Factor out the greatest common factor from this expression using the distributive property.
90 + 60

A) 30(3+2)
B) 10(9+6)
C) 15(6+4)
D) 6(15+10)

Answer:

C.1/16

Step-by-step explanation:

When a coin is tossed 4 times, the number of outcomes are:

2^4 = 16

So,

From the outcomes, only one outcome will be when there will be all heads

So, the probability will be:

One out of the 16 outcomes

Hence, the probability of a coin landing on heads all 4 times is:

C.1/16

Check the picture below.

recall that OM is an angle bisector, so those two "green" angles are equal, the same goes for ON which is also an angle bisector, those two "red" angles are also equal.

Answer:

hello

Step-by-step explanation:

i'm just making this answer so the other guy who obviously worked VERY hard on his answer can get a brainliest. :) don't mind me

Answer:

amount of miles traveled

Step-by-step explanation:

The dependent variables depends on another variable.

What that variable depends on is called the independent variable.

So the cost of the cab fare depends on the mile traveled variable.

The amount of miles traveled is the independent variable because the cost of the cab fare depends on it.

Answer:

The independent variable is the initial fee of $4

Step-by-step explanation:

Initial fee of $4

Additional fare of $0.25 per mile

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=0.25(x+5)^2\implies y=0.25[x-(\stackrel{h}{-5})]^2+\stackrel{k}{0}~\hfill \stackrel{\textit{vertex}}{(-5,0)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{the y-intercept occurs when x =0}~\hfill }{y=0.25(0+5)^2\implies y=0.25(5)^2}\implies y=6.25~\hfill \stackrel{\textit{y-intercept}}{(0, 6.25)}[/tex]

To identify the vertex and the y-intercept for the function \( y = 0.25(x + 5)^2 \), we will use our knowledge of quadratic functions and their properties.
Vertex:
The given function is in the form of \( y = a(x - h)^2 + k \), where (h, k) is the vertex of the parabola. This form is commonly referred to as the vertex form.
For the given function, \( y = 0.25(x + 5)^2 \), we can see that it is equivalent to \( y = 0.25(x - (-5))^2 + 0 \), indicating that the vertex (h, k) is at (-5, 0). This means the parabola opens upwards (because the coefficient of \( (x + 5)^2 \) is positive) and has its vertex point at x = -5 and y = 0.
Y-intercept:
The y-intercept of a function is found by evaluating the function when x = 0.
So we'll substitute x = 0 into the function to find the y-coordinate of the y-intercept:
\( y = 0.25(0 + 5)^2 \)
Now, we'll calculate the value inside the parentheses:
\( 0 + 5 = 5 \)
Then, we raise it to the power of 2:
\( 5^2 = 25 \)
Finally, we multiply by 0.25:
\( y = 0.25 \times 25 = 6.25 \)
Therefore, the y-intercept where the graph crosses the y-axis is at the point (0, 6.25), where the x-coordinate is 0 and the y-coordinate is the value we just calculated, 6.25.
In summary, the vertex of the function \( y = 0.25(x + 5)^2 \) is (-5, 0), and the y-intercept is at (0, 6.25).

The steps are shown below. From here, we can write:

[tex]\frac{x^3-2x^2-14x+3}{x+3}=x^2-5x+1+\frac{0}{x+3} \\ \\ \therefore \boxed{\frac{x^3-2x^2-14x+3}{x+3}=x^2-5x+1}[/tex]

Answer:

x^2-5x+1

Step-by-step explanation:

this is correct

Answer:

120

Step-by-step explanation:

A: D: 10 ≤ b ≤ 12

R: 0 ≤ W(b) ≤ 120

B: D: 0 ≤ b ≤ 10

R: 12 ≤ W(b) ≤ 120

C: D: 0 ≤ b ≤ 120

R: 0 ≤ W(b) ≤ 10

D: D: 0 ≤ b ≤ 10

R: 0 ≤ W(b) ≤ 120

W(b) = 12b.

he has enough to build 10 birdhouses, he doesn't have for more than that, he can either build no birdhouses or build 10 birdhouses, since "b" is the independent variable and thus the domain will come from it, what values can "b" safely take?   "b" can be either 0 or more than 0 but nor more than 10, because Owen doesn't have enough for more than that, 0 ≤ b ≤ 10.

let's say owen chooses to build 0 birdhouses, then W(0) = 12(0) => W(0) = 0.

let's say owen chooses to build 10 birdhouses, then W(10) = 12(10) => W(10) = 120.

so the amount of wood needed for those birdhouses, namely the range, can be either 0, if he chooses to build none, or 120 if he chooses to build 10, 0 ≤ W(b) ≤ 120.

Answer:

(9,7)

Step-by-step explanation:

F(a)=b means the point (a,b) is on the graph of F

The point that is on the graph of the function f, given f(9)=7, is (9, 7). This results because 9 is the input (x-coordinate) and 7 is the output (y-coordinate) of the function.

In mathematics, particularly in graphing functions, each point on the graph of a function f is represented by an ordered pair: the input (x-coordinate) and the output (y-coordinate). When you are given that f(9)=7, this essentially means that when the input is 9, the output is 7. Therefore, the point that is on the graph of the function f is (9, 7).

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Answer:

k = 29

Step-by-step explanation:

(5k -3) + (9+k) = 180

5k-3+9+k = 180

6k + 6 = 180

6k = 180 - 6 = 174

k = 29

The value of k is:

                     k = 29

We know that when two angles lie on a straight line then the sum of the two angles is equal to 180 degree.

Here we have two angles on a straight line as:

first angle = (5k-3)°

and second angle= (9+k)°

Hence, we have:

(5k-3)°+(9+k)°=180°

i.e.

5k-3+9+k=180

on combining the like terms on the left hand side of the equation we have:

5k+k+9-3=180

6k+6=180

6k=180-6

6k=174

i.e.

k=174/6

i.e.

k=29

Answer:

0,-9

Step-by-step explanation:

To solve [tex]x^2[/tex] + 9x = 0, we factor out the common x to get x(x + 9) = 0 and set each factor equal to zero, which gives us the solutions x = 0 and x = -9.

To solve the equation x2 + 9x = 0, we can apply factoring techniques. The first step is to factor out the common factor x from both terms in the equation. This yields:

x(x + 9) = 0

Then you have to realize that a product of two multiplicands is equal to zero if either multiplicand is equal to zero. Setting either multiplicand equal to zero and solving for x yields the solutions. Therefore, we have two multiplicands:

x = 0

x + 9 = 0, which simplifies to x = -9

The solutions to the equation are x = 0 and x = -9. As a check, we can substitute these values back into the original equation and confirm that both satisfy the equation.

Answer:

C

Step-by-step explanation:

Given that the triangles are congruent then corresponding sides are congruent.

YZ = BC = 12 and XZ = AC = 13, thus

cosZ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{12}{13}[/tex]

The solution is, the value of cos(z) is C.) 12/13.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

here, we have,

Given that the triangles are congruent then corresponding sides are congruent.

YZ = BC = 12

and XZ = AC = 13,

thus,

we get,

cosZ = base/hypotenuse

        =YZ/XZ  

        = 12/13

Hence, The solution is, the value of cos(z) is C.) 12/13.

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Answer:

It will take 5 years.

Step-by-step explanation:

Let's find how long it will take, but first let's understand the equation.

For simple interest, we use the equation:

T=(1/R)*(((A+B)/B)-1) where,

A= interest amount

B=invested money

R=interest rate (in decimal form)

T=time

Because we want to earn $1800 in interest, then A=1800.

Because we invested $6000, then B=6000.

Because we are investing under an interest rate of 6%, then R=0.06.

'How long will it take' means that T= not given, but its value is in 'years', since an annual rate was given.

Using the equation for simple interest we write:

T=(1/0.06)*(((1800+6000)/6000)-1), the solution is then:

T=5; remember, because is an annual rate, T solution means 5 years.

