2
A circle has the equation x^2+ y^2 + 6x - 8y + 21 = 0.
a) Find the coordinates of the centre and the radius of the circle.

The point P lies on the circle.
b) Find the greatest distance of P from the origin.

Answer:

a=[tex]\frac{vf - vi }{t}[/tex]

Step-by-step explanation:

vf=vi + at

vf-vi= at

divide  both sides by t

[tex]\frac{vf - vi }{t}[/tex] =[tex]\frac{at}{t}[/tex]

a=[tex]\frac{vf - vi }{t}[/tex]

Answer:

95.44%

Step-by-step explanation:

We can find the percentage of area lies within 2 standard deviations of mean by computing P(-2<Z<2).

So,

P(-2<Z<2)=P(-2<Z<0)+P(0<Z<2)

Using normal area table P(0<Z<2)=0.4472. So,

P(-2<Z<2)=0.4472+0.4772

P(-2<Z<2)=0.9544

Thus, the 95.44% of area lies within 2 standard deviations of mean.

Answer:

(A) 70°

(B) 67°, because they are alternate interior angles

Step-by-step explanation:

For a:

The angles of a triangle will all add up to 180°. Using the "feathers" (lines that signify congruence), we can tell that the angle connecting the two congruent lines will be different than the other two, which will be equivalent to each other.

This means that the angle measure of x will be [tex]180-55-55[/tex], or just [tex]180-110[/tex].

This is equal to 70°.

For b:

We know that the 67° angle and y are formed by the same line intersecting two parallel lines. This means that the angle measures of each intersection point will be the same as the other intersection point, however they will be flipped. This makes the concept of alternate interior angles. We know that the 67° angle and y are formed by the same line, this means that their angle lengths are the same - therefore y is 67°.

Hope this helped!

Answer:

7cm

Step-by-step explanation:

Your question has been heard loud and clear

Passive voice

The matter will be looked into by him.

Thankyou

Answer:

C. The statement is an equation because there is an equality symbol.

Step-by-step explanation:

Equation:

Combination of terms joined by the sign minus, plus, multiplication, and division and has equality sign.

Example

5x+45=-5

Term:

A Numbers. (Only)

Example:

9

Combination of a number and a variable joined by multiplication or division.

Example:

9x, 6ab, 10n

Variable:

a symbol that is written with a number or a term.

6ab

Expression:

Terms joined by the sign plus or minus

Hope this helps ;)❤❤❤

Answer:

22

Step-by-step explanation:

replace -2 for every in the equation:

-(-2)x2-9x-2=22

Answer:

f(-2)=14

Step-by-step explanation:

[tex]f(x) = -x^2 - 9x\\\\f(-2) = -(-2)^2-9(-2)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(-2\right)^2\::\quad 4\\=-4-9\left(-2\right)\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:9\left(-2\right)\::\quad -18\\\\=-4-\left(-18\right)\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:-4-\left(-18\right)\:\\f(-2):\quad 14[/tex]

Answer:

(D) [tex]x>-10[/tex]

Step-by-step explanation:

If we have the inequality [tex]-7x + 4 > -8x - 6[/tex], we can simplify it down and get [tex]x[/tex] isolated on one side of the equation.

Add 6 to both sides:

[tex]-7x + 4 + 6 > -8x - 6 + 6\\\\-7x + 10 > -8x[/tex]

Add [tex]8x[/tex] to both sides of the inequality:

[tex]-7x + 10 + 8x > -8x+8x\\\\x + 10 > 0[/tex]

Subtract 10 from both sides of the inequality:

[tex]x + 10 - 10 > 0 - 10\\\\x > -10[/tex]

So (D) [tex]x>-10[/tex] is the correct simplification.

Hope this helped!

Answer:

The possible values are less than 4 but greater than –4

Step-by-step explanation:

If the absolute value of integer number is less than 4 then it is 0, 1, 2 or 3.

so the possible integer numbers are: -3, -2, -1, 0, 1, 2 or 3.

All of them are greater than -4 and less than 4

Answer:

Answer is C.

Step-by-step explanation:

She would use 9/7 of a bottle of conditioner for a full year.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

We have been given that Martina used 3/4 of a bottle of conditioner in 7/12 of a year.

Let the amount of conditioner would be x she uses in a full year

As per the given condition, we can write a proportion as

3/4 of a bottle : 7/12 of a year = x : 1

⇒ (3/4) / (7/12) = x / 1

Reciprocal the terms of the denominators,

⇒ (3/4) × (12/7) = x

⇒ 36 / 28 = x

⇒ x = 9/7

Therefore, she would use 9/7 of a bottle of conditioner for a full year.

Learn more about the proportion here:

brainly.com/question/1504221

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the answer is 1 because when x is a variable by it self it is 1

Answer: 1

Step-by-step explanation: f(x)=1

Answer:

2 meters

Step-by-step explanation:

The formula for finding the volume of a triangular prism is:

V = 1/2ba * h where b = base length, a = height of base and h = height of prism. In this case, we're solving for a. We know that V = 4.5, b = 1.5 and h = 3 so:

4.5 = 1/2 * 1.5 * a * 3

4.5 = 2.25a

a = 2 meters

Answer:

First of all snog can you please say something in comments man you the best mod out there.

1.5 m because that is the height of the tent. It says so as a measurement.

Step-by-step explanation:

Answer:

-7(x+2)

Step-by-step explanation:

-3(2x+5)-(x-1)

↦ -6x+(-15)-x+1

↦-6x-x-15+1

↦7x-14

↦2(x-7)

Answer:  No it does not .

Step-by-step explanation:

First use the coordinates of point A and B to write an equation.

A (-3,-2)

B(2,1)

We will need to use these points to find the slope first and by doing that we will find the difference in the y values and divide it by the difference in the x values.

-2-1= -3

-3-2 = -5

-3/-5= 3/5  

The slope is 3/5 and now we need to find the y intercept using the same points. As you can see the equation will have to be in slope intercept form which uses the formula y=mx+b  where m is the slope and b is the y-intercept.

We will plot the first points in and solve for b.

-2=3/5(-3) + b

-2= -9/5 + b  

+9/5  +9/5

b = -1/5  

We will now write the equation  y=3/5x - 1/5   .

Now using the equation try point c to see if it fits the graph.  

Point C is (5,3)  so again plot in the x and y coordinates and solve,

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

3 = 3 - 1/5

3[tex]\neq[/tex] 14/5

In this case 3 does not equal 14 over 5 so Point c does not fit the graph

Answer:

the answer is: [tex]\{3, 9\}[/tex]

Step-by-step explanation:

Given a set:

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Two subsets,

One subset of odd numbers:

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, ......}

Other subset of multiples of 3:

B = {3, 6, 9, 12, 15, .....}

To find:

Which number in set S are elements in both A and B.

So, we need to find intersection of A and B provided the number is between 1 to 10 (1 to 10 are the elements of S).

First of all, let us have intersection (i.e. common elements) of A and B:

[tex]A\cap B = \{3, 9, 15, 21, ......\}[/tex]

Now, the numbers between 1 to 10 are:

[tex]\{3, 9\}[/tex]

So, the answer is: [tex]\{3, 9\}[/tex]

The value of the angle x will be 40°. Then the correct option is B.

The circle is at equidistant of points drawn from the center. The radius of a circle is the distance between the center and the circumference.

The minor arc  is 75°. And the another arc is 130°.

We know that the complete circle subtends 360 degrees.

Then the measure of the major arc will be

Major arc + 130° + 75° = 360°

       Major arc + 205° = 360°

                   Major arc = 155°

Then the value of the angle x will be given by the half of the difference of the major arc to minor arc.

x = (Major arc – minor arc) / 2

x = (155 – 75)/2

x = 80 / 2

x = 40°

Thus, the value of the angle x will be 40°.

Then the correct option is B.

More about the circle link is given below.

https://brainly.com/question/11833983

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Answer:

is this for a test?

Step-by-step explanation:

Answer:

Hey there!

We can let x be that number.

2x+9=31

2x=22

x=11

The number is 11.

Let me know if this helps :)

Answer:

The whole number is 11.

