Find the exact value for tan7/8 using half angle identities

Answer:

220

Step-by-step explanation:

216+4

The next day+ the first day=220

To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

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Answer:i dont know

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply the price by 0.09, then add that number to the price

47.25 x 0.09 = 4.25

47.25 + 4.25 = 51.50

Step 1: Concept

Draw the image after rotated 90 degrees counterclockwise about Q.

Step 2: Find the coordinates of the points.

The transformation rule is (-y, x)

Next, subtract Q from the other points

New coordinate

Q' = (0,0)

P' = (3,0)

R' = (3, -2)

Next, using the transformation rule, find the image of the triangle P'Q'R'

Q'' = (0,0)

P'' = (0,3)

R'' = (2,3)

Step 3: Final answer

The final coordinates

Q''' = (0+1, 0+2) = (1,2)

P''' = (0+1, 3+2) = (1,5)

R''' = (2+1, 3+2) = (3,5)

Answer:

D) The answer is 16.

Step-by-step explanation:

1) An even exponent will make any negative number turn into a positive number, so your answer must be positive.

2) You can just go by 2*2*2*2=16 to find out that the answer is 16.

Take into account that the area of the given trapezoid is the sum of the area of two right triangles and one square. The area of the triangles is the same, then, we have:

A = 2A1 + A2

where A1 is the area of the triangle and A2 the area of the square.

Let's calculate the area of triangle OSH, as follow:

A1 = (OS)(SH)/2

OS and SH are segments which we can calculate by using the following formula for the distance between two points with coorindates (x1,y1) and (x2,y2):

Based on the given coordinates points for O, S and H, we have:

Then, the area of triangle OSH is:

Next, let's calculate the area of the square. As you can notice on the given image, the length of the sides of the square is the same that the length of the segment OS, then, we have for the area of the square:

Finally, let's replace the obtained values of A1 and A2 into the expression for the total area A:

A = 2(2.5) + 5 = 5 + 5

A = 10 squared units

Being a girl and playing a sport are C. No, they are not independent events, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62.

Let's consider the probabilities:

P(girl) = (number of girls) / (total number of students) = 135 / 275 ≈ 0.49

P(girl plays a sport) = (number of girls playing a sport) / (total number of students) = 76 / 275 ≈ 0.276

If being a girl and playing a sport were independent events, the joint probability would be the product of the individual probabilities:

P(girl) × P(girl plays a sport) ≈ 0.49 × 0.276 ≈ 0.13524

However, the actual joint probability is different from the expected value:

P(girl, plays a sport) ≈ 76 / 275 ≈ 0.276

Since the joint probability does not match the product of the individual probabilities, we can conclude that being a girl and playing a sport are not independent events based on the given data.

Therefore, option C. No, they are not independent, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62. is the correct answer.

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Answer: = 143.94%

Step-by-step explanation:

Multiply 1.4394 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

1.43941×100100=143.94100

143.94/100 is 143.94 over 100 and means 143.94 per 100. 143.94 "per 100" means 143.94 "percent" or 143.94%

Therefore, we have shown that

1.4394 = 143.94%

Answer:

143.94%                                                                                                                

It is a whole number so it is 100% plus the 43 so it is 143.94

By definition, the domain of a function is the set of all the input values for which the function is defined.

Given the function:

You can identify that it is a Rational Function because it has this form:

Where these are polynomials:

For Rational Functions:

Then, since the denominator cannot be zero, you need to find the values of "x" that make it equal to zero. To do this, you have to set up that:

Now you have to solve for "x":

Therefore, the answer is:

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.

Given that:

Perimeter = sum of all sides

Perimeter = AB + BC + CA

Estimate each distance using the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

AB = √(1 - 5)² + (5 - 3)²

AB = √(-4)² + (-2)²

AB = √(16 + 4)

AB = √20

BC = √(3 - 1)² + (0 - 5)²

BC = √(2)² + (-5)²

BC = √(4 + 25)

BC = √29

CA = √(5 - 3)² + (3 - 0)²

CA = √(2)² + (3)²

CA =  √(4 + 9)

CA = √13

Perimeter = AB + BC + CA

Perimeter = √20 + √29 + √13

Perimeter = 4.47 + 5.38 + 3.60

Perimeter = 13.45 units.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

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The height of the stump is 3 ft.

The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.

In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:

h(0) = -16(0)² + 64(0) + 3

Since any term multiplied by zero is zero, we can simplify further:

h(0) = 0 + 0 + 3

Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.

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Same strategy as before: transform X ∼ Normal(76.0, 12.5) to Z ∼ Normal(0, 1) via

Z = (X - µ) / σ   ↔ X = µ + σ Z

where µ is the mean and σ is the standard deviation of X.

P(X < 79) = P((X - 76.0) / 12.5 < (79 - 76.0) / 12.5)

… = P(Z < 0.24)

… ≈ 0.5948

Answer:

Gary did not use the greatest common factor in the expression.

Step-by-step explanation:

Both factors of 36 and 66 are correct.

Gary also used equivalent expressions. I hope this helps.

Answer: Gary did not use the greatest common factor in the equation.

Step-by-step explanation: Gary did not use the Greatest common factor because the greatest common factor would be 33

Answer:

We conclude that there is not a linear correlation.

Step-by-step explanation:

We are given that a sample of 6 head widths of seals (in cm) and the corresponding weights of the seals (in kg) was recorded.

Given a linear correlation coefficient of 0.948.

Let ρ = population correlation coefficient.

So, Null Hypothesis, \(H_0\) : ρ = 0     {means that there is a linear correlation}

Alternate Hypothesis, \(H_A\) : ρ \(\neq\) 0      {means that there is not a linear correlation}

The test statistics that would be used here One-sample t-test statistics for testing population correlation coefficient;

                            T.S. =  \(\frac{r \times \sqrt{n-2} }{\sqrt{1 -r^{2} } }\)  ~  \(t_n_-_2\)

where, r = sample correlation coefficient = 0.948

           n = sample of head widths of seals = 6

So, the test statistics  =  \(\frac{0.948 \times \sqrt{6-2} }{\sqrt{1 -0.948^{2} } }\)  ~ \(t_4\) 

                                     =  5.957

The value of t-test statistics is 5.957.

Now at 0.01 level of significance, the t table gives a critical value of 4.604 at 4 degrees of freedom for a two-tailed test.

Since our test statistics is more than the critical value of t as 5.957 > 4.604, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that there is not a linear correlation.

Answer:

A. 55

Step-by-step explanation:

hope this helps have a good day :)

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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The equations x² + 4x + 3 = 0 and x² -6x + 13 = 0 are equivalent to (x + 2)² = 1 and (x - 3)² = -4

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The standard equation of a quadratic function is:

y = ax² + bx + c

1) Given that:

x² + 4x + 3 = 0

subtract 3 from both sides:

x² + 4x = -3

add to both sides the square of half the coefficient of x:

x² + 4x + 4 = -3 + 4

(x + 2)² = 1

2) Given that:

x² - 6x + 13 = 0

subtract 13 from both sides:

x² - 6x = -13

add to both sides the square of half the coefficient of x:

x² - 6x + 9 = -13 + 9

(x - 3)² = -4

The equations are (x + 2)² = 1 and (x - 3)² = -4

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Answer:

∠Q≅∠F

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides of the triangles are equal and all the three angles are equal.

Given that: In triangle DEF, DE=8 in., DF=23 in., and ∡D=16°. In triangle PQR, PQ=23 in., PR=8 in., and ∡P=16°.

Hence we can say that ΔDEF is congruent to ΔPQR. According to the side-angle-side (SAS) triangle congruence theorem: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Therefore:

DF = PQ, DE = PR, EF = RQ, ∠D = ∠P, ∠E = ∠R and ∠F = ∠Q

Answer/Step-by-step explanation:

1. Only one side and an included angle is known. To prove that both triangles are congruent by the SAS Congruence Theorem, an additional information such as a corresponding second side (KJ, and HJ) must be given to be equal to each other.

KJ = HJ

2. Additional information such as a second corresponding angle (angles C and W must be known to prove both triangles are congruent by SAS.

<C = <W

3. Additional information needed is a second corresponding angles must be known to prove the AAS.

4. Additional information needed is the corresponding angles, R and L, which should be equal to prove the ASA.

<R = L

5. Additional information needed: <C = <H

6. Additional information needed: equal hypotenuse lengths of both traingles.

Answer:

3x²+9x+8

Step-by-step explanation:

x²+x+x(x+2)+1(x+2)+x(x+3)+2(x+3)

x²+x+x²+2x+x+2+x²+3x+2x+6

x²+x²+x²+x+2x+x+3x+2x+2+6

3x²+9x+8

Answer:

\(3 x^{2}\) + 9\(x\) + 8

(This is an expression, not an equation so you can't find x with this expression. Equations have an = sign which can help isolate x on one side to find the value of x. This is the closest thing you could do for an answer for this expression.)

Step-by-step explanation:

x(x+1)+(x+1)(x+2)+(x+2)(x+3)

= (x)(x) + (x)(1) + (x)(x) + (x)(2) + (1)(x) + (1)(2) + (x)(x) + (x)(3) + (2)(x) + (2)(3)

= x^2 + x + x^2 + 2x + x+ 2 + x^2 + 3x + 2x + 6

= (x^2+x^2+x^2) + (x+2x+x+3x+2x) + (2+6)

= \(3x^{2}\) + 9\(x\) + 8

So first you expand the brackets and then you combine like terms.

Complete question is;

Some car jacks are constructed like a collapsed rhombus. When used to raise a car, the rhombus is easily seen. If the sides of the rhombus are 15 inches, what is the maximum length of the shaft?

Answer:

Maximum length of shaft = 30 inches

Step-by-step explanation:

To understand this clearly, I've attached a real life image of a car jack that's in the shape of a rhombus.

From the attached image, we can see that it has four sides which are equal in length.

Now, if this jack is collapsed, the shaft will just be like a straight line with a maximum length equal to twice a side of the rhombus which represents the maximum length of the diagonal.

Since we are told that one side of the rhombus is 15 inches, it means that the maximum length of shaft = 2 × 15 = 30 inches

Answer:

multiply, add, then subtract so your answer should be 4

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(please excuse my dear aunt sally)

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Answer:

A

Step-by-step explanation:

Sorry i'm late, but we in the same boat my dude

Answer:

answe is a

Step-by-step explanation:

Answer:

D

Step-by-step:

The y-coordinates will change, not the x. Size and shape will also remain the same.