Find the missing length.

Answer:

c. x - 2/3

Step-by-step explanation:

The given equation is f(x) = [tex]3x^4 - 5x^3 - 71 x^2 + 157x + 60[/tex]

To test if the given equations are factors of the polynomial, check if the remainder is equal to zero if substituted into the equation.

For x - 3, x = 3

Substituting x = 3 into the given polynomial:

[tex]f(3) = 3(3)^4 - 5(3)^3 - 71 (3)^2 + 157(3) + 60\\f(3) = 0[/tex]

x - 3 is a factor

For x - 4, x = 4

Substituting x = 4 into the given polynomial:

[tex]f(4) = 3(4)^4 - 5(4)^3 - 71 (4)^2 + 157(4) + 60\\f(4) = 0[/tex]

x - 4 is a factor

For x - 2/3, x = 2/3

Substituting x = 2/3 into the given polynomial:

[tex]f(2/3) = 3(2/3)^4 - 5(2/3)^3 - 71 (2/3)^2 + 157(2/3) + 60\\f(2/3) = 132.22[/tex]

x - 2/3 is  not a factor

For x + 1/3, x = -1/3

Substituting x = -1/3 into the given polynomial:

[tex]f(-1/3) = 3(-1/3)^4 - 5(-1/3)^3 - 71 (-1/3)^2 + 157(-1/3) + 60\\f(-1/3) = 0[/tex]

x + 1/3 is  a factor

Answer:

Step-by-step explanation:

Distribute 7 to the first number

7 * -3/4 = -21/4

-21/4 = 5  -1/4

Distribute 7 to the second number

7 * -3

= -21

Put the numbers together

They separated the parenthesis.

So it is still 7 * -3/4

and

7*-3.

Hope this helps,

Kavitha

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

9,020,406.27

Step-by-step explanation:

The proofing is as follows:

Given that,

|LO|=|MN| and |LM|=|ON|

It means that  Opposite sides of a parallelogram are equa

Now, LN⊥OM

So,

∠LPO = ∠NPO = 90° ( by definition of perpendicular lines)

LPO ≅ ∠NPO (by definition of congruent angles)

|LP|=|PN| (diagonals of a parallelogram bisect each other)

based on this LMNO is a rhombus

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Answer:

All right angles are congruent

Reflexive property

Opposite sides of a parallelogram are congruent

Step-by-step explanation:

That what i got on my assignment

Answer:

it could be angle DGF or CGA (they are both supplementary to angle CGD)

Step-by-step explanation:

Answer:

40m³

Step-by-step explanation:

[tex]\sqrt[3]{5}[/tex] = 1.709975947

1.709975947 × 2 = 3.419951893

3.419951893³ = 40

Answer:

volume of the box multiply scale factor

=5 × 2

=10m

Answer:

The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle

Use rule ; SOHCAHTOA .Where sin x = opp/hyp

cos x = adj/hyp

tan x= opp/adj

Substitute the given values for the three sides

into any of the above rules

[tex]example = Hyp = 2\\opp = 1\\sin- x = 1/2\\x = sin^{-1} 1/2\\x = 30[/tex]

Step-by-step explanation:

I Hope It Helps :)

Answer:

-200, 0 and -5

Step-by-step explanation:

Area can never be zero or negative.

Answer:

2:8 is the ratio to an equal ratio

Hey there! :)

Answer:

x = -6.

Step-by-step explanation:

Given:

[tex]\sqrt[3]{5x-4} = \sqrt[3]{7x + 8}[/tex]

Cube both sides:

5x - 4 = 7x + 8

Subtract 5x from both sides:

-4 = 2x + 8

Subtract 8 from both sides:

-12 = 2x

x = -6.

Answer:

I guess that we want to create 4 digit numbers that are divisible by 5, only using the odd numbers in the image.

We know that a number is divisible by 5 only if the last digit (the units digit) is a zero or a five, in the image we only have a five, so our 4-digit numbers need to end with a five, so we have a digit fixed in five and the other 3 digits can be other numbers.

We have two different approaches to this:

First, if each odd number can be used only once, we already used the five, so we can use the other 4 numbers.

Then, for the first digit, we have 4 options.

for the second digit, we have 3 options (because we already used one)

for the third digit, we have 2 options (because we already used 2)

then the number of combinations is equal to the product of the number of options for each selection:

C = 4*3*2 = 24 combinations.

The second approach is If the numbers in the image can be repeated (for example, 5555 or 3435 are allowed)

we still have our last digit fixed in 5, and for the first digit we have 5 options, for the second we also have 5 options, and for the third, we also have 5 options, then, with the same reasoning as above, we have:

C = 5*5*5 = 25*5 = 125 combinations.

Answer:

4. -1/2 and 2

5. N and R

Step-by-step explanation:

Well if you want me too do 5 I’ll do 4 too.

So for #4 it’s actually pretty simple we just have to seperate y that’s it.

So first we have to get y by itself by subtracting 3x to the other side so the equation looks like this now [tex]6y=-3x+12[/tex].

Now we have to take away the 6 and to do that we divide it to all the numbers and variables. Which gets us [tex]y=-1/2x+2[/tex].

So m and b are -1/2 and 2.

So we have to graph y = -1/2x + 2 so look at the image below.

So looking at the image we can see it passes through the points N and R.

Answer:

The line passes through points N and R.

Step-by-step explanation:

I graphed the equation on the graph below.

Answer:

P(XX) = 69/190

Step-by-step explanation:

Given:

20 balls, 10R, 3B, 7W.

Two taken without replacement.

Find probability of two identical colours.

P(XX)

Solution:

We use the multiplication rule for the probability of each of the 2 draws

P(RR) = 10/20*9/19 = 90/380

P(BB) = 3/20*2/19 = 6/380

P(WW) = 7/20*6/19 = 42/380

Probability of drawing two identical coloured balls

P(XX) = (90+6+42)/380 = 138/380 = 69/190

Answer:

Hey there!

Let x be the price he paid for.

2x-8=34

2x=42

x=21

He bought the stock for 21 dollars.

Hope this helps :)

Answer:

The price per share  when he bought it was 21

Step-by-step explanation:

Let x = price he paid for the stock

34 = 2x-8

Add 8 to each side

34+8 = 2x-8 +8

42 = 2x

Divide by 2

42/2 = 2x/2

21 = x

The price per share  when he bought it was 21

Answer:

143.6F

Step-by-step explanation:

Entonces la ecuación establecida es;

C = [tex]\frac{5F-160}{9}[/tex]

Entonces, para resolver el Celsius, debes hacer de F el tema que hago a continuación.

[tex]C = \frac{5F - 160}{9}\\C * 9 =( \frac{5F-160}{9}) *9\\9C - 5F = 5F -160 - 5F\\9C-5F =-160 \\-5F = -160 - 9C\\\frac{-5F}{-5} = \frac{-160-9C}{-5}\\[/tex]

∴[tex]F = \frac{-160-9C}{-5}[/tex]

Ahora ingresamos los valores y resolvemos para F

F = [tex]\frac{-160 - 9(62)}{-5}[/tex]

  =[tex]\frac{-160-558}{-5}[/tex]

  = [tex]\frac{-718}{-5}[/tex]

  = 143.6

∴ 62C = 143.6F

Answer:

a. 800 litros

b. 500 litros

Step-by-step explanation:

Aquí, se nos dice que 1/4 del total se usa para lavar la ropa.

Lo que queda sería 1-1 / 4 = 3/4 Fuera de esto, 5/6 se usa para cocinar.

La fracción utilizada para cocinar es 5/6 * 3/4 ​​= 15/24 = 5/8

Y todavía nos quedan 100 litros.

La cantidad utilizada ya sería 1/4 + 5/8 = (2 + 5) / 8 = 7/8

Entonces la fracción no utilizada = 1-7 / 8 = 1/8

Ahora, es este 1/8 que corresponde a 100 litros.

Digamos que el volumen total es x litros inicialmente, Eso significa 1/8 * x = 100 x / 8 = 100 x = 800 litros

La fracción utilizada para cocinar es 5/8 del total, por lo que el valor sería 5/8 * 800 = 500 litros

Answer:

              [tex]\underline{x\in\left\{-6\,,\ 1\right\}}[/tex]

Step-by-step explanation:

[tex]x^2+5x-6=0\\\\a=1\,,\ \ b=5\,,\ \ c=-6\\\\x_1=\dfrac{-5-\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5-\sqrt{25+24}}2=\dfrac{-5-\sqrt{49}}2=\dfrac{-5-7}2=-6\\\\x_2=\dfrac{-5+\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5+7}2=1[/tex]

Answer:

Step-by-step explanation: Answer is B-6,1

Answer:

A ; -4

Step-by-step explanation:

3a = 12b then a = 4b (dividing by 3)

we put 4b in the equation instead of a:

(-4b / b) = -4

.. ..

Answer:

A. -4

Step-by-step explanation:

3a/b = 12

Let b = 2

3a/2 = 12

3a = 24

a = 8

( - a/b)

( - 8/2)

( - 4)

Answer:

3:2

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles

The cost of each white tile was £2

The cost of each blue tile was £4

Therefore the total cost of 48 white tiles is

= 48×2

= £96

The total cost of 16 blue tiles is

= 16×4

= £64

The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor

The greatest common factor of £96 and £64 is 32

96/32 = 3

64/32= 2

Ratio= 3:2

Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2

Answer:

A

Step-by-step explanation:

First, let's do the difference of two squares:

[tex](1-cos^4(\theta))=(1-cos^2(\theta))(1+cos^2(\theta))[/tex]

Note that [tex]sin^2(\theta)=1-cos^2(\theta)[/tex] (Pythagorean Identity)

Thus, we can substitute:

[tex]sin^2(\theta)(1+cos^2(\theta))[/tex]

Now, and I'm serious, you just have to use your creativity. After a while, you will find that:

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

So:

[tex]1+sin^2(\theta)+cos^2(\theta)=1+1[/tex]

Thus, we have [tex]1+cos^2(\theta)=2-sin^2(\theta)[/tex]

Now, we can substitute:

[tex]sin^2(\theta)(2-sin^2(\theta))=2sin^2(\theta)-sin^4(\theta)[/tex]

Answer:

The perimeter of the actual playground is 22000 units

Step-by-step explanation:

By measurement, the width of the scale drawing = 16 units

The breadth of the scale drawing = 6 units

Therefore, given that the scale is 1:500, we have that the actual dimensions of the playground are;

Actual width of the playground = 500×16 = 8,000 units

Actual breadth of the playground = 500×6 = 3,000 units

Therefore;

The perimeter of the actual playground = 2 × 8000 + 2 ×3000 =  22000 units.