Step-by-step explanation:

Let's call the whole number x. We can write the following equation:

2x + 9 = 31

Subtracting 9 from both sides of the equation gives us:

2x + 9 - 9 = 31 - 9

2x = 22

Dividing both sides of the equation by 2 gives us:

2x / 2 = 22 / 2

x = 11

Answer:

The height of the pole is 167 m

Step-by-step explanation:

The given parameters are;

Increase  in the length of the shadow = 90 m

Initial angle of elevation of the Sun = 58°

Final angle of elevation of the Sun = 36°

We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase  in the length of the shadow  

We have by sin rule;

90/(sin (22°)  = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)

Let the initial ray from the top of the pole to the end of the shadow's length = l₁

90/(sin (22°)  = l₁/(sin(122°)

l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m

Therefore;

The height of the pole = 283.3 m × sin(36°) = 166.52 m

The height of the pole= 167 m to three significant figures.

Answer:

height of pole = 121 m (to 3 significant figures

Step-by-step explanation:

From the diagram attached to this solution:

Let the length of the shadow = b

Let the height of the triangle = h

[tex]Triangle\ 1\\\\Tan\ (58)\ =\ \frac{h}{b}\\1.60\ =\ \frac{h}{b} - - - - - -(1)\\\\[/tex]

[tex]Tan\ (36) = \frac{h}{b+90} \\0.73\ =\ \frac{h}{b+90} - - - - (2)[/tex]

[tex]From\ equation\ (1)\\1.60 = \frac{h}{b}\\ cross-multiplying\\1.60b = h - - - - - (3)\\\\\\from\ equation\ (2)\\0.73\ =\ \frac{h}{b+90}\\ corss-multiplying\\0.73b\ +\ 65.7 = h\\h\ =\ 0.73b\ +\ 65.7- - - - - -(4)\\[/tex]

Notice that equation (3) = equation (4) = h

[tex]1.60b = 0.73b\ + 65.7\\1.60b\ -\ 0.73b\ = 65.7\\0.87b\ =\ 65.7\\b\ =\ \frac{65.7}{0.87} = 75.52\ m\\[/tex]

Now let us find the height of pole from equation (3)

1.60b = h - - - - - - (3)

where b = 75.52

h = 1.60 × 75.52

h = 120.83 m

= 121 m (to three significant figure

Answer:

1/2, 3/6 and 2/4 are equivalent fractions.

Step-by-step explanation:

To know if the fractions are equivalent, their simplest form should be the same.

So we must simplify all the fractions to their simplest form.

To find the simplest form of a fraction, we must divide the numerator and denominator with their GCF (Greatest Common Factor)

So:

1/2 = 1/2

1/3 = 1/3

3/4 = 3/4

3/6 = 1/2 ( The GCF for 3 and 6 is 3)

2/4 = 1/2 ( The GCF for 2 and 4 is 2)

4/10 = 2/5 ( The GCF for 4 and 10 is 2)

Because 1/2, 3/6 and 2/4 has the same simplest form, they are equivalent fractions.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

Step-by-step explanation:

a.

[tex]AC=\sqrt{AB^2-BC^2} =\sqrt{13^2-5^2} =\sqrt{169-25} =\sqrt{144} =12\\[/tex]

applying sine formula

AB=c

AC=b

BC=a

[tex]\frac{a}{sin A} =\frac{b}{sin B} =\frac{c}{sin C} \\\\\frac{5}{sin A} =\frac{12}{sin B} =\frac{13}{sin 90} \\using~last~two\\\frac{12}{sin B}= \frac{13}{1} \\sin B=\frac{12}{13}\\ B=sin^{-1}(\frac{12}{13}) \approx 67.38 ^\circ[/tex]

b.

third angle ∠Y=180-(30+90)=180-120=60

using sine formula

[tex]\frac{xz}{sin Y} =\frac{xy}{sin Z} = \frac{yz}{sin X} \\\frac{30}{sin 60} =\frac{xy}{sin 90} =\frac{h}{sin 30} \\using ~first~and~last\\\frac{30}{\frac{\sqrt{3} }{2} } =\frac{h}{\frac{1}{2} } \\2h=\frac{60}{\sqrt{3} } \\h=\frac{30}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } =10\sqrt{3}[/tex]

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Hi my lil bunny!

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Let's simplify step-by-step.

[tex]-a - b + 1 + ab[/tex]

[tex]= -a + -b + 1 + ab[/tex]

So the answer is : [tex]\boxed {-a + -b + 1 + ab}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

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Have a great day/night!

❀*May*❀

Ok so we need to find out the different kinds of variables/constants.

1st kind: -a

2nd kind: -b

3rd kind: 1

4th kind: ab

-a and -b are different because they are different variables, and since their value is not known, you can't add or subtract them together.

-a, -b, and 1 are not the same because -a and -b are variables and their value is unknown. However, 1 is a constant, and it's value is constant and known.

-a, -b, and ab are different because ab are "fused together" (multiplied) and that means you cannot add them separately.

So this expression cannot be factorized.

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer: -2b-4

Ok, so I assume you meant b-4-3b. If not, then B-4-3b is the best you can get, since B and b are different in math.

Anyways, we can rearrange b-4-3b into b-3b-4. Calculating b-3b = -2b. That means -2b-4 is the answer.

Hope that helped,

-sirswagger21

Answer:

B - 4 - 3B

=> -2B - 4

Answer:

23 mpg

Step-by-step explanation:

We simply need to evaluate the given function at the speed requested (60 mph):

[tex]f(x)=32-0.15\,x\\f(60)=32-0.15\,(60)\\f(60)=23\,\,mpg[/tex]

Answer:

Option A must be true.

Step-by-step explanation:

Answer:

[tex] \overline{TQ} \cong \overline {TR} [/tex]

Step-by-step explanation:

Since, endpoints of a segment are equidistant from any point situated on the perpendicular bisector of that segment.

T is a Point on the perpendicular bisector of segment AB.

[tex] \therefore \overline{TQ} \cong \overline {TR} [/tex]

Answer:

x = 21

Step-by-step explanation:

1. Write the equation

(18 + 2x) ÷ 5 = 12

2. Multiply both sides by 5

18 + 2x = 60

3. Subtract 18 from both sides

2x = 42

4. Solve for x by dividing both sides by 2

x = 21

Answer:

the equation is 18+2x/5 =12

Step-by-step explanation:

now

18+2x= 60

or 2x= 60-18

or 2x= 42

or x=21

so the no is 21 (ans)

thank u

Answer:

90i

Step-by-step explanation:

18 * sqrt(-25) = 90i

Answer:

The correct options are;

A. 1·2 = 2

B. 1·1 = 1

E. 1 + 1 = 2

Step-by-step explanation:

Given that the equations 1.2 = 2 and 1.1 = 1 are correctly written as 1·2 = 2 and 1·1 = 2, we have;

The product of any number and one is equal the same number, that is a × 1 = a

Whereby we have the expression 1·2 which is 1 × 2,  we therefore have;

1 × 2 = 1 · 2= 2

B. Similarly we have;

1 · 1 = 1 × 1 = 1

Also, 1 + 1 = 2 is correct as the sum of two numbers is equal to the sum of the count of the numbers, therefore;

E. 1 + 1 = 2 is correct.

Answer:

0.0000375, 3.75x10^-3, 37.5x10^5, 37,500,000, 3.75x10^9

Step-by-step explanation:

0.0000375

37.5x10^5  = 37.5 * 100,000 = 3,750,000

3.75x10^9  = 3.75 * 1,000,000,000 = 3,750,000,000

3.75x10^-3  = 3.75 * 0.001 = 0.00375

37,500,000

Answer:

0.0000375

3.75x10^-3

37.5x10^5

37,500,000

3.75x10^9

Answer:

2000

Step-by-step explanation:

Salim will need to get 2000 clicks in order to get $50 per month or more.

First: 5 cents goes into one dollar 20 times.

Second: You multiply 20 times 50. This is how you get 2000. There is your answer.

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

A linear equation is in the form:

y = mx + b;

where y, x is variable, m is the rate of change and b is the y intercept.

Let y represent the total pay Salim earns and x represent the number of clicks.

Salim's Website earns $15 per month plus $0.05 every time a visitor clicks, hence:

y = 0.05x + 15

To earn for than $50 per month:

0.05x + 15 > 50

0.05x > 35

x > 700

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

Find out more at: https://brainly.com/question/13911928