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1. In the scale drawing shown the room is 3 centimeters long. What is the actual length of the
room if 1 cm = 3 m?

Answer:

c.) 28

Step-by-step explanation:

I hope this helped. I know it probably doesn't. But I hope you get the question right. And I am sorry if you get it wrong.

Answer:

the exact form is 3/8

in a decimal it's 0.375

Step-by-step explanation:

Answer:

hope this helps you

We want to see if the two given lines are perpendicular or not.

We will see that yes, the lines are perpendicular.

First, let's define a general linear equation, it is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the slope of one is equal to the inverse of the opposite of the slope of the other.

Also, if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope of the line is given as:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So we can get the slopes of the two given lines, for line PQ we have:

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

For line RS we have:

[tex]a = \frac{-6 - (-1)}{15 - 10} = -1 = -(1/1)[/tex]

So you can see that the slope of line RS is equal to the inverse of the opposite of line PQ.

Then yes, the lines are perpendicular.

If you want to learn more, you can read:

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Answer:

b/e/g=63

d/c/f/h=117

Step-by-step explanation:

b , e and g=63

d,c,f, and h = 63

Answer:

a=b=e=g= 63°

d=c=h=f= 180°-63°= 117°

Answer:

-4

Step-by-step explanation:

2a2+5a2

2(-6)2=-24

5(2)2=20

-24+20=-4

Answer: -4

Step-by-step explanation:

(2x-6×2)(5×2×2)

-24+20

-4

Answer:

y = - 3x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + y = 3 ( subtract 3x from both sides )

y = - 3x + 3 ← in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + c ← is the partial equation

To find c substitute (- 1, 2) into the partial equation

2 = 3 + c ⇒ c = 2 - 3 = - 1

y = - 3x - 1 ← equation of parallel line

The required equation of line which passes through points (-1, 2) and parallel to line 3x + y = 3 is 3x + y = -1

Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.

y - y₁ = m(x - x₁)

The given equation of line,

3x + y = 3,        

The slope of the given line is -3,

The equation of the line that passes through points (-1, 2) and which is parallel to line 3x + y = 3

The slope of the required line will be same as slope of line 3x + y = 3.

The equation of line,

y - 2 = -3 (x - (-1))

y - 2 = -3 (x + 1)

y - 2 = -3x - 3

3x + y = -1

To know more about Slope on :

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Answer:

(f/g)(5) = 22

Step-by-step explanation:

All we need to do is plug in 5 for x in both f(x) and g(x) then divide the result of f(x) and g(x) to find our final answer.

Step 1: Plug in 5 for x

f(x) = 7(5) + 4(5) = 55

g(x) = 1/2(5) = 2.5

Step 2: Divide f(x) by g(x)

f(5)/g(5) = 55/2.5 = 22

And we have our final answer!

Answer:

Its A and B uwu

Answer:

i got A

Step-by-step explanation:

trust me and u welcome

Answer:

1.15 m³

Step-by-step explanation:

i hope its correct and i hope its helpful

Step-by-step explanation:

hey can yuh show work by step by step...since its hard plzz

Answer: 3/8

Step-by-step explanation:

Answer:

0.52

Step-by-step explanation:

0.52 is a decimal and 52/100 or 52% is the percentage for 13/25.

hope this is helpful:)

Answer:

The scale factor is 1/5

Step-by-step explanation:

Each of the lengths of the lengths of this triangle are divided by 5 (or multiplied by 1/5)

Answer:

So lets calculate, we know that the common multiplier is 3. So we can use the geometric sequence formula.

(ar)^(n-1)

So we have 1*3 = 3. 3 to the power of 11-1 = 10. So our answer is 3^10 or 59049. Thats the answer

The 11th term of the geometric progression is 59049

What is Geometric Progression?

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

The first term of the geometric progression is a = 1

The common ratio r = second term / first term

                                 = 3/1

                                 = 3

The number of terms n = 11

So , the equation to calculate the nth term of a GP is

aₙ = arⁿ⁻¹

Substituting the value of a , n and r  we get

a₁₁ = ar¹¹⁻¹

a₁₁ = ar¹⁰

a₁₁ = 3¹⁰

a₁₁ = 59049

Therefore the value of a₁₁ is 59049

Hence , The 11th term of the geometric progression is 59049

To learn more about geometric progression click :

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Step-by-step explanation:

To help solve this question we will put it into a ratio:

MILES:KM

5        :8              This ratio shows that 5 miles equals 8km.

47.5         :76       We can put 76 on the km side because we are told that in                                    

                            in the question. Lets find out how many times 8 was

                            multiplied to equal 76. 76 divided by 8=9.5 Because 8 was

                            multiplied by 9.5 we shall multiply 5km by 9.5  5x9.5=47.5

Therefore 76km is equal to 47.5miles.

Answer:

180°

Step-by-step explanation:

In bearing the protractor is placed in the North-South direction(eastside) thus directly north is on a bearing of 0°.After you mark the point B. A will be directly south which is on a bearing of 180°

Step-by-step explanation:

position your compass at point A and using the same distance mark arcs on line AB(mark the point it meets the line D)and AC(mark the meeting point of the arc and the line E).Place your compass at D and draw an arc at the middle of the angle,using the same measurements position your compass at point E and draw an arc.Where the two arcs meet label F using a ruler draw a straight line from F to meet point A.

Note;the width of the compass when making the arcs should be the same always

Answer:

60 buns

Step-by-step explanation:

Assuming that the 5 people eat 20 steamed buns between them and not each, that is an average of 4 buns per person. this means that they eat one bun every 50 seconds. therefore, in 5 minutes one person can eat a total of 6 buns, meaning 10 people can eat 60.

Answer:

La respuesta correcta es;

D) 55 grados

Step-by-step explanation:

Por el cual el telescopio G está ubicado en el centro del círculo con radio = HG, tenemos por teorema de círculo;

El ángulo sostenido por un arco en el centro del círculo es dos veces el ángulo sostenido por el mismo arco en la circunferencia del círculo.

Por lo tanto, por el cual el ángulo subtendido por el arco que describe el campo de visión requerido de los telescopios se da como 110° para el telescopio H en el centro del círculo con radio HG, el ángulo que el arco del campo de visión subtiende en la circunferencia, en telescopio G = 110°/2 = 55°

Por lo tanto, el telescopio G tiene que ajustar el campo de visión en 55° para cubrir la misma área que el telescopio H.

Answer:

(-1, 4)

Step-by-step explanation:

11x+5y=9

11x+3y=1

subtract side-by-side

Answer:

x=6

Step-by-step explanation:

......................

Answer:

x=6

Step-by-step explanation:

7x+2y = 48

Let y = 3

7x +2(3) = 48

7x+6 = 48

Subtract 6 from each side

7x+6-6 = 48-6

7x = 42

Divide each side by 7

7x/7 = 42/7

x = 6

Answer:

Mehmut is 8 years old.

Step-by-step explanation:

From the statement we can get the following information, let M be Mehmut's age and b brother's age:

M = 4 * b

M + 1 = 3 * (b + 1)

We replace the first equation in the second and we are left with:

4 * b + 1 = 3 * b + 3

4 * b - 3 * b = 3 - 1

b = 2

Now, we replace to calculate M:

M = 4 * b

M = 4 * 2

M = 8

Mehmut is 8 years old.

[tex]answer = 136 °\\ solution \\ x + 44 = 180(opposite \: angles \: of \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a \: cyclic \: quadrilateral \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: are \: supplementary) \\ or \: x = 180 - 44 \\ x = 136° \\ hope \: it \: helps[/tex]

Answer:

0.3

Step-by-step explanation:

3/10 = 3 : 10 = 0,3

Answer:

0.7673

Step-by-step explanation:

We have the following:

The null and alternative hypothesis is,

H0: m = 290

Ha: m> 290

x = 285.2

m = 290

sd = 59.3

n = 82

is m the mean, sd the standard deviation and n the population size

Now we calculate the value of z like this:

z = (x - m) / sd / (n ^ (1/2))

z = (285.2 - 290) / 59.3 / (82 ^ (1/2))

z = -0.73

now

P (z> -0.73) = 1 - P (z <-0.73)

we look at the normal distribution table

P = 1 - 0.2327 = 0.7673

Therefore the value of p is equal to 0.7673

Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the  first experiment she uses 6g of the chemical and in the second experiment she uses 7.8 g of the chemical

(i)Given that the amounts of the chemical used form an arithmetic progression find the total amount of  chemical used in the first 30 experiments

(ii)Instead it is given that the amounts of the chemical used for a geometric progression. Sarah has a  total of 1800 g of the chemical available. Show that the greatest number of experiments possible satisfies the inequality: [tex] 1.3^N \leq 91[/tex] and use logarithms to calculate the value of N.

Answer:

(a)963 grams

(b)N=17

Step-by-step explanation:

(a)

In the first experiment, Sarah uses 6g of the chemical

In the second experiment, Sarah uses 7.8g of the chemical

If this forms an arithmetic progression:

First term, a =6g

Common difference. d= 7.8 -6 =1.8 g

Therefore:

Total Amount of  chemical used in the first 30 experiments

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2*6+(30-1)1.8] \\=15[12+29*1.8]\\=15[12+52.2]\\=15*64.2\\=963$ grams[/tex]

Sarah uses 963 grams in the first 30 experiments.

(b) If the increase is geometric

First Term, a=6g

Common ratio, r =7.8/6 =1.3

Sarah has a total of 1800 g

Therefore:

Sum of a geometric sequence

[tex]S_n=\dfrac{a(r^N-1)}{r-1} \\1800=\dfrac{6(1.3^N-1)}{1.3-1} \\1800=\dfrac{6(1.3^N-1)}{0.3}\\$Cross multiply\\1800*0.3=6(1.3^N-1)\\6(1.3^N-1)=540\\1.3^N-1=540\div 6\\1.3^N-1=90\\1.3^N=90+1\\1.3^N=91[/tex]

Therefore, the greatest possible number of experiments satisfies the inequality

[tex] 1.3^N \leq 91[/tex]

Next, we solve for N

Changing [tex] 1.3^N \leq 91[/tex] to logarithm form, we obtain:

[tex] N \leq log_{1.3}91\\N \leq \dfrac{log 91}{log 1.3}\\ N \leq 17.19[/tex]

Therefore, the number of possible experiments, N=17

Answer:

6

Step-by-step explanation:

3 is the bottom the height is 4 because if you go to the top and count it 4 the 3x4 / 2= 6

Answer:

1. C. 1 + cot²θ = cos²θ

D. 1 - sec²θ = tan²θ

2. D. 0

3. C. Any square is a rectangle

4. C. Parallelogram

5. B. 30 m

6. A. cos(-890°) is Negative

Sin(-890°) is negative

7. A. 100·√3 m

8. [tex]\left (\dfrac{-8}{3} , \dfrac{1}{3} \right )[/tex]

9. First option, A. 68 unit

10. A. 150

Step-by-step explanation:

1. C. 1 + cot²θ = cos²θ

The correct identity is given as follows;

1 + cot²θ = csc²θ

Also

D. 1 - sec²θ = tan²θ

The correct identity is given as follows;

1 - sec²θ = -tan²θ

2. cot(-8550)

We convert -8550 to degrees by dividing by 360 and multiplying the remaining fraction by 360 as follows;

[tex]\dfrac{-8550}{360} = -23\dfrac{3}{4}[/tex]

Therefore, -8550 ≅ -3/4×360 = -270

-270 ≅ 360 - 270 = 90°

Therefore, cot(-8550) = cot(90) = 1/(tan(90)) = 1/∞ = 0

Therefore, the correct option is the option D. 0

3. The correct option is any square is a rectangle as a square (a rectangle with all sides equal) is a subset of the set of rectangles

The correct option is C. Any square is a rectangle.

4. Where the diagonals bisect each other, we have a shape where the two opposite triangle areas across the bisector are equal

Therefore, the quadrilateral is necessarily a C. Parallelogram

5. Where by the angle of depression = 45°

Therefore, the angle of elevation = 45° (Alternate angles)

The height of the building = 30 m

Therefore, tan(45°) = (30 m)/(Distance of point A from the building) = 1

∴ The distance of point A from the building = 30 m

The correct option is therefore;

B. 30 m

6. A. -890° = 190° which is in the second quadrant

Therefore, cos(190°) = Negative

B. -1200° = -120° = 240 which is in the third quadrant

Hence, tan(-1200) = tan(240) is positive

C. Sin(1200) = Sin(120) which is in the second quadrant

Hence, sin(1200) is positive

D. Sin(-890°) = Sin(190°) which is in the third quadrant

Hence, sin(-890) is negative

7. The distance from the wall where the measurement is taken = 100/(tan(30)) = 100·√3 = 173.21 m

The total height of the antenna from the ground = 173.21 × tan(45) = 100·√3 m

The total height of the antenna from the ground is 100·√3 m

The correct option is therefore;

A. 100·√3 m

8. The coordinates of the point of intersection of the medians is given by the relation;

[tex]Centroid = \left (\dfrac{x_{1}+x_{2}+x_{3}}{3} , \dfrac{y_{1}+y_{2}+y_{3}}{3} \right )[/tex]

Where:

x₁, y₁ x₂, y₂, x₃, y₃ are the coordinates of the vertices

We therefore have;

[tex]Median \, point= \left (\dfrac{(-2) +(-2)+(-4)}{3} , \dfrac{3+(-7)+5}{3} \right ) = \left (\dfrac{-8}{3} , \dfrac{1}{3} \right )[/tex]

9. The perimeter of the rhombus = 4×√(First diagonal)/2)

[tex]The \, perimeter \, of \, the \, rhombus = 4\times \sqrt{\left (\dfrac{First \, diameter}{2} \right )^{2}+ \left (\dfrac{Second \, diameter}{2} \right )^{2}}[/tex]

[tex]= 4\times \sqrt{\left (\dfrac{16}{2} \right )^{2}+ \left (\dfrac{30}{2} \right )^{2}} = 68 \ unit[/tex]

The correct option is A. 68 unit

10. The exterior angle of a regular polygon > 180°, therefore, the correct option is A. 150

Answer:

B. 46

Step-by-step explanation:

10% is equal to 1/10, so we have x/10 = 20. We multiply by 10 on both sides, leaving us with x = 200. 23% of 200 is equal to 46.