Henry had $24.12. His friend Greg had one-
half as much as Henry. Another friend Kasey
had one-fourth of what Henry has. How much
money do the three friends have altogether?
Henry:
Greg:
Kasey
Total:

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:

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:

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

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:

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:

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.

To solve more questions on size scaling, visit the link below-

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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]

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.

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]

Answer:

[tex]a_1=7[/tex]

[tex]a_2=7\\a_3=10\\a_4=13\\a_5=16[/tex]

Step-by-step explanation:

The arithmetic series is [tex]S_{5}=\sum_{k=1}^5(1+3k)[/tex]

From the given series the general term of the series is [tex]a_k=1+3k[/tex]

When [tex]k=1[/tex], we substitute into the general formula to get:

[tex]a_1=1+3(1)=4[/tex]

When k=2, we get: [tex]a_2=1+3(2)=7[/tex]

When k=3, we substitute to get:

[tex]a_3=1+3(3)=10[/tex]

When k=4, we substitute to get:

[tex]a_4=1+3(4)=13[/tex]

When k=5, we get:

[tex]a_5=1+3(5)=16[/tex]

Answer:

a1= 4

a2=7

a3=10

a4=13

a5=16

s5=50

Step-by-step explanation

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.

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: answer is C

Step-by-step explanation:

Answer:

Sales Warehouse

Step-by-step explanation:

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:

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]

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.

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: 7.2 * 10 to the negative four

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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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:

Andre scored 14 points in the game.

Step-by-step explanation:

Question :

Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego. If

Noah scored 10 points, how many points did Andre score?

Given:

Diego scored 9 points less than Andre in the basketball game.

Noah scored twice as many points as Diego.

Noah scored 10 points

To find Andre's points.

Solution:

Let Andre's score be = [tex]x[/tex] points

Then, Diego's points will be = [tex](x-9)[/tex] points

Noah's points will be = [tex]2(x-9)[/tex] points

Noah's points given = 10 points.

Thus, the equation can be given as:

[tex]2(x-9)=10[/tex]

Solving for [tex]x[/tex].

Dividing both sides by 2.

[tex]\frac{2(x-9)}{2}=\frac{10}{2}[/tex]

[tex]x-9=5[/tex]

Adding 9 both sides.

[tex]x-9+9=5+9[/tex]

∴ [tex]x=14[/tex]

Thus, Andre scored 14 points in the game.

The score of Andre and Diego is 14 and 9 points, respectively.

Given information:

Diego scores 9 points less than Andre in the basketball game.

Noah scores twice as many points as Diego.

Noah's score is 10 points.

Let x be the score of Diego.

So, the score of Andre will be x+9 and that of Noah will be [tex]2x[/tex].

Compare Noah's score to get the value of x as,

[tex]2x=10\\x=5[/tex]

So, Diego's score is 5 points.

Now, the score of Andre will be calculated as,

[tex]x+9=5+9\\=14[/tex]

Therefore, the score of Andre and Diego is 14 and 9 points, respectively.

For more details, refer to the link:

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The item most likely to be bought with an installment loan is A. A couch, as installment loans are used for significant purchases paid over time. Groceries, calculators, and school books are generally less expensive and paid for upfront.

The question posed is, "Which of these items are you most likely to buy with an installment loan?" The correct answer is A. A couch. Installment loans are typically used for larger purchases that require payment over time. These include items such as furniture, cars, and appliances.

On the other hand, groceries (B), calculators (C), and school books (D) are generally more affordable and are usually paid for upfront rather than through installment loans. Installment loans often come with interest, making them more suitable for more expensive items that cannot be paid for in full immediately.

It is essential to carefully consider the necessity and the ability to repay before taking out any loan, especially for substantial purchases like a couch, to avoid financial strain.

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:

3/5 x d = 345

Step-by-step explanation:

got the question right on the quiz

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:

98up-'[y;adsdsfsafafdespenol es mi amigos si

Step-by-step explanation: