Solve the following system of equations. Show all work and solutions.

y = 2x^2 + 6x + 1
y = −4x^2 + 1

Answer:

[tex]y = 85[/tex]

[tex]x = 95[/tex]

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:

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!

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:

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

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

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:

mRQ = 50

Step-by-step explanation:

180-130=50

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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[tex] \sqrt{12} + 1 - \sqrt{5} \\ = \sqrt{4} \times \sqrt{3} + 1 - \sqrt{5} \\ = 2 \sqrt{3} + 1 - \sqrt{5} [/tex]

Answer: C

Step-by-step explanation:

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.

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:

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:

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:(-6,0)

Step-by-step explanation:

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

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

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:

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:

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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Answer: B, C, D

Step-by-step explanation:

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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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:

Herman is wrong.  Latoya got the better deal.

Step-by-step explanation:

Latoya bought 8 pounds of potatoes for $18.

    ► 18 / 8 = $2.25 per pound

Herman bought 6 pounds of potatoes for $15.

    ► 15 / 6 = $2.50 per pound

Cheaper per pound is better!

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:

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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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