Madison has reserved x hours this week for activities. He uses 1/4 of his hours for basketball. He uses 1/3 of his hours to practice playing his saxophone. Write an expression to show how much time he has left for other activities.

Answer:

See explanation

Step-by-step explanation:

    Statement                              Reason

1. [tex]\overline{PS}\perp \overline{SQ}[/tex]                           Given

2. [tex]m\angle PSQ = 90^{\circ}[/tex]          Definition of perpendicular lines

3. [tex]\triangle PSQ[/tex] is right triangle   Definition of right triangle

4. [tex]\overline{RQ}\perp \overline{SQ}[/tex]                          Given

5. [tex]m\angle RQS = 90^{\circ}[/tex]          Definition of perpendicular lines

6. [tex]\triangle RQS[/tex] is right triangle   Definition of right triangle

7. [tex]m\angle PSQ=m\angle RQS[/tex]       Substitution property of equality

8. [tex]\overline {SQ}\cong \overline {QS}[/tex]    Reflexive property

9. [tex]\overline {PQ}\cong \overline {RS}[/tex]                        Given

10. [tex]\triangle PSQ\cong \triangle RQS[/tex]               HL postulate

Answer:

x=-27

Step-by-step explanation:

x/-9=3

x=3*-9=-27

Plant B produced 8000 panels.

Let's denote the number of panels produced by Plant B as B .

The total number of defective panels from Plant A is [tex]\( 0.05 \times 16000 = 800 \)[/tex] , and the total number of defective panels from Plant B is [tex]\( 0.02 \times B \)[/tex].

The total number of panels from both plants is 16000 + B .

The overall percentage of defective panels is given as 4%, so:

[tex]\[ \frac{800 + 0.02 \times B}{16000 + B} = 0.04 \][/tex]

Now, let's solve for  B :

[tex]\[800 + 0.02 \times B = 0.04 \times (16000 + B) \][/tex]

[tex]\[ 800 + 0.02 \times B = 640 + 0.04 \times B \][/tex]

Subtracting [tex]\( 0.02 \times B \)[/tex] from both sides:

[tex]\[ 800 = 640 + 0.02 \times B \][/tex]

Subtracting 640 from both sides:

[tex]\[ 160 = 0.02 \times B \][/tex]

Now, divide by 0.02 to find B :

[tex]\[ B = \frac{160}{0.02} \][/tex]

B = 8000

So, Plant B produced 8000 panels.

The number of panels produced by Plant B is 8,000.

The number of panels produced by Plant A  = 16,000

The number of defective panels from A = 5%

Now, 5% of 16,000 =

So, out of  16,000 panels produced by pant A , 800 are defective. .. (1)

Let us assume number of panels produced by Plant B  = m

The number of defective panels from B = 2%

Now, 2% of m

So, out of total m panels produced by pant B , 0.02 m are defective. .. (2)

Now, total panels produced over all = Panels by A  + Panels by B

= 16,000 + m

The percentage of defective panels over all = 4%

Now, 4% of (16,000 + m)

Also, the total number of defective panels = Defective from A  + Defective from B

⇒(0.04)(16,000 + m)  =  800 +   0.02 m   from (1) and (2)

0.02 m = 160

⇒ m = 160 /0.02 = 8,000

or, m = 8,000

Hence, Number of panels produced by Plant B is 8,000.

Answer: 24

Step-by-step explanation:

2-(8-5x6) = 24

Deb can use 6.5 ounces of cheese per loaf of bread. The calculation is made by dividing the total amount of cheese by the number of loaves.

Deb has 26 ounces of shredded cheese and she is making 4 small loaves of garlic cheese bread. To equally distribute the cheese across each loaf, we perform division.

We divide the total amount of cheese by the number of loaves: Thus, 26 ounces divided by 4 loaves equals 6.5 ounces of cheese per loaf.

The reasoning here is simple: we are equally distributing the cheese across each loaf, so we divide the total amount by the number of loaves. This ensures each loaf gets the same amount of cheese.

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Answer:

x=-5, y=-5. (-5, -5).

Step-by-step explanation:

-x-5y=30

10x+5y=-75

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

9x=-45

x=-45/9

x=-5

-(-5)-5y=30

5-5y=30

5y=5-30

5y=-25

y=-25/5

y=-5

Answer:

If by bi-weekly you mean once every two weeks, then the friend who is payed bi-weekly has a higher annual salary. The same for if he is payed twice a week.

