Given the triangle, find the length of y. Give your answer in simpliest radical form.

Answer:

300

Step-by-step explanation:

20÷2=10

60÷2=30

30x10=300

Answer:

  45°

Step-by-step explanation:

The acute angles of a right triangle are complementary. The base angles of an isosceles triangle are congruent. If x is the measure of the base angles, this requires ...

  x = 90-x . . . . . the base angle is congruent to the other base angle

  2x = 90 . . . . . add x

  x = 90/2 = 45 . . . . divide by 2

The measure of a base angle of an isosceles right triangle is 45°.

__

It can be useful to remember this fact.

If the Sahas were reading a best-sellingnovel as a family. The person who read the greatest fraction and who read the same fraction of the book is: A. Maddie read the greatest; Mr. Saha and Mrs. Saha read the same.

Fraction of each are:

Mr. Saha - 2/6

Mrs. Saha - 1/3

Maddie - 3/4

George - 2/3

Now let find the person who read the greatest and same fraction

Mr. Saha - 2/6 = 0.33

Mrs. Saha - 1/3 = 0.33

Maddie - 3/4 = 0.75

George - 2/3 =0.66

So,

Mr. Saha - 2/6 = 0.33 ( Same fraction)

Mrs. Saha - 1/3 = 0.33 (Same fraction)

Maddie - 3/4 = 0.75  (Greatest fraction)

Therefore the correct option is A.

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The complete question is:

The Sahas were reading a best-selling novel as a family. They checked in with each other to see how much of the book each had read.

Fraction Read:

Mr. Saha - 2/6

Mrs. Saha - 1/3

Maddie - 3/4

George - 2/3

Who read the greatest fraction and who read the same fraction of the book.

answer choices

Maddie read the greatest; Mr. Saha and Mrs. Saha read the same.

Mr. Saha read the greatest; Maddie and George read the same.

Mrs. Saha read the greatest; Mr. Saha and Mrs. Saha read the same.

George read the greatest; Maddie and Mr. Saha read the same.

Answer:

D. 73.6 ft^2

Step-by-step explanation:

Using trigonometry to get our answer: (we can use SAS to find the area)

A = 0.5 * side a (10ft