Pls help. ASAp. Im confused

The radius x for the circle is derived to be 10.92 using the Pythagoras rule for the right triangle.

Since the line with length 12 is tangent to the circle, then the triangle is a right triangle and the Pythagoras rule can be applied as follows:

x² + (x + 6)² = 12²

x² + x² + 12x + 36 - 144 = 0

2x² + 12x - 108 = 0

x² + 6x - 54 = 0

x² + 6x + 9 = 54 + 9 {completing the square}

(x + 3)² = 63

x + 3 = ±√63

x = 3 + √63 or x = 3 - √63

x = 10.92 or x = -4.92

Therefore, the radius x for the circle is derived to be 10.92 using the Pythagoras rule for the right triangle.

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Answer:

11. (D) 90 degrees

12. (C) 93

13. (D) 90 degrees

14. (C) 46

Step-by-step explanation:

11. this is a square so each angle is 90 degrees.

12. as each side is the same, we create the equation 9x + 3 = 11x - 17. Solve.

13. With diagonals, MGQ, QGE, QEO, QOM, QMG become 45 degrees, while the intersection of the diagonals become 90 degrees

Hope this answers your question

please give Brainliest, would really appreciate it! :)

According to chances:

10. If you and your five friends are sitting together in a row of 6 empty seats, then you can be seated in any of the 6 seats, your first friend can be seated in any of the remaining 5 seats, your second friend can be seated in any of the remaining 4 seats, and so on. Therefore, the total number of ways in which you all can sit together in a row of 6 empty seats is given by:

6 x 5 x 4 x 3 x 2 x 1 = 720

Hence, there are 720 different ways in which you all can sit together in a row of 6 empty seats.

11. Since you can purchase 5 out of 7 different flavors of hot sauce, the number of possible ways of purchasing the hot sauces can be calculated using the combination formula. The number of ways to choose 5 sauces out of 7 is given by:

C(7,5) = 7! / (5! x 2!) = 21

Therefore, there are 21 possible ways for you to purchase 5 different flavors of hot sauce.

(a) If the order of the five numbers does not matter, then we need to find the number of combinations of 5 numbers that can be selected from 20 numbers. This can be calculated using the combination formula, and is given by:

C(20,5) = 20! / (5! x 15!) = 15,504

Therefore, the probability of winning the lottery is 1/15,504.

(b) If the order of the five numbers matters, then we need to find the number of permutations of 5 numbers that can be selected from 20 numbers. This can be calculated using the permutation formula, and is given by:

P(20,5) = 20! / 15! = 3,584,000

Therefore, the probability of winning the lottery is 1/3,584,000.

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Image transcribed:

10. You and five of your friends go to the local theatre to watch a famous orchestra perform. In how many, different ways, can you all sit together in a row of 6 empty Seats? (7pts)

11. A local grocery store has 7 different kinds of hot sauce that you would love try. However, you only have enough money to purchase 5 of the different flavors. How many of the flavors of hot sauce are possible for you to purchase? (7 pts)

12. You are testing your recent luck and want to find out how unlikely it is to win a lottery with a jackpot $1, 000, 000. In order to win, you must correctly select 5 numbers where each is an integer between 0-19 inclusive. Find the probability that you randomly select a lottery ticket and win if: (6 pts each)

(a) The order of the five numbers does not matter.

(b) The order of the five numbers do matter.

Answer:

1.52

Step-by-step explanation:

divide 152 by 100

The  completed  table is shown below:

starting elevation (feet)

change (feet)

final elevation (feet)

A

+200

75 up

275

B

+200

75 down

125

C

+200

200 down

0

D

+200

+25

225

the additional equation for B is:

final elevation for B = +200 feet - 75 feet

c. The line diagram is attached below.

We can use the formula, to write an addition equation for B

final elevation = starting elevation + change

final elevation for B = +200 feet - 75 feet

We simplify  this equation as:

final elevation for B = +125 feet

We draw a number line diagram for B, we can start at +200 feet (the starting elevation) and then move 75 units down (since the elevation is decreasing by 75 feet).

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So, the value of P (X=2 or X=0) is 0.4.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that it is certain to occur.

For example, if you flip a fair coin, the probability of it landing on heads is 0.5 or 50%, as there are only two possible outcomes (heads or tails) and they are equally likely to occur.

