Find the quotient.
-245 - 35
a. -7
b. - 5
C. 5
d 7

Answer:

x² + y² = z²

Step-by-step explanation:

(a)

Using the right triangle altitude theorem,

x/z = p/x

x² = pz

(b)

y/z = q/y

y² = qz

(c)

x² + y² = pz + qz

x² + y² = z(p + q)

z = p + q

x² + y² = z × z

x² + y² = z²

Answer: 63.5

Step-by-step explanation:

90 - 26.5 = 63.5

Her home is 3km far from the bicycle repair shop;

Her avg speed = 2*6*20/(6+20) = 60/13 km/h

d = r*t = (60/13)*(39/60)

d = 3 km;

What is Avg Speed?

In normal use and in kinematics, the speed (normally known as v) of an object is the significance of the change of its position over time or the value of the change of its role consistent with unit of time; it is for this reason a scalar amount.

The common speed of an item in an c programming language of time is the distance travelled by using the item divided by the length of the c program languageperiod

the instant pace is the restriction of the common speed because the length of the time c program languageperiod methods 0. velocity isn't similar to pace.

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By using the given pair of values we can see that the constant of proportionality is 8, and the proportional relation is:

y = 8*x

A proportional relation is a linear relation with an y-intercept of 0, so these are written as:

y = a*x

Where a is the constant of proportionality.

By knowing a pair of values x and y, we can find the value of a. In this case we can see that when x = 3, y = 24, replacing that in the general equation we get:

24 = a*3

24/3 = a = 8

Then the constant of proportionality is 8, and the proportional relation is:

y = 8*x

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The equation of the line in function notation is y.=-2x + 5

The standard equation of a line is expressed as y = mx + b

where

m is the slope

b is the y-intercept

Given the equation

2y=x-4

y = 1/2x - 2

The slope perpendicular will be -2

Substitute into y-y₁ = m(x-x₁)

y-(-7) = -2(x-6)

y+7 = -2x +12

y = -2x  + 5

Hence the equation of the line in function notation is y.=-2x + 5

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Answer:

-61

by both methods

Step-by-step explanation:

Let's first see what the terms direct substitution and synthetic substitution mean.

Direct Substitution

In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)

Synthetic Substitution

In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]

Solving using direct substitution

The given polynomial is

[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]

Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]

Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]

Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)

This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex]  in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 2
Carry down the leading coefficient as is to below the division symbol

[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 4

Add down the column

[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]

Step 5

Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12

2 | 3     0      -1        6     -1       1
  |        -6      12  
  -------------------------------------------------
     3    -6      

Step 6
Add down the column
-1 + 12 = 11

2 | 3     0      -1        6     -1       1
  |        -6      12    
  -------------------------------------------------
     3    -6      11

Repeat this process for the other two coefficients

The final result is

2 | 3     0      -1        6     -1       1

  |        -6      12    -22   32   -62
  -------------------------------------------------
     3    -6     11       -16   31   -61

The last carry-down value s the remainder and the value of f(-2) = - 61

The given statement is true that for a given non-zero vector v in r³ there is a unique unit vector parallel to it.

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The height of the building = 1026.328ft

Given the angle of elevation = 11°

The angle of elevation is the angle formed between the horizontal distance to the base of the building and the line of sight to the top of the building.

We know that tan x = opposite side/adjacent side.

Here the opposite side gives the height of the building and the adjacent side is the distance to the base of the building on the ground.

Distance to the base of the building on the ground = 1 mile = 5280 ft.

So tan 11° = h/5280

⇒ h= tan 11° x 5280 = 0.194 x 5280 = 1026.328 ft

So the height of the building = 1026.328 ft

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The answer is most probably to round the the numbers to nearest 10 digits and multiply

697x82 =  56,154

700 x 80 = 56000

A rounded number is less precise but roughly equal to the original number in value.

To the closest hundred, 341 is equivalent to 300. This is due to the fact that 341 is more similar in value to 300 than to 400. Because $1.89 is closer to $2.00 than to $1.00, when rounded off to the nearest dollar, it becomes $2.00.

The standard rounding rule is as follows:

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Round to nearest 10 digits and multiply

697x82=________x________=________

The secant line connects two points on a graph's curve:

Point P: (15, 1257)

(a) The secant lines' slopes PQ.

The points are as follows:

The slope (m) is calculated using:

Therefore, the secant line connects two points on a graph's curve:

The slope (m) is calculated as follows:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So far, we have:

The slope of the secant line for Q = (5,3410) is:

[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]

The slope of the secant line for Q = (10, 2210) is:

[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]

The slope of the secant line for Q = (20, 550) is:

[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]

The slope of the secant line for Q = (25, 145) is:

[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]

The slope of the secant line for Q = (30, 0) is:

[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]

(b) The average slope of the tangent.

The secant lines that are closest to tangent P are:

This is because point P (15, 1275) is located between the two previous points.

The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:

[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]

The average slope (m) is as follows:

[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]

Hence, the average slope is -166.

Therefore, the secant line connects two points on a graph's curve:

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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).

Part a: The size of the game in standard form is 240000 kilobytes

Part b: The game was 5 times larger than the patch file

Part A:

Size of the game downloaded by Ryan on his computer = 2.4 * 10^5

Size of the patch file for the game = 48000 kilobytes

Therefore, converting the size of the game into the standard form:

Size of the game = 2.4 * 10^5

= 2.4 * 100000

= 240000 kilobytes

Therefore, the size of the game is 240000 kilobytes in standard form

Part B:

Size of the game = 240000 kilobytes

Size of the patch file = 48000 kilobytes

Computing the size of the game with respect to the patch file we get:

=240000/48000

= 5

Hence, the game was 5 times larger than the patch file

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the combinations that work are "A" and "B" as they both equal to 80

Answer:

a) A = 1, C = 0, and D > 0 --> Graph B

b) A = 1, C = 0, and D < 0 --> Graph C

c) A > 1, C > 0, and D > 0 --> Graph D

d) 0 < A < 1, C < 0, and D < 0 --> Graph A

The least and the greatest amounts are $98 and $112

The food budget is modeled by 0.5|x - 110| = 6

So, we have:

0.5|x - 110| = 6

Divide both sides by 0.5

|x - 110| = 12

Remove the absolute bracket

x - 110 = 12 and x - 110 = -12

Add 110 to both sides

x = 112 and x = 98

Hence, the least and the greatest amounts are $98 and $112

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to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]

true!!!

school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room

Answer: 9x^2+6x

Step-by-step explanation:

(4x^2 - 2x) - (-5x^2 - 8x)=

4x^2 - 2x +5x^2 + 8x=

4x^2+5x^2 - 2x + 8x=9x^2+6x

Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

Given the data in the question;

Since Q is a point between P and R.

PR = PQ + QR

Plug in the given values and solve for x.

5x - 3 = ( 2x + 8 ) + ( x + 11 )

5x - 3 = 2x + 8 + x + 11

5x - 3 = 3x + 19

5x - 3x = 19 + 3

2x = 22

x = 22/2

x = 11

Numerical value of segment PQ when x = 11 will be;

PQ = 2x + 8 = 2(11) + 8 = 30

Numerical value of segment QR when x = 11 will be;

QR = x + 11 = (11) + 11 = 22

Numerical value of segment PR when x = 11 will be;

PR = 5x - 3 = 5(11) - 3 = 52

Given that Q is a point between P and R, the numerical values of x, segment PQ, QR and PR are 11, 30, 22 and 52 respectively.

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Answer:

b=2/3

Step-by-step explanation:

Let's solve the equation step by step

( b ) = 2/3

Remove bracket

b=2/3

Answer:

The question states four less than twice its width so we first find twice the width. The width is 6 and twice that is 12. Note that it says four less than, so four less than 12 is 8. so the length of the triangle is 8.

Step-by-step explanation:

Hope it helps! =D

The expression is simplified to 7(-x + 9)

Algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.

They are also made up of mathematical or arithmetic operations

Given the expression;

9 – 3(4x – 18) + 6x

expand the bracket

9 - 12x + 54 + 6x

collect like terms, we have;

-12x + 5x + 54 + 9

Add or subtract like terms

-7x + 63

Factor out 7

7(-x + 9)

Thus, the expression is simplified to 7(-x + 9)

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Answer:

12x-94

---------------------

Hope this helps!

Have a great day and God bless! :)

Answer:

8 milkshakes

Step-by-step explanation:

16 cups in a gallon. 2 cups per milkshake.

16/2=8

Answer:
Study a Times Tables map each day if you can soon you will get the hang of it

The location of point D on the number line is -5.15625

The given parameters are:

A = 5

B = -10

AC : CB = 1 : 3

This means that

C = AC/(AC + AB) * (A - B)

This gives

C = 1/4 * (5 + 10)

Evaluate

C = 3.75

Also, we have:

BD : DC = 3 : 5

So, we have:

D = BD/(BD + DC) * (B - C)

This gives

D = 3/8 * (-10 - 3.75)

Evaluate

D = -5.15625

Hence, the location of point D on the number line is -5.15625

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I don't see why my answer got deleted from last time as nothing was wrong with it, but your answer is: x = 5/6.

--------------------------------------------------------

Hope this helps!

Have a great day and God bless! :)

The factors of the expression is 3x²(x+5)(x+5) .

Factors of a number are defined as the numbers which divide the given number completely.

For an algebraic expression the factors of the expression are smaller polynomials which divide the given expression completely.

Factors of algebraic expression can be  calculated by the following methods:

The given polynomial is of the form:

3x⁴ + 30x³ + 75x²

Taking 3x² common from all the terms we get:

3x² (x² + 10x + 25)

Now we use middle- term factorization method to factor (x² + 10x + 25)

3x² (x² + 5x + 5x + 25)

or, ( 3x² ){x ( x + 5 ) + 5 ( x + 5 )}

or, 3x² (x + 5) (x + 5)

or, 3x²  (x + 5)²

Hence the factors of the expressions are: 3x²  (x + 5)²

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Factor completely:  3x⁴ + 30x³ + 75x²

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Answer: 24/54

Step-by-step explanation:

[tex]\displaystyle\\\frac{4}{9}=\\\\ \frac{4}{9}*1=\\\\ \frac{4}{9}*\frac{6}{6} =\\\\\frac{4*6}{9*6} =\\\\\frac{24}{54}[/tex]