16. CRITICAL THINKING
Two figures are congruent. Are the areas of the two figures
the same? the perimeters? Explain your reasoning.​

Lenny's hourly rate is calculated by dividing his gross pay of $196.90 by the total number of hours worked, which is 22 hours. The calculation gives an hourly rate of $8.95.

The question is asking to calculate Lenny's hourly rate based on his gross pay for work done over three days. To find this rate, we will add the total number of hours worked and divide the total gross pay by this number.

Therefore, Lenny's hourly rate is $8.95.

Answer:

36 ft. tall

Step-by-step explanation:

We can easily solve this problem with a simple proportion:

12 feet / height    =     2 feet / 6 feet

6 * 12 = 2h

72 = 2h

h = 36 ft.

It's found that the tree is 36 feet tall.

To find the height of the tree using the lengths of the shadows and the person's height, we can use a proportion based on similar triangles. Since the sun's rays hit both the tree and the person at the same angle, the ratio of the height of the tree to the length of its shadow is the same as the ratio of the person's height to the length of their shadow.

Let's let 'h' represent the height of the tree. We can set up the proportion as follows:

Person's height / Person's shadow length = Tree's height / Tree's shadow length

6 feet / 2 feet = h / 12 feet

Now we solve for 'h' by cross-multiplying:

6 feet * 12 feet = 2 feet * h

72 feet2 = 2 feet * h

Divide both sides by 2 feet to get:

h = 36 feet

Therefore, the tree is 36 feet tall.

To find what percent 9 is of 20, you divide 9 by 20 and multiply the result by 100. The answer is 45%.

To determine what percent 9 is of 20, you'd set up an equation based on the mathematical definition of percentage:

p = (part/whole) * 100%

Here, our part is 9 and our whole is 20. So you arrange the numbers in the given formula:

p = (9/20) * 100%

Solving the equation gives us 45%

Therefore, 9 is 45% of 20.

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To find out what percent 9 is of 20, we can use the formula part/whole = percent/100. Using this equation, we can solve for p and find that 9 is 45% of 20.

To find out what percent 9 is of 20, we can set up an equation using the formula:

part/whole = percent/100

In this case, the part is 9, the whole is 20, and we want to find the percent. So the equation becomes:

9/20 = p/100

To solve for p, we can cross multiply:

9 * 100 = 20 * p

Dividing both sides of the equation by 20 gives us:

900 = 20p

Finally, dividing both sides by 20 gives us the value of p:

p = 900/20 = 45

Therefore, 9 is 45% of 20.

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Answer:

Step-by-step explanation:

Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).

[tex]4=\frac{2+x_2}{2}[/tex]                    [tex]2=\frac{7+y_2}{2}[/tex]

Multiply by 2 we get                             Multiply by 2 we get  

[tex]4(2)=2+x_2[/tex]                                           [tex]2(2)=7+y_2[/tex]

[tex]8=2+x_2[/tex]                                                [tex]4=7+y_2[/tex]

Subtracting 2 on both

the sides                                    Subtracting 7 on both the sides

[tex]8-2=2+x_2-2[/tex]                                [tex]4-7=7+y_2-7[/tex]

[tex]6=x_2[/tex]                                                       [tex]-3=y_2[/tex]

Rewritting the above equation      Rewritting the equation

[tex]x_2=6[/tex]                                                      [tex]y_2=-3[/tex]

Solution:

We have to find the height of lamppost

From the figure in question,

Given is a right angled triangle

Where,

base = 40 inches

height = ?

By definition of tan,

[tex]tan\ 70 = \frac{opposite}{base}\\\\tan\ 70 = \frac{height}{40}\\\\height = tan\ 70 \times 40\\\\height = 2.7474 \times 40\\\\height = 109.89 \approx 110[/tex]

Thus height of lamp post to nearest inch is 110 inches

great someone deleted all my answers again

Answer:

100

Step-by-step explanation:

1. 100 divided by 5 = 20

2. 20 x 100 = 2000

3. Final Answer = 100

A company plans to ship 2,000 packages of chocolate, the number of packages is  X=100. This is further explained below.