Probability is used extensively in fields such as statistics, mathematics, and science to model and analyze uncertainty and randomness. It is also used in practical applications such as gambling, risk assessment, and decision making.

o find the probability of X being 2 or 0, we need to add the probabilities of the two events.

P(X=2 or X=0) = P(X=2) + P(X=0)

From the given table, we can see that:

P(X=2) = 0.1

P(X=0) = 0.3

Therefore,

[tex]P (X=2 or X=0) = 0.1 + 0.3 = 0.4[/tex]

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Therefor option C  graph for this identity  will be best . This function has all real numbers as its domain and all real numbers as its range.

The collection of all potential input values (typically denoted by x) for which a mathematical function is specified is known as the domain of the function. For instance, the domain of a function f(x) = 1/x, with the exception of x = 0, is all real numbers. This is due to the illogical nature of division by zero.

Another illustration is the formula g(x) =.(x - 2). All real numbers larger than or equal to 2 fall under the domain in this situation. This is due to the fact that a negative number cannot be squared.

A cube root function is the one with the formula m(x) = x + 5. Similar to a square root function, but more spread out, is the graph of a cube root function. This function has all real numbers as its domain and all real numbers as its range.

We can start by locating a few points on the graph in order to graph this function for example,

when x = 0, m(x) = ∛0 + 5 = 5.

When x = 1, m(x) = ∛1 + 5 ≈ 6.

When x = -1, m(x) = ∛(-1) + 5 ≈ 4.

We can plot these points on a coordinate plane and connect them with a smooth curve to get the graph of the function.

Therefor option C  graph for this identity  will be best

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Answer:

Step-by-step explanation:

if your on computer jus press refresh when your by the answer, it will show u for a split sec

Answer:

Step-by-step explanation:

You want the formula for angle C in triangle ABC with area D.

The relevant formula for the area of the triangle is ...

  Area = 1/2ab·sin(C)

When the area is D, this is ...

  D = 1/2ab·sin(C)

You are being asked to rearrange the formula to give an expression for C.

  2D/(ab) = sin(C) . . . . divide by the coefficient of sin(C)

  [tex]C=\sin^{-1}\left(\dfrac{2D}{ab}\right)=\sin^{-1}\left(\dfrac{m}{n}\right)[/tex]

Comparing parts of the expressions, we see that ...

The equation of the circle is x²2 - 2x + y²2 - 4y = -3.

How to solve?

The equation for a circle centered at the point (h, k) with a radius of length r is given by:

(x - h)²2 + (y - k)²2 = r²2

In this case, the circle is centered at the point (1, 2) and has a radius of length 2. So, we have:

h = 1

k = 2

r = 2

Substituting these values into the equation, we get:

(x - 1)²2 + (y - 2)²2 = 2²2

Simplifying and expanding the squared terms, we get:

(x²2 - 2x + 1) + (y²2 - 4y + 4) = 4

Moving the constant term to the right-hand side, we get:

(x²2 - 2x) + (y²2 - 4y) = -1

Adding 1 to both sides, we get the final equation of the circle in standard form:

(x²2 - 2x + 1) + (y²2 - 4y + 4) = 4

x²2 - 2x + y²2 - 4y = -3

The equation of the circle is x²2 - 2x + y²2 - 4y = -3.

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All points on this line are equidistant from the two arms of the parabola, and the line passes through the vertex of the parabola.

What is quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable, where the variable is typically denoted by x.

According to question:

A quadratic equation's vertex form is provided by:

y = a(x - h)² + k

where an is a constant that governs the parabola's shape and (h, k) is the parabola's vertex.

In this case, the vertex form of the quadratic equation with a = 3, h = -4, and k = 1 is:

y = 3(x + 4)² + 1

To find the equation of the axis of symmetry, we need to determine the x-coordinate of the vertex, which is given by -h. In this case, -h = -(-4) = 4.

The line that represents the axis of symmetry has the following equation, then:

x = 4

This is because all points on this line are equidistant from the two arms of the parabola, and the line passes through the vertex of the parabola.

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a)The term 1-16t²represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple

b)Interpreting the domain, we can say that h(t) makes sense only for non-negative values of t. In other words, we can use the function h(t)to find the height of the apple at any time t a

what is gravity ?

Gravity is a fundamental force of nature that causes objects with mass to attract each other. It is the force that keeps planets in orbit around stars, and stars in orbit around the center of their galaxies.

