Gilberto’s grandfather gives him $5 for his birthday and then $.50 for each math question he answers correctly on his math exams for the year. Write an equation that represents the amount of money that Gilberto receives during the school year. Explain what the variables and numbers mean.

Answer:

If two parallel lines  [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.

Below is the prove of this.

Step-by-step explanation:

As we know that Alternate interior angles are two angles that are on the interior of [tex]p[/tex] and [tex]q[/tex], but on opposite sides of the transversal.

In other words,  If two parallel lines  [tex]p[/tex] and [tex]q[/tex] are cut by a transversal, then the alternate interior angles are congruent.

Lets prove this.

Given: p ║ q

Prove: ∠1 ≅ ∠2

Statement                                  Reasons

1. p ║ q                                        1. Given

2. ∠1 ≅ ∠3                                  2. Corresponding Angles Postulate

3. ∠3 ≅ ∠2                                 3. Vertical Angles Congruence Theorem

4. ∠1 ≅ ∠2                                  4. Transitive Property of Congruence

Answer:jennie has 536 songs and diamond has 359

Step-by-step explanation:

Answer:

For plato users: Option C.

Step-by-step explanation:

Answer:

30%?

Step-by-step explanation:

im not really sure but 30 percent of 280 is 84 and i couldnt find anything else

since 280-129=88 i thought 84/30% was closest

Answer:

i) this does not show direct variation.

ii) this shows direct variation

iii) this shows direct variation

iv) (2x-5y) + (x+y)  =  3x - 4y

v) (7x-5) - (3x-2)  = 4x - 3

Step-by-step explanation:

i.) y - x  = 4                      this does not show direct variation.

ii) x - y = 0   [tex]\Rightarrow[/tex]  x = y       this shows direct variation

iii) 8 = xy    [tex]\Rightarrow[/tex]  8/x = y      this shows direct variation

iv) the sum of (2x-5y) and (x+y)    [tex]\Rightarrow[/tex] (2x-5y) + (x+y)  =  3x - 4y

v) expression that is equivalent to (7x-5) - (3x-2)

[tex]\Rightarrow[/tex]  (7x-5) - (3x-2)  =  4x - 5 + 2 = 4x - 3

Answer:

volume is 432 cubic inches

Step-by-step explanation:

A box measures 1 ft. long, 1/2 ftwide, and  1/2 ft high.

we need to find the volume of the box

Volume of the box formula is

[tex]volume = length \cdot width \cdot height\\[/tex]

convert all the measurement into inches

1 feet = 12 inches

1/2 feet = 6 inches

length = 12 inches, width = 6 inches , height = 6 inches

now we plug in the values in volume

[tex]volume = 12 \cdot 6 \cdot 6= 432 in^3[/tex]

Answer:

216

Step-by-step explanation:

1. √{6^6}

2. √(6^3)^2}

3.6^3

4.216

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Hope this helps!

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The value of the given expression is 216.

The given expression is,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5[/tex]

Square Root Computations:

The square root of a number is the number that we require to multiply by itself to obtain the original number

Now, solving the given expression as,

[tex]\sqrt{2\cdot 6^5 + 2\cdot 6^5 + 2\cdot 6^5}=\sqrt{2\cdot6\cdot6^4+2\cdot6\cdot6^4+2\cdot6\cdot^4}\\ =6^2\sqrt{12+12+12}\\ =36\sqrt{36}\\ =36\sqrt{4\cdot9}\\ =36\cdot2\cdot3\\=216[/tex]

Learn More information about the simplification:

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if you have a scientific calculator type in y=4/3x+4

and you should find your answer

Answer:

$8.75

Step-by-step explanation:

You and three friends = 4 people

$35 / 4 people = $8.75

The cost of one ticket is $8.75

Hope this helps :)

Answer:

27 > b

Step-by-step explanation:

7 > -20 + b

7 + 20 > -20 + 20 + b

27 > b

Answer:

-2

Step-by-step explanation:

8x+7=-9

8x=-9-7

8x=-16

x=-16/8

x=-2

Answer:

-5-4x

Step-by-step explanation:

7-3(4-2x)-10x

7-12+6x-10x

-5+6x-10x

-5-4x

7-12+6x-10x

or

-5-4x

Simplify the answer to get equivalent expressions

Answer:

it the same number.

Step-by-step explanation:

Answer:

11 feet

Step-by-step explanation:

Area of rectangle (170.5cm) = length (15.5) x width

170.5/15.5=width

Width = 11

Hope this helps! :)

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Solution:

Given expression is the inequality.

