I need help with this puzzle

To find the area of the given shape, we need to identify the shape and then calculate the total area. the correct answer is: Area [tex]= 72 mm^2[/tex] .

To find the area of the given shape, we need to identify the shape and then calculate the total area.

Based on the provided dimensions, it appears that the shape is a composite figure made up of multiple rectangles. Let's calculate the total area by finding the area of each rectangle and then adding them together.

Rectangle 1: Length = 6 mm, Width = 7 mm

Area of Rectangle 1 = Length × Width = 6 mm × 7 mm = 42 mm²

Rectangle 2: Length = 15 mm, Width = 2 mm

Area of Rectangle 2 [tex]= Length × Width = 15 mm × 2 mm = 30 mm^2[/tex]

Total Area = Area of Rectangle 1 + Area of Rectangle  [tex]2 = 42 mm^2 + 30 mm^2 = 72 mm^2[/tex]

So, the correct answer is: Area [tex]= 72 mm^2[/tex]  .

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Answer:

degree of -2x^4 is 4

degree of -3 is 0

degree of 4x^6 is 6

degree of -6x^7 is 7

degree of the polynomial 17

Step-by-step explanation:

the degree of a term is the exponent of the variable. so for the terms, just write down the exponent of X. since -3 does not have a variable, it has a degree of 0. the degree of a polynomial is the sum of the exponents on all variables so 4+6+7=17.

Answer:

Ther answers are in the photo I've added

Step-by-step explanation:

Use trigonometry:

4.

[tex] \tan(60°) = \frac{bc}{15} [/tex]

Cross-multiply to find the value of BC:

[tex]bc = 15 \times \tan(60°) = 15 \sqrt{3} [/tex]

∠B = 180° - 60° - 90° = 30° (the sum of all triangle's angles is 180°)

To find AB, we can use the Pythagorean theorem:

[tex] {ab}^{2} = {ac}^{2} + {bc}^{2} [/tex]

[tex] {ab}^{2} = {15}^{2} + ({15 \sqrt{3} )}^{2} = 225 + 675 = 900[/tex]

[tex]ab > 0[/tex]

[tex]ab = \sqrt{900} = 30[/tex]

Now we the others one the same way

.

5.

[tex] \tan(45°) = \frac{40}{qs} [/tex]

[tex]qs = \frac{40}{ \tan(45°) } = 40[/tex]

∠R = 180° - 90° - 45° = 45°

[tex] {rs}^{2} = {qr}^{2} + {qs}^{2} [/tex]

[tex] {rs}^{2} = {40}^{2} + {40}^{2} = 3200[/tex]

[tex]rs > 0[/tex]

[tex]rs = \sqrt{3200} = 40 \sqrt{2} [/tex]

.

6.

[tex] \sin(53°) = \frac{dc}{21} [/tex]

[tex]dc = 21 \times \sin(53°) ≈16.77[/tex]

∠D = 180° - 90° - 53° = 37°

[tex] {bc}^{2} = {bd}^{2} - {dc}^{2} [/tex]

[tex] {bc}^{2} = {21}^{2} - ({16.77})^{2} = 159.7671[/tex]

[tex]bc > 0[/tex]

[tex]bc = \sqrt{159.7671} ≈12.64[/tex]

Answer:

6 hours tutoring and 8 hours landscaping.

Step-by-step explanation:

Helping in the name of Jesus.

8 feet is the distance between the ground and the top of the ladder

Given the following sides

length of ladder = hyp = 10foot

Distance from ladder to the base = adjacent  = 6 feet

Substitute the given parameters into the formula to have:

10² = opp² + 6²

opp²=100 - 36

opp² = 64

Take square root on both sides

opp = 8 feet

Hence, 8 feet is the distance between the ground and the top of the ladder

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Answer: 3237 photos

Step-by-step explanation:

Let the number of photos of size 3R that the school ordered be 'x', and the number of photos of size 6R be 'y'.

