3. Given the graph below, determine whether each statement is true or false.

Answer:

A.]A chord of a circle of diameter 40 cm subtends an angle of 70° at the centre of the circle.

Solution given;

diameter [d]=40cm

centre angle [C]=70°

(a) Find the perpendicular distance be tween the chord and the centre of the circle.

Answer:

we have

the perpendicular distance be tween the chord and the centre of the circle=[P]let

we have

P=d Sin (C/2)

=40*sin (70/2)

=22.9cm

the perpendicular distance be tween the chord and the centre of the circle is 22.9cm.

(b) Using = 3.142, find the length of the minor arc.

Solution given;

minor arc=[tex]\frac{70}{360}*πd=\frac{7}{36}*3.142*40[/tex]

=24.44cm

the length of the minor arc. is 24.44cm.

B.]In the diagram, XZ is a diameter of the cir cle XYZW, with centre O and radius 15/2 cm.

If XY = 12 cm, find the area of triangle XYZ.

Solution given:

XY=12cm

XO=15/2cm

XZ=2*15/2=15cm

Now

In right angled triangle XOY [inscribed angle on a diameter is 90°]

By using Pythagoras law

h²=p²+b²

XZ²=XY²+YZ²

15²=12²+YZ²

YZ²=15²-12²

YZ=[tex]\sqrt{81}=9cm[/tex]

:.

base=9cm

perpendicular=12cm

Now

Area of triangle XYZ=½*perpendicular*base

=½*12*9=54cm²

the area of triangle XYZ is 54cm².

Answer:

a)

d = 40 cm ⇒ r = 20 cm

Let the perpendicular distance is x.

Connecting the center with  the chord we obtain a right triangle with hypotenuse of r and leg x with adjacent angle of 70/2 = 35°.

From the given we get:

b)

The minor arc is 70° and r = 20

The length of the arc is:

Since XZ is diameter, the opposite angle is the right angle, so the triangle XYZ is a right triangle.

Find the missing side, using Pythagorean:

The area of the triangle:

Answer:

x = -3

y= 3

Step-by-step explanation:

y =  x + 6 -----------------------(I)

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

Substitute y =x +6 in equation (II)

x + 6  = -2x - 3

Add 2x to both sides

x + 2x +6 = -3

Combine like terms

3x + 6 = - 3

Subtract 6 from both sides

3x = - 3 - 6

3x = -9

Divide both sides by 3

x = -9/3

x = -3

Plug in s = -3 in equation (I)

y = -3 + 6

y = 3

Answer:

119?

Step-by-step explanation:

Answer:

Value of given expression x is -4

Step-by-step explanation:

Given equation in question;

4 + 2|3x + 4| = -4

Find:

Value of given expression

Computation:

4 + 2|3x + 4| = -4

Using BODMAS rule;

⇒ 4 + 2|3x + 4| = -4

⇒ 2|3x + 4| = - 4 - 4

⇒ 2|3x + 4| = - 8

⇒ |3x + 4| = - 8 / 2

⇒ |3x + 4| = - 4

⇒ 3x + 4 = - 8

⇒ 3x = -8 - 4

⇒ 3x = -12

⇒ x = -12 / 3

⇒ x = -4

Value of given expression x is -4

Answer:

Yes it can

Step-by-step explanation:

To check wether it's a right angle triangle we need to apply the Pythagoras theorem

h^2= a^2 +b^2

Hypotenuse is always the longest side so

5^2 = 3^2 + 4^2

This is correct, so the triangle is a right angle triangle

Answer from Gauthmath

Answer:A(1,-5)

B(6,-8)

Step-by-step explanation:

Answer:

answer C

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&-2x^2\\y&=&x-2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2(y-2)^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&y-2\\y&=&-2y^2-8y-8\\\end{array}\right.\\\\[/tex]

Answer:

7 units

Step-by-step explanation:

In similar triangles, corresponding sides are same ratio.

[tex]\frac{LN}{JH}=\frac{LM}{JI}\\\\\frac{LN}{14}=\frac{5}{10}\\\\LN=\frac{5}{10}*14\\\\LN=7[/tex]

Answer:

Step-by-step explanation:

Yes. The zeroes of a graph are the values of x where the graph touches (or crosses) the x-axis.

Answer:

17 lb I guess 8 don't think the question is full

Step-by-step explanation:

the question is half

Answer:

30 words per minute

Step-by-step explanation:

Take the number of words and divide by the number of minutes

150/5 = 30

300/10 =30

450/15 = 30

600/20 = 30

30 words per minute

Answer:

janae types 30 words each minutes.

Step-by-step explanation:

if 5minutes = 150 words

[tex]1 \: minute = \frac{150words}{5minutes} [/tex]

[tex] = \: 30words[/tex]

In case of Nina:

slope of graph = speed = 48-32/6-4 = 16/2 =8

y-32 =8(x-4)

y-32=8x-32

y=8x

d=8t

at x= 0 i.e at t= 0

d= 0m

In case of Ryan:

slope =speed = 47.5-35=6-4 = 12.5/2 =6.25

y-35=6.25(x-4)

y-35=6.25x-25

y=6.25x+10

d=6.25t+10

at t = 0, d= 10m

RYAN had a head start of 10 m

AB: 20

BC: 12

AC: 16

AD: 10

DE: 6

AE: 8

Answer:

The midpoint of the data when it is arranged in order.

Step-by-step explanation:

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

For example, the median of the following set of numbers is 5

1, 2, 5, 10, 20

Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

X=7

c is the answer:

[tex]3x + 50 = 10x + 1 \\ 10x - 3x = 50 - 1 \\ 7x = 49 \\ x = \frac{49}{7} \\ x = 7[/tex]

Answer: -2. Bc if you look on the graph of the y axis you'll see its located at -2.

Hope this helps :)

Step-by-step explanation:

The function is negative for all real values of x where x < -3 or x > -1 and the domain of the function is -∝ < x < ∝

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = - ( x + 3 ) ( x - 1 )   be equation (1)

Now , the values of x which makes the function negative are

when x < -3

f ( x ) = - ( -ve ) ( -ve ) = -ve

when x > 1

f ( x ) = - ( +ve ) ( +ve ) = -ve

So , the domain of the function is all real numbers and -∝ < x < ∝

Hence , the function is solved

To learn more about domain and range click :

https://brainly.com/question/28135761

#SPJ7

Answer:

4.5 hours in minutes = 270

Every 45 minutes, bacteria triples

You start with 50

Divide 270 (total time) by 45 (every time bacteria triples)

270/45 = 6

36,450 bacteria

Answer:

75°

Step-by-step explanation:

First, we need to know that the interior angle sum of a triangle is always 180°.

Now, to find the missing angle aside from x, we need to complete the sum 180-155=25, seeing 155° lies on a straight line. Remembering the interior angle sum of a triangle is always 180°, it is thus clear that 25+80+x=180. If we complete this equation, x=75.

Hope this helps!

Answer:

Step-by-step explanation:

The domain are all the x values in order, no repeats allowed:

D = {-2, 2, 5}

Same thing for the range, except these are the y values:

R = {-7, 2, 4}

The coordinates stated this way don't match up to what they are in coordinate form, but they don't have to.

Answer:

Domain : {-2,2,5}

Range:{ -7,2,4}

Step-by-step explanation:

The domain is the inputs

Domain : {-2,2,5}

The range is the outputs

Range:{ -7,2,4}

Answer:

Lateral surface area= circumference*height

120=12*h

h=10cm

Answer:

h=10 cm

Step-by-step explanation:

cicumference of a circle C=2πr=12

lateral surface area of cylinder=2πrh

120=12h

h=120/12=10 cm

Answer:

[tex]{ \tt{m \sqrt{p} + n \sqrt{p} - \sqrt{p} }} \\ = { \tt{ \sqrt{p}(m + n - 1) }}[/tex]

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

[tex](3x + 1)(x + 4)[/tex]

[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]

Multiply it by x.

[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]

[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

[tex]x = 5[/tex]

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

[tex]1 - 2 - 5 + 6 = 0[/tex]

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

[tex] {x}^{2} - x - 6[/tex]

We can then factor this into

[tex](x - 3)(x + 2)[/tex]

So our roots or factors is

[tex](x - 1)(x - 3)(x + 2)[/tex]

Answer:

The numbers you're looking for are 54, 55, and 56.

Step-by-step explanation:

x + (x + 1) + (x + 2) = 5 * (x + 1 - 22)

3x + 3 = 5x - 105

3 = 2x - 105

108 = 2x

x = 54

x + 1 = 55

x + 2 = 56

Answer:

32 years

Step-by-step explanation:

8x12 because there are 12 inches in a foot

8x12=96

96/3

96/3=32

Answer:

32 years

Step-by-step explanation:

y = years

1 foot  = 12 inches

12 × 8 = 96

Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.

3y

3 × 10 = 30

3 × 20 = 60

3 × 30 = 90

3 × 31 = 93

3 × 32 = 96

It will take the pine tree 32 years to grow 8 feet, or 96 inches.

Answer:

A) (0,-3)

Step-by-step explanation:

to get the y-intercept let x = 0, then

y = 0 + 0 -3

y = -3

Answer:

(0,-3)

Step-by-step explanation:

The y intercept is where x=0

ƒ(x) = –x^2 + 4x – 3?

f(0) = -0^2 +4(0)-3

f(0) = -3

(0,-3)

First, we'll set up two equations. One for the amount of each coin and another for the value of the coins.

N will represent nickels

D will represent dimes

N + D = 30

---The problem tells us that there are 30 total coins

0.05N + 0.10D = 2.95

---Nickels are worth 5 cents and dimes are worth 10 cents, and the total value of the coins is 2.95

Now that we have our equations, we need to solve for one of the variables in the first equation. I will solve for N.

N + D = 30

N = 30 - D

Then, we take that equation and substitute our new value for N into the second equation (value) and solve for D.

0.05(30 - D) + 0.10D = 2.95

1.5 - 0.05D + 0.10D = 2.95

1.5 + 0.05D = 2.95

0.05D = 1.45

D = 29

Now that we know how many dimes there are, we can plug that value into our equation for N and solve for N.

N = 30 - D

N = 30 - 29

N = 1

Therefore, there are 29 dimes and 1 nickel.

Hope this helps!

Answer:

= 50%

Step-by-step explanation:

There is one point, random number = 1

There are two circles, sample space = 2

[tex]{ \tt{probability = \frac{1}{2} }} \\ { \tt{percentage = \frac{1}{2} \times 100\% }} \\ = 50\%[/tex]

Answer:

25%

Step-by-step explanation:

1. Find the area of both Circles: [tex]A = \pi r^{2}[/tex] [tex]A = \pi 2^{2}[/tex] = [tex]4\pi[/tex]   [tex]A = \pi 1^{2} = \pi[/tex]

2. [tex]\frac{\pi }{4\pi }[/tex] to find the percentage

3.  0.25 = 25%