Help for points! please

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

The given equation is:

[tex]3-k=\sqrt{3k+1}[/tex]

Square both sides of the equation

[tex](3-k)^2=3k+1[/tex]

Expand the left side of the equation above

[tex](3-k)^2=3k+1\\\\(3-k)(3-k)=3k+1\\\\3^2-3k-3k+k^2=3k+1\\\\9-6k+k^2=3k+1[/tex]

Write the quadratic equation in standard form

[tex]k^2-6k-3k+9-1=0\\\\k^2-9k+8=0\\\\[/tex]

Factor the quadratic equation

[tex](k-8)(k-1)=0[/tex]

Use the zero product property

k - 8 = 0

k = 8

k - 1 = 0

k = 1

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

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answer

first one: 8 and 1

second one: is 1

Step-by-step explanation:

slay

Answer:

30/6 is correct

Step-by-step explanation:

Answer: -1/6

You can multiply 2/6 by 2 to get 4/12 which you can subtract from 6/12.

4/12 - 6/12 = -2/12 which you can simplify further to get -1/6

Answer:

Step-by-step explanation:

The area of each trapezoid can be found using the relevant formula:

  A = 1/2(b1 +b2)h . . . . b1, b2 are the base lengths; h is the height

For the top trapezoid, the height is 13 m-7 m = 6 m, so the area is ...

  A = 1/2(8 m +5 m)(6 m) = 39 m²

The area of the bottom trapezoid is ...

  A = 1/2(10 m +17 m)(7 m) = 94.5 m²

The area of the shape is the sum of the areas of the two trapezoids.

  area = 39 m² +94.5 m² = 133.5 m² . . . . area of the figure

__

The horizontal lengths are all marked, but the slant lengths are not. There are no angles or other information given that can help determine the slant lengths. In order to answer the question, we can assume that the trapezoids are isosceles. Then the base of the right triangle shown in the top trapezoid is (8 -5)/2 = 1.5 m. The height is 6 m. The Pythagorean theorem tells us the slant length is ...

  s1 = √(1.5² +6²) ≈ 6.1847 . . . . meters

Similarly, the base length of the right triangle shown next to the bottom trapezoid is (17 -10)/2 = 3.5 m. The height is 7 m. The slant length of that one is ...

  s2 = √(3.5² +7²) ≈ 7.8262 . . . . meters

__

The perimeter is the sum of the lengths of the sides. Note that the 17 m dimension includes 8 m that are not part of the boundary of the figure. The sum of lengths of the horizontal edges is ...

  10 m +(17 -8 m) +5 m = 24 m

The sum of the lengths of the slant edges is ...

  2·s1 +2·s2 = 2(6.1847 +7.8262) ≈ 28.02 . . . . meters

The perimeter of the figure is the sum of horizontal lengths and slant lengths:

  24 m + 28.02 m = 52.02 m . . . . perimeter of the figure

b. gh is a perp. bisector .

Answer:

a=19

Step-by-step explanation:

In this equation you want to solve for a

In this case you simply add 6 to 13 because -6 is attached to the a on the left side and you want a on it's own.

a - 6 = 13  

+6       +6       (-6+6 = 0) (6+13=19)

a = 19

Its 1/-2, or in other words it is -(1/2), so it would be the third option you have there.

Your welcome! :D

Answer:

the Domain would be represented by Time in this problem, since time can only be positive, the domain would start at zero seconds and end at 5 seconds when the soccer ball hits the ground.

Step-by-step explanation:

Answer:

EFGH, HFGE, EGFH, HGFE

Step-by-step explanation:

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

Answer:

-1 / 2.

Step-by-step explanation:

The Slope of a line when given two points:

First establish the two points as (X1, Y1) and (X2,Y2)

you can decide which point is (X1, Y1) and which point is (X2,Y2) in any order

So I choose (X1, Y1) = (-10,1) and (X2,Y2) = (0,-4)

Next use this equation to find the difference in rise/run (rise over run): (Y2 - Y1) / (X2 - X1)

Now we're ready to solve by plugging in our points: ( (-4) - 1 ) / ( 0 - (-10) ) **DON'T FORGET negatives attached to numbers when plugging in**

Solve: (-5) / 10 = -5 / 10 or -1 / 2 reduced by taking out a 5 from top and bottom. So your slope is equal to -1 / 2.

Answer:

-1/2

Step-by-step explanation:

Answer:

  A.  y ≥ -3x +4

Step-by-step explanation:

The boundary line crosses the y-axis at +4, so the y-intercept of it is +4. This eliminates choices C and D.

The shading is above the line, where y-values are greater than those on the line. This eliminates choice B.

The correct inequality is ...

  A. y ≥ -3x +4

Work Shown:

(3 mm)/(17 m) = (x mm)/(55 m)

3/17 = x/55

3*55 = 17*x

165 = 17x

17x = 165

x = 165/17

x = 9.706 approximately

Side note: I used the cross multiplication rule for the third step.

Answer:

B

Step-by-step explanation:

Each tick = + or - 2 depending on which quadrant and axis

So the first line (the slanted one) intersects the y axis at (0,5) and continues until (2,5)

Then the line becomes straight (the y remains constant) from (2,5) (the points x value is 2) to (2,10) (the points x value is now 10)

Answer:

-16.1y + 14

Step-by-step explanation:

–7(2.3y − 2)

=> -16.1y + 14

Therefore, -16.1y + 14 is the simplified form.

Hoped this helped

[tex]GeniusUser[/tex]

Answer:

53

Step-by-step explanation:

sorry if im incorrect

Answer:

p = (-15)/14

Step-by-step explanation:

Solve for p:

5 + 1/28 = p/2 + 4/7 + 5

Put 5 + 1/28 over the common denominator 28. 5 + 1/28 = (28×5)/28 + 1/28:

((28×5)/28 + 1/28) = p/2 + 4/7 + 5

28×5 = 140:

140/28 + 1/28 = p/2 + 4/7 + 5

140/28 + 1/28 = (140 + 1)/28:

((140 + 1)/28) = p/2 + 4/7 + 5

140 + 1 = 141:

141/28 = p/2 + 4/7 + 5

Put each term in p/2 + 4/7 + 5 over the common denominator 14: p/2 + 4/7 + 5 = (7 p)/14 + 8/14 + 70/14:

141/28 = ((7 p)/14 + 8/14 + 70/14)

(7 p)/14 + 8/14 + 70/14 = (7 p + 8 + 70)/14:

141/28 = ((7 p + 8 + 70)/14)

Grouping like terms, 7 p + 8 + 70 = 7 p + (70 + 8):

141/28 = (7 p + (70 + 8))/14

70 + 8 = 78:

141/28 = (7 p + 78)/14

141/28 = (7 p + 78)/14 is equivalent to (7 p + 78)/14 = 141/28:

(7 p + 78)/14 = 141/28

Multiply both sides of (7 p + 78)/14 = 141/28 by 14:

(14 (7 p + 78))/14 = (14×141)/28

(14 (7 p + 78))/14 = 14/14×(7 p + 78) = 7 p + 78:

(7 p + 78) = (14×141)/28

14/28 = 14/(14×2) = 1/2:

7 p + 78 = 141/2

Subtract 78 from both sides:

7 p + (78 - 78) = 141/2 - 78

78 - 78 = 0:

7 p = 141/2 - 78

Put 141/2 - 78 over the common denominator 2. 141/2 - 78 = 141/2 + (2 (-78))/2:

7 p = (141/2 - (78×2)/2)

2 (-78) = -156:

7 p = 141/2 + (-156)/2

141/2 - 156/2 = (141 - 156)/2:

7 p = ((141 - 156)/2)

141 - 156 = -15:

7 p = (-15)/2

Divide both sides by 7:

p = ((-15)/7)/2

2×7 = 14:

Answer: p = (-15)/14

Use the multinomial theorem to compute some polynomial expansions:

(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)

(a + b + c)³ = a³ + b³ + c³

… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)

… … … … … … + 6 abc

(a + b + c)⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

Now, given that

a + b + c = 4

a² + b² + c² = 10

it follows that

ab + ac + bc = (4² - 10)/2 = 3

We use this result to simplify the extra terms in the 3rd-degree expansion.

a²b + a²c + ab² + b²c + ac² + bc²

= a (ab + ac) + b (ab + bc) + c (ac + bc)

= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc

… … I underline the terms that are added and subtracted … …

= (a + b + c) (ab + ac + bc) - 3abc

= 4 • 3 - 3abc

= 12 - 3abc

Given that

a³ + b³ + c³ = 22

this tells us that

4³ = 22 + 3 (12 - 3abc) + 6abc

4³ = 58 - 3abc

and so

abc = (4³ - 58)/(-3) = -2

from which it follows that

a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18

Now we similarly simplify the extra terms in the 4th-degree expansion.

a³b + a³c + ab³ + b³c + ac³ + bc³

= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)

= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²

= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)

= 10 • 3 - (a²bc + ab²c + abc²)

which means

4⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (30 - a²bc - ab²c - abc²)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

reduces to

136 = a⁴ + b⁴ + c⁴

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 8 (a²bc + ab²c + abc²)

Now, we know a + b + c = 4 and abc = -2, so we have

a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8

and so

136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)

200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)

Finally, we know that ab + ac + bc = 3. Squaring this gives

(ab + ac + bc)² = 3²

a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9

but we also know that a²bc + ab²c + abc² = -8, so

a²b² + a²c² + b²c² + 2 • (-8) = 9

a²b² + a²c² + b²c² = 25

Therefore, we end up with

200 = a⁴ + b⁴ + c⁴ + 6 • 25

⇒   [[[   a⁴ + b⁴ + c⁴ = 50   ]]

Answer:

8m

Step-by-step explanation:

Answer:

if im correct the answer is 63 + 36 = 9 (7 + 4)

Step-by-step explanation:

Answer:

The guy above was correct! I hope people see this so that they can trust the provided answer above.

Step-by-step explanation:

Answer:

264 cm³

Step-by-step explanation:

Answer:

the amount paid for the loan would be $6700.80

Answer:

$7.01

Step-by-step explanation:

Answer:

$7.01

Step-by-step explanation:

You have seven whole dollars, which goes before the decimal point, then your cents go behind the decimal point.

Answer:

=35

Step-by-step explanation:

3(3) ^2 + 2(4)

= 3(9) + 8

= 35

Where you see a, substitute with 3 and where you see b, substitute with 4

Just follow the steps above.

[tex]\\ \sf\Rrightarrow 3a^2+2b[/tex]

[tex]\\ \sf\Rrightarrow 3(3)^2+2(4)[/tex]

[tex]\\ \sf\Rrightarrow 3(9)+8[/tex]

[tex]\\ \sf\Rrightarrow 27+8[/tex]

[tex]\\ \sf\Rrightarrow 35[/tex]

Answer:

EI = FI and EG is twice the length of EI. Try setting up algebraic equations 3x + 8 = 6x -4 to find the value of x. Then substitute it back into the equation to find the length.

Step-by-step explanation:

Step-by-step explanation:

The first inequality has solution

 4p > -8 . . . . . . subtract 1

 p > -2 . . . . . . . divide by 4

This is graphed as an open dot at -2, with shading to the right.

Neither inequality symbol includes "or equal to", so both dots are open dots. The appropriate choice is the first one:

 a number line with open circles at negative 2 and 5 with shading in between

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If there are 20 girls in a class of 30 students, find out the percentage of boys in the class?​

>> If the class has 30 students and 20 girls then;

>> Therefore;

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The percentage of boys in the class is 33.3%

If the class has 30 students and 20 girls then;

Boys = (30 - 20 = 10)

Percentage that are boys = (no.of boys/total students) x 100

10/30 * 100 = 33.3%

The percentage is a relative fee indicating the hundredth component of any amount. One percentage (symbolized 1%) is one centesimal part; as a result, 100 percent represents everything and 2 hundred percent specifies twice the given amount. percentage. associated subjects: mathematics percentile.

Multiply the number by means of 100. If you are required to convert a decimal number like 0.57 to a %, you simply multiply it through one hundred. that is 0.57 x 100 = 57. therefore, 0.57 as a percent equals 57%.

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The speed of this car is equal to 1.6 km/min.

Given the following data:

To calculate the speed of this car:

Speed can be defined as the distance travelled by an object per unit time and it is usually measured in meter per seconds (m/s). Also, speed has magnitude but no direction and as such it is a scalar quantity.

Mathematically, speed is given by the formula;

[tex]Speed = \frac{distance}{time}[/tex]

Substituting the given parameters into the formula, we have;

[tex]Speed = \frac{50}{30}[/tex]

Speed = 1.6 km/min.

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Answer:

49

Step-by-step explanation:

9*7=63

7*7=49

There are 49 questions did Jackson answer correctly.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

Jackson answered every 7 out of 9 questions correctly on a Spanish Quiz.

Total number of questions = 63

Now,

Let number of correct questions = x

So, By the definition of ratio, we can formulate;

⇒ 7 : 9 = x : 63

Solve for x as;

⇒ 7 : 9 = x : 63

⇒ 7 / 9 = x / 63

⇒ 7 × 63 / 9 = x

⇒ x = 7 × 63 / 9

⇒ x = 7 × 7

⇒ x = 49

Thus, There are 49 questions did Jackson answer correctly.

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