What is the sum (6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)?

A.9x^6 + 8x^4 + 4x^2 – 1
B.8x^4 + 9x^3 + 4x – 1
C.8x^4 + 3x^3 – 10x^2 + 4x – 1
D.8x^4 – 3x^3 + 10x^2 – 2x + 9

[tex](a)\\\\\\\text{Given that,}~~\\\\ f(t) =\dfrac 6{\sqrt{t-8}}\\\\\\\\\implies f'(t) = 6\left[\dfrac{\left(\sqrt{t-8}\right) \cdot 0 - \dfrac 1{2\sqrt{t-8 }}}{\left(\sqrt{t-8}\right)^2}\right]\\\\\\\\\implies f'(t) = -6\left(\dfrac {\dfrac 1{2\sqrt{t-8}}}{t-8}\right)\\\\\\\implies f'(t) = -6\left(\dfrac{1}{2\sqrt{t-8} (t-8)}\right)\\\\\\\implies f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}[/tex]

(b)

[tex]\text{Given that,}\\\\y=f(t)\\\\\text{Slope of y,} ~~ f'(t) =-\dfrac 3{(t-8)^{\tfrac 32}}\\\\\text{At point (33, 6/5)}\\\\\\f'(t) = -\dfrac 3{(33-8)^{\tfrac 32}} = - \dfrac 3{ (25)^{ \tfrac 32}} = - \dfrac 3{5^3} = -\dfrac 3{125}\\\\\\\text{Equation with given points,}\\\\y - \dfrac 65 = -\dfrac 3{125} ( t - 33)\\\\\\\implies y =-\dfrac 3{125} t +\dfrac{99}{125} + \dfrac 65\\\\\\\implies y = -\dfrac 3{125} t +\dfrac{249}{125}[/tex]

Answer:

The equation for the axis of symmetry is x=3

Step-by-step explanation:

Because the vertex is (-2,3) then the axis of symmetry must pass that point.

Answer:

can you give more context to the question and I will answer it in the comments? thanks!

Answer:

Slope-intercept form y=10x-37

Point slope form y-3=10(x-4)

Step-by-step explanation:

Answer:

150.72 in³

Step-by-step explanation:

We know that

Radius = Diameter/2

Radius = 8/2

Radius = 4 in

Now,

Volume of cylinder = πr²h

=> 3.14 × (4)² × 3

=> 3.14 × 16 × 3

=> 150.72 in³

Answer:

The correct answer is option 150.72 in³.

Step-by-step explanation:

Given :

To Find :

Using Formula :

[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]

[tex]\star{\small{\underline{\boxed{\sf{\pink{V = \pi{r}^{2}h}}}}}}[/tex]

Solution :

Firstly, finding the radius of cylinder by substituting the values in the formula :

[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \dfrac{8}{2}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{8}{2}}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Radius_{(Cylinder)} = 4 \: in}}}[/tex]

[tex]{\star{\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 4 \: in}}}}}}[/tex]

Hence, the radius of cylinder is 4 in.

[tex]\rule{300}{1.5}[/tex]

Now, finding the volume of cylinder by substituting the values in the formula :

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \pi{r}^{2}h}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4)}^{2} \times 3}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(4 \times 4)} \times 3}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times {(16)} \times 3}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = 3.14 \times 16 \times 3}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314}{100} \times 16 \times 3}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 16 \times 3}{100}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{314 \times 48}{100}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = \dfrac{15072}{100}}}}[/tex]

[tex]\dashrightarrow{\small{\sf{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}[/tex]

[tex]\star{\small{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} = Rs.150.72 \: {cm}^{3}}}}}}}[/tex]

Hence, the volume of cylinder is 150.72 in³.

[tex]\rule{300}{1.5}[/tex]

Answer:

6.93

Step-by-step explanation:

hope this helps

Answer:

98.6° Fahrenheit ( i did it in celsius sorry if i got it wrong)

Step-by-step explanation:

Answer:

Step-by-step explanation:

across x axis:(-4,2)

across y-axis:(4,-2)

Answer:

no it is really easy question to answered so do it your self

[tex]\\ \sf\Rrightarrow 1\dfrac{2}{5}m-\dfrac{3}{5}(\dfrac{2}{3}m+1)[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{7}{5}m-\dfrac{3}{5}(\dfrac{2m+3}{3})[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{7m}{5}-\dfrac{6m+9}{15}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{21m-6m-9}{15}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{15m-9}{15}[/tex]

[tex]\\ \sf\Rrightarrow m-\dfrac{3}{5}[/tex]

The simplified form of the expression is m - 3/5

Given the expression 1 2/5 m - 3/5 (2/5m + 1)

We need to simplify the term. Expand the bracket to have:

1 2/5 m - 3/5 (2/3m + 1)

1 2/5 m -2/5 m - 3/5

7/5 m - 2/5 m - 3/5

(7m-2m)/5 - 3/5

5m/5 - 3/5

m - 3/5

Hence the simplified form of the expression is m - 3/5

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Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

Ignore this, I posted the wrong answer and I don't know how to delete it.

Answer:

Yes/true

Step-by-step explanation:

-2(z+9)-(-5)=-2⋅z-2⋅9+5

sostituisco la lettera dandogli un valore

=-2(-6+9)-(-5)=-2⋅(-6)-2⋅9+5

calcolo e tolgo le parentesi

=-2⋅3+5=12-18+5

Elimino i termini uguali

=-2⋅3=12-18

Somma e moltiplicazione tra i numeri

=-6=-6

Answer:

A. (A) Yes

B. (A) Yes

C. (B) No

Step-by-step explanation:

A is Categorical because it is not based on numbers.

B is Categorical because it is not based on numbers.

C is Not Categorical because it is based on numbers.

Answer:

19 is a prime number, thus making the only factors 1, 2, 19. (Not necessary to include 1)

Step-by-step explanation:

Answer:

A probability cannot be more than 100%

Answer:

if a pyramid and a prism have the base and height also their volumes are always in the ratio 1:3

step by step

as the volumes of prism is 108 cubic meters

1/3 x 108 = 36 cubic meters

Answer:

8 for tens, 9 for hundredths and thousandths is 1

Step-by-step explanation:

you can find the number by looking at the place of the numbers if it is tens look at the tens place which is the number eight as tens are 2 digit numbers

Answer:

3

Step-by-step explanation:

Answer:

why has the speaker come to the earth

Answer:

the two numbers are 3x and -x.

Step-by-step explanation:

product = -3x²

sum = 2x

hope this helps you.

The angle relationship and their reasons are:

The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:

∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are  equal based on the vertical angles theorem.

∠KFE and ∠FEJ are alternate interior angles, therefore, they are  equal based on the alternate interior angles theorem.

∠LFG and ∠FEJ are alternate exterior angles, therefore, they are  equal based on the alternate exterior angles theorem.

∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.

∠DEJ and ∠EFL are corresponding angles, therefore, they are  equal based on the corresponding angles theorem.

∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.

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Answer:

y= -x -3

Step-by-step explanation:

A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).

Let's find the slope of the line segment.

\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }slope=x1−x2y1−y2

Slope of line segment

= \frac{4 - ( - 8)}{5 - ( - 7)}=5−(−7)4−(−8)

= \frac{4 + 8}{5 + 7}=5+74+8

= \frac{12}{12}=1212

= 1

The product of the slopes of 2 perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

m(1)= -1

m= -1

y= -x +c

To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.

Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.

\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}midpoint=(2x1+x2,2y1+y2)

Midpoint of line segment

= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )=(25−7,24−8)

= ( \frac{ - 2}{2} , \frac{ - 4}{2} )=(2−2,2−4)

= (-1, -2)

y= -x +c

When x= -1, y= -2,

-2= -(-1) +c

-2= 1 +c

c= -2 -1

c= -3

Thus, the equation of the perpendicular bisector is y= -x -3.

Answer: 36!

Step-by-step explanation:

Answer:

B . 34

Step-by-step explanation:

simply subtract the lowest value from the greatest value, ignoring the others.

Answer:

3546 ft

Step-by-step explanation:

First find length of base to center of mountain.

(3150*sin 16 deg)/(sin 74 deg) = ~903 ft

Then dist of point from centre of mountain

903+725=1628 ft

Then cable length

(3150^2 + 1628^2)^0.5 = ~3546 ft

2. The number of adults who live in the house is 3 (1,200/400).

3.a. If an adult recycled the glass, paper, and card that have 42% of the rubbish, the adult will generate 232 kg (400 kg x (1 - 42%) of rubbish.

b. If the adult, in addition, had a composite for vegetable and decomposable material, he will generate 152 kg (400 kg x (1 - 62%).

Data and Calculations:

1 ton = 1,000 kg

Weight of rubbish produced by an adult per year = 400 kg

Total kg of rubbish produced by the family = 1,200 kg (1,000 x 1.2)

Percentage of Vegetable and decomposable material = 20%

Percentage of glass, paper, and card = 42% (33% + 9%)

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Answer:

B) 13/8

Step-by-step explanation:

First we need to understand what a terminating decimal is: It is a decimal that has a finite number of decimal values that are not zero, meaning that its decimal values end at some point

Let's go through our possible answers with trial and error:

A) 8/9

8/9 = 0.888888888888...9 (Incorrect)

B) 13/8

13/8 = 1.625 (Correct)

C) 4/3

4/3 = 1.3333333333...4 (Incorrect)

D) 6/11

6/11 = 0.545454545454...54 (Incorrect

13/8 is our answer because in decimal form it is a terminating decimal.

Answer:

Surface area = 6l^2

Volume = l^3

If total surface area increased by 2, then the length increased by [tex]\sqrt{2}[/tex]

Volume then is increased by ([tex]\sqrt{2}[/tex]l)^3 = 2[tex]\sqrt{2}[/tex]l^3

1 :2 [tex]\sqrt{2}[/tex]

Which is not an option in the question so this question clearly has a problem.

First of all It's supposed to be "then" not "than," so I'm not sure who teaches math without even knowing this basic grammar.

Second of all, if the answer is 8:1 the question should be "If each sides of a cube is doubled" not "the lateral surface area." Come to think of it what even is lateral surface area of a cube if all sides of the cube is supposed to be same.

Or, if the answer is 2:1 then, it should be If height lateral surface area of a cube is doubled by doubling the height and without changing the length and width"  But, then the the shape would no longer be a cube.

Who even wrote this garbage question what.

Answer:

8

Step-by-step explanation:

The diagonals of a parallelogram divide each other into two equal parts.

Answer:

here p=0.65 and n=100 hence standard error =(p*(1-.

Step-by-step explanation:

Answer:

Step-by-step explanation:

0 can't have a direction. It does not move. It has no speed component. Therefore 0 m/s south is not the answer.

45 m/s has no direction stated. It is just a speed, not a velocity.

45 m/s north is a velocity. It has both speed and direction.