[tex]$\frac{5 x-3}{(x-1)(x+1)} \leq 0[/tex]

Substitute x = –2 in the inequality.

[tex]$\frac{5 (-2)-3}{(-2-1)(-2+1) }=\frac{-13}{(-3)(-1) }[/tex]

                            [tex]$=\frac{-13}{3 }[/tex]

                            < 0

For test point x = –2, the inequality is true.

Substitute x = 0 in the inequality.

[tex]$\frac{5 (0)-3}{(0-1)(0+1) }=\frac{-3}{(-1)(1) }[/tex]

                      [tex]$=3[/tex]

                      > 0

For test point x = 0, the inequality is false.

Substitute [tex]x=\frac{4}{5}[/tex] in the inequality.

[tex]$\frac{5 (\frac{4}{5} )-3}{((\frac{4}{5} )-1)((\frac{4}{5} )+1) }=\frac{1}{(-\frac{1}{5} )(\frac{9}{5} ) }[/tex]

                            [tex]$=\frac{-25}{9 }[/tex]

                            < 0

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

Substitute x = 2 in the inequality.

[tex]$\frac{5 (2)-3}{(2-1)(2+1) }=\frac{7}{(1)(3) }[/tex]

                      [tex]$=\frac{7}{3 }[/tex]

                      > 0

For test point x = 2, the inequality is false.

Hence,

For test point x = –2, the inequality is true.

For test point x = 0, the inequality is false.

For test point [tex]x=\frac{4}{5}[/tex], the inequality is true.

For test point x = 2, the inequality is false.

Answer:

In the picture below

Step-by-step explanation:

Edge 2021

Answer:

Step-by-step explanation:

When you talk about "unit price," you need to define the unit of interest. Unit prices on grocery store shelves don't always use the same unit, even for like items. Here it might be convenient to use any of the following as the "unit":

The "unit price" is computed as ...

  unit price = (price for some number of units)/(the number of units)

The "number of units" may be larger, smaller, or equal to 1.

Then the price per cup (8 ounces) would be ...

  unit price = (price for 15 oz)/(15/8 cups) = ($2.79)(8/15)

  = $1.488 per cup

__

The price per ounce would be ...

  unit price = ($2.79)/(15 oz) = $0.186/oz

__

We assume that the unit of interest is probably 1 ounce, but it could be something else. Your grader may expect the value to be rounded to the nearest cent, $0.19 per ounce.

The unit price of shampoo is approximately $0.186 per ounce.

To find the unit price of shampoo, divide the cost of the bottle by the number of ounces it contains. In this case, the cost is $2.79 and the bottle is 15 ounces. So, the unit price can be calculated as $2.79 divided by 15 ounces, which gives us approximately $0.186 unit price per ounce.

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The simplified ratio that correctly compares 27 feet to 36 feet is 3:4

Step-by-step explanation:

Step 1: Simplify the ratio by finding common factor

Step 2: Here, in this case the lowest common factor is 3. Divide both numerator and denominator by 3.

⇒ 27/36 = 9/12 (on dividing by 3)

⇒ 9/12 = 3/4 (again on dividing by 3)

Answer:

the answer to your question is b

Answer:

.5 or l/2 liter

Step-by-step explanation

4 liters x 5= 20 liters / 40 people =.5 or 1/2  liter

Answer: 1.9

Step-by-step explanation:

because you keep adding 1.9 to get your result

Answer:

11.1

Step-by-step explanation:

3.9 - 1.5 = 2.4

if you add 2.4 to one of the numbers in the sequence it will be the next number.

1.5 + 2.4 = 3.9

3.9 + 2.4 = 6.3

6.3 + 2.4 = 8.7

if this is the case then 8.7 + 2.4 = 11.1

Answer:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

Step-by-step explanation:

Assuming we want to write a quadratic function with intercepts x=13 and x=2.

Then we can work backwards.

This means that:

x-13=0 and x-2=0

The factored form of this quadratic function becomes:

[tex]f(x) = (x - 13)(x - 2)[/tex]

We expand to get:

[tex]f(x) = {x}^{2} - 2x - 13x + 26[/tex]

We simplify to obtain:

[tex]f(x) = {x}^{2} - 15x + 26[/tex]

Answer: x = 995

Step-by-step explanation:

In this equation our log doesn't have a base so it is given the default base of 10. This makes our equation really.

