Name:
6. Graph the following function in factored form and identify all key features

f(x) = 2(x - 1)(x + 3)
Zeros:
Axis of symmetry: x =
Vertex:
Y-Intercept:

Answer:

y = 1/5x + 2 3/5

Step-by-step explanation:

lmk if you want an explanation

The solution to the system is x = -6 and y = 4.

To solve the system by the addition method, we want to add the equations together in a way that will eliminate one of the variables.

Let's start by multiplying the first equation by -3 to get -3x - 9y = -18, and then add the second equation to it:

-3x - 9y = -18

+ 3x + 4y = -2

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

    -5y = -20

Now we can solve for y by dividing both sides by -5:

y = 4

We can substitute y=4 into one of the original equations, say x+3y=6, to solve for x:

x + 3(4) = 6

x + 12 = 6

x = -6

So the solution to the system is x = -6 and y = 4.

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13 is the range, 17.0 is the population variance, and 4.1 is the population standard deviation.

The range of a collection of data is a measurement of its variability. It is the difference between a set of data's highest and lowest value.

Given ,

11,11,16,17,15,13,9,18,5,7

Highest value = 18

Lowest value = 5

Range = 18-5 = 13

The following formula works well for population variance:

Population Variance = Σ(x-mean)²/N

N is total element in the data = 10

x are the individual data

Calculating the mean is necessary before we can obtain the variance and standard deviation.

mean = Σfx/N

Mean = 122/10

Mean = 12.2

Variance = 170.16/10

Population variance = 17.016

Population variance ≈ 17.0 (to 1 d.p)

Population standard deviation = √Population Variance

Population standard deviation = √17.016 = 4.125

≈ 4.1 (to 1 d.p)

The complete question is:

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 11,11,16,17,15,13,9,18,5,7

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You roll a fair number of cube. The Probability of P(2 then 2) would be 1/36.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Here is a complete description You roll a fair number cube to find probability of p(2, then2)

Given the sample space for a die

S = (1, 2,3,4,5,6) = 6

The Probability of 2 then 2 = (1/6) x (1/6)

= 1/36

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Given:

The numbers are 160, 192, 240​.

To find:

The LCM of 160, 192, 240.

Solution:

The given numbers are  160, 192, 240​. Write the factor forms of these numbers.

\(160=2\times 2\times 2\times 2\times 2\times 5\)

\(160=2^5\times 5\)

\(192=2\times 2\times 2\times 2\times 2\times 2\times 3\)

\(192=2^6\times 3\)

\(240=2\times 2\times 2\times 2\times 3\times 5\)

\(240=2^4\times 3\times 5\)

Now, the LCM of given numbers is the product of all prime factors with highest degrees.

\(LCM=2^6\times 3\times 5\)

\(LCM=64\times 15\)

\(LCM=960\)

Therefore, the LCM of given numbers is 960.

Answer:

Step-by-step explanation:

Solve for y:

\(2y-3x=10\\2y=3x+10\\y=\frac{3}{2} x+5\)

Therefore:

y = 3/2x + 5

m = 3/2

b = 5

Graph below courtesy of Desmos.

Answer:

The length of PR is 15.8 cm

Step-by-step explanation:

We will solve the question using the cosine rule

In ΔPQR

∵ (PR)² = (PQ)² + (RQ)² - 2(PQ)(RQ)(cos∠Q)

∵ PQ = 17.8 cm

∵ RQ = 26.3 cm

∵ m∠Q = 36°

→ Substitute them in the rule above

∵ (PR)² = (17.8)² + (26.3)² - 2(17.8)(26.3)(cos36)

∴ (PR)² = 316.84 + 691.69 - 936.28(cos36)

∴ (PR)² = 251.0635685

→ Take √ for both sides

∴ PR = 15.8449856

→ Correct it to 3 significant figures

∴ PR = 15.8 cm

∴ The length of PR is 15.8 cm

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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Answer:

4.9 in

Step-by-step explanation:

6/11 = x/9

6/11 times 9 = x

x = 4.9

Area of a polygon formula: = 2(1+\(\sqrt{2}\)) side²

To find one side: 96 ÷ 8 = 12

implement formula

≈695.29351

Answer:

2,575 grams of blood plasma are in the typical adult human body

Step-by-step explanation:

Density is the property that matter, whether solid, liquid or gas, has to compress into a given space, so it relates the amount of mass per unit volume. So the density of a substance is the quotient between mass and volume:

\(density=\frac{mass}{volume}\)

In this case, you know:

Replacing:

\(1.03\frac{g}{mL} =\frac{mass}{2,500 mL}\)

and solving, you get:

mass= 1.03 \(\frac{g}{mL}\) *2,500 mL

mass= 2,575 g

2,575 grams of blood plasma are in the typical adult human body

Answer:

4.75

Step-by-step explanation:

helppddcskdilfsl

Answer:

-216

Step-by-step explanation:

use the rule bodmas

bracket,othersign, division, multiplication, addition, subtraction

Last one.

Hope this helps.

Answer:

\(k=35\)°

Step-by-step explanation:

The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.

\(130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95\)

The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;

\((unknown_1)+(unknown_2)+(k)=180\)

Substitute,

\(50+95+k=180\)

Simplify,

\(50+95+k=180\\\\145+k=180\\\\k=35\)

\(\sf \bf {\boxed {\mathbb {TO\:FIND :}}}\)

The measure of angle \(k\).

\(\sf \bf {\boxed {\mathbb {SOLUTION:}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}\)

\(\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}\)

➪ \(x\) + 85° = 180°

➪ \(x\) = 180° - 85°

➪ \(x\) = 95°

Also,

Exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ 130° = \(k\) + \(x\)

➪ \(k\) + 95° = 130°

➪ \(k\) = 130°- 95°

➪ \(k\) = 35°

Therefore, the value of \(k\) is 35°.

\(\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}\)

\(\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ 50° + 35° + 95° = 180°

( where 50° = 180° - 130°)

➪ 180° = 180°

➪ L. H. S. = R. H. S.

Hence verified.

(Note: Kindly refer to the attached file.)

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Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer: $4840

Step-by-step explanation:

A = p(1+r/n)^nt

A = 2800(1+0.043)^13

A = 4840

Answer:

4123 for 9 years

Step-by-step explanation:

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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Answer:

initial value         opposite value             absolute value

15                                -15                                   |15|

-93                                93                                 |93|

56                                 -56                                 |56|

-87                                87                                   |87|

Step-by-step explanation:

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

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Answer:

area of triangle = 1/2 ×base×height

Answer: 20

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

Factors of 40: 1,2,4,5,8,10,20,40

Factors of 80: 1,2,4,5,8,10,16,20,40,80

Factors of 100: 1,2,4,5,10,20,25,50,100

The greatest common factor is 20

Answer:

75%

Step-by-step explanation:

Answer:

Step-by-step explanation:

square     square

yards         feet

4                 36

10                 x

 \(x = \dfrac{36\cdot10}{4}=9\cdot10=90\)

Answer:

6 of x and 5 of y

Step-by-step explanation:

x = number of closets of the first type

y = number of closets of the second type

1200 = 100x + 120y

100 = 10x + 8y

10x = 100 - 8y

10x(100 - 8y) + 120y = 1200

1000 - 80y + 120y = 1200

40y = 200

y = 5

100 = 10x + 8×5 = 10x + 40

60 = 10x

x = 6

20x + 24y = max

20×6 + 24×5 = 120 + 120 = 240

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

The five more known rotation rules are given as follows:

The original coordinates for this problem are given as follows:

A(0,0), B(5,2), C(5,-5), D(0,-3).

Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:

A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).

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Answer: All real numbers

Step-by-step explanation:

Let's find the critical points of the inequality.

2y2+1=

−9

5

y−6

2y2+1−(

−9

5

y−6)=

−9

5

y−6−(

−9

5

y−6)(Subtract (-9)/5y-6 from both sides)

2y2+

9

5

y+7=0

For this equation: a=2, b=1.8, c=7

2y2+1.8y+7=0

y=

−b±√b2−4ac

2a

(Use quadratic formula with a=2, b=1.8, c=7)

y=

−(1.8)±√(1.8)2−4(2)(7)

2(2)

y=

−1.8±√−52.76

4

Answer: 16, 24, 32

Step-by-step explanation:

Since the ratio is 8:3, and the girl's rate is added to itself by 3, you need to add 8 for each boy's rate.

Answer:

16, 24, 32

In that order

Step-by-step explanation: