The product of a 25 and a number, increase by 8 is 68. find the number.
​

Find the values a, b, and c to substitute into the quadratic formula.

Notice how there are a, b, and c. Everything is left of the equal sign, leaving 0 on the right.

ax² + bx + c = 0

Notice how there are a, b, and c too, just like in standard form. After we find standard form, we can substitute a, b and c values into the quadratic formula.

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

Here are the steps we will follow:

Move everything to the left while keeping both sides equal.

x² + 1 = 2x – 3                 Equation from the question

x² + 1 + 3 = 2x – 3 + 3     Add three to both sides.

x² + 1 + 3 = 2x                 -3 + 3 cancels out to 0.

x² + 4 = 2x                      Simplify.

x² + 4 – 2x = 2x – 2x     Subtract 2x from both sides.

x² + 4 – 2x = 0                No numbers on the right side is the same as 0.

x² – 2x + 4 = 0                Rearrange to follow ax² + bx + c = 0.

Find a, b, and c from standard form.

ax² + bx + c = 0         Standard form

x² – 2x + 4 = 0           No number attached to x² means a = 1.

a = 1,  b = –2,  and  c = 4

Substitute a = 1, b = –2, and c = 4 into the quadratic formula.

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

Here is how our formula set up should look:

[tex]\displaystyle{x=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(4)}}{2(1)} }[/tex]

Let's compare formula set up to the options in the question.

The denominator is 2(1). So, the answer is not option B.

Inside the square root, it says –4(1)(4). So, the answer is not option D.

This leaves us with either option A or option C.

Before the ±, it says –(–2). When simplified, –(–2) is 2.

Option C has –2. So, the answer is not option C.

Inside the square root, it says (–2)², which is equal to 2².

When solving exponents of negative numbers,

The exponent 2 is even.

(–2)² = 4

∵ (–2)² = 4 and 2² = 4

∴ (–2)² = 2²

(–2)² is the same as 2².

Therefore, the answer is option A.

Answer:

Brother has $6

I have $18

Step-by-step explanation:

To answer - you have to write the equation out. Money I have is (3x) and Brother's money is x. :)

Answer:= 0.124688 oz per fl

Step-by-step explanation:

This is a fraction equal to

3.99 oz ÷ 32 fl

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 32

3.99 oz ÷ 32

32 fl ÷ 32

=

0.124688 oz

1 fl

=

0.124688 oz

fl

= 0.124688 oz pe

Answer:

CF is a diagonal through the interior of the cube.

The system of the equations 3x = 5y - 22 and 12x = 20y - 11 are parallel lines. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The equations are given below.

− 3x + 5y = 22 or 3x = 5y − 22   ...1

 20y − 11 = 12x or 12x = 20y − 11   ...2

The system of the equations follows the condition that will be

12/3 = 20/5 ≠ 11/22

4 = 4 ≠ 1/2

This is the condition for the parallel lines or no solution.

More about the linear system link is given below.

https://brainly.com/question/20379472

#SPJ1

Answer:

2x + y = 4, 5y = 10x + 4

is a system of linear equations representing intersecting lines.

2x + 3y = 21, -6y = 4x + 1

is a system of linear equations representing parallel lines.

-2x + 4y = 9, 8y = 4x + 18

is a system of linear equations representing coincidental lines.

Step-by-step explanation:

Graphed them all.

Answer:

38

Step-by-step explanation:

add 189+115 = 304

then 304÷8 =38

Answer:

well when its simplyfied its 91

Step-by-step explanation:

27 + 64 mutipliction first

27 + 64 = 91

Answer:

E empty set

Step-by-step explanation:

The answer is empty at

Answer:

A = 50.24 inch^2

Step-by-step explanation:

Area = πr^2

So we have r =4inch and let π = 3.14

A = 3.14 * 4^2

A = 50.24 inch^2

Answer:

See below ~

Step-by-step explanation:

Circle 1

Circle 2

Answer:

circumference with diameter 5=15.7m

area with diameter 5=19.625m²

499

199

+-------  the answer is 698 you have to add 499 and 199.

Part A: The IQR for the males' data.  23

Part B: The difference between the median values of each data set. 13

Part C: The distribution of the data and if the mean or median would be a better measure of center for each Median for the males and Mean for the females

Part D:The possible reason for the outlier in the data set. The day the movie premiered

The likely missing part of the question; The Box Plots are to compare The Number of Males and The Number of Females attending the latest superhero movie every day in a given month

The known parameters

The 5 number summary in a are;

Minimum                                         0           0

FIrst Quarlite Q1                             2           5

Second Quarlite, Mediun Q2        20         7

Third Quarlite                                 25         40

Maximum                                        50         18

Outlier                                                           46

Part A:

The Inter Quartile Range, IQR = Q₃ - Q₁

For the males, we have, IQR = 25 - 2 = 23

Part B:

The difference between the median values for the males and females is given as follows;

Difference between median = Q₂ Males - Q₂ Females

∴ Difference between median = 20 - 7 = 13

The difference between the median values for the males and females = 13

Part C:

The distribution of the data for the males is skewed left, with almost all the data in the first half

The better measure of center for the skewed data is the median, given

that three quarter of the data have values that are less than half of the

range of values in the data set, and that the median is close to the third

quartile, the mean will be located further towards the minimum value of

the data than the median

The distribution of the data for the females consists of the interquartile range located approximately in the middle between the max and the min values with the median being close to the first quartile, therefore, the mean will be a better measure of center as it will be located further from the first quartile and closer midway in the IQR

Part D;

The possible reason for the outlier in the data set may be due to the first day the latest super hero movie is premiered

To know more about data sets follow

https://brainly.com/question/4219149

#SPJ1

Answer:

For rectangulasr prism

a. [tex]72cm^3[/tex]

b. [tex]108cm^{3}[/tex]

Step-by-step explanation:

For rectangulasr prism

a. Equation: Volume = length x width x height

length: 6cm

width: 4cm

height: 3cm

Volume = 6cm x 4cm x 3cm

Volume = 24cm x 3cm

b. Equation: A = 2[(width x length) + (height x length) + (heigth x width)]

A = 2[(4cm x 6cm) + (3cm x 6cm) + (3cm x 4cm)]

A = 2[(24cm) + (18cm) + (12cm)]

A = 2[(24cm) + (30cm)]

A = 2[(54cm)]

Answer:

268.08 cubic inches

Step-by-step explanation:

I'm sorry if this isn't helpful

Moving 5 one digit to the left, one number in which the value of digit 5 is 10 times as great as in 253,829 is in 538,290.

It means that the value of the digit is multiplied by 10.

Hence, moving the digit 5 one position to the left, and appending a zero at the end, generating the number 538,290, the value of digit 5 is 10 times as great as in 253,829.

More can be learned about the value of a digit at https://brainly.com/question/2041524

#SPJ1

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$99.931\\ r=rate\to 14\%\to \frac{14}{100}\dotfill &0.14\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (99.931)(0.14)(5)\implies I\approx 70[/tex]

Answer: [tex]i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-5}=\sqrt{(-1)(5)}=\sqrt{-1} \sqrt{5}=\boxed{i\sqrt{5}}[/tex]

Answer:

6[tex]\sqrt{17}[/tex] or 24.738634

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of the sides. We will only need to find the length of AB and AD, as AB = DC and AD = BC.

The picture shows the Pythagorean theorem being used to find AB and AD.

AB = [tex]\sqrt{17}[/tex]

AD = [tex]\sqrt{68}[/tex]

Now we can find the perimeter

2([tex]\sqrt{17}[/tex]) + 2([tex]\sqrt{68}[/tex]) = 6[tex]\sqrt{17}[/tex]

Answer:

1 / 64

Step-by-step explanation:

(2^2)^-3

apply exponent rule: (a^b)^c = a^(bc)     a ≥ 0

2^((2) - 3)

((2) - 3) = -6

2^-6

apply exponent rule: a^-b = 1 / a^b

2^-6 = 1 / 2^6

2^6 = 64

1 / 64

Let me know if you have any questions !

If the volume of the aluminum will be 48 cubic m. Then the density of the aluminum will be 2700 kg per cubic m.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Density = mass/volume

A solid aluminum sculpture in the shape of a rectangular prism has a mass of 129,600 kilograms.

The length of the sculpture is 6 meters, the width is 2 meters, and the height is 4 meters.

Then the density of the aluminum will be

The volume of the aluminum brick will be

V = 6 x 2 x 4

V = 48 cubic m

Then the density will be

D = 129600/48

D = 2700 kg per cubic m

To learn more about the density refer to the link;

brainly.com/question/952755

#SPJ1

The three medians are = CL, AM, and BN. The centroid is point Z. The value of BN, if BZ=30 units, is 45 units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

The problem can be solved as,

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ1

Answer:

option b, 205

Step-by-step explanation:

Each dot on the line plot represents a different length of the ribbon,

To find the total length of the ribbon you add all the different length that was cut,

3(11.5) + 5(12) + 1(12.5) + 2(13.5) + 4(14) + 1(15)

34.5 + 60 + 12.5 + 27 + 56 + 15 = 205

205

hope it helps...!!!

thx for points

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

The given linear inequality is,

[tex]2y > x - 2[/tex]

Solve it further,

[tex]2y > x - 2\\2y-x > - 2[/tex]

Change the inequality with changing the sign of it,

[tex]x-2y < 2[/tex]

The inequality equation is graphed, which can be shown in the image provided below. In this graphed equation,

Thus, on a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

Learn more about the graph of the inequality here;

https://brainly.com/question/62792

#SPJ1

Answer:

[tex]-20\sqrt{3}-5\sqrt{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]4 \sqrt{12}-\sqrt{50}-7\sqrt{48}[/tex]

Rewrite 12 as 4 · 3  and 50 as 25 · 2 and 48 as 16 · 3 :

[tex]=4 \sqrt{4 \cdot 3}-\sqrt{25 \cdot 2}-7\sqrt{16 \cdot 3}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a \cdot b}=\sqrt{a}\sqrt{b} :[/tex]

[tex]=4 \sqrt{4}\sqrt{3}-\sqrt{25}\sqrt{2}-7\sqrt{16}\sqrt{3}[/tex]

As [tex]\sqrt{4}=2[/tex] and [tex]\sqrt{25}=5[/tex] and [tex]\sqrt{16}=4[/tex] then:

[tex]=4 \cdot 2 \sqrt{3}-5\sqrt{2}-7 \cdot 4\sqrt{3}[/tex]

Simplify:

[tex]=8\sqrt{3}-5\sqrt{2}-28\sqrt{3}[/tex]

Collect like terms:

[tex]=8\sqrt{3}-28\sqrt{3}-5\sqrt{2}[/tex]

Combine like terms:

[tex]=-20\sqrt{3}-5\sqrt{2}[/tex]

Answer:

x = 30

Step-by-step explanation:

x = 90 - 60 = 30

x = 30

.................................................

Answer:

a.......4880

Step-by-step explanation:

b.......180 per year

Answer:

2.75

Step-by-step explanation:

Answer:

$8.8 per hour

Step-by-step explanation:

Well, the equation is simple.

Time (hours) * Money (per hour) = Total

We know the time he worked for and the total amount he earned, so just replace in this equation and find the unknown number

12.5 * money = 110

To find the money he earns per hour we should just simply divide the total amount he earned by the hours he spent working

money = 110/12.5

money = 8.8$

You can also check it out to make sure it's correct.

If he earns 8.8$ per hour and worked for 12.5 hours how much he'll earn? Let's find out

8.8 * 12.5 =?

8.8 * 12.5 = 110, the same total amount so our solution must be correct.