Identity all obtuse angles in the drawing below

To achieve his goal of paying off $430,000 in 10 years, Rob Herndon needs to make $34,186.97 at 5% compounded annually.

A future value refers to a value on a future date based on an assumed growth rate of interest over time.

The future value can be determined using the FV formula or table.

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $430,000

Results:

PMT = $34,186.97

Sum of all periodic payments = $341,869.70

Total Interest= $88,130.30

Thus, for Rob Herndon to achieve his goal of paying off $430,000 in 10 years, he needs to make $34,186.97 at 5% compounded annually.

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Answer:

  23.20°

Step-by-step explanation:

All three sides of this right triangle are given, so the acute angle of interest can be found using any of the inverse trig functions.

The tangent of the angle is the ratio of opposite and adjacent sides:

  Tan = Opposite/Adjacent

Here, that means ...

  tan(α) = 3/7

To find the value of α, we need to use the inverse tangent function, also called the arctangent function.

  α = arctan(3/7) ≈ 23.19859°

  α≈ 23.20°

[tex]\sf{\qquad\qquad\huge\underline{{\sf Answer}}}[/tex]

An equation is called any equality that contains one or more unknown quantities, which are called unknowns, and that are only generally verified for certain values of the unknowns.

Thus, for example: 4x - 2 = 3x + 1~4x−2=3x+1 is an equation because it is an equality in which there is one unknown, xx .

⇝Equation resolution:

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]

We transpose the term 3x to the first member.

3x to the first member.We will have:

[tex] \qquad \sf \dashrightarrow4x - 2 - 3x = 14x−2−3x=1[/tex]

Next we transpose the term -2 to the second member.

We will have:

[tex] \qquad \sf \dashrightarrow4x - 3x = 1 + 24x−3x=1+2[/tex]

[tex] \qquad \sf \dashrightarrow \: x = 3x = 3[/tex]

Let's check that x = 3x=3 satisfies the given equation:

[tex] \qquad \sf \dashrightarrow4x - 2 = 3x + 14x−2=3x+1[/tex]

[tex] \qquad \sf \dashrightarrow4(3) - 2 = 3(3) + 14(3)−2=3(3)+1[/tex]

[tex] \qquad \sf \dashrightarrow12 - 2 =9+ 112−2=9+1[/tex]

[tex] \qquad \sf \dashrightarrow10 = 10 \: \: \: \: \:10=10[/tex]

That is, 10 = 10, as we wanted to verify.

I hope I've helped : )

Answer:

The value of x is 3

When x = 3 then both the LHS and RHS of the equation equal to the same number; 10.

Step-by-step explanation:

[tex]4x - 2 = 3x + 1 \\ 4x - 3x = 1 + 2 \\ x = 3 \\ [/tex]

When we substitute the value for x in the expression, we see that the expression represents the same number. i.e

[tex]4x - 2 = 3x + 1 \\ 4(3) - 2 = 3(3) + 1 \\ 12 - 2 = 9 + 1 \\10 = 10 \\ [/tex]

The length of the flagpole is x - 5  yards

The complete question is in the image

The area of the flagpole is given as:

Area = x^2 - 10x + 25

Expand the expression

Area = x^2 - 5x -5x + 25

Factorize the expression

Area = (x - 5)(x - 5)

Express as squares

Area =(x - 5)^2

The area of a square is

Area = Length^2

So, we have:

Length = x - 5

Hence, the length of the flagpole is x - 5  yards

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Answer:

x = 45°

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent (equal).

From inspection of the given diagram, the straight line with points C and D and the straight line with points F and G intersect at point E.

Therefore, angles ∠FEC and ∠DEG are vertically opposite, and so they are equal.

From inspection of the diagram:

Therefore:

⇒ ∠FEC =∠DEG

⇒  x = 45°

Answer:

Step-by-step explanation:

Solution

There are 28 students

There are 7 equal groups

There must by 28/7 = 4

Answer

Each group will have 4 students in it..

Answer:

Step-by-step explanation:

5 + 1 = 6 units

90 : 6 = 15 (one unit)

15 * 5 = 75°

The natural antilogarithm of the given logarithm can be evaluated as; 1.014.

The natural logarithm of the number given in the task content can be evaluated by multiplying by 2.303 as follows;

Natural logarithm value is; 2.303 × 0.0058887

= 0.01356.

On this note, it follows that the natural antilogarithm of the result can be evaluated as;

= 1.014.

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1) Identify the statement you want to prove is true

2) Assume temporarily that the statement is false; assume the opposite is true

3) Obtain statements that logically follow from your assumption.

4) Reason logically until you reach a contradiction of a known fact.

5) Point out that your assumption must be false, and the statement must then be true.

The probability that the student will answer 5 correct questions is; P(5) = 0.053

The formula for binomial probability is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

Where;

p = probability of success.

n = number of trials, or the sample size.

x = the number of successes in the probability we are trying to calculate.

Now, we want to find P(5). We are given;

n = 12

x = 5

p = 1/5 = 0.2

Thus;

P(5) = 12C5 * (0.2)⁵ * (1 - 0.2)⁽¹² ⁻ ⁵⁾

P(5) = 0.053

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Answer:

overfishing

Step-by-step explanation:

I'm not completely sure but i think it's overfishing because it has more to relate to the food chain which would be most likely to lead to a shortage

Answer: plug in the coordinates for x and y

Step-by-step explanation:

take a look at my work if you still need some help

Answer: Then the graph of the function f(x) will change shifting vertically down (because the negative sign in 4) by 4 tons.

Answer:

$4.5

Step-by-step explanation:

We apply sales tax to the total cost, which in this case is $40 + $50 = $90.

Thus, we have 5% * $90 = $4.5

It even works individually if you apply the tax to both orders separately and add them together:

(50 * 5%) + (40 * 5%) = 4.5

2.5 + 2 = 4.5

7 evaluates the expression a2 + b.

option a.7 is the correct choice which evaluates the given expression.

Given values are a = 2 and b =3

the given expression is = a2 + b

To evaluate an expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

Substitute these value in the given expression.

=2 × 2 ₊ 3

=7

Every time we replace the variables with its values  we get the answer as 7. The other options present does not satisfy the equation.

For ex: 25 , we don't get this number when we substitute the given values in the expression. 10 is also not what we get when we solve the expression. Likewise other options are also invalid.

Hence we get the answer as 7.

Your question is incomplete. Please find the missing content here.

Which of the following choices will evaluate the expression a2 + b when a = 2 and b = 3?

a. 7

b. 10

c. 25

d. None of these choices are correct

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The factors of the trinomial to the given quadratic expression are (x+1) and (x-4)

Given the quadratic equation below

f(x) = x^2 - 3x - 4

Factorize

f(x) = x^2 - 4x + x - 4 = 0
f(x) = x(x - 4) + 1(x - 4) = 0
(x+1)(x-4) = 0

Hence the factors of the trinomial to the given quadratic expression are (x+1) and (x-4)

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Answer:

4.  Horizontal shrink by a factor of ¹/₅

5.  Left 5, Up 5

6.  Right 5, Down 5

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 4

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(5x)^3[/tex]

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by 5.

Therefore, the transformation is:

[tex]y=f(5x) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{5}[/tex]

As a > 1, the transformation visually is a compression in the x-direction, so we can also say:  Horizontal shrink by a factor of ¹/₅

Question 5

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x+5)^3+5[/tex]

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been added to the x-value of the parent function.

[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]

Step 2

5 has then been added to function.

[tex]f(x+5)+5 \implies f(x+5) \: \textsf{translated}\:5\:\textsf{units up}[/tex]

Transformation:  Left 5, Up 5

Question 6

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x-5)^3-5[/tex]

Comparing the parent function with the given function, we can see that there are a series of transformations:

Step 1

5 has been subtracted from the x-value of the parent function.

[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]

Step 2

5 has then been subtracted from function.

[tex]f(x-5)-5 \implies f(x-5) \: \textsf{translated}\:5\:\textsf{units down}[/tex]

Transformation:  Right 5, Down 5

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Answer:

4) Horizontal shrink by a factor of 1/5

5) Left 5, Up 5

6) Right 5, Down 5

Explanation:

Main parent function: f(x) = x^3

4.) f(x) = (5x)^3

Comparing it with f(ax) which gives horizontal compression when a > 1 or horizontal stretch when 0 < |a| < 1 by a factor of 1/a

The function has been compressed horizontally by a factor of 1/5.

5.) f(x) = (x+5)^3 + 5

Comparing with f(x + c) + d, gives function moved c units left, d units up.

The function has moved 5 units left and 5 units up.

6.) f(x) = (x-5)^3 - 5

Comparing with f(x - c) - d, gives function moved c units right, d units down.

The function has moved 5 units right, 5 units down.

Answer:

x=1,2,3,4 y=3,7,11,15

firstly find d such that d=7-3=4

afunction f(x)= 3+4(x-1)

and x= 1,2,3,4 y=3,9,27,81

y=x²

The probability that a randomly selected riverside high school student is in twelfth grade is 0.4

The complete question is in the attached image

From the image, we have:

The probability is then calculated as:

P = 200/500

Divide

P = 0.4

Hence, the probability that a randomly selected riverside high school student is in twelfth grade is 0.4

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Answer:

the answer is C

Step-by-step explanation:

Answer:

d

Step-by-step expladnation:

The polynomial which is equivalent to fog(x) is 2/x + 1.

A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).

Here,

given functions are;

f(x) = x + 1   ;     g(x) =  2/x

Now, we need to compose fog(x) from the given function;

fog(x)  =   f ( g(x) )

          =  f( 2/x)

          = 2/x + 1

Thus, the polynomial which is equivalent to fog(x) is 2/x + 1.

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The value of 'x' is 10°

We have that supplementary angles sum up to 180

M∠A = (6x +4)° and m∠B = (10x + 16)°.

Then,

6x + 4 + 10x + 16 = 180

Collect like terms

16x + 20 = 180

16x = 180 - 20

16x = 160

x = 160/ 16

x = 10°

Thus, the value of 'x' is 10°

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Answer:

6.5 %

Step-by-step explanation:

Full commission would then be   2 * 3152.50 = 6305

Full commission percentage of sale is then:

6305 / 97000   * 100 % = 6.5 %

The equivalent form of the  compound inequality  are −2x − 8 < -44 and −2x − 8 ≥ −4

Inequality are expression not separated by an equal sign. Given the compound inequality

−44 > −2x − 8 ≥ −48?

Add 8 to all the sides

−44 + 8> −2x − 8+8 ≥ −48 + 8

−36 > −2x  ≥ −40

This can be also be written as

−44 > −2x − 8 and −2x − 8 ≥ −48

Changing the sides will change the sign to have

−2x − 8 < -44 and −2x − 8 ≥ −48

Hence the equivalent form of the  compound inequality  are −2x − 8 < -44 and −2x − 8 ≥ −4

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Answer:

4$

Step-by-step explanation:
The ratio between the $5.80 spent for 58 text messages is $0.10. This means that each text message sent is $0.10. So you just multiply $0.10 and 40 text messages to find that it costs $4 to send 40 messages.

Answer:

100744

Step-by-step explanation:

14392

       7

______

        4    (carry the 1)

14392

       7

______

     44    (carry the 6)

14392

       7

______

   744   ( carry the 2)

14329

        7

______

 0744       (carry the 3)

14329

        7

______

 100744      (final answer)

The values of x in x²-x-2=0​ are x = 2 or -1

The equation is given as:

x²-x-2=0​

Add 2 to both sides

x² - x = 2

Take the coefficient of x

k = -1

Divide by 2

k/2 = -1/2

Square both sides

(k/2)² = 1/4

Add 1/4 to both sides of x² - x = 2

x² - x + 1/4= 2 + 1/4

Evaluate

x² - x + 1/4= 9/4

Express as perfect square

(x - 1/2)² = 9/4

Take the square roots

x - 1/2 = ±3/2

This gives

x = 1/2 ±3/2

Evaluate

x = 2 or -1

Hence, the values of x in x²-x-2=0​ are x = 2 or -1

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Answer:What is the magnitude of 3i?

3i invested c.

Step-by-step explanation: $182m in Magnitude Software in 2019 to accelerate its global growth ambitions through new product development and investments in sales & marketing, and to build a more integrated enterprise software business.

Answer: $201.81

Step-by-step explanation:

The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.

Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]