2 points How Did I Do? The cost of renting a car is $42 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=42+0.25x , where x is the number of miles traveled.

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!

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 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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After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.

A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.

given,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.

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The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.

Here we have two perfect square trinomials, these are:

(A + B)^2

(A - B)^2

Notice that the only difference between these is the sign of the second element.

Now we can expand these two expressions as:

(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2

The second expression gives:

(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2

                                       = A^2 - 2AB + B^2

There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.

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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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Answer:

3x - y = 2

Step-by-step explanation:

pick 2 points on the line:  (0, -2), (2, 4)

find slope (m):

m = (4-(-2))/(2-0) = 6/2 = 3

write the equation in point-slope form first:

y - y1 = m(x - x1)

plug in a point: (2,4)

y - 4 = 3(x - 2)

y - 4 = 3x-6

now write it in standard form:  Ax + By = C

3x - 6 = y - 4

3x - y = 2

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

On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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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:

  (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.

Answer:

A) Technically he/she can, but they shouldn't really.

B) Yes

C) Yes

D) Yes he/she can but is not necessary to solve the equation

E) Yes

Answer: 800 more hours is required to fly an aircraft

Step-by-step explanation:

The amount of syrup she needs is 3/4 cups of syrup. Option A

A fraction can be described as the part of a whole variable, element or number.

The several types of fractions are;

Also, proportion can be defined as a mathematical comparison between two numbers

From the information given, we have that;

6 cups of soap = 1 /4 cup of syrup

Then 18 cups of soap = x cups of syrup

cross multiply, we get;

6x = 18(1/4)

multiply the values

6x = 18/ 4

Divide both sides by the coefficient of x , we get;

x = 18/ 4 × 1/6

x = 3/ 4 cup of syrup

Hence, the value is 3/4

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Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

The 95% confidence interval for the proportion of people who prefer Candidate A is given as follows:

(0.438, 0.522).

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The parameters for this problem are given as follows:

[tex]n = 550, \pi = \frac{264}{550} = 0.48[/tex]

Hence the lower bound of the interval is obtained as follows:

[tex]0.48 - 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.438[/tex]

The upper bound of the interval is obtained as follows:

[tex]0.48 + 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.522[/tex]

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Solving the provided question, we can say that the quadratic equation is [tex]-16t^2 +vt +s[/tex] so answer is -16+48+3 = 35

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

[tex]-16t^2 +vt +s[/tex]

v = 16

s =3

t =

so answer is -16+48+3 = 35

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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!

Answer:

which of the following is not a true statement 4/6 equals 8/12 2/3 equals 10/15 2/10 equals 3/15 3/4 equal 6/9

Step-by-step explanation:

Answer:

8 hours and 45 minutes.

Step-by-step explanation:

Step-by-step explanation:

system 1 :

3x + 2y = 7

4x + 7y = 17

system 2 :

12x + 2y = 28

4x + 7y = 17

the first equation in the second system is not a multiple of either equation in the first system, and the second equation in the second system is the same as the second equation in the first system.

thus, the systems are not equivalent.

"12x" gives us the idea what the factor would have to be (4 or 3), if the second equation of the second system would be a multiple of any of the equations in the first system.

as we would have to multiply 3x by 4 to get 12x, and 4x by 3 to get 12x.

but then 2y×4 = 8y, or 2y×3 = 6y, and that is not the same as 2y (part of the first equation of the second system).

that is why this first equation of the second system is not a multiple of either equation in the first system.

and that makes it impossible for both systems to be equivalent. that the second equations are identical, is then not relevant anymore.

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

The distance between points E(-8, 7) and L(-1, 4) on the coordinate plane is √58 units

An equation shows how two or more numbers and variables are related to each other.

The distance between two points in the coordinate plane is given as:

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

The distance between points E(-8, 7) and L(-1, 4) is:

[tex]EL = \sqrt{(4-7)^2+(-1-(-8))^2}=\sqrt{58}[/tex]

The distance is √58 units

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Answer:

226a³b² - 824ab³ + 984b⁴

Step-by-step explanation:

We can factorize the given expression by expanding the two binomials and then combining like terms.

First, expand the two binomials:

10ab (a − 2b)³ +24ab² (3a − 6b)² = 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

Then, combine like terms:

= 10ab(a³ - 6a²b + 12ab² - 8b³) + 24ab²(9a² - 36ab + 36b²)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= (10a³b + 216a³b² - 60a²b² - 864ab³ + 120ab³ + 864b⁴ - 80b⁴)

= (10a³b - 60a²b² + 120ab³ - 80b⁴) + (216a³b² - 864ab³ + 864b⁴)

= 226a³b² - 824ab³ + 984b⁴

Given ,

To Find : The Circumference of a circle

Radius can be the determined by the formula

[tex]r = \frac{d}{2} \\r = \frac{18}{2} \\r = 9yd[/tex]

Now we can apply the formula of the circumference of a circle which is,

[tex]Circumference = 2\pi r[/tex]

[tex]Circumference = 2X3.14X9[/tex]

[tex]Circumference = 56.52[/tex]

Hence , the Circumference of a circle is 56.52yd

So the person talked for 6 minutes.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

To solve this problem, we can use the following equation:

Cost = (Number of minutes x $0.31) + $0.89 + $1.23

We know that cost is $6.15 and the call lasted 6 hours. Since there are 60 minutes in an hour, we can convert the time in hours to minutes by multiplying 6 hours by 60 minutes/hour

So the number of minutes is 6 hours * 60 minutes/hour = 360 minutes

Now we can substitute the values into the equation:

Cost = (360 minutes x $0.31) + $0.89 + $1.23

Cost = $111.6 + $0.89 + $1.23

Cost = $113.72

The equation does not match the $6.15 cost, which means that the person talked for 6 minutes

So the person talked for 6 minutes.

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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

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

Answer: 1000 times less

Step-by-step explanation: multiply 0.054x1000

Answer:

1000 times

Step-by-step explanation:

To find how many times less 0.054 is than 54,

we can divide 54 by 0.054.

This gives us 54/0.054 = 1000

This means that 0.054 is 1000 times less than 54.

Answer:

x–2, x ≠ -3

Step-by-step explanation:

Solution in the diagram