Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?

try attaching a photo tso we can see the shapes

Answer:

Step-by-step explanation:

here x1=8 , y1=9 , x2=4 , y2=4

using formula

slipe(m)=y2-y1/x2-x1

=4-9/4-8

=-5/-4

=5/4

By solving a system of equations we will see that she sold 80 phones and 240 accessories.

Let's define the variables:

x = number of phones.

y = number of accessories.

We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:

y = 3x

x*$8 + y*$4 = $160

To solve the system, we can replace the first equation into the second one.

x*$8 + (3x)*$4 = $160

x*$8 + x*$12 = $160

x*$20 =  $160

x  = $160/$20 = 80

She sold 80 phones, and the number of accessories is:

y = 3x

y = 3*80 = 240

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer:

(b.) Angles 6 and 8 are supplementary

(c.) Angle 1 is congruent to Angle 4

(d.) Angle 2 is congruent to Angle 7

Step-by-step explanation:

Explaining b. Angles 6 and 8 are supplementary:

There are four pairs of these supplementary angles in this diagram including:

Explaining c. Angle 1 is congruent to Angle 4:

There are also four sets of vertical angles in the diagram including:

Explaining d. Angle is congruent to Angle 7:

There are two pairs of alternate exterior angles in the diagram:

x + y = 15------(1)

x/y = 2------(2)

y = 15 - x

put this value in eq 2

x/(15-x) = 2

x = 2 (15 - x)

x = 30 - 2x

2x + x = 30

3x = 30

x = 10

y= 15 - x

y = 15 - 10

y = 5

Solution:

Given:

Let’s simplify the second equation to find out the value of x.

Now, let’s substitute the value of x into the first equation.

Now, let’s substitute the value of y into the simplified second equation.

Hence, the value of x and y are 5 and 10 respectively.

The required regression equation is y = -2.78x + 48.5 for the line of best fit where x represents the month and y represents the time.

The table is given in the question.

As per the given table, the required solution would be as:

Let x represents the month and y represents the time

\(\bar{x}\) = (1+2+3+4+5+6)/6 = 21/6 = 3.5

\(\bar{y}\) = (47+43+39+36+35+33)/6 = 233/6 = 38.83

Sum of x = 21

Sum of y = 233

Mean x = 3.5

Mean y = 38.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = -48.5

Regression Equation = y = bx + a

b = SP/SSX = -48.5/17.5 = -2.77143

a = MY - bMX = 38.83 - (-2.77×3.5) = 48.53333

y = -2.78x + 48.5

Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.

To learn more about the Regression Equation click here:

https://brainly.com/question/14184702

#SPJ1

Answer:

y = -2.78x + 48.5

Step-by-step explanation:

I just took the test like 2 seconds ago...

Answer: 0= y x (x)

Step-by-step explanation: y x x ≠ 0.1x

The required inequality for the height of the building around the park should be y < 0.9x.

Given that,
A city has a building code that limits the height of buildings around the central park. The code says that all buildings must be less than 0.1x in height where x is the distance of the building from the center of the park and y is height in feet. Assume that the par center is located at 0.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
The height of all the buildings must be,
y < x - 0.1x
y < x(0.9)
y < 0.9x

Thus, the required inequality for the height of the building around the park should be y < 0.9x.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ2

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

Read more about Economic Order Quantity at: https://brainly.com/question/26814787

#SPJ1

Answer:  y = -320

Steps:  ³⁄₂y + 12 = ⁷⁄₅y - 20

Subtract 12 from both sides:  ³⁄₂y + 12 - 12 = ⁷⁄₅y - 20 - 12

Simplify: ³⁄₂y = ⁷⁄₅y -32

Subtract ⁷⁄₅y from both sides: ³⁄₂y -  ⁷⁄₅y = ⁷⁄₅y -32 -  ⁷⁄₅y

Simplify: ⅒y = -32

Multiply both sides by ten: 10  ·  ⅒y = 10  · -32

Simplify: y = -320

Plz mark brainliest:)

Answer:

\(Y=\frac{c}{a}-\frac{b}{a}\)

Step-by-step explanation:

Answer:

y=c+b/a (The a is under c+b)

Step-by-step explanation:

Add the b over to c.

ay=c+b

Now divide both sides by a, which will remove the a from y.

y=c+b/a

Answer:

160 trust me

Step-by-step explanation:

we multiply the length by the width which is the formula of finding rectangular areas'  

Answer:

No, a triangle cannot be created with these measurement.

Step-by-step explanation:

It must follow these rules:

a + b > c

b + c > a

a + c > b

Answer:

it is y=-3/2x+6 and then you subtract it by 2 and then add 7 and then u get 49

Step-by-step explanation:

The probability that it is in a winning position will be 0.8036.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.

Then the probability of winning is calculated as,

P = [a² - πd² / 4] / (a²)

P = [4² - 3.14 x 2² / 4] / (4²)

P = (16 - 3.14) / 16

P = 0.8036

The probability that it is in a winning position will be 0.8036.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ1

The events A and B are not mutually exclusive, so the probability of A∩B cannot be equal to 1/12.

(a) The probability of A∩B is given by the intersection of the probabilities of A and B:

P(A∩B) = P(A) * P(B)

Substituting the given probabilities:

P(A∩B) = (3/4) * (1/3) = 1/4

Since 1/4 is smaller than 1/3, we have shown that the probability of A∩B is smaller than 1/3.

The situation where the probability of A∩B is equal to 1/3 would occur if and only if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event. However, in this case, A and B are not independent events, so the probability of A∩B cannot be equal to 1/3.

(b) Similar to part (a), we have:

P(A∩B) = P(A) * P(B) = (3/4) * (1/3) = 1/4

Since 1/4 is larger than 1/12, we have shown that the probability of A∩B is larger than 1/12.

The situation where the probability of A∩B is equal to 1/12 would occur if and only if A and B are mutually exclusive events, meaning that they cannot occur at the same time. In this case, the events A and B are not mutually exclusive, so the probability of A∩B cannot be equal to 1/12.

To know more about probability, visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

8

Step-by-step explanation:

Okay, let's break this down:

Given: (7+3²)3/|-8|-|-2|

Write as a fraction: \(\frac{(7+3^{2} )3}{ |-8|-|-2|}\)

Now for the denominator:

Absoulte value: \(\frac{(7+3^{2} )3}{ 8-+2}\)

Simplifying bottom: \(\frac{(7+3^{2} )3}{ 6}\)

Numerator:

Exponent: \(\frac{(7+9)3}{6}\)

Add: \(\frac{(16)3}{6}\)

Multiply: \(\frac{48}{6}\)

Answer:

Divide: 48 / 6 = 8

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

It is concluded that the alternative hypothesis H1: σ² < 100 is true.

The variance is the square of the standard deviation of a sample of observations. In order to test whether a given variance of the population is equal to a given value, we make use of the chi-square distribution.

Thus, let X be a random variable that has a normal distribution with mean μ and variance σ². The formula to calculate chi-square distribution is as follows:

chi-square (x²) = (n-1) * S² / σ²Where n = sample size, S² = sample variance, and σ² = population variance.

Now, let's perform a hypothesis test with the given data:

Null hypothesis:H0: σ² = 100

Alternative hypothesis:

H1: σ² < 100

The value of the test statistic is:chi-square (x²) = (n-1) * S² / σ²= (25-1) * 131.29 / 100= 33.82

The degrees of freedom (df) for the test is

:df = n - 1= 25 - 1= 24

The critical value for chi-square distribution at df = 24 and α = 0.01 is 9.7097.

Since the calculated test statistic (33.82) is greater than the critical value (9.7097), we reject the null hypothesis and conclude that there is evidence to suggest that the variance of the miles per gallon (mpg) is less than 100.

Therefore, it is concluded that the alternative hypothesis H1: σ² < 100 is true.

Know more about alternative hypothesis here:

https://brainly.com/question/13045159

#SPJ11

You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

To learn more about scatter plot refer to:

https://brainly.com/question/6592115

#SPJ4

The balloon artist will charge Mrs. Abara $55 as an additional supply fee since there are more than 10 children at the party, and the party duration is irrelevant to the fee calculation.

1. Given that there will be 16 children at the party, which is more than 10, the balloon artist will charge an additional supply fee.

2. The additional supply fee is $55, as stated in the question.

3. The duration of the party, which is 4.5 hours, is not mentioned as a factor affecting the fee calculation.

4. Therefore, regardless of the party's duration, the balloon artist will charge Mrs. Abara $55 as the additional supply fee due to the number of children exceeding 10.

Learn more about additional  : brainly.com/question/29783548

#SPJ11

Answer:

A. (2,5), (3,6), (6,9)

Step-by-step explanation:

In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.

The hash of the given message is 135.

In computing, a message digest is a fixed-sized string of bytes that represents the original data's cryptographic hash. This hash is used to authenticate a message, guaranteeing the integrity of the data in the message.

Here, it is given the message m = 23  

The formula to calculate hash is him) - (m*7;2 MOD 7793.

So, let's calculate the hash : him) - (m*7;2 MOD 7793(him) - (23*7;2 MOD 7793

⇒ (8*23) - (49 MOD 7793)

⇒ 184 - 49= 135.

So, the hash of the given message is 135.

To know more about message digest, please click here:

https://brainly.com/question/6384456

#SPJ11

Answer:

-13

Step-by-step explanation:

Answer: 2(-4x+y)

Step-by-step explanation:

rewrite -8 as 4*2

4*2x+2y

factor out the common term (2)

2(-4x+y)

Answer:

Set your calculator to degree mode.

cos(48°) = y/35

y = 35cos(48°)

tan(20°) = x / 35cos(48°)

x = 35cos(48°)tan(20°) = 8.5 inches

Answer:

8.5 in

Step-by-step explanation:

Find height, h, of the triangle:

cos48 = h/35

h = cos48(35) = 23.42

tan20 = x/23.42

x = tan20(23.42) = 8.524 ≈ 8.5 in

Answer:

what show me a picture of it

According to given conditions, the solution for c is (P - 5)/2.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a numerical value. Expressions can also contain functions, parentheses, brackets, and other symbols that indicate the order of operations.

Starting equation: P = 2c + 5

Add 5 to both sides of the equation:

P + 5 = 2c + 5 + 5

Simplify:

P + 5 = 2c + 10

Subtract 5 from both sides of the equation:

P + 5 - 5 = 2c + 10 - 5

Simplify:

P = 2c + 5

Substitute c with (P - 5)/2:

P = 2((P - 5)/2) + 5

Simplify:

P = P - 5 + 5

Simplify further:

P = P

Therefore, according to given conditions, the solution for c is (P - 5)/2.

To know more about expressions visit :

https://brainly.com/question/1859113

#SPJ1

Answer:

0.3 lbs

Step-by-step explanation:

4.2/14 = 0.3 lbs of trail mix in each bag

Answer:

First, if we have a function defined as:

\(G(x) = \int\limits^x_0 {f(t)} \, dt\)

then:

G'(x) = f(x)

\(F(x) = \int\limits^x_0 {cos(t)^2} \, dt\)

then:

F' = dF/dt = cos(t)^2

F'(1) = cos(1)^2 = 0.2919

If we round it up to the third digit after the decimal point we get:

F'(1) = 0.292

The correct option is the second one.