Answer:

D) 5 7/9

Work Shown:

-52/-9 = 5 7/9 = 5.7777777778

Final answer:

The linear equation is solved by distributing the number outside the parentheses, combining like terms, and then isolating the variable x. The final answer is x = 1/4.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, let's follow the standard steps for solving a linear equation.

Distribute the 3 to both terms inside the parentheses: 3 × (−4x) + 3 × 5 = 12, which simplifies to −12x + 15 = 12.

Subtract 15 from both sides of the equation to get the x term by itself: −12x + 15 − 15 = 12 − 15, which simplifies to −12x = −3.

Finally, divide both sides of the equation by −12 to solve for x: −12x / −12 = −3 / −12, which simplifies to x = 1/4.

By following these steps, we've found that the value that satisfies the equation is x = 1/4.

Final answer:

To solve the equation 3(−4x + 5) = 12, distribute the 3, subtract 15 from both sides, and then divide by −12, yielding the solution x = 1/4 or 0.25.

Explanation:

To solve the linear equation 3(−4x + 5) = 12, we'll start by expanding the equation and then isolating x.

Therefore, the solution to the equation 3(−4x + 5) = 12 is x = 0.25.

Answer:

0.1 or 1/10

Step-by-step explanation:

100% --> 1

9/10 --> 0.9

1 - 0.9 = 0.1

The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.

This means

[tex]82^\circ=m\angle 2[/tex]

[tex]\implies82=10x+12[/tex]

[tex]\implies10x=70[/tex]

[tex]\implies\boxed{x=7}[/tex]

Answer:

Catherine's sister ate 2/15 gallons of the ice cream.

[tex]\displaystyle \frac{2}{15}[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the amount of ice cream that Catherine's sister ate, in gallons.

Consider the relationship:

[tex]\text{Original amount - What Catherine ate - What Catherine's Sister ate}\\ =\text{ What's left.}[/tex].

That is:

[tex]\displaystyle 1- \frac{1}{5} - x = \frac{2}{3}[/tex].

Add [tex]x[/tex] to both sides of this equation:

[tex]\displaystyle 1 - \frac{1}{5} = \frac{2}{3} +x[/tex]

Substract [tex]\displaystyle \frac{2}{3}[/tex] from both sides:

[tex]\displaystyle 1 - \frac{1}{5} - \frac{2}{3} = x[/tex].

Convert the denominator of all three numbers on the left-hand side to [tex]3 \times 5 = 15[/tex]

[tex]\displaystyle \frac{15}{15} - \frac{3}{15} - \frac{10}{15} = x[/tex].

[tex]\displaystyle x = \frac{2}{15}[/tex].

In other words, Catherine's sister ate [tex]\displaystyle \frac{2}{15}[/tex] gallons of the ice cream.

To solve this, we need to add the 1/5 of the ice cream to the 2/3 left of ice cream to find out how much her sister ate.

First, we need a common denominator. We can multiply 3 by 5 to get a common denominator easiest, since they are both multiples of it.

3*5=15

Now multiply the numerators by the amount the denominators were multiplied by.

1*3=3 so 3/15

2*5=10 so 10/15

Now, add them together.

10/15+3/15= 13/15.

Finally, subtract that amount from the original full amount of ice cream (15/15) to get the amount her sister ate, since that is the only unknown value left.

15/15-13/15=2/15.

Because 15 isn’t divisible by 2, we can’t simplify this fraction anymore.

Her sister ate 2/15 of a gallon of ice cream.

Hope this helps!

The requried, to make the game fair, the first place prize should be worth 4n - 13 dollars. None of the options are correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The second place prize is worth $8 and the third place prize is worth $5, so the total value of these two prizes is $8 + $5 = $13.

If the game is fair, then the total amount of prize money awarded should be equal to the total amount of entry fees collected. If n players enter the game, then the total entry fees collected will be 4n.

Let x be the value of the first-place prize, which we want to find. The probability of winning any of the three prizes is 1/n, so the total amount of prize money awarded is,

1/n × x + 1/n × $8 + 1/n × $5 = ($4)n
x + 8 + 5 = 4n
x = 4n - 13

Therefore, to make the game fair, the first place prize should be worth 4n - 13 dollars.