Step-by-step explanation:

1458 x 24 = 34992

1346 x 26 =34996

Answer:

7 weeks

Step-by-step explanation:

500-200=300. 300 divided by 40 is 7.5 so 7 weeks

Answer:

(4y +8 )÷6 -12

Variable = y

Sum = 4y +8

Quotient = 6

coefficient =4

Answer:

-1

Step-by-step explanation:

if x = 0...

2(0) + 8(0) - 1 =

0 + 0 - 1 =

0 - 1 =

-1

Answer:

60°

Step-by-step explanation:

Jenny drew a figure in art school and the figure is shown in the attached diagram.  

The diagram is a regular hexagon and it has rotational symmetry.  

Two of its sides is placed parallel to the x-axis.

Therefore, by rotating 60° the adjacent sides will become parallel to the x-axis and the figure remains the same and symmetric with respect to the coordinate axes. (Answer)

Answer:

Step-by-step explanation:

The fiven figure is a hexagon, which is a regular polygon with six equal sides.

Now, the symmetry of a hexagon is based on a 60° rotation, because each symmetrical portion of the figure enclosed a 60° angle.

Therefore, the right answer is 60°.

Answer: Percy, None, 288

Step-by-step explanation:

Divide to find the rate.

Divide 33/2= about 16. 43/3= about 14.

Percy is faster.

Second problem: 50/12=4

120/30=4

No one, they grade the same amount.

Third:

72/2= 36 per hour

36x8= 288

Answer:

20

Step-by-step explanation:

I assume you mean discriminant.

For a quadratic y = ax² + bx + c, the discriminant is b² − 4ac.

Here, a = -4, b = 2, and c = 1.  So the discriminant is:

(2)² − 4(-4)(1) = 20

Answer:

x-intercept: (9,0)

y-intercept: (0,7)

Step-by-step explanation:

x-intercept: when y = 0

7x + 9(0) = 63

7x = 63

x = 9

y-intercept: when x = 0

7(0) + 9y = 63

y = 7

Answer:

x-intercept : (9,0)

y-intercept : (0,7)

Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Hope this helps you out! ☺

We can see here that the cost of the food bill and tip before sales tax was approximately $253.20.

To find the cost of the food bill and tip before sales tax, you first need to calculate the tip amount and then add it to the food bill.

Given:

Food bill = $214.58

Tip rate = 0.18 (18% expressed as a decimal)

First, calculate the tip amount:

Tip = Food bill × Tip rate

Tip = $214.58 × 0.18

Tip = $38.6244 (rounded to two decimal places)

Tip ≈ $38.62

Now, add the food bill and the tip to find the total cost before sales tax:

Total cost = Food bill + Tip

Total cost = $214.58 + $38.62

Total cost = $253.20

Therefore, the cost of the food bill and tip before sales tax was approximately $253.20.

Answer:

0

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-7)/(8-0)

m=0/8=0

Answer:

0

Step-by-step explanation:

Answer:

[tex](x-2)(8x+4)[/tex]

Step-by-step explanation:

we have

[tex]8x^{2} -12x-8[/tex]

Equate to zero and find the roots of the quadratic equation

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]8x^{2} -12x-8=0[/tex]

so

[tex]a=8\\b=-12\\c=-8[/tex]

substitute in the formula

[tex]x=\frac{-(-12)(+/-)\sqrt{-12^{2}-4(8)(-8)}} {2(8)}[/tex]

[tex]x=\frac{12(+/-)\sqrt{400}} {16}[/tex]

[tex]x=\frac{12(+/-)20} {16}[/tex]

[tex]x_1=\frac{12(+)20} {16}=2[/tex]

[tex]x_2=\frac{12(-)20} {16}=-\frac{1}{2}[/tex]

therefore

[tex]8x^{2} -12x-8=8(x-2)(x+\frac{1}{2})=(x-2)(8x+4)[/tex]

Answer:

y - 2 = 3(x - 5)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (5, 2), thus

y - 2 = 3(x - 5) ← equation of line

Answer:

y - 2 = 3(x - 5)

Step-by-step explanation:

Start with the general point-slope equation:

y - k = m(x - h)

Now substitute 2 for k, 5 for h and 3 for m:

y - 2 = 3(x - 5)

Answer:

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

Step-by-step explanation:

we know that

In a parallelogram, opposite sides are parallel and congruent

In this problem we have a parallelogram

so

[tex]DC=AB[/tex]

[tex]AD=BC[/tex]

substitute the given values

[tex]5x-18=2x+12[/tex]

[tex]5x-2x=12+18[/tex]

[tex]3x=30[/tex]

[tex]x=10[/tex]

Find the length of side AB

[tex]AB=2x+12[/tex]

substitute the value of x

[tex]AB=2(10)+12=32\ units[/tex]

Find the length of side CB

[tex]BC=3x-6[/tex]

substitute the value of x

[tex]BC=3(10)-6=24\ units[/tex]

therefore

[tex]AB=DC=32\ units[/tex]

[tex]AD=BC=24\ units[/tex]

Let X = Individual ticket and y = couples tickets.

Set up two equations:

X + Y = 47 tickets sold

1X + 8y = $200

Rewrite the first equation as X = 47-y

Replace x in the second equation and solve:

1(47-y) = 8y = 200

Simplify:

47 - y + 8y = 200

Combine like terms:

47 +7y = 200

Subtract 47 from both sides:

7y = 153

Divide both sides by 7:

y = 153 / 7

y = 21.857

Because Y does not equal a whole number, the extra dollar does belong in the box.

Final answer:

Given the ticket prices and attendance, total sales amount to $71. The extra dollar found doesn't fit this, so it shouldn't be in the box.

Explanation:

To determine if the dollar Nola found belongs in the box, let's analyze the ticket sales. With individual tickets priced at $1 and couples tickets at $8 for two, we can calculate the total number of tickets sold. If there were 47 students in attendance, and assuming each couple bought the couples' ticket deal, the number of individual tickets sold would be (47 - number of couples) * 2 + number of couples.

Since each couple buys two tickets, the number of couples is 47 / 2 = 23.5, which means there were 23 couples and 1 individual. So, the total number of tickets sold is (47 - 23) * 2 + 23 = 71. Thus, the revenue from ticket sales should be $71.

If the cash box contains $200 and ticket sales total $71, then the extra dollar Nola found does not belong in the box. It's possible someone overpaid for a ticket or dropped a dollar accidentally, but it shouldn't be included in the revenue from ticket sales. Therefore, Nola should keep the dollar aside, perhaps to return it to its rightful owner.

Answer:

The first option:

Prove that the area of the two small squares combined is equal to the area of the larger square

Step-by-step explanation:

The Pythagorean Theorem in an equation would be:

a² + b² = c²

Where:

c = hypotenuse (longest side of the triangle)

a and b = two other legs of the triangle

The theorem states that the sum of the squares of the shorter sides is equal to the square of the longest side in a right triangle or a triangle that has a right angle (90°)

Let's say that we have a right triangle with the lengths of 3cm , 4cm, and 5cm.

(3cm)² + (4cm)² = (5cm)²

9cm² + 16cm² = 25cm²

25cm² = 25cm²

Look at the attached image to see what happens when we draw the squares of each leg.

Answer: 20 ÷ 2.5 = 8

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 divided by 0.5 equals 8.

Answer:

7.5 pounds of muscles.

Step-by-step explanation:

Mr. Tan gained 5 pounds of solid fast twitching muscles during his last bulking phase lasting 24 days.

If this rate remains the same, then we can use the unitary method to calculate the amount of muscle he will gain in 36 days bulking phase.

Hence, within 24 days of the bulking phase, he gains 5 pounds of muscles.

So, within 36 days of the bulking phase, he will gain [tex]\frac{5}{24} \times 36 = 7.5[/tex] pounds of muscles. (Answer)

First, we calculated Mr. Tran's rate of muscle gain by dividing the total amount gained by the number of days. We then applied this rate to the asked time frame of 36 days. The result was approximately 7.48 lbs of muscle gain.

To solve this problem, we need to determine the rate of gain. Mr. Tran gained 5 lbs of solid fast twitching muscles in 24 days, so his rate of gain is 5 lbs / 24 days = 0.208 lbs/day. If Mr. Tran continues this rate for an extended period of 36 days, we can calculate the total gain by multiplying his daily rate by the number of days, i.e., 0.208 lbs/day * 36 days = 7.48 lbs. rounded to two decimal places.

