i’ve been struggling for hours and i still can’t get it!! someone please help

Ive Been Struggling For Hours And I Still Cant Get It!! Someone Please Help

Answers

Answer 1

Answer:

40.1 cm

Step-by-step explanation:

For this problem we will use trigonometry. To find x, we have to remember SOH CAH TOA

Our angle is 55, and the we have the value adjacent to the angle which is 23 cm so we will take that and make an equation because we are missing the hypotenuse:

CAH = adjacent/hypotenuse

cos = ^

cos ( 55 ) = 23/x

multiply x both sides

xcos(55) = 23

divide cos(55) from left

x = 23/cos(55)

input in calculator (make sure in right mode degrees)

23/(cos(55))

x = 40.09927 cm

x = 40.1 cm


Related Questions

A company is planning to manufacture a certain product. The fixed costs will be $428136 and it will
cost $126 to produce each product. Each will be sold for $639.
Find a linear function for the profit, P, in terms of units sold x

Answers

Answer:

Step-by-step explanation:

The profit function for a company is calculated as the difference between the revenue and the total cost. The revenue is calculated by multiplying the number of units sold by the price per unit. The total cost is calculated by adding the fixed costs to the variable costs (calculated by multiplying the number of units produced by the cost per unit).

In this case, we can calculate the profit function P(x) as follows:

P(x) = Revenue - Total Cost P(x) = (Price per unit * Units sold) - (Fixed Costs + Variable Costs) P(x) = (639x) - (428136 + 126x) P(x) = 639x - 428136 - 126x P(x) = 513x - 428136

So for this company, a linear function for their profit in terms of units sold x would be P(x) = 513x - 428136.

I will mark you brainiest!
Given that QRVTSU is a regular hexagon, what are the lengths of QR and ST ?

A) 37
B) 28
C) 14
D) 10

Answers

Answer:

QR & ST = 37

Step-by-step explanation:

Because this is a regular hexagon, all the sides are equal.

Thus, since the length of QR = the length of ST, we can set the equations for both sides equal to each other and solve for y:

[tex]3y+19=6y+1\\3y+18=6y\\18=3y\\6=y[/tex]

Now, we can plug in 6 for y into any of the two equations to find the length of both QR and ST:

[tex]QR=3(6)+19\\QR=18+19\\QR=37[/tex]

ath-5th grade Add, subtract, and multiply fractions and mixed numbers: word problems ZD2
At Polk High School, 2/3 of the students play a sport. Of the students who play a sport,
2/3 play football. What fraction of the students at Polk High School play football?
Simplify your answer and write it as a fraction or as a whole or mixed number.
of the students
Submit
Work it out
Yo

Answers

4/9 of the students at Polk High School play football.

How to solve fraction?

If 2/3 of the students play a sport and 2/3 of those who play a sport play football, then the fraction of students who play football can be found by multiplying the two fractions:

(2/3) x (2/3) = 4/9

Therefore, 4/9 of the students at Polk High School play football.

To understand more clearly :-

Polk High School has a certain number of students, and 2/3 of them play a sport. Out of those who play a sport, 2/3 of them play football. The question asks what fraction of the students at Polk High School play football.

To solve the problem, we first need to find the fraction of students who play both a sport and football. We can do this by multiplying the fractions representing each of these groups of students. The product of 2/3 and 2/3 is 4/9, which represents the fraction of students at Polk High School who play both a sport and football.

Therefore, 4/9 of the students at Polk High School play football. This means that out of every 9 students, 4 of them play football and 5 of them do not. Alternatively, we can express this answer as a percentage by multiplying 4/9 by 100. This gives us 44.4%, meaning that approximately 44.4% of the students at Polk High School play football.

It is important to note that this answer assumes that all students at Polk High School play either a sport or no sport at all, and that all sports are equally likely to be played by students. If these assumptions are not true, the answer may not be accurate.

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Peace's average score on 5 tests was 88. If she dropped her lowest score, her average would be 90. What is her lowest score?

Answers

Answer:

Her lowest score was 80.

Step-by-step explanation:

5 x 88 = 440

4 x 90 = 360  

An equation we can use to find her lowest score:

Let x represent her lowest score

440 - x = 360

440 - 360 = x

x= 80

Type in the coordinates of the vertices of the image of quadrilateral WXYZ after it is reflected over the y-axis.

