Solve the following system of equations and show all work.
y = 2x2
y =
3x -1 (10 points)

Answers

Answer 1

Answer: [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]

Step-by-step explanation:

We have [tex]y=2x^{2}[/tex] and [tex]y=3x-1[/tex].

Since both of the equations are set equal to y, we can conclude that:

[tex]2x^2 = 3x-1\\\\2x^{2}-3x+1=0\\\\(2x-1)(x-1)=0\\\\x=\frac{1}{2}, 1[/tex]

If [tex]x=\frac{1}{2}[/tex], then [tex]y=3\left(\frac{1}{2} \right)-1=1[/tex]

If [tex]x=1[/tex], then [tex]y=3-1=2[/tex]

Therefore, the solutions are [tex]\left(\frac{1}{2}, 1 \right), (1, 2)[/tex]


Related Questions

The formula M = 5/8 K gives the approximate distance in miles as a function of kilometers. Use the inverse to express 25 miles in kilometers.​

Answers

M = 5/8 K
8/5 M = 8/5 x 5/8 K = K
K = 8/5 x 25 = 40 km

Alaric wants to determine if he can get a better grade in math by studying for longer periods of time.
He plans to experiment for 4 weeks.
Which statement is true of this experiment?
a.) The duration of Alaric's experiment is the explanatory variable.
b.) Alaric's math grade is the explanatory variable.
c.) The amount of time Alaric spends studying is the response variable.
d.) Alaric's math grade is the response variable.

Answers

The statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.

What is an explanatory variable?

It is defined as the variable which is independent. They show the expected results and the result is known as the response variable which is dependent on the explanatory variable.

We have given:

Alaric wants to determine if he can get a better grade in maths by studying for longer periods of time.

The duration of the experiment is 4 weeks which is known or constant.

But the number of hours she studied is a variable, and it is independent.

The maths grade is the dependent variable which is on the number of hours Alaric study variable.

Thus, the statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.

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Assume that the function f is a one-to-one function.
a. if f(3)=9, find ^-1 (9)

b. if f^-1(-8)=-9 , find f(-9)

Answers

Answer:

a. 3

b. -8

Step-by-step explanation:

let me know if you want an explanation

Solve the equation x³ - 5x²+2x+8 = 0 given that - 1 is a zero of f(x)= x3 - 5x²+2x+8.
The solution set is? (Use a comma to separate answers as needed.)

Answers

Answer:

added in the picture

Step-by-step explanation:

added in the picture

Find the area of the trapezoid. TOP 11ft, RIGHT4√3ft , BOTTOM 15ft ,LEFT 8ft

Answers

Answer:

[tex]52\sqrt{3} ft^{2}[/tex]

Step-by-step explanation:

Please refer to the attached picture.

First we will find the area of rectangle BCDE.

Area of Rectangle = Length x Breadth = DE x CD

= 11 x [tex]4\sqrt{3}[/tex]

[tex]=44\sqrt{3} ft^{2}[/tex]

Next we will find Area of Triangle ABE.

Area of Triangle = 0.5 x Base x Height

[tex]0.5*4*4\sqrt{3} \\=8\sqrt{3} ft^{2}[/tex]

Area of Trapezoid = Area of Rectangle + Area of Triangle

[tex]=44\sqrt{3} +8\sqrt{3} \\=52\sqrt{3} ft^{2}[/tex]

Answer:

A = 52[tex]\sqrt{3}[/tex] ft² ≈ 90.1 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height and b₁ , b₂ the parallel bases

here h = 4[tex]\sqrt{3}[/tex] , b₁ = 15 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{3}[/tex] × (15 + 11)

   = 2[tex]\sqrt{3}[/tex] × 26

   = 52[tex]\sqrt{3}[/tex] ft²

   ≈ 90.1 ft² ( to the nearest tenth )

Complete the recursive formula of the geometric sequence 56, -28, 14, -7,....

Answers

Step-by-step explanation:

each term in the sequence is half of the value of the previous term, and in the opposite sign.

therfore, the quotient between terms is (-2)

so, to get one term from the previous term, we multiply by 1/(-2), so:

d(n) = d(n-1) × 1/(-2)

the first term is 56 so d(1)=56

Answer:

56 and -1/2

Step-by-step explanation:

khan

There are 60 students studying Sciences (Biology, Chemistry or Physics). 7 students study Biology, Chemistry and Physics. 12 students study Biology and Chemistry. 15 students study Biology and Physics. 20 students study Chemistry and Physics. 35 students study Biology. 32 students study Physics. B Complete the Venn diagram. E P C There are 60 students studying Sciences ( Biology , Chemistry or Physics ) . 7 students study Biology , Chemistry and Physics . 12 students study Biology and Chemistry . 15 students study Biology and Physics . 20 students study Chemistry and Physics . 35 students study Biology . 32 students study Physics . B Complete the Venn diagram . E P C​

Answers

Answer:

8 in the box.

Step-by-step explanation:

As, it is given that 35 students study Biology.

So, in Biology circle,

15+7+5+x=35

27+x=35

x=35-27

x=8

X -6,-3,0,3,6 y 0 1 2 3 4 which equation contains the coordinate parts given in the table

Answers

The linear equation that contains the coordinate parts in the given table is: y = 1/3x + 2.

How to Find the Equation of a Linear Equation?

To find the linear equation that contains the coordinate parts in the table given, find the slope (m) and y-intercept (b), then substitute the values into y = mx + b.

Slope (m) using two coordinate parts, (0, 2) and (3, 3):

Slope (m) = change in y / change in x = (3 - 2)/(3 - 0)

Slope (m) = 1/3

y-intercept (b) = 2 [this is the value of y when x = 0)

Substitute the values into y = mx + b

y = 1/3x + 2.

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-3 5/7 X -2 1/2
I really don't understand

Answers

Answer:

[tex] - 3 \frac{5}{7} x - 2\ \frac{1}{2} [/tex]

[tex] \frac{ - 26}{7} - \frac{5}{2} [/tex]

LCM of 7 and 2 is 14

Multiplying (-26/7) with 1/2 (to make the denominator 14) and -5/2 with 1/7

[tex] \frac{ - 26}{7} \times \frac{1}{2} - \frac{5}{2} \times \frac{1}{7} [/tex]

[tex] \frac{ - 26}{14} - \frac{5}{14} [/tex]

[tex] \frac{ - 26 - 5}{14} [/tex]

[tex] - \frac{31}{14} [/tex]

I think the X is multiplication

-3 5/7 x -2 1/2 = 26/7 x 5/2 = 130/14 = 65/7 = 9 2/7

look at the picture

Answers

Answer:

The x-intercept is 2.

Step-by-step explanation:

[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]

[tex]2 \sqrt[3]{x - 10} = - 4[/tex]

[tex] \sqrt[3]{x - 10 } = - 2[/tex]

[tex]x - 10 = - 8[/tex]

[tex]x = 2[/tex]

A sample has a sample proportion of 0.3. Which sample size will produce the
widest 95% confidence interval when estimating the population parameter?
A. 46
B. 68
C. 56
D. 36

Answers

Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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One positive number is 8 times another number. Their difference is 70.
Which of the following equations could be used to find the numbers?

Answers

Answer:

X equals 10.

8x - x = 70

Step-by-step explanation:

8 x 10 = 80

80 - 10 = 70

. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the smaller bottle holds.The length of the larger bottle is 10cm.the length of the smaller bottle is 5cm

Answers

Answer:

The smaller bottle holds 12.5 ml of perfume.

====================

Given

Two bottles of similar shape;Larger bottle has volume of 100 ml;The length of larger bottle is 10 cm;The length of smaller bottle is 5 cm.

To find

The volume of smaller bottle.

Solution

Find the scale factor, the ratio of corresponding dimensions:

[tex]k = 5/10 = 1/2[/tex]

We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:

[tex]V_{small}/V_{large} = k^3\\[/tex]

Substitute the known values and find the volume of small bottle:

[tex]V_{small}/100= (1/2)^3\\[/tex][tex]V_{small}/100= 1/8[/tex][tex]V_{small}= 1/8*100=12.5[/tex]

The smaller bottle holds 12.5 ml of perfume.

The smaller bottle holds 12.5 ml of perfume.

I solved it and came with this result.

Out of 310 racers who started the marathon, 289 completed the race, 18 gave up, and 3 were disqualified. What percentage did not complet

Answers

Answer:

7.1%

Step-by-step explanation:

Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%

Two vertical angles are complementary. Statement is always, sometimes, or never true. Explain your reasoning

Answers

Answer:

depends upon the degree of the angle

Step-by-step explanation:

vertically opposite angles are always equal like

80 = 80 sum is equal to 160 degrees not equal to 90

45 = 45 , sums equal to 90 degrees ,equal to 90

30 = 30 sum is equal to 60 degrees, not equal to 90

so we can say it depends what is the no of degrees if it is  45 only we can say  the vertically opposite angles are  complementary angle

I really need help on this question. Im stuck any help?

Answers

Answer:

170

Step-by-step explanation:

[tex]x+40=210\\x=170[/tex]

If a number, x, is increased by 40 (+40) and is now equal to 210 (=210), then the number, x, is equal to 170.

Giving a test to a group of students, the grades and gender are summarized below
Grades vs. Gender
A B C
Male 17 18 5
Female 12 3 14
If one student was chosen at random,
find the probability that the student was female.

Probability = (Round to 4 decimal places)

Answers

It would be 1/6 because there are 6 students and if you’re picking one it would be one out of six : 0.1666

The exterior angles of a triangle are (2x+10),(3x+15)and (4x+20). What is the value of x and what is the largest interior angle of the triangle?

Answers

Answer:

x = 35 and 100°

Step-by-step explanation:

the sum of the exterior angles of a triangle = 360° , then

2x + 10 + 3x + 15 + 4x + 20 = 360 , that is

9x + 45 = 360 ( subtract 45 from both sides )

9x = 315 ( divide both sides by 9 )

x = 35

then each exterior angle is

2x + 10 = 2(35) + 10 = 70 + 10 = 80°

3x + 15 = 3(35) + 15 = 105 + 15 = 120°

4x + 20 = 4(35) + 20 = 140 + 20 = 160°

the sum of an exterior angle and corresponding interior angle = 180°

then

180° - 80° = 100°

180° - 120° = 60°

180° - 160° = 20°

the largest interior angle of the triangle is 100°

Answer:

x = 35

largest interior angle = 100°

Step-by-step explanation:

The exterior angles of a triangle sum to 360°

⇒ (2x + 10) + (3x + 15) + (4x + 20) = 360

⇒ 2x + 10 + 3x + 15 + 4x + 20 = 360

⇒ 9x + 45 = 360

⇒ 9x = 315

x = 35

Therefore, the three exterior angles are:

(2x + 10) = 2(35) + 10 = 80°(3x + 15) = 3(35) + 15 = 120°(4x + 20) = 4(35) + 20 = 160°

If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.  As angles on a straight line sum to 180°:

⇒ interior angle + exterior = 180°

So the largest interior angle will be the supplementary angle to the smallest exterior angle.

The smallest exterior angle is 80°, so:

⇒ largest interior angle + 80° = 180°

⇒ largest interior angle = 180° - 80°

largest interior angle = 100°

solve the following inequality, algebra 1.

will give brainliest answer !!

Answers

Answer:

See below

Step-by-step explanation:

r/6 <-6      multiply both sides by 6 to get

r < - 36

  or    4r+2 > 18     subtract 2 from both sides of the equation

            4r > 16        divide both sides by 4

             r > 4

Step-by-step explanation:

[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]

[tex]4r + 2 > 18 \: \: \: \: \: \: \: \: \: \: ...2[/tex]

Solving for inequality 1:

[tex] \frac{r}{6} < - 6 \: \: \: \: \: \: \: \: \: \: ... 1[/tex]

Multiplying both sides by 6:

6 * 1/6 r < -6*6r < -36

Hence the solution is r < -36

Solving for inequality 2:

4r + 2 > 18

Subtract 2 from both sides:

4r + 2 - 2 > 18 - 24r > 16

Divide both sides by 4:

[tex] \cfrac{4r}{4} > \cfrac{16}{4} [/tex][tex]r > 4[/tex]

Hence the answer is r > 4.

determine weather y varies directly with x. if so, find the constant variation and write the equation

Answers

Answer:

Yes, k = 1/3 and y = 1/3x

Step-by-step explanation:

[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]

[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]

[tex]\text{This implies that,}[/tex]

[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]

Which of the following are square roots of the number below? Check all that
apply.
4
A. 41/2
B. 8
C. -41/2
D. 2
E. -2
F. 16

Answers

Answer:

D. 2

E. -2

Step-by-step explanation:

What is the solution to the following system?
4x+3y-z=-6
6x-y+3z=12
8x+2y+4z=6
x= 1, y = -3, z = -1
x= 1, y=-3, z = 1
x = 1, y = 3, z = 19
x = 1, y = 3, z = -2

Answers

The solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

What is a linear equation?

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 three linear equations in three variable:

4x + 3y - z = -6 ..(1)

6x - y+ 3z = 12 ..(2)

8x + 2y + 4z = 6 ...(3)

From the equation (1)

[tex]\rm x=\dfrac{-6-3y+z}{4}[/tex]

Substitute the above value in the equation (2) and (3):

[tex]\rm 6\cdot \dfrac{-6-3y+z}{4}-y+3z=12\\\\ 8\cdot \dfrac{-6-3y+z}{4}+2y+4z=6[/tex]

After simplification:

[tex]\rm -11y+9z-18=24\\ -4y+6z-12=6[/tex]

After solving the above two equations by substitution method:

z = 1

y = -3

Plug the above two values in the equation (1), we get:

x = 1

Thus, the solutions are x = 1, y = -3, z = 1 after solving with substitution method option second x= 1, y=-3, z = 1 is correct.

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Which function is represented by this graph? A line is graphed in an x y plane, where the x and the y axes range from negative 10 to 10 in increments of 2. The line falls through (negative 6, 10), (0, 4), (4, 0) to (7, negative 3), and then it rises through (10, 0). A. f(x) = |x + 7| − 3 B. f(x) = |x − 7| − 3 C. f(x) = |x + 3| − 7 D. f(x) = |x − 3| − 7

Answers

The line that represents the graph satisfying all condition is  f(x) = |x − 7| − 3.

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

As, the points are given.

We have to find which equation  satisfies all the points.

f(x) = |x − 7| − 3

put x= -6

y=  13-3 = 10

Similarly by putting all the values the only condition that satisfies is

f(x) = |x − 7| − 3

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y=2x^2-4x-3
Solve quadratic questions

Answers

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

How to find the roots of a quadratic equation

All quadratic equations of the form a · x² + b · x + c = 0 have two roots that can be found by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]     (1)

If we know that a = 2, b = - 4 and c = - 3, then the roots of the quadratic equations are:

[tex]x = \frac{4 \pm \sqrt{(-4)^{2}-4\cdot (2) \cdot (- 3)}}{2\cdot (2)}[/tex]

[tex]x = 1 \pm \frac{\sqrt{40}}{4}[/tex]

[tex]x = 1 \pm \frac{\sqrt{10}}{2}[/tex]

By applying the quadratic formula we conclude that the roots of the quadratic equation y = 2 · x² - 4 · x - 3 are 1 + 0.5√10 and 1 - 0.5√10, respectively.

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PLEASE HELP I WILL GIVE BRAINLEST!!!!!!

Below is the graph of a polynomial function with real comedic fangs. All local extreme of the function are shown in the graph.
Use the graph to answer the following questions.

(a) over which intervals is the function decreasing? Choose all that apply.
(-∞,-8) (-8,-4) (-4,0) (0,5) (-4,5) (9, ∞)

(b) At which x-values does the function have local minima? If there is more than one value seepage them with commas.

(C) what is the sign of the function’s leading coefficient?
Answers are positive, negative, not enough time

(D) which of the following is a possibility for the degree of the function? Choose all that apply
4 , 5 , 6 , 7 , 8 , 9

Answers

Part (a)

Decreasing means that as x increases, y decreases.

So the intervals are [tex](-8, -4), (0, 5), (9, \infty)[/tex]

Part (b)

A local minimum is where the function changes from decreasing to increasing.

So, the local minima are at [tex]x=-4, 5[/tex]

Part (c)

The function is approaching negative infinity as x approaches both positive and negative infinity, so the leading coefficient is negative

Part (d)

The degree is given by the number of roots (including multiplicity).

From the graph, we see there is a single root at x = -6, a single root at x = -1, a single root at x = 1, a single root between x=6 and x=8, and a single root at around x = 10.

Thus, there are a minimum of 5 roots for the graph (there could be more outside of the given section)

However, since the graph has the same end behavior in both directions, the degree must be even.

So, the possible answers are any even number that is at least 6

Can y’all please help me with this ! Everybody have a good day!

Answers

Answer: A. She substituted incorrectly into the distance formula


She should be subtracting x from x and y from y but she is subtracting y from x.

Answer is A they are supposed to minus one set of x and y but Helen subtracted the x values and y values

need help with this question im stuck

Answers

Answer:

answer is B. 100°

Step-by-step explanation:

if correct please I need brainlist

Answer:

100°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, i.e., they add up to 180°.

The 80° angle and angle x are opposite each other, so:
x + 80° = 180°

x = 180° - 80°

  x = 100°

Which sequences are geometric? Check all that apply.
5, 10, 20, 50,...
3, 12, 48, 192,...
3, 15, 75, 375,...
8, 15, 75,375,...
14, 21, 28, 35,...
17, 20, 23, 26,...
2, 10, 50, 250,...

Answers

Answer:

The first, third and last sequences

[tex]\frac{1}{28} + \frac{1}{70} + \frac{1}{130} + \frac{1}{208} + \frac{1}{304} = ?[/tex]

Evaluate this expression.

Answers

Considering the least common multiple of the denominators, it is found that the result of the expression is given by:

[tex]\frac{9100}{138320}[/tex]

How do we add fractions?

We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.

In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.

Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:

[tex]\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}[/tex]

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Construct the truth table and determine the truth value of the following compound statement.
a)p⟾¬(p ʌ r)
b) (q ʌ r) ⟾(p ⇔ q)​

Answers

See the attached truth tables.

• A ∧ B is true only when both A and B are true

• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B

• ¬A is true only when A is false

• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)

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