Which statement describes what these four powers have in common?

Answer:

Step-by-step explanation:

When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.

That translates into

(x + 8)/10 = (2x - 5)/14            Cross multiply

14* (x + 8) = 10* (2x - 5)          Remove the brackets on both sides.

14x + 112 = 20x - 50               Subtract 14x from both sides.

112 = 20x - 14x - 50                Combine

112 = 6x - 50                           Add 50 to both sides.

112+50 = 6x - 50 + 50             Combine

162 = 6x                                   Switch

6x = 162                                   Divide by 6

x = 27

Answer:

The son's age is 10 and the daughter's age is 5 now

Step-by-step explanation:

Let

x-----> the son's age now

y----> the daughter's age now

we know that

x=2y ----> equation A

(x+15)+(y+15)+(40+15)=100

x+y+85=100

x+y=15 -----> equation B

Substitute equation A in equation B and solve for y

2y+y=15

3y=15

y=5 years

Find the value of x

x=2(5)=10 years

therefore

The son's age is 10.

The daughter's age is 5

For this case we have that variable "m" represents the cost of Jake's food. They tell us that he left an 18% tip. That is to say:

m -------------> 100%

tip ------------> 18%

Where "tip" is the cost of the tip based on the cost of the meal.

[tex]tip = \frac {18 * m} {100}\\tip = 0.18m[/tex]

The amount Jake pays is represented by:

[tex]m + 0.18m[/tex]

Where 0.18m is the tip

ANswer:

Tip

Answer:

the tip amount jake pays

Step-by-step explanation:

Answer:

B. 1/10 or 0.10

Step-by-step explanation:

The question asks what's the probability that a student picked randomly will be playing both basketball and soccer.

The answer is right in the diagram.

We have only one student who plays both basketball and soccer: Ella

Since we have 10 students in the selected group, the probably you'll pick Ella is:

1 / 10 = 0.10 = 10%

So, the answer is B.

The value of P(A/B) is 0.33.

Given that, the Venn diagram shows sports played by 10 students.

P(A/B) is known as conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B". The formula for P(A/B)=P(A∩B) / P(B).

Now, P(A/B)=1/3≈0.33

Therefore, the value of P(A/B) is 0.33.

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Answer:

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

Step-by-step explanation:

* Lets explain how to solve the problem

- We need to find the product of the monomials (8x 6y)² and

   [tex]x^{3}y^{4}[/tex]

- At first lets solve the power of the first monomial

- Because the power 2 is on the bracket then each element inside the

  bracket will take power 2

∵ (8x 6y)² = (8)²(x)²(6)²(y)²

∵ (8)² = 64

∵ (x)² = x²

∵ (6)² = 36

∵ (y)² = y²

∴ (8x 6y)² = [64x² × 36y²]

∵ 64 × 36 = 2304 x²y²

∴ The first monomial is 2304 x²y²

∵ The first monomial is 2304 x²y²

∵ The second monomial is [tex]x^{3}y^{4}[/tex]

- Lets find their product

- Remember in multiplication if two terms have same bases then we

  will add their powers

∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =

   2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]

∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]

∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]

∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

A. His solution is accurate

You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x

Charles' solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]

Taking common as (1/3)x

[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]

The above expression is similar to Charles factor's of expression.

Thus, Charles solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

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ANSWER

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

[tex]\sec( \theta) = \frac{17}{8} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]

[tex] {h}^{2} = 289[/tex]

[tex]h = \sqrt{289} [/tex]

[tex]h = 17[/tex]

The sine ratio is negative in the fourth quadrant.

[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

The cosecant ratio is the reciprocal of the sine ratio.

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

The cosine ratio is positive in the fourth quadrant.

[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

The secant ratio is the reciprocal of the cosine ratio.

[tex]\sec( \theta) = \frac{17}{8} [/tex]

The tangent ratio is negative in the fourth quadrant.

[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

The reciprocal of the tangent ratio is the cotangent ratio

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

Answer:

sin=-15/17

cos=8/7

tan=-15/8

csc=-17/15

sec=17/8

cot=-8/15

Answer:

[tex]6\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

its D

Answer:

x = 20

Step-by-step explanation:

Formula

x1/x2 = x3/x4

Givens

x = 11

x2 = 11 + 121 = 132

x3 = 10

x4 = 10 + 5x + 10

Solution

11/132 = 10 / (5x + 10 + 10)        Combine

11/132 = 10/(5x + 20)                Cross multiply

11*(5x + 20) = 132 * 10              Combine on the right.

11(5x + 20 ) = 1320                   Divide by 11. (You could remove the brackets, but this is easier.

11(5x + 20)/11 = 1320/11            Do the division

5x + 20 = 120                          Subtract 20 from both sides

5x + 20-20 = 120 - 20             Combine

5x = 100                                   Divide by 5

5x/5 = 100/5

x = 20

Answer: Third option

[tex]f(x) - 2[/tex]

Step-by-step explanation:

The function [tex]y=log_3 (x)[/tex] passes through the point (1,0) since the function [tex]y=log_a (x)[/tex] always cuts the x-axis at [tex]x = 1[/tex].

Then, if the transformed function passes through point (1,-2) then this means that the graph of [tex]y=log_3(x)[/tex] was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

[tex]y = f (x) + k[/tex]

Where k is a negative number. In this case [tex]k = -2[/tex]

Then the transformation is:

[tex]f(x) -2[/tex]

and the transformed function is:

[tex]y = log_3 (x) -2[/tex]

Answer:

Step-by-step explanation:

This is a negative x^2 quadratic.  I'm not sure if there's anything else you need.

Answer:

a=16

Step-by-step explanation:

Given

(y-4)(y^2+4y+16)

To find the value of a in the resulting polynomial we have to solve the given expression

=y(y^2+4y+16)-4(y^2+4y+16)

= y^3+4y^2+16y-4y^2-16y-64

To find the value of a, both the polynomials will be compared

y^3+4y^2+16y-4y^2-16y-64  

y^3+4y^2+ay-4y^2-ay-64

Comparing the coefficients of both polynomials gives us that

a=16

So, the value of a is 16 ..  

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

x=44

Step-by-step explanation:

33+103+x=180

136+x=180

x=44

The sum of all the angles of a triangle is 180 degrees.  

Add all the angles together and set it equal to 180, then solve for x

33 + 103 + x = 180

(136 - 136) + x = 180 - 136

x = 44

Hope this helped!

The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.

Volume of cone = 3.14 x 7^2 x 12/3

Volume of cone = 3.14 x 49 x 4

Volume of cone = 615.44 cubic inches.

The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)

Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)

= 1/2 x 4/3 x 3.14 x 343

= 718.01 cubic inches.

Total volume = 615.44 + 718.01 = 1333.45 cubic inches.

Rounded to the nearest tenth = 1,333.5 cubic inches.

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75

The greatest common factor is 5.

12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.

66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.

13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.

14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.

15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.

16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.

17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.

18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.

If you want a further explanation step by step just ask :)

Answer:

(0,3) and (3,0)

Step-by-step explanation:

The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.

I take it the first equation is a typo and should be y = x^2 - 4x + 3

Equate the two equations.

-x + 3 = x^2 -4x + 3    Subtract 3 from both sides

-x = x^2 - 4x + 3-3

-x = x^2 - 4x                Add x to both sides.

0 = x^2 - 4x + x

0 = x^2 - 3x                Factor

0 = x(x - 3)

So x can equal 0

or x can equal 3

In either case the right side will reduce to 0.

Case 1. x = 0

y= - x + 3

y = 0 + 3

y = 3

So the point is (0,3)

Case 2. x = 3

y = - x + 3

y = - 3 + 3

y = 0

So the point is (3,0)

Answer:

X=-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

-8x+4=36

          -4

-8x     =32

/-8       /-8

  x      = -4

ANSWER

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

EXPLANATION

The recursive formula is given as:

[tex]a_n= \frac{1}{3} a_{n-1}[/tex]

where

[tex]a_1=2[/tex]

The explicit rule is given by:

[tex]a_n=a_1 {r}^{n-1}[/tex]

From the recursive rule , we have

[tex]r = \frac{1}{3} [/tex]

We substitute the known values into the formula to get;

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Therefore, the explicit rule is:

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Answer:178

Step-by-step explanation: I took the test :)

Answer:

The mass of the container is 178 kg.

Step-by-step explanation:

Since, the volume of a cylinder is,

[tex]V=\pi (r)^2 h[/tex]

Where r is the radius of the cylinder

And, h is its height

Here, r = 0.2 meters,

h = 1 meter,

So, the volume of the cylindrical container is,

[tex]V=\pi (0.2)^2(1)[/tex]

[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]

Now,

[tex]Density = \frac{Mass}{Volume}[/tex]

[tex]\implies Mass = Density\times Volume[/tex]

Given, Density of the container = 1417 kg/m³,

By substituting the values in the above formula,

[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

[tex]at ^ 2 + bt + c[/tex]

So

the t coordinate of the vertice is:

[tex]t =-\frac{b}{2a}[/tex]

In this case the equation is:

[tex]h(t)=72t-16t^2[/tex]

So

[tex]a=-16\\b=72\\c=0[/tex]

Therefore

[tex]t =-\frac{72}{2(-16)}[/tex]

[tex]t=2.25\ s[/tex]

Finally the maximum height that the ball will reach is

[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]

[tex]h=81\ ft[/tex]

The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.

To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.

So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.

To find out the maximum height, we just need to substitute this value of t into the equation for h(t):

h(2.25)=72*2.25-16*2.25^2

The above calculation gives a maximum height of 81 feet.

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Answer:

Area of triangle = 6 in^2

Step-by-step explanation:

We need to find the area of triangle. The formula used is:

Area of triangle = 1/2 * b*h

where b=base and h= height

In the given question, b =2 and h= 6

Putting values in the formula:

Area of triangle = 1/2 *2*6

                          = 12/2

                          =  6 in^2

Answer:

The area is 6 in^2

Step-by-step explanation:

The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse

Step-by-step explanation:

The measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse option third is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a right angle triangle with dimensions shown in the picture:

From the sin ratio in the right angle triangle:

sin∠C = 15/17

Thus, the measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse.

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Rewrite [tex]f[/tex] as

[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]

and recall that for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],

[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]

Then the radius of convergence is 2.

The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula  ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.

Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.

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Answer:

  x = (4r +3)/(r +2)

Step-by-step explanation:

Collect x terms, then divide by the coefficient of x.

  x(r +2) = 4r +3

  x = (4r +3)/(r +2)

Answer:

3/1

Step-by-step explanation:

Well there's 6 sides on a dice and only 2 winning numbers. 6/2=3/1. You have a good chance of losing lol. Is this what you're looking for?

~Keaura/Cendall.

Follow below steps:

To find the expected winnings for the game described, we need to calculate the expected value of one roll of the die based on the outcomes and their corresponding probabilities and payoffs. This is a classic example of a discrete probability distribution problem where the random variable X represents the winnings from one roll of the die.

There are two winning outcomes, rolling a four and rolling a five, each of which has a probability of 1/6 and a payoff of 8 dollars. There are four losing outcomes, rolling a one, two, three, or six, each with the same probability of 1/6 and a loss of 4 dollars.

Therefore, the expected value E(X) is calculated as follows:

E(X) = (2/6) * 8 + (4/6) * (-4) = (16/6) - (16/6) = 0

So the expected winnings for this game are 0 dollars, which means that, on average, a player neither wins nor loses money in the long term.

Answer:

[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]

Step-by-step explanation:

[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]

Answer: Last option

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Step-by-step explanation:

Note that: [tex]-3\frac{1}{4} =-3-\frac{1}{4} =-3.25[/tex]

The inequality is:

[tex]k<-3 \frac{1}{4}[/tex]

The inequality is:

This means that the inequality includes all values of the number line that are less than -3.25 or that are to the left of -3.25

__-8.4_________-3.25_-3____0___0.9____________7.1__

Note that the number -8.4 is less than -3.25, because it is to its left on the number line.

Then the correct statement is:

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Answer:

the last option!!!

Step-by-step explanation:

i took the unit test

Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.

In your case, we have to substitute "x" with "a+h":

[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]