Generally, the number of packages is given as

X=(No Packages* incorrect weight)/ random selections

Therefore

X=2000*5/100

X=100

In conclusion, the number of packages predicted to have an incorrect weight is

X=100

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Answer:

x=2 and y= -3

Step-by-step explanation:

This is a simultaneous equation. To solve this type of equation, there are three methods; substitution, Elimination and Graphical.

But here, we would be using the substitution method.

3x-y=9 Equation 1

2x-y=7. Equation 2

Getting y from equation 2, we have

-y= 7-2x

Multiply both sides by -

y= 2x-7 Equation 3

Substituting y for 2x-7 in equation 1, we have

3x- (2x-7)=9

3x-2x+7=9

x+7=9

x=9-7

x=2

Substituting x as 2 in equation 3

y=2x-7

y= 2(2)-7

y= 4-7

y= -3

Answer:

x=6

Step-by-step explanation:

You are correct. x does equal 6

Answer:

Yes

x = 6

Step-by-step explanation:

Given

2x - 5 = 3(1 - x) + 22

First distribute 3 into (1 - x)

We have

2x - 5 = 3 x 1 -3 x X + 22

2x - 5 = 3 - 3x + 22

The expression can be rearranged as

2x - 5 = 3 + 22 - 3x

2x - 5 = 25 - 3x

Add 3x to both sides

3x + 2x - 5 = 25 - 3x + 3x

5x - 5 = 25

Add five to both sides

5x - 5 + 5 = 25 + 5

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

Answer:

$3600

Step-by-step explanation:

Cost of the car = $8000

The car loses value at 11% each year .

That’s

11% /100% x $8000

0.11 x 8000

$880

11% decrease each year means that the cost of the car is reduced by $880 per year.

Therefore,

Worth of the car in 5 years

= $8000 - ($880 x 5)

= $8000 - $4400

= $3600

The car will be worth $3600 in five years

Answer:

YES

Step-by-step explanation:

If both the fractions are greater than .5, then yes.

Ex. 3/4 and 4/5

Yes if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

If both the fractions are greater than .5, then yes. examples are 3/4 and 4/5.

Sum = 3 / 4 + 4 / 5

Sum = 31 / 20

We can see that the sum is greater than one.

Therefore if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.

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Answer:

B

Step-by-step explanation:

The formula is Y-Y1= M(X-X1)

So y-4=3(x+2)

Answer:

3

Step-by-step explanation:

18*x=54   (divide both sides by 18)

x = 54 ÷ 18

x = 3

Hello!

The answer to your problem is A) 3

Move all terms to the left

[tex]18x-(54)=0[/tex]

Move all terms containing x to the left, all other terms to the right

[tex]18x=54[/tex]

[tex]x=54/18[/tex]

Get your answer

[tex]x=3[/tex]

Hope This Helps!

Answer:

220.5

Step-by-step explanation:

:3

Answer:

220.5 lb

Step-by-step explanation:

1 kg = 2.20462262185 lb

100 kg = 100×2.20462262185 lb

100 kg = 220.462 lb

100 kg = 220.5 lb

There was a minor mistake in the second step. The sum should be 2/3 + 4/9, not 2/9 + 4/9. After finding the common denominator and converting the fractions, we add the numerators to get 10/9, which simplifies to 1 1/9.

The process Rodrigo followed is correct, but there was a small mistake in the second step. Here, the problem should be 2/3 + 4/9, not 2/9 + 4/9. To add fractions like this, it's critical to ensure they have common denominators. The lowest common denominator (LCD) of 3 and 9 is 9.

So, the fraction 2/3 should be converted to its equivalent fraction with 9 as the denominator. Multiplying both the numerator and the denominator of 2/3 by 3, we get 6/9. So now our problem becomes 6/9 + 4/9.

Now, we can add them by combining their numerators: 6+4 = 10. So, the answer would be 10/9. But in simplest form, we would write this as 1 1/9. Hence, the sum of 2/3 and 4/9 in simplest terms is 1 1/9.

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Answer:

3/10

mark brainliest

Step-by-step explanation:

The measure of angle B is 65°

Explanation:

Given that ∠A and ∠B are supplementary angles.

The measures are ∠A = (3x - 17)° and ∠B = (2x-23)°

The value of x:

Since, supplementary angles add up to 180°, then we have,

[tex]\angle A+ \angle B=180^{\circ}[/tex]

Substituting the values, we have,

[tex]3x-17+2x-23=180[/tex]

               [tex]5x-40=180[/tex]

                       [tex]5x=220[/tex]

                        [tex]x=44[/tex]

Thus, the value of x is 44

Measure of angle B:

Let us determine the measure of angle B by substituting the value of x in ∠B = (2x-23)°

Thus, we have,

[tex]\angle B=(2(44)-23)^{\circ}[/tex]

[tex]\angle B=(88-23)^{\circ}[/tex]

[tex]\angle B=65^{\circ}[/tex]

Thus, the measure of angle B is 65°

Miss C weight before she started her diet is 80 kg.

Solution:

Weight before diet = x

Weight loss percent = 8%

Present weight of Miss C = 73.6 kg

[tex]$ x-x\times \ 8 \% =73.6[/tex]

[tex]$ x-x\times \frac{8}{100} =73.6[/tex]

The denominators must be same to add/subtract the fractions.

LCM of 1 and 100 = 100

Multiply first term by [tex]\frac{100}{100}[/tex] and 73.6 by [tex]\frac{100}{100}[/tex] to make the denominator same.

[tex]$ \frac{100x}{100} - \frac{8x}{100} =\frac{7360}{100}[/tex]

[tex]$ \frac{100x-8x}{100} =\frac{7360}{100}[/tex]

Multiply by 100 on both sides, we get

100x - 8x = 7360

92x = 7360

Divide by 92 on both sides, we get

x = 80

Miss C weight before she started her diet is 80 kg.

Answer:

The intersection is (1,-2) I am really sure.

Here in question, the table is not given to complete the table with ordered pairs. So, in general, found the possible integer ordered pairs to create the table as in attached figure are [tex](x,y) =(0,3), (12,0),(4,2),(8,1)[/tex].

Step-by-step explanation:

We have the following given linear equation : [tex]x+4y = 12[/tex].Let's find out ordered pairs that satisfies this linear equation .

At x=0 ,

[tex]0 + 4y = 12 \\4y=12\\y=3[/tex]

So, one pair is [tex](x,y) = (0,3)[/tex].

Similarly, At y=0,

[tex]x +4.0 = 12\\x=12[/tex]

SO, another pair is [tex](x,y) = (12,0)[/tex].

At x=4,

[tex]4+4y=12\\4y=8\\y=2[/tex]

Pair is [tex](x,y) = (4,2)[/tex].

At x=8,

[tex]8+4y=12\\4y=4\\y=1[/tex]

Pair is [tex](x,y) = (8,1)[/tex].

Therefore all the possible integer ordered pairs are [tex](x,y) =(0,3), (12,0),(4,2),(8,1)[/tex].

Answer:

x=-1

x=-2

Step-by-step explanation:

4x2 + 12x + 8

To solve a quadratic equation, factorisation Method, formulae method or completing the square method can be used. But for the purpose of this question, the formulae method will be used.

(-b±√(b²-4ac))2a

Where a=4, b=12 and c=8

(-12±√(12²-4(4)(8))/2(4)

(-12±√(144-128)/8

(-12±√16)/8

(-12±4)/8

(-12+4)/8 or (-12-4)/8

-8/8 or -16/8

-1 or -2

Part A: For 100 miles, the cost will be same for both companies.

Part B: Alex should use Drive and Move company as it will cost him less money.

Step-by-step explanation:

Given,

Starting amount of YMI= $40

Per mile charges = $1.99

Let,

x be the number of miles.

y be the total charges.

y = 1.99x+40    Eqn 1

Starting amount of DM = $60

Per mile charges = $1.79

y=1.79x+60    Eqn 2

Part A:

For same charges;

Eqn 1 = Eqn 2

[tex]1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100[/tex]

For 100 miles, the cost will be same for both companies.

Part B:

Total miles = x = 150

Putting x=150 in Eqn 1

y=1.99(150)+40

y=298.5+40

y=$338.50

Putting x=150 in Eqn 2

y=1.79(150)+60

y=268.5+60

y=$328.50

Alex should use Drive and Move company as it will cost him less money.

Answer:

The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = 25 blocks.

Step-by-step explanation:

Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.

So, Reyna's house, the school, and the Shaquille's house form a right triangle and the shortest distance from Shaquille's house to Reyna's house is the hypotenuse of the right triangle.

So, the shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = [tex]\sqrt{12^{2} + 5^{2}} + 12 = 13 + 12 = 25[/tex] blocks. (Answer)

The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.

Since Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.

So, here the shortest distance is

[tex]= \sqrt{(12)^2 + (5)^2}+ 12\\\\[/tex]

= 13 + 12

= 25

Hence, The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.

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Answer:

D)M(x)=70x

Step-by-step explanation:

The function that represents the remaining distance after x hours is M(x) = 617 - 70x (option C).

The question asks about the function that represents the number of remaining miles, M(x), Kyle has to travel after x hours at a speed of 70 miles per hour. To calculate the remaining distance, we subtract the distance traveled (70 miles per hour times x hours) from the total distance of the trip, which is 617 miles. Therefore, the correct function is M(x) = 617 - 70x, which corresponds to option C.

To further illustrate this with an example, if Kyle drives for 1 hour at 70 miles per hour, he would have traveled 70 miles, so the remaining distance would be M(1) = 617 - 70(1) = 547 miles.

Answer:

d > -5

Step-by-step explanation:

Step 1:  Subtract 15 from both sides

15 + d > 10

15 + d - 15 > 10 - 15

d > -5

Answer:  d > -5

Jim's income tax liability for the $45,000 he earned from his three employers would be $9,500.

To calculate Jim's income tax, we first need to find his total income. Since he worked for three different employers, his total income would be the sum of his earnings from each employer, which is $15,000 * 3 = $45,000.

Next, we need to know the tax rates that apply to Jim's income. Income tax rates are usually progressive, meaning different portions of income are taxed at different rates.

Using the hypothetical tax rates mentioned above, we can calculate Jim's income tax liability:

First $10,000 at 10%: $10,000 * 0.10 = $1,000

Next $20,000 at 20%: $20,000 * 0.20 = $4,000

Remaining $15,000 at 30%: $15,000 * 0.30 = $4,500

Now, summing up the tax amounts from each tax bracket: $1,000 + $4,000 + $4,500 = $9,500.

Therefore, Jim's income tax liability should have been $9,500.

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Final answer:

Jim earned a total of $45,000 from three employers. Using a simplified marginal tax rate example, his total income tax comes to approximately $7,106.25. This calculation method demonstrates how the marginal tax rate system works in a basic form.

Explanation:

To determine how much income tax Jim should have paid on his earnings from three different employers, where each paid him $15,000, we first need to calculate his total income. Jim's total income is $15,000 from each job, multiplied by 3, because he worked for three different employers, resulting in a total income of $45,000.

Assuming a simple tax rate example (for illustrative purposes), let's use the marginal tax rates provided in the reference:

Income from $0 to $9,075 is taxed at 10%

Income from $9,075 to $36,900 is taxed at 15%

Income from $36,900 and beyond is taxed at 25%

Since Jim earns $45,000, here is how his taxes would be calculated:

The first $9,075 is taxed at 10%, amounting to $907.50.

The next $27,825 ($36,900 - $9,075) is taxed at 15%, amounting to $4,173.75

The remaining $8,100 ($45,000 - $36,900) is taxed at 25%, amounting to $2,025.

Add up these amounts to get the total tax:

$907.50 + $4,173.75 + $2,025 = $7,106.25

Therefore, applying this simplified tax calculation, Jim should have paid a total of roughly $7,106.25 in income tax on his total earnings of $45,000 from three different employers.

The equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]

Explanation:

The equation of the line is perpendicular to [tex]y=-14 x-8[/tex]

The equation is of the form [tex]y=mx+b[/tex] where m=-14

Slope:

The slope of the perpendicular line can be determined using the formula,

[tex]m_1 \cdot m_2=-1[/tex]

[tex]-14 \cdot m_2=-1[/tex]

       [tex]m_2=\frac{1}{14}[/tex]

Thus, the slope of the line is [tex]m=\frac{1}{14}[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the slope [tex]m=\frac{1}{14}[/tex] and the point (2,-4), we get,

[tex]y+4=\frac{1}{14}(x-2)[/tex]

Simplifying, we get,

[tex]y+4=\frac{1}{14}x-\frac{1}{7}[/tex]

     [tex]y=\frac{1}{14}x-\frac{1}{7}-4[/tex]

     [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]

Thus, the equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]