We know that the school ordered 308 photos of size 3R, so:

x = 308

We also know that the total amount spent on photos was Rs 18500, so:

3x + 6y = 18500

Substituting the value of x from the first equation:

3(308) + 6y = 18500

924 + 6y = 18500

6y = 17576

y = 2929.33 (rounded off to the nearest whole number)

Since the number of photos must be a whole number, we can assume that the school ordered 2929 photos of size 6R.

Therefore, the total number of photos that the school ordered together is:

x + y = 308 + 2929 = 3237

Hence, the school ordered a total of 3237 photos.

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(1) The closest answer choice is B. 0.148 repeated, which is equivalent to 0.148148... (2) The closest answer choice to the value of the shaded area is A. 0.148.

Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value.

(1) If the shaded area is 2/12 of the total area, we can simplify 2/12 by dividing both the numerator and denominator by 2, which gives us 1/6. So, the shaded area is 1/6 of the total area.

Let's assume that the total area of the diagram is 1 unit, then the shaded area would be:

1/6 x 1 = 0.166666...

This value is equal to 0.166666... or 0.1666 with 4 decimal places, which is not exactly equal to any of the answer choices provided.

The closest answer choice is B. 0.148 repeated, which is equivalent to 0.148148... with the digits repeating infinitely. However, this is not exactly equal to the calculated value of 0.166666....

Therefore, none of the answer choices provided is an exact match for the calculated value of the shaded area.

(2) If the shaded area is 2/15 of the total area, then we can find the value of the shaded area as follows:

Let's assume that the total area of the diagram is 1 unit, then the shaded area would be:

2/15 x 1 = 0.133333...

This value is equivalent to 0.1333 with 4 decimal places, which is not exactly equal to any of the answer choices provided.

The closest answer choice is A. 0.148, which is approximately equal to the calculated value of 0.133333... but is not an exact match.

Therefore, the closest answer choice to the value of the shaded area is A. 0.148.

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Answer:

x = 9

PR = 10.4

PT = 13

Step-by-step explanation:

We are given a circle, with secants PR and PT. Secant PR is made up of PQ and QR, while Secant PT is made up of PS and ST.

We know that PQ = 5, QR = 5.4, PS = 4, and ST = x

As stated by your problem, we want to find the length of x (which is ST) and the length of each segment (i.e. we want to find the lengths of both PR and PT).

You're correct in setting up the Secant-Secant Product Theorem; it will be PR * PQ = PT * PS

Now, we substitute the values into the equation.

As stated above, PR is made up of PQ and QR, which means that PR = PQ + QR (segment addition postulate).

Substituting in the values, PR = 5 + 5.4 = 10.4

We also know that PT is made up of PS and ST. In other words, PT = PS + ST (also segment addition postulate).

Substituting in the values, PT = 4 + x

We already know the values of PQ and PS, so when we substitute the values in, the the equation becomes:
10.4 * 5 = (4 + x) * 4

We can simplify this to become:

52 = 16 + 4x

Subtract 16 from both sides.

36 = 4x

Divide both sides by 4.

9 = x

We found the value of x, however we aren't done yet. Remember that we need to find the lengths of the secants as well.

We have already found the length of PR (which was 10.4), but remember that PT was 4 + x

Substituting 9 as x, PT is 13.

Answer:

1/15

Step-by-step explanation:

you write down 1/5÷3= 1/5x1/3= 1/15

The value of the percentage 64% of 35 is 22.4

To find 64% of 35, we can use the following formula:

percent × whole = part

where percent is the percentage we want to find, whole is the total value, and part is the result we are looking for.

In this case, we want to find 64% of 35, which means that percent = 64 and whole = 35.

Let's substitute these values into the formula:

64% × 35 = part

To calculate the product of 64% and 35, we can convert 64% to a decimal by dividing it by 100:

64% ÷ 100 = 0.64

Substituting this value into the formula, we get:

0.64 × 35 = part

Multiplying 0.64 by 35, we get:

22.4 = part

Therefore, 64% of 35 is 22.4.

