Solve for x:
4(x-5)
8
= 9y
X =
= [?]y + []
Enter

Answer:

substitute means to use or add in place of something.

Step-by-step explanation:

Example: Substitute 1 for x: therefore x now is equal to 1.

The required value of focus of the parabola is (3, 2).

A parabola is set of all places in a plane which are an equivalent separation away from a given point and given line. The fact is known as the focal point of the parabola and the line is known as the directrix. The emphasis lies on the hub of balance of the parabola.

parabola: f(x) = 1/4 (x – 3)^2 + 1

On comparing with general formula y = a(x - h)^2 +k

We get,

a = 1/4

h = 3

k = 1

vertex is (3, 1)

Now, we need p  the distance from the vertex to the focus.

⇒ 1/4a

⇒ 1/4/4

⇒  1

Then focus of parabola is( h, k+p ) = (3, 2)

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Answer:-2, 0, 2, 3, 4

Step-by-step explanation:

-2 is smaller than 0, 0 is smaller than 2, 2 is smaller than 3, and 3 is smaller than 4.

Answer:

4, 3, 2, 0, -2

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equivalent to -(1/6)y + 1/3 is,

-(1/6)y + 1/3

Take 1/6 common from both first and the last term,

1/6 (-y + 2)

Hence, the correct option is C.

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The distance between the waterfall and the lake is 12.25 km.

The distance between the waterfall and the lake as "d".

We have a triangle with two sides given: 13.6 km (south) and an included angle of 228 degrees.

Using the law of cosines, the formula for finding the third side is:

d² = a² + b² - 2abcos(C)

Where:

a = 13.6 km

b = unknown (d)

C = 180 degrees - 228 degrees (to convert the bearing to an angle)

Now we can calculate:

C = 180° - 228° = -48° (since we need to use the interior angle)

d²= (13.6 km)² + (d)² - 2(13.6 km) (d)cos(-48°)

Simplifying and solving for "d":

d² = 184.96 km² + d²- 27.2 km.d.cos(-48°)

d = 184.96 km² / (27.2 km×cos(-48°))

cos(-48°) = 0.6691.

d = 184.96 km² / (27.2 km × 0.6691)

d = 12.245 km

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The meaning of the statement, "if the function has no parameters, then the class C is definable" is that if there are no parameters given then the class c can be defined with an empty set but if there are no parameters, then the class cannot be defined.

The meaning of the above statement is that if no parameters are provided for this function, then the given class represented as c can be defined with an empty set that is enclosed in parameters.

Also, if the parameters are given then the class c is not defined.

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The equations that could be used to solve for the number of male runners (m) in the race are (m+75)/m = 3 / 2 and 150 + 2m = 3m. The correct options are A and B.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that at a running race, the ratio of female runners to male runners is 3 to 2. There are 75 more female runners than male runners.

The ratio is written as,

f/ m = 3 / 2

There are 75 more female runners than male runners.

f = m + 75

The equation can be written as,

f / m = 3 / 2

( m + 75 ) / m = 3 / 2

Or

150 + 2m = 3m

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Solution:

5/8 of the students in a school are girls.

This simply means 5 out of every 8 students is girl and 3 out of every 8 children is boy.

Thus, there are 5 girls to 3 boys.

Hence, the ratio of girls to boys is 5:3

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

The five key points of the parent function are:

The function is given as:

y = -2 sin[2(x - 45)] + 1

The above function is a sine function, and the parent function of a sine function is

y = sin(x)

The properties of the above function are:

The transformed function is given as:

y = -2 sin[2(x - 45)] + 1

A sine function is represented as:

y = A sin[Bx + C] + D

Where:

Using the above representations, we have:

See attachment for the graph of the sine function y = -2 sin[2(x - 45)] + 1

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Answer:

about 440,000

Step-by-step explanation:

Here 438,105 you can round of the 38,000as 40,000 so will get 440,000.

Answer:

2

Step-by-step explanation:

Given,

6x-3y=18

or, -3y=18-6x

dividing by 3 into both sides and multiply by -1

we get,

y=2x-6

comparing above eq with linear equation y=mx+c

we get,

m=2 Ans.

Answer: -8

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

In the Pythagorean theorem the sum of the 2 shortest side's squares add up to the square of the longest side (a²+b²=c²).

58²+58² = 64²

3,364+3,364 = 4,096

6,728 = 4,096

This is false so these sides can not make up a right triangle

According to the unitary method,

A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.

B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.

Unitary method:

In math, unitary method refers the process of finding the value of a single unit, and based on this value.

Given,

Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.

Here we need to find the following:

A) The time take for Peter to finish the job alone

B) The time taken for Emily and Peter to finish the job together

Let us consider x be the time taken for Peter to finish the job alone.

So, based on the given question we can write it as,

=> 1/6 + 1/8 + 1/x = 1/2

=> (8 + 6)/48 + 1/x = 1/2

=> 14/48 + 1/x = 1/2

=> 7/24 + 1/x = 1/2

=> 1/x = 1/2 - 7/24

=> 1/x = 12 -7/24

=> 1/x = 5/24

=> x = 24/5

=> x = 4.8

So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.

Then the time taken for Emily and Peter to finish the job together is calculated as,

=> 5/24 + 1/6

=> 5 + 4/ 24

=> 9/24

=> 3/8

Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.

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Answer:

There is now 3 cups of m ilk left in the jug.

Step-by-step explanation:

12+1=13 | 13-16=3

ANSWER: 3

Answer:

The probability is  \(P(\= X > 12 ) = 0.72688\)

Step-by-step explanation:

From the question we are told that

   The  mean is  \(\mu = 12.3 \ years\)

    The standard deviation is  \(\sigma = 0.7 \ years\)

    The sample size is  n = 14

Generally the standard error of the mean is mathematically represented as

         \(\sigma _{x} = \frac{\sigma}{\sqrt{n} }\)

=>       \(\sigma _{x} = \frac{0.7}{\sqrt{14} }\)

=>       \(\sigma _{x} = 0.1871\)

Generally the probability that their mean life will be longer than 12 years is mathematically represented as

      \(P(\= X > 12 ) = P(\frac{\= X - \mu }{\sigma} > \frac{12 - 12.3}{ 0.1871 } )\)

\(\frac{\= X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \=  X )\)

       \(P(\= X > 12 ) = P(Z > -0.6034 )\)

From the z table  the area under the normal curve to the left corresponding to    -0.6034  is

=>    \(P(Z > -0.6034 ) = 0.72688\)

=>   \(P(\= X > 12 ) = 0.72688\)

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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Answer:

8 ft², 21.8ft², and 11.2ft²

Step-by-step explanation:

Answer: 10 ounces for $2.40

Step-by-step explanation: The trick behind these problems, always divide. 2.40/10ounces is $0.24. 2.08/8ounces is $0.26. Better deal, therefore smaller answer of the 2, because it's cheaper.

The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.

The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.

We are given that the price of the case is $7.50. Substituting this value in the equation, we get:

24b = 7.50

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:

b = 7.50/24

Simplifying this expression, we get:

b = 0.3125

Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.

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Option C. triangle 1 and triangle 3 are congruent.

By SAS Congruence Criterion.

Sides and Angles Are equal in both the triangles

Answer: triangle 1 and triangle 3

Step-by-step explanation:

The compound interest rate of the investment is 1.10%

The given parameters about the compound interest are

Principal, P = $11,000

Amount, A = $20,000

Time, t = 9

Number of times, n = 12 i.e. monthly interest

To calculate the amount, we have:

A = P(1 + R/n)^nt

Substitute the known values in the above equation, so, we have the following representation

20000 = 11000 * (1 + r/12)^(12 * 9)

This gives

1.82 = (1 + r/12)^108

Take the 108th root of both sides

1 + r/2 = 1.0055

Subtract 1 from both sides

r/2 = 0.0055

Multiply by 2

r = 0.011

Express as percentage

r = 1.10%

Hence, the value of the interest rate is 1.10%

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Answer:

6.66%

Step-by-step explanation:

Compounded Monthly:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

20000

�

=

11000

�

=

9

�

=

12

A=20000P=11000t=9n=12

Given values

20000

=

20000=

11000

(

1

+

�

12

)

12

(

9

)

11000(1+

12

r

​

)

12(9)

Plug in values

20000

=

20000=

11000

(

1

+

�

12

)

108

11000(1+

12

r

​

)

108

Multiply

20000

11000

=

11000

20000

​

=

11000

(

1

+

�

12

)

108

11000

11000

11000(1+

12

r

​

)

108

​

Divide by 11000

1.8181818

=

1.8181818=

(

1

+

�

12

)

108

(1+

12

r

​

)

108

(

1.8181818

)

1

/

108

=

(1.8181818)

1/108

=

[

(

1

+

�

12

)

108

]

1

/

108

[(1+

12

r

​

)

108

]

1/108

Raise both sides to 1/108 power

1.0055509

=

1.0055509=

1

+

�

12

1+

12

r

​

−

1

−1=

−

1

−1

Subtract 1

0.0055509

=

0.0055509=

�

12

12

r

​

12

(

0.0055509

)

=

12(0.0055509)=

(

�

12

)

12

(

12

r

​

)12

Multiply by 12

0.0666108

=

0.0666108=

�

r

6.66108

%

=

6.66108%=

�

r

Convert to percent (multiply by 100)

�

≈

r≈

6.66

%

6.66%

Round to the nearest hundredth of a percent

Answer:

\(\huge\boxed{\sf x = 5}\)

Step-by-step explanation:

g(x) = -3x + 8

Given that, g(x) = -7

-7 = -3x + 8

Subtract 8 to both sides

-7 - 8 = -3x

-15 = -3x

Divide -3 to both sides

5 = x

OR

x = 5

\(\rule[225]{225}{2}\)