x+y=5
3x-4y=8
please i need the steps

The x values of the polynomial expression given as x^2 - 324 = 0 are x = 18 and x = -18

The polynomial expression is given as:

x^2 - 324 = 0

Rewrite as

x^2 + 0 - 324 = 0

Express 0 as 18x - 18x

So, we have:

x^2 + 18x - 18x - 324 = 0

Factorize the polynomial expression

x(x + 18) - 18(x + 18) = 0

Factor out x + 18

(x - 18)(x + 18) = 0

Split the factors

x - 18 = 0 and x + 18 = 0

Solve for x

x = 18 and x = -18

To use a table, we have

x^2 - 324 = 0

Set x = some values and calculate the expression

x      x^2 - 324

3     -315

6      -288

9       -243

18       0

Hence, the values of x are x = 18 and x = -18

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Answer:

See attached picture

Step-by-step explanation:

We rarionalize by multiplying with the conjugate of the denominator

Answer:

\(\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}\)

Step-by-step explanation:

\(\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }\)

To rationalize the above fraction multiple both numerator and denominator by the conjugate of its denominator.

\(\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }\)

We can simplify √8 like this :

√8 = √4 × √2

√8 = 2√2

Let us rationalize the above fraction now.

\(\frac{4+\sqrt{ 5}}{\sqrt{15}-\sqrt{8} }*\frac{\sqrt{15}+\sqrt{8} }{\sqrt{15} +\sqrt{8} }\\ \\\\\frac{(4+\sqrt{ 5})}{(\sqrt{15}-\sqrt{8}) }*\frac{(\sqrt{15}+2\sqrt{2} ) }{(\sqrt{15} +\sqrt{8})}\)

Solve the brackets and roots.

\(\frac{4(\sqrt{15}+2\sqrt{2})+\sqrt{5} (\sqrt{15} +2\sqrt{2}) }{\sqrt{ 15} * \sqrt{15} - \sqrt{8} * \sqrt{8} } }\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}\)

Simplify the roots.

√75 = √25 × √3

√75 = 5√3

\(\frac{4\sqrt{15} +8\sqrt{2}+\sqrt{75}+2\sqrt{10} }{15-8}\\\\\\\frac{4\sqrt{15} +8\sqrt{2}+5\sqrt{3} +2\sqrt{10} }{7}\)

Answer: 11/15

Hope this helps! ^^

Answer: The answer in improper form is 11/15 or in mixed number form it is 12 1/5... I did this by dividing the Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

2/3 * 11/10

For fraction multiplication, multiply the numerators and then multiply the denominators to get

2*11/3*10=  22/30

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 22 and 30 using 22 divided by 2/30 divided by 2 which equals 11/15.

Therefore 2/3 divided by 10/11 equals 11/15

Hope this helps... Plz mark me brainliest... Stay safe and have a great weekend!!! :D

The grocer should combine 2 lbs of the $1.75/lb trail mix with 3 lb of the $3.75/lb trail mix to get $2.95/lb trail mix.

A grocer is a retailer who sells food and household items. Grocery stores are typically stocked with a wide variety of products, including fresh fruits and vegetables, meat, dairy, bread, canned goods, frozen foods, and other packaged food items. Grocers may also offer non-food items such as cleaning products, health and beauty supplies, and pet supplies.

The total cost of the combined trail mix must be equal to the cost of the desired $2.95/lb trail mix. So, we can set up the following equation:
1.75x + 3(3.75) = 2.95(x+3)
where x is the number of pounds of the $1.75/lb trail mix.
Solving for x, we get:
1.75x + 11.25 = 2.95x + 8.85
Subtracting 2.95x from both sides, and subtracting 8.85 from both sides, we get:
-1.2x = -2.4
Dividing both sides by -1.2, we get:
x = 2
So, the grocer should combine 2 lbs of the $1.75/lb trail mix with 3 lb of the $3.75/lb trail mix to get $2.95/lb trail mix.

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Answer:

10 units and 157.84 units

Step-by-step explanation:

4

substitute t = 1 into the equation

h = - 16(1)² + 6 = - 16 + 6 = - 10

the value is negative since the ball travels down

the ball has travelled 10 units after 1 second

5

substitute t = 3.2 into the equation

h = - 16(3.2)² + 6 = - 16(10.24) + 6 = - 163.84 + 6 = - 157.84

the well is 157.84 units deep

Answer:

(a) The median estimate is 450.

(b) The first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is 450.

(d) The particular value which is less than 150 or it is more than 1200, is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed.

Step-by-step explanation:

We are given that the box plot shows the undergraduate in-state tuition per credit hour at four-year public colleges. 0, 300, 600, 900, 1,200, 1,500.

(a) As we can see in the box plot that the middlemost data lies between 300 and 600, that means;

Median is given by the average of the two numbers, i.e;

             Median =  \(\frac{300+600}{2}\)

                           =  \(\frac{900}{2}\)  = 450

So, the median estimate is 450.

(b) As we know that the first quartile represents 25% of the data values and the third quartile represents 75% of the data values.

So, from the box plot given; we can observe that the first quartile, \(Q_1\) = 300 and the third quartile lies between the values of 600 and 900, i.e;

Third quartile, \(Q_3\) = \(\frac{600+900}{2}\)

                             =  \(\frac{1500}{2}\)  = 750

So, the first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is given by the following formula;

          Interquartile range = Third quartile - First quartile

                                          =  \(Q_3-Q_1\)

                                          =  750 - 300 = 450

(d) From the box plot; it is clear that if the particular value is less than 150 or it is more than 1200, then it is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed because the more values are on the right side of the curve and it skewed towards the right.

Answer:

−8x^4 + 5x^3 + x^2

Step-by-step explanation:

3x^3  + x^2  + 2 (x^3  − 4x^4)

Apply the distributive property.

3x^3  + x^2  + 2x^3  + 2 (−4x^4)

Multiply −4 by 2.

3x^3 + x^2 + 2x^3 − 8x^4

Simplify by adding terms.

Add 3x^3 and 2x^3.

5x^3 + x^2 − 8x^4

Simplify the expression.

Move x2.

5x^3 − 8x^4 + x^2

Reorder 5x^3 and −8x^4.

−8x^4 + 5x^3 + x^2

Answer:

A

Step-by-step explanation:

-4x+5y=10. -4x+5y=10. -4x+5y=10

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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Answer:

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Step-by-step explanation:

From the information given :

An exit poll of 200 voters finds that 94 voted for the referendum.

How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52​? Based on your​ result, comment on the dangers of using exit polling to call elections.

This implies that ;

the Sample size n = 200

the probability p = 0.52

Let X be the random variable

So; the Binomial expression can be represented as:

X \(\sim\) Binomial ( n = 200, p = 0.52)

Mean \(\mu\) = np

Mean \(\mu\)  = 200 × 0.52

Mean \(\mu\)  = 104

The standard deviation \(\sigma\) = \(\sqrt{np(1-p)}\)

The standard deviation \(\sigma\) = \(\sqrt{200 \times 0.52(1-0.52)}\)

The standard deviation \(\sigma\) = \(\sqrt{200 \times 0.52(0.48)}\)

The standard deviation \(\sigma\) = \(\sqrt{49.92}\)

The standard deviation \(\sigma\) = 7.065

However;

P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .

The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5

Now;

x = 94.5

Therefore;

\(z = \dfrac{x- \mu}{\sigma}\)

\(z = \dfrac{94.5 - 104}{7.065}\)

\(z = \dfrac{-9.5}{7.065}\)

z = −1.345

P(X< 94.5) = P(Z < - 1.345)

From the z- table

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where:

x1 and x2 are the sample means of the two sheets,

s_p is the pooled standard deviation,

n1 and n2 are the sample sizes.

The pooled standard deviation (s_p) can be calculated using the following formula:

s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))

where:

s1 and s2 are the sample standard deviations.

To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.

Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.

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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.

The t-statistic for a paired t-test is calculated as follows:

t = (X1 - X2) / (s / √n)

where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.

Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.

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Given that:

A 15-foot log is cut into two pieces.

Longer piece is 1.5 feet shorter than twice the shorter piece.

Solution:

Let the length of shorter piece be x feet. So,

Length of longer piece = 2x-1.5 feet

Total length = x+(2x-1.5) feet

Now,

\(x+(2x-1.5)=15\)

\(3x-1.5=15\)

\(3x=15+1.5\)

\(3x=16.5\)

\(x=\dfrac{16.5}{3}\)

\(x=5.5\).

So, length of shorter piece is 5.5 feet.

\((2x-1.5)=2(5.5)-1.5\)

\((2x-1.5)=11-1.5\)

\((2x-1.5)=9.5\)

So, length of longer piece is 9.5 feet.

Answer:

30%

Step-by-step explanation:

The value of the voltage of the electricity is 6 + j + 2j²

From the question, we have the following parameters that can be used in our computation:

C = 2 - j

I = 3 + 2j

The formula of voltage is given as

V = CI

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

V = (2 - j) * (3 + 2j)

Open the brackets

So, we have

V = 6 + 4j - 3j + 2j²

Evaluate the like terms

V = 6 + j + 2j²

Hence, the voltage is 6 + j + 2j²

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Answer:

the first one

Step-by-step explanation:

because I know the answer

The quadratic function represented in the graph is f(x) = -5 (x - 1) (x + 5).

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given a graph of a quadratic function.

The graph is directed downwards. So the leading coefficient is negative.

The function touches the X axis at two points, x = -5 and x = 1.

So -5 and 1 are the zeroes of the function.

So the function can be factored as,

f(x) = (x + 5)(x - 1)

So the quadratic equation is,

f(x) = -5 (x - 1) (x + 5)

Hence the equation of the given quadratic equation is f(x) = -5 (x - 1) (x + 5).

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Answer:

28.8

Step-by-step explanation:

4% * 720

.04 * 720

28.8

a) The position function for the object is s(t) = t4 +t² + 3t with s in feet and t in minutes.b) The velocity function of the object v(t) = 4t³ + 2t + 3 in feet per minute.c) The acceleration at time t = 3 is 114 feet per minute squared (ft/min²).

Explanation: Given that the object's position is s(t) = t4 +t² + 3t, we can find its velocity function v(t) by taking the derivative of s(t).v(t) = s'(t) = d/dt (t⁴ + t² + 3t) = 4t³ + 2t + 3Therefore, the velocity function of the object is v(t) = 4t³ + 2t + 3 in feet per minute. To find the acceleration at time t = 3, we take the derivative of the velocity function. v'(t) = d/dt (4t³ + 2t + 3) = 12t² + 2At time t = 3, the acceleration is:v'(3) = 12(3)² + 2 = 114 feet per minute squared (ft/min²).Therefore, the acceleration at time t = 3 is 114 ft/min².

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If two points are at different heights on a graph, we would need to check the values of the dependent variable (y-axis) to establish if they are actually different.

To establish if two points on a graph at different heights are actually different, we should check the values of the dependent variable (y-axis) being plotted

We should check the numerical values of the variable being plotted on the y-axis to see if they are different between the two points. This would tell us whether there is a statistically significant difference between the two groups or not.

To determine whether the difference between the two points is statistically significant, we can perform a hypothesis test or a statistical analysis to compare the means or distributions of the data at the two points.

Alternatively, we can also look at confidence intervals or p-values to establish the statistical significance of the difference between the two points.

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a. The images coincide because rotations preserve rays.

b. Transformations preserve distances, so the image of point A and point E are the same distance along the same ray from C and they have to coincide.

c. The rotation would also make the image of B equal with D. So there is a rigid motion that takes CBA onto CDE.

Transformations are classified into rigid and non-rigid, according to the definitions presented as follows:

In this problem, the transformation was a rotation of triangle BAC over vertex C, generating triangle EDC.

A rotation is a rigid transformation, hence the distances are preserved.

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Answer:

x=5

Step-by-step explanation:15x - 10x -2 = 23

5x= 23 = 2

5x = 5

x=5

Answer:

X=5

Step-by-step explanation:

15x - 2 = 10x + 23

5x - 2 = 23

5x = 25

x = 5

Hope this helps. Pls give brainliest.

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

What diagram below?

Step-by-step explanation:

There's no picture.

Answer: 16,200 Seconds

Step-by-step explanation:

Data: 4.5 hours(h)=x seconds(s)

Step One, Convert Hours Into Minutes

4.5h=4h and 30 minutes(m)

1h=60mx4=240m+30=270m

Reason: Since to convert to seconds, minutes are needed, you have to convert everything to minutes. And with 60 minutes in an hour you have to multiply 60 by 4 to get 240 and add 30 minutes to it(since it's 4.5 hours) to find ourselves at 270 minutes.

Step two, Convert Minutes Into Seconds

1m=60s

270mx60=16,200s

Reason: Since we are ultimately trying to get 4.5 hours into seconds, we have to convert the minutes we have into seconds by multiplying 270 minutes by 60(since 60 seconds are in a minute) to get our final answer of 16,200 seconds.

I hope this helps!

By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.

A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.

The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.

The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.

In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.

On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.

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Answer:

0

Step-by-step explanation:

-4(2x+5)+8x+20

-8x-20+8x+20

0+0=0

0

Answer:

54 and 42

Step-by-step explanation:

add 9 and 7

use your answer as a denominator

to find the value for 9 you do 9/16 *96

which will give you 54

then do the same for 7 but replace the 9 with seven

according to question the surface integral is (32π - 192)/15.

To evaluate the surface integral, we need to parameterize the surface and find the surface element ds.

Let's consider the parameterization:

x = y^2 + z^2

y = y

z = z

The surface element can be found as:

ds = √(1 + (dx/dy)^2 + (dx/dz)^2) dy dz

ds = √(1 + 4y^2) dy dz

Now, we can rewrite the integral as:

∫∫s z^2 ds = ∫∫R (y^2 + z^2)^2 √(1 + 4y^2) dy dz

where R is the projection of the surface S onto the yz-plane, which is the region 0 ≤ y ≤ 2, -√(4 - y^2) ≤ z ≤ √(4 - y^2).

Let's evaluate the integral:

∫∫s z^2 ds = ∫0^2 ∫-√(4-y^2)^√(4-y^2) (y^2 + z^2)^2 √(1 + 4y^2) dz dy

Using cylindrical coordinates, we can rewrite the integral as:

∫0^2 ∫0^π/2 ∫0^2r (r^2 cos^2θ + r^2 sin^2θ)^2 r √(1 + 4r^2 sin^2θ) dr dθ dy

Simplifying and solving the integral, we get:

∫∫s z^2 ds = (32π - 192)/15

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Given:

According to an Automobile Association of America report, 11.5% of Americans traveled by car over the 2019 Memorial Day weekend and 87.0% stayed home.

Required:

What is the probability that a randomly selected American stayed home or traveled by car over the 2019 Memorial Day weekend?

Explanation: