Consider the trapezoid shown below.
6 in.
4 in.
6 in.
6 in.
(not drawn to scale)

Answer:

[tex]h^2-3h+5\:\text{remainder }3 \text{ or }h^2-3h+5-\frac{3}{h+3}[/tex]

Step-by-step explanation:

Question: [tex]\frac{h^3-4h+12}{h+3}[/tex] (divide using long division)

To start, our quotient must have a degree of 2, since [tex]h\cdot h^2=h^3[/tex].

From long division, multiply by the highest degree possible with appropriate constants to ride terms of the dividend when necessary. When you finish, the final term at the bottom will be your remainder and your quotient will be on top (in long division form).

The result is [tex]\frac{h^3-4h+12}{h+3}=h^2-3h+5\text{ with a remainder of } 3[/tex]. You can write it in quotient-remainder form, or as one long polynomial: [tex]\implies h^2-3h+5-\frac{3}{h+3}[/tex].

Verify:

[tex](h^2-3h+5)(h+3)=h^3-4h+15=\bold{h^3-4h+12}+\underline{3} \:\checkmark[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]

7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]

[tex] \huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]

[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]

[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]

[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{7.)\:13}}}}[/tex]

8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]

[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{8.)-14}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

a rule in quadratic equ states that

if summation of the roots should be -b/a of the equa

comparing the equ x² - 6x + y=0

with. ax² + bx +c =0

we see that in the equ, a= 1, b=-6

so the sum of the roots is -(-6)/1= +6

looking the the option the only one that agreed is option A

-2 + 8= 6

there fore the values of x are -2 or 8

Answer:

True

Step-by-step explanation:

A system of equations can be solved by Translating the system of equations into a matrix by following theses steps

write out the resulting answer in form of equations.

Answer:

x=4.34 seconds

Step-by-step explanation:

-16x^2+70x-2=0

[tex]x=\frac{35+\sqrt{1193}}{16}[/tex]

x=4.34

Answer:

Total Distance Michelle Covered is 26.14 miles

Step-by-step explanation:

According To the Question, We Have

Michelle First Ride Her bike In 12 miles South, then Changed her Direction & Ride Bike For A long While, and when she stopped she find Herself 2 miles south and 10 miles west from starting point. that shows she change direction and start walking in South-West Direction.  

(For Diagram, Please Find in attachment)

In Triangle ABC , Apply Phythagorus Theorem

AB² = BC² + AC²

AB² = 10² + 10²

AB² = 200

AB = √2×10 ⇔ 14.14 miles

Now The Total Distance Travelled by Michelle Would be

OA + AB = 26.14 miles

Answer:

x=0;y=2

Step-by-step explanation:

4(-x+2)=2x+8 -4x+8=2x+8 -4x-2x=8-8 -6x=0 x=0 y=-x+2 y=0+2 y=2

Answer:

See Explanation

Step-by-step explanation:

You posted an incomplete question with little and unclear details.

I will answer this question with a more complete version (see attachment)

Given that:

[tex]Scores: 100\ 95\ 88\ 62\ 76\ 90\ 100\ 58\ 72\ 60\ 85\ 90\ 70\ 72\ 54\ 100\ 60\ 80\ 75\ 51[/tex]

Required

The fraction that passed the test

Rearrange the score in ascending order:

[tex]Scores: 51\ 54\ 58\ 60\ 60\ 62\ 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

The total number of students is:

[tex]n =20[/tex]

Extract the students that passed (scored 70 and above)

[tex]Passed: 70\ 72\ 72\ 75\ 76\ 80\ 85\ 88\ 90\ 90\ 95\ 100\ 100\ 100[/tex]

Their numbers are:

[tex]Passed: 14[/tex]

So, the fraction of those that passed is:

[tex]Fraction = \frac{Passed}{n}[/tex]

[tex]Fraction = \frac{14}{20}[/tex]

Reduce fraction

[tex]Fraction = \frac{7}{10}[/tex]

Answer:

Step-by-step explanation:

Answer/Step-by-step explanation:

The diagram of the circular track is missing, and so also its dimensions.

However, let's assume the dimensions of the circular track given is diameter (d) = 20 meters or radius (r) = 10 meters.

Since it's a circular track, the circumference of the track would give us the number of meters she runs in 1 lap.

Circumference = πd

d = 20 m (we are assuming the diameter is 20 meters)

π = 3.14

Circumference of circular track = 3.14 × 20 = 62.8 m.

This means that 1 lap = 62.8 m that she would have to run.

Therefore,

6 laps would be = 6 × 62.8 = 376.8 m

Therefore, if she completes 6 laps around the circular track that has a diameter of 20 m, she will have to run about 376.8 m.

Answer: 12 and 24

Step-by-step explanation:

Answer:

Step-by-step explanation:

length = Pi.radius.15degree/180degree

= Pi.2.15/180 = about 0,5 feet

The length of the arc that is subtended by 15° is: 0.5 ft.

Formula for the arc length in a circle with a radius of r and a central angle of ∅ is, ∅/360 × 2πr.

Given the following:

Arc length = 15/360 × 2π(2)

Arc length = 0.5 ft.

Thus, the length of the arc that is subtended by 15° is: 0.5 ft.

Learn more about the arc length on:

https://brainly.com/question/17329757

Answer:

x = 80

Step-by-step explanation:

x + .1x = 88

or

x(1+.1) = 88

which ever makes more sense to you

1.1 x = 88

x = 88/1.1

x = 80

Answer:

I've attached the Answer

Answer:

a = - 2

Step-by-step explanation:

Given x = a, y = 3 lies on the equation. That is the values satisfies the equation when substituted.

Find a :

Equation : 5x + 2y = - 4

                5 ( a ) + 2 ( 3) = - 4

                5a + 6 = - 4

                 5a + 6 - 6 = - 4 - 6               [ subtracting both sides by 6 ]

                 5a  + 0 = - 10

                   5a = - 10

                    a = - 2                               [ dividing both sides by 5]

[ fact check : If (-2 , 3 ) lies on the equation : 5x + 2y = - 4

                                                                    5(-2) + 2( 3 ) = - 4

                                                                   - 10 + 6 = - 4

                                                                         - 4 = - 4 ]

Answer:

x = ±2

 x = ±i

Step-by-step explanation:

(x^2+4)^2 – 11(x^2+4) + 24 = 0

Let m = x^2 +4

(m)^2 – 11(m) + 24 = 0

Solving this quadratic

What two numbers multiply to 24 and add to -11

-8*-3 =24

-8-3 = -11

(m-8)(m-3) =0

m = 8   m=3

Now substitute back

x^2 +4 = 8    x^2 +4 = 3

x^2 +4-4 = 8-4    x^2+4-4 = 3-4

x^2 = 4                      x^2 = -1

Taking the square root

sqrt(x^2) = sqrt(4)                      sqrt(x^2) = sqrt(-1)

x = ±2                                           x = ±i

Answer:

one value of x = 2

Step-by-step explanation:

[tex](x^2 + 4 )^2 - 11(x^2 + 4 ) + 24 = 0\\\\x^4 + 16 + 8x^2 - 11x^2 -44 + 24 = 0\\\\x^4 - 3x^2 -4 = 0\\\\[/tex]   ------ ( 1 )

[tex]Let \ x^2 \ = \ u[/tex]

( 1 ) => [tex]u^2 - 3u - 4 = 0[/tex]

         [tex]u^2 -4u + u - 4 = 0\\\\u(u - 4) + 1 (u - 4) = 0\\\\(u + 1) (u - 4) = 0\\\\u = -1 \ , \ u = 4[/tex]

   [tex]=> x^2 = - 1 \ and \ x^2 = 4[/tex]

      [tex]x = \sqrt {-1} = i[/tex]

      [tex]x = \sqrt{4} = \pm 2[/tex]

Answer:

250

Step-by-step explanation:

4/16 = 1/4 = .25

When dividing exponents, subtract the bottom from the top, so [tex]10^{5}[/tex]÷[tex]10^{2}[/tex] = [tex]10^{3}[/tex]

So, .25 * [tex]10^{3}[/tex] = 250

Answer:

Can I get the full question please

Step-by-step explanation:

x + y = 10 - - - 1

x=2y - - - - - 2

Putting the value of x in eqn 1,

2y+y=10

y=10/3

=3.33 yrs

Which i feel is incorrect

Answer: the 24 oz hazelnuts

Step-by-step explanation:

Answer:

hazelnuts

Step-by-step explanation:

pecans = $15.2/16= .95

cashews = 5.60/8=.7

almonds = 20.48/32= .64

hazelnuts = 13.5/24 = .56

QUESTION:- Given 3x+y=1

Write the equation in general form Ax+By+C =0

3x-y+1=0

-3x +y-1=0

3x-y=-1

[tex]3x + y - 1 = 0 \: \: ✔[/tex]

ANSWER:-

[tex]3x + y = 1 [/tex]

Form of the given equation->

[tex]Ax + By = C[/tex]

so we need to change the side of the C !

while changing side of C we need to change the sign of C !

[tex] \bold{ \red{SO :- }}[/tex]

[tex]3 x + y = 1 \\ 3x + y - 1 = 0[/tex]

FORM OF THE RESULTED EQUATION:-

[tex]Ax + By + C = 0 \\

A = 3 \\ B = 1 \\ C = - 1[/tex]

Answer:

Step-by-step explanation:

volume of reqd. figure=10×5×1+3×3×1=50+9=59 cm³

Answer:

12.21

Step-by-step explanation:

Explanation:

This is a right triangle, so the Pythagorean Theorem applies.

The Pythagorean Theorem states that the sum of the squared legs of a triangle is equal to the squared hypotenuse.

The legs of a triangle are the sides that form the right angle.

The hypotenuse of a triangle is the longest side.

Formula/solve:

[tex]a^2+b^2=c^2[/tex]

[tex]a,b-legs[/tex]

[tex]c-hypotenuse[/tex]

Here, I am solving for the hypotenuse.

[tex]7^2+10^2=c^2[/tex]

[tex]49+100=c^2[/tex]

[tex]149=c^2[/tex]

Conclude:

The last step is the cancel out c² by finding the square root of 149.

149 is not a perfect square, so I must round the square root to the nearest hundredth.

[tex]12.2065556157[/tex] ≈ [tex]12.21[/tex]

I, therefore, believe the length of the hypotenuse is 12.21 feet.

Answer:

$ 5.98

Step-by-step explanation:

20/100 × 22.42/1 = $ 4.48

$ 22.42 - $ 4.48 = $ 17.94

If they split that bill in two each would pay $ 5.98

I hope this helps.

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28°  ∠ACD=31°  &  line AB=AC .

According To the Question,

        thus , ∠ABC=76° .

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°)  ⇔  104˚

For Diagram, Please Find in Attachment  

Answer:

circumference of a circle =2 pi r

radius=14/2=7

2×3.14×7=43.96ft

The circumference of the circle is 43.96 ft.

Given,

Diameter of the circle = 14 ft

π = 3.14

We need to find the circumference of a circle.

The circumference is the total length of the surface of the circle.

The circumference is given by:

= 2πr

r = radius of the circle

Diameter = 2radius

Example:

We have,

Diameter = 14 ft

π = 3.14

Radius = diameter / 2 =  14/2 = 7 ft

Circumference:

= 2πr

= 2 x 3.14 x 7

= 43.96 ft

Thus the circumference of the circle is 43.96 ft.

Learn more about circles here:

https://brainly.com/question/16125353

#SPJ2

Answer:

275, 300, 450, 490, 675

Median: 450

Q1: 287

Step-by-step explanation:

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } [/tex]

[tex]\huge\underline{\sf{\red{Problem:}}}[/tex]

[tex]\huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{mass \: 1 \: = \: 6000 \: kg}[/tex]

[tex]\quad\quad\quad\quad\sf{velocity\: 1\: = \: 2.0\: m/s}[/tex]

[tex]\quad\quad\quad\quad\sf{mass \: 2\: = \: 3000 \: kg}[/tex]

[tex]\quad\quad\quad\quad\sf{velocity\: 2\: = \: 3.0\: m/s}[/tex]

[tex]\huge\underline{\sf{\red{Fomula:}}}[/tex]

[tex]\quad\quad\quad\quad\boxed{\sf{vf\: = \frac{ \small{m }\tiny{1} \small{v} \tiny{1} \small{ \: + \: m} \tiny{2} \small{v} \tiny{2}}{( \small{m} \tiny{1}\small{ \: + \: m} \tiny{2} \small{)} }}}[/tex]

[tex]\huge\underline{\sf{\red{Solution:}}} [/tex]

[tex]\quad\quad\quad\quad\sf{vf\: = \frac{ \small{m }\tiny{1} \small{v} \tiny{1} \small{ \: + \: m} \tiny{2} \small{v} \tiny{2}}{( \small{m} \tiny{1}\small{ \: + \: m} \tiny{2} \small{)} }}[/tex]

[tex]\quad\quad\quad\quad\sf{vf\: = \frac{(6000 \: kg)(2.0\:m/s)+(3000\:kg)(3.0\:m/s)}{(6000\:kg)+(3000\:kg)}}[/tex]

[tex]\quad\quad\quad\quad\sf{vf\: = \frac{(12,000kgm/s)+(9,000\:kgm/s)}{(9,000kg)}}[/tex]

[tex]\quad\quad\quad\quad\sf{vf\: = \frac{21,000 \: kgm/s}{9000kg}}[/tex]

[tex]\quad\quad\quad\quad\sf{vf\: = \frac{21,000 \cancel{ \red{ kg}}m/s}{9000 \cancel{ \red{kg}}}}[/tex]

[tex]\quad\quad\quad\quad \sf{vf\: = \boxed{ \sf{ 2.33 \:m /s}}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad\quad \underline{ \sf{\boxed{ \sf{ \red{ 2.33 \:m /s}}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } [/tex]

[tex]\sf{\red{︎✰}ShineBrighter\red{︎✰}}[/tex]

[tex]\sf{✍︎ C.Rose\red{❀}}[/tex]

ฅ^•ﻌ•^ฅ