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The table that correctly shows these ratios in a three-column table is shown below:

Classroom Brown      Green

1                     10         18

2                     12         23

3                          15        35

4                          32         64

The correct three-column table would be:

Classroom    Brown            Green

1                        5                  9

2                     12/2              23/2

3                       3/7                 5/7

4                       1/2                   1/2

To create the table, we can simplify each ratio by dividing both the numerator and denominator by their greatest common factor. For example, in Classroom 1, the greatest common factor of 10 and 18 is 2, so we can divide both by 2 to get the simplified ratio of 5:9.

Similarly, for Classroom 2, we divide both the numerator and denominator by 2 to get 6:23/2 or 12:23. We can simplify the remaining ratios in the same way.

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Answer:y = 9x - 1

Step-by-step explanation:

Calculate the slope (m) using the two points (x1, y1) = (2, 17) and (x2, y2) = (-7, -64):

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

m = (-64 - 17) / (-7 - 2)

m = (-81) / (-9)

m = 9

Now that we have the slope (m = 9), we can use one of the points (either (2, 17) or (-7, -64)) to find the y-intercept (b). Let's use (2, 17):

y = mx + b

17 = 9 * 2 + b

17 = 18 + b

b = -1

Now we have the slope (m = 9) and the y-intercept (b = -1), so we can write the equation of the line in the form y = mx + b:

y = 9x - 1

(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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check the image for the explanation

Kristen have 8 cups more than Chris.

We will use unitary method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Kristen has 8 gallons of water. Chris has 28 quarts of water.

We need to convert gallons and quarts to cups and subtract the values

1 gallon = 16 cups

7 gallons = 7 x 16 = 112 cups

1 quart = 4 cups

Therefore,

26 quarts = 26 x 4 = 104 cups

112 - 104 = 8 cups

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The solution to the equation is [tex]? = 2/13[/tex] .

the variable (?) in order to solve this problem. By multiplying both sides by the fraction's denominator (2 and 1/2 or 5/2) we can first get rid of the fraction.

[tex](5/2) \times ? times 2[/tex]  and  [tex]1/2 = (5/2) \times 1/4[/tex]

Simplifying the left-hand side, we get:

[tex](5/2) \tmes ? times 2[/tex] and [tex]1/2 = (5/2) \times (5/2) \times 1/10[/tex]

Now, we can simplify the right-hand side:

[tex](5/2) \times ? \times 2 \ and\ 1/2 = 1/2[/tex]

Next, we need to get rid of the coefficient of ? by dividing both sides by  [tex](5/2) \times 2[/tex] and 1/2:

[tex][(5/2) ? \times 2[/tex]  and  [tex]1/2] / [(5/2) \times 2[/tex] and  [tex]1/2] = (1/2) / [(5/2) \times 2 and 1/2][/tex]

Simplifying the left-hand side, we get:

[tex]? = (1/2) / [(5/2) \times 2 and 1/2][/tex]

Now, we need to simplify the right-hand side:

[tex]? = (1/2) / (13/4)[/tex]

To divide by a fraction, we multiply by its reciprocal:

[tex]? = (1/2) \times (4/13)[/tex]

Simplifying the right-hand side, we get:

[tex]? = 2/13[/tex]

Therefore, the solution to the equation is   [tex]? = 2/13.[/tex]

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The height of John's room walls is roughly 7.98 feet.

We would use lateral surface area (LSA) to solve the problem:

The LSA of the room, or sum of the areas of all four walls, is determined with an equation as follows:

LSA = 2(LH) + 2(WH), since there are two pairs of opposing walls.

In this case, we have been provided with the overall LSA at 335 square feet, thus:

335 = 2(14H) + 2(7H).

To find our answer for H, we must next solve accordingly:

335 = 28H + 14H, which then simplifies to 335 = 42H.

Subsequently, divide both sides by 42:

H = 335 / 42 or, expressed differently, H ≈ 7.98 feet.

Therefore, it can be concluded that the height of John's room walls is roughly 7.98 feet.

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The possible solutions are (1,2), (1,5), (3,4). So correct options are B, C, and D.

In mathematics, an inequality is a statement that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities are used to represent a range of values that satisfy a certain condition, rather than just a single value.

For example, the inequality x > 5 represents all the possible values of x that are greater than 5. This can include 6, 7, 8, and so on. Similarly, the inequality y ≤ 2x + 1 represents all the possible values of y that are less than or equal to 2 times x plus 1.

Inequalities can be graphed on a number line or in the coordinate plane to show the range of values that satisfy the inequality. They are commonly used in solving problems involving equations, functions, and systems of equations.

We can graph the two inequalities to find the solutions that satisfy both.

The graph of y > 4x - 3 is a blue dashed line with a slope of 4 and y-intercept of -3. We shade the region above the line since the inequality is "greater than".

The graph of y ≥ -2x + 3 is a green dashed line with a slope of -2 and y-intercept of 3. We shade the region above the line since the inequality includes "greater than or equal to".

The shaded regions overlap in the upper-right quadrant, so any point in that region satisfies both inequalities. Looking at the options given:

A. (1,1): Does not satisfy y > 4x - 3

B. (1,2): Satisfies both inequalities

C. (1,5): Satisfies both inequalities

D. (3,4): Satisfies both inequalities

E. (0,5): Satisfies y ≥ -2x + 3 but not y > 4x - 3

Therefore, the possible solutions are B, C, and D.

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Answer:

The highest card already drawn is the 10 of hearts, so we need to find the probability that the next card drawn is a jack, queen, king, or ace. There are 16 of these cards in the deck (4 jacks, 4 queens, 4 kings, and 4 aces) out of a total of 47 cards left in the deck (since 5 cards have already been drawn).

Therefore, the probability of drawing a winning card is 16/47, which is approximately 0.34 or 34%. None of the given answer choices match this calculation, so there must be a mistake in the problem or in the answer choices.

The required, probability of drawing a winning card is 25%. Option D is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

There are 52 - 4 = 48 cards remaining in the deck after the 4 cards have been drawn. To win, the player needs to draw a card with a value higher than 10. There are 3 aces and 3 jacks, 3 queens, and 3 kings left in the deck that can satisfy this condition, for a total of 12 winning cards.

Therefore, the probability of drawing a winning card is:

P(winning) = number of winning cards/number of remaining cards

= 12 / 48

= 1 / 4

= 25%

So, the answer is D. 25%.

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The total area of the entire space is 1728.72 feet².

We have,

From the figure,

It has 4 shapes:

Semicircle, Rectangle, trapezium, and a smaller rectangle.

Now,

Diameter of the semicircle = 4 units

Radius = 2 units = 2 x 7 = 14 feet

Area = 1/2 x π x r² = 1/2 x 3.14 x 14 x 14 = 307.72 feet²

And,

Area of the Rectangle.

= 5 units x 3 units

= 5 x 7 x 3 x 7

= 15 x 49

= 735 feet²

And,

Area of the trapezium.

= 1/2 x 1 unit x (3 units + 5 units)

= 1/2 x (1 x 7) x (8 x 7)

= 1/2 x 7 x 56

= 196 feet²

And,

Area of the rectangle.

= 5 units x 2 units

= 5 x 7 x 2 x 7

= 35 x 14

= 490 feet²

Now,

The total area of the entire space.

= 307.72 + 735 + 196 + 490

= 1728.72 feet²

Thus,

The total area of the entire space is 1728.72 feet².

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Answer:

b= 51°  c= 129°

Step-by-step explanation:

We know that angle b = 51° as it is a verticle angle to 51°. To find angle c, we must know that on a straight angle, there is a total of 180°.

180° = angle 1 + angle 2.

Since we know one of the angles, we can plug it into the equation,
180° = 51° + c

-51°         -51°

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

180° - 51° = c

129° = c

Answer:

Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

Step-by-step explanation:

According to the given information, Diego wants to make a shade of green paint that requires 3 parts yellow and 7 parts blue.

This means that for every 7 gallons of blue paint, Diego needs 3 gallons of yellow paint.

