Don has a box of colored pencils. He uses 53 pencils And has 118 pencils left in the box.Write an equation to showing how many pencils are in the box before he starts drawing.

The features that Michael should include on the graph of the parabola are given as follows:

The parabola for this problem is defined as follows:

y = -0.5(x - 3)² - 1.

Comparing to the vertex form definition, the coordinates of the vertex are given as follows:

(3, -1).

The equation can also be written as follows:

-0.5(x - 3)² = y + 1

(x - 3)² = -2(y + 1).

Then the coefficient p is obtained as follows:

4p = -2

p = -0.5

Then the coordinates of the focus are given as follows:

(3, -1 - 0.5) = (3, -3/2),

The equation of the directrix is then given as follows:

y = 1 - 0.5

y = 1/2.

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In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time

so finding intersection point of the y=4/x and y=16x

4/x=16x

=>  = 1/4

=> x = 1/2 as x>0

and y=16x

=> y =8

now finding intersection point of y=4/x and y=1/16x

=> 4/x =x/16

=>  = 64

=> x = 8 as x>0

and y= 4/x

=> y=1/2

now finding intersection point of y=16x and y=1/16x

the intersection point of both line is x=0

so y=16x

=> y=0

so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.

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The length of the curve x = 1/3 √y (y − 3)  is 64/3.

The distance between two point along a segment of a curve is known as the arc length.

The equation of the curve is given by:

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) between point  x =a to x = b is given by:  

[tex]\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx[/tex]

 √1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 * [tex]y^\frac{3}{2}[/tex] - [tex]y^\frac{1}{2}[/tex]

Let's find the first derivative of x.

dx/dy = 1/3. 3/2.  [tex]y^\frac{1}{2}[/tex]- 1/2 .  [tex]y^\frac{1}{2}[/tex]

dx/ dy = 1/2 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])

(dx/dy)^2= 1/4 (  [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])^2

= 1/4(y + [tex]y^-^1[/tex]-2)

1 + {f′(x)}2 = 1 + 1/4(y +[tex]y^-^1[/tex]-2)

= 1/4 y + 1/4[tex]y^-^1[/tex]+ 1/2

1 + {f′(x)}2= 1/4 (y + [tex]y^-^1[/tex] + 2)

√[1 + {f′(x)}2] = 1/2 (  [tex]y^\frac{1}{2}[/tex] +  [tex]y^\frac{-1}{2}[/tex])

Length of curve  is given by:  

25

∫   [tex]\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }[/tex] dy

16

= [tex]\left \{ {{y=25} \atop {x=16}} \right.[/tex] [[tex]y^\frac{3}{2}[/tex]/3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

So the length of the curve is 64/3

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The given statement is true that the points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

A line that splits another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to create a perpendicular bisector.

When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.

"Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints".

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Answer:

3/5

Step-by-step explanation:

AB = AC · cos A

18 = 30 · cos A

cos A = 18/30

cos A = 3/5

The two simultaneous equations are 50x + 25y = 250 and x + y = 7

Simultaneous equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations

Assuming the bottle of soda has 50 grams of sugar in each bottle (since this information is not given). Let the bottles of soda bought be x and bottles of juice bought be y. Two equations will be formed so that we can solve them simultaneously.

50x = total amount of sugar in soda bottles

25y = total amount of sugar in juice bottles

50x + 25y = 250 (total amount of sugar in all bottles)

x + y = 7 (total number of bottles)

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Both equations y = 0.5x + 2.75 and y – 0.5x = 2.75 are equal. Hence, these systems will have infinite solutions. Hence, Option a is the most suitable answer to this question.

The system of equations having an infinite number of solutions must be the same.

In option a -

we have, y = 0.5x + 2.75 and 2y = x + 2.75

Rewriting the second equation 2y = x + 2.75 in slope-intercept form, we get,

2y = x + 2.75

y = x/2 + 2.75/2

y = 0.5x + 1.375

Both equations are not similar.

Hence this option is not the right choice.

Similarly, we will check for option b -

we have, y = 0.5x + 2.75 and y – 0.5x = 2.75

From the second equation y - 0.5x = 2.75, this can be expressed as y = 0.5x + 2.75 in the slope-intercept form.

Here, we get both equations equal.

Thus,  y = 0.5x + 2.75 and y – 0.5x = 2.75 will have infinite solutions.

Similarly, checking for other options, we do not get any similar equations.

Hence, option b is the correct answer to this question.

