which equation has the solutions x=5+-2(sqrt)7/3

Which Equation Has The Solutions X=5+-2(sqrt)7/3

Answers

Answer 1

Answer:

the solution is the last one.

Step-by-step explanation:

We know that for a second grade equation of the type:

ax^2 + bx + c = 0

The solution will be given by the quadratic formula, which states that:

x1 = [-b + sqrt(b^2 - 4ac)]/2a

x2 = [-b - sqrt(b^2 - 4ac)]/2a

So, according to the solution, we have:

x1 = [-5 + 2sqrt(7)]/3

Then:

2a = 3

-b = 5

b^2 - 4ac = 28

Solving each equation:

a = 2/3

b= -5

c = 9/8

None of the alternatives equals the values obtained before. So we can say that the expression is simplified.

Now we knoe what the first and second equation are wrong because b is not equal to -5.

So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:

then:

2a = 6

b= -10

b^2 - 4ac = 112

Then b=-10, a = 3 and c=-1

So the solution is the last one.

Answer 2

Final answer:

The correct quadratic equation with the solutions x = 5 ± 2√7 / 3 is 3x² - 10x - 1 = 0, determined by matching the given solution to the quadratic formula.

Explanation:

The student is asking which of the given quadratic equations has the solutions x = 5 ± 2√7 / 3. The correct equation that yields these solutions must be in the form ax² + bx + c = 0, where a, b, and c are constants.

To determine the right equation, we can work backwards from the given solutions using the quadratic formula:

x = ∛( -b ± √(b² - 4ac) ) / 2a

Comparing the solutions to the standard form obtained by the quadratic formula, we need to match the coefficients such that:

a equals the denominator (3) after the ± symbol,b is opposite in sign to the middle term (5),The discriminant b² - 4ac results in 4×7.

After testing each equation, we find that:

33x² - 5x + 7 = 0 (Incorrect)3x² - 5x - 1 = 0 (Incorrect)3x² - 10x + 6 = 0 (Incorrect)3x² - 10x - 1 = 0 (Correct)

The discriminant for the last equation is (10)² - 4×3×(-1) = 100 + 12 = 112, which is 4×7, confirming that x = 5 ± 2√7 / 3 are indeed the solutions.


Related Questions

128.75+_______=143.62

Answers

Answer:

14.87

143.62

- 128.75

________

14.87

At a pizza restaurant a large cheese pizza cost $8.99 plus $1.25 per topping if Laura paid $13.99 for a large pizza before taxes how many toppings did Laura put on her pizza

Answers

Answer:

4 toppings

Step-by-step explanation:

13.99-8.99=5

5÷1.25= 4

Laura put 4 toppings on her pizza.

The answer would be 4 toppings.

First you must subtract $13.99 by $8.99 which gives you $5. Then you divide that by the price of a topping which is $1.25. When you divide you get 4.

Hope this helps

Your friend George is 6 feet tall and his shadow is 10 feet long. At the same time, the shadow of the flagpole was 85 feet long. What is the height of a flagpole?



1.4 feet

60 feet

51 feet

141.6 feet

Answers

Answer:

51 feet

Step-by-step explanation:

Let

x -----> the height of a flagpole

we know that

Using proportion

[tex]\frac{6}{10}=\frac{x}{85} \\\\x=6*85/10\\\\x=51\ ft[/tex]

Given ABCD, AC=38, and AE=3x+4, find the value of x

Answers

ANSWER

D 5

EXPLANATION

The diagonals bisect each other so,

AE=CE

This implies that

3x+4+3x+4=38

6x+8=38

Group similar terms

6x=38-8

6x=30

x=5

Answer: 5

Step-by-step explanation:

help plz asap!!!!!!!!!

Answers

Answer:

a. 7(5 + 1/7) = 35 + 1 = 36

b. 5(4 + 7) = 20 + 7

c. 1/7(28 + 84) = 4 + 12 = 16

I hope this helps! :)

plsss help will give brainliest

Answers

Answer:

C, A, B, D

Hope This Helps!  Have A Nice Day!!

Number 9 is scalene

Number 10 is equilateral

Sorry I can’t help you on the other two I see.

The ratio of boys to girls in a room is 6:5. If three boys leave the room, the ratio is 1:1. How many girls are in the room?

Answers

Answer:

If the current price of $\$30$ is after a $50\%$ reduction, then the Lux basketball shoes must have been $30 \times 2 = \$60$ before. That $\$60$ price was after a $25\%$ reduction. When $25\%$ of the price is removed, the remaining portion is $75\%$, or $3/4$ of the price, which means the original price must have been $\$60 \times 4/3 = \boxed{\$80}$.

What is the area of triangle TUV?

A.
3 square units
B.
5.25 square units
C.
7 square units
D.
20.5 square units
E.
35 square units

Answers

The area of a triangle is 1/2*base*height and in this case it would be 1/2*7*1.5 which is B. 5.25 square units

Answer:

Yes it's B. 5.25

A=hbb

2=1.5·7

2=5.25

Step-by-step explanation:

What is the area of the obtuse triangle given below?

Answers

It's 49 sq. units because of the formula:

Area of triangle = 1/2 base × perpendicular height

Area = 14/2 × 7

Area = 7 × 7

= 49 sq. units

The area of the obtuse triangle is 49 sq. units.

What is the area of the obtuse triangle?

Given:

The base of the obtuse triangle is 14 units.The height of the obtuse triangle is 7 units.

Find:

The area of the obtuse triangle.

Solution:

As we know that the area of an obtuse triangle is equal to 1/2 * base * height.

So, as base and height of the obtuse triangle is given.

Now, we will calculate the area.

Area of the obtuse triangle = 1/2 * base * height

                                          = 1/2 * 14 * 7

                                          = 49 sq. units.

Hence, the area of the obtuse triangle is 49 sq units.

Therefore, Option A is the correct answer.

To learn more about an obtuse triangle, refer to:

https://brainly.com/question/12453859

#SPJ2

Working together, Joy and Steve collected 39 pounds of aluminum cans for recycling. If Joy collected j pounds, which of the following shows the number of pounds collected by Steve?

Answers

Answer:

The number of pounds collected by Steve is [tex]39-j[/tex]

Step-by-step explanation:

Let

j----> the number of pounds collected by Joy

s ---> the number of pounds collected by Steve

we know that

[tex]j+s=39[/tex]

Solve for s

That means-----> Isolate the variable s

Subtract j both sides

[tex]s=39-j[/tex]


10x² – 5x = 0 Solved for x

Answers

Answer:

Exact Form:

x = 0, 1/2

Decimal Form:

x =0, 0.5

Point A, locayed at (-2, 4), is translated down 6 units. What are the coordinates of A​

Answers

Answer:

(-2,-2)

Step-by-step explanation:

you would be going down the cooridante plane so that would only change the y value.

the vertex of this parabola is at (-3,2). which of the following could be its equation?

Answers

Answer:

B

Step-by-step explanation:

Notice that the vertex is 2 units above the x-axis.  The equation of this parabola must end in +2 to reflect this fact.  Thus, we narrow down our answer choices to B and C.

(x + 3) in choice B is correct, since the vertex is to the left of the y-axis.

Does this make sense?
0.88 is greater because after decimal point the hundreds place is eight in 0.88

Answers

It depends. Greater than what?

Not really, the hundredths place won't determine which number is larger, usually the largest place will do, which here is the tenth place.

1/4 = 0.25

0.88 > 0.25 because 0.8 > 0.2.

Would a scatter plot of the side length and perimeter of the side length and area represent a linear relationship?

Answers

Yes it would be because the perimeter is the out side and the area.is inside

from a boat on the lake, the angle of elevation to the top of a cliff is 16°38'. if the base of the cliff is 1250 feet from the boat, how high is the cliff?​

Answers

Check the picture below.

make sure your calculator is in Degree mode.

recall that there are 60 minutes in 1 degree.

How would I find the square root of 49531.25 without a calculator?

Answers

That’s a good question for google haha

well, without a calculator, what you can do is

round each choice to a "metric" value, namely 312.5 use 310, and then you can simply multiply it manually 310*310, which is 96100, well, that's too large, so nope.

don't bother with 323.4 because that's even larger.

likewise, check 239.3 with say 230 * 230, to see if it's close enough.

then check 222.5 with 220*220.

Point O is the center of the circle.
what is the area of the shaded portion of the circle

Answers

The area of the shaded portion of the circle is option G. 28.5cm²

How did we get the value?

To find the shaded area of a circle, you need to know the radius of the circle and the central angle of the sector that forms the shaded region. The formula for the area of a sector (a portion of a circle) is given by:

[tex]\[ \text{Area of Sector} = \left( \frac{\text{Central Angle}}{360^\circ} \right) \times \pi r^2 \][/tex]

where:

- [tex]\( \text{Central Angle} \)[/tex] is the measure of the angle at the center of the circle (in degrees),

- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159, and

- [tex]\( r \)[/tex] is the radius of the circle.

If the shaded region is not a complete sector but a segment (a portion of the circle bounded by a chord and an arc), you may need to subtract the area of the triangle formed by the radius and the two radii extending to the endpoints of the chord. The formula for the area of the segment is then:

[tex]\[ \text{Area of Segment} = \text{Area of Sector} - \text{Area of Triangle} \][/tex]

One can find the shaded area by:

1. Determine the radius [tex](\( r \))[/tex] of the circle.

2. Find the measure of the central angle [tex](\( \text{Central Angle} \))[/tex] of the sector or segment.

3. Apply the formula to calculate the area of the sector [tex](\( \text{Area of Sector} \))[/tex].

4. If it's a segment, find the area of the triangle formed by the radii and the chord and subtract it from the area of the sector.

[tex]\[ \text{Area of Quarter Circle} = \frac{1}{4} \times \pi r^2 \][/tex]

Given that the radius [tex](\( r \))[/tex] is 10, you can substitute this value into the formula:

[tex]\[ \text{Area of Quarter Circle} = \frac{1}{4} \times \pi \times (10)^2 \][/tex]

Let's calculate this:

[tex]\[ \text{Area of Quarter Circle} = \frac{1}{4} \times \pi \times 100 \][/tex]

[tex]\[ \text{Area of Quarter Circle} = \frac{1}{4} \times 100 \pi \][/tex]

[tex]\[ \text{Area of Quarter Circle} = 25 \pi \][/tex]

1/2 × 10 × 10 = 50cm²

25π - 50 = 25 × 3.14 - 50

              = 78.5 - 50

              = 28.5cm²

What is the value of 3 1/3 ÷ 2/3​

Answers

Answer:

5

3 1/3 / 2/3 = 5

Answer:

5

Step-by-step explanation:

"What is the value of 3 1/3 ÷ 2/3​"

3 1/3= 10/3

10/3 / 2/3 = 5/1=

5

Which linear inequality is represented by the graph

Answers

Answer:

[tex]y\leq \frac{1}{2} x+2[/tex]

Step-by-step explanation:

Firstly, as seen in the graph, the shaded area is below the graph. This means that [tex]y \leq[/tex]

Next we can look at the slope. It is seen that m=[tex]\frac{1}{2}[/tex]

From these two observations, the only inequality that fits the critera is

[tex]y\leq \frac{1}{2} x+2[/tex]

Answer:

Option A

Step-by-step explanation:

(1) In the given graph a solid line has been given which represent the sign of inequality between two variables.

(2) Moreover this, a should area has been given below the solid line. which represents the sign of "less than" between the variables.

In total between y and x there should be a sign of (≤)

(3) Now this line passes through two points (0,2) and (-4,0) so slope of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]

Therefore, slope =[tex]\frac{2-0}{0+4}=\frac{1}{2}[/tex]

y-intercept of the line has been given as 2

So inequality for this graph will be

y ≤ [tex]\frac{1}{2}[/tex]x + 2

Option A is the answer.

For the inverse variation equation p=8/v what is the value of v when p=1/2

Answers

The value of V is 16.

V=16

Explanation

Answer: v=16

Step-by-step explanation:

Given: The inverse variation equation :

[tex]p=\dfrac{8}{v}[/tex]

To find the value of v when p = 1/2, replace the value of p by 1/3 in the above  inverse equation, we get

[tex]\dfrac{1}{2}=\dfrac{8}{v}[/tex]

Multiply 2v on both the sides , we get

[tex]\dfrac{1}{2}\times2v=\dfrac{8}{v}\times2v\\\\\Rightarrow\ v=16[/tex]

Hence, the the value of v =16.

Donald has xxx twenty-dollar bills and 111 ten-dollar bill.
How much money does Donald have?

Answers

The expression representing the total amount of money Donald has is:

[tex]\[ \text{Total money} = 20x + 1110 \][/tex]

To find the total amount of money Donald has, we need to calculate the sum of the value of all the bills.

The value of each twenty-dollar bill is $20, and the value of each ten-dollar bill is $10.

Let's represent the number of twenty-dollar bills as x and the number of ten-dollar bills as 111.

So, the total amount of money Donald has can be expressed as:

[tex]\[ \text{Total money} = \text{Value of twenty-dollar bills} + \text{Value of ten-dollar bills} \]\[ \text{Total money} = 20x + 10(111) \][/tex]

A little help? I've been using a calculator since i'm in 7th grade, but part of the AIR (State Test) for 7th graders is without a calculator. Can someone re-teach me how to do this problem without a calculator?

1.36 divided by 0.08

Answers

The answer is 17. I will put the other side in a comment. It took me forever to do this, so someone else has probably answered already.

the sides of 2 similar hexagons are in a ratio of 1:3. The area of the smaller hexagon is 12in². Find the area of the larger hexagon

Answers

Answer:

374.12

Step-by-step explanation:

A=33

2a2=3·3

2·122≈374.12297

To solve this problem, we will use the fact that if two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Let's start by identifying the given information:
1. The ratio of the sides of the two similar hexagons is 1:3.
2. The area of the smaller hexagon is 12 square inches.
We are asked to find the area of the larger hexagon.
Now, since the ratio of the sides of the two hexagons is 1:3, the square of this ratio will tell us the ratio of the areas of the two hexagons. So we must square the side ratio to get the area ratio:
Ratio of sides of hexagons = 1 : 3
Ratio of areas of hexagons = (1^2) : (3^2) = 1 : 9
This means that the area of the larger hexagon is 9 times larger than the area of the smaller hexagon. Now we can find the area of the larger hexagon by multiplying the area of the smaller hexagon by 9:
Area of larger hexagon = Area of smaller hexagon * 9
                       = 12 in² * 9
                       = 108 in²
Therefore, the area of the larger hexagon is 108 square inches.

The area of a trapezoid is 30 square centimeters. The height is 4 centimeters. The shorter base measures 6 centimeters. What is the measure of the longer base?

Answers

Answer:

The other base would be 9 centimeters.

Step-by-step explanation:

This is because the formula for the area of a trapezoid is base+the other base/2 x height. if you have two of the three values and the answer all you have to do is put in numbers for the third value until it equals the area you were given.

Four expressions are shown bellow
A. 2(4x + 2)
B. 2(3x + 3)
C. 6x + 6
D. 8x + 4
Which two expressions are equivalent to 2(3x + 2 + x)?

Answers

Answer:

A

[tex]2(4x + 2)[/tex]

and

D

[tex]8x + 4[/tex]

Step-by-step explanation:

Because if you simplify the equation theb you get 8x+4 therefore D is equivalent to it. A is also equal to D which make it equivalent to the equation as well.

Answer:

A and D

Explanation:

A. 2 multiply by 4x give 8x and 2 multiply by 2 give 4 so the answer is 8x+4

D. When we expand the bracket, 2 multiply by 3x give 6x and 2 multiply by 2 give 4 and 2 multiply by x give 2x so the answer will be 6x+4+2x and we will gather the like terms so it will be 6x+2x=8x so the final answer is 8x+4

I need your help please because I do not understand that I have to find the diameter and the radius of a circle 3.14 • 1.5 • 1.5
2) 3.14 • 1.5 • 1.5
3) 3.14• 1•1
4) 3.14•6•6
5)3.14•2•2
6)3.14•1.5.1.5

And the other is the area 3.14•3
2) 3.14•1.25
3) 3.14•2
4) 3.14•12
5) 3.14•4
6) 3.14•3
Pleaseeeeeeeseeeeee

Answers

Answer:

Step-by-step explanation:

If you are given  3.14 · 1.5 · 1.5, you actually have 3.14 · 1.5²

If you match this up to the area-of-a-circle formula A = πr²

you can see right away that r = 1.5.  If r = 1.5, d = 2(1.5) = 3.0

I do not quite understand what you were trying to present in your

"And the other is the area 3.14•3

2) 3.14•1.25" so am unable to help you with it.

Final answer:

To find the diameter and radius of a circle, divide the given circumference by 3.14 to find the diameter, and then divide the diameter by 2 to find the radius. To calculate the area, use the formula A = πr², where π is approximately 3.14 and r is the radius of the circle.

Explanation:

To find the diameter and radius of a circle, we need to understand the formulas and calculations involved. The diameter is the distance across the circle passing through the center, and it is twice the length of the radius. The radius is the distance from the center of the circle to any point on its edge.

Finding the Diameter and Radius:

To find the diameter, you need to divide the given circumference by 3.14. For example, to find the diameter of 3.14 • 1.5 • 1.5, you would divide this value by 3.14. To find the radius, you divide the diameter by 2. For example, if the diameter is 6, then the radius is half of that, which is 3.

So, depending on the given values, you can use the formulas mentioned above to solve for the diameter and radius of a circle.

Calculating the Area:

To calculate the area of a circle, you need to use the formula A = πr², where π is approximately 3.14 and r is the radius of the circle. Substitute the given value of the radius into the formula and solve for the area. For example, if the radius is 3, then the area would be 3.14 • 3².

Using the formulas and steps above, you can find the diameter, radius, and area of a circle based on the given values.

Geometry semester 2 ; what’s the surface area of the regular pyramid below ?

Answers

Answer:

The correct answer is option B.  756 units²

Step-by-step explanation:

Points to remember

Surface area of pyramid = Base area  + (4 * area of side triangle)

To find the base area

Base area = side * side

 = 14 * 14 = 196 units²

To find the area of side triangle

Area of triangle = bh/d

Area = (14 * 20)/2 = 140 units²

To find the surface area of pyramid

Surface area = Base area  + (4 * area of side triangle)

 = 196 + (4 * 140)

 = 756  units²

Answer: 756

Step-by-step explanation:

What is the perimeter of the figure?



180 in.

64 in.

65 in.

72 in.

Answers

the perimeter is adding all the lenghts. the answer that i got isn't in there since i got 118 if you add all of them. hopefully that helped

Answer:

180

Step-by-step explanation:

i just did 18x10

Describe the end behavior of f(x) = 1/3^x-5. [note: this is an exponential function where 1/3 is the base and x is the exponent.]

( answer choices are above, please only answer if you know I really need help and I can’t retake it) Thank you and if it’s correct I promise to mark brainlest!!!

Answers

Answer:

c

Step-by-step explanation:

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