A student is trying to prove that the triangle XAB is similar to triangle XYZ.

The equivalent trigonometric expression to sin(2x)cos(x) is given as follows:

sin(2x)cos(x) = 2sin(x)cos²(x).

The expression for this problem is defined as follows:

sin(2x)cos(x).

The trigonometric identity used to simplify sin(2x) is given as follows:

sin(2x) = 2sin(x)cos(x).

Hence the expression can be written as follows:

sin(2x)cos(x) = 2sin(x)cos(x)cos(x)

sin(2x)cos(x) = 2sin(x)cos²(x).

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The lengths for which the area will be less than 175 cm² are less than 25 cm

From the question, we have the following parameters that can be used in our computation:

Width = 7 cm

Area = Less than  175 cm²

The formula of area is represented as

Area = Length * Width

Using the above as a guide, we have the following:

Length * Width < 175

substitute the known values in the above equation, so, we have the following representation

Length * 7 < 175

Divide by 7

Length < 25

Hence, the length is less than 25

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The coordinates of points where the two lines intersect, is the solution of the equations/lines, that is (6, 64)

In the given equilateral triangle XYZ the relation which is true is WX = 2WZ. So option C is correct.

An equilateral triangle is a particular kind of triangle in which the lengths of the three sides are equal. These are a few of its main characteristics:

Congruent angles exist for all three: An equilateral triangle has 60 degrees for each angle.

The three parties all agree: The perimeter of an equilateral triangle is three times the length of any one side because each side is the same length.

For any side, the same line serves as the altitude, median, and angle bisector:

A line segment perpendicular to the other side and drawn from one vertex is the altitude. A line segment called the median is drawn from one vertex to the middle of the other side. The line segment known as the angle bisector divides the angle made up of two sides.

Given that,

The triangle XYZ,

It is known that,

All the sides in the equilateral triangle are equal,

So it can be written as,

⇒ WX = WY = XY

⇒ WY = 2WZ = 2ZY

Therefore,

⇒ WX = 2WZ

Hence, the correct relationship is WZ = 2WZ.

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Answer:

WX=2 times WZ

Step-by-step explanation:

i just took the quiz on apex

Answer:

$29.68 to drive 350 miles

Step-by-step explanation:

To find the cost of driving 350 miles, we first need to calculate the amount of gasoline required for driving 350 miles. We can use the formula:

gasoline = distance ÷ miles per gallon

Plugging in the given values:

gasoline = 350 ÷ 33

gasoline = 10.606060606060606

So, we need 10.61 gallons of gasoline to drive 350 miles.

Next, we multiply the amount of gasoline needed by the cost per gallon to find the total cost:

total cost = gasoline × cost per gallon

total cost = 10.61 × 2.80

total cost = 29.6780

Therefore, it would cost approximately $29.68 to drive 350 miles when gasoline costs $2.80 per gallon and your car gets 33 miles per gallon.

Answer: 350 mi * 1 gal / 33 miles * $2.80 / 1 gal  = 29.69$

which means the cost is 2.8*(350/33)=29.69$

Step-by-step explanation:

Here, 2.80$/1 Gal.

Now we need to cancel out gallons, so we add a ratio with gallons.

2.80$/1 Gal. x 1 Gal/33 mi.

Now add the last data element to cancel out miles.

2.80$/1 Gal. x 1 Gal/33 mi. x 350 mi.

Cancelling out units and numbers gives,

(2.80$ x 350)/33. Continue reducing to an answer:

980$/33 = 29.69$

Answer:

Step-by-step explanation:

y=16. There are sixteen 1/2 in 8

PREMISES

y=8/.5

CALCULATIONS

y=8/.5

y=8(2)

y=

16

PROOF

If y=16, then the dependent value D(y) 8/.5 returns

y(.5)=8

Answer:

Step-by-step explanation:

The length of the line segment between two points in a plane can be calculated using the distance formula. Given two points (x1, y1) and (x2, y2), the distance between them is given by the following formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3, 5) and (7, 3). Plugging these values into the formula, we get:

d = √((7 - 3)^2 + (3 - 5)^2)

d = √((4^2) + (2^2))

d = √(16 + 4)

d = √20

So, the length of the line segment between the two points (3, 5) and (7, 3) is √20.

The requried two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.

A triangle with two sides and two congruent angles is called an isosceles triangle.

To determine the value of x and the third side of the triangle, we need to first ensure that the triangle is a valid triangle, meaning that the sum of the lengths of the two shorter sides must be greater than the length of the longest side.

In this case, the two shorter sides are 2 and 3x, and the longest side is 9. We have,

2 + 3x > 9

Solving for x, we get:

3x > 7

x > 7/3

Since x must be a whole number, the smallest possible value for x that would make the triangle valid is 3. With x = 3, the third side of the triangle would be 3 × 3 = 9, which is equal to the longest side.

