Copy and complete the prime factor trees
for 21 and 33.
What is the highest common factor (HCF)
of 21 and 33?
21
33

If A is 5, b is 5, and C is 6 the quadratic equation is in standard form using those numbers will be y = 5x² + 5x + 6 and the vertex of the parabola is (-0.2, 5.2)

Any equation of the form  [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

It is given that,

a = 5, b = 5 and c = 6

The quadratic equation is in standard form as,

y = ax² + bx + c

Put the values as

y = 5x² + 5x + 6

Differentiate the above equation and equate to 0 to obtain the vertex point,

y' = 10x + 5

0=10x + 5

5x + 1 = 0

5x = -1

x = -0.2

Substitute the value of x as

y = 5x² + 5x + 6

y = 5(-0.2)² + 5(-0.2) + 6

y = 5.2

The vertex of the parabola is (-0.2, 5.2)

Thus, if A is 5, b is 5, and C is 6 the quadratic equation is in standard form using those numbers will be y = 5x² + 5x + 6 and the vertex of the parabola is (-0.2, 5.2)

Learn more about quadratic equations here:

brainly.com/question/17177510

#SPJ1

Using the properties of complementary angles we can represent the solution as (a) definition of a right angle (b) substitution property of equality (c) angle addition postulate .

If the sums of two angles equal exactly 90 degrees, they are said to be complimentary.

To learn more about complimentary angles visit:

https://brainly.com/question/5708372

#SPJ1

Answer:

a

Step-by-step explanation:

if you substitute for example in the first 2 boxes you have -1 for x and 5 for y so substitute these in for x and y so 5=2(-1)+7. Next do 2 time -1 = -2 the add 7. -2+7=5 so 5=5 hope this helps

Expression is a combination of numbers, operators and variables. the value of the expression −51 − 17 − (−37) is -31.

Expression is a combination of numbers, operators and variables.

The given expression is minus fifty one minus seventeen minus of minus thirty seven.

−51 − 17 − (−37)

We have to use BODMAS rule to solve this expression

-51-17+37

Now add  minus fifty one and minus seventeen

We get minus 68

-68+37

Now subtract 37 from 68 and put minus sign in the answer.

We get answer as minus thirty one.

-31

Hence option C is correct. the value of the expression −51 − 17 − (−37) is -31.

To learn more on expressions click:

brainly.com/question/14083225

#SPJ1

Answer:

v = 3D - x - r

99%

Step-by-step explanation:

D = (x + r + v)/3

x + r + v = 3D

v = 3D - x - r

(b) When x = 85, r = 86 and D = 90%:

v = 3*90 -85 - 86

  = 270 - 171

  = 99.

Gavin worked 7 hours on his tutoring job and 3 hours on his landscaping job

A system of equations is a group of two or more equations with the same variables. A solution to a system of equations is the values of the variables that make all of the equations in the system true. A solution to a system is also an intersection point of the graphs of the equations in the system.

Let;

We need to write system of equations to solve this problem.

14x + 13y = 137 ...eq(i)

x + y = 10 ...eq(ii)

Solving equation (i) and (ii),

x = 7 and y = 3

He worked 7 hours tutoring and 3 hours landscaping

Learn more on system of equations here;

https://brainly.com/question/13729904

#SPJ1

First, determine the number of miles covered per day:

Her car already has 45,300 miles on it.

(a)The total number of miles, f(x), Stefanie's car will have been driven after x more days will be:

(b) Stephanie works 4 days a week.

After 3 weeks, the number of days worked = 4 x 3 = 12 days

Therefore, when x=12:

Answer:

limit = 1

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

175 x 3 = 525. Divide that by 25 and you get 21.

Answer:

An equivalent function to the given function is;

Explanation:

Given the function;

we want to find an equivalent function to the given function;

Applying the rules of exponent;

Therefore, An equivalent function to the given function is;

The value of x when he equation given is solved is x = 4/27.

To solve for x in an equation, we have to apply all necessary properties of equality to will enable us isolate x to one side of the equation. The value of x is the solution to the equation that will make the equation a true statement.

Given the equation:

4(4/4x) + 5 = 32

Subtract 5 from both sides

4(4/4x) + 5 - 5 = 32 - 5 [subtraction property of equality]

4(4/4x) = 27

4/x = 27

Cross multiply

4 = 27(x)

4 = 27x

Divide both sides by 27 [division property of equality]

4/27 = 27x/27

4/27 = x

x = 4/27

Learn more about equations on:

https://brainly.com/question/25678139

#SPJ1

Answer:

6.75

Step-by-step explanation:

I've had this question before. You solve like this:

4/4 = 1 so x.

so 4 times x is 4x. You then subtract 5 from each side.

4x+5-5=32-5

4x=27 Divide both sides by 4 to get

x=27/4 which as a decimal is 6.75.

if two parallel lines are cut by a transversal then each pair of alternate interior angles are congruent.

Two straight lines are parallel if they intersect a horizontal line so that their corresponding angles are coincident. Two line segments are parallel if they intersect the transverse line so that the alternating interior angles are congruent. When two parallel lines cross a horizontal line, they form an equilateral interior angle, and their sum equals 180 degrees.

The angles are complementary because the sum of the interior angles on equal sides is 180 degrees. The sum of the interior angles formed by one side of a horizontal line is two right angles. Alternating interior angles are formed by a horizontal line intersecting two parallel lines. They lie between two parallel lines, but on opposite sides of the horizontal line, creating two pairs of alternating interior angles four angles total.

Learn more about The interior angles here:-https://brainly.com/question/24966296

#SPJ1

The gradient of a line perpendicular to a line with a gradient of −2/3 is 3/2.

Gradient of a line

The gradient of a line is defined as the change in the "y" coordinate with respect to the change in the "x" coordinate of that line. The gradient of a line is helpful to find the inclination or steepness of a line.

We know that,

The product of gradient of two lines perpendicular to each other is equal to -1.

Let the gradient of the other line be m.

Hence, according to the data given in the question, we can write,

(-2/3)*m = -1

m = -1*(-3/2)

m = 3/2

To learn more about  gradient of a line, here:-

https://brainly.com/question/24200465

#SPJ1

For given two state parks Elm Grove and Cathedral Rock, the range of visitors per day to Elm Grove Park is equal to the range of visitors per day to Cathedral Rock Park.

Also, the maximum number of visitors to Elm Grove Park is less than the minimum number of visitors to Cathedral Rock Park.

The correct statements are statement 1 and statement 2

Here, we have been given two state parks Elm Grove and Cathedral Rock. Each recorded the number of visitors to the park each day for 15 days.

We were given line graphs of this data.

We have to choose the correct statements about the two plots.

For Elm Grove Park,

Maximum number of visitors: 350

Minimum number of visitors: 50

Range of visitors per day,

350-50 = 300

And in case of Cathedral Rock Park,

Maximum number of visitors 600

At least 300 visitors and the range of visitors per day is 600-300 = 300

This means that the range of visitors per day to Elm Grove Park is equal to the range of visitors per day to Cathedral Rock Park.

Also, the maximum number of visitors to Elm Grove Park is less than the minimum number of visitors to Cathedral Rock Park.

The correct statements are statement 1 and statement 2

Learn more about the range here:

https://brainly.com/question/20259728

#SPJ1

Answer:

A and C

Step-by-step explanation: The range of visitors in a day to Cathedral Rock is equal to the range of visitors in a day to Elm Grove.

The range of visitors in a day to Cathedral Rock is equal to the range of visitors in a day to Elm Grove.

The greatest number of visitors in a day to Elm Grove is greater than the least number of visitors in a day to Cathedral Rock.

The greatest number of visitors in a day to Elm Grove is greater than the least number of visitors in a day to Cathedral Rock.

Answer: The answer is m^2

Step-by-step explanation:

Using the given description < NOP is found to be 46 degrees

given data]

< OPQ = ( 9x - 19 ) degrees

< PNO = ( 2x + 5 ) degrees

< NOP = ( 3x + 16 ) degrees

From the figure described

let < NPO = y

< PNO + < NOP + y = 180 degrees ( sum of angles of triangle )

< OPQ + y = 180 degrees ( linear pair theorem )

Hence we equate both

< PNO + < NOP + y = < OPQ + y

< PNO + < NOP  = < OPQ + y - y

< PNO + < NOP  = < OPQ

( 2x + 5 ) + ( 3x + 16 ) =  ( 9x - 19 )

2x + 3x + 5 + 16 = 9x - 19

5x + 21 = 9x - 19

21 + 19 = 9x - 5x

40 = 4x

x = 40 / 4

x = 10

< NOP = ( 3x + 16 ) degrees

< NOP = ( 3 * 10 + 16 ) degrees

< NOP = ( 30 + 16 ) degrees

< NOP = 46 degrees

Read more on angles here: https://brainly.com/question/25716982

#SPJ1

The statements that are true about the solution to the system of equations are

y coordinate, of the solution is = (-8) ,

x coordinate, of the solution is = (9) , and

The ordered pair that is solution to the system lies in Quadrant IV .

In the question ,

the system of equations are given as

4x+3y = 12   ...(1)

and 2x +3y = -6    ...(2)

to solve for x and y , we subtract equation (2) from equation(1) .

So , On subtracting , we get

(4x+3y)-(2x+3y)= 12-(-6)

4x+3y-2x-3y = 12+6

4x-2x +3y-3y = 18

2x = 18

x = 18/2

x = 9

Put x=9 in equation [tex](1)[/tex], we get

4(9)+3y=12

36+3y=12

3y = 12-36

3y = -24

y= -24/3

y = -8

Since x coordinate is +9 and y coordinate is -8 ,

so the solution lies in Quadrant IV.

Therefore , The statements that are true about the solution to the system of equations are

y-coordinate, of the solution is =  (-8) ,

x-coordinate, of the solution is =  (9) , and

The ordered pair that is solution to the system lies in Quadrant IV .

Learn more about Equations here

https://brainly.com/question/27911202

#SPJ1

The ratio of 5 days to 60 hours is 2:1.

So, the ratio of 5 days to 60 hours:

Then, ration os 5 days to 2.5 days

Therefore, the ratio of 5 days to 60 hours is 2:1.

Know more about ratios here:

https://brainly.com/question/2328454

#SPJ13

Answer: B: 1

Step-by-step explanation:

Since we already know 3 + 18 = 21, then it would only make sense for 3 x 1 + 18 to equal 21. Even then, the other answers are incorrect by process of elimination

The variance of the sample mean x = 7 is 18(option c).

Given table:

X          7  5  11   1   11

(x₁ - x)² 0  4  16 36 16​

n = number of observations = 5

Variance σ² = 1/n-1 Σ[tex]\ \ n} \atop {i=1} \right.[/tex] ([tex]X_{1}[/tex] - X)²

= 1/5-1 (0 +4 + 16 + 36 + 16)

= 1/4(72)

= 18

Therefore variance σ² = 18

Hence the variance of the sample mean x = 7 is 18.

so option c is correct.

Learn more about the variance and sample mean here:

https://brainly.com/question/16032058

#SPJ1

​

There are 2 tusks for every  8 whiskers.

There is 1 tusk for every 4 whiskers.

How are the ratios calculated?

First image:

Number of whiskers in the first image = 4

Number of tusks in the first image = 0

Second image:

Number of whiskers in the second image = 4

Number if tusks in the second image = 2

Total number of whiskers = 4+4

                                           = 8

Total number of tusks = 0 + 2

                                     = 2

Rewriting as ratios,

a) Tusks: whiskers

     2: 8

So, from the ratio, there are 2 tusks for every 8 whiskers.

b) Tusks: whiskers

     2: 8

     1 : 4

So, from the ratio, there is 1 tusk for every 4 whiskers.

To learn more about ratios, refer:

https://brainly.com/question/2914376

#SPJ9

lilkyky67, this is the solution:

Let's recall that the angles in the image are consecutive interior angles and they add up to 180 degrees.

Therefore,

12x - 29 + 4x + 1 = 180

16x - 28 = 180

Adding 28 at both sides:

16x - 28 + 28 = 180 + 28

16x = 208

Dividing by 16 at both sides:

16x/16 = 208/16

x = 13

Now, we can find out the measures of the two angles, as follows:

First angle:

12x - 29 = 12 * 13 - 29

156 - 29 = 127

Second angle:

Answer:

88

Step-by-step explanation:

Answer:

c i think because you can factor it

Answer:

y = x - 5

Point Slope form: y + 8 = 1 (x + 3)

Step-by-step explanation:

(-3,-8) and (-7,-12)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁        -12 - (-8)         -12 + 8         -4

m = ------------ = --------------- = -------------- = -------- = 1

        x₂ - x₁          -7 - (-3)          -7 + 3          -4

y - y₁ = m(x - x₁)

y - (-8) = 1(x - (-3))

y + 8 = x + 3

   -8         -8

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

y = x - 5

I hope this helps!

The number of times that 3.08 × 10^8 is greater than 4.4 ×× 10^6 as a scientific notation is 0.7 × 10^2.

Scientific notation simply means the way of expressing numbers that are too big or too small.

In this case, the numbers that are given are 3.08 × 10^8 and 4.4 ×× 10^6

Then we have to divide them to know the number of times that it's greater. This will be:

= (3.08 × 10^8) / (4.4 × 10^6)

= 0.7 × 10^2

This illustrates scientific notation.

Learn more about scientific notation on:

brainly.com/question/1767229

#SPJ1

Answer: 50 mph

Step-by-step explanation:

Answer:

C is the correct answer.