If a line is tangent to a circle, then it is ___________ to the radius drawn to the point of tangency.

Answer:

10=10

Step-by-step explanation:

_1(12)+14=2(12)+2

3.

The Venn diagram of each situation is a diagrammatic way of representing what the situation stands for

Diagram 1: A ∩ B ∩ C

This means that we shade all intersection points of the sets A, B and C

Diagram 2: (A ∩ B) ∪ C

This means that we shade the intersection points of the sets A and B and the whole of set C

Diagram 3: A ∩ (B ∪ C)

This means that we shade the where the set A intersects with the whole of sets B and C

Diagram 4: (A ∩ B) \ C

This means that we shade the intersection point of the sets A and B without shading any point on set C

Diagram 5: (A\B) ∪ (B\C) ∪ (A\C)

This means that we shade all set A without set B, all set B without set C and all set A without set C. In other words, we shade everything in the set without shading set C

See attachment for the diagrams

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There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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Answer:

Step-by-step explanation:

on the 250ml ÷ 140 ml = 1L and 78757ml

on the 200 ml ÷ 150 ml = 1L and 333ml

on the 150 ml ÷ 160 ml = 9375ml

on the 100 ml ÷ 170 ml = 58832ml

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Given:

At a certain time, a 5 m vertical pole casts 2 m shadow.

Required:

What is the angle of elevation of the sun?

Explanation:

We will first draw the figure

We will use trigonometric ratio:

Now,

Answer:

Hence, answer is above.

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

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Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

Answer:

The answer is A

Step-by-step explanation:

0=1/8(0)

Answer:

D. (2,0)

Step-by-step explanation:

The amount of money that each person would get for the three days of work is $92.

The first step is to add all the money earned on the three days together. Addition is the process of determining the sum of two or more values.

Total amount earned in the 3 days = amount earned on the first day + amount earned on the second day + amount earned on the third day

= $93 + $75 +$108  =$276

The next step is to divide the total amount of money earned in the three days by the total number of people that would share the money. Division is the process of determining the quotient of a number.

The amount of money gotten by each person = total earnings / total number of people

$276 / 3 = $92

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Answer:

6 ounces of red beads

6 ounces of gold beads

Step-by-step explanation:

x + y = 12

x + 3y = 24

We can solve this with substitution or elimination.  In this case, I would suggest elimination.  Subtract the first equation from the second:

2y = 12

y = 6

Plug back into either equation to find x.

x = 6

Answer:

How many ounces of red beads will Juanita buy to break even?

6

How many ounces of gold beads will she buy?

6

Step-by-step explanation:

Because I got 100 percent on EDG 2020

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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We have a triangle △RST where the measure of angles are given as

m∠R = x + 17

m∠S = 2x - 2

m∠T = 5x + 5

We know that the sum of all three angles in a triangle must be equal to 180°

So, we can write the following equation

Let us substitute the given values and solve for x.

So, the value of x is 20

Now we can find the measure of angle m∠S

Therefore, the measure of angle m∠S is 38°

Answer:

g(x) is a dilation of function f(x), and \(g(x) = \frac{1}{4}x^2\)

Step-by-step explanation:

Function f is \(f(x) = x^2\)

So:

When \(x = 0, f(x) = 0\)

When \(x = 1, f(x) = 1\)

When \(x = 2, f(x) = 4\)

When \(x = 3, f(x) = 9\)

Now

For function g, looking at the graphic, we have that:

When \(x = 0, g(x) = 0\)

When \(x = 2, g(x) = 1\)

When \(x = 3, g(x) = 2.5\)

That is, g(x) is a fourth of f(x).

This means that we have a dilation by a factor of 1/4, so \(g(x) = \frac{1}{4}x^2\)

The given number in the standard form is 0.00000252

The given number is 2.52 × 10⁻⁶.

The given number is in scientific notation.

The general format of scientific notation is a × 10ⁿ  where a is a number or decimal number satisfying the condition, 1 ≤ |a| < 10. n is the power of 10 required so that the scientific notation is equivalent to the original number.

2.52 × 10⁻⁶

= 2.52 × (1/10⁶) (Apply the exponent rule: a⁻ⁿ = 1/aⁿ)

= (2.52 × 1)/10⁶ (Multiplication of fractions a × (b/c) = (a × b)/c)

= 2.52/10⁶

= 2.52/1000000 (Use 10⁶ = 1000000)

Divide the number 2.52 by 1000000, and we get

= 0.00000252

Therefore, the given number in the standard form is 0.00000252.

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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The value of x in the similar triangle is 6 units.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Therefore, let's use the similarity ratio to find the value of x in the similar triangle as follows:

Hence,

5 / 40 = x / 48

48 × 5 = 40x

240 = 40x

divide both sides by 40

x = 240 / 40

x = 6

Therefore,

x = 6

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The expression y ÷ [3(4 - 2) + 5.5] in the simplified form will be y ÷ 11.5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ y ÷ [3(4 - 2) + 5.5]

Simplify the denominator, then we have

⇒ [3(4 - 2) + 5.5]

⇒ [3(2) + 5.5]

⇒ [6 + 5.5]

⇒ 11.5

Then the expression is written as,

⇒ y ÷ [3(4 - 2) + 5.5]

⇒ y ÷ 11.5

The expression y ÷ [3(4 - 2) + 5.5] in the simplified form will be y ÷ 11.5.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Step-by-step explanation:

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Slope = change in y / change in x

Slope = (-2 -8) / (1-0)

Slope = -10/1

Slope = -10

Answer: slope = -10

The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.

The sum of the interior angles of a regular 18-gon can be found using the formula:

S = (n - 2) × 180 degrees

n is the number of sides of the polygon.

Substituting n = 18 we get:

S = (18 - 2) × 180 degrees

= 2880 degrees

The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.

Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.

The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.

Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.

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The equation of the relationship is f(200) = 0.75 * 200

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

Total number of drinks = 200

Cost of each drink = 0.75

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

f(x) = Cost of each drink * Total number of drinks

Where

f(x) = Total cost

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

f(200) = 0.75 * 200

Hence, the equation is f(200) = 0.75 * 200

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Answer:

She will need a time of 1024 units to complete the 10th station.

Step-by-step explanation:

A. As the quotient between consecutive terms is the same, the data is a geometric sequence.

B. The recursive formula is:

C. She will need a time of 1024 units to complete the 10th station.

In a sequence, if the difference between consecutive terms is the same, the sequence is arithmetic.

If the quotient between consecutive terms is the same, the sequence is geometric.

Item a:

When x increases by 1, y is multiplied by 2, hence, as the quotient between consecutive terms is the same, the data is a geometric sequence.

Using correlation and it's value of coefficient , The answer is b. 0.50

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.

we have 25% variance confidence.

\(r ^ {2} = 0.25\)

\(r=\sqrt {0.25}\)

\(r=0.50\)

The answer is b.0.50

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If a linear regression equation predicts more than 25% of the variance in the Y scores, then the correlation between X and Y must be greater than (c) r = 0.35.

Correlation (r) quantifies the strength and direction of the linear relationship between two variables. A correlation of 0.35 indicates a moderate positive linear association, suggesting that as X increases, Y tends to increase as well, and vice versa.

When the correlation surpasses this threshold, it implies that a substantial portion of the variability in Y can be explained by changes in X. However, it's important to interpret the correlation value within the context of the specific data and the field of study.

Other factors like sample size and potential outliers can also influence the significance of the correlation. In summary, a correlation greater than (c) 0.35 signifies a meaningful connection between X and Y, contributing to the prediction of Y scores using the linear regression equation.

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The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

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Answer:

the answer is a

Step-by-step explanation:

radius is the diameter divided by 2

Answer:

31.2

Step-by-step explanation:

Answer:

32 : 3

Step-by-step explanation:

Answer- 32 : 3

Divide Both Sides By 20

Answer:

5,6,7 because they are in line with the letter

The equivalent exponential equations are given as follows:

\(2^{4x} = 2^{3(x - 3)}\)

The exponential expression for this problem is defined as follows:

\(2^{4x} = 8^{x - 3}\)

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)

Meaning that the correct option is given by the fourth option.

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Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25