Answer: the value of the integral is in the range:

0.006  ≤  int ≤  0.008

Step-by-step explanation:

First, we have the function

5*tan(3x), and the range in this case is: pi/12 ≤ x ≤ pi/9

Then, the first step is find the maximum and minimum of f(x) in this range.

We know that between 0 and pi/2, tan(x) is a growing function, then

then the limits are

5*tan(3*pi/9) = 5*tan(pi/3) = M=  0.091

5*tan(3*pi/12) = 5*tan(pi/4) =m = 0.069

Then the value of the integral is between:

0.069*(3.14/9 - 3.14/12) ≤  int ≤  0.091*(3.14/9 - 3.14/12)

0.006  ≤  int ≤  0.008

Answer:

6

Step-by-step explanation:

From the blue graph of f(x) we can see that the function value is -6 when x = 6.  Similarly, g(5) = -5.

Then:  4*f(6) - 6*g(5) becomes:

           4*(-6) - 6*(-5), or

              -24 +  30  = 6

The value of ⋅f(6)−6⋅g(5)= 6

An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

Given:

From the blue graph we can see that

f(x)= -6 when x = 6.

Similarly, g(5) = -5.

thus,

4*f(6) - 6*g(5)

=3 4*(-6) - 6*(-5)

=-24 +  30

= 6

Learn more about this concept here:

https://brainly.com/question/20379727

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Answer:

  $52.46

Step-by-step explanation:

We are told that ...

  8.75% · purchase = $4.59

Dividing by the percentage, we have ...

  purchase = $4.59/0.0875 = $52.46

Yasmin's pre-tax total was $52.46.

Answer:

the correct answer is b aka 52.46

Answer:

∠BAD = 100°

∠ADC = 105°

∠DCB = 50°

∠ABC = 105°

Step-by-step explanation:

∠BAD is given.

∠ADC is supplementary to the 75°, so it is 180-75 = 105°

∠DCB is 50° just like its opposite angle

The sum of all angles in a quadrilateral must be 360, so ∠ABC = 360-100-105-50 = 105.

Answer:

-3

Step-by-step explanation:

Given the function f(x) = -(-x)

we want to evaluate f(-3)

What we do simply here is substitute the value of -3 for x in the equation

That would be ;

f(-3) = -(-(-3)) = -(3) = -3

Answer:

125°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 8 (octagon), thus

sum = 180° × 6 = 1080°

let x represent one of the equal angles, then

3x + 705 = 1080 ( subtract 705 from both sides )

3x = 375 ( divide both sides by 3 )

x = 125

Thus the size of one equal angle = 125°

Answer:

b) y = -x2 + 6x + 2

Step-by-step explanation:

Answer:

The answer is explained below

Step-by-step explanation:

The location of point A = (-5, -1) and point B = (4, 1).

To find the coordinate of the point that divides a line segment PQ with point P at [tex](x_1,y_1)[/tex] and point Q at [tex](x_2,y_2)[/tex] in the proportion a:b, we use the formula for the x and y coordinates:

[tex]x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1[/tex]

P is One-fourth the length of the line segment from A to B, Therefore AB is divided in the ratio 1:4. The location of point A = (-5, -1) and point B = (4, 1).Therefore:

[tex]x-coordinate:\\\frac{1}{1+3}(4-(-5))+(-5)=\frac{1}{4}(9)-5=-\frac{11}{4} \\\\While \ for\ y-coordinate:\\\frac{1}{1+3}(1-(-1))+(-1)=\frac{1}{4}(2)-1=\frac{-1}{2}[/tex]

Therefore the coordinate of P is (-11/4, -1/2)

Answer:

the coordinate of P is (-11/4, -1/2)

x= -11/4

y= -1/2

c on edu

Step-by-step explanation:

edu 2021

Step-by-step explanation:

The formula the amusement parc use is  100y-39000=55(x-800)

The slope intercept form of a function is wriiten generally as:

y = mx+c

Let's rewrite our equation in the precedent form

The slope intercept form of this equation is:

y= 0.55x-50

Answer:

y=55x+38992

Explanation:

You have to turn the equation into the form y=mx+b

Step 1: Get y by itself(divide both sides by 100)

100y-39,000=55(x-800)

100/100y-39,000=55(x-800)/100

y-39,000=55(x-800)/100

Step 2: Get y by itself(+ 39000 to both sides)

y-39,000=55(x-800)/100

 +39,000=55x-800/100+39,000

y=55x-800/100=39,000

Step 3: Simplify

y=55x+38992