The pie chart shows how 36 pupils travel to school.
Use the pie chart to complete the table.
Bike
Walk
Travel to
school
Number
of pupils
Walk
9
120°
Car
Bus
Bus
Car
Bike
Total
36

Answer:

Step-by-step explanation:

You just need to sum up the values according to arc addition postulate:

Now we have to find,

The measure of arc AD according to the Arc Addition Postulate.

AD is the sum of the measures of the other two arcs. Then measure of AD is,

→ AC + CD

→ 35° + 45°

→ 80° (final answer)

Hence, the measure of arc AD is 80°.

Answer:

Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°

Step-by-step explanation:

To find the measure of Angle a, we add 55 and 45, then subtract the sum from 180.

180 - 100 = 80

Angle a is 80°.

Then, we solve for Angle b. Line segment CD is congruent to Line AB, so Angle b is congruent to 55°.

After that, we find Angle c. Line segment AC is congruent to Line segment BD, so Angle c is congruent to 45°.

Lastly, we solve for Angle d using the same method we used for Angle b and Angle c. Angle d is congruent to Angle a, so it measures 80°.

So, Angle a = 80°, Angle b = 55°, Angle c = 45°, Angle d = 80°.

Answer:

[tex]y = 5x + 3[/tex]

Step-by-step explanation:

Given

[tex]y = 3x - 2[/tex]

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Required

The second equation in slope intercept form

We have:

[tex]10(x + \frac{3}{5}) = 2y[/tex]

Divide both sides by 2

[tex]5(x + \frac{3}{5}) = y[/tex]

Open bracket

[tex]5x + 3 = y[/tex]

Rewrite as:

[tex]y = 5x + 3[/tex]

Hence, the equation in slope intercept form is: [tex]y = 5x + 3[/tex]

Answer: I agree with the other person

Step-by-step explanation:

The ordered pairs of the transformation are A'(1,2), B'(1,-2), C'(-2,2) of the coordinates of the triangle ABC are A(2,3),B(2,-1),C(-1,-1).

What is meant by coordinates?

They are the points which together when jointed form a triangle.

How to do transformation of a triangle?

The transformation of triangle whose coordinates are as A(2,3), B(2,-1), C(-1,-1) is done as follows:

A'=(2-1,3-1)=(1,2)

B'=(2-1,-1-1)=(1,-2)

C'=(-1-1,-1-1)=(-2,-2)

Hence the ordered pairs are (1,2)(1,-2)(-2,-2).

Learn more about transformation of a triangle at https://brainly.com/question/4289712

#SPJ2

Answer:

gradient = slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{rise}{run}[/tex]

Slope intercept Form equation : y = mx + b

m = slope or gradient

b = y - intercept ( where the line crosses the y = axis)

x and y = are place holders for a coordinate pair that makes the equation true

c) y = -6x + 8

The -6 is the m. It's the slope or gradient.

the + 8  is the b. It's the y- intercept.

d) y = 4

This is a horizontal line. It intercepts the y-axis at 4.

That means the 4 is the y-intercept.

There is no x. That means the slope is 0. The line rises 0 as it runs left to right.

e) y -4x= 0  

equation needs to be is standard form y = mx + b.

add 4x to both sides in order to isolate the y variable.

y = 4x + 0.

The slope or gradient is 4. The y - intercept is 0. The line crosses through the origin.

f) y -x = -8

Add x to both sides.

y = x - 8

There is one x.  That means the gradient is 1. The y-intercept is the -8

g) y + 3x = 7

Subtract 3x from both sides.

y = -3x + 7

-3 = gradient. 7 = y-intercept.

h) y + [tex]\frac{1}{2}[/tex]x = -4

Subtract [tex]\frac{1}{2}[/tex]x from each side.

y = -[tex]\frac{1}{2}[/tex]x - 4

One last thing. If you are presented with an equation without a y, the gradient is  'undefined'.

example : x = 4

This a vertical line passing through 4 on the x-axis. There is no 'b' because its not crossing the y-axis.

Why is it 'undefined' ?

As the line rises it, it does not 'run' left or right. [tex]\frac{rise}{0}[/tex] . Zero can never, ever be in the denominator. Denominators can't be zero. That is why we say it's 'undefined'.

Hope this helps.

Answer:

B 720

Step-by-step explanation:

same process as the previous image I sent ya

Answer:

B) 720.

Step-by-step explanation:

We can use the Binomial Expansion Theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^kb^{n-k}[/tex]

We have the expression:

[tex]\displaystyle (2x-3)^5[/tex]

Therefore, a = 2x, b = -3, and n = 5.

We want to find the coefficient of x³. To get x³, we can cube a. Therefore, we can find our coefficient by letting k = 3. Hence:

[tex]\displaystyle \binom{5}{3}(2x)^3(-3)^{5-3}[/tex]

Evaluate:

[tex]\displaystyle =10(8x^3)(9)=720x^3[/tex]

Our answer is B.

Answer: Angles of Elevation and Depression are used in measuring heights and distances in trigonometric applications using right triangles. These angles are made when we look up or down to view objects. Devices are available to measure angles of elevation and depression. These measured angles can be used in measuring heights and distance which are either tedious or impractical to measure, by modelling the situation into right triangles

Answer:

Angles of Elevation and Depression are used in measuring heights and distances in trigonometric applications using right triangles. These angles are made when we look up or down to view objects. Devices are available to measure angles of elevation and depression. These measured angles can be used in measuring heights and distance which are either tedious or impractical to measure, by modelling the situation into right triangles

Step-by-step explanation:

correct on EDGE2021

Answer:

His average speed is

12 km/hr

.

Step-by-step explanation:

Remember the triangle of Speed, Distance and Time. If you remember it, you'll ace these kinda questions.

I had trouble with these formulas but the triangle helped me a LOT! Anyways, let's get back to the question. The formula for average speed is pretty much the same as the formula for just speed. The average speed formula is

Average speed

=

Total Distance

Total Time

So......

48 km

4 hr

=

12 km/hr

My source

I hope this explanation helps you!

Answer:

3x

Step-by-step explanation:

We need to find the HCF of given two numbers .HCF is the Highest Common factor for two or more than two numbers . The given numbers are ,

[tex]\implies Numbers = 3x \ and \ 6x [/tex]

Let's factorise the numbers , we get .

[tex]\implies 3x = 3 \times x [/tex]

[tex]\implies 6x = 3\times 2 \times x [/tex]

The common factors are 3 and x . Therefore the HCF is 3 × x = 3x .

[tex]\implies\underline{\underline{ HCF = 3x }}[/tex]

Answer:

Step-by-step explanation:

the statement  0 < t < 52.5  represents all the time values for when Riko is behind Yuto,   she catches up to Yuto at 52.5 minutes into her ride.   Her ride starts at time of zero , so she can't have a negative time,  like -4  because she isn't involved in the activity of riding her bike.  

Answer:

The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.

Step-by-step explanation:

Answer:

the above answer help you.

Answer:

6

Step-by-step explanation:

Set your formula up as

15 = 2y+3

15 - 3 = 2y

12 = 2y

12 / 2 = y

6 = y

Answer:

[tex] \large{ \tt{❃ \: TAKING \: \angle \: \: A \: AS \: A \: ANGLE \: OF \: REFERENCE : }}[/tex]

[tex] \large{ \tt{❁ \: sin \: 60 \degree = \frac{perpendicular}{hypotenuse} }}[/tex]

[tex] \large{ \tt{➝ \: \frac{ \sqrt{3} }{2} = \frac{6}{y} }}[/tex]

[tex] \large{ \tt{➝ \sqrt{3}y = 6 \times 2 }}[/tex]

[tex] \large{ \tt{➝ \: \sqrt{3} \: y = 12 }}[/tex]

[tex] \large{ \tt{➝ \: y= \frac{12}{ \sqrt{ 3} } }}[/tex]

[tex] \boxed{ \large{ \tt{➝ y = \: 4 \sqrt{3} }}}[/tex]

[tex] \large{ \tt{❇ \: TAKING \: \angle \: B \: AS \: THE \: ANGLE \: OF \: REFERENCE}} : [/tex]