Therefore, the triangle has sides 2, 9, and 9.

Since two sides are equal, this triangle is an isosceles triangle, which means that two of the angles are equal to 45 degrees or less, and the triangle is acute.

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The least possible total number of cookies are 21.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, Bailey is making festive cookie bags. She tried to split all her cookies evenly by putting 15 per bag, but the last bag had only 14 cookies.

Here, 15+14=29

29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.

Now, 10+9+2=21

21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.

Therefore, the total number of cookies are 21.

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The values of the composite functions are (f + h)(5) = 7, (h - f)(2) = 0, (fh)(3) = 0 and (h/f)(0) = 3/5

From the question, we have the following parameters that can be used in our computation:

The graphs

Using the graphs as a guide, we have the following:

(f + h)(5) = f(5) + h(5)

(f + h)(5) = 3 + 4

(f + h)(5) = 7

(h - f)(2) = h(2) - f(2)

(h - f)(2) = 1 - 1

(h - f)(2) = 0

(fh)(3) = f(3) * h(3)

(fh)(3) = 4 * 0

(fh)(3) = 0

(h/f)(0) = h(0)/f(0)

(h/f)(0) = 3/5

Hence, the value of the function (h/f)(0) is 3/5

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Answer:

$90.12

Step-by-step explanation:

The principal amount of the loan is ...

 (sale price)(1 + sales tax rate) - (down payment)

 = $19,725×1.0475 -2175 = $18,486.94

For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is

 i = Prt = ($18,486.94)(0.0585)(1/12)

 i = $90.12

Answer:

Below

Step-by-step explanation:

