Find all solutions to 8x³-10x² - 21x + 18 = 0 if x= 2 is one solution.

Answer:

The vertex is (4,-4)

Step-by-step explanation:

Plug in x=4 in the equation

The value of the modulus function |5x| = 3 is x = 3/5 or x = -3/5.

In  mathematics modulus function is the absolute or numerical value of the function irrespective of the sign.It represents magnitude.We modulus functions when we want length, mass and for other variables when we want to represent their weight.

According to the given question |5x| = 3.

We know |x| = a implies x = a or x = -a.

∴ |5x| = 3 is

5x = 3

x = 3/5

Or

5x = -3.

x = -3/5.

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Answer:

x² + 5x + 8

Step-by-step explanation:

This issue is about "function composition",

(g ° f) means

g(f(x)) = g(x² + 5x +6)

= x² + 5x +6 + 2

= x² + 5x +8

Answer:

22

Step-by-step explanation:

add ab and bc to get ac

Answer:

0.99 or 99%

Step-by-step explanation:

This is actually much more simple than it sounds

Take 95% and add 80% of 5 because 5% of the time the QK piece will not work. 80% of 5 is 4. 95+4=99

Answer:

112

Step-by-step explanation:

3y^2 + 7y + 2

if y = 5, then 3(5^2) + 7(5) + 2

= 3(25) + 35 + 2

= 75 + 37

= 112

From the given distribution, we have that:

a) The distribution is skewed to the left.

b) The median is of 74.

c) The mean will be smaller than the median.

Since life expectancies are clustered at the high end, the outliers are small life expectancies, meaning that the mean will be smaller than the median and the distribution is skewed to the left.

The median of a data-set is the 50th percentile, the value that separates the bottom 50% of the data-set from the upper 50%.

In this problem, we have that about half of all the countries having a life expectancy between about 74 and the maximum of 84.7, meaning that 74 is the median.

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The expression becomes 3log₁₀2-3log₁₀3

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

logₐb where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logₐbc where a is the base is given as logₐb + logₐc

logₐbc where a is the base is given as logₐb-logₐc

Now it is given to us to find the logarithmic form of 8/27=(2/3)^3

Let us consider the base of the logarithm to be 10

thus log₁₀8/27=log₁₀(2/3)^3

log₁₀8/27=log₁₀(2/3)^3

We know that logₐb can be written as log₂b/log₂a

Hence

log₁₀8/27= 3(log2/3)

log₁₀8/27=3(log2-log3)

log₁₀8/27= 3log2-3log3

Hence the expression becomes 3log2-3log3

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The total percentage decrease in the number of students on the honor roll is 16.67%.

Percentage is a measure of frequency that is used to express a number as a fraction of an amount out of 100. The sign used to denote percentage is %. In order to convert a number to percentage, multiply the number by 100.

The first step is to determine the number of boys on the honor roll this year.

Number of  boys on the honor roll this year : (1 - percentage decrease) x number of boys last year

(1 - 0.12) x 150

0.88 x 150 = 132

The second step is to determine the number of girls on the honor roll this year.

Number of girls on the honor roll this year : (1 - percentage decrease) x number of girls last year

(1 -0.25) x 84

0.75 x 84 = 63

Total number of students on the honor roll last year = 150 + 84 = 234

Total number of students on the honor roll this year = 63 + 132 = 195

Percentage decrease :[ (195 /234) - 1] x 100 = 16.67%

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Step-by-step explanation:

BQS=78

BQN=48

BQS+BQN=78+48=126

180-126=54°

NQS=54°

comfirm=BQN+BQS+NQS=180

48+78+54=180

Answer:

30°

Step-by-step explanation:

∠NQS + ∠BQN = ∠BQS

Knowing this information, we use the known measures to find ∠NQS

∠NQS + 48° = 78°

∠NQS = 78° - 48°

∠NQS = 30°

Thus, angle NQS is 30 degrees.

Hope this helps!

The approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The complete question is added at the end of the solution

The equation of the height function is given as

h(t) = -5t² + 10t+4

After 1,2 seconds, we have:

t = 1.2

Substitute t = 1.2 in the equation h(t) = -5t² + 10t+4

So, we have

h(t) = -5 x 1.2² + 10 x 1.2 + 4

Evaluate the exponent

So, we have

h(t) = -5 x 1.44 + 10 x 1.2 + 4

Evaluate the products

So, we have

h(t) = -7.2 + 12 + 4

Evaluate the sum

So, we have

h(t) = -7.2 + 16

Evaluate the difference

So, we have

h(t) = 8.2

Hence, the approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

This means that the required approximate height of the gymnast above the ground level after 1.2 seconds is 8.2 feet

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Complete question

The function h(t) = -5t² + 10t+4 models the height of a gymnast on a trampoline over time, where is feet above the ground level and is the number of seconds since the start of their jump.

Using the function, approximately how high is the gymnast above the ground level after 1.2 seconds?

The equation of the line in the graph in slope-intercept form is: y = -5x - 30.

To be able to write the equation of a line in slope-intercept form, y = mx + b, find the value of the slope (m) = rise/run, and the value of the y-intercept (b), which is the value of y where the line intercepts the y-axis.

From the given graph, we have:

Slope (m) = rise/run = -50/10

Slope (m) = rise/run = -5

The y-intercept (b) = -30

Substitute m = -5 and b = -30 into y = mx + b:

y = -5x + (-30)

y = -5x - 30

Thus, the equation of the line in the graph in slope-intercept form is: y = -5x - 30.

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Correct answer is D. Nothing can be determined from the given graph.

A graph is a type of graphic used to display data and show relationships. Graph analysis is helpful for identifying the overall trend, connecting experiment findings to the hypothesis, and creating hypotheses for next studies.

You may compare various figures, comprehend how various components affect the overall, or examine patterns using a chart or graph. Charts and graphs can also be helpful for seeing data that deviates from what you're used to or for assisting in the understanding of group relationships.

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Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².

Newton's first equation of motions states that;

v = u + at

Where v is final velocity, u is initial velocity, a is acceleration and t is time.

Given the data in the question;

First, convert the unit of the initial velocity from kilometer per hour to meter per seconds

Initial velocity = 80 km/h = ( 80 × 5/18 )m/s = 2.2222 m/s

Now, plug these values into the equation above and solve for a.

v = u + at

0 = 22.2222m/s + ( a × 4s )

a × 4s = -22.2222m/s

a = 22.2222m/s ÷ 4

a = -5.56m/s²

Negative sign shows that the car is slowing down.

Given the initial speed and time elapsed by the car, the negative acceleration that brings the car to a stop at the red light is -5.56m/s².

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1.  The probability given as P(Y∩X) is; 2/25

2. The probability given as P(Y) * P(X) is; 4/15

We are given the following probabilities;

P(X) = 2/3 , P(Y) = 2/5 , and P(X|Y) = 1/5

1. We want to find P(Y ∩ X).

This means probability of the set intersection of Y and X

Since  P(X) = 2/3 , P(Y) =2/5 , and P(X|Y) =1/5, it means that we have a conditional probability.

Thus;  P(Y∩X) = P(Y) * P(X|Y)

P(Y∩X) = 2/5 × 1/5

P(Y∩X) = 2/25

2. We want to find P(Y) * P(X)

Plugging in the relevant values gives;

P(Y) * P(X) = 2/3 × 2/5

P(Y) * P(X) = 4/15

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Complete question is;

For two events X and Y, P(X) =2/3 , P(Y) =2/5 , and P(X|Y) =1/5 . Find the probabilities.

1.  P(Y∩X) = ____

2. P(Y)· P(X) =____

Answer:

[tex] {6}^{12} \times 36 =[/tex]

Answer:

216

Step-by-step explanation:

If x = 8 & y = -9
Put in place -3 (8)(-9)
-24 * -9 = 216

Answer:

5.16666666,...

Step-by-step explanation:

5 + (5/3) - (3/2)

5 + 1.66666666667 - 1.5

5 + 0.16666666666

5.16666666666,...

Nhân chia trc cộng trừ sau

Answer:

31/6 ( or 5 1/6)

Step-by-step explanation:

5 + 5/3 - 3/2 =

5 + 1/6 =

31/6

Answer: its (2,5) or (2,-5)

Step-by-step explanation:

basically it depends on the location like for example: if a dot is in the Q4 area which is (-x,-y) or Q3 is (-x,y) and Q2 is (x,-y) and Q1 is (x,y) so yeah hope it helps

Answer:

B - 5

Step-by-step explanation:

Amy = 8 packs × 7 snacks

Amy = 56 snacks altogether

Mary = Amy - 11

Mary = 56 - 11

Mary = 45 snacks altogether

Mary = 45 snacks / 9 tropical fruit snacks

Mary = 5 packs of tropical fruit snacks

Hope this Helps! :)

- Riona

On multiplying and then simplifying 3∛2x² . 7 ∛32x⁴, we get, 84x⁶

1. Split the radicands in half. A number known as a radicand appears underneath the radical symbol.

2. To multiple radicands, multiply the integers as if they were whole numbers. Always keep the item beneath a single radical sign.

3. Use factoring to exclude any perfect squares from the radicand. To achieve this, check whether any perfect squares have the radicand as a factor.

4. Position the square root of the ideal square before the radical sign. Don't change the second component of the radical symbol.

5. Square the square's root. Sometimes it is necessary to multiply a square root by itself.

Given,

3∛2x² . 7 ∛32x⁴

⇒ [tex]21 (2^{1/3} ) x^{2+4} . 32^{1/3}[/tex]

⇒ [tex]21 (2^{1/3} ) x^{6} . 2^{5/3}[/tex]

⇒ [tex]21 (2^{1/3 + 5/3} ) x^{6}[/tex]

⇒ [tex]21 (2^{2} ) x^{6}\\84x^{6}[/tex]

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Answer:

Its 3D 6U

or -2/-2

Step-by-step explanation:

Using division and the graph, the zeroes of the function are given as follows:

The function in this problem is defined as follows:

f(x) = -3x³ -4x² + x + 2.

From the graph, we have that x = -1 is a zero of the function, meaning that it can be written as follows:

-3x³ -4x² + x + 2 = (x + 1)(ax² + bx + c).

The other zeros will be the zeros of ax² + bx + c. To find the coefficients, we use a system of equations, hence:

(x + 1)(ax² + bx + c) = -3x³ -4x² + x + 2

ax³ + (a + b)x² + (c + b)x + c = 2.

Hence the coefficients are given by:

Thus the quadratic equation that we have to solve is:

-3x² - x + 2 = 0

3x² + x - 2 = 0.

Hence:

The zeroes of the function are given as follows:

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Joy was charged the labor of 11 hours .

Joy was charged a total of $1215 from the landscaper for listed parts and labor.

He was charged $445 for listed parts

He was charged the rest for labor

The hourly rate for labor is $ 70

Let the number of hours worked by labor be x

so, we can form a linear equation here as 445 + 70x = 1215

Now we have to solve this linear equation

445 + 70x = 1215

70x= 1215 - 445

70x = 770

x = 770/ 70

x = 11

Therefore, 11 hours of labor were needed to complete the job.

The correct question is Joy recently hired a landscaper to do some necessary work. On the final bill, Joy was charged a total $1215.  $445 was listed for parts and the rest for labor. If the hourly rate for labor was $70, how many hours of labor were needed to complete the job?

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Answer:

q=10, r=8

Step-by-step explanation:

You have to first cancel one of the variables.

8q-15r=-40

4q+2r=56

To do this, multiply the second equation by -2.

8q-15r=-40

-2(4q+2r)=(56)(-2)

Multiply it out.

8q-15r=-40

-8q-4r=-112

Combine like terms.

-19r = -152

Divide by -19 to get the value of r.

r=8

Substitute r back into one of the equations, it does not matter which one. I'll do both.

8q-15(8)=-40

8q-120=-40

8q=80

q=10

4q+2(8)=56

4q+16=56

4q=40

q=10

You should get the same value for q for both.

In the instance where the variables are x and y, which they usually are, you would write your answer as an ordered pair, (x, y).

(10, 8)

Answer:

q=10 and r=8

Step-by-step explanation:

8q-15r=-40 ...........equation(i)

4q+2r=56................eqn(ii)

Now,

Multiplying eqn (ii) by 2 then we get,

8q+4r=112..........eqn(iii)

Here, Subtracting eqn (i) and (iii)

8q-15r=-40

8q+4r=112

(-) (-) (-)

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

-19r=-152

r= -152/-19

r= 8

Again, Putting the value of r in eqn (ii)

4q+2r=56

4q+2×8=56

4q=56-16

q=40/4

q=10

Answer:

Step-by-step explanation:

12z=108 what’s the value of z

12z = 108

z = 108 : 12

z = 9

check

12 * 9 = 108

108 = 108

the answer is good

Answer:

15

Step-by-step explanation:

Answer:

The number is 1

Step-by-step explanation:

Let the number be x
Subtract 8 from x ==>   x - 8

Multiply by -3 ==>         -3(x - 8) = -3(x) -3(-8) = -3x - 24

This equals 21

So
-3x + 24 = 21

Subtract 24 from both sides:
-3x + 24 - 24 = 21 - 24

==> -3x + 0 = - 3

-3x = -3

Divide by -3

==> -3x/-3 = -3/-3

x = 1

Check

1 - 8 = -7

-3(1-8) = -3 x -7 = 21

The cost per cup of milk as required in the task content is; $0.14375.

The cost per fluid ounce of milk as required in the task content is; $0.018.

The cost per quart of milk as required in the task content is; $0.575.

It follows from the task content that the cost of each unit measure of milk is to be determined. Therefore, since the cost per gallon of milk is; $2.30.

1). Since there are 16 cups of milk per gallon, it follows that the cost per cup of milk is; 2.30/16 = $0.14375

2). Also, Since there are 128 fluid ounces of milk per gallon, it follows that the cost per fluid ounce of milk is; 2.30/128 = $0.018

3). Also, Since there are 4 quarts of milk per gallon, it follows that the cost per quart of milk is; 2.30/4 = $0.575

Ultimately, the cost per unit measure of milk in each case scenario has been determined and is as represented above.

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value of x in given logarithmic equation is =  2000

In, mathematics a logarithmic function is inverse of exponential function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function

           x is the expression

Mathematically, if [tex]a^x = N[/tex] is and exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

Some important formulas of logarithms :

According to given statement,

log x - log 2 =3

using formula, log a - log b = log a/b

=> log x/2 = 3

=> x / 2 = 10³

=> x = 2 . 10³ = 2000

Thus solution for this equation is x =2000.

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The temperature at dawn is -7 F.

If it is  8 degrees colder at dawn than it is at dawn, it means that the temperature is lower in the dawn than it is in the dusk. Thus, to determine the temperature at dawn, subtract 8 from the temperature at dusk.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -.

Temperature at dawn = termpature at dusk - difference in termpature

1 - 8 = -7

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