a 500-foot weather
tower used to measure wind speed has a guy wire attached to it 200 feet above the ground. The angle between the wire and the vertical tower is 47 degrees. Approximate the length of the guy wire to the nearest foot.

Answer:

y-1=-3/5(x-3)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-1)/(-2-3)

m=3/-5

m=-3/5

y-y1=m(x-x1)

y-1=-3/5(x-3)

Answer:

Step-by-step explanation:

△ABC is isosceles. So ∠3 = ∠4

given 1 ≅ 3.

therefore, 1 ≅ 4

alternate interior angles are equal if only AB//CD

Answer:

10.5 units (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

Note that AB and CD are horizontal lines because A and B have the same y coordinate, and C and D have the same y coordinate. As a result, I can simply subtract their x coordinate values to find length of AB and CD.

Answer:

Step-by-step explanation:

Answer:

f(x) = x³ - x² - 6x

Step-by-step explanation:

If a polynomial f(x) has roots x = a and x = b then the factors are

(x - a) and (x - b) and the polynomial is the product of the factors, that is

f(x) = (x - a)(x - b)

Here the roots are x = 3, x = - 2 and x = 0, thus

(x - 3), (x - (- 2)) and (x - 0) are the factors, that is

(x - 3), (x + 2) and x , hence the polynomial is

f(x) = x(x - 3)(x + 2) ← expand the pair of factors

     = x(x² - x - 6) ← distribute parenthesis by x

     = x³ - x² - 6x

Answer:

y= 3x +1

Step-by-step explanation:

Let's write the equation of the line in slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Start by finding the slope with the formula below:

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Slope

[tex]=\frac{10-(-2)}{3-(-1)}[/tex]

[tex]=\frac{10+2}{3+1}[/tex]

[tex]=\frac{12}{4}[/tex]

= 3

Substitute m= 3 into the equation:

y= 3x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -1, y= -2,

-2= 3(-1) +c

-2= -3 +c

c= -2 +3

c= 1

Thus, the equation of the line is y= 3x +1.

_______

Alternatively, we can write the equation in the point-slope form.

[tex]\boxed{y-y_1=m(x-x_1)}[/tex]

Substitute m= 3 and a pair of coordinates into [tex](x_1,y_1)[/tex]:

y -10= 3(x -3)

Additional:

For more questions on writing equations of line, check out:

The equation which passes through the points  (-1,-2)and(3,10) will be y= 3x +1

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Let's write the equation of the line in slope-intercept form. That is, y= mx+c, where m is the slope and c is the y-intercept.

Start by finding the slope with the formula below:

[tex]\rm Slope =\dfrac{y_1-y_2}{x_1-x_2}[/tex]

Slope

[tex]\rm Slope =\dfrac{10-(-2)}{3-(-1)}[/tex]

[tex]\rm Slope=\dfrac{12}{4}[/tex]

Slope = 3

Substitute m= 3 into the equation:

y   =  3x +  c

To find the value of c, substitute a pair of coordinates into the equation.

When x= -1, y= -2,

-2   =   3(-1) +  c

-2= -3  +  c

c  =  -2  +  3

c  =   1

Thus, the equation of the line is y  =   3x +  1.

Alternatively, we can write the equation in the point-slope form.

y  -  y₁  =  m ( x - x₁ )

Substitute m= 3 and a pair of coordinates into :

y  - 10  =  3 ( x  - 3 )

Therefore the equation which passes through the points  (-1,-2)and(3,10) will be y= 3x +1

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To find the width of each strip, divide the total width of the cloth by the number of strips required.

To find the width of each strip, we need to divide the total width of the cloth by the number of strips required. Let's assume the width of the cloth is W. So, each strip would get a width of W/10.

Answer:

[tex]x=115^o[/tex]

Step-by-step explanation:

Angles Inside a Polygon

A polygon of n sides must have the sum of its internal angles  

[tex]S=180^o(n-2)[/tex]

The polygon shown in the figure has n=5 sides, so the sum of its internal angles is

[tex]S=180^o(5-2)=540^o[/tex]

The construction of the internal angles of the polygon is shown in the image below. The sum of them is

[tex]50+180-x+180-x+360-x+x=540[/tex]

Reducing

[tex]-2x+770=540[/tex]

Solving

[tex]\displaystyle x=\frac{770-540}{2}[/tex]

[tex]\boxed{x=115^o}[/tex]

Answer:

x is 115 degrees

Step-by-step explanation:

Answer:

The distance cover by Mai's bike is 2 time the distance cover by Noah's bike

Step-by-step explanation:

Given as :

The distance cover by Mai's bike = [tex]d_1[/tex] = 7 [tex]\dfrac{1}{4}[/tex] miles

I.e [tex]d_1[/tex] = [tex]\dfrac{28+1}{4}[/tex] miles

Or, [tex]d_1[/tex] = [tex]\dfrac{29}{4}[/tex] miles

The distance cover by Noah's bike = [tex]d_2[/tex] = 3 [tex]\dfrac{5}{8}[/tex] miles

I.e [tex]d_2[/tex] = [tex]\dfrac{24 + 5}{8}[/tex] miles

Or,  [tex]d_2[/tex] = [tex]\dfrac{29}{8}[/tex] miles

let the number of times that Noah's bike ride was Mai's bike ride = n

So, The distance cover by Mai's bike = n × The distance cover by Noah's bike

Or, [tex]d_[/tex] = n ×  [tex]d_[/tex]

Or, [tex]\dfrac{29}{4}[/tex] miles =  n × [tex]\dfrac{29}{8}[/tex] miles

Or, n = [tex]\frac{\frac{29}{4}}{\frac{29}{8}}[/tex]

∴ n = [tex]\dfrac{8}{4}[/tex]

I.e n = 2

Hence The distance cover by Mai's bike is 2 time the distance cover by Noah's bike  . Answer

Explanation: All fractions positive or negative are rational numbers so 3/2 must be rational. Another way to think about rational numbers is that if you can turn the number into a fraction, it's rational. Since 3/2 is already in fraction form, it's a rational number.

Answer:

See explanation

Step-by-step explanation:

a1) Given

[tex]\angle A\cong \angle C\\ \\\angle ABD\cong \angle CDB[/tex]

   Statement               Reason

1. [tex]\angle A\cong \angle C[/tex]   - Given

2. [tex]\angle ABD\cong \angle CDB[/tex]   - Given

3. [tex]\overline{BD}\cong \overline{DB}[/tex]  - Reflexive property

4. [tex]\triangle ABD\cong \triangle CDB[/tex]  - AAS postulate

5. [tex]\overline {AB}\cong \overline{CD}[/tex] - Congruent triangles have congruent corresponding parts

6. [tex]AB=CD[/tex]   - Definition of congruent segments

a2) Given

[tex]\overline{H O}\parallel \overline{E N}\\ \\H W=N W[/tex]

Statement Reason

1. [tex]H W=W N[/tex] - Given

2. [tex]\overline{H O}\parallel \overline{E N}[/tex] - Given

3. [tex]\angle O H W\cong \angle E N W[/tex] - Alternate interior angles theorem (two parallel lines H O and E N are cut by transversal H N)

4. [tex]\angle H W O\cong \angle N W E[/tex] - Vertical angles theorem

5. [tex]\triangle H O W\cong \triangle N E W[/tex] - ASA postulate

b) Given

[tex]PO=PR\\ \\OS=RS\\ \\\angle O\cong \angle R\\ \\m\angle P=90^{\circ}[/tex]

   Statement               Reason

1. [tex]m\angle P=90^{\circ}[/tex]   - Given

2. [tex]\triangle OPE, \triangle RPN[/tex] are right triangles   - Definition of right triangles

3. [tex]\angle O\cong \angle R[/tex]  - Given

4. [tex]PO=PR[/tex]  - Given  

5. [tex]\triangle POE\cong \triangle PRN[/tex]  - HA postulate

6. [tex]OS=RS[/tex] - Given

7. [tex]\angle O\cong \angle R[/tex] - Given

8. [tex]\angle OSN\cong \angle SRE[/tex] - Vertical angles theorem

9. [tex]\triangle SON\cong \triangle SRE[/tex] - ASA postulate

c1) Given

[tex]\overline{SA}\parallel \overline{NE}\\ \\\overline{SE}\parallel \overline{NA}[/tex]

   Statement               Reason

1. [tex]\overline{SA}\parallel \overline{NE}[/tex]   - Given

2. [tex]\angle ENS\cong \angle ASN[/tex]   - Alternate interior angles theorem (two parallel lines SA and NE are cut by transversal SN)

3. [tex]\overline{SE}\parallel \overline{NA}[/tex]  - Given

4. [tex]\angle ESN\cong \angle ANS[/tex]   - Alternate interior angles theorem (two parallel lines SE and NA are cut by transversal SN)  

5. [tex]\overline{SN}\cong \overline{NS}[/tex] - Reflexive property

6. [tex]SN=NS[/tex] - Definition of congruent segments

7. [tex]\triangle ENS\cong \triangle ASN[/tex]  - ASA postulate

8. [tex]\overline{SA}\cong \overline {NE}[/tex]  - Congruent triangles have congruent corresponding parts

9. [tex]SA=NE[/tex]   - Definition of congruent segments

c2) Given

[tex]\angle BTO\cong \angle IWE\\ \\\overline{WI}\cong \overline{BT}\\ \\\overline{OW}\cong \overline{ET}[/tex]

   Statement               Reason

1. [tex]\angle BTO\cong \angle IWE[/tex]   - Given

2. [tex]\overline{WI}\cong \overline{BT}[/tex]   - Given

3. [tex]\overline{OW}\cong \overline{ET}[/tex]  - Given

4. [tex]\overline{WT}\cong \overline{TW}[/tex]   - Reflexive property  

5. [tex]WI=BT[/tex] - Definition of congruent segments

6. [tex]OW=ET[/tex] - Definition of congruent segments

7. [tex]WT=TW[/tex] - Definition of congruent segments

8. [tex]OT=OW+WT[/tex] - Segment addition postulate

9. [tex]WE=WT+TE[/tex] - Segment addition postulate

10. [tex]OW+WT=ET+WT[/tex] - Substitution property

11. [tex]OT=WE[/tex] - Substitution property

12. [tex]\triangle BOT\cong \triangle IEW[/tex]  - SAS postulate

Answer:

What he said

Step-by-step explanation:

Answer:

9 * 10^7.

Step-by-step explanation:

(3 * 10^5) * (3 * 10^2)

= 3 * 3 * 10^5 * 10^2

= 9 *  10^(5+2)

= 9 * 10^7.

Question:

before last nights game a basketball player has scored an average ( arithmetic mean) of 20 points per game . she scored 25 points in last nights game raising her average go 21 points per game. how many games did she play before last night's game

Answer:

She played 4 games before last night's game

Step-by-step explanation:

Given:

Average of last night basketball games = 20

Points scored in last night game =  25

Rise in average after last night game =  21

To Find:

The number  of games played last night = ?

Solution:

Let the number of games played before last night's game be x

Then

The average of x games =20

That is

[tex]\frac{\text{ Total points scored in x games}}{x}= 20[/tex]

Total  points scored in x games = 20x

In last night game she scored 25 points

So now the total score will be  = 20x+25 and

the number of games will be x+1

Now the

The average of x+1 games = 21

[tex]\frac{20x+25}{x+1}[/tex] =21

[tex]20x+25 =21 \times (x+1) [/tex]

[tex]20x+25 =21x+ 21[/tex]

[tex]25-21 =21x-20x[/tex]

x=4

Answer:

16

Step-by-step explanation:

8(19-17)=8(2)=16

Check the picture below.

Answer:

9%

Step-by-step explanation:

9/100 = 0.09

To convert to a percent, multiply by 100 and add a percent sign:

0.09 * 100 = 9%

Answer: 9%

Step-by-step explanation:

I Looked it up online.

2.14 kilometers of road is built each day

Solution:

Given that road is 10 kilometers long

The crew worked for [tex]4\frac{2}{3}[/tex] days

To find: Kilometers of road build each day

Assume they built the same amount each day

Length of road = 10 km

number of days worked = [tex]4\frac{2}{3} = \frac{3 \times 4 + 2}{3} = \frac{14}{3}[/tex]

Kilometers of road build each day is given as:

Kilometers of road build each day = total length of road divided by number of days the crew worked

[tex]\rightarrow \frac{10}{\frac{14}{3}}=\frac{10}{1} \times \frac{3}{14}=2.14[/tex]

Thus 2.14 kilometers of road is built each day

Answer:

16.5.

Step-by-step explanation:

This is an arithmetic series because the increase is a constant 0.30.

Sum of n terms = (n/2)[a + l)    where n = no.of terms a = first term , l = last term.

There are 3/ 0.3 = 10 terms so

Sum = (10/2) (0.3 + 3.0)

= 5 * 3.3

= 16.5.

Answer:

1. Emily scored 60 points in the first round

2. Emily scored minus 30 points in the second round

3. Emily's final score is 15 points.

Step-by-step explanation:

1. Let's review all the information given to us to answer the questions correctly:

Points awarded for a correct answer = 20

Points deducted for a incorrect answer = 10

2. Let's calculate the score of Emily in the first round:

Score = 7 * 20 - 8 * 10

Score = 140 - 80

Score = 60

Emily scored 60 points in the first round

3. Let's calculate the score of Emily in the second round:

Score = 4 * 20 - 11 * 10

Score = 80 - 110

Score = - 30

Emily scored minus 30 points in the second round

4. Let's calculate the final score of Emily:

Final score = (Score 1st round + Score 2nd round)/2

Final score = (60 + - 30)/2

Final score = (60 - 30)/2 = 30/2 = 15

Emily's final score is 15 points.

Domain of the function f(x)=3x^3 is 2,5 what is the function range?

Answer:

The range of given function is {24, 375}

Solution:

Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)

So we can substitute the given domain values of "x" in f(x) and find the range of function

As per the given question:

The domain of the function [tex]f(x) = 3x^3[/tex] is, [2, 5]

We have to find the range of the function

Substitute x = 2 in f(x)

[tex]f(x) = 3x^3[/tex]

[tex]f(2) = 3 (2)^3 = 3(8) = 24[/tex]

Substitute x = 5 in f(x)

[tex]f(5) = 3(5)^3 = 3 \times 125 = 375[/tex]

Therefore range of given function is {24, 375}

The value of x is 30

Solution:

Given that measure of exterior angle of regular polygon is 2x

The measure of interior angle is 4x

To find: value of x

The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)

measure of exterior angle + measure of interior angle = 180

2x + 4x = 180

6x = 180

x = 30

Finding the measure of an exterior angle

measure of exterior angle = 2x = 2(30) = 60 degrees

Finding the measure of interior angle

measure of interior angle = 4x = 4(30) = 120 degrees

Answer:

y=4x+8

Step-by-step explanation:

I assume you want this rewritten in slope intercept form. That means we need to isolate the y.

-4x+y=-8

Add 4x to both sides

y=-8+4x

Now let's rewrite it in slope intercept form. Recall slope intercept form is y=mx+b. That means our 'b' (8) must be on the end of the equation.

y=4x+8

Answer:

B, C, D

Step-by-step explanation:

The information given about the teachers is limited to the fact they teach preschool.

B and D. If a teacher has more experience teaching, they are probably better at teaching. Even if the subject is not reading, they gain transferable teaching skills with experience.

C. Although both teachers teach preschool, one may have many more years of experience or other qualifications, which will likely help them to teach better in generally.

A. The samples 30 and 40 students in a typical class are enough to show different students' various learning styles and strengths. The sample size is big enough.

Answer:

Step-by-step explanation:

2x^2 - 98 = 2 * ( x^2 - 49)

          = 2 * (x^2 - 7^2)

          = 2 * (x+7) * (x-7)    {a²-b² = (a+b)(a-b)}

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

Answer:

114791256

Step-by-step explanation:

27*17=486

486^3=114791256

Answer:

y + 9 = 6(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 6 and (a, b) = (4, - 9), thus

y - (- 9) = 6(x - 4), that is

y + 9 = 6(x - 4)

Answer:

384 + c = m.

Step-by-step explanation:

You can use another variable such as t to represent "total." I used m to represent total "miles." The variable you use to represent the total shouldn't matter but these two variables make the most sense. 384 for last year's miles plus c, which is this year's miles, equals the total miles. A very simple, straight forward and easy equation to write.

Answer:

6 plus or minus square root of 37/2

Step-by-step explanation:

Is the quadratic formula allowed or no?

Answer:

t = 3 ± ½√37

Step-by-step explanation:

0 = -16t² + 96t + 4

This isn't factorable, so complete the square or use quadratic formula.  Completing the square:

16t² − 96t = 4

t² − 6t = 1/4

t² − 6t + 9 = 1/4 + 9

(t − 3)² = 37/4

t − 3 = ±½√37

t = 3 ± ½√37

Answer: The variable is 3.

Step-by-step explanation: 5x3=15. 15+8=23

Please Mark Me Braineilest

Answer:

The probability of winning = 0.001 and hence the expected payoff = $0.

Step-by-step explanation:

There is a lottery contest and there are 1000 entries.

Only one will win and will get a prize of $710. All others would be given nothing.

We have to find the probability of the person winning.

Probability = [tex]\frac{number of favorable events}{total number of events}[/tex]

Number of favorable events = 1

Total number = 1000

So probability of winning the payoff = [tex]\frac{1}{1000}[/tex] = 0.001

Hence the expected payoff = $0

The school council will have 216 small sandwiches.

Step-by-step explanation:

Sandwiches ordered = 12

Length of one sandwich = 6 feet

1 foot = 12 inch

6 feet = 12*6 = 72 inches

Length of one sandwich in inches = 72 inches

As one small sandwich is 4 inches,

Number of small sandwiches in one sandwich = [tex]\frac{72}{4}=18[/tex]

One sandwich = 18 small sandwiches

12 sandwiches = 18*12 = 216 small sandwiches

The school council will have 216 small sandwiches.

Keywords: multiplication, division

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