Help!! Factor the common factor out of each expression

Answer: $26.81

Step-by-step explanation: the tank holds 16.5 gallons. Meaning, half of the tank is 8.25 gallons. Multiply that by the cost of the gas, 3.25, and you get 26.81

Answer:

Step-by-step explanation:

You want the angles associated with different arc lengths and radii.

The length of an arc is given by the formula ...

  s = rθ . . . . . θ is the angle in radians, r is the radius

Solving for θ gives ...

  θ = s/r

For s=17 in, r=4 in, ...

  θ = (17 in)/(4 in) = 4.25 . . . . radians

For s=12 ft, r=5 ft, ...

  θ = (12 ft)/(5 ft) = 2.4 . . . . radians

For s=8.5 mm, r = 13.6 mm, ...

  θ = (8.5 mm)/(13.6 mm) = 0.625 . . . . radians

The height of the rock ledge will be 20.35 meters.

The height of the tree will be 58.75 meters

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The angle of elevation to the top of a tree is 22°.

And, The angle of depression to the base of the tree is 12°.

Now,

Let the height of the rock ledge = x

So, By figure, we get;

⇒ tan 12° = x / 96

⇒ x = 96 × tan 12°

⇒ x = 20.35 meters

And, Let total height of the tree = x + y

                                                = 20.35 + y

Hence, By figure, we get;

⇒ tan 22° = y / 96

⇒ y = 96 × tan 22°

⇒ y = 96 × 0.40

⇒ y = 38.4 meter

Thus, The height of tree = 38.4 meters + 20.35 meters

                                      = 58.75 meters

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To find:-

Answer:-

Part A :-

Here we can see that the distance between the rock ledge and the base of the tree is 96m . Also the angle of elevation to the top of the tree from the rock is 22° .

Firstly, we can see that,

[tex]\implies \angle CAD =\angle EDA = 12^o\\[/tex]

This is so because they are alternate interior angles .

Now , in ∆ADE ,

[tex]\implies \tan\theta =\dfrac{p}{b}=\dfrac{AE}{ED}\\[/tex]

[tex]\implies \tan 12^o =\dfrac{AE}{96m} \\[/tex]

[tex]\implies AE = 96\tan12^o m \\[/tex]

[tex]\implies AE = 96 (0.21)m \\[/tex]

[tex]\implies AE = 20.16 \ m \\[/tex]

Hence the height of the rock ledge is 20.16 m.

_______________________________________

Part B :-

Now in ∆ACB , we have;

[tex]\implies \tan\theta =\dfrac{BC}{AC} \\[/tex]

[tex]\implies \tan 22^o =\dfrac{BC}{96m} \\[/tex]

[tex]\implies BC = 96\tan 22^o \ m \\[/tex]

[tex]\implies BC = 96(0.4) m \\[/tex]

[tex]\implies BC = 38.4 \ m \\[/tex]

Now the total height of the tree will be = BC + AE

[tex]\implies h_{tree}= BC + AE \\[/tex]

[tex]\implies h_{tree}=38.4\ m + 20.16 \ m =\boxed{58.56\ m} \\[/tex]

Hence the height of the tree is 58.56m.

and we are done!

Answer:

  (b)  No solution

Step-by-step explanation:

You want the solution to 0.5(-2+ 4d) - 2d = -13.

Eliminating the parentheses using the distributive property, we have ...

  -1 +2d -2d = -13

Collecting terms gives ...

  -1 = -13 . . . . . false

No value of d will make this true. There is No Solution.

The total displacement made by her to go from home to the school is given by the sum of the distances of P to Q, Q to R and then R to S.

The total displacement is obtained as the distance that she walks to go to the school from her home.

The check-points that she passes to go to the school are given as follows:

Hence the total displacement is given by the sum of each of these distances.

These distances are calculated using the formula for the distance between two points, given as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.

The problem is incomplete, hence the answer is given in general terms.

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The tax rate of an Item that costs $450 Before tax. and the sales tax is $31.50 is 7%

The tax rate is the percentage of an income or an amount of money that has to be paid as tax.

To find the tax rate of $31.50 from $450

The formula is

Amount taxed/Principal amount x 100

= $31.50/$450 x100

=$3150/450

=7%

Hence, the tax rate is 7%

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The distance from the top of the tree of height 30 tall to the end of the shadow is 50.

Distance is the length between two point.

To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.

Note: The tree and the shadow form a right angle.

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1

Hence, the distance from the top of the tree to the end of the shadow is 50.

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One possible equation is (6b+2)+40 = 90

That equation solves to b = 8

======================================================

Explanation:

The angles (6b+2) and 40 degrees combine to form a right angle, aka 90 degree angle. This is because the upper angle is 90 degrees, so the remaining portion is 180-90 = 90.

So (6b+2)+40 = 90 is one possible equation.

Let's solve for b.

(6b+2)+40 = 90

6b+42 = 90

6b = 90-42

6b = 48

b = 48/6

b = 8

---------------

A slight alternative.

The angles (6b+2), 40, and the 90 degree angle form a straight line.

The three angles add to 180

(6b+2)+(40)+(90) = 180 is another possible equation

6b+132 = 180

6b = 180-132

6b = 48

b = 48/6

b = 8

The rates of change in attendance in week 1-4 is 33, week 4-6 is -11, week 6-10 is -37 people per week

The rate of change in attendance with respect to time is calculated by taking the difference in attendance between two weeks and dividing by the number of weeks between those weeks. This is done to find the average rate of change in attendance per week. The formula used is:

[tex]Rate =\frac{Attendance at week 2 - Attendance at week 1}{week 2 - week 1}[/tex]

Weeks 1-4:

The rate of change in attendance with respect to time is 33 people per week. This can be calculated by taking the difference in attendance between weeks 1 and 4 (230-131) and dividing by the number of weeks between those weeks (4-1 = 3).

[tex]rate =\frac{230-131}{4-1}\\[/tex]

hence rate is 33 people per week

Weeks 4-6:

The difference in attendance between weeks 4 and 6 (230 - 208)

The number of weeks between those weeks (6-4 = 2).

[tex]rate =\frac{208-230}{6-4}[/tex]

Hence rate is -11 people per week

Weeks 6-10:

The difference in attendance between weeks 6 and 10 (60-208)

The number of weeks between those weeks (10-6 = 4).

[tex]rate=\frac{60-208}{10-6}[/tex]

Hence rate is -37 people per week

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The value of y is 130°

The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

Given here:

Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.

Thus the angle adjacent to the 50-degree angle will be 130

but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines

Hence, The value of y is 130°

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The cookies that each person bake will be:

A = 4 1/2 dozen cookies

B = 6 3/4 dozen cookies

C = 15 3/4 dozen cookies.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

Person A baked 4 1/2 Dozens of cookies for a bake sale. Person B Baked 1 1/2 as many as Person A. This will be:

= 1 1/2 × 4 1/2

= 6 3/4

Person C Baked 2 1/3 as many as Person B. This will be:

= 2 1/3 × 6 3/4

= 7/3 × 27/4

= 15 3/4

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Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.

The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.

Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.

Thus, total possibility = 10.

probability of getting 100 = 1/10

There are 5 volumes which are  less than 100 here,  [95, 99]. Thus, the probability = 5/10 = 1/2.

There are 5 values between 98 and 102 including these two values.

Hence, probability of getting these range  = 5/10 = 1/2.

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Answer:

Step-by-step explanation:

(49/72)-(13/14)

-125/504

Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.

Here,

In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.

The given function is f(x)=(5x)^2 on [1, 5].

Ax = (5-1)/N

Ax = 4/N

X = 1+iAx

X = 1+i4/N

f(x) = 25X^2

f(x) = 25(1+i4/N)^2

f(x) = 25(1+i8/N+16/N^2 i^{2})

R(N) = 1ƒ(X) Ax

Now putting the value of f(x) and Ax

R(N)==1 [25 (1+ &i + 16i2)]

R(N) = 1001 (1 +Ni + 16i2)

N100 (1+i+12)N

100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)

R(N)=100 (N + √2/ N(N+1) x 100

R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2

[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3

[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67

[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)

Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).

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The constant cost call c is $0.7 and the cost of per minute call m is $0.93.

In algebra, a system of equations consists of two or more equations and looks for ways to solve them all together. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.

Let the constant cost be c and the per minute cost be denoted by m.

The equation for 5 minutes of the call is:

5.91 = 5m + c

c = 5.91 - 5m

The equation for 10 minutes of the call is:

10.06 = 10m + c

Substitute the value of c in the above equation:

10.06 = 10m + 5.91 - 5m

10.06 - 5.91 = 5m

4.69 = 5m

m = 0.93

Substitute the value of m:

10.06 = 10(0.93) + c

c= 0.7

Hence, the constant cost call c is $0.7 and the cost of per minute call m is $0.93.

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Answer: $305

Step-by-step explanation:

1) 12.50 multiplied by 10= 125

2) 12% of 1500 is 180

3) 125+180=305

Answer: A y-intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

Slope - A number that describes both direction and steepness of the line.

Step-by-step explanation: If a line intersects the y-axis at point 5 then its y-intercept will be c= 5. As we denote y-intercept with c.

The slope is denoted by m.

Answer: 130

Step-by-step explanation:

The original price of the sweater is $303.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.

The discounted price is $91

Let the original price of the sweater be x.

So, 30% of x=91

30/100 ×x=91

0.3x=91

x=91/0.3

x=$303

Therefore, the original price of the sweater is $303.

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Answer:

x = -5

y = 2

Step-by-step explanation:

1)  -5x-4y = 17

2) 3x-4y = -23

subtract equation 2 from equation 1:

-8x + 0 = 40

-8x = 40

x = -5

substitute x = -5 into equation 1 and solve for y:

-5(-5) - 4y = 17

-4y = -8

y = 2

test answers by substituting x and y values into eqation 2:

3(-5) - 4(2) = -23   Answers are correct!

Two equations that have the same solution as the given equation are;

2.3p – 10.1 =  6.49p – 4

230p – 1010 = 650p – 400 – p

Both sides of an equation will remain equal, when both sides are

multiplied by the same amount.

The given equation: 2.3·p - 10.1 = 6.5·p - 4 - 0.01·p

Simplifying the above equation by collecting like terms gives;

2.3·p - 10.1 = 6.5·p - 0.01·p - 4 = 6.49·p - 4

2.3·p - 10.1 = 6.49·p - 4

Multiplying both sides of the original equation by 100 gives

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

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a) The portion of the garden is made up of beef steak tomatoes is 8.

b) he Equation for beef steak tomatoes is 4/5 x (portion of tomatoes).

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Portion of Garden have Tomatoes = 2/3

and, 4/5 of the tomato plants are beefsteak tomatoes.

a) The total section in model is 15.

so, Tomatoes in the garden = 2/3 x 15

                                               = 10

and, the portion of the garden is made up of beef steak tomatoes

= 10 x 4/5

= 8 portion.

b) The Equation for beef steak tomatoes

= 4/5 x (portion of tomatoes)

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Using the given function and the ordered pairs, we observed that Mr. Poppen pays more initially, to join the club

From the question, we are to determine who pays more initially to join the club between Mr. Poppen and Mrs. Zagorski  

From the given information,

"Mr. Poppen joins a fitness club which has a cost represented by the function y = 10x + 70"

The initial amount paid by Mr. Poppen is the value of y when x is 0

y = 10x + 70

y = 10(0) + 70

y = 0 + 70

y = 70

From the given ordered pairs

(0, 50)

(1, 60)

(2, 70)

(3, 80)

We can conclude that the initial amount paid by Mrs. Zagorski is 50

Hence, Mr. Poppen pays more initially

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On solving the provided question, we can say that F= The lifting force is 27135 0.003357*250*180*180 = F=27135, surface area

The total area that all of a 3D object's faces cover is the surface area. The surface area of a cube is its surface area, for instance, if we are trying to determine how much paint is needed to paint it. Always expressed in square units.

The entire surface of a three-dimensional shape is referred to as its surface area. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. Alternatively, you can label the cuboid's length, width, and height (l, w, and h), then calculate its surface area (SA) using the formula: SA=2lw+2lh+2hw.

F= k*a*v^2

a= 250

v=190

30300=k*250*{190^2}

k= 0.03357

F= 0.003357*250*180*180

F=27135

The lifting force is 27135

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Answer:

  To get black from red ...

Step-by-step explanation:

You want the know the transformation that is applied to the red graph to make it be the black graph.

We note that the vertex of the black graph is (-1, 4), which is 1 unit left and 4 units up from the vertex of the red graph.

The black graph opens downward, and has a slope of ±3 compared to the slope of ±1 for the red graph. This means it has been reflected across the x-axis and scaled by a factor of 3.

The reflection and scaling can both be accomplished by multiplying the function by -3. The translation is accomplished by adding 4 to the function value to shift it up 4 units, and adding 1 to the x-value to shift the graph left 1 unit.

The transformations applied to the red graph are ...

Answer:

x = -11, 2/3

Step-by-step explanation:

-3x^2-11x+2=0

-(3x^2+11x-2) = 0

3x^2 + 11x - 2 = 0

3x^2 + 33x - 22x - 2 = 0  ==> 33-22=11 and 33/11=3 and -22/11=-2

3x(x + 11) - 2(x + 11) = 0  ==> factor

(3x - 2)(x + 11) = 0

3x - 2 = 0                x + 11 = 0

3x = 2                x + 11 - 11 = 0 - 11

{ x = 2/3                         x = -11 } ==> x = -11, 2/3

Answer:

-15y

Step-by-step explanation:

The square root of any squared number is always the number itself.

So in this case, it is -15y

Brainliest please. It'll help a lot.

Answer:

---------------------------------

Simplify the expression:

We know the square root is never negative and since y is positive, we get:

Answer:

-3w2-11w-3

Step-by-step explanation:

take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets

2y-8x-8-5y-3x+5

note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs

then you collect like terms:

2y-5y-8x-3x-8+5= -3y-11x-3

now put substitute back w2=y and w=X

-3w2-11w-3

if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same