Which angle is a vertical angle with Angle EFD?

Answer:

last option

Step-by-step explanation:

(x-h)²+(y-k)²=r²

(x--7)²+(y-4)²=5²

(x+7)²+(y-4)²=25

The equation of the circle is (x + 7)² + (y - 4)² = 25.

Option D is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

The equation of a circle with center (h,k) and radius r.

(x - h)² + (y - k)² = r²

Substituting the given values, we get:

(x - (-7))² + (y - 4)² = 5²

Simplifying the equation:

(x + 7)² + (y - 4)² = 25

Therefore,

The equation of the circle is (x + 7)² + (y - 4)² = 25

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Answer:

40

Step-by-step explanation:

The value of Sin(90) is equal to 1.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: Sin(90) and to find the value using the unit circle

Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.

The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.

The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.

Hence, Sin (90) is equal to 1.

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The 11th term of the geometric sequence 1, 4, 16,... is 4¹⁰.

A sequence is a grouping of objects in a particular order that permits repetitions. It has members, just like a set does. The length of the sequence is determined by the number of items.

Consider the geometric sequences 1, 4, 16......

For a geometric sequence a, ar, ar²,.....

Where a is the first term, and r is the common ratio of the sequence.

Then for the sequence 1, 4, 16,...

a = 1 and r = 4

The nth term of a geometric sequence is given as:

aₙ = ar⁽ ⁿ ⁻ ¹⁾

Therefore, the 11th term of the sequence will be:

a₁₁ = 1 × r¹¹ ⁻ ¹

a₁₁ = (4)¹⁰

a₁₁ = 4¹⁰

Hence, the 11th term of the sequence is 4¹⁰.

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Answer:

To add mixed numbers, we need to add the whole numbers separately and fractions separately.

Starting with the whole numbers, we have:

9 1/2 − 3 7/8 + 4 4/5 − 1 1/2

= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)

= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)

= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)

= 5 7/20 (expressing the result as a mixed number in simplest form)

Therefore, the value of the expression is 5 7/20.

The fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in²

Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.

Surface area of  triangular prism with isosceles triangle base is find out using the following formula,

\(A_s=[(2a+b)\times l]+2\times A_b\)

Gavin is making a scale replica of a tent for his social studies project.

The replica is in the shape of a triangular prism. It has an isosceles triangle base with side lengths 6 inches, 5 inches, and 5 inches.

The base area of the prism is,

\(A=\dfrac{1}{2}\sqrt{5^2-\dfrac{6^2}{4}}{\times6}\\A=12\rm\; in^2\)

The height of the triangle is 4 inches, and the depth of the tent is 7 inches.

Put the values in the above formula as,

\(A_s=[(2\times5+6)\times 7]+2\times12\\A_s=136\rm \; in^2\)

Thus, the fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in².

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Answer:

A

Step-by-step explanation:

According to the described situation, we have that:

The decision rule is:

The value of the test statistic is of z = -0.866.

The claim is:

"Forty percent or more of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job were available"

At the null hypothesis, we consider that the claim is false, that is, the proportion is of less than 40%, hence:

\(H_0: p < 0.4\)

We have a right-tailed test, as we are testing if a proportion is less/greater than a value. Since we are working with a proportion, the z-distribution is used.

Using a z-distribution calculator, the critical value for a right-tailed test with a significance level of 0.01 is of z = 2.327, hence, the decision rule is:

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

In this problem, the parameters are:

\(p = 0.4, n = 200, \overline{p} = \frac{74}{200} = 0.37\)

Hence:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.37 - 0.4}{\sqrt{\frac{0.4(0.6)}{200}}}\)

\(z = -0.866\)

The value of the test statistic is of z = -0.866.

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Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

Answer:

No triangle possible

Step-by-step explanation:

Answer:130/4 ×5 112÷8 ×7 and 156÷12 ×10

Step-by-step explanation:can't work them out right now don't have a calculator on me but that's the basic

The best way to solve an equation of the form Ax+by=c could be either substitution, completing the squares or graphical method depending on the type of equation given.

