Find all of the missing angles of sides of the triangle below. Note that side lengths are in centimeters. Show and/or explain your work thoroughly and round answers to the nearest hundredth if needed.

Answer: D. The quadratic function has two distinct real zeros.

There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.

This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.

Answer:

x = 9

Step-by-step explanation:

first remove the brackets

2x - 5 = 48 - 4x + 1

then take numbers to the opposite sides

2x + 4x = 48 + 5 + 1

I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4

now solve

2x + 4x= 6x

48+5+1= 54

6x = 54

now solve for x

divide both sides by 6x

x = 9

Answer:

Step-by-step explanation:

Given that Top Hat Soda has 300,000 millilitres of cola to bottle and,

a bottle is 500 millilitres in capacity.

To find the amount of bottles that will fill the Top Hat Soda,

we have to divide Top Hat Soda by the 500 millilitres bottle

we have:

Number of bottles needed to fill Top Hat Soda=  300,000/500 = 600 bottles.

Hence 600 bottles will fill the Top Hat Soda

Answer:

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] of 600 is 150

hope this helps

plz mark as brainliest!!!!!!

Answer:

91.67inch^3

Step-by-step explanation:

The volume of a cone can be calculated using below formula

V= 1/3 π.r^2h

Where h= height of the cone

r= radius of the cone

V= volume of the cone

Given :

height= 11inches

radius= 5inches

π= 3.14

Then substitute into the formula we have

V= 1/3 × 3.14× 5^2 ×11

V= 91.67inch^3

Therefore volume of the cone is 91.67inch^3

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?

Answer:

the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Step-by-step explanation:

Given that :

the current population of insect A to be 1.3 million

the current population of insect B to be 2.1 million.

As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:

[tex]\mathtt{y = pe^{-rt}}[/tex]

where;

P represents the population of each species of insect in millions

t represents the elapsed time in years

r is the rate of decrease

So, we can have:

[tex]\mathtt{p_1 = 1.3 }[/tex] in million   and  [tex]\mathtt{p_2 = 2.1}[/tex] in million

Also for rate of decrease;

[tex]\mathtt{r_1 = 0.038}[/tex]     and [tex]\mathtt{r_2 = 0.046}[/tex]

Therefore;

the exponential decay for Population of insect A can now be:

[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]

the exponential decay for Population of insect B can now be:

[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]

Hence, the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Answer:

A!

Step-by-step explanation:

Plato

Answer:

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x [tex]{}[/tex]       F(x)

-4[tex]{}[/tex]       30

-3[tex]{}[/tex]       0

-2[tex]{}[/tex]       6

-1[tex]{}[/tex]        0

0 [tex]{}[/tex]      -18

1[tex]{}[/tex]         0

2[tex]{}[/tex]       150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.

Answer:

C

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

75%   of what number is 150

75          150

----- =  ---------

100       x

75*2 = 150

So multiply the left by 2/2

75*2          150

----- =  ---------

100*2       x

150

------

200

Answer:

The last question

Step-by-step explanation:

I took the test

Answer:

[tex]\boxed{\sf Option \ 1}[/tex]

Step-by-step explanation:

The profit is revenue (R ) - costs (C ).

Subtract the expression of costs (C ) from revenue (R ).

[tex]10x-0.01x^2-(2x+100)[/tex]

Distribute negative sign.

[tex]10x-0.01x^2-2x-100[/tex]

Combine like terms.

[tex]8x-0.01x^2-100[/tex]

The first option has a positive 100, which is wrong.

The rest options are right, when we expand brackets the result is same.

Answer:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b) x = 24

(c) y = 17; z = 51

Step-by-step explanation:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b)

15/45 = 8/x

1/3 = 8/x

x = 3 * 8

x = 24

(c)

a^2 + b^2 = c^2

x^2 + 45^2 = z^2

24^2 + 45^2 = z^2

576 + 2025 = z^2

z^2 = 2601

z = 51

15/45 = y/z

1/3 = y/51

3y = 51

y = 17

if [tex] x\times e=x[/tex] for all x, then e is the Multiplicative Identity.

is this enough for you to get the answer?