2^3  /  2^7 =   2^(3-7)   =   2^(-4)   =   1/ (2^4)   =   1/16   =   .0625  

   ~~~~pick your poison

The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.

To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.

In this case, the base is 2.

Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:

[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]

The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:

[tex]2^{-4} = 1/2^4[/tex]
      = 1/16

Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.

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Answer:

Simplifying

-27 = 19 + -2x

Solving

-27 = 19 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.

-27 + 2x = 19 + -2x + 2x

Combine like terms: -2x + 2x = 0

-27 + 2x = 19 + 0

-27 + 2x = 19

Add '27' to each side of the equation.

-27 + 27 + 2x = 19 + 27

Combine like terms: -27 + 27 = 0

0 + 2x = 19 + 27

2x = 19 + 27

Combine like terms: 19 + 27 = 46

2x = 46

Divide each side by '2'.

x = 23

Simplifying

x = 23

The solution is, the value of  (f• Hºg)(x) = 4x+2.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

f(x) = x-4

g(x) = x+ 2,

and h(x) = 4x+1

now, (f• Hºg)(x)

= (f•(4(x+2)+1)(x)

=((4x+6)-4)

=4x+2

Hence, The solution is, the value of  (f• Hºg)(x) = 4x+2.

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Answer:  

Translates to x-(x+6) which simplifies to -6

=====================================================

Explanation:

x = some number

x+6 = the sum of x and 6

x-(x+6) = subtract the previous amount from x

x-x-6 .... distribute the negative through to each term

-6

No matter what number you started with, you'll always end up with -6 as the fully simplified answer. The x variables cancel.

Example:

Pick 10 as the starting number. Subtract off 10+6 = 16 to get 10-16 = -6.

The range of ages that are within one standard deviation of the mean age are given as follows:

M - 14.8 ≤ M ≤ M + 14.8.

In which M is the mean age.

The standard deviation of a data-set is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations.

The values that are within one standard deviation of the mean M have the bounds given as follows:

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Answer:do homework

Step-by-step explanation:

The production possibility frontier based on the information is attached.

PPF0 is the curve before technological progress. PPF1 is the the curve after the advance in technology.

Before the advance in technology, the opportunity cost of treating HIV/AIDS increases as the world moves down along its PPF.

After the advance in technology, the opportunity cost of treating more HIV/ AIDS cases decreases as the world has to give up less other goods and services to treat additional HIV/AIDS patients. Or, by giving up the same amount of other goods and services, world can treat more HIV/AIDS patients now.

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The values of the vacant spaces are $3.75, 4 oranges, 10 oranges, $15 and 20 percent of 160 is 32

The table can be completed using the following values

If 8 oranges cost $10,

Then 1 orange will cost 10/8 = $1.25

This means that  3 oranges will cost 1.25*3 = $3.75

$5 can buy 8/10*5 = 40/10 = 4 oranges

In the same way, $12.50 will buy 8/10 * 12.50 = 10 Oranges

In the same manner, 12 oranges will cost 1.25*12 = $15

20% of 160 can be calculated as follows

Recall that percentage is a proportion of 100

This implies that 20/100 * 160 = 3200/100 = 32

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Answer:

Step-by-step explanation:

75 x 0.40= £30

The required value of x is equivalent to 30 units.

The state of likeness can be referred to as a similarity. When two elements, things, ideas, or people resemble one another, they are said to be similar. Example: In terms of the number of sides, a square and a rectangle are comparable ( four sides for each). The state of being different can be used to define a difference.

To find the value of x we will use the similarity which corresponding sides of similar triangle are Proportional.

So;

50/x = 75/45

2/x = 3/45

x = 30 units

Thus, required value of x is  30 units.

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Answer:

Step-by-step explanation:

12

144 divided by 12 is 12

Answer:

To perform a t-test for the equality of two population means with unequal variances, we can use the Welch's t-test. In this test, the formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

Where x1 and x2 are the sample means, s1^2 and s2^2 are the sample error variances, and n1 and n2 are the degrees of freedom for the two samples.

Plugging in the given values, we have:

t = (52.8 - 48.4) / sqrt(20.31/36 + 45.06/24) = 4.25

Next, we need to find the critical t-value from the t-distribution table with degrees of freedom equal to the smaller of n1 and n2, which is 24. With a 95% confidence level, the critical t-value is approximately 2.492.

Since our calculated t-statistic (4.25) is greater than the critical t-value (2.492), we reject the null hypothesis that the two population means are equal. This suggests that there is strong evidence that the mean yield of oats is different between the two experiments.

Step-by-step explanation:

The amount of money that Amelia is expected to raise is given as follows:

£78.13.

The outcomes of a person winning, and their probabilities, as given as follows:

Hence the probabilities of winning and losing are given as follows:

Then the distribution of earnings for each person is given as follows:

Hence, considering 250 people, the expected amount raised is given as follows:

E(X) = 250/16 x (2.5 x 6 - 1 x 10)

E(X) = £78.13.

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Answer:

Step-by-step explanation:

ax+bx=c

x(a+b)=c

x(a+b)/(a+b)=c/(a+b)

x=c/(a+b)

Answer:

[tex]x=\dfrac{c}{a+b}[/tex]

Step-by-step explanation:

To make x the subject of the equation ax + bx = c, rearrange the equation using algebraic operations to isolate a single x-variable.

Given equation:

[tex]ax + bx = c[/tex]

Factor out x from the left side of the equation:

[tex]x(a+b)=c[/tex]

Divide both sides of the equation by (a + b):

[tex]\dfrac{x(a+b)}{(a+b)}=\dfrac{c}{(a+b)}[/tex]

Simplify:

[tex]x=\dfrac{c}{a+b}[/tex]

To determine the total energy consumption of refrigerator A in a day, we need to first convert the power usage from watts to kilowatts.

500 watts/hour * 1 kilowatt/1000 watts = 0.5 kilowatts/hour

Next, we can calculate the energy consumption in kilowatt-hours (kWh) per day:

0.5 kilowatts/hour * 12 hours/day = 6 kilowatt-hours/day

To find the daily cost of running the refrigerator, we can multiply the energy consumption by the cost per kWh:

6 kWh/day * $0.12/kWh = $0.72/day

To calculate the yearly cost of running the refrigerator, we can multiply the daily cost by 365 days:

$0.72/day * 365 days = $262.80/year

To calculate the total cost of running the refrigerator for 20 years, we can multiply the yearly cost by 20:

$262.80/year * 20 years = $5,256.00

In addition to the cost of running the refrigerator, there is also the cost of purchasing the unit itself. In this case, the cost is $1,000.

Therefore, the total cost of owning and operating Refrigerator A for 20 years is:

$5,256.00 (operating cost) + $1,000.00 (purchase cost) = $6,256.00

It's worth noting that this calculation assumes that the cost of electricity remains constant over the 20-year lifespan of the refrigerator. In reality, the cost of electricity may increase over time, which would increase the overall cost of running the refrigerator.

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Answer:

aiaiiwakkaoajdjsjzjhsjaj

The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]

Your system might not require the "0≤x", but it technically should be there.

The value of delta such that the statement is true is:

δ = 0.0002

We want to find δ such that:

if |x -3| < δ, then |5x - 15| < ε

So we have two absolute value inequalities to work with.

With ε = 0.001

If we take the second inequality and replace epsilong, we will get:

|5x - 15| < 0.001

We can take 5 as a common factor on the left side to get:

5*|x - 3| < 0.001

Dividing both sides by 5 gives:

|x - 3| < 0.001/5

|x - 3| < 0.0002

Then the value of delta is 0.0002.

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