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The complete question is -

Which systems have infinite solutions? Check all that apply.

a) y = 0.5x + 2.75 and 2y = x + 2.75

b) y = 0.5x + 2.75 and y – 0.5x = 2.75

c) y = 0.5x + 2.75 and 0.5x + y = 2.75

d) y = 0.5x + 2.75 and y = 0.5(x + 5.5)

e) y = 0.5x + 2.75 and y = –2(–0.25x )+ 2.75

Answer: look at the screenshot below I hope it helps you, my friend

have a lovely day :3 :) :D

UWU

Step-by-step explanation:

Answer:

750 ft

Step-by-step explanation:

the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.

let h be the height of the cell phone tower

We require the dimensions to be the same, using the conversion

1 foot = 12 inches , then

10 ft = 10 × 12 = 120 in

125 ft = 125 × 12 = 1500 in

then we obtain

[tex]\frac{h}{1500}[/tex] = [tex]\frac{120}{20}[/tex] =  6 ( multiply both sides by 1500 to clear the fraction )

h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )

h = 9000 in ÷ 12 = 750 ft

that is the cell phone tower is 750 ft tall.

Confounding variables is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers.

Confounding variables are those that have an effect on other factors in such a way that misleading or distorted relationships between two variables result. They misinterpret the "real" relationship between two variables. Confounding variable illustration You track sunburns and ice cream consumption. You discover that eating more ice cream increases your chances of becoming sunburned. To establish if a particular risk factor produced confounding, compare the estimated measure of association before and after controlling for confounding. To put it another way, compute the measure of association before and after correcting for a potential confounding factor.

Here,

Confounding variables are the terms used to explain these other elements that may have an influence on tea users' stress levels.

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A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.

The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.

This ratio can be expressed as a fraction: 8/5.

To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.

We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.

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Answer:

78

Step-by-step explanation:

The answer is 78 or 87 dear friend its a mystery

[tex]-\cfrac{5}{7}(-42k-56)\implies -\cfrac{5}{7}(-42k)\left[ -\cfrac{5}{7}(-56) \right]\implies +\cfrac{5}{7}(42k)+\left[ \cfrac{5}{7}(56) \right] \\\\\\ \cfrac{5(42k)}{7}+ \cfrac{5(56)}{7}\implies 5\cdot \cfrac{42}{7}k + 5\cdot\cfrac{56}{7}\implies 5\cdot 6k+5\cdot 8\implies {\Large \begin{array}{llll} 30k+40 \end{array}}[/tex]

The time that has elapsed since Gerardo started walking away from car will be equal to 5 seconds.

We solve this problem by converting it into a linear equation that has three variables in it. Since we have distance, time and speed the three variables will be d, t and s respectively. The expression which shows the distance of Gerardo will be expressed as

d = (s×t) + 9; we have the constant as 9 because Gerardo was 9 feet away from his car.

Now, we have the distance as d = 24 feet and the speed is constant that is equal to 3 feet per second and we need time which will be

24 = (3×t) + 9

15 = 3×t

=> t = 15/3

=> t = 5 seconds

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Answer:

first equation = red line

second equation = blue line

Step-by-step explanation:

First, we solve for y for both equations

4x + 2y = -12

2y = -12 - 4x

2y = -4x -12

y = -2x - 6

3x - 5y = -35

-5y = -35 - 3x

-5y = -3x - 35

y = (-3/5)x + 7

It's equation in point-slope from is -1/6x+5/2.

An equation is a formula that is express the equality of two equation.

Based on the given condition the formula

M= -1/6

Substitute {m -1/6

                        { X= 9

                        {Y = 1

(Into y= mx+b)

1=-1/6×9+b

Reduce the expression into the Lowest term

1=-1/2×3+b

Write as a single fraction

1=-3/2+b

Rearrange variables to the left side of the equation.

-b= -3/2-1

Now we have to find the denominator and write the numerators above common denominator

-b=-3-2/2

Calculate the sum or difference

-b=-5/2

b=5/2

Substitute {m=-1/6 b=5/2 into y mx+b

Y=-1/6x+5/2

Rewrite the equation of the line

Y= -1/6x+5/2 in point-slope

Y-1 = -x-9/6

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they belong to high-performance athletes

It may be a sign of a family history of early heart disease.  If one of your close relatives, such as a parent or sibling, has experienced a heart attack, a stroke, or was previously diagnosed with heart disease before the age of 60. Thus, option B, C is correct.

The CDC's Response to the Risk Factors in the Country. Leading causes of heart disease and stroke risk factors include high blood pressure, high levels of low-density lipoprotein (LDL) cholesterol, diabetes, smoking, exposure to second-hand smoke, obesity, a poor diet, and inactivity.

People who are aware of their situation make wiser decisions, live longer, and experience greater well-being. Even if you have heart failure, it is still possible to lead a regular life. The secret to success is realizing heart failure and taking charge of it.

Therefore, They are from well-trained professional athletes, and They are from individuals with a history of heart disease.

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The question is incomplete, complete question with option given below:

Three hearts are dissected from individuals with unknown histories. Two of the three hearts are enlarged. Select all of the possible reasons the two hearts may be enlarged.

A. They are from individuals who had low blood pressure histories.

B. They are from well-trained professional athletes.

C. They are from individuals with a history of heart disease.

D. They are from individuals who had arthritis issues.

The value of y in the equation 14.25y = 99.75 is C. 7.00.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is given as:

14.25y = 99.75

Divide through by 14.25

y = 99.75 / 14.25

y = 7

The value of y is 7.

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The correct expression that has a product greater than 4 is one hundred and one hundredths times four.

There are four expressions given as

(a) four hundredths of a percent

= 4 × 99/100

= 4 × 0.99

= 3.96

(b) four times the eighth

= 4 × 8/8

= 4 × 1

= 4

(c) four times three-fourths

= 3/4 × 4

= 3

(d) one hundred and one hundredths multiplied by four

= 1.01 × 4

= 4.04

As a result, the expression with a product greater than four is one hundred and one hundredths times four.

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The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.

The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.

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Answer:

[tex]\frac{3}{5\pi}[/tex]

Step-by-step explanation:

[tex]\frac{f(5\pi/6)-f(0)}{5\pi/6}=\frac{3}{5\pi}[/tex]

Answer:

-5/4

Step-by-step explanation:

the main answer is -5/4

Answer:

0 Joules (No work)

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.

Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.

the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in is[tex]487.5lb .[/tex]

Calculate the moment of inertia by using following expression,

\begin{aligned}

[tex]I & =\frac{1}{12} b d^3 \\& =\frac{1}{12} \times 6 \times(4)^3 \\& =32 \mathrm{in}^4\end{aligned}\\[/tex]

The centroid at center is,

[tex]\begin{aligned}Q & =\bar{y}_1 A \\& =1 \times 6 \times 2 \\& =12 \mathrm{in}^3\end{aligned}$$[/tex][tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}$$[/tex]

The shear flow is,

[tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}[/tex]

Since, there is 3 rows of nails so the shear force resisted by each nail is,

[tex]\begin{aligned}\tau & =\frac{1}{3} q s \\& =\frac{1}{3} \times 243.75 \times 6 \\& =487.5 \mathrm{lb}\end{aligned}$$[/tex]

Therefore, the shear force resisted by each nail is 487.5

[tex]487.5lb .[/tex]

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The true statement is (d) the angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

From the question, we have the following parameters that can be used in our computation:

Trapezoid PQRS

The transformation is given as

As  a general rule of transformation, reflection and rotation are rigid transformations and they do not change the size and angles in a shape

This means that we get a congruent figure to that figure after the transformations

Thus, when PQRS is reflected and rotated 90° about the origin to form trapezoid KLMN, the trapezoid KLMN is congruent to trapezoid PQRS.

⇒  By the definition of congruence,

The corresponding sides and angle of trapezoid KLMN are congruent to that of trapezoid PQRS.

⇒ ∠P ≅ ∠K, ∠Q ≅ ∠L, ∠R ≅ ∠M and  ∠S ≅ ∠N

⇒ Option D) is correct.

Note:  KMLN is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

Since, trapezoid KMLN is congruent to trapezoid PQRS.

⇒ Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid KMLN = Area of trapezoid PQRS

Thus, Option C) is incorrect.

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Complete question

Trapezoid PQRS is shown on the coordinate plane. If trapezoid PQRS is reflected across the y-axis and rotated 90° clockwise about the origin to form trapezoid KLMN, which must

A) The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid KLMN.

B) Trapezoid PQRS is not congruent to trapezoid KLMN

C) The area of trapezoid PQRS is less than the area of trapezoid KLMN

D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

Answer:

The observation in the upper right corner of the plot is influential for the least-squares regression line.

Step-by-step explanation:

Answer:

6i-4

Step-by-step explanation:

To simplify the expression 4i+(8-3i) - 12+√-25, you can start by combining like terms.

First, you can combine the terms 4i and -3i to get 1i. You can also combine the constants 8 and -12 to get -4.

So, the expression becomes 1i - 4 + √-25.

Next, you can simplify the square root. √-25 is the same as √(-25) which is the same as √(5*-5), which is the same as 5√(-1). √(-1) is equal to i, so 5√(-1) is equal to 5i.

Therefore, the final simplified form of the expression is 1i - 4 + 5i, which is equal to 6i - 4.

Answer:

op

Step-by-step explanation:

Approximately, Brianne percentage rate of contribution is 0.5%.

Brianne's annual contribution to her union dues is $200. Her salary is $38,500.

Approximately, her percentage rate of contribution can be calculated as follows:

percentage rate of contribution = union dues / salary × 100

union dues = 200 dollars

salary = 38500

percentage rate of contribution = 200 / 38500 × 100

percentage rate of contribution = 20000 / 38500

percentage rate of contribution =  0.51948051948

Therefore,

percentage rate of contribution ≈ 0.5%

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