So, if Mr. Tran’s bulking phase continues at the same rate for 36 days, he will gain approximately 7.48 lbs of muscle.

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Answer:

Step-by-step explanation:

5/10 and 1/2 are both equivalent ratios resulting in half of themselves you can multiply these by any numbers but they will stay as half ratios such as 1:2 x 6 it would be 6:12 divide it by 6 and you have a half

Equivalent ratios have a multiplicative relationship, where multiplying both terms of a ratio by the same number results in another equivalent ratio. For example, multiplying the ratio 1:2 by 2 gives the equivalent ratio 2:4, showing that the ratios are proportional to each other.

Understanding Equivalent Ratios through Multiplication

We can explore the concept of equivalent ratios by looking at their multiplicative relationship. For instance, let's consider the ratios 1:2 and 2:4. These two ratios are equivalent because if we multiply both terms of the first ratio by 2, we get the second ratio. Mathematically, this can be expressed as 1x2/2x2 = 2/4, which is the same as the second ratio. Hence, the multiplication of both the numerator and the denominator of the first ratio by the same number (in this case, 2) maintains the ratio's equivalence to the second ratio.

This concept is crucial when dealing with proportions, unit rates, and unit scales. For example, if a map uses a unit scale of 1 inch = 100 feet, doubling the distance on the map to 2 inches would also double the actual distance to 200 feet, showing a direct multiplicative relationship between the two equivalent ratios.

Understanding how to use multiplication to find equivalent ratios is fundamental in solving problems that involve scaling, such as converting units or working with maps and models.

The correct answer is option 4: [tex](8.\frac{1}{4}).\frac{3}{5}[/tex]

Step-by-step explanation:

Given expression is:

[tex]8.(\frac{1}{4}.\frac{3}{5})[/tex]

The associative property states that for any three terms that are being multiplied, different order of multiplication (i.e. which two terms are multiplied first) will give the same answer.

Let a,b and c be the three terms

then

[tex]a.(b.c) = (a.b).c[/tex]

So applying the associative property on given expression

[tex]8.(\frac{1}{4}.\frac{3}{5}) = (8.\frac{1}{4}).\frac{3}{5}[/tex]

Hence,

The correct answer is option 4: [tex](8.\frac{1}{4}).\frac{3}{5}[/tex]

Keywords: Associative property, Properties

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Answer:

A

Step-by-step explanation:

You are dividing not multiplying

Answer:

1/4

Step-by-step explanation:

You go up 2 and right 8, which translates to 2/8.

Simplify that to 1/4

Answer:

The town received approximately 44.29 inches of rain during a 31−day month.

Step-by-step explanation:

Given;

The amount of rain for two weeks = 20 inches.

For finding amount of rain for 31 days, we use the unitary method.

∵ Amount of rain for 14 days = [tex]20\ inches[/tex]

∴ Amount of rain for 1 day = [tex]\frac{20\ inches}{14}[/tex]

∴ Amount of rain for 31 day = [tex]\frac{20\ inches}{14}\times31=\frac{620}{14}\ in=44.285\approx 44.29\ in[/tex]

Hence the amount of rain the town received is 44.29 inches approximately.

Answer:

B

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( isolate r by dividing both sides by 2π )

C ÷ 2π = r → B

Answer:

b=[tex]\frac{c}{2\pi }[/tex]

Step-by-step explanation:

Answer:

[tex]y = \frac{ - 4}{3} x + 3[/tex]

Step-by-step explanation:

[tex]using \: point \: slope \: form \\ y - y1 = m(x - x1) \\ y + 9= \frac{ - 4}{3} (x - 9) \\ y + 9= \frac{ - 4}{3}x + 12\\ y = \frac{ - 4}{3} x + 3[/tex]

The equation of the line in point-slope form passing through (9, -9) with a slope of -4/3 is y + 9 = -4/3 * (x - 9).

The point-slope form of a line's equation is expressed as y - y1 = m(x - x1). In this equation, 'm' represents the line's slope and (x1, y1) defines a particular point through which the line passes. In this scenario, the slope is given as '-4/3' and the point (9, -9). Consequently, by substituting these parameters into the point-slope form, we obtain the equation y - (-9) = (-4/3)(x - 9) or y + 9 = -4/3 * (x - 9).

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