Use the long division method to find the result when x^3+9x² +21x +9 is divided
by x+3

Answer:

  (a)  85 - (35 x 2) - 6

Step-by-step explanation:

The miles Mr. Richardson has left to drive will be the difference between the distance to his goal and the miles he has alread driven. The relation between distance, speed, and time can be used to find the miles he drove before lunch.

__

  distance = speed × time

  miles before lunch = (35 mi/h) × (2 h) = (35 × 2) mi

The total miles driven before stopping for gas will be ...

  miles before stopping for gas = (miles before lunch) + (6 more miles)

  = 35 ×2 +6 . . . miles

Then the remaining miles are ...

  remaining = trip miles - miles driven

  = 85 -(35 ×2 +6)

  = 85 - (35 ×2) -6 . . . . . miles left to drive

Answer:

The formula for semicircle area is [tex]\frac{1}{2} \pi r^2[/tex]

Very similar to the formula for finding area of a circle, but since a semicircle is half of a circle, the formula will be revolving around halves.

Answer:

[tex]8 \frac{1}{25} [/tex]

Step-by-step explanation:

[tex]4 \frac{3}{5} + 3 \frac{11}{25} \\ (4 + 3) + ( \frac{3}{5} + \frac{11}{25} ) \\ 7 + \frac{26}{25 } \\ 7 + 1 \times \frac{1}{25} \\ 8 \frac{1}{25} [/tex]

[tex]4 \frac{3}{5} + 3 \frac{11}{25} [/tex]

the simplest form.

[tex] \frac{23}{5} + \frac{86}{25} [/tex]

[tex] = \frac{(23 \times 25) + (86 \times 5)}{5 \times 25} [/tex]

[tex] = \frac{575 + 430}{125} [/tex]

[tex] = \frac{1005}{125} [/tex]

[tex] = 8 \frac{1}{25} [/tex]

Answer:

The mean would be 4

Step-by-step explanation:

Steps to find the mean.

1. Least to greatest.

2,3,4,4,5,6

2. Add all the numbers.

2+3+4+5+5,6

=24

3. Divided by how many numbers you have.

24÷6

=4

Hope this helps! Mark me brainlest if you want, have a great day!! :))

Answer: It would be 4

Step-by-step explanation: Hope that helps!

Answer:

SA = 54π cm^2

A

Step-by-step explanation:

[tex]{\pi}rs + {\pi} {r}^{2} [/tex]

radius = 3cm

slant height = 15 cm

follow the formula

Answer:

Each son received from their mother $287.50

Step-by-step explanation:

3(x - 275) = x - 250

2x = 825 - 250

x = 287.50

$287.50 - $275 = $12.50

Check the answer:

After spending the older son has $12.50  

$287.50 - $250 = $37.50

After spending the younger son has $37.50

$37.50 ÷ $12.50 = 3 times

Answer:

Step-by-step explanation:
I need more explanation to answer

The given statement is false statment because the line drawn has an inclination of 45°.

Given that,
On a grid, moving from 0,0 to 4,4 makes a line at a 90-degree angle. whether the statement is true or false is to be justified.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

Here,
According to the question,
Moving from 0,0 to 4,4
Calculating the slope,
m = 4 - 0 / 4 - 0
m = 1
m = tanФ = 1
tanФ = 1
tanФ = tan 45°
Ф = 45°

Thus, the given statement is a false statment because the line drawn has an inclination of 45°.

learn more about lines here:

brainly.com/question/2696693

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Answer:

C) 24

Step-by-step explanation:

Alternate interior angles are equal

so angle 1 equals angle 6

3x+10=x+58

subtract 10 from both sides

3x=x+48

then subtract x from both sides

2x=48

dived each side by two

x=24

Answer:

is it (3,3)

Step-by-step explanation:

(x,y)=(-2+5,1+2)

(x,y)=(3,3)

Answer:

x = 2/9 or 0.2

Step-by-step explanation:

6 x 2 - 54x = 0

(6x2) = 12

12 - 54x = 0

Rearange the terms

-54x + 12 = 0

subtract 12 from both sides

-54x = -12

Divide both sides by the same factor

-54x/54 = -12/-54

then simplify

x=2/9 or 0.2

5,870,000,000,000 miles.

The distance light travels in 100 years.

The distance of the light travels in 100 years is:

5,870,000,000,000 × 100 miles.

= 587,000,000,000,000 miles

= 587 × 10^12 miles.

answer= option d

[tex]1 \: year = 5870000000000 \: miles[/tex]

The distance which light can travel in 100 years.

to find the distance which light can travel in 100 years, multiply the distance which light can travel in 1 year (5,870,000,000,000 miles) by 100.

[tex] = 5870000000000 \times 100[/tex]

[tex] = 587000000000000 \: miles[/tex]

[tex] = 587 \times {10}^{12} [/tex]

Hence, the correct answer is option D

[tex]\sqrt{196} + \sqrt{441}\\\\=\sqrt{14^2} + \sqrt{21^2}\\\\=14+21\\\\=35[/tex]

The combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

[tex]S=\dfrac{a(1-r^n)}{1-r}[/tex]

Here, [tex]a_1[/tex] is the first term of the sequence, n is the number of terms, and r is the common ratio.

The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it.

The second doll is half of the first doll. Thus, the height of the second doll is,

[tex]a_2=\dfrac{1}{2}\\a_2=0.5\rm\;m[/tex]

Similarly, height of third doll,

[tex]a_3=\dfrac{0.5}{2}\\a_3=0.25\rm\;m[/tex]

Here, we see a pattern or sequence in the height of doll,

1,0.5,0.25......

For this series, the value of first term [tex]a_1[/tex] is 1, the number of dolls n is 8 and common ratio r is 0.5. Put the value in the above formula,

[tex]S=\dfrac{1(1-0.5^8)}{1-0.5}\\S=1.992\\S\approx 2\rm\; meters[/tex]

Thus, the combined height of the dolls when the tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it is 2 meters.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

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Answer:

4 units left

Step-by-step explanation:

if u look at point C and count the amount of lines it takes to get to its next spot, it us 4 units left

u can tell which shape is the original because it does not have little 1's next to its letters

Answer: I write more than one choice . The book is on the table , desk , bed , chair or shelf.

Step-by-step explanation: hope it helps

Answer:

j=12

Step-by-step explanation:

Answer:

11-1 equals 10

Step-by-step explanation:

Answer:

C  and D

Step-by-step explanation:

Use Pythagorean theorem to test

a^2 + b^2 = c^2    ?      a   and b  are the shorter two sides   c = longest side

Doing this for each data set shows   C   and D   ARE rt triangles

Answer:

[tex]0.55[/tex]

Step-by-step explanation:

[tex]\displaystyle \sin C=\frac{opposite}{hypotenuse}=\frac{11}{20}=0.55[/tex]

Answer:

Step-by-step explanation:

You must solve the slope-intercept form with the graph of the linear function g passing through the points.

Use the slope-intercept form.

[tex]\underline{\text{SLOPE-INTERCEPT FORM:}}[/tex]

[tex]\Longrightarrow: \sf{y=mx+b}[/tex]

Use the slope formula.

[tex]\underline{\text{SLOPE:}}[/tex]

[tex]\Longrightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

(-7,-4) and (7,6)

[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}}[/tex]

Solve.

[tex]\sf{\dfrac{6-\left(-4\right)}{7-\left(-7\right)}=\sf{\dfrac{10}{14}=\dfrac{10\div2}{14\div2}=\dfrac{5}{7} }}[/tex]

I hope this helps. Let me know if you have any questions.

Answer:

[tex]2-3x=6x-7\\x=1[/tex]

(There are a lot more combinations tho. Read more!)

Step-by-step explanation:

The first thing to notice is that the answer has to be a whole number and that there are only 5 spaces.

Another thing to notice is that one of the x's is negative.

So the easiest thing is to set [tex]x=1[/tex].

The we can work backwards. There are multiple solutions that we can use. But any combination that adds to the same number will work.

Such as:

[tex]2-3x=6x-7\\x=1[/tex]

or

[tex]2-5x=3x-6\\x=1[/tex]

And so on.

Answer:

Quadrant 4

Step-by-step explanation:

The x value is positive so it is either in 1 or 4

The y value is negative so it is either 3 or 4

To meet both conditions, it must be 4

Answer: C

Step-by-step explanation:

The area of the larger square is a^2 and the area of the smaller square is b^2, so the area is a^2 + b^2, not (a+b)^2.

In this case, the equation is in vertex form. To graph the parabola, we need to determine the y-intercept, x-intercept(s), and the vertex.

Vertex form: y = a(x + h)² - k

Assume "y" as 0.

[tex]\implies 0 = 3(x + 2)^{2} - 1[/tex]

[tex]\implies 1 = 3(x + 2)^{2}[/tex]

Take square root both sides and simplify:

[tex]\implies\sqrt{1} = \sqrt{3(x + 2)^{2}}[/tex]

[tex]\implies1 = \sqrt{3 \times (x + 2) \times (x + 2)}[/tex]

[tex]\implies1 = (x + 2) \times \sqrt{3[/tex]

Divide √3 both sides:

[tex]\implies \±\huge\text{(}\dfrac{1 }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]    

[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} }{\sqrt{3}} \huge\text{)} = (x + 2)[/tex]    

Multiply √3 to the numerator and the denominator:

[tex]\implies \±\huge\text{(}\dfrac{\sqrt{1} \times \sqrt{3} }{\sqrt{3\times \sqrt{3}}} \huge\text{)} = (x + 2)[/tex]

[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} = (x + 2)[/tex]

[tex]\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} - 2 =x[/tex]

[tex]\implies x = \underline{-2.6...} \ \text{and} \ \underline{-1.4...} \ \ \ \ (\text{Nearest tenth})[/tex]

Assume "x" as 0.

y-intercept = 11 ⇒ (0, 11)

Since the first cooeficient is positive (+3), the direction of the parabola will be upwards.

Axis of symmetry line: x-coordinate of vertex

Axis of symmetry line: x = -2

Plot the following on the graph:

Refer to graph attached.

Answer:

Vertex form of a quadratic equation:

[tex]y=a(x-h)^2+k\quad \textsf{where }(h,k)\:\textsf{is the vertex}[/tex]

Given equation:  [tex]y=3(x+2)^2-1[/tex]

Therefore, the vertex is (-2, -1)

The x-intercepts are when [tex]y=0[/tex]:

[tex]\implies 3(x+2)^2-1=0[/tex]

[tex]\implies 3(x+2)^2=1[/tex]

[tex]\implies (x+2)^2=\dfrac13[/tex]

[tex]\implies x+2=\pm\sqrt{\dfrac13}[/tex]

[tex]\implies x+2=\pm\dfrac{\sqrt{3}}{3}[/tex]

[tex]\implies x=-2\pm\dfrac{\sqrt{3}}{3}[/tex]

[tex]\implies x=\dfrac{-6\pm\sqrt{3}}{3}[/tex]

Therefore, the x-intercepts are at -2.6 and -1.4 (nearest tenth)

The y-intercept is when [tex]x=0[/tex]:

[tex]\implies 3(0+2)^2-1=11[/tex]

So the y-intercept is at (0, 11)

The axis of symmetry is the x-value of the vertex.  Therefore, the parabola is symmetrical about x = -2

**You don't need to plot the axis of symmetry - I have added it so that it is easier to draw the curve**

Answer:

6000cm

Step-by-step explanation:

multiply all figures given

Answer:

92 Degrees.

Step-by-step explanation:

As this is a Quadliateral inscribed in a circle, you can use a trick that is always true for these types of problems. Opposite angles will always be the same, since 92Degrees is A and is opposite to C, this means C is also 92Degrees, these type of shapes are also known as cyclic quadrilaterals

Answer:

5. 2612.5 ≈ $2613

6. 848.4 ≈ $849