[tex] \large{ \tt{❊ \: sin \: 30 \degree = \frac{perpendicular}{hypotenuse} }}[/tex]

[tex] \large{ \tt{⟶ \: \frac{1}{2} = \frac{x}{4 \sqrt{3} } }}[/tex]

[tex] \large{ \tt{⟶ \: 2x = 4 \sqrt{3} }}[/tex]

[tex] \large{ \tt{⟶ \: x = \frac{4 \sqrt{3} }{2} }}[/tex]

[tex] \boxed{\large{ \tt{⟶ \: x = 2 \sqrt{3} }}}[/tex]

[tex] \boxed{ \large{ \tt{❈ \: OUR \: FINAL \: ANSWER : \boxed{ \tt \: x = 2 \sqrt{3} \: \: y = 4 \sqrt{3} }✓}}}[/tex]

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

a = 4

b = -2

Step-by-step explanation:

If the given function is continuous at x = 1

[tex]\lim_{x \to 1^{-}} f(x)=(x+1)[/tex]

                     [tex]=2[/tex]

[tex]\lim_{x \to 1^{+}} f(x)=ax+b[/tex]

                     [tex]=a+b[/tex]

[tex]\lim_{x \to 1} f(x)=ax+b[/tex]

                   [tex]=a+b[/tex]

And for the continuity of the function at x = 1,

[tex]\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)[/tex]

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

[tex]\lim_{x \to 2^{-}} f(x)=ax+b[/tex]

                     [tex]=2a+b[/tex]

[tex]\lim_{x \to 2^{+}} f(x)=3x[/tex]

                     [tex]=6[/tex]

[tex]\lim_{x \to 2} f(x)=3x[/tex]

                   [tex]=6[/tex]

Therefore, [tex]\lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)[/tex]

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2

Answer:

100

Step-by-step explanation:

add positive numbers. then subtract the negative numbers.

Answer:

1500

Step-by-step explanation:

The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,

[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]

And , the number of tiles required will be ,

[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]

Hence the required answer is 1500 .

Answer:

A) [tex]3x^{2} - x - 4[/tex]

B) [tex]-3x^{2} -4x -5[/tex]

Step-by-step explanation:

Answer:

836.8

Step-by-step explanation:

Answer:

Option number B

Step-by-step explanation:

As per the statement:

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level.

Given the equation as:

7h - 5 ( 3h -8 ) = -72

Using distributive property, 

a ⋅ ( b + c ) = a ⋅ b + a ⋅ c

7h - 15h + 40 = - 72

Combine like terms;

-8h + 40 = -72

Subtract 40 from both sides we have;

-8h 8= -112

Divide both sides by -8 we have;

h = 14 hours

Therefore, the statement is true about Pieter’s solution is, It must be a positive number since it represents a number of hours.

Answer:

4 days at least

Step-by-step explanation:

Step-by-step explanation:

angle e = 50 degree,,,,,,,

Answer:

Step-by-step explanation:

Volume of a sphere is

[tex]V=\frac{4}{3}\pi r^3[/tex] And using r = 11 and pi = 3 (which is so far off, it's ridiculous):

[tex]V=\frac{4}{3}(3)(11)^3[/tex] which gives us that

V = 5324 in³

Sin (angle) = opposite leg / hypotenuse

Sin(x) = 2.1/4

x = arcsin(21./4)

x = 31.7 degrees

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

Explanation:

I'm assuming that segments AD and CD are tangents to the circle.

We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.

By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.

----------------------------

Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.

Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.

We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.

---------------------------

Here's what we have so far for quadrilateral DAEC

Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees

A+E+C+D = 360

90+100+90+D = 360

D+280 = 360

D = 360-280

D = 80

Or a shortcut you can take is to realize that angles E and D are supplementary

E+D = 180

100+D = 180

D = 180-100

D = 80

This only works if AD and CD are tangents.

Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.

Answer:

5√2

Step-by-step explanation:

Finding distance :-

Answer:

. JUST LOAD

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Firstly, we solve for x

-x ≥ 2 * 4

-x ≥ 8

Multiply both sides by -1

x ≤ -8

So we look at the inequality represented by this;

We can see that the correct inequality is option B;