Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.

Dana owns      [tex]\frac{3}{14}[/tex] fraction of the business

How to calculate the fractions?

*Identify a fraction: When writing fractions, one number is placed above the dividing line and one number is written underneath it.

*Find the numerator: The numerator—the number at the top—indicates the number of elements that make up the fraction.

*find the denominator: The denominator is the figure at the bottom. This number reveals how many components there are in the total number.

Let us take the fraction shared by Dana and Randi as x

So the equation becomes

[tex]\frac{2}{7} +\frac{2}{7} +x+x=1[/tex]

⇒ [tex]\frac{4}{7}+2x=1[/tex]

⇒2x=1-[tex]\frac{4}{7}[/tex]

⇒[tex]2x=\frac{7-4}{7}[/tex]

⇒[tex]2x=\frac{3}{7}[/tex]

⇒[tex]x=\frac{3}{7*2}[/tex]

⇒[tex]x=\frac{3}{14}[/tex]

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The equation that represent the given situation is y = 15x + 70

When she plants 3 stalks, each plant yields 115 ounces of beans

The first point = (3, 115)

When she plants 8 stalks, each plant yields 190 ounces of beans

The second point = (8, 190)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (190-115) / (8-3)

= 75/5

= 15

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Choose one point and substitute the values in the equation

y - 115 = 15(x - 3)

y - 115 = 15x - 45

y = 15x - 45 + 115

y = 15x + 70

Hence, the equation that represent the given situation is y = 15x + 70

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The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86

What is a probability?

The probability of an event in an experiment is calculated by the division of the number of desired outcomes by the number of total outcomes in the experiment.

From the tree diagram, there are two ways to obtain the promotion:

0.41 of 0.68 (hit the quota).

0.14 of 0.32 (did not hit the quota).

Hence the probability of getting a promotion is:

P(A) = 0.41 x 0.68 + 0.14 x 0.32 = 0.3236.

The probability of both getting a promotion and hitting the quota is:

P(A and B) = 0.41 x 0.68 = 0.2788.

Hence the conditional probability is:

P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.86. (approximately).

The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86

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The limit Lim x→1 (sinx - sin1)/(x - 1) = cos1

The limit of a function f(x) as x tends to a is the value of the function f(x) as x tends to a. It is written as [tex]\lim_{x \to a} f(x) = L[/tex]

GIven that we require the limit given as  [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1}[/tex]

So, substituting the value of x = 1 into the given equation, we have that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{sin1 - sin1}{1 - 1} \\= \frac{0}{0}[/tex]

Since 0/0 is one of the inderterminate forms, we use the L'hopital's rule to find the limit of the given function.

L'hopital's rule states that if [tex]\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0[/tex] and f'(x) and g'(x) exist then [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

Let the variables be

So, since we know that

[tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = \frac{0}{0}[/tex],

So,  [tex]\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}[/tex]

So, we differentiate both the numerator and denominator and find the limit.

So,

[tex]\lim_{x \to 1} \frac{f'(x)}{g'(x)} = \lim_{x \to 1} \frac{\frac{d(sinx - sin1)}{dx} }{\frac{d(x - 1)}{dx} } \\= \lim_{x \to 1} \frac{cosx - 0}{1 - 0} \\= \lim_{x \to 1}cosx \\= cos1[/tex]

So, [tex]\lim_{x \to 1} \frac{sinx - sin1}{x - 1} = cos1[/tex]

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Answer:

30

Step-by-step explanation:

Supplementary angles add to 180°.

[tex]4x+30+2x-30=180 \\ \\ 6x=180 \\ \\ x=30[/tex]

Option D is correct answer, The given model in the picture shows the division problem as: 0.78 ÷ 3 = 0.26.

What is division?

Along with addition, multiplication, and subtraction, division is one of the four basic mathematical operations. The act of separating anything into smaller groups so that each one has the same amount of items is known as division. It is a mathematical operation that is used to distribute and group things equally.

we can count that, there are 26 cubic blocks in each square in the picture,

10 each are vertically in two rows and 6 are horizontally present.

And there are total of 3 such squares present each with 26 cubic blocks.

So these all totals to 78 cubic blocks which is divided in 3 squares and in each squares there are 26 cubic blocks.

Therefore, the division problem representing this can be written as:

0.78 ÷ 3 = 0.26

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On that date, 110.66 euro was worth 160.38 dollars.

On that date, 77.65 dollars was worth 53.58 euro.

Given that one U.S. dollar was worth 0.69 euro, the dollar that was 110.66 euro worth will be:

= Amount of euro / Rate

= 110.66 / 0.69

= 160.38 dollars

The euro that 77.65 dollars was worth will be:

= 77.65 × 0.69

= 53.58 euro

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Answer: divide the area value by 1e+6

Step-by-step explanation:

The numeric value of the function f(x) = 2x² - x + 3 at x = x + 1 is given as follows:

f(x + 1) = 2x² + 3x + 4.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 2x² - x + 3.

The point at which the numeric value is calculated as given by:

x = x + 1.

Hence the numeric value is obtaining replacing the two instances of x in the function by x + 1, as follows:

f(x + 1) = 2(x + 1)² - (x + 1) + 3

f(x + 1) = 2(x² + 2x + 1) - x - 1 + 3

f(x + 1) = 2x² + 4x + 2 - x - 1 + 3

f(x + 1) = 2x² + 3x + 4.

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The coordinates of pre-image point H is (c) (3, 2)

The graph represents the given parameter

On the graph, we have the coordinate of point H' (i.e. the image) to be

H' = (-3, -2)

The transformation rule is given as

Rotation 180° about the origin

Mathematically, this is represented as

(x, y) = (-x, -y)

This implies that:

H = (3, 2)

So, the coordinates are (3, 2)

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From the graph, the ordered pair that is included in the solution to the given system is (-6, -2). The correct option is the second option (−6, −2)

From the question, we are to determine the ordered pair that is included in the solution to the given system of inequalities

The given system of inequalities is

y ≥ 2/3(x) + 2

y < -1/3(x) + 1

To determine the ordered pair that is included in the solution, we will graph the given system of linear inequalities.

The graph of the system of linear inequalities is given below.

From the graph, we can observe that (-6, -2) is a solution to the given system of linear inequalities.

Hence, the ordered pair that is a solution is (-6, -2)

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Answer:

Option B: (-6, -2)

Step-by-step explanation:

i took the test xx

Answer:

×= -7½

Step-by-step explanation:

2x<15

2x<15=0

2x= -15

x= -15/2

x= -7½

Answer:

Step-by-step explanation:

Let the trapezium be B.

Draw a line from the top of the trapezium to it's base and call the triangle formed B.

The base of is 2cm (8cm - 6cm

The area of the triangle = 40cm² ( 5cm x 4cm x 2cm)

Area of the trapezium =. ½ (base x height)

. = 18cm²

Add area of trapezium and triangle.

 = 40cm² + 18cm² = 58cm²

.

Answer:

Step-by-step explanation:

abcdefgh

The solution of the exponential equation is x = -1

We want to solve the exponential equation:

2^(3x + 1) = 1/4

If we apply the natural logarithm in both sides of that equation, we will get:

ln( 2^(3x + 1) ) = ln( 1/4)

(3x + 1)*ln(2) = ln(1/4)

3x*ln(2) = ln(1/4) - ln(2)

x = (ln(1/4) - ln(2))/(3*ln(2)) = -1

The value of x is -1

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Answer: $10,252.87

Step-by-step explanation:

Based on the linear model of data, the price of the car that is 10 year old is approximately 10,000.

Linear model.

Basically, the linear model describes the relationship between a dependent variable, y, and one or more independent variables, X. Where the dependent variable is also called the response variable. And the independent variables are also called explanatory or predictor variables.

Given,

Here we have the table of data that contains the fourteen cars were randomly chosen at a used car lot and the age of each car and its sale price.

Now, we have to find the sale price for the 10 year old car.

In order to find the price of the 10 year old car, we have to plot these given table on the graph.

Then we get the graph like the following.

By looking at the graph, the sales price of the 10 year old car is predicted as approximately 10,000,

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Answer:

Step-by-step explanation:

The area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

First, let us understand the area under the curve:

A definite integral between two points is used to calculate the area under a curve between them. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a and x = b. This area can be estimated by integrating with specified limitations.

We are given:

y = x^2 - 3x

We need to find the area between the curve y = x^2 - 3x for x between 1 and 8.

Now,

Integrate the given function:

Integration y = Integration  x^2 - Integration 3x

y = [x^(2 + 1) / (2 + 1)] ^ 8 _1 - [3x^(1 + 1) / (1 + 1)] ^ 8 _1

y = [x^3 / 3] ^ 8 _1 - [3x^2 / 2] ^ 8 _1

y = [8^3 / 3 - 1^3 / 3] - [3 * 8^2 / 2 - 1 * 8^2 / 2]

y = [512 / 3 - 1 / 3] - [96 - 32]

y = 1535 / 3 - 64

y = 1535 - 192 / 3

y =  1343 / 3 square units.

So, the area is 1343 / 3 square units.

Thus, the area between the curve y = x^2 - 3x for x between 1 and 8 is 1343 / 3 square units.

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The end behavior of the given graph is as x → -∞, f(x) → ∞ and as x → ∞ f(x) = ∞.

End behavior of graph

End behavior of the graph refers the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. And the degree and the leading coefficient of a polynomial function will determine the end behavior of the graph.

Given,

Here we have the graph with some function as y = f(x).

Here we have to find the end behavior of the graph.

Here we can see that the value of x goes to the positive side (the right side of the graph), the graph increases upwards, and this is shown with the arrow pointing up.

So, which means that the value of x goes to ∞,  then the value of y will also go to ∞.

Similarly, we can see the exact same behavior for the negative side of x (the left side of the graph), then as x goes to -∞, y will go to ∞.

Therefore, the correct option will be the second option, counting from the top.

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Answer:

[tex] \huge{ \boxed{y = - 3x - 12}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = -3

In order to find c we substitute the point (−5,3) into the equation y = mx + c

We have

[tex]3 = - 3( - 5) + c \\ 3 = 15 + c \\ c =3 - 15 \\ c = - 12 [/tex]

We now substitute c and m into the main equation

We have the final answer as

[tex]y = - 3x - 12[/tex]

Hope this helps you

Answer:

can you show me it so i can help

Step-by-step explanation:

In order to get the total amount $91,000 at the end of the 7 year, the interest rate is 2.2% on compound interest basis.

Compound Interest:

The general form to calculate the compound interest is written as,

A = P(1 + r/n)ⁿˣ

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

n = number of compounding periods per unit of time

x = time in decimal years

Given,

Naomi is going to invest $78,000 and leave it in an account for 7 years. Assuming the interest is compounded daily.

Here we need to find the  nearest hundredth of a percent, would be required in order for Naomi to end up with $91,000.

Here we have to solve for rate r as a decimal

[tex]r = n[(A/P)^{1/nt} - 1][/tex]

r = 365 × [(91,000.00/78,000.00)1/(365)(7) - 1]

r = 0.022022202

Then convert r to R as a percentage

R = r * 100

R = 0.022022202 * 100

R = 2.202%/year

Therefore, the interest rate required to get a total amount of $91,000.00 from compound interest on a principal of $78,000.00 compounded 365 times per year over 7 years is 2.202% per year.

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The expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

According to the question,

We have the following information,

The given verbal phrase is one-half times a number m plus twenty-five.

Now, we will solve it step by step.

Now, we will first find one-half times a number m. We know that we will replace the word times with multiplication. So, we have the following expression:

m/2

Now, adding 25 to this term, we have the following final expression:

m/2+25

Hence, the expression that represents the verbal phrase, one-half times a number m plus twenty-five, is m/2+25.

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Answer:

$80

Step-by-step explanation:

hunter+ kid 1+kid 2+kid 3+kid 4= 60 dollars just for tickets

4 snacks= 20 dollars for snacks

$60+$20=$80

PLEASE MARK BRAINIEST

The solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.

In the given question we have to solve the system using the Cramer's rule.

The given equations are

-4x-5y+6z = 5

-3x+6y-2z = 4

5x+9y-3z = 1

From the Cramer's rule

[tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]

Here,

A = [tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right][/tex]

X= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]

Now D=|A|

D= [tex]\left|\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right|[/tex]

D= [tex]-4\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]

D= -4[6×(-3)-(-2)×9]+5[(-3)×(-3)-(-2)×5]+6[(-3)×9-5×6]

D= -4[-18+18]+5[9+10]+6[-27-30]

D= -4×0+5×19+6×(-57)

D= 0+95-342

D= -247

[tex]D_{x}=\left[\begin{array}{ccc}5&-5&6\\4&6&-2\\1&9&-3\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{x}=5\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|+6\left|\begin{array}{ccc}4&6\\1&9\end{array}\right|[/tex]

[tex]D_{x}[/tex] = 5[6×(-3)-(-2)×9]+5[4×(-3)-(-2)×1]+6[4×9-1×6]

[tex]D_{x}[/tex] = 5[-18+18]+5[-12+2]+6[36-6]

[tex]D_{x}[/tex] = 5×0+5×(-10)+6×30

[tex]D_{x}[/tex] = 0-50+180

[tex]D_{x}[/tex] = 130

[tex]D_{y}=\left[\begin{array}{ccc}-4&5&6\\-3&4&-2\\5&1&-3\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{y}= -4\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|-5\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|[/tex]

[tex]D_{y}[/tex] = -4[4×(-3)-(-2)×1]-5[(-3)×(-3)-(-2)×5]+6[(-3)×1-4×5]

[tex]D_{y}[/tex] = -4[-12+2]-5[9+10]+6[-3-20]

[tex]D_{y}[/tex] = (-4)×(-10)-5×19+6×(-23)

[tex]D_{y}[/tex] = 40-95-138

[tex]D_{y}[/tex] = -193

[tex]D_{z}=\left[\begin{array}{ccc}-4&-5&5\\-3&6&4\\5&9&1\end{array}\right][/tex]

Simplifying the matrix

[tex]D_{z}=-4\left|\begin{array}{ccc}6&4\\9&1\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|+5\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]

[tex]D_{z}[/tex] = -4[6×1-4×9]+5[1×(-3)-4×5]+5[(-3)×9-5×6]

[tex]D_{z}[/tex] = -4[6-36]+5[-3-20]+5[-27-30]

[tex]D_{z}[/tex] = (-4)×(-30)+5×(-23)+5×(-57)

[tex]D_{z}[/tex] = 120-115-285

[tex]D_{z}[/tex] = -280

As we know that;  x=Dx/D, y=Dy/D, z=Dz/D

x=130/(-247)

x= -0.53

y=(-193)/(-247)

y=0.78

z=(-280)/(-247)

z=1.13

Hence, the solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.

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The most appropriate interpretation for the slope of the data given is the height of water in the pool increases by 2 inches per minute. Option (1) is correct.

The slope of a line, also known as its gradient, is the value of the steepness or direction of a line in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

Given that

Time                       Height

2                                 8

4                                12

6                                16

8                                20

10                              24

The slope of the line = 2

A line's slope is also known as its gradient or rate of change.

The slope can be positive or negative; positive slope values indicate an increase in x as y increases and vice versa.

A negative slope indicates that one variable decreases as the other increases.

Because the slope value given here is positive, we can conclude that the height of the water increases over time.

As a result, the height of the water rises by 2 inches per minute.

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The number line which represents the number of exams Ms. Filer had left to grade is "number line with an open circle on number 15 and line shaded left". option B

five eighths plus h equals eleven over eight, determine the value of h.

5/8 + h = 11/8

substract 5/8 from both sides

h = 11/8 - 5/8

h = 6/8

h = 3/4

Water boils at a minimum temperature of 100 degrees Celsius.

The inequality:

100 ≥ b

Mario total goal for the month = Number of miles Mario has left to run this month to reach her goal + number of miles Mario has run so far

150 = m + 75

substract 75 from both sides

150 - 75 = m

75 = m

The equation f + 24 = −3, solve for f.

f + 24 = -3

substract 24 from both sides

f = -3 - 24

f = -27

Number of gifts each family donates = 4

Number of families = 12

Total gifts donated = g

The equation:

g / 12 = 4

cross product

g = 12 × 4

g = 48

The equation 17 equals y over -3, solve for y.

17 = y / -3

cross product

17 × -3 = y

-51 = y

Number of cookies Bella is baking = 42

Number of cookies she has baked = 29

Number of cookies left for Bella to bake = x

The equation:

42 = x + 29

substract 29 from both sides

42 - 29 = x

13 = x

The inequality:

6(n − 5) < 3(n + 4)

open parenthesis

6n - 30 = 3n + 12

6n - 3n = 12 + 30

3n = 42

divide both sides by 3

n = 42/3

n = 14

The equation 5.24w = 16.506, solve for w.

5.24w = 16.506

divide both sides by 5.24

w = 16.506 / 5.24

w = 3.15

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Answer:

No solutions

Step-by-step explanation:

-5y+7/2y=-5-3/2y-4

+3/2y.           +3/2y

-5y+3/2y+7/2y=-5-4

-5y+10/2y=-9

-5y+5y=-9

0=-9

No solutions

Hopes this helps please mark brainliest

Answer:

1=180 2=90

Step-by-step explanation:

1=∠1 and ∠2 are supplementary, so m∠2 = 180° - x°. ∠2 and ∠6 are corresponding angles. So, m∠6 = 180° - x°.

2=Their measures are equal, so m∠4 = 90 . When two lines intersect to form one right angle, they form four right angles.

Answer:

∠4 = 55°

∠6 = 35°

Step-by-step explanation:

    In ΔABC,

         35 + 90 + ∠4 = 180° {Sum of all angles of triangle}

                  125 +∠4 = 180

                           ∠4 = 180 - 125

                             ∠4 = 55°

Linear pair: If in two adjacent angles, the  non-common arms form a straight line, then the two angles are called linear pair and they add up to 180.

∠7 + ∠8 = 180°  {linear pair}

   90 + ∠7  = 180°

            ∠7 = 180 - 90

                 ∠7 = 90°

In ΔACD,

         ∠6 + ∠4+ ∠7 = 180  {Sum of all angles of triangle}

           ∠6 + 55 + 90 = 180

                   ∠6 + 145 = 180

                             ∠6 = 180 - 145

                   ∠6 = 35°

Answer: 25 questions

Step-by-step explanation: