them.

6y – 9z – 6y – 16z = 36 + 14

⇒ –25z = 50

⇒ z = –2

Substitue z = –2 in equation (4), we get

⇒ 2y – 3(–2) = 12

⇒ 2y  = 12 – 6

⇒ y = 3

Substitute, z = –2 and y = 3 in equation (1), we get

⇒ x – 3 – 2(–2) = 4  

⇒ x – 3 + 4 = 4  

⇒ x + 1 = 4  

⇒ x = 3

Hence the point to the system of solution is (3, 3, –2).

Answer:

(3, 3, –2).

Step-by-step explanation:

Answer:

The family bought approximately 2 bags of chips.

Step-by-step explanation:

Given:

Total spent by family = $5.50

We need to find bags of chips did the family buy.

Solution:

Let number of bags of chips bought be 'x'.

Also Given:

The number of candy bars was twice as much as the number of bags of chips.

number of candy bars = [tex]2x[/tex]

Now we can say that;

Total spent by family is equal to sum of the number of bags of chips bought and number of candy bars.

framing in equation form we get;

[tex]x+2x=5.5\\\\3x=5.5[/tex]

Dividing both side by 3 we get;

[tex]\frac{3x}{3}=\frac{5.5}{3}\\\\x=1.83\approx2[/tex]

Hence the family bought approximately 2 bags of chips.

Equation shows the relationship between  distance traveled (d), speed (s), and time taken (t) is:

[tex]s = \frac{30}{3}\\\\s = 10\ miles\ per\ hour[/tex]

Solution:

Given that,

Alice traveled 30 miles in 3 hours

To find: Equation shows the relationship between  distance traveled (d), speed (s), and time taken (t)

The speed is given by:

[tex]Speed = \frac{distance}{time}[/tex]

From given,

Distance = d = 30 miles

Time = t = 3 hours

Therefore,

[tex]s = \frac{d}{t}[/tex]

[tex]s = \frac{30}{3}\\\\s = 10\ miles\ per\ hour[/tex]

Thus the equation is found and speed is calculated

Answer:

3/5 x d = 345

Step-by-step explanation:

got the question right on the quiz

Answer:

A. 178.35°F

B. ≅ 5.64 minutes or 5 minutes 38 seconds approximately

C. 76°F.

Step-by-step explanation:

1. Let's review the information given to us to answer the questions correctly:

Temperature of the pizza in the oven = 400°F

Temperature of the kitchen = 76°F constantly

Temperature of the pizza after 3 minutes = 267°F

2. A. What is the temperature  T(t)  of the pizza after 5 minutes?

We will use the ratio of how much degrees the temperature of the pizza decreases per minute, this way:

Ratio = (Temperature of the pizza in the oven - Temperature of the pizza after 3 minutes)/ Minutes

Ratio = (400 - 267)/3 = 133/3 = 44.33 (Rounding to two decimal´places)

It means that the temperature of the pizza diminishes 44.33°F per minute.

Therefore, the temperature  T(t)  of the pizza after 5 minutes, will be:

T(5) = 400 - (44.33 * 5) = 400 - 221.65 = 178.35°F

B. Determine the time when the temperature of the pizza is 150°F.

min.

Time when the pizza is 150°F = (400 - 150)/44.33 = 250/44.33 = 5.64 minutes or 5 minutes 38 seconds approximately

C. After a very long period of time, what is the approximate temperature of the pizza? It will be the temperature of the kitchen, 76°F.

Answer:

F, G, H

Step-by-step explanation:

$9/6 = $1.5

$6/4 = $1.5

The price is $1.50 per notebook.

Every point on the graph must have a y-coordinate that is 1.5 times the x-coordinate.

The function is y = 1.5x

F(3,4.50)     3 * 1.5 = 4.5    Yes

G(8,12)    8 * 1.5 = 12     Yes

H(7,10.50)    7 * 1.5 = 10.5    Yes

J(12,16)   12 * 1.5 = 18     No

Answer:2/3

Step-by-step explanation:

So you add 8 plus 2 And keep the denominator the same and then simplify with 5

Answer:

x = -30*1/3

Step-by-step explanation:

(3x+10)+81=0

3x + 10 + 81 = 0

3x + 91 = 0

3x = -91

x = -91/3

x = -30*1/3

Answer:

Step-by-step explanation:

The simple answer is "yes".

The reason is that Distance = Speed (Velocity) * time taken.

d = v*t

Given that the distance is fixed, the velocity and time become inversely related such that an increase in velocity will mean that the distance is covered in a shorter time while an increase in time will mean that the distance is covered at a slower velocity.

A = number of flavors = 3

B = number of toppings = 4

C = number of syrups = 2

D = number of different sundaes (picking one flavor, topping and syrup)

D = A*B*C

D = 3*4*2

D = 24

There are 24 different sundaes possible.

Answer: answer is C

Step-by-step explanation:

Answer:

Sales Warehouse

Step-by-step explanation:

See the explanation

Theorem:

A perpendicular dropped from the center of the circle to a chord bisects it. It means that both the halves of the chords are equal in length.

In my own words, I'd explain this by drawing a circle and the diameter of the circle drawn in red. Also, we have a chord of the circle drawn in blue. The theorem says that the diameter bisects the chord in a right angle, so we will have two halves that measure the same so that's why we drew two  hash marks on each half of the chord.

A problem about this is indicated in figure 2. Suppose you have a perpendicular dropped from the center of the circle to a chord and you know that the left half measures 2 cm, so we want to know the x-value of the right half. Since the diameter bisects the chord, then it is true that [tex]x=2cm[/tex] as well.

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To solve for 'y' in the equation 'y + 1.05 = 7.26', subtract 1.05 from both sides of the equation, the answer is 'y = 6.21'.

In mathematics, solving for 'y' involves rearranging the equation to isolate the 'y' variable. In this case, the equation is 'y + 1.05 = 7.26'.
To solve for y, begin by performing the inverse operation of addition on both sides of the equation. This means subtracting 1.05 from both sides.
After doing so, the equation would look like this:

So the solution for y in this equation is 6.21.

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Answer:

slope-intercept form: y = 3x - 14

slope: 3

y-intercept: -14

Step-by-step explanation:

To find the equation in slope-intercept form, isolate the "y" variable by moving everything to the other side. Slope-intercept form looks like y = mx + b.

"x" and "y" mean points that are on the line.

"m" is the slope.

"b" is the y-intercept.

Rearrange the equation to isolate "y"

3x - y = 14

3x - 3x - y = 14 - 3x          Subtract 3x from both sides

-y = 14 - 3x          Multiply both sides by -1.

y = -14 + 3x          Put "3x" in front of "-14" because it has the 'x'

y = 3x - 14          Looks like y = mx + b

State the "m" and "b".

m = 3     (Slope of the line)

b = -14    (y-intercept of the line)

Therefore the equation of the line in slope-intercept form is y = 3x - 14. The slope is 3 and the y-intercept is -14.

Answer:

Step-by-step explanation:

Assuming the problem you want to solve is finding the number of each coin, you can let variables represent those numbers. I like to use mnemonic variables, such as q for the number of quarters, and d for the number of dimes.

The two equations you can write are based on the given information:

  q + d = 60 . . . . . . you have 60 coins

  .25q +.10d = 9.45 . . . . . their value is 9.45

_____

You have 23 quarters and 37 dimes.

_____

I like to solve these by substitution, using an expression to replace the variable representing the lowest-value coin.

  d = 60 -q . . . . . . . expression for the number of dimes

  .25q +.10(60 -q) = 9.45

  .15q +6.00 = 9.45 . . . . . eliminate parentheses, collect terms

  .15q = 3.45 . . . . . . . . . . .subtract 6.00

   q = 23 . . . . . . . . . . . . . . . divide by 0.15

   d = 60 -q = 37

Answer:

The volume of the Prism=[tex]629.2cm^3[/tex]

Step-by-step explanation:

A right rectangle prism shape is that in which the faces of the prism are in the shape of a rectangle making it a cuboid.

Volume of a right rectangle prism= [tex]length*width*Height[/tex]

Given: length=12.1 cm

           width=8 cm

          Height= 6.5 cm

Putting the given values in the formula

   Volume of the right rectangular prism:

                                                                [tex]=12.1cm*8cm*6.5cm\\\\=629.2cm^3[/tex]

The volume of the Prism=[tex]629.2cm^3[/tex]