A VERTICAL POLE OF CAST A SHADOW OF 4.5m LONG AT THE SAME TIME A TREE OF HEIGHT 24m LONG CAST A SHADOW OF 6m LONG. FIND THE HEIGHT OF THE POLE.​

Answer:

d. [tex]\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG[/tex]

Step-by-step explanation:

Here, we are given a diagram in which there are two triangles to be considered:

[tex]\triangle CJG \ and\ \triangle BJI[/tex].

We can consider the whole diagram in the form as attached in the answer area.

To find:

The conditions to prove [tex]\triangle CJG \sim \triangle BJI[/tex].

Solution:

First of all, let us learn about AAA similarity.

AAA stands for Angle Angle Angle.

i.e. when we prove that the all the three corresponding angles of two triangles are equal ,the triangles are similar.

There is one more property of the triangles, that if two angles of two triangles are equal then the third angle of the triangles will also be equal to each other.

So, actually, to prove that [tex]\triangle CJG \sim \triangle BJI[/tex], we need the conditions that two corresponding angles of the triangles are equal to each other, then we can say that third angle will also be equal. Therefore the triangles will be similar to each other.

Let us consider the corresponding angles:

[tex]\angle BIJ \ and \ \angle CGJ\ ,\ \angle BJI \ and \ \angle CJG\ , \ \angle IBJ\ and \ \angle GCJ[/tex]

So, if we are given that any of the two above three pairs are equal/congruent to each other, we can prove [tex]\triangle CJG \sim \triangle BJI[/tex].

Therefore, the correct answer is:

d. [tex]\angle BIJ \cong \angle CGJ\ and\ \angle BJI \cong \angle CJG[/tex]

Answer:

y = -3/4 x + 25/2

Step-by-step explanation:

x² + y² = 100

Take derivative with respect to x.

2x + 2y dy/dx = 0

2y dy/dx = -2x

dy/dx = -x/y

Evaluate at (6, 8).

dy/dx = -6/8

dy/dx = -3/4

Use point-slope form to write equation:

y − 8 = -3/4 (x − 6)

Simplify.

y − 8 = -3/4 x + 9/2

y = -3/4 x + 25/2

Answer:

17 quarters

Step-by-step explanation:

Let q = quarters

n = nickels

.25q + .05n = 5.90

we have 16 more nickels than quarters so add 16 quarters to make them equal

n = q+16

Substitute

.25q + .05( q+16) = 5.90

Distribute

.25q+.5q+.80=5.90

Combine like terms

.30q +.8 = 5.90

Subtract .8 from each side

.30q = 5.10

Divide each side by .3

.3q/.3 = 5.1/.3

q = 17

Answer:

Gisel have:

17

quarters

Step-by-step explanation:

1 nickel = 5 cents

1 quarter = 25 cents

1 dollar = 100 cents

5,90 dollars = 5,9*100 = 590 cents

then:

n = t + 16

5n + 25t = 590

n = quantity of nickels

t = quantity of quarters

5(t+16) + 25t = 590

5*t + 5*16 + 25t = 590

5t + 80 + 25t = 590

30 t = 590 - 80

30 t = 510

t = 510 / 30

t = 17

n = t + 16

n = 17 + 16

n = 33

Check:

5n + 25t = 590

5*33 + 25*17 = 590

165 + 425 = 590

Answer:

32

Step-by-step explanation:

We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.

Answer:

32.

Step-by-step explanation:

Let's say the number we are trying to find is x.

24 = 0.75x

0.75x = 24

x = 24 / 0.75

x = 32

Hope this helps!

The area is:

A = πR² ------- 2π

A = x --------- π/6

x = πR²/12

x = π.(10)²/12

x =  26.18 in²

Hope it helps x

━━━━━━━☆☆━━━━━━━

▹ Answer

2 5/6

▹ Step-by-Step Explanation

[tex]\frac{17}{6} \\\\6 * 2 = 12\\12 + 5 = 17\\\\2\frac{5}{6}[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

2 5/6

Step-by-step explanation:

17/6

6 goes into 17 2 times  

2*6 = 12

17-12 = 5  

There is a remainder of 5  this goes over the denominator

2 5/6

Hey there! I'm happy to help!

We see that 500 languages is a certain percent of the 7,111 total languages. When working with percent equations, the word "is" means "equals", and "of" usually means "multiplied by" This means that 500 is equal to a certain percent multiplied by 7,111. We can use p to represent this certain percent and create an equation below.

500=7,111p

Let's flip the equation around so the p is on the left side. Variables are usually supposed to be on the left.

7,111p=500

We divide both sides by 7,111.

p=0.0703

As a percent, this is about 7.03%. Therefore, about 7.03% of the total languages spoken globally are represented on WikiTongues.

I hope that this helps! Have a wonderful day! :D

Answer:

7.03 %

Step-by-step explanation:

500 / 7,111 = 0.07031359865

0.07031359865  x 100 = 7.03 %

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

Explanation:

Arcs CBH and FGH are given, while arc CDF is unknown. Let's call this y

y = measure of arc CDF

Adding the three arcs forms a full circle of 360 degrees

(arc CBH)+(arc FGH)+(arc CDF) = 360

170+64+y = 360

y+234 = 360

y = 360-234

y = 126

arc CDF = 126 degrees

Then notice how inscribed angle x cuts off arc CDF. By the inscribed angle theorem, we take half of the arc measure to get the inscribed angle measure.

inscribed angle = (arc measure)/2

x = (arc CDF)/2

x = 126/2

x = 63

Answer:

rewrite the fromula 126

Step-by-step explanation:

Answer:

Length of the longest side = 17 units

Step-by-step explanation:

Given:

Three sides of triangle

A = 7

B = x+4

C = 2x + 1

Perimeter of the triangle = 36

Find:

Length of the longest side

Computation:

We know that

Perimeter of the triangle = A + B + C

Perimeter of the triangle = 7 + x + 4 + 2x + 1

36 = 12 + 3x

24 = 3x

x = 8

So

Side B = 8 + 4 = 12 unit

Side C = 2(8) + 1 = 17 units

Length of the longest side = 17 units

Answer:

17.

Explaination:

Dunno. I just put it on paper, and did the calculations there.

Answer:

[tex] y = x + 4 [/tex]

Step-by-step explanation:

Use the two-point form of the equation of a line.

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

[tex] y - 4 = \dfrac{16 - 4}{12 - 0}(x - 0) [/tex]

[tex] y - 4 = \dfrac{12}{12}x [/tex]

[tex] y - 4 = x [/tex]

[tex] y = x + 4 [/tex]

Answer:

y = x + 4

Step-by-step explanation:

An equation for a line looks like:

=> y = mx +b

=> In this equation "m" is the slope.

=> "b" is the y-intercept.

To find the slope:

=> y/x - y1/x1

=> 16/12 - 4/0

=> 16 -4 / 12 - 0

=> 12 / 12

=> 1

So, the slope is 1.

Now our equation looks like:

y = 1x + b

=> y = x + b

Let's take some the values of "x" and "y"  of (0,4)

So, our now look like:

=> 4 = 1 (0) + b

=> 4 = b

So, b (y-intercept) = 4

Now, our final equation is:

=> y = x + 4

The equation that could best represent the line of best fit for the given data is; y = 0.625x

The formula for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept which is the point where the line intersects the y-axis

Now, in this question, we see that the line intersects the y-axis at 0. Thus;

y-intercept; c = 0

Now, let us find the slope from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

Using the first and penultimate coordinate which are;

(0, 0) and (8, 5), we have;

m = (5 - 0)/(8 - 0)

m = 0.625

Thus, the equation is;

y = 0.625x

Read more about Scatter plot equation at; https://brainly.com/question/6592115

#SPJ1

Answer:

y=0.625x

Step-by-step explanation:

plato

Answer:

See below.

Step-by-step explanation:

[tex]f(x)=-x^2+6x-11\\f(x-3)=-(x-3)^2+6(x-3)-11\\f(x-3)=-(x^2-6x+9)+6x-18-11\\f(x-3)=-x^2+6x-9+6x-29\\f(x-3)=-x^2+12x-38[/tex]

Step-by-step explanation:

First you have to add up all of the numbers that make up the perimeter of this arrow.

3+3+1+.5+.5+1.8+1.8=11.6

You than want to divide this number by 2 to find the half perimeter you have to work with, which is 5.8.

A simple shape you can make is a square, with each side being 1.45 m.

Answer:

P = 27.2c-7.2d

Step-by-step explanation:

It is given that,

The width of a rectangle is (8.3c-8.4d)

The length of a rectangle is (5.3c+4.8d)

The perimeter of a rectangle is equal to the sum of its all sides i.e.

P = 2(l+b)

P = 2(8.3c-8.4d+5.3c+4.8d)

P = 2[(8.3c+5.3c)+(4.8d-8.4d)]

P = 2(13.6c-3.6d)

⇒P = 27.2c-7.2d

Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.

Answer:

Graph D

Step-by-step explanation:

(h)t = -16t^2 + 80

At time t = 0 the screwdriver is at 0+80 =80 ft

As time increases the height will decrease so we can eliminate graph B

We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A

We need to find where it meets the x axis

0 = -16t^2 + 80

-80 = -16t^2

5 = t^2

t = sqrt(5)

t =2.23

This is Graph D

Answer:

x = -2/3 , 2

Step-by-step explanation:

Factor 2  out of   6 x^ 2 − 8 x − 8

2 ( 3 x^ 2 − 4 x − 4 ) = 0

Factor

2 ( 3 x + 2 ) ( x − 2 ) = 0

Set  3 x + 2  equal to  0  and solve for  x

x = -2/3

Set  x − 2  equal to  0  and solve for  x

x = 2

The final solution is all the values that make 2 ( 3 x + 2 ) ( x − 2 ) = 0

x = -2/3 , 2

Hope this can help you

Answer:

x+5=19

Step-by-step explanation:

i think that right let me know...:/

Answer:

x= 14

Step-by-step explanation:

a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes

x+5=19

19-5=x

14=x

Answer:  20

Step-by-step explanation:

Given: Total students at the dinner = 100

Number of fish entrees = 40

Number of pasta entrees = 60

Number of students chose neither entree = 20

Now , Number of students chose either fish or pasta = (Total students) - (Number of students chose neither entree)

= 100-20

= 80

Now , Number of students chose either fish or pasta = (Number of fish entrees) + (Number of pasta entrees)- (Number of students chose both)

⇒ Number of students chose both = (Number of fish entrees) +(Number of pasta entrees)-(Number of students chose either fish or pasta)

= 40+60-80

= 20

Hence, the number of students were served two entrees = 20

20 students were served two entrees.

Given,

total student pass through cafeteria line and were served meal is 100.

No. of students choose fish entries is 40.

No. of students choose pasta entrees is 60.

No. of student choose neither entree is 20.

We have to calculate the no. of students served two entrees.

Now Number of students chose either fish or pasta will be,

[tex]N=100-20[/tex]

[tex]N=80[/tex]

Now no. of students choose both will be,

[tex]N=(fish\ entree+\ pasta \ entree )-Entree\ either \ pasta \ or \ fish[/tex]

[tex]N=60+40-80[/tex]

[tex]N=20[/tex]

Hence 20 students were served two entrees.

For more details follow the link:

https://brainly.com/question/24550771

[tex]-25(x - 4) = -55(x - 10)\\-25x+100=-55x+550\\30x=450\\x=\dfrac{450}{30}=15[/tex]

Answer:

x=15

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer

y>2/3 x +1 is your answer (B)

Answer:

Option B is the correct option.

Step-by-step explanation:

point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1

point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3

Now, let's find the slope:

Slope ( m ) = [tex] = \frac{y2 - y1}{x2 - x1} [/tex]

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

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

[tex] = \frac{4}{6} [/tex]

[tex] = \frac{2}{3} [/tex]

At ( 3 , - 1 )

y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis

[tex] - 1 = \frac{2}{3} \times ( - 3) + c[/tex]

Solve for c

[tex] - 1 + 2 = c[/tex]

[tex]c = 1[/tex]

Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.

The answer would be:

[tex]y > \frac{2}{3} x + 1[/tex]

Hope I helped!

Best regards!

Answer:

$240 extra

Step-by-step explanation:

1/3(7200) + 12(420) = 2400 + 5040 = 7440

7440 - 7200 = 240

The customer had to pay 1720 extra.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A car is priced at $7200.

If the deposit is one third = 7200/3

                                          = 240

The amount after 12 payments will be

= 240 x 12

= 2880

total cost will be

= 2880 + 2400

= 5280

and, The customer had to pay extra amount

= 7200 - 5280

= 1720

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ5

Answer:

x=8

Step-by-step explanation:

4:3=x:6

Multiply the first set by 2

4*2 : 3*2

8:6

That means x =8

Answer:

That Ratios aren't equal.

Step-by-step explanation:

Given: DE is || to BC.

So in order to make this false then we have to say that the sides aren't proprtional, making it not possible to get the ratios equal.

(See the Triangle proprtionality theorem or the triangle midsegment theorem)      

Answer:

4:10 ≠ 6:14

Step-by-step explanation:

bc i said so

Answer:

18 : 30

Step-by-step explanation:

Our ratio could look like this:

Number of games won : Number of games played

6 : 10

=> .6 : 1

Let's check whether the 1st option is correct.

=>  18 : 20

=> 1 x 20 = 20

=> .6 x 20 = 12

=> 12 : 20 is not equal to 18 : 20

The second option is 100% incorrect because the number of games won is greater than the number of games played.

let's check whether the 3rd option is correct.

=> 18 : 30

=> 1 x 30 = 30

=> .6 x 30 = 18

18 : 30 = 18: 30

So, the 3rd option is correct.

Answer:

18:30

Step-by-step explanation:

The ratio of games is 6 won out of 10 games

The ratio at the bottom that is 6:10 is

18:30

Divide each side by 3

18/3 : 30/3

6:10

Answer:

Value of x is -3

Step-by-step explanation:

Given:

5x + 15 = 0

Find:

Value of x

Computation:

5x + 15 = 0

From subtracting 15 from both side (LHS and RHS)

5x + 15 – 15 = 0 – 15

5x = -15

From dividing 5 from both side (LHS and RHS)

5x / 5 = -15 / 5

x = -3

So,

Value of x is -3

Answer:

LN = 6

Step-by-step explanation:

Since M is on LN, then

LN = LM + MN = 4 + 2 = 6

Answer:

[tex]\huge \boxed{6}[/tex]

Step-by-step explanation:

Point M is on the line segment LN.

LM = 4

MN = 2

LN = LM + MN

LN = 4 + 2 = 6

Answer:

m∠C = 102°

Step-by-step explanation:

This is a quadrilateral inscribed in a circle

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

We know what m∠B

We have external angles outside the circle.

m∠CDA is opposite m∠B

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA is the sum of m∠CD and m∠DA

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

m∠DAB is an exterior angle also, hence,

m∠DAB is the sum of m∠DA and m∠AB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Finally we can solve for m∠C

m∠DAB is Opposite m∠C

So, m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Answer:

Step-by-step explanation:

Yes, due to the presence of that operator " i "

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

Use law of cosines to find angle A

a^2 = b^2 + c^2 - 2*b*c*cos(A)

9^2 = 6^2 + 14^2 - 2*6*14*cos(A)

81 = 36 + 196 - 168*cos(A)

81 = 232 - 168*cos(A)

81 - 232  = -168*cos(A)

-151  = -168*cos(A)

-168*cos(A) = -151

cos(A) = (-151)/(-168)

cos(A) = 0.8988095

A = arccos(0.8988095)

A = 25.9979801

A = 26 degrees approximately

The angle m∠A will be 27. so option C is correct.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

Use law of cosines to find angle A

a^2 = b^2 + c^2 - 2*b*c*cos(A)

9^2 = 6^2 + 14^2 - 2*6*14*cos(A)

81 = 36 + 196 - 168*cos(A)

81 = 232 - 168*cos(A)

81 - 232  = -168*cos(A)

-151  = -168*cos(A)

-168*cos(A) = -151

cos(A) = (-151)/(-168)

cos(A) = 0.8988095

A = 25.9979801

A = 26 degrees approximately

Therefore, the angle m∠A will be 27. so option C is correct.

Learn more about sine to cosine conversion here:

https://brainly.com/question/1421592

#SPJ5

Answer:

m<C = 102°

Step-by-step explanation:

Step 1: find measure of arc BC.

According to the Inscribed angle theorem of a circle, an inscribed angle is half the measure of the arc it intercepts.

m<D intercepts arc ABC

thus, 80° = ½(120+BC)

Solve for BC. Multiply both sides by 2

80*2 = 120 + BC

160 = 120 + BC

BC = 160 - 120 = 40°

Step 2: Find m < A

According to the Inscribed angle theorem, m < A = ½ of arc BCD = ½(40 + 116)

m < A = 78°

Step 3: find m < C

m < A + m < C = 180 (opposite angles of an inscribed quadrilateral are supplementary)

m < C = 180 - 78 = 102°