In the given question,

a. The function h(t)=-16t²+36 represents the height of an apple above the ground at time t after falling off a tree. The term1 -16t² represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple when it fell off the tree.

b. The domain of h(t) in this situation is the set of all possible values of t that make sense in the context of the problem. Since h(t) represents the height of the apple at time t after it fell off the tree, the domain of h(t)is the set of all non-negative real numbers, or [0,\infty) This is because time cannot be negative, and the apple cannot fall for an infinite amount of time.

Interpreting the domain, we can say that h(t)makes sense only for non-negative values of t. In other words, we can use the function h(t) to find the height of the apple at any time t after it fell off the tree, as long as t is non-negative..

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This is not true, so there is no point c in the interval  [tex](1, 8)[/tex] that satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = x-3.[/tex]

To apply the Mean Value Theorem, we need to check that the function   [tex]f(x) = x-3[/tex] satisfies the following conditions:

f(x) is continuous on the closed interval [1, 8].

f(x) is differentiable on the open interval (1, 8).

Condition 1 is satisfied because f(x) is a polynomial function, and all polynomial functions are continuous everywhere.

To check condition 2, we can take the derivative of f(x) to get:

f'(x) = 1

The derivative is a constant function, so it is defined and continuous on the entire interval (1, 8).

Therefore, we can apply the Mean Value Theorem, which states that there exists a point c in the open interval (1, 8) such that:

[tex]f'(c) = (f(8) - f(1))/(8 - 1)[/tex]

Plugging in the values, we get:

[tex]1 = (8-3)/(8-1)[/tex]

Simplifying, we get:

[tex]1 = 5/7[/tex]

Therefore, This is not true, so there is no point c in the interval (1, 8) that satisfies the conclusion of the Mean Value Theorem for f(x) = x-3.

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Therefore, the solution of the given problem of equation comes out to be adding 7x to both sides of the equation might be the initial step towards solving the equation 7x 5 = x + 3.

Variable words are often employed in complex algorithms to show consistency between two contradictory statements. Academic expressions called equations are used to show the equality of various academic figures. Think of the specifics with y + 7 proposals. In this situation, elevating results in b + 7 when building y + 7 is combined, in contrast to another method of splitting 12 equally sized pieces into two halves.

Here,

We can start by reducing the equation by using various algebraic operations in order to find the solution to the equation 7x 5 = x + 3.

The variable term on the right side of the equation would be eliminated, and the variable on the left side would be isolated, by adding 7x to both sides of the equation as a possible initial step:

=> -7x - 5 + 7x = x + 3 + 7x

Combining similar terms to make the left side simpler:

=> -5 = 8x + 3

After that, we may take 3 off of both sides:

=> -5 - 3 = 8x + 3 - 3

Making the right side simpler:

=> -8 = 8x

By multiplying both sides by 8, we may finally find the value of x:

=> x = -1

As a result, adding 7x to both sides of the equation might be the initial step towards solving the equation 7x + 5 = x + 3.

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Answer:

42° and 95°

Step-by-step explanation:

1

the inscribed angle EFD is half the measure of its intercepted arc , that is

∠ EFD = [tex]\frac{1}{2}[/tex] × DE = [tex]\frac{1}{2}[/tex] × 84° = 42°

2

ABCD is a cyclic quadrilateral.

the opposite angles sum to 180° , that is

∠ B + ∠ D = 180°

∠ B + 85° = 180° ( subtract 85° from both sides )

∠ B = 95°

Answer:

36

Step-by-step explanation:

It's the biggest number.

The surface areas for each figures are:

1. The surface area of the cuboid is:

Top and bottom: 2(10 ft x 4 ft) = 80 ft²

Front and back: 2(10 ft x 5 ft) = 100 ft²

Sides: 2(4 ft x 5 ft) = 40 ft²

Total surface area = 80 + 100 + 40 = 220 ft²

2. The surface area of the cuboid is:

Top and bottom: 2(18 cm x 5 cm) = 180 cm²

Front and back: 2(18 cm x 5 cm) = 180 cm²

Sides: 2(5 cm x 5 cm) = 50 cm²

Total surface area = 180 + 180 + 50 = 410 cm²

3. The surface area of the prism is:

Top and bottom: 2(5 cm x 14 cm) = 140 cm²

Front and back: 2(5 cm x 12 cm) = 120 cm²

Sides: 2(12 cm x 14 cm) = 336 cm²

Total surface area = 140 + 120 + 336 = 596 cm²

4. The surface area of the stacked cuboids is:

Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²

Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²

Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²

Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²

Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²

Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²

Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²

Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²

5. The surface area of the cylinder is:

Top and bottom: 2π(6 mm)² = 72π mm²

Side: 2π(6 mm)(5 mm) = 60π mm²

Total surface area = 72π + 60π = 132π mm²

6. The surface area of the cylinder is:

Top and bottom: 2π(1 ft)² = 2π ft²

Side: 2π(1 ft)(10 ft) = 20π ft²

Total surface area = 2π + 20π = 22π ft²

7. The surface area of the cylinder stacked on a cube is:

Top and bottom of cylinder: 2π(5 m)² = 50π m²

Side of cylinder: 2π(5 m)(8 m) = 80π m²

Surface area of cube: 6(10 m x 13 m) = 780 m²

Total surface area = 50π + 80π + 780 = (130π + 780) m²

8. The surface area of the cylinder is:

Top and bottom: 2π(9 in)² = 162π in²

Side: 2π(9 in)(4 in) = 72π in²

Therefore, the total surface area of the cylinder is:

2(162π in²) + 72π in² = 396π in²

So the surface area of the cylinder is 396π square inches.

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Image transcribed:

Find the surface area of each figure.

10 ft

18 cm

5 cm

4 ft

5 ft

3.

4.

6 cm

7 cm

2 cm

5 cm

12 cm

14 cm

4 cm

10 cm

8 cm

Find the surface area of each cylinder. Leave your answer in terms of π.

5.

6 mm

6.

1 ft

5 mm

10 ft

7.

5 m

8.

4 in.

8 m

10 m

9 in.

13 m

11 m

247

Journal and Practice Workbook

Geometry

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

We use the fact that parallel lines have the same slope to determine the equation of a line that is perpendicular to a given line and passes through a point. provided that it takes the form y = mx + b, where m is the slope, the provided line has a slope of -8/7. The parallel line will therefore similarly have a slope of -8/7.

The point-slope form of a line is used to determine the y-intercept of a parallel line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. We obtain: y - 4 = (-8/7)(x + 6) by substituting (-6, 4) and -8/7 for m.

This equation can be simplified to y = (-8/7)x - 40/7.

We make use of the fact that perpendicular lines have opposing reciprocal slopes to determine the equation of a line that is perpendicular to the supplied line and passes through (-6, 4). provided that the provided line has a slope of -8/7, the perpendicular line will have a slope of 7/8.

Again using the point-slope representation of a line, we arrive at: y - 4 = (7/8)(x + 6)

This equation can be simplified to: y = (7/8)x + 25/4

Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.

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Answer: Sure, here's an example survey result in tabular form:

Color Number of Students

Grey 10

Green 20

Blue 35

Pink 15

Yellow 20

Total 100

Step-by-step explanation:

Answer:132 tenths are equivalent to 13.2.

Step-by-step explanation:

Answer: 132 tenths.

Step-by-step explanation:

Since it's tenths, all you have to do is move the decimal place over 1 space.

The condensed expression in to a single logarithm is In(6x⁷).

Using the property of logarithms that states "the logarithm of the quotient is the difference of the logarithms", we can write:

In(6x⁹/x²)

Simplifying the expression within the parentheses, we get:

In(6x⁷)

Therefore, the condensed expression is In(6x⁷).

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Answer: 172z + 19u

Step-by-step explanation: To look up to the power of, use: "^"

2^6

4^5 etc.

Answer:

[tex]y = 2x+1[/tex]

Step-by-step explanation:

Let y = mx + b.

We can find two points, (0, 1) and (1, 3).

Substituting both into the equation:

[tex]\left \{ {{1 = 0m + b} \atop {3 = m+b}} \right.[/tex]

We find that b = 1, m = 2.

Thus, y = 2x + 1.

We have demonstrated that the middle of a right triangle's hypotenuse is equally spaced from its three vertices, MA = MB = MC.