As Diego is using 49 gallons of blue paint, we can set up the following proportion:

7/49 = 3/x

where x is the amount of yellow paint needed.

To solve for x, we can cross-multiply and simplify:

7x = 3 * 49

7x = 147

x = 21

Therefore, Diego will need 21 gallons of yellow paint to make the shade of green paint he desires.

The area of the regular polygon, or equilateral triangle, is determined as  27.71 mm².

The area of a regular polygon can be calculated using the formula:

Area = (perimeter * apothem) / 2

where;

Assuming the regular polygon is an equilateral triangle, the following formula will be used to find the area of the triangle.

A = a² × √3/4

where;

a is the side length of the  equilateral triangle = 8 mm

The area of the equilateral triangle is calculated as follows;

A = ( 8² ) x √ ( 3 ) / 4

A = 27.71 mm²

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The surface area of the solid is 56m²

Surface area is the amount of space covering the outside of a three-dimensional shape. Therefore the total surface area is the addition of all the areas.

Face 1,

area = l× b

= 4× 2 = 8m²

for face 2,

area = 5× 2

= 10m²

face 3,

area = 1+( 4×3)

= 1+12 = 13m²

face 3 = face 4

therefore, face 4 = 13m²

Face 5,

area = 3×2 = 6m²

Face 6,

area = 2+(2×2)

= 2+4 = 6m²

therefore the total surface area = 10+13+13+6+6+8

= 56m²

therefore the surface area of the solid is 56m²

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The surface area of the solid as shown in teh diagram is 26 m².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the solid, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the surface area is 26 m².

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Step-by-step explanation:

to find the percentage you have to take 5 as 100% so to find the percentage of 4 you have to divide 100 by 5 making 20%. then do 20 multiplied by 4 which is 80%. so the answer is 80^

Taylor series will be

4 - 2x² + (2x⁴ / 3) - (2x⁶ / 45) + ...

The Taylor series for a function f(x) centered at a is given by:

f(x) = Σ [[tex]f^n[/tex](a) / n!] * [tex](x-a)^n[/tex](n from 0 to infinity)

where [tex]f^n[/tex])(a) denotes the nth derivative of f evaluated at x=a.

To find the first four nonzero terms of the Taylor series for f(x) = 4cos²(x) centered at a=0, we need to compute the derivatives of f(x) and evaluate them at x=0.

f(x) = 4cos²(x)

f'(x) = -8cos(x)sin(x) = -4sin(2x)

f''(x) = -8cos(2x)

f'''(x) = 16sin(2x)

f''''(x) = 32cos(2x)

Now we can plug these values into the formula for the Taylor series to obtain:

f(x) = f(0) + f'(0)x + (f''(0)x² / 2!) + (f'''(0)x³ / 3!) + (f''''(0)x⁴ / 4!) + ...

f(0) = 4cos²(0) = 4

f'(0) = -4sin(2*0) = 0

f''(0) = -8cos(2*0) = -8

f'''(0) = 16sin(2*0) = 0

f''''(0) = 32cos(2*0) = 32

Therefore, the first four nonzero terms of the Taylor series for f(x) = 4cos²(x) centered at a=0 are:

4 - 4x² + (8x⁴ / 4!) - (16x⁶ / 6!) + ...

Simplifying, we get:

4 - 2x² + (2x⁴ / 3) - (2x⁶ / 45) + ...

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The exponential function graphed is defined as follows:

y = 4(3)^x - 1.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function in this problem has an horizontal asymptote at y = -1, hence it is defined as follows:

y = ab^x - 1.

When x increases by one, y is multiplied by 3, hence the parameter b is given as follows:

b = 3.

Hence:

y = a(3)^x - 1.

When x = 0, y = 3, hence the parameter a is given as follows:

a - 1 = 3

a = 4.

Thus the function is:

y = 4(3)^x - 1.

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Answer:

FD = 16 units

Step-by-step explanation:

If the given integer is positive, then it is plotted to the right of zero on the number line. If the given integer negative, then it is plotted to the left of zero on the number line.