Quadratic equation

The equation in the form Ax+by=c is a quadratic problem which could be approached in different ways depending on the specific equation given and the information provided.

The methods of approach are substitution, completing the squares or graphical method which all have proven to be suitable ways to arrive at the solution.

Hence, either of the three methods are good ways to solve such equation.

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Answer:

16 more than 23 = 23 + 16 or 16 + 23

Hope it helps :)

Answer:

hbgvfcdxcfgvbh

Step-by-step explanation:

Answer:

I'm so confused

Step-by-step explanation:

did you forget to add a picture

Answer: 48

Step-by-step explanation: 60-12=48

Answer:

B.

Step-by-step explanation:

B is the least expensive

Using the Multiplication Principle of Counting, 18 unique codes can be formed.

There are 6 possible choices for the first character (2, 3, 4, 5, 6, or 7) and 3 possible choices for the second character (A, B, or C). Therefore, by the multiplication principle of counting, there are 6 × 3 = 18 unique codes that can be formed from two characters where the first character can be from 2 to 7 and the second character can be from A to C.

The multiplication principle of counting is a basic principle in combinatorics that states that if there are k ways to do one thing and m ways to do another thing, then there are k × m ways to do both things together. In other words, if there are a ways to choose the first element of a sequence and b ways to choose the second element of the same sequence, then there are a × b ways to choose the two elements together. This principle can be extended to more than two choices as well.

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The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

\(o = a=9\)

The side labelled "f" is the hypotenuse of the triangle. Therefore:

\(f= 2a = 2 \cdot 9=18\)

Therefore:

The correct statement is: On a coordinate plane, an absolute value graph has a vertex at (0, 1).

The function p(x) = |x - 1| represents an absolute value function. The vertex of an absolute value function in the form f(x) = |x - h| + k is given by the point (h, k). In this case, the function p(x) = |x - 1| has a vertex at (1, 0).

Therefore, none of the provided options accurately represents the vertex of the function p(x) = |x - 1|. The correct vertex for this function is (1, 0), which means the vertex is at x = 1 and y = 0 on the coordinate plane. It is important to note that the vertex is located at (h, k) where h represents the x-coordinate and k represents the y-coordinate.

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Answer:

80 points

Step-by-step explanation:

If score in English is x points and score in math is 5% higher then score in math

y = x + 0.05x

where 0.05 = 5% expressed as decimal

0.05x refers to the 5% increase in score

y = math score

y = x(1 + 0.05)

y = 1.05x

Given score in math = 84 this becomes

84 = 1.05x

x = 84/1.05

x = 80

So Emily's score in English was 80 points

This solids are similars if the quotients between their correspondent sides are all the same. In this cases the quotients would be:

If you calculate those quotients you'll see that they all give 1.5 so the first question is answered, the solids are similar.

The scale factor determinates the relationship between two similar solids or geometric figures. It's usually used while constructing scale models of bigger things like building. To calculate we are going to use the rule of three since the factor tells how many inches in one solid represents an inch in the other one.

We know that 28 inches in the smaller one represent 42 in the bigger one so:

28 in --------- 42 in

1 in ------------ x

Where:

So the value of the quotients I mentioned before is the scale factor of this pair of solids and it's 1.5

x + 8x = 9x

(like 1 + 8 but with x's)

Answer:

-5.5

Step-by-step explanation:

1. -3.1 + (-7.2) + 4.8

remove parentheses

add/subtract the numbers.

-3.1-7.2+4.8 = -5.5

Answer:

Step-by-step explanation:

y=-3x-1

format for formula:

y=mx+b

b=1  that is your y-intercept.  where it hits the y-axis

m= -3    this is your slope    \(\frac{rise}{run} =\frac{-3}{1}\)  

from a point you have, the y-intercept, you go down 3 (because of the negative in front of it), this is your rise,
and to the right 1, this is your run

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

\(5^{15} * 5^{5}\)

= \(25^{20\\}\)