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The balance in Josie's account at the beginning of year 3, with a $400 investment at 5% annual compound interest, can be calculated using the compound interest formula A = P(1 + r)^n, which results in $441.

The explicit formula to find the account's balance at the beginning of year 3 for Josie's investment with an annual compound interest rate can be determined using the compound interest formula:

A = P(1 + r)^n

Where:

In Josie's case, she invested $400 at a 5% annual interest rate for 2 years. The formula will look like this:

A = 400(1 + 0.05)^2

Now, calculate the amount:

A = 400(1 + 0.05)^2

A = 400(1.05)^2

A = 400(1.1025)

A = $441

Hence, the balance in Josie's account at the beginning of year 3 would be $441.

For this case we must find the inverse of the following function:

[tex]g (x) = 2x + 4[/tex]

Replace g(x) with y:

[tex]y = 2x + 4[/tex]

We exchange the variables:

[tex]x = 2y + 4[/tex]

We solve for "y":

We subtract 4 on both sides of the equation:

[tex]x-4 = 2y[/tex]

We divide between 2 on both sides of the equation:

[tex]y = \frac {x} {2} -2[/tex]

We change y by [tex]g ^ {-1} (x)[/tex]:

[tex]g ^ {- 1} (x) = \frac {x} {2} -2[/tex]

Answer:

[tex]g ^ {- 1} (x) = \frac {x} {2} -2[/tex]

Answer:

[tex]f^{-1}=\frac{x}{2} -2[/tex]

Step-by-step explanation:

the inverse function of g(x) = 2x + 4

To find the inverse of a function we replace g(x) with y

[tex]y=2x+4[/tex]

Replace x with y and y with x

[tex]x=2y+4[/tex]

Solve the equation for y

Subtract 4 from both sides

[tex]x-4= 2y[/tex]

Divide both sides by 2

[tex]\frac{x}{2} -2=y[/tex]

[tex]y=\frac{x}{2} -2[/tex]

Replace y with f inverse

[tex]f^{-1}=\frac{x}{2} -2[/tex]

The answer is:

The option that represents the matrix is the option D:

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

From the statement we know that the matrix is formed with the information obtained from a system of equations:

Being the values of the first column the values of the variable "x"

Being the values of the second column the values of the variable "y"

Being the values of the third column the values of the variable "z"

Being the values of the fourth column the values of the constant numbers (after the equality)

Knowing that, we are looking for a system equation that contains the following equations:

First equation:

[tex]3x+6y-z=8[/tex]

Second equation:

[tex]-2x+3y=4[/tex]

Third equation:

[tex]4x+5y+4z=-2[/tex]

Hence, we can see that the option that matches with the matrix is the option D.

[tex]3x+6y-z=8\\-2x+3y=4\\4x+5y+4z=-2[/tex]

Have a nice day!

Answer:

the one on the bottom left

Step-by-step explanation:

Note that the cube on the bottom left is composed of

4 × 4 × 4 = 64 ← unit cubes

Thus the volume of the cube = 64 units³

The volume of a cube = s³ ← where s is the side length

Thus s³ = 64

To find s given the volume take the cube root of both sides, that is

s = [tex]\sqrt[3]{64}[/tex] = 4

Answer:

95.1893

Step-by-step explanation:

The distance between points (16, -43) and (1, 51) is 95.1893

Answer:

36°

Step-by-step explanation:

134° is the exterior angle of the triangle.

By the exterior angle theorm

134° = 98° + y

y = 134° - 98°  = 36°

Answer:

The value of b is 28.28

Step-by-step explanation:

We would use Law of sines to find the value of b

The law of sines is:

[tex]\frac{a}{sinA}=\frac{b}{sinB}[/tex]

We are given

a= 20

A = 30°

B = 45°

b=?

Putting values in the formula:

[tex]\frac{20}{sin(30)}=\frac{b}{sin(45)}\\\frac{20}{0.5}=\frac{b}{0.707}\\b = \frac{20}{0.5} * 0.707\\b = 40 * 0.707\\b= 28.28\\[/tex]

The value of b is 28.28

Answer:

4n+2

Step-by-step explanation:

The common difference between the terms is 4 which means that the sequence is an arithmetic sequence.

The general formula for arithmetic sequence is:

[tex]a_{n}=a_{0}+(n-1)d[/tex]

where a_n is the nth term, a_0 is the first term and d is the common difference between them.

We know that

[tex]a_{0}=6\\d=4[/tex]

Putting the value in general formula:

[tex]a_{n}=6+4(n-1)\\a_{n}=6+4n-4\\a_{n}=4n+6-4\\a_{n}=4n+2\\[/tex]

So the generalized pattern is 4n+2 ..

Answer:

13 and 14

Step-by-step explanation:

13+ (2*13) +6= 45 which is less than 50

14+ (2*14) +6= 48 which is also less than 50.

When you do the same with 15,16, and 17 the answers all come out to be  51, 54, and 57 which are all greater than 50

Answer:

13 and 14

Step-by-step explanation:

Given : [tex]x + 2x + 6 < 50[/tex]

To Find : From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are .

Solution:

Inequality :  [tex]x + 2x + 6 < 50[/tex]

Substitute x =  13

[tex]13 + 2(13) + 6 < 50[/tex]

[tex]45 < 50[/tex]

Substitute x = 14

[tex]14 + 2(14) + 6 < 50[/tex]

[tex]48 < 50[/tex]

Substitute x = 15

[tex]15 + 2(15) + 6 < 50[/tex]

[tex]51 > 50[/tex]

Substitute x = 16

[tex]16+ 2(16) + 6 < 50[/tex]

[tex]54 > 50[/tex]

Substitute x = 17

[tex]17+ 2(17) + 6 < 50[/tex]

[tex]57 > 50[/tex]

So,  the values of x for which the inequality holds true are 13 and 14.

Answer:

3/8

Step-by-step explanation:

Slope is the same as rise over run, or y/x. In this case, rise over run is 15 over 40, or 15/40. Simplified, this is 3/8.

Answer:

4 cups of candies and 8 cups of nuts

Step-by-step explanation:

Cost per cup = $1.29

Total number of cups = 12

Total cost of cups = 12 x $1.29

                              = $15.48

Cost of candies = $2.49 per cup

Total number of candies = x

Cost of nuts = $0.69 per cup

Total number of nuts = y

Equations :

x + y = 12 (because total cups of nuts and candies will be equal to 12)

2.49x + 0.69y = 15.48 (Total cost of the 12 cups should be 15.48)

Step 1 : Find x in terms of y

x = 12 - y

Step 2 : substitute x in terms of y from step 1 in the second equation

2.49x + 0.69y = 15.48

2.49 ( 12 - y) + 0.69y = 15.48

29.88 - 2.49y + 0.69y = 15.48

-1.8y = -14.4

y = 14.4/1.8

y = 8

Step 3 : Find x

x + y = 12

x = 12 - y

x = 12- 8

x = 4

Yumi should use 4 cups of candies and 8 cups of nuts.

!!

The number of cups of candies and nuts, Yumi should use is 4 and 8 cups respectively.

Given the following data:

Translating the word problem into an algebraic expression, we have;

For total number of cups:

[tex]C + N = 12[/tex]  .....equation 1

For cost of candies and nuts:

[tex]2.49C + 0.69N = 1.29(12)\\\\2.49C + 0.69N = 15.48[/tex].....equation 2

From equation1:

[tex]C = 12 - N[/tex]   ....equation 3

Substituting eqn 3 into eqn 1, we have:

[tex]2.49(12 - N) + 0.69N = 15.48\\\\29.88 - 2.49N + 0.69N = 15.48\\\\1.8N = 29.88 - 15.48\\\\1.8N = 14.4\\\\N = \frac{14.4}{1.8}[/tex]

Number of nuts, N = 8 cups

For candies:

[tex]C = 12 - N\\\\C = 12 - 8[/tex]

Number of candies, N = 4 cups

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