Let A be the vertex of the right angle, B and C be the other two vertices, and let their (x,y) coordinates be as follows:

A: (a,b)

B: (c,d)

C: (e,f)

The midpoint M of the hypotenuse BC can be found by averaging the (x,y) coordinates of B and C:

[tex]M: $\left(\frac{c+e}{2},\frac{d+f}{2}\right)$[/tex]

To calculate the lengths of MA, MB, and MC, we can use the distance formula:

[tex]MA = \sqrt{(a - \frac{c+e}{2})^2 + (b - \frac{d+f}{2})^2}$\\$MB = \sqrt{(c - \frac{c+e}{2})^2 + (d - \frac{d+f}{2})^2}\\$MC = \sqrt{(e - \frac{c+e}{2})^2 + (f - \frac{d+f}{2})^2}$[/tex]

Simplifying each of these equations, we get:

[tex]MA = \sqrt{(2a - c - e)^2 + (2b - d - f)^2}/2$\\$MB = \sqrt{(c - e)^2 + (d - f)^2}/2$\\$MC = \sqrt{(2e - c - e)^2 + (2f - d - f)^2}/2$[/tex]

We want to show that the midpoint M of the hypotenuse BC is equidistant from the three vertices, i.e., that MA = MB = MC.

Substituting the coordinates of M into the expressions for MA, MB, and MC, we get:

[tex]$MA = \sqrt{(2a - c - e)^2 + (2b - d - f)^2}/2$$MB = \sqrt{(c - e)^2 + (d - f)^2}/2$$MC = \sqrt{(2e - c - e)^2 + (2f - d - f)^2}/2$[/tex]

To simplify these expressions, notice that[tex]$(c+e)/2$[/tex]  is the x-coordinate of M, which is halfway between the x-coordinates of B and C. Similarly, [tex]$(d+f)/2$[/tex]  is the y-coordinate of M, which is halfway between the y-coordinates of B and C. Therefore, we can rewrite the expressions as:

[tex]MA = \sqrt{(a - \frac{c+e}{2})^2 + (b - \frac{d+f}{2})^2}\\MB = \sqrt{(c - \frac{c+e}{2})^2 + (d - \frac{d+f}{2})^2}\\MC = \sqrt{(e - \frac{c+e}{2})^2 + (f - \frac{d+f}{2})^2}[/tex]

Notice that these are the same expressions we obtained in step 3 for the lengths of the three segments.

Therefore, we have shown that MA = MB = MC, which means that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

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You can expect to receive the increase of percentage that is 2.5%.

The term "percentage" in mathematics can refer to either numbers or ratios that are stated as fractions of 100. In most cases, they are indicated by "%" or "percent."In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. A% is a number that has neither dimensions nor a defined unit of measurement.

Given,

You received a score of 3.4 on annual review. Merit increases are given out at .5% at a score of 2.6 and it goes up 1% every .4 points.

Score received in the beginning = 2.6

Increase in score as a percentage equals 0.5%

Score increases by 1% for every 0.4 points.

The following rise will occur at 2.6 + 0.4 = 3.0 points.

Increase in percentage: 0.5 + 1= 1.5%

Score = 3.0 + 0.4 = 3.4 points will be the following point increment.

Score increase as a percentage: 1.5 + 1 = 2.5%

You can expect to receive the increase 2.5%

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{ 1 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{ 1 }{ 3 }}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 3 }x+2 \end{array}}[/tex]

Answer:

No

Step-by-step explanation:

(x,y)=(2,7) is the solution for y=3x+1, but not for y=2x+5, so (2,7) isn't the solution to the system of equations.

The calculated value of the length of the segment HK is 7.8 units

Given the circle

And the intersecting chords IJ and GH

When two chords cross each other inside a circle, the product of the lengths of their respective line segments are equal.

In this particular circle, chords IJ and GH intersect at a point called K.

As a result, the product of the length of segments IK and KJ is equal to the product of the length of segments GK and HK.

So, we have

IK * KJ = GK * HK

This gives

6 * 26 = 20 * HK

This gives

HK = 7.8

Hence, the segment HK is 7.8 units long

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Answer:

Yes, the c.o.p. is 2.

Step-by-step explanation:

The question of proportionality is answered by directly dividing each y-value (distance) by its associated x-value (time). If ALL of the related pairs give the same quotients, the relationship is proportional and the common quotient is the constant of proportionality.

4/2=2

8/4=2

12/6=2

16/8=2

The elements of the sets are;

'D = { 4, 6 , 8}

C∪D = { 2, 3, 5, 7}

C∩'D = { }

A Venn diagram is defined as a widely used diagram style showing the logical relation between sets.

The different sets in a Venn diagram are determined with the symbols;

From the Venn diagram shown, we have that;

Universal set = {4, 6, 8}

C = { 7}

D = { 2, 3 , 5}

Then, we have that;

'D = { 4, 6 , 8}

C∪D = { 2, 3, 5, 7}

C∩'D = { }

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