[tex]log_{10}(x+3) + log_{10}(2) = 3[/tex]

Now we put every equation as the exponent of our base 10 looks like this:

[tex]10^{log_{10} (x+3)} + 10^{log_{10} (2)} = 10^{3}[/tex]

Now we cancel out the log base 10 and the 10. We are left with:

(x+3) + (2) = 10^3

Lastly solve for x

x + 5 = 1000

x = 995

It takes about 14.55 years for quadruple your money

Solution:

Given that,

At 10 percent interest, how long does it take to quadruple your money

Rule of 144:

The Rule of 144 will tell you how long it will take an investment to quadruple

Here,

Rate of interest = 10 %

Therefore, number of years to quadruple your money is obtained by dividing 144 by 10

Rule of 144 Formula:

[tex]N = \frac{144}{R}[/tex]

Where:

N = Number of many years times.

144 = Is the constant variable.

R = Rate of interest.

[tex]\rightarrow N = \frac{144}{10} = 14.4[/tex]

Thus it takes about 14.4 years for quadruple your money.

Another method:

If initial amount is $ 1 and it if quadruples it should be $ 4

We have to find the number of years if rate of interest is 10 %

Let "n" be the number of years

Then we can say,

[tex]Amount = Principal(1+\frac{R}{100})^n[/tex]

[tex]4 = 1(1+\frac{10}{100})^n[/tex]

[tex]4 = 1(1+0.1)^n\\\\4= 1(1.1)^n\\\\4 = 1.1^n\\\\We\ know\ that,\\\\(1.1)^{14.55} = 1.1^n\\\\We\ know\ that\\\\If\ a^m = a^n\ then\ m = n\\\\Therefore,\\\\14.55 = n\\\\n = 14.55[/tex]

Thus Option D 14.55 years is correct

Answer: 95 sold



Step-by-step explanation:

995 horses and cows - 510 horses and 390 cows left = 95 sold

Answer:

95

Step-by-step explanation:

add 510 + 390 to find out the total number of horses and cows he has left. this equals 900

then you subtract the total of horses and cows he started with by what he has left to find out how many he sold

995-900=95

Answer:

See photo

Step-by-step explanation:

The line is in slope-intercept form which looks like y = mx + b.

"x" and "y" represent points on the line.

"m" is the slope (how steep the line is) and if the line goes up (+) or down (-).

"b" is the y-intercept, which is where the graph hits the y-axis.

Take information from the equation y=-2x+6. Use the slope and the y-intercept to graph to line.

m = -2  =  [tex]-\frac{2}{1}[/tex]   (Fraction form).

b = 6

Plot a point at the y-intercept on the y-axis

If the y-intercept is 6, so you plot the point at (0, 6). (The y-intercept occurs when x = 0).

Find another point

Count the number of rise and run from the y-intercept.

Remember the slope is [tex]\frac{rise}{run}[/tex]

Run is the number of squares moving right. Rise is the number of squares moving up (if positive) or down (if negative).

Since the slope is -2/1, move two squares down and one square to the right to find another point on the line.

Connect the points

You only need two points to make a line. If you want the line to be longer, you can extend it with a ruler.

Other formatting rules

Remember to add arrows at the ends of the x and y axis.

Also, add arrows to the ends of the the line that you graphed.

Most teachers ask you to label the line with the equation.

Answer:

Step-by-step explanation:

(5x+17)+(2x+50)

5x+2x + 17+50

7x+67

IF 7x+67 = 0

7x = -67

x = - 67/7 OR x = -9.57

Answer:

(4,5)

Step-by-step explanation:

We are to find the circumcenter of triangle EFG with vertices

E(2,6), F(2,4), and G(6,4)

Let S(x,y) be the circum center.  Then this point is equidistance from E, F and

G

i.e. [tex]ES=FS=GS\\ES^2 =FS^2 =GS^2[/tex]

[tex](x-2)^2+(y-6)^2 =(x-2)^2+(y-4)^2 =(x-6)^2+(y-4)^2 \\i.e. x^2-4x+4+y^2-12y+36 = x^2-4x+4+y^2-8y+16 = x^2-12x+36+y^2-8y+16 \\4y = 20: y =5\\8x=32\\x=4[/tex]

Thus circumcenter is (4,5)

Option B: 5.25 is the length of XZ

Explanation:

The triangles PQR and XYZ are similar.

To determine the length of XZ, let us use the similarity theorem.

The theorem states that, "if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar".

Thus,

[tex]\frac{QR}{YZ} =\frac{PR}{XZ}[/tex]

Let us substitute the values from the diagram, we have,

[tex]\frac{4}{3} =\frac{7}{XZ}[/tex]

Multiplying both sides by 3, we get,

[tex]4 =\frac{21}{XZ}[/tex]

Thus,

[tex]XZ =\frac{21}{4}=5.25[/tex]

Thus, the length of XZ is 5.25

Hence, Option B is the correct answer.