A quadratic equation is shown below:

3x2 − 11x + 10= 0

Part A: Find the vertex. Show your work.

Part B: Solve for x using an appropriate method. Show the steps of your work.

ANSWER

60 buttons.

EXPLANATION

Let the number of buttons in the container be x.

Then the number of buttons that are black are:

[tex] \frac{7}{10} x[/tex]

The number of buttons that are white

[tex] \frac{3}{10} x[/tex]

The difference between the white and the black buttons

[tex] \frac{4x}{10} = 24[/tex]

Solve for x.

[tex]4x = 240[/tex]

[tex]x = \frac{240}{4} [/tex]

[tex]x = 60[/tex]

Hence there are 60 buttons in the container.

ANSWER

[tex]11 .6[/tex]

EXPLANATION

x is the radius of the circle.

It is equal to the hypotenuse of the right triangle created by connecting the center and the end of the chord with a straight line.

[tex] {x}^{2} = {5}^{2} + {( \frac{21}{2} )}^{2} [/tex]

[tex]{x}^{2} = 25 + 110.25[/tex]

[tex] {x}^{2} = 135.25[/tex]

[tex]x = \sqrt{135.25} [/tex]

[tex]x = 11.6[/tex]

Answer:

see explanation

Step-by-step explanation:

For 2 similar figures

linear ratio = a : b, then

area ratio = a² : b²

volume ratio = a³ : b³

Given linear ratio = [tex]\frac{2}{5}[/tex], then

(a)

perimeter is a linear ratio = [tex]\frac{2}{5}[/tex]

(b)

surface area ratio = [tex]\frac{2^2}{5^2}[/tex] = [tex]\frac{4}{25}[/tex]

(c)

volume ratio = [tex]\frac{2^3}{5^3}[/tex] = [tex]\frac{8}{125}[/tex]

Answer:

3.5 feet / per minute

Step-by-step explanation:

3 1/2 feet / minute = 3.5 feet / minute

hope this helps :)

Answer:360

Step-by-step explanation:

35% of of 100% with 126 being as the part and the whole is missing.You multiply 126 by 100 which equals 12600 divided by 35 which is equals 360.

Answer:

C)

Step-by-step explanation:

If you multiply twice, you will get 70%. If you multiply by three, you will get 378. That is higher than 360. So it's 360(c)

7lb in 12 oz equals blank ounces = 124 ounces

To find the total number of children who attended the fair on opening day, add 351 to 4000, giving a result of 4351 children.

The number of children who attended the fair on opening day is calculated by adding 351 to the value of 4 thousands. To find the answer, we follow these steps:

Therefore, 4351 children attended the fair on the opening day.

Answer:

13.6

Step-by-step explanation:

Use the a^2 + b^2 = c^2 formula.

Answer:

A = 7.55

Step-by-step explanation:

Answer:

the answer is 71

Step-by-step explanation:

On a box and Quaker plot the median is the middle dot is the median so 71

Answer:  D. |6.7| > |-45|

Step-by-step explanation:

When in these | | then any negative number becomes positive. 6.7 is NOT grater than 45.

Answer:

8, substitute 12 into the equation and then subtract it from 12

Step-by-step explanation:

V≈301.59

I think this is the answer.

Hope this helps!

The answer is 96pi units^3

Answer:

x = - 5

Step-by-step explanation:

The line with equation x = - 2 is a vertical line parallel to the y- axis

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

The line passes through (- 5, 4) with x- coordinate - 5, thus

equation of parallel line is x = - 5

Answer: 75 students

Step-by-step explanation:

15% of 500= 75

Answer:

I would do answer B if not A.

Step-by-step explanation:

I would do this because then they would be relatively closer in skill set.

The appropriate way to label the age intervals on the x-axis is:  Option: B

               B) 7−10; 11−14; 15−18; 19−22

            The rule for determining the number of intervals is:

Here we have 13 observations

and √(13)=3.6055≈4

Hence, we have a total of four intervals.

                 The width of each interval is calculated as:

                       i.e.   (22-7)/4=15/4=3.75≈4

We know that for classifying a class interval in a histogram the width of each of the interval must be equal.

A) 7−11; 11−14; 15−19; 20−22

In option: A--

the width of first interval is: 4

width of second interval is: 3

Width of third interval is: 4

Width of fourth interval is: 2

Hence, the width of each interval is not equal.

Hence, option: A is discarded.

C) 7−10; 10−15; 15−19; 19−22

In option: C--

the width of first interval is: 3

width of second interval is: 5

Width of third interval is: 4

Width of fourth interval is: 3

Hence, the width of each interval is not equal.

Hence, option: C is discarded.

D)  7−13; 15−19; 20−22

In option: D--

the width of first interval is: 6

width of second interval is: 4

Width of third interval is: 2

Hence, the width of each interval is not equal.

Hence, option: D is discarded.

B)  7−10; 11−14; 15−18; 19−22

There are a total of 4 intervals and also width of each interval is equal and equal to 4.

         Hence, option: B is the correct answer.

Answer:

1 and 1/4

Step-by-step explanation:

3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1 1/4

Answer:

[tex]1\frac{1}{4}[/tex]

Step-by-step explanation:

In order to calculate this you just have to add up both of the values that you are given, and to do that, you first have to convert the the values into the same denominator:

[tex]\frac{1}{2} +\frac{3}{4} =\frac{2}{4}+\frac{3}{4}  =\frac{2+3}{4} =\frac{5}{4} =1\frac{1}{4}[/tex]

So the value of the addition of both would be: [tex]1\frac{1}{4}[/tex]

Answer:

log 13 = 1.1139

Step-by-step explanation:

log 13 = 1.1139

Answer:

log 13 = 1.1

Step-by-step explanation:

Given  : log 13.

To find : What is the value round your answer to the nearest tenth.

Solution : We have given log 13.

log 13 = 1.113.

Nearest tenth = 1.1

Therefore, log 13 = 1.1

Answer:

centre = (2, - 1), radius = 6

Step-by-step explanation:

Rearrange the equation by placing the x and y terms together and adding 31 to both sides

Given

x² + y² - 4x + 2y - 31 = 0, then

x² - 4x + y² + 2y = 31

Use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(- 2)x + 4 + y² + 2(1)y + 1 = 31 + 4 + 1

(x - 2)² + (y + 1)² = 36

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r the radius

compare to (x - 2)² + (y + 1)² = 36, then

centre = (2, - 1) and r = [tex]\sqrt{36}[/tex] = 6

The center of the circle is  (2, - 1) and the radius is 6 units.

The equation for a circle has the generic form x² + y² + 2gx + 2fy + c = 0.

The standard equation of a circle is x² + y² = r².

The polar form of the equation of the circle is (rcosθ)² + (rsinθ)² = p².

Given, The equation of a circle is x² + y² - 4x + 2y - 31 = 0.

We know, In x² + y² + 2gx + 2fy + c = 0, The center of the circle is,

(- g, - f) and radius is [tex]\sqrt{g^2 + f^2 - c[/tex].

Therefore, 2gx = - 4x and 2fy = 2y.

2g = - 4 and 2f = 2.

g = - 2 and f = 1.

- g = 2 and - f = - 1.

So, The center is (2, - 1).

And the radius is, [tex]\sqrt{2^2 + -1^2 + 31[/tex].

= [tex]\sqrt{4 + 1 + 31[/tex].

= [tex]\sqrt{36[/tex].

= 6 units.

learn more about circles here :

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Answer:

Step-by-step explanation:

f,d,e

Answer:

F, C, B

Step-by-step explanation:

Just look at where the two graphs intersect and then correspond that point with the color and letter.

Given : One carton of eggs contains 12 eggs.

By unitary method we can find the number of eggs in following cartoons :

1 cartoon = 12 eggs

5 cartoons = 12 × 5 = 60 eggs

6 cartoons = 12 × 6 = 72 eggs

7 cartoons = 12 × 7 = 84 eggs

8 cartoons = 12 × 8 = 96 eggs

Answer:

D

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

Given  

Two Data sets

Class A :{ 2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}

Class B : {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}

In order to check the options we will have to find the mean and median of both data sets.

So for Class A:

Mean= x =(Sum of values)/(Number of values)

=96/20

=4.8

For median the data has to be arranged in ascending order, so

2, 2,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8

Median will be the average of middle two values as the number of items are odd.

Median=(5+5)/2

=10/2

=5

Range = 8-2 = 6

For Class B:

Mean= x =(Sum of values)/(Number of values)

=80/20

=4

For median, arranging the values

2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7

Median=(4+4)/2

=8/2

=4

Range = 7-2 = 5

We get,

Mean of class A > Mean of Class B

Median of Class A > Median of Class B

Range of Class A > Range of Class B

We observe that only option B is correct for the given data sets..

Answer: p(x) = a (x-b)(x-c)(x-d)

Step-by-step explanation:

The first step is to determine the degree of the polynomial.

It shall depend totally on the linear factors given for the polynomial.

If there is one, it is a linear polynomial.

If there are 2, then it is a quadratic polynomial.

If there are three then it shall be a cubic polynomial.

Now let us assume that there are three linear factors.

We multiply those factors and write the polynomial.

If x-b, x-c & x-d are the factors we write

p(x) = (x-b)(x-c)(x-d)

But as we may have a leading coefficient so we write the polynomial as

Then we go on to expand this to get the polynomial in the standard form.

Answer with Step-by-step explanation:

First we find the degree of polynomial.

Consider two linear factors

(x-a) and (x-b)

Multiplying these two factors to get the polynomial.

[tex]p(x)=(x-a)(x-b)=x^2-(a+b)x+ab[/tex]

There are two linear factors .

Therefore, the degree of polynomial is 2 and the polynomial is quadratic.

Degree of polynomial=Number of linear factors

If the linear factors are three then the polynomial formed by multiplying theses factors .

Then, we get the polynomial of degree 3 and the polynomial is cubic polynomial.

It we have four linear factors.

After multiplying these four factors, we get a polynomial of degree 4.

The polynomial is bi quadratic.

Answer:

it is the first one

Step-by-step explanation:

the width is equal to a cm.

the length is twice the width, therefore the length is equal to 2a cm.

the height is twice the length, therefore the height is equal to 4a cm.  

the volume is equal to width times length times height which is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

For Example:

let a = 5

then 2a = 10

then 4a = 20  

a is the width

2a is the length

4a is the height.  

the length is twice the width.

the height is twice the length  

the volume is equal to a * 2a * 4a which is equal to 8a^3 cubic cm.  

this is equivalent to 8 * 5^3 which is equal to 8 * 125 which is equal to 1000 cubic cm.  

5 * 10 * 20 = 50 * 20 = 1000 cubic cm.  

formula works and so is considered to be good.  

the volume is equal to 8a^3 cubic cm.

* hope you understand*

The volume of a rectangular solid where width equals a cm, length equals twice the width, and the height is twice the length is calculated to be 8a³ cubic cm.

Based on the question, we know that the width of the rectangular solid is a cm. Where the length equals twice the width, so it is 2a cm; likewise, the height, which is twice the length, turns out to be 4a cm. The equation for calculating the volume of a rectangular solid is width * length * height. Therefore, if we substitute the given values, we have a cm * 2a cm * 4a cm, which equals 8a³ cubic cm. As a result, the volume of this given rectangular solid is 8a³ cubic cm.

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Answer:

B

Step-by-step explanation:

7 serving multiplied by 2 is equal to 14

Answer:

the answer is prob B i am i on usatest prep and it is correct

Step-by-step explanation:

Hence, the correct answer is:

             Option : a

             a.   5.6 amps

It is given that:

The current (I) in an electrical conductor varies inversely as the resistance (R) of the conductor.

This means that:

[tex]I\propto \dfrac{1}{R}[/tex]

Hence, we get the relation as:

[tex]\dfrac{I_1}{I_2}=\dfrac{R_2}{R_1}[/tex]

where [tex]R_1[/tex] is the resistance corresponding to the current [tex]I_1[/tex]

and  [tex]R_2[/tex] is the resistance corresponding to the current [tex]I_2[/tex]

We have:

[tex]I_1=6\ ,\ R_1=722\ ,\ R_2=768[/tex]

Hence, we get:

 [tex]\dfrac{6}{I_2}=\dfrac{768}{722}\\\\\\i.e.\\\\\\I_2=\dfrac{722\times 6}{768}\\\\\\I_2=5.6406\ amperes[/tex]

        Hence, the answer is:

             Option : a

To find the missing value in the equation, we add -4.5 and 4.4 first, then solve for the missing value.

To find the missing value, we need to solve the equation. Start by adding -4.5 and 4.4. (-4.5 + 4.4 = -0.1)

Now we have: -0.1 + ___ = 0

To solve for the missing value, subtract -0.1 from both sides of the equation: ____ = 0 + 0.1 = 0.1

The missing value is 0.1.

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Final answer:

The missing value is 0.1.

Explanation:

This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4.90, b = -14.3, and c = -20.0.

To solve for the missing value, we can rearrange the equation:

-4.5 + 4.4 + ____ = 0

Simplifying the equation, we get:

-4.5 + 4.4 + ____ = 0

-0.1 + ____ = 0

By adding 0.1 to both sides of the equation, we can isolate the missing value:

____ = 0.1

Therefore, the missing value is 0.1.

Answer:

2 hours 33 mins

Step-by-step explanation:

Arrives = 8.12 pm

Leaves = 10.45 pm

8.12 pm to 10.12 pm = 2 hours

10.12 pm tp 10.45 pm = 33 minutes

Total

= 2 hours + 33 mins

= 2 hours 33 mins

Answer:

2:33

Step-by-step explanation:

For 8:00 to get to 10:00 add two which means two hours then subtract :45 by :12 which gives you 33 so tyler stayed there for 2 hours and 33  minutes.

The area of the yellow sector is 15/8 π in² in pi form.

Answer:

96

Step-by-step explanation:

for every 3 cars there is 2 trucks

If you have 144 cars then we divide 144 by 3 to get 48

That is not the answer though because that would be a 3/1 ratio

We then multiply 48 by 2 to get 96

To find the number of trucks at the dealership, we interpret the ratio 3:2, meaning that for every 3 cars, there are 2 trucks. We figure out that '1' in the ratio is equivalent to 48 vehicles. So, we multiply the trucks component of the ratio (2) by this value to get 96 trucks.

To solve this problem, you must interpret the ratio of cars to trucks as 3:2. This means for every 3 cars, there are 2 trucks. We need to use this ratio to find out how many trucks there are if there are 144 cars.

The first step is to figure out what proportion 144 cars represents within the ratio. To find this, we can divide the number of cars by the cars component of the ratio (3) which gives us: 144 ÷ 3 = 48.

Now we know that '1' in our ratio represents 48 vehicles. So to find out how many trucks, we multiply the trucks component of the ratio (2) by this value, which gives us: 48 x 2 = 96 trucks.

Therefore, if there are 144 cars at the dealership, there are 96 trucks.

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