Answer:

FALSE.

Step-by-step explanation:

1 is the multiplicative identity of the set of rationals.

Answer:

c as in neither.

Step-by-step explanation:

the question does not give enough info because there are not two variables to be dependant on

Answer:

68

Step-by-step explanation:

Hello, the number is 'ab' meaning that we can write it as 10a +b

For instance 42 = 10*4 + 2

So, a = b - 2

and 10a + b + 10b + a = 154

11(a+b)=154

a+b = 154/11 = 14

We replace a by b - 2

b+b-2 = 14

2b = 14 + 2 = 16

b = 8 and then a = 6

the original number is 68.

Thanks

Answer:

No

Step-by-step explanation:

Linear equations must have no squares, roots, cubes, or any powers. If the graph has an asymptote or any restrictions, it is not a linear function.

A linear function will only appear in either point-slope form or slope-intercept form. These forms will not have square roots or powers in them.

-x + 3y² = 18

We know here that this is not a linear function. But we can try to write it in slope-intercept form:

3y² = x + 18

y² = x/3 + 6

y = √(x/3 + 6)

We can see from here that our graph is a square root function and has a restricted domain (no negative numbers).

Alternatively, we can graph the equation to see if it is a constant line (linear equation) or not. When we do so, we see that it is definitely not a linear function:

Answer:

(x1,y1) = (2x - x2, 2y - y2)

Step-by-step explanation:

Given:

Midpoint = (x , y)

End point = (x2, y2)

Find:

(x1, y1)

Computation:

Mid-point formula

x = (x1 + x2) / 2 , y = (y1 + y2) / 2

So,

2x = x1 + x2 , 2y = y1 + y2

x1 = 2x - x2 , y1 = 2y - y2

So,

(x1,y1) = (2x - x2, 2y - y2)

Answer:

(4x2 +5)⋅(4x2 −5)

Answer:

3

Step-by-step explanation:

6(x+4)=42

x=3

check:

6*(3+4)=42

Answer:

299.99 miles

Step-by-step explanation:

Since the plane traveled due west,

The total angle is 49.17 + 90

Represent that with θ

θ = 49.17 + 90

θ = 139.17.

Represent the sides as

A = 170

B = 150

C = unknown

Since, θ is opposite side C, side C can be calculated using cosine formula as;

C² = A² + B² - 2ABCosθ

Substitute values for A, B and θ

C² = 150² + 170² - 2 * 150 * 170 * Cos 139.17

C² = 22500 + 28900 - 51000 * Cos 139.17

C² = 51400 - 51000 (−0.7567)

C² = 51400 + 38,591.7

C² = 89,991.7

Take Square Root of both sides

C = 299.9861663477167

C = 299.99 miles (Approximated)

Hence, the distance between the plane and the airport is 299.99 miles

Answer:

x = 60

Step-by-step explanation:

Given

[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )

[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )

([tex]\sqrt{x+4}[/tex] )² = 8² , that is

x + 4 = 64 ( subtract 4 from both sides )

x = 60

Answer:

893.42

Step-by-step explanation:

1kg=2.205pounds

so 20mg is for 2.205pounds

therefore for 197pounds will be 1784.84mg

but the dose is once every 12hrs meaning twice a day so divide 1784.84/2 to get the pounds

Answer:

  451. No, the angles are wrong.

Step-by-step explanation:

450. AB = 15, BC = 10, and CD= 7. Find the length DA.

  This cannot be done without additional information about the sort of figure that ABCD is. If these are points on a line segment, we need to know their order. If these are points on a quadrilateral, we need to know its description in more detail.

If these are points ordered ABCD on a line, then AD = 15+10+7 = 32.

__

451. See the attached figure. BPQD is not a parallelogram: BCQ is not a straight line. (The internal angles of a pentagon are 108°, but would need to be 120° for BCQ to be a straight line, making BP parallel to DQ.) Instead, BPQD is an isosceles trapezoid.

Step-by-step explanation:

the answer to the question is C. 64.

Answer:$60,000

Step-by-step explanation:

If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because

60,000 - 55,000 = 5,000

Answer:

Step-by-step explanation:

Let the number of files he had be x

He gave 3/5 of the files

That's

3/5x

After that he still had 14 files left which means when we subtract 14 from the original files we should get 3/5 of the original files

So we subtract 14 from the original number of files

That's

x - 14

We equate the two statements

that's

[tex] \frac{3}{5} x = x - 14[/tex]

Multiply through by 5

[tex]5 \times \frac{3}{5} x = 5x - 70[/tex]

We have

3x = 5x - 70

3x - 5x = 70

-2x = - 70

Divide both sides by -2

We have the final answer as

Therefore he had 35 files at first

Hope this helps you

Answer:

35 files

Step-by-step explanation:

gave=3/5

left=2/5 = 14f

had= 5/5

2/5=14

5/5

5×14÷2 = 35

Answer:

60 miles per hour

Step-by-step explanation:

Total distance= 180 miles

Total time =3 hours

Average rate of change= ?

Distance= Rate × time

Make Time the subject of the formula

Time= Distance / Rate

Make average rate of change the subject of the formula

Average rate of change = Distance / time

= 180 miles / 3 hours

= 60 miles per hour

Answer:

B. 4x2 + 9x – 28

Step-by-step explanation:

Multiply out the factors and see what polynomial you end up with.

(4x – 7)(x + 4) = 4x^2 + 16x - 7x - 28 = 4x^2 + 9x - 28

The polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

To determine which polynomial has factors of 4x – 7 and x + 4, we can use the fact that if a polynomial has a factors.

So, if a polynomial has factors of 4x – 7 and x + 4, then it can be written as:

(4x – 7)(x + 4)

Multiplying these factors together using the distributive property, we get:

4x²+ 16x - 7x - 28

Simplifying, we get:

4x² + 9x - 28

Hence, the polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.

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Step-by-step explanation:

Hey, there!!

According to the question,

There is given circumference = 6pi in.

or, 2.pi.r = 6pi.in

or, r = 6 pi.in/ 2

Therefore, the radius (r)= 3in.

now,

area = pi.r^2

a= pi× (3in)^2

Therefore, the area is 9.pi.in^2.

Hope it helps....

Answer:

A ≈ 2.86

Step-by-step explanation:

Using the formulas

A = πr²

C = 2πr

Solving for A

A = C²/ 4π = 6²/ 4·π ≈ 2.86479

Answer:

G. $70

Step-by-step explanation:

$420 for 7 hours

$270 for 4 hours

Each of the above already includes the fixed fee.

Now we subtract the bottom line from the top line:

$420 - $270 = $150

$7 hours - 4 hours = 3 hours

$150/3 hours = $50/hour

For 4 hours, the hourly fee is $50/hour * 4 hours = $200.

Since the total charge for 4 hours is $270, then fixed fee is

$270 - $200 = $70

Answer: $70

The fixed fee that the mechanic charges is $70. Therefore, option G is the correct answer.

Given that, a mechanic charges a fixed fee plus an hourly rate for each hour he works. He charges $420 for 7 hours and $270 for 4 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the mechanic charges x dollars per an hour.

The difference in the charges = $420 - $270 = $150

Difference in the hours = 7 hours - 4 hours = 3 hours

Now, x=150/3 = 50

So, $50 per hour is the mechanic charges for service.

For 4 hours, the hourly fee is 50 × 4 = $200.

Since the total charge for 4 hours is $270, then fixed fee is

$270 - $200 = $70

The fixed fee that the mechanic charges is $70. Therefore, option G is the correct answer.

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