Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?

A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

  | 2  -7    8  -3

1 |      2   -5   3

  | 2   -5    3  0

1 |      2     -3  

    2   -3     0

So the factorization is (x-1)² (2x-3)=0. So:

                     [tex]\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

      |  1  -1  0  -4

  2  |     2  2    

         1  2  2  0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

                   [tex]\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}[/tex]

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

   | 6    7       9      2

-2 |      -12    10     -2

     6    -5     1       0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

         [tex]\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}[/tex]

                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}[/tex]

Answer:

it would be a vertical shift of 5 down

Step-by-step explanation:

I'm learning the same thing rn and that's right

The first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1

The complete question is as given below:-

The angle by which turns clockwise about point B to coincide with is degrees. If from point B, a point E is drawn directly opposite point C so that B, E, and C are on the same straight line, the angle by which turns counterclockwise to coincide with is degrees.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

I have attached the figure for this problem and there are two questions for this problem. The first is the angle needed for AB to turn to coincide with BC.

Simply, get add the measures of the angles ABD and DBC. So,

33.3 + 30.6 = 63.6 degrees

The second question is the angle needed for AB to turn to coincide with EB. Angle EBA is complementary with angle ABC. So,

180 - 63.6 = 116.4 degrees

Therefore for first drop-down menu answer is 63.9 And the second drop-down menu answer is 116.1

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Answer:

90

Step-by-step explanation:

90

Answer:

[tex]\textbf{C.}~2x^4 -9x^3-8x^2 +15x[/tex]

Step-by-step explanation:

[tex]~~~~(x^2 -5x)(2x^2 +x-3)\\\\=2x^4+x^3 -3x^2 -10x^3 -5x^2 +15x\\\\=2x^4 -9x^3-8x^2 +15x[/tex]

Answer:

$699.80

Step-by-step explanation:

$640 - 18% = 524.80

(640x18)/100 = 115.20

640-115.20 = 524.80

524.80+175 = 699.80

Answer:

$699.80

Step-by-step explanation:

640(18%)

640 x 18

100

reduce fraction

640 x 9

50

simplify

64 x 9

5

576

5. or 115 1

5. of 115.20

640 - 115.20 = 524.80 (dishwasher)

524.80 + 175 = 699.80 (total including installation)

Answer:

x = 3

Step-by-step explanation:

6x - 2 = 8x - 8 ( subtract 8x from both sides )

- 2x - 2 = - 8 ( add 2 to both sides )

- 2x = - 6 ( divide both sides by - 2 )

x = 3

Answer:

x=3

Step-by-step explanation:

Step-by-step explanation:

using elimination method because this is a simultaneous equation

3×x+6×y=111

x+y=27

1×[3x+6y=111]

3×[x+y=27]

3x+6y=111—equation 1

3x+3y=81—equation 2

substrate equation 1 from equation 2

3y=30

divide both sides by 3

y=10

substitute 10 for y in equation 1

3x+6y=111

3x+6(10)=111

3x+60=111

3x=111-60

3x=51

divide both sides by 3

x=17

Answer: A

Step-by-step explanation: BIG BRAIN

Answer:

2 I believe

Step-by-step explanation:

you do 4x12 then divide it by 6x4 then it would be n equals 2

Inspired by the works of Neil Dawson and Bert Flugelman, Kassidy drafts a design for a modern sculpture, the amount of steel Kassidy will need is mathematically given as

SA=16.094711 ft^2

Generally, the equation for the surface area of a cone is mathematically given as

SA=πr(rπ+√(h^2+r^2))

Therefore

SA=πr(rπ+√(h^2+r^2))

SA=π*1(1+√(4^2+1^2))

SA=16.094711 ft^2

In conclusion,  the amount of steel Kassidy will need is

SA=16.094711 ft^2

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Answer: B

Step-by-step explanation:

    We will test the options and see if they apply to the given values.

[A]  ✗

1 * 6 = 6 ✓

4 * 6 ≠ 15✗

[B] ✓

1 * 3 = 3, 3 + 3 = 6 ✓

4 * 3 = 12, 12 + 3 = 15 ✓

6 * 3 = 18, 18 + 3 = 21 ✓

[C] ✗

1 * 8 = 8, 8 - 2 = 6 ✓

4 * 8 = 32, 32 - 2 = 30, 30 ≠ 15 ✗

The given shape in the image is not an equilateral triangle.

The triangle with all three sides equal and all the angles equal is called an equilateral triangle.

In the given figure we can see a triangle this triangle is not an equilateral triangle because the figure is formed between a square grid now if you see closely the base of the triangle can not be equal to the two sides of the triangle.

Because these two sides are the hypotenuse for the remaining right-angle triangle. So the base of the highlighted triangle can not be equal to the other two sides of the triangle.

Therefore given shape in the image is not an equilateral triangle.

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Question has errors in typing that 572 should be √57/2

Because if it's 572 then 2a=1 so

Also

c also comes different

If it's like what I said

then

and

By putting values

Option B can be correct

Answer:

B: a = 1, b= 7, c = -2

Step-by-step explanation:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

Given:

[tex]x=\dfrac{-7\pm\sqrt{57}}{2}[/tex]

Comparing the terms of the given x-value with those of the quadratic formula:

[tex]\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}[/tex]

Therefore:

Using the found values of a and b to solve for c:

[tex]\implies b^2-4ac=57[/tex]

[tex]\implies (7)^2-4(1)c=57[/tex]

[tex]\implies 49-4c=57[/tex]

[tex]\implies -4c=57-49[/tex]

[tex]\implies -4c=8[/tex]

[tex]\implies c=-2[/tex]

In summary:   a = 1,  b = 7,  c = -2

[tex]\implies x^2+7x-2=0[/tex]

Therefore, option B is the correct solution.

Answer:

[tex]\text{1st term} = 3\\\\\text{Common ratio} = 2[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\\text{5th term} = ar^{5-1} = ar^4 = 48~~~~~~~~...(i)\\ \\\text{8th term} = ar^{8-1} = ar^7 = 384~~~~~~~...(ii)\\\\\text{1st term,}~ a = ?\\\\\text{Common ratio,}~ r = ?\\\\(ii) \div (i):\\\\~~~~~~\dfrac{ar^7}{ar^4}=\dfrac{384}{48}\\\\\implies r^{7-4} = 8\\\\\implies r^3 = 8\\\\\implies r^3 = 2^3\\\\\implies r =2\\\\\text{Substitute r = 2 in eq (i):}\\\\~~~~~~a\cdot 2^4 = 48\\\\\implies 16a =48\\\\\implies a = \dfrac{48}{16}\\\\\implies a = 3\\[/tex]

The heights of plant A and plant B will be equal on the day 8.

The height of the tree can be found as follows:

The equation for plant A can be described as follows:

y = 1 + 0.5x

where

x = number of days

y = height

The equation for plant B can be described as follows:

y = 3 + 0.25x

Therefore, for the height to be equal

1 + 0.5x =  3 + 0.25x

1 - 3 = 0.25x  - 0.5x

-2 = -0.25x

x = 2 / 0.25

x = 8 days

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Answer:

D.3x²+x-6

Step-by-step explanation:

4x²-x²+3x-2x-2-4

3x²+x-6

Answer:

The meal was $20

Step-by-step explanation:

20%= 1/5

1/5=4/? ---> one converts to four by multiplying it by 4 so you should do the the same with the denominator which is five.

5×4= 20

Answer:

y=3x-10

Step-by-step explanation:

Slope: (y2-y1)/(x2-x1)

(2-8)/(4-6)

slope= -6/-2 = 3

Point: (6,8)

Slope-intercept: y-y1=m(x-x1)

y-8=3(x-6)

y-8=3x-18

y=3x-10

Answer:

1328.88 cm^2

Step-by-step explanation:

Area = 6 * 1/2 * 22.6 * 19.6

= 1328.88 cm^2

Answer:

2/3

Step-by-step explanation:

Probability (b or e) :

⇒ There are 3 b's and 3 e's in the word "bumblebee"

⇒ P (b or e) = No. of b's and e's / Total letters

⇒ P (b or e) = 3 + 3 / 9

⇒ P (b or e) = 6/9

⇒ P (b or e) = 2/3

Answer:

1. I went to a store four days in a row and only bought chocolate bars each day. All chocolate bars were the same and cost the same. On the first day, I bought 2 chocolate bars for $2.38. On the second day I bought 1 chocolate bar for $1.19. On the third day, I bought 10 chocolate bars for $11.90. On the fourth day, I bough 4 chocolate bars for $4.76.

2. A sink is full. It contains 20 gallons of water. The stopper is removed and water starts draining out. One minute after the stopper is removed, the volume of water in the sink is 18 gallons.  Two minutes after the stopper is removed, the volume of water in the sink is 16 gallons.  Four minutes after the stopper is removed, the volume of water in the sink is 12 gallons.  Ten minutes after the stopper is removed, the sink is empty.  

Answer:

Step-by-step explanation:

Let the shorter sides be x.

The angle at common vertex of congruent sides is less than 90°, since it is acute triangle.

It means the other congruent angles are greater than 45°, according to angle sum theorem.

The vertical bisector divides the triangle in half, with base 8/2 = 4 cm and hypotenuse x.

It gives us the inequality:

Correct choice is D

The graph that shows the information on the table is On a coordinate plane, the x-axis is labeled ounces of salad dressing and the y-axis is labeled Total calories. A line goes through points (2, 300) and (4, 600).

The independent variable is the number of ounces of salad dressing which means that it will be shown on the x axis.

The total calories is the dependent variable which means that it will be on the y axis.

The line drawn will pass through the points on the table of (2,300) and (4 ,600) so option A is correct.

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A force F, of 25 newtons pulls at an angle of 20° above due east

A force F₂ of 35 newtons pulls at an angle of 55° below due west

Find the magnitude and direction of the resultant force

Answer:

26 display cases

Please give brainliest!
Hope this helps :)

if Jamaal has 1920 stamps, and he wants to place them in diplay cases that can each hold 72 stamps, we figure out how many display cases can be filled with stamps by finding out 1920/72

This gives us 26 2/3, but 2/3 isn't 1.

he can fill 26 cases

Answer:

d

Step-by-step explanation:

your answer to your question is D

Using compound interest, it is found that Dante was 6.6 years old when the balance in the account reached $13,000.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

A(t) = 13000, A(0) = 10000, r = 0.04, n = 12.

Hence the time in years is found as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]13000 = 10000\left(1 + \frac{0.04}{12}\right)^{12t}[/tex]

[tex](1.0033)^{12t} = 1.3[/tex]

[tex]\log{(1.0033)^{12t}} = \log{1.3}[/tex]

[tex]12t\log{1.0033} =  \log{1.3}[/tex]

[tex]t = \frac{\log{1.3}}{12\log{1.0033}}[/tex]

t = 6.6

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The length of the second pen is 11.25 units.

A rectangle is a polygon with four sides , the opposite sides are parallel and equal .

it is given in the question that

Saif is building a rectangular pen for his dog. the dimensions are 15 units long and 7 units wide

length new = 75% length initial

Length new = (75/100) * 15

Length new = 0.75 * 15

Length new = 11.25 units

The length of the second pen is 11.25 units.

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