4x^2+2y=8 and 2x^2=7, then find y

Answers

Answer 1
The value of y is –3

Step 1

Equation obtained from the question.

4x² + 2y = 8 .............(1)

2x² = 7..... (2)

Step 2:

Determination of the value of x².

From equation 2,

[tex]2x^{2} = 7[/tex]

Divide both side by 2

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

Step 3:

Determination of the value of y

From equation 1,

[tex]4x^{2} + 2y = 8\\ \\But\\\\x^{2} = \frac{7}{2}\\\\Thus\\\\4(\frac{7}{2}) + 2y = 8[/tex]

Clear bracket

[tex]14 + 2y = 8[/tex]

Collect like terms

Divide both side by 2

[tex]y = \frac{-6}{2}[/tex] y = –3

Therefore, the value of y is –3

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Related Questions

Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What are their present ages?

Answers

Answer:

Amira is currently 24 years old and Pam is currently 12 years old

Step-by-step explanation:

Let Amira's age be [tex]a[/tex] and Pam's age be [tex]p[/tex]. Currently, Amira is twice as old as Pam. Therefore, we can write the equation [tex]a=2p[/tex].

We can write a second equation using the other information given in the question. Nine years ago, Amira and Pam's combined ages was 18. If Amira and Pam are currently [tex]a[/tex] and [tex]p[/tex] years old, respectively, then their respective ages 9 years ago would ben [tex]a-9[/tex] and [tex]p-9[/tex]. Since these add up to 18, we have the equation [tex](a-9)+(p-9)=18[/tex].

Therefore, we have a system of equations:

[tex]\begin{cases}a=2p,\\a-9+p-9=18\end{cases}[/tex]

Substitute the first equation into the second one:

[tex]2p-9+p-9=18[/tex]

Combine like terms:

[tex]3p-18=18[/tex]

Add 18 to both sides:

[tex]3p=36[/tex]

Divide both sides by 3:

[tex]p=\frac{36}{3}=\boxed{12}[/tex]

Now substitute this into any of the equations (I'll choose the first):

[tex]a=2p,\\a=2(12),\\a=\boxed{24}[/tex]

Therefore, Amira is currently 24 years old and Pam is currently 12 years old.

The width of a rectangle measures (8x + 2) centimeters, and its length measures
(6x + 6) centimeters. Which expression represents the perimeter, in centimeters, of
the rectangle?
20x + 24
28x + 16
Submit Answer
O 8 + 14x
O 10x + 12

Answers

Answer:

(28x+16)cm

Step-by-step explanation:

2(8x+2)+2(6x+6)

16x+4+12x+12

28x+16

S O L U T I O N

Perimeter = 2(Length + Breadth)

Perimeter = 2(6x + 6 + 8x + 2) cm

Perimeter = 2(14x + 8) cm

Perimeter = 28x + 16

CORRECT ANSWER IS OPTION B, 28x + 16

How many 3-digit numbers can you write if you cannot use any other digits except 4 and 6?

Answers

Answer:

Step-by-step explanation:

4 4 4

4 4 6

4 6 6

4 6 4

6 6 6

6 6 4

6 4 4

6 4 6

Jessica is traveling at a speed of 60 miles per hour in her truck. After 4 hours, how far will she have traveled?

Answers

Answer:

240 miles

Step-by-step explanation:

60*4=240

Answer: 240

Step-by-step explanation: If she is traveling 60 miles per hour you can multiply it by 4, which is 240.

If 65% of a number is 1105 what is 82% of the number

Answers

Answer:

1394

Step-by-step explanation:

Set up equation to find the number:

Variable n = number

65/100 = 1105/n

Cross multiply:

65 × n = 100 × 1105

65n = 110,500

n = 1700

Check your work:

1700 × 65%

Convert percentage into decimal:

1700 × 0.65

1105

Correct!

Find 82% of 1700:

Variable x = 82% of 1700

82/100 = x/1700

82 × 1700 = 100 × x

139,400 = 100x

1394 = x

Check your work:

1700 × 82%

1700 × 0.82

1394

Correct!

The 82% of the original number (1700) is approximately 1394.

Let's denote the original number as N. We know that 65% of N is equal to 1105. We can write this as:

65% of N = 0.65 * N = 1105

Now, to find the value of N, we can rearrange the equation to solve for N:

N = 1105 / 0.65

Now, calculate the value of N:

N ≈ 1700

So, the original number N is approximately 1700.

Next, we need to find 82% of this number. We can express this as:

82% of N = 0.82 * N

Now, substitute the value of N:

82% of 1700 = 0.82 * 1700

                     ≈ 1394

Thus, 82% of the original number (1700) is approximately 1394.

To summarize, first, we found the value of the original number (N) using the given information that 65% of N is equal to 1105. Then, we calculated 82% of N, which turned out to be approximately 1394.

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In Exercises 51−56, the letters a, b, and c represent nonzero constants. Solve the equation for x

ax – 2 = 12.5

Answers

Answer:

x = 14.5/a

Step-by-step explanation:

ax – 2 = 12.5

Add 2 to each side

ax – 2+2 = 12.5+2

ax = 14.5

Divide by a

ax/a = 14.5/a

x = 14.5/a

arc length of an oval that is 6ft by 5ft. i just want 1/4 of the oval. i want to find out how long i would need a wire to go from the ground to the middle of the "dome".
the picture explains it better.

in the end i want to have a wire frame around the garden and than take some netting and use that to keep out the big bugs and birds. i will of course use zip ties to attach the screen/netting to the frame. unless there is a easier and cheaper way to do this.​

Answers

You can model the ellipse with the equation

(x/6)² + (y/5)² = 1

If you're comfortable with calculus, read on.

Let x = 6 cos(t ) and y = 5 sin(t ), with 0 ≤ t ≤ π/2. Then the curve C parameterized by (x(t), y(t)) traces out one quarter of the ellipse. The arc length of this curve is given by the integral,

[tex]\displaystyle\int_C\mathrm ds = \int_0^{\pi/2}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{36\sin^2(t)+25\cos^2(t)}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{25+11\sin^2(t)}\,\mathrm dt \\\\ = 5\int_0^{\pi/2}\sqrt{1+\frac{11}{25}\sin^2(t)}\,\mathrm dt[/tex]

Unfortunately, you cannot find the exact value of this integral. (Well, you can, but it involves introducing a special kind of function; I'll link it in a comment.)

But you can approximate it, and the integral above comes out to about 8.657.

I'm not sure if there's a simpler, purely geometric way to estimate the arc length. But since the semiaxes (5 ft and 6 ft) are fairly close, you could try a circle with a radius somewhere in between. The arc length would range between 7.854 ft and 9.425 ft. If the material isn't too expensive, you can always overshoot and trim off the excess or repurpose it.

Decide whether the graphs of the given euqations are parallel perpendicular or neither

Answers

Answer: C) perpendicular

Explanation:

Each equation given to you is in y = mx+b form (aka slope intercept form).

The slope m is what we'll focus on.

The first equation has slope of 1, while the second equation has slope -1.

The two slopes multiply to -1. This is a property of any pair of perpendicular lines, as long as neither line is vertical nor horizontal.

Or you could note that -1 is the negative reciprocal of 1, or vice versa.

So there are a few options to see why the lines are perpendicular.

The definition of a circle

Answers

Answer:

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

Explanation:

Oxford dictionary definition

Step-by-step explanation:

a circle is a shape consisting of all points in a plane that are at a given distance from a given point the center

Which geometric terms are modeled by the Eiffel Tower

Answers

Point and line are geometric terms for the Eiffel Tower

B
16 m
A
С
20 m -
Find the area of AABC.
[?] ml
Enter

Answers

Answer:

A = 60 m^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 (20)*6

A = 60 m^2

Jun made a round tablecloth for his kitchen table. The tablecloth is 4.5 feet in diameter. Approximately how much fabric did Jun use for the tablecloth?

Answers

Answer:

the correct answer is 16ft^2

The test statistic of z=2.93 is obtained when testing the claim that p≠0.523. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of α=0.01​, should we reject H0 or should we fail to reject H0​?

Answers

Answer:

Step-by-step explanation:

Confidence Level - "P" values  

99%  2.58

Confidence Interval - "P" values  

(0.5289 , 0.6097 )  

Reference=0.523 Reject H0

Could someone please help me with this

Answers

Answer:

what are the questions

Step-by-step explanation:

GIVING BRAINLIEST Graph and solve the inequality y>-|x-5|-1

Answers

Answer:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For:

x

=

0

y

=

0

+

5

y

=

5

Or

(

0

,

5

)

For:

x

=

2

y

=

2

+

5

y

=

3

Or

(

2

,

3

)

We can now plot the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line will be solid because the inequality operator contains an "or equal to" clause.

graph{(x^2+(y-5)^2-0.125)((x+2)^2+(y-3)^2-0.125)(y-x-5)=0 [-20, 20, -10, 10]}

Now, we can shade the left side of the line.

graph{(y-x-5) >= 0 [-20, 20, -10, 10]}

what is the volume of the cylinder

Answers

Answer:

B

Step-by-step explanation:

Volume of the figure = Volume of cylinder + Volume of cone

Note: A cone having the same radius and height as cylinder have a volume (1/3) of cylinder

Volume of cone=(1/3)*96=32

Volume of the figure = 32+96=128

find the measure of the indicated angle to the nearest degree​

Answers

Answer:

71°

Step-by-step explanation:

12/36 = 1/3

inverse cos(1/3) = 70.53 = 71

7.2b + 6.5 > 4.8b – 8.1

Answers

Answer:

[tex]7.2b+6.5>4.8b-8.1[/tex]

Multiply both sides by 10

[tex]72b+65>48b-81[/tex]

Subtract both sides by 65

[tex]72b>48b-146[/tex]

Subtract both sides by 48b

[tex]24b>-146[/tex]

Divide both sides by 24

[tex]b>-\frac{73}{12}[/tex]

OAmalOHopeO

WILL GIVE BRAINLIEST. Given: SLant Prism, m

Answers

Hi! I ran into a similar problem so i will try, but sorry if i get it wrong, so basically all you do i

Pls what is the formula for finding the base and the height of a triangular pyramid.

Answers

Answer:

Take the Cubits and multiply

Step-by-step explanation:

This is a problem i had so just fill it in to your numbers etc.

A= 43.3 cubits squared

SA= the base of A +1/2 (p x slant h)

SA= 43.3 cubits squared + 1/2 (30 x 14 cubits)

To sum it up u can message me ur numbers and ill help

Suppose there are approximately 220 calories in 3 servings of a particular brand of cereal and 362 calories in 5 servings of the same cereal. Find the rate of change.

Answers

Answer:

.93 calories per serving

Step-by-step explanation:

220 ÷ 3 = 73.3333333 calories per serving

3 ÷ 220 = 0.0136363636

362 ÷ 5 = 72.4

5 ÷ 362 = 0.0138121547

73.3333333 - 72.4 = 0.9333333 = around .93

Sausages come in packets of 12. Bread rolls come in packets of 9. Brian wants to buy enough packs of sausages and rolls so that there are an equal number of sausages and rolls. What is the minimum number of sausages and rolls he needs to buy?

Answers

Answer: packet of sausage = 3, packet of roll = 4

Explanation:

I do guess and check.

12(1) + 9(1) = 12 + 9
12(2) + 9(2) = 24 + 18
12(3) + 9(3) = 36 + 27
12(3) + 9(4) = 36 + 36

So that’s the answer

What are the factors of the expression below -2x^2+5-3


A -1(2x-3)(x-1)

B -1(2x+3)(x-1)

C -1(2x+3)(x+1)

D -1(2x-3)(x+1)

Answers

d got it right hope you do

Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

f (x) = -x^2 + x + 14 Find f(2)

Answers

f(x) = -x² + x + 14

f(2) = -2² + 2 + 14 = -4 + 16 = 12

f(2) = 12

Answer:

12

Step-by-step explanation:

f (x) = -x^2 + x + 14

Let x= 2

f(2) = - (2)^2 +2+14

     = -4 +2+14

  = -2 +14

  = 12


Write a verbal expression for (c-2)d

Answers

Answer:

the sum of c minus 2 multiplied by d ------> (c-2)d

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Which of the following statements is true?
A. A data set will always have exactly one mode
B. A data set can have multiple modes
C. A data set will always have at least one mode
D. A data set will never have a mode

Answers

Answer:

B

Step-by-step explanation:

Let's go over each option with the process of elimination!

A. A data set will always have exactly one mode.

Contradiction: 2, 2, 3, 3, 4, 5, 6

in this data set, both 2 and 3 are modes, so it is incorrect.

B. A data set can have multiple means.

True, example as A.

C. A data set will have at least one mode.

Contradiction: 2, 3, 4, 5, 6

There are no modes in here.

D. A data set will never have a mode.

Contradiction: 2, 2, 3, 4, 5

The mode is 2.

The only true statement is answer B.

I hope this helped! :D

Answer:

b

Step-by-step explanation:

if a data set had 1,1,3,4,4 how would you have 2 modes, 1,4. If you had 1,1,2,2,3,3 you would have 1,2,3 as your modes

a is wrong, c is wrong, d is wrong

a:my example has more that one

c:i have no explanation

d:is well already wrong

Name the property: i) (-15) X (-56)
ii) (-72) X 26 = 26 X (-72)
iii) [8 X (-46)] X 32 = 8 X [(-46)] X 32]
iv) (-15) X 105 = [(-15) X (100 +5)] = [(-15) X100] + [(-15) X 5]

Answers

Answer:

Open in answr appOpen_in_app

(i)

15

7

=

30

x

⇒x=

15

7×30

=14

(ii)

3

x

=

18

12

⇒x=

18

12×3

=2

(iii)

x

30

=

24

45

⇒x=

45

30×24

=16

(iv)

16

8

=

x

25

⇒x=

8

25×16

=50

Step-by-step explanation:

yeah

Pls help me this is due tomorrow

Answers

Step-by-step explanation:

Claim: There's 14 Goats and 9 Chickens!!

Data:

Working with the Provided Information.

Let the Number of goats be x

let the Number of Chickens be y

x + y = 23..... (i)

Since the goat Possesses Two Pair of Legs... Which is a Total of 4 Legs... We say Let its Contribution be 4x.

The Chicken has Only a Pair Of Legs...Which is a total of 2 legs.... We say let its contribution be 2y

4x + 2y = 74 .....(ii)

BRINGING BOTH EQUATIONS TOGETHER.

x + y = 23

4x + 2y = 74

From Eqn i

x= 23 - y

Substitute into eqn ii

4(23 - y ) + 2y = 74

92 - 4y + 2y = 74

92 - 2y = 74

2y = 92 - 74

2y = 18

y= 9.

Substitute y into any of the eqns to get x

x + y = 23

x + 9=23

x = 23 - 9

x = 14

This simply proves that there are 14 Goats and 9 Chickens!!!.

HAVE A GREAT DAY!

(a + b)2 = 1a2 + 2ab + 1b2
(a + b)3 = 1a3 + 3a2b + 3ab2 + 1b3
How are binomial expansions related to Pascal’s triangle?

Answers

The Pascal triangle terms and binomial are related by the binomial theorem fomrula:

The row of the Pascal triangle is the same as

where n is the same as the row of the Pascal triangle.

For example,

.

is the same as the 2nd row of the Pascal triangle.

.

Also know the leading coefficient and last term degree will be the nth row of the Pascal triangle.

The first term, a will be 1 less than the previous terms and the second term, b will be 1 more than the previous terms. For example, look at

.

Another example is

.

The third row of Pascal Triangle

.

.

Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

Binomial expansions are directly related to Pascal's triangle.

Pascal's triangle is a triangular arrangement of numbers in which each number is the sum of the two numbers directly above it. The first and last numbers in each row of Pascal's triangle are always 1.

The coefficients of the terms in a binomial expansion correspond to the numbers in Pascal's triangle. Each row of Pascal's triangle represents the coefficients of the corresponding power of the binomial.

For example, in the expansion of (a + b)², the coefficients are 1, 2, and 1. These coefficients can be found in the third row of Pascal's triangle: 1, 2, 1. Similarly, in the expansion of (a + b)³, the coefficients are 1, 3, 3, and 1, which can be found in the fourth row of Pascal's triangle: 1, 3, 3, 1.

In summary, Pascal's triangle provides a systematic way to determine the coefficients of binomial expansions, making it a valuable tool in algebra and combinatorics.

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In the first quadrant, you start at 2, 6 and move 2units rights and 3 units down what point will you end up on?

Answers

Answer:

[tex]End = (4, 9)[/tex]

Step-by-step explanation:

Given

[tex]Start = (2,6)[/tex]

Transformation: 2 units right and 3 units down

Required

The new point

First, we take the right translation;

When a point is translated right by 2 units, the rule is:

[tex](x,y) \to (x + 2, y)[/tex]

So, we have:

[tex](2,6) \to (2 + 2, 6)[/tex]

[tex](2,6) \to (4, 6)[/tex]

Next, we take the down translation;

When a point is translated down by 3 units, the rule is:

[tex](x,y) \to (x, y + 3)[/tex]

So, we have:

[tex](4,6) \to (4, 6+3)[/tex]

[tex](4,6) \to (4, 9)[/tex]

Hence, the endpoint is:

[tex]End = (4, 9)[/tex]

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Uruguay _______________ Argentina in the final match of the first World Cup. a. passed b. defeated c. wined d. managed 29. Brazil became the first team to ______________ the trophy five times. a. win b. succeed c. beat d. bite 30. How many countries took part in the first World Cup?a. interested b. participated c. competed d. cooperated31. 'Look outside. ........... sky is getting very dark.' a. A b. The c. d. An32. I'd like to invite him to ........... dinner next week if that's OK with.a. a b. the c. d. an33. 'I'm going out for a walk. Have you seen my shoes?' 'Yes, they're on ............ floor in .......... kitchen.'a. a/ the b. the/ the c. a / a d. the/ a34. 'Would you like .............. ice cream? There's one in ....... fridge.' 'Thanks.'a. an/ the b. an/ a c. / the d. a/ the35. Don't forget we're meeting on ............ Friday for ............ lunch Which Benin product was regulated to the point of issuing executions for unlicensed workers? A capacitor consists of two parallel conducting plates, each of area 0.4 m2 and separated by a distance of 2.0 cm. Assume there is air between the plates. While connected to a battery the electric field within the plates is 500 N/C. The potential difference between the plates is: ________ a) 5.0 V b) 10 V c) 30 V d) 20 V . What was the point of difference between the two sects of Jainism? Fred just purchased an expensive new refrigerator and is considering purchasing the overpriced warranty. In making his decision on the warranty, Fred ignores better ways that his money could be spent, including paying off high-interest credit card debt. According to prospect theory, the process that leads Fred to ignore the debt and buy the overpriced warranty is anchoring. confirmation bias. framing bias. mental accounting. what is contour line Before you move forward, summarize the changes you will need to make to your new budget. Describe these changes in at least two sentences.