W (6, 2) → W' ( , )

X (12, 2) → X' ( , )

Y (10, -3) → Y' ( , )

Z (4, -3) → Z' ( , )

Answers

The coordinates of the vertices after the given reflection is:

W (6, 2) → W' ( -6, 2)X (12, 2) → X' (-12 ,  2)Y (10, -3) → Y' ( -10, -3)Z (4, -3) → Z' (-4, -3)

Which are the coordinates after a reflection over the y-axis?

Remember that for a general point (x, y), a reflection over the y-axis only changes the sign of the x-coordinate.

Then we will have the transformation:

(x, y) --> (-x, y)

Now we need to apply that to each one of the given vertices, we will get:

W (6, 2) → W' ( -6, 2)X (12, 2) → X' (-12 ,  2)Y (10, -3) → Y' ( -10, -3)Z (4, -3) → Z' (-4, -3)

These are the coordinates of the vertices of the quadrilateral after the reflection over the y-axis.

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what is 5% of $26.50

Answers

Answer:1.325

Step-by-step explanation:

Any body know the answer to this ?

Answers

Answer:

Step-by-step explanation: its 13

What is the translation for this graph?

O(x-3.y-4)
O(x-4. y 3)
O(x-3, y+4)
O(x-4.y-3)

Answers

The translation for this graph is represented by this transformation rule: C. (x + 3, y + 4)

What is a translation?

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N while a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N).

Where:

N represents an integer.g(x) and f(x) represent a function.

Based on the graph of the parent function, is given by the following transformation rule:

x - 3 = 0

x = 3.

y - 2 = 2

y = 4

Therefore, the transformation rule is (x, y)     →   (x + 3, y + 4)

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Complete Question:

What is the translation for this graph?

O(x-3.y-4)

O(x-4. y 3)

O(x+3, y+4)

O(x-4.y-3)

A game requires you to toss a 10-sided numbered solid
and a 6-sided numbered solid to determine how to move
on a game board. Find the following probabilities.

a. P(same number on both)

b. P(odd, even) or P(even, odd)

Answers

P(same number on both) = 10/60 = 1/6 and P(odd, even) or P(even, odd)  = 1/4

How to find the probabilities

There are 10 possible outcomes on the 10-sided die and 6 possible outcomes on the 6-sided die

The total number of possible outcomes is 10 x 6 = 60.  

To get the same number on both, we need to get one of the 10 numbers on the first toss and then get the same number on the second toss. There are 10 ways to do this. Therefore, the probability of getting the same number on both is:

P(same number on both) = 10/60 = 1/6

b. To get an odd and an even number, we need to get an odd number on the first toss and an even number on the second toss, or vice versa.

There are 5 odd numbers and 5 even numbers on the 10-sided solid, and 3 even numbers and 3 odd numbers on the 6-sided solid.

Therefore, the probability of getting an odd and an even number, or an even and an odd number, is:

P(odd, even) or P(even, odd) = (5/10) x (3/6) + (5/10) x (3/6) = 1/4

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The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentage

If their wage went from $7.00 to $13.27 in 12 years what is the doubling time?

Answers

The doubling time for the hourly wage is approximately 14.54 years.

We can use the formula for exponential growth to solve for the doubling time: [tex]A = P * (1 + r)^t[/tex]

Where:

A = final amount (doubled hourly wage = $7.00 * 2 = $14.00)

P = initial amount (hourly wage = $7.00)

r = annual growth rate (unknown)

t = time (doubling time = unknown)

We can also use the given information to set up another equation:

[tex]13.27 = 7 * (1 + r)^{12[/tex]

To solve for r, we can isolate the exponential term and take the 12th root of both sides:

[tex](1 + r)^{12} = 13.27 / 7[/tex]

[tex]1 + r = (13.27 / 7)^{(1/12)[/tex]

[tex]r = (13.27 / 7)^{(1/12)} - 1[/tex]

r ≈ 0.0477

Now that we know the annual growth rate is approximately 0.0477, we can use the doubling time formula:

t = log(2) / log(1 + r)

t = log(2) / log(1 + 0.0477)

t ≈ 14.54

Therefore, the doubling time for the hourly wage is approximately 14.54 years.

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What is the value of x?

Answers

Answer:

It was 8

Step-by-step explanation:

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semangat belajar

painting outside of a cylinder and finding the amount of paint. cylinder will be used without the top

Answers

Approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

how to calculate the amount of paint?

To calculate the amount of paint required to paint the outside of a cylinder, you will need to find the surface area of the cylinder. Since the cylinder is without a top, we only need to find the lateral surface area.

formula of surface area

Lateral Surface Area = 2πrh

when r is the cylinder's radius, h is its height, and is a constant value roughly equivalent to 3.14.

Once you have calculated the lateral surface area of the cylinder, you can use the following formula to find the amount of paint required:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

where coverage per unit of paint refers to the area that can be covered by one unit of paint. This will depend on the type of paint you are using and its thickness.

For example, if the cylinder has a radius of 3 meters and a height of 5 meters, the lateral surface area would be:

Lateral Surface Area = 2πrh

Lateral Surface Area = 2 x 3.14 x 3 x 5

Lateral Surface Area = 94.2 square meters

If the coverage per unit of paint is 10 square meters, the amount of paint required would be:

Amount of Paint = Lateral Surface Area / Coverage per unit of paint

Amount of Paint = 94.2 / 10

Amount of Paint = 9.42 units of paint

Therefore, approximately 9.42 units of paint would be required to paint the outside of a cylinder with a radius of 3 meters and a height of 5 meters, without the top.

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SUN The temperature of the Sun's surface is about 5.5×10^3
degrees Celsius. The temperature of the Sun's core is about 2.7×10^3
times hotter than the surface. What is the approximate temperature of the Sun's core? (In Celsius) PLEASE BE QUICK!!

Answers

According to the given information, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

The Sun is a massive ball of gas that generates heat and light through nuclear fusion at its core. The temperature of the Sun's core is much hotter than its surface temperature, and this difference in temperature is responsible for the Sun's energy output.

The temperature of the Sun's surface is approximately [tex](5.5*10^{3})[/tex] degrees Celsius, which is also known as the photosphere. However, the temperature at the Sun's core is estimated to be about [tex](2.7*10^{3})[/tex] times hotter than the surface temperature. This is because the core is the site of intense nuclear fusion reactions that convert hydrogen into helium and release huge amounts of energy in the form of heat and light.

To find the approximate temperature of the Sun's core, we can start with the temperature of the Sun's surface, which is given as [tex](5.5*10^{3})[/tex] degrees Celsius. We need to multiply this by the factor of  [tex](2.7*10^{3})[/tex]  to get the temperature of the core.

The approximate temperature of the Sun's core

= [tex](5.5*10^{3}) * (2.7*10^{3})[/tex]

=[tex]14.85*10^{6}[/tex]degrees Celsius

= [tex]1.485*10^{7}[/tex] degrees Celsius (in scientific notation)

Therefore, the approximate temperature of the Sun's core is [tex]1.485*10^{7}[/tex]degrees Celsius.

This extremely high temperature is necessary to sustain the nuclear reactions that power the Sun's energy output. The high temperature and pressure in the core create the ideal conditions for nuclear fusion to occur, which releases energy that eventually makes its way to the surface of the Sun and out into space in the form of light and heat.

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Find the square root of 8!/70

Answers

Answer:

We can write 8! as:

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

To simplify the square root of 8!/70, we can first simplify the denominator:

8!/70 = (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/70

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(2 x 5 x 7)

= (8 x 6 x 4 x 3 x 2 x 1)/2

= 8 x 6 x 4 x 3 x 1

= 576

Now, we can write the original expression as:

sqrt(8!/70) = sqrt(576/1)

= sqrt(576)

= 24

Therefore, the square root of 8!/70 is 24.


Find the critical numbers of the function. (Enter your answers as a comma-separated list.)
f(x) = 3x² - 4x

Answers

Answer:

Critical points are :       2/3, -4/3

Step-by-step explanation:

Use the Fundamental Counting Principle to find the total number of possible outcomes.you didn't show me the steps

Answers

Therefore , the solution of the given problem of unitary comes out to be 105 different meal combos that could be made.

What is an unitary method?

By combining the information obtained using this variable technique with all supplementary data from two individuals who used a specific tactic, the job can be completed. This mean that, if indeed the desired outcome materialises, either the stated person will be recognized or, in actuality, the colour by both huge processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.

Here,

b. The following formula can be used to determine the total interest charged over the loan's term:

=>  total interest = (monthly payment X n) - P .

There have been a total of:

=>  120 = ten years times one year.

The entire interest paid is thus:

=>  ($3,943.80) (total monthly installments * n) - P

=>  (131.19 * 120) - 9900 (rounded to the nearest dollar)

So, rounded to the closest dollar, Reh will pay about $3,944 in interest for the duration of his loan.

=>  7 entree choices, 5 drink options, and 3 dessert options are available.

We must add the number of drink options, entree options, and dessert options together to get the total number of potential meal combinations:

=> 5 x 7 x 3 = 105

There are 105 different meal combos that could be made.

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Please help
please click on the documents that's attached...
Please show work

Answers

The factored form of trinomial equation 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).

What is the difference between factoring and expanding polynomials?

The parenthesis must be dropped in order to expand the equation. One need just multiply the value outside the value, which is 2 to each of the values inside the parenthesis, to arrive at an equation without parentheses. The opposite of factoring out, which entails adding parenthesis to an equation, is expanding, which entails removing parentheses from an equation.

The given trinomial equation is 10m² + 29mn + 10n².

Multiply the coefficients of the first and last term that is:

(10)(10) = 100

Now factor the term using two factors to make the given middle term, here the factor of 100 are 4 and 25.

Now, rewrite the equation with the factors as follows:

(10m² + 4mn) + (25mn + 10n²)

= 2m(5m + 2n) + 5n(5m + 2n)

Factor out the common binomial factor (5m + 2n):

(5m + 2n)(2m + 5n)

Hence, the factored form of 10m² + 29mn + 10n² is (5m + 2n)(2m + 5n).

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Write two numbers that multiply to the value on top and add to the value on bottom.
Submit Answer
9
-10

Answers

Answer:

-9 & -1

Step-by-step explanation:

-9*-1=9

-9+(-1)=10

done lol

Answer:

-9 and - 1

Step-by-step explanation:

Because it is two negatives they will become a positive 9 when multiplied and when you add them - 9+(-1) the positive and negative sign become a negative so it is negative nine minus 1 which gives you - 10

Noa flies a drone in a circular path around an object that is 210 meters west and 150 meters south of her
position. The drone's path takes it over a point that is 170 meters east and 190 meters north of her.

Find an equation for the drone's path. (Assume Noa is located at the origin, with the horizontal axis running
east-west and the vertical axis running north-south)

The drone's path follows the equation________

When the drone passes due north of Noa's position, it will be ___________ feet north of
her (round your answer to three decimal places).

Answers

We can solve this problem using the standard equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Since Noa is at the origin, the center of the circle is the midpoint between the object and the point where the drone passes:

h = (210 - 170)/2 = 20

k = (190 - 150)/2 = 20

The radius is the distance between the center and the point where the drone passes:

r = √((170 - 20)² + (190 - 20)²) = √(150² + 170²) = √(62500) = 250

So the equation of the drone's path is:

(x - 20)² + (y - 20)² = 250²

When the drone passes due north of Noa's position, its x-coordinate is 20, so we can substitute that into the equation:

(20 - 20)² + (y - 20)² = 250²

y - 20 = ±√(250²)

y = 20 ± 250

y ≈ -230 or y ≈ 270

So the drone will be approximately 230 feet north of Noa's position.

The population of a town was 821 in 1970. The population has been growing at a rate of 11% each year. What is the population of the town in the year 1995? i have 30 minutes until the quiz is submitted

Answers

The pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.

Hοw tο determine the percentage grοwth rate?

The grοwth factοr (b) is given as: b = 3.76

The grοwth factοr (b) is greater than 1.

We can sοlve this prοblem by using the fοrmula fοr expοnential grοwth:

[tex]P(t) = P0(1 + r)^t[/tex]

where:

P0 is the initial pοpulatiοn (821 in 1970)

r is the annual grοwth rate (11% οr 0.11)

t is the number οf years since the initial pοpulatiοn (25 years frοm 1970 tο 1995)

Substituting the given values, we get:

[tex]P(25) = 821(1 + 0.11)^25\\\\P(25) = 821(1.11)^25[/tex]

Using a calculatοr tο evaluate this expressiοn:

P(25) ≈ 4,261.9

Therefοre, the pοpulatiοn οf the tοwn in the year 1995 was apprοximately 4,262.

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a rectangular garden has dimensions of 5 feet by 12 feet. if the length and width of the garden are increased by the same amount, and the resulting area is 144 square feet, how much was each side increased?​

Answers

Based on the data, we can infer that the difference in length after the garden increment is 4 feet on each side.

How to find how much the garden increased in length and width?

To find how much the garden increased in length and width we must carry out the following procedure:

First of all we must calculate the area of the garden:

side * side = area5 * 12 = 60

According to this result we know that the increase is more than half in the values. Therefore, we can add 3 or more feet to each side and recalculate the area of the garden.

5 + 3 = 812 + 3 = 158 * 15 = 120

In this case we add 3 feet to each side and calculate the area that would give these side measurements 8 and 15. The area would be 120, you still wouldn't have enough length on the sides to have an area of 144.

5 + 4 = 912 + 4 = 1616 * 9 = 144

In this case we add 4 feet on each side and calculate the area that would be given with these side measurements 9 and 16. The area would be 144, it would be the measurement mentioned in the statement.

Based on the above, we can infer that the rise is 4 feet on each side.

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MARKING AS BRAINLIST |!! PLEASE HELP

Answers

Answer:

39

Step-by-step explanation:

First you need to find the other missing angle, by subtracting 156.5 from 180. (because 180 is the angle of a straight line)

180-156.5=23.5

Then we can add the two angles

117.5+23.5=141

Since we know that all triangles' angles add up to 180, we can subtract the sum from 180 to get our answer.

180-141=39

We can check if this is right by adding all the angles again.

39+23.5+117.5=180

Therefore, c=39

Marbles are divided among Tom, Gary, and Mary in the ratio 2:3:5, respectively. If Tom gets 30 marbles, how many do Gary and Mary receive?

Answers

Answer:

Gary would have 45 and Mary would have 75

trey paid 42 dollars for 2/3 ton of concrete. he wants to know the price of 3 tons of concrete.

Answers

Answer:

To find the price of 3 tons of concrete, we need to use a proportion:

If 2/3 ton of concrete costs $42, then 1 ton of concrete costs:

$42 ÷ (2/3) ton = $42 × (3/2) = $63

Therefore, 3 tons of concrete will cost:

$63 × 3 = $189

So Trey would need to pay $189 for 3 tons of concrete.

Solve the problem. This is for my practice test.

Answers

The bearing of the plane to the nearest degree is 357°, which is answer choice (c).

What is vector addition?

Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for the vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.

To find the bearing of the plane, we need to determine the direction in which it is traveling with respect to the true north. To do this, we need to use vector addition to combine the velocity of the plane with the velocity of the wind.

Let's break down the velocity vectors into their north-south and east-west components, using positive directions to the north and east.

The airspeed of the plane is 213 mph due south, so its velocity vector can be written as:

Vp = (0, -213)

The wind velocity is 16 mph at a direction of 52.0°. We can find its components using trigonometry:

Vw,x = 16 cos(52.0°) = 10.91 mph to the east

Vw,y = 16 sin(52.0°) = 12.18 mph to the south

So the wind velocity vector is:

Vw = (10.91, -12.18)

To find the total velocity vector of the plane relative to the ground, we can add the velocity vectors of the plane and the wind:

Vtot = Vp + Vw

Vtot = (0 + 10.91, -213 - 12.18)

Vtot = (10.91, -225.18)

The direction of the total velocity vector, measured from true north, can be found using the arctangent function:

θ = arctan(Vtot,x / Vtot,y)

θ = arctan(10.91 / -225.18)

θ ≈ -2.8°

Since the result is negative, this means the direction is to the left of true north. We can convert this to a bearing by adding 360° to get the positive equivalent:

θ = 360° + θ

θ ≈ 357.2°

Therefore, the bearing of the plane to the nearest degree is 357°, which is answer choice (c).

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Find the distance between the pair of points.
N(-3,-11), P(-3,-2)
d=
(Simplify your answer. Type an exact answer, using radicals as needed.)

Answers

The distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

How to find the distance between the pair of points.

Given the points

N(-3,-11) and P(-3,-2)

To find the distance between two points, we can use the distance formula:

d = √((x2 - x1)²+ (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between the two points N(-3, -11) and P(-3, -2) as follows:

d = √((-2 + 11)²+ (-3 + 3)²)

This gives

d = √9²+ 0²)

So, we have

d = √81

Evaluate

d = 9

Therefore, the distance between the two points N(-3, -11) and P(-3, -2) is 9 units.

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In circle A, secant EC and tangent BC intersect at point C.
mEB 163° and mBD = 77°.
What is m∠BCD?

Answers

Therefore, m angles for BCD is 98.5°.

Describe angle?

An angle is formed when two straight lines or rays meet at a single terminal. The vertex of an angle is the location where two points converge. The Latin word "angelus," which means "corner," is where the term "angle" originates.

These two theorems allow us to calculate the angle BCD's measure as follows:

To establish the angle ECB's measure first, apply Theorem 1:

m ∠ECB = m ∠DBC = 77°

Next, we can use theorem 2 to find the measure of the arc ED:

m(arc ED) = 1/2 (m∠EBD + m∠ECD) = 1/2 (163° + m∠ECB)

Since arc ED is an exterior arc to angle BCD, we can find the measure of angle BCD as:

m ∠BCD = 1/2 (m(arc BD) + m(arc ED)) = 1/2 (77° + m(arc ED))

Substituting the value we found for m(arc ED), we get:

m ∠BCD = 1/2 (77° + 1/2 (163° + m ∠ECB))

Now, we can substitute the value we found for m ∠ECB to get:

m ∠BCD = 1/2 (77° + 1/2 (163° + 77°)) = 1/2 (77° + 120°) = 98.5°

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simplity: 2x3 + 3y3 + 5x3 + 4y

Answers

7x³ +3y³ +4y

Simplify the expression by Removing parentheses and brackets by multiplying factors, use the exponent rule to remove grouping if the term contains exponents, combine like terms by adding or subtracting coefficients and combine the constants.

Answer: The answer is  7x^3 + 3y^3 + 4y. Or in simpler terms choice A is correct

Step-by-step explanation:

Write an equivalent expression in expanded form.



`8\left(-x+\frac{1}{4}\right)`

Answers

The equivalent οf the expressiοn 8(-x + 1/4) is -8x + 2.

What is an expressiοn?

A mathematical expressiοn is a phrase that cοntains a minimum οf twο numbers οr variables and at least οne mathematical οperatiοn. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. An expressiοn's structure is as fοllοws:

Expressiοn: (Math Operatοr, Number/Variable, Math Operatοr).

The given expressiοn is 8(-x + 1/4)

The distributive prοperty:

Accοrding tο the distributive prοperty, it is mandatοry tο multiply each οf the twο numbers by the factοr befοre adding them tοgether when a factοr is multiplied by the sum οr additiοn οf twο terms. A (B+ C) = AB + AC is a symbοlic representatiοn οf this prοperty.

Apply the distributive prοperty:

= 8×(-x) + 8×(1/4)

= -8x + 2

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You have a 5" by 7" photo that you would like to have enlarged to fit an 7.5" by 10.5" frame. Would the two photographs be similar? Explain your answer using Similarity Transformations.

Answers

The photos are similar because the enlarged photo is 1.5 times the size of the original photo.

What is meant by similarity transformations?

Similarity transformations turn items in space into similar objects. If two items have the same shape or have the same shape as their mirror images, they are said to be similar. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

Here the initial dimension of the photo is  5" by 7" and after enlarging it has dimensions 7.5" by 10.5".

The scale factor is = 7.5/5 = 10.5/7 = 1.5

Since the scale factor is constant for all sides, the pictures before and after enlargement are similar.

Therefore the photos are similar because the enlarged photo is 1.5 times the size of the original photo.

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