Don was thinking about buying a flat screen TV. The store marks it as
55 inches. (TV dimensions are given as diagonals.) If the length of the
TV is 35.51 inches, how tall is the TV?

Answer:

BC = 1 [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AB}{DE}[/tex] ( substitute values )

[tex]\frac{BC}{4}[/tex] = [tex]\frac{\frac{3}{4} }{\frac{5}{2} }[/tex] ( 2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex] )

cross- multiply

[tex]\frac{5}{2}[/tex] BC = 4 × [tex]\frac{3}{4}[/tex] = 3 ( multiply both sides by 2 to clear the fraction )

5 BC = 6 ( divide both sides by 5 )

BC = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex]

Answer:

20

Step-by-step explanation:

so if you do 3 -1 = 2

so 2 portions = 10

divide by 2

so 1 portion = 5

so do 5 x 1 = 5

5 x 3 = 15

5 + 15 = 20

so 20 students in total

if you do inverse you can check if it's right

hope this works :)

The total number of students who went on the field trip will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The proportion of young men to young ladies on the school field trip was 3:1. assuming there were 10 a larger number of young men than there were young ladies.

Let 'B' be the number of boys and 'G' be the number of girls. Then the equations are given as,

B/G = 3/1

B = 3G                 ....1

B = G + 10          ....2

From equations 1 and 2, then we have

3G = G + 10

2G = 10

G = 5

Then the number of boys is given as,

B = 5 + 10

B = 15

Then the total number of students who went on the field trip will be given as,

⇒ 5 + 15

⇒ 20

The total number of students who went on the field trip will be 20.

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Answer:

X=6,2

Step-by-step explanation:

If the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

Given that the top 2% of athletes will go pro.

We are required to find the Z-Score that is required to be the top 2%.

A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured basically in terms of standard deviations from the mean.

Because only 2% of the top is pro then it will be a two tailed test. The required percentage will be 2/2=1%

The value which we will require to catch up from table=0.01

Z value will be 0.0438 (Z table is attached)

Hence if the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

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The distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

Two points J(-2 , 6) and K(1 , 4) are given .

We have to find out the distance between two points.

What is the distance formula ?

The distance formula is [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] where two points are ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]).

As per the question ;

J ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) = J (-2 , 6) and K ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = K (1 , 4)

and

The distance formula is ;

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex]

So ,

The distance between points J(-2 , 6) and K(1 , 4) will be ;

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

= [tex]\sqrt{(-3)^{2} + (2)^{2} }[/tex]

= [tex]\sqrt{(9)+ (4)}[/tex]

= √13

= 3.6 ( round to nearest tenth)

Thus , the distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

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The following is the absolute value equation for figuring out the maximum and minimum period of time: t = |d/v| + |25/v|.

The parameters provided;

The number of hours required for the plane to travel just at given values is determined as follows:

Time= distance / speed

The equation for calculating the maximum number of hours is as follows:

t = (d + 25)/v = (160 + 25)/150

t = 1.23 hours.

The equation and for shortest number of hours is as follows:

t = (d - 25)/v = (160 - 25)/150

t = 0.9 hours.

Thus, the absolute value equation for determining the maximum and minimum amount of time is as follows:

t = |d/v| + |25/v|.

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None of the equations are correct.

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. In other languages, the word equation and its cognates may have slightly different meanings. In French, an équation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

For perpendicular equations, the product of slope is -1, but none of the options here is have slope whose product with the given equation is -1.

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Answer:

NAH THIS ANSWER IS EASY: ANSWER 2500

Step-by-step explanation:

Answer:

198.5

Step-by-step explanation:

The unit rate represented by the information is  6/5 mile per hour

The given parameters are

Distance = 2/5 mile

Time = 1/3 hour

The ratio of distance in time is calculated as

Ratio = Distance : Time

This gives

Ratio = 2/5 mile : 1/3 hour

Divide both ratio by 1/3

So, we have

Ratio = 6/5 mile : 1 hour

Express as fraction

Ratio = 6/5 mile/1 hour

This gives

Ratio = 6/5 mile per hour

Hence, the unit rate represented by the information is  6/5 mile per hour

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150 is   the cost of renting a car from YourPal.

What is surface area of cuboid ?

Let y = total charge for a car rental and x = miles driven

Proxy car equation: y = 0.32x + 18

YourPal equation: y = 0.36x + 12

Set equations right sides equal to each other... meaning their cost, y, are equal

0.32x + 18 = 0.36x + 12

18 = 0.04x + 12  (subtract 0.32x from both sides of the equation)

6 = 0.04x            (subtract 12 from both sides of the equation)

150 = x               (divide both sides of the equation by 0.04)

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The common difference of arithmetic sequence is 10.

according to a = 2 and d = 3, the sequence. Solution: We apply the method for finding the nth term to locate a specific term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the numbers a = 2 and d = 3 into the formula to determine the nth term.

This is an arithmetic sequence.

a = 11

d = a2 - a1

d = 22 - 11

d = 10

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Answer:

[tex] \frac{2}{10} \\ \\ 0.2[/tex]

Answer:

40

Step-by-step explanation:

accumulated vacation Minus used vacation = remaining vacation

55  -15 = 40

A chord is a segment with endpoints on the circle. EF, DF are chords of the circle.

The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.

A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.

A chord is a segment with endpoints on the circle.

Therefore, EF, DF are chords of the circle.

The complete question is:

Identify each.

a chord

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With the help of linear equtions it can be concluded that we downloaded 54 songs in which 28 songs were free and 26 songs were paid.

A linear equation is an algebraic equation in which each term has an exponent of one and when graphed produces a straight line. That's why it is considered a 'linear equation.'

Let a represent paid downloaded songs.

Total cost of songs downloaded = a x cost of each additional download.

a x $0.59 = $0.59a

The overall cost of downloaded songs is $15.34.

$15.34 =   $0.59a

Divide both sides of the equation by  $0.59.

a = 26 songs

We downloaded 26 paid songs.

Total songs downloaded = total free songs + total paid songs

Total songs downloaded = 26 + 28 = 54 songs

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Answer:

[tex]\boxed{y = \dfrac{1}{4}x -4}[/tex]

Step-by-step explanation:

The slope-intercept form of a line equation is y = mx + b[tex]\sf\\\\To\;find\;b, \;plug \;in \;the \;values\; of\; (4, - 3) \;which \;corresponds\; to\; x = 4, y = -3 \;into \;the \;above \;equation:\\== > - 3 = \dfrac{1}{4}\cdot 4 + b\\\\Switching\;sides,\\\dfrac{1}{4}\cdot 4 + b = -3\\\\Simplifying\\1 + b = -3\\\\b = -3 -1 = -4\\So\; the\; equation \;of \;the\; perpendicular\; line \;is: \boxed{y = \dfrac{1}{4}x -4}[/tex]

A perpendicular line will have slope is  [tex]-\dfrac{1}{m}[/tex]

The perpendicular line will have a slope which is the negative of the reciprocal of the first line

Here the line is 4x + y =3

This can be re-written as y = -4x + 3

Slope of this line is -4

[tex]\sf Reciprocal \; of-4 = -\dfrac{1}{4}[/tex]

[tex]\sf Negative \; of \; reciprocal = -(-\dfrac{1}{4}) = \dfrac{1}{4}[/tex]

[tex]\sf So\;slope\;of\;perpendicular\;line=\dfrac{1}{4}\\Equation \;of \;the \;perpendicular\; line\; is \;y = \dfrac{1}{4}x + b \;where \;b \;is \;the\; y\; intercept[/tex]

Answer:

17

Step-by-step explanation:

3(2)2+(35÷5) = 12+7 = 19

[hope it helps, im not sure if its exactly what you need]

Answer: 88

Explanation: You always round up if the number before is greater than 4!

The midpoint is at (3/10 , 3/2 , 4/10)

In the given statement is

To find the midpoint of the line segment joining the pair of points

F (3/5, 0, 4/5) and G(0,3,0)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points F (3/5, 0, 4/5) and G(0,3,0)

Solving for the midpoint , we have,

m = ([tex]\frac{3/5+0}{2} , \frac{0+3}{2} ,\frac{4/5+0}{2}[/tex])

m = (3/10 , 3/2 , 4/10)

Therefore, the midpoint is at (3/10 , 3/2 , 4/10)

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Answer:

x=ay/4 +3

Step-by-step explanation:

Answer: [tex]2x^{2} +17x+36[/tex]

Step-by-step explanation:

FOIL:
[tex]2x^{2} +8x+8x+36[/tex]

Combine like terms:

[tex]2x^{2} +17x+36[/tex]

The linear equation, he makes approximately 9 balls in the next three baskets and the balls in the first match.

According to the statement

We have to find that the Number of the basket in the each of the game.

So, For this purpose, we know that the

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

From the given information:

Marcus made 6 baskets in his first basketball game. In each of the next 4 games,he made the same number of baskets. If he made a total of 34 baskets.

Then

In first game = 6 basket ball.

The linear equation form is a

3x +6 = 34

Then

3x =  34 - 6

3x  = 28

x = 28/3

x = 9.3

After conclusion, The basket in the first game is a 6 baskets and in the next 3 games he makes a 28 baskets.

So, The linear equation, he makes approximately 9 balls in the next three baskets and the balls in the first match.

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A. For every 4 apples, there are 3 oranges.

B. The ratio of bananas to oranges is 6:3

C. The ratio of apples to bananas is 4 to 6.

D. For every 1 orange, there are 2 bananas.

The team's expected value for a hand is 0.75.

Probability:

Probability refers the possible occurrence of any required event.

Given,

You are playing a team card game where a team can get 0 points, 1 point, or 3 points for a hand.

The probability of your team getting 1 point for a hand is 60% and of getting 3 points for a hand is 5% .

Here we need to find the team's expected value for a hand.

The expected value is calculated by the sum of the product of each point value and its corresponding probability.

So, the sum of the each probability value is,

E = sum ( point value x probability)

E = 0 + (1 x 60%) + (3 x 5%)

Convert the percentage values onto decimal,

Then

E = 0 + ( 1 x 0.60) + (3 x 0.05)

E = 0 + 0.60 + 0.15

E = 0.75

Therefore, the team's expected value for a hand is 0.75.

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2.4 f of snow would fall in March.

Given that

Delphine's home received 40% 40% 40% 40% more snowfall in March compared to February.

now find the Delphine's house had fff centimeters of snowfall in February.

Let f represent the volume of snow that fell in February.

If there is 40% more snowfall in February than there was in March,

Consequently, the snowfall would be

[tex]f+( \frac{100+40}{100} )f[/tex]

[tex]f+( \frac{140}{100} )f[/tex]

f + 1.4f

2.4f

Therefore, 2.4f of snow would fall in march.

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When dividing 28 by 263.2, the approximate quotient is 0.1062 (rounded to four decimal places).

To divide 28 by 263.2, we can perform the division operation as follows:

Dividend ÷ Divisor = Quotient

Here, the dividend is 28, and the divisor is 263.2.

To simplify the division, we can remove the decimal point by multiplying both the dividend and divisor by a power of 10. In this case, we can multiply by 10 to eliminate the decimal point.

28 * 10 = 280

263.2 * 10 = 2632

Now, we can perform the division:

280 ÷ 2632 ≈ 0.10621761658

Hence, when dividing 28 by 263.2, the approximate quotient is 0.1062 (rounded to four decimal places).

In summary, to divide a number by another number, we divide the whole numbers and the decimal numbers separately, considering the appropriate place values, and then combine the results to obtain the final quotient.

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The value of HI is 28.

Given that HJ=7x-27, HI=3x-5 and IJ=x-1 as shown in the attached image.

We have to find the value of HI.

As a line given in image it shows that the line HJ is the sum of Hi and IJ and we can write it as

HI+IJ=HJ

Now, we will substitute all the given values which is shown in the attached image, we get

3x-5+x-1=7x-27

Now, we will simplify the left-hand side by combining all the like terms, we get

4x-6=7x-27

Further, we will subract 4x from both sides, we get

4x-6-4x=7x-27-4x

6=3x-27

Furthermore, we will add 27 on both sides, we get

6+27=3x-27+27

33=3x

Now, we will divide by 3 from both sides, we get

33/3=3x/3

11=x

Further, we will simplify the value of HI by substituting the value of x, we get

HI=3x-5

HI=3(11)-5

HI=33-5

HI=28

Hence, the value of HI when HJ=7x-27 and the attached image is 28.

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2)Main Answer: a)1,8,27,64,125,216,343,512

                        b)I,II,III,IV,V,VI,VII,VIII,IX,X,XI                                    

Concept and definitions should be there:

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

Given data

a)Next five terms 1,8,27,64

b)Next five terms I,II,III,IV,V

Solving part

using conjecture

a)Next five terms 1,8,27,64,125,216,343,512

Notice that the difference between consecutive terms is 7.

Conjecture: n3, n=1,2,3...

Final Answer:1,8,27,64,125,216,343,512

b))Next five terms I,II,III,IV,V,VI,VII,VIII,IX,X,XI

Conjecture: n, n=i,ii,iii,...

Final Answe:I,II,III,IV,V,VI,VII,VIII,IX,X,XI

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3)Quastion incompleted

4)Main answer :The number 14 is even and therefore is divisible by 2. This is the correct statement.

Given data

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

Solving part

The number 14 is even and therefore is divisible by 2. This is the correct statement.

Final Answer:The number 14 is even and therefore is divisible by 2. This is the correct statement.

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5)Main Answer:X = -2

Concept and definitions should be there:This solution deals with linear equations with one unknown.

Given data

18x-2(3x+1)=5x-16

Solving part

We simplify the equation first:

18x−2(3x+1)=5x−16

18x+(−2)(3x)+(−2)(1)=5x+−16 (Distribute)

18x+−6x+−2=5x+−16

(18x+−6x)+(−2)=5x−16 (Combine Like Terms)

12x+−2=5x−16

12x−2=5x−16

Then we cancel out:

12x−2−5x=5x−16−5x

7x−2=−16

7x−2+2=−16+2

7x=−14

7x/7 = −14/7

x = -2

Final Answer:x = -2

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Using the Factor Theorem, the quadratic functions are given as follows:

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

[tex]x_1 = -3, x_2 = 8[/tex]

Hence:

f(x) = a(x + 3)(x - 8)

f(x) = a(x² - 5x - 24).

It opens upward with a positive leading coefficient, that is, a > 0, hence one example is a = 1 as follows:

f(x) = x² - 5x - 24.

It opens downward with a negative leading coefficient, that is, a < 0, hence one example is a = -1 as follows:

f(x) = -x² + 5x + 24.

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