How do I factor quadratics?

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

Geometric mean of two numbers of the square root of their product:

[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]

The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].

The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.

The following formula is used to calculate the geometric mean;

[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]

Where a is the first term and b is the second term.

Therefore,

The geometric mean of 5 and 4 is;

[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]

Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].

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Answer:

Look below. The answers are bolded!

Step-by-step explanation:

1.   10x + 23

5+6(2x+3)-2x

Distribute first!

5 + 12x + 18 -2x.

Now you can combine like terms.

23 + 10x

2.   18x + 6

3(4x+8) + 3(2x-6)

Distribute first!

12x + 24 + 6x - 18

Now you can combine like terms.

18x + 6

3. -2x + 8

(32-8x)

____ ___

     4

Divide 32 and -8x by 4.

32/4 = 8

-8x/4 = -2x

-2x + 8

4. 4x + 3

24x+18

______

    6

Divide 24x and 18 by 6

24x/6 = 4x

18/6 = 3

4x + 3

Answer:

formula

Step-by-step explanation:

3rd option is correct which is formula.

A mathematical relationship or rule which expressed only in symbols and which is the connection between two or more variable.

An equation that expresses a mathematical rule or relationship is a formula.

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept fprm is

y = mx + b ( m is the slope and b the y-intercept )

y = [tex]\frac{5}{4}[/tex] x - 4 is in this form

with m = [tex]\frac{5}{4}[/tex] and b = - 4

Plot the point (0, - 4)

using the slope add 5 to the y-coordinate and 4 to the x-coordinate

(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1)  ← point on the line

Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph

Answer:

Step-by-step explanation:

Answer:

A.  Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.

B. Total number of 6-ounce jars = 551

Total money earned from 6-ounce jars = $4408

Step-by-step explanation:

A. Jian's family's collection = 3311 ounces

Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]

= 827.75

Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.

Cost per 4-ounce jar = $5.

Total cost = 827 × 5 = 4135

B. Now, number of 6-ounce jars =  [tex]\frac{3311}{6}[/tex]

= 551.83

≅ 551 jars

Cost per 6-ounce jar = $8

Total cost = 551 × 8 = 4408

Answer:

6400 fans will be pleased.

Step-by-step explanation:

Out of 150 fans, 120 were pleased. Assuming the same ratio, out of 8000 fans, 8000x120/150 = 6400 will be pleased.

Answer:

6400

Step-by-step explanation:

We need to find the fraction of fans that are pleased

120 out of 150 are please

120/150  = 12/15 =4/5

We multiply this fraction by the fans at the game

4/5 * 8000 = 6400

6400 fans should be pleased

Answer: x = 12.5

Step-by-step explanation:

P = (2, 5)

Q = (x, -3)

R = (7, 9)

[tex]d_{PQ}=d_{QR}[/tex]

[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]

[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]

[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]

[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]

[tex]4x+68 = -14x+193[/tex]

[tex]10x+68 = 193[/tex]

[tex]10x= 125[/tex]

x = 12.5

Answer: cis (ln x) ; x > 0

Step-by-step explanation:

  [tex]x^i[/tex]

[tex]= e^{ln(x^i)}[/tex]

[tex]=e^{i \ln(x)}[/tex]

= cos (ln x) + i sin (ln x)

AKA: cis (ln x)

NOTE: I found this following formula which you may find useful:

[tex]A^i = x + iy[/tex]

Answer:

1.  B. BD

2. C. 15

3. A. 2

Step-by-step explanation:

1.  From the figure,

∠DAB = ∠DAC

Therefore, BD is the bisector of ∠ABC.

2.  From the figure, IG = GH

3x = 5x - 10

10 = 5x - 3x

2x = 10

x = 5

So, GH = 5x - 10

= 5(5) - 10

= 25 - 10

= 15

Therefore, GH = 15.

3.  From the figure,

∠DAB = ∠DAC

10y = 8y + 4

10y - 8y = 4

2y = 4

y = 2

Answer:

The month-to-month contract will cost an extra $1356.

Step-by-step explanation:

"An annual contract is $502.00/month with a 2-month penalty if you break the lease."

If you stay the whole year, and you pay $502 per month, you pay 12 * $502 = $6024 for the entire year.

"The month-to-month contract is $615.00/month."

If you stay the entire year, you pay 12 * $615 = $7380.

The difference is $7380 - $6024 = $1356

Answer:

3) TB and NT

4) ∠KLM and ∠MLK

Step-by-step explanation:

3) those two rays intersect to form the angle shown in the diagram

4) an angle can always be named from left to right or right to left as long as the middle letter is always the vertex of the angle

It's a vertical line. The slope of vertical line is undefined.

The equation of a vertical line is x = a (a - any real number).

Answer:

Slope = undefined

Step-by-step explanation:

A vertical STRAIGHT line that represents a slope is undefined.

Answer:

11/20

Step-by-step explanation:

Answer:  [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.

Step-by-step explanation:

Since we have given that

Percentage of guest who order the signature dish = 55%

Total percentage = 100

We need to find the fraction of guests order the signature dish.

So, Fraction of guests order the signature dish is given by

[tex]\dfrac{\text{Percentage of guest order the signature dish}}{\text{Total percentage}}\\\\=\dfrac{55}{100}\\\\=\dfrac{11}{20}[/tex]

Hence, [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.

Answer:

Mr. Wright taught 1,050 students in 25 years.

Step-by-step explanation:

Given,

The number of students Mr. Wright taught = 18,

Also, every year the number of student is increased by 2,

So, in second year, the number of students = 18 + 2 = 20,

In third year = 20 + 2 = 22,

In fourth year = 22 + 2 = 24,

.............., so on,

Hence, we get an A.P. that shows the given situation,

18, 20, 22, 24, ............. till 25 years.....

First term, a = 18,

Common difference, d = 2,

And, number of terms, n = 25,

Hence, the total number of students that have been taught by him are,

[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

[tex]S_{25}=\frac{25}{2}[36+(25-1)2][/tex]

[tex]=\frac{25}{2}[36+24\times 2][/tex]

[tex]=\frac{25}{2}[36+48][/tex]

[tex]=\frac{25}{2}(84)[/tex]

[tex]=\frac{2100}{2}[/tex]

[tex]=1050[/tex]

Third option is correct.

It these triangles are similar, then the sides of the triangles are in proportion:

[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex]      cross multiply

[tex]15y=10(y+4)[/tex]    use distributive property

[tex]15y=10y+40[/tex]       subtract 10y from both sides

[tex]5y=40[/tex]           divide both sides by 5

[tex]\boxed{y=8}[/tex]

[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex]            cross multiply

[tex]8x=(4)(6)[/tex]

[tex]8x=24[/tex]           divide both sides by 8

[tex]\boxed{x=3}[/tex]

Answer:

8P1 = 8

Step-by-step explanation:

Permutation  

The number of elements can be selected from a set of elements.

Let r be the number of elements want to select and n be the set of elements.

It can be written as nPr

nPr = n!/(n - r)!

To find 8P1

n= 8 and r = 1

8P1 = 8!/(8-1)! = 8!/7! = (8 x 7!)/7! = 8

Therefore 8P1 = 8

Answer:

x=4.4

Step-by-step explanation:

To get from A to B, the scale factor is 2.5, since 4*2.5 = 10

So, to get from B to A, you divide by 2.5.

11/2.5 = 4.4

Answer:

Darin drove '2m - 20' miles.

Step-by-step explanation:

We are given that Sam drove 'm' no. of miles.

As, it is also given that Kara drove twice as many miles as Sam. Therefore we get that Kara drove '2m' no. of miles.

Now, it is given that Darin drove 20 miles fewer than Kara .i.e. Darin drove '2m - 20' no. of miles.

Hence, in terms of m, Darin drove '2m - 20' miles.

Answer: 2268 miles

Step-by-step explanation: 1 hour = 567 miles

4 hours= n miles

multiply 567 miles by four hours

= 2268 miles

Answer:

2304

Step-by-step explanation:

567 x 4

Answer:

t=5

Step-by-step explanation:

Add 3t to the other side to cancel it out

2t+3t+15=40

Subtract 15 to the other side to cancel it out

2t+3t=40-15

Simplify

5t=25

t=5

Answer:

Gabe needs 20 liters of the 40% solution.  

He also needs 40 liters of the 70% solution.

Step-by-step explanation:

Equation:

acid + acid = acid

0.40x + 0.70(60-x) = 0.60*60

40x + 70*60 - 70x = 60*60

-30x = -10*60

x = 20 liters

Gabe needs 20 liters of the 40% solution.  

He also needs 40 liters of the 70% solution.

Answer:

14

Step-by-step explanation:

The LCD is the LCM of the denominators, 7 and 2. Since these numbers have no common factors, their LCM is simply their product:

... 7·2 = 14

Answer:

50 and 26

Step-by-step explanation:

Make an equation! That makes it much simpler and has helped me a lot.

x+x-24=76

Combine like terms

2x+24=76

Add 24 on both sides

2x=52

Divide both sides by 2

x=26

72-26=50

To check that their difference is correct, subtract 26 from 50

50-26=24

Hope this helps!

Answer:

For every 15 students scoring in the 60's there were 9 students scoring in the 70's.

Step-by-step explanation:

Your first step would be to rewrite the numbers into an easier to understand form like fractions, 45/3 and 27/3. Then you divide both numbers by 3, so you get comparable numbers. 45/3= 15, 27/3=9.

Answer:

LM=12

V =90

Step-by-step explanation:

4.  If it is a parallelogram, the two sides have to be equal.

2x-6 = x+3

Subtract x from each side

2x-x -6 = x+3-x

x-6 =3

Add 6 to each side

x-6+6 = 3+6

x=9

LM =2x-6

    = 2*9 -6

   = 18-6

   = 12

5.  

<U + < T = 180   Adjacent corners in a parallelogram are supplementary

11x+2 + 12x-6 = 180

Combine like terms

23x -4 = 180

Add 4 to each side

23x-4+4 = 180+4

23x = 184

Divide by 23

23x/23 = 184/23

x=8

<V = <T  Opposite corners in a parallelogram are equal.

<V = 12x-6

<V = 12(8) -6

<V = 96-6

<v =90

The question involves solving algebra and geometry problems related to parallelograms, focusing on transformations, coordinates, and area calculations to find the equation for y.

The student is asked to solve a series of algebra and geometry problems related to the properties of a parallelogram. These include finding coordinates, proving algebraic expressions, computing distances, and determining areas. The goal is to find the equation for y given a series of transformations and conditions on a square that becomes a parallelogram. Important concepts include the area of a parallelogram, vector addition using the parallelogram rule, and the determinant relating to a change of basis in vectors.

For example, part (e) involves finding the area of the parallelogram by computing twice the area of triangle PQO, using PQ as the base of the triangle. Solving for y in part (f) by setting this area equal to 1 involves understanding the effects of transformation on geometrical shapes and employing algebra to arrive at the desired equation.

Answer:

Huma's share =Rs x =  Rs. 1.35392881

Seema's share =Rs. 12x =  Rs (12 *  1.35392881) = Rs. 16.2471457

Hubna's share =Rs. 123*12x =  Rs. (123*16.2471457) = Rs. 1998.39892

Step-by-step explanation:

Given :

Huma , Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother.

Seema gets 12 of what Huma gets

Hubna gets 123 times Seema’s share

To find : How much money do the three sisters get individually?

Solution :

Let  Huma's share be Rs. x.

Since we are given that Seema gets 12 of  Huma's share

⇒ Seema's share = Rs 12x.

Since we are given that Hubna gets 123 times Seema’s share

⇒Hubna's share = Rs. (123 * 12x) = Rs. 1476x.

We are given that they received together Rs. 2016 in total .

⇒[tex]x+12x+1476x= 2016[/tex]

⇒[tex]1489x= 2016[/tex]

⇒[tex]x = \frac{2016}{1489}[/tex]

⇒[tex]x = 1.35392881[/tex]

Thus Huma's share =Rs x =  Rs. 1.35392881

Thus Seema's share =Rs. 12x =  Rs (12 *  1.35392881) = Rs. 16.2471457

Thus Hubna's share =Rs. 123*12x =  Rs. (123*16.2471457) = Rs. 1998.39892

[tex]\left\{\begin{array}{ccc}2y+4x=18\\2y-3x=4&\text{add 3x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2y+4x=18&(**)\\2y=3x+4&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\3x+4+4x=18\qquad\text{subtract 4 from both sides}\\7x=14\qquad\text{divide both sides by 7}\\\boxed{x=2}\\\\\text{Put the value of x to the first equation:}\\\\2y+4(2)=18\\2y+8=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}\\\\Answer:\ \boxed{x=2\ and\ y=5}[/tex]

The smallest diameter needed to drill through the wall is 0.75 inches, which is calculated by multiplying the inside diameter of the pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). Always measure and plan ahead to avoid mistakes.

The subject matter of this question is mathematics, specifically ratios. To find the smallest diameter you would need to drill into the wall, you would need to multiply the inside diameter of your pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). So, 0.5 inches * 1.5 = 0.75 inches.

This means, to allow the pipes to pass through the wall, you will need to drill a hole at least 0.75 inches in diameter. This is assuming the wall is thin enough that the entire length of the pipe that needs to pass through the wall is less than the thickness of the wall.

Remember, it's always better to pre-measure and plan ahead to avoid unnecessary work and potentially costly mistakes.

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