Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

The shaded region in the graph represents the solutions of this system of linear inequalities:

y ___

4x + ___

y ≤ ___

x + ___


Note: Use the symbols <, >, <=, and >= for inequality signs.

The values of x, y, and z are 1, 2, and 3 respectively after using the substitution method.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a linear equation in three variable:

2x + 3y - z = 5 ...(1)

4x - y - z = -1 ...(2)

x + 4y + z = 12 ...(3)

[tex]\rm \mathrm{Substitute\:}x=\dfrac{5-3y+z}{2}[/tex]   (from the equation 1 and 2)

After solving:

[tex]\rm \begin{bmatrix}-7y+z+10=-1\\ \dfrac{5y+3z+5}{2}=12\end{bmatrix}[/tex]

From the above, two equations:
y =2

z =3

Plug the above values in equation 1

x = 1

Thus, the values of x, y, and z are 1, 2, and 3 respectively after using the substitution method.

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Inequalities help us to compare two unequal expressions. The inequality for this scenario in standard form is 2x + 3y > 30.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Let the safety counts be represented by x, while the field goal count is represented by y.

Part A: The inequality for this scenario in standard form.

2x + 3y > 30

Part B: The inequality in slope-intercept form.

2x + 3y > 30

3y > 30 - 2x

y > 10 - (2/3)x

y < (2/3)x - 10

PartC: The inequality is represented below.

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Answer:

[tex]y = 85[/tex]

[tex]x = 95[/tex]

Answer:

C

Step-by-step explanation:

Lower rectangle =  4 * 12 =   48  in^2

Upper trapezoid  1/2 ( 5 + 12 ) *  6 = 51 in^2

total = 48 +  51 = 99 in^2

Answer:

x=-2

Step-by-step explanation:

Given equation:

8^x= 1/64

Ensure both sides of the equation are in power format by changing 1/64

1/64 = 64^-1

8^x = 64^-1

2^3(x) = 2^6(-1)

The bases will cancel out each other

3(x) = 6(-1)

3x = -6

x = -6/3

x = -2

Check

8^x = 1/64

x = -2

8^-2

= 1/8²

= 1/8*8

= 1/64

Answer:

The cliffs are home to many seabirds. Despite its name, there are few puffins (around 50 pairs during the April-July breeding season).

Step-by-step explanation:

Answer:

C.) y = -2x + 5

Step-by-step explanation:

The general structure of an equation in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

You were given the value of "m" (-2). You were also given an "x" variable and "y" variable from a point (3,-1). You can plug these variables into the equation and simplify to find "b".

m = -2        x = 3       y = -1

y = mx + b                         <---- General structure

y = -2x + b                         <---- Plug -2 in for "m"

-1 = -2(3) + b                      <---- Plug "x" and "y" values in from point

-1 = -6 + b                          <---- Multiply -2 and 3

5 = b                                  <---- Add 6 to both sides

Therefore, the equation of the line is:

y = -2x + 5

Answer:

x = 25

Step-by-step explanation:

First turn this into an equation:

[tex]\frac{4}{5}[/tex] times x = 20

Now divide both sides by [tex]\frac{4}{5}[/tex]. You can't divide by a fraction, instead you multiply by flipping the fraction. So now you're multiplying both sides by [tex]\frac{5}{4}[/tex].

20 times 5 = 100. Next you divide [tex]\frac{100}{4}[/tex]. This is equal to 25. You have completed the equation and now have the answer:

x = 25

Have a great day!

Answer:

Step-by-step explanation:

(2x + 4x + 6x) * 2  = 360*

2x + 4x + 6x = 180°

12x = 180°

x = 180 : 12

x = 15

(2x + x) * 2 = 360

2x + x = 180

3x = 180

x = 180 : 3

x = 60°

Answer: C

Step-by-step explanation:

Answer:

Rounded to 0.42. Not rounded: 0.41729656785

Step-by-step explanation:

24/25 = 0.96

11/61 = 0.180327869

Add those together.

Answer for that: 1.14032787

Find the cos for the answer.

Which is 0.41729656785 to 0.42

The solutions of the given quadratic equation are:

[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]

Here we have the quadratic equation:

[tex]x^2 = -7x - 8[/tex]

To solve it, we can rewrite it as:

[tex]x^2 + 7x + 8 = 0[/tex]

Now if we use Bhaskara's formula, we get the solutions:

[tex]x = \frac{-7 \pm \sqrt{(7)^2 - 4*1*(8)} }{2} \\\\x = \frac{-7 \pm \sqrt{17} }{2}[/tex]

Then the two solutions are:

[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]

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Make the equations equal and solve for x

For x=0

For x=-1

The solutions are

Graph attached

Answer:(-6,0)

Step-by-step explanation:

Answer:

mRQ = 50

Step-by-step explanation:

180-130=50

Answer:

I disagree.

Step-by-step explanation:

The reasoning may be wrong but I believe it is disagree.

I am going to keep it simple.

On the spinner there are 4 options, 3 for red and 1 for yellow.

Therefore, we have a 1/4 chance to get a yellow once.

If we get a yellow again, it is another. 1/4 chance.

1/4 x 1/4 is 1/16, considerably smaller than 1/3.

Answer:

From inspection of the diagram, we can see that the spinner is divided into 4 equal parts, where 3 parts are red and 1 part is yellow.

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Therefore,

[tex]\implies \textsf{Probability of getting a red} = \sf \dfrac{3}{4}[/tex]

[tex]\implies \textsf{Probability of getting a yellow} = \sf \dfrac{1}{4}[/tex]

Multiplication Rule for Independent Events

For independent events A and B:

Therefore,

[tex]\begin{aligned}\implies \sf P(yellow\:and\:yellow) & = \sf P(yellow) \times P(yellow)\\\\ & = \sf \dfrac{1}{4} \times \dfrac{1}{4}\\\\ & = \sf \dfrac{1}{16}\end{aligned}[/tex]

Ari is incorrect.  The spinner is divided into 4 parts, where only one part is yellow.  Therefore, the probability of spinning a yellow is 1/4.  As the events are independent, the Multiplication Rule should be used to calculate the probability of spinning 2 yellows.  So the probability of spinning 2 yellows is 1/4 x 1/4 = 1/16.

Answer:

2(12 + π)

Step-by-step explanation:

This will get you about 30and even by just counting squares you will get the closest to this answer.

Rhombus RSTU is congruent to WXYZ, and are translational images of each other because all their sides and angles are equal

Some of the properties of a rhombus are;

If Rhombus RSTU is congruent to WXYZ, then they are both translation images of each other because all their sides and angles are equal.

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Answer:

1 kilometre = 1000 metres
2.5km = 2.5 × 1000m = 2500m
2500 - 1950 = 550m

Therefore Justin rides 550m farther than Luke walks to school.

Answer:

2 days

Step-by-step explanation:

275 miles times 0.05 = $13.75 for mileage

200-13.75=186.25 left

186.25/63.41(daily fee)= 2.93

She can rent it for 2 days

The events are not independent.

The probability of selecting a football card and a basketball card is 0.16.

Probability is the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of selecting a football card and a basketball card = (number of football cards / total number of cards) x (number of basketball cards / total number of cards)

2/10 x 8/10 = 0.16

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Answer: B, C, D

Step-by-step explanation:

i think you just have to do 3 + 14+2+2+3and then solve i guess

Answer:

The answer is 21

Step-by-step explanation:

This should help you

Answer:

D

Step-by-step explanation:

If you imagine the dots continued in a connected line, (imagining where the data points will likely go), the line's slope informs you if it is a negative (going down/negative slope) linear association or if it's a positive (going up/positive slope) linear association.

For A, it has a positive slope [as it increases].

For B, it also has a positive slope

For C, there is no correlation, the dots are not showing any trends

For D, there is a negative slope.

This means that the scatter plot D shows a negative linear association.

Option (D) shows a negative linear association between the variables is the correct answer.

A scatter plot is a type of data visualization that shows the relationship between different variables. Scatter plots are used to plot data points on a horizontal and a vertical axis in an attempt to show how much one variable is affected by another.

For the given situation,

The graph shows the data points on a horizontal and a vertical axis.

A scatter plot with an increasing value of one variable and a decreasing value for another variable can be said to have a negative correlation.

Among graphs, in option (D) when one variable tends to increase in the x-axis, the other variable decreases in the y-axis.

Hence we can conclude that option (D) shows a negative linear association between the variables is the correct answer.

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An explanation for 4 < x < 7 is that 4 is less than and x is less than 7.

The mathematical expression that is given is 4 < x < 7. It should be noted that this implies that 4 is less than and x is less than 7.

In this case, the appropriate values that can fit x in this situation will be 5 and 6.

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A function assigns the values. The value of (f+g)(x) is (5x³ - 4x² - 6x - 7).

A function assigns the value of each element of one set to the other specific element of another set.

Given F(x)=2x²+6x-4 and G(x)=5x³-6x²-3, therefore, the value of (f+g)(x) is,

(f+g)(x) = f(x) + g(x)

           = 2x²+6x-4 + 5x³-6x²-3

           = 5x³ - 6x² + 2x² - 6x - 4 - 3

           = 5x³ - 4x² - 6x - 7

Hence, the value of (f+g)(x) is (5x³ - 4x² - 6x - 7).

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Answer:

It's at the beginning of x+4, the 2nd symbol of 4x-4, and the beginning of X+1.

Step-by-step explanation:

No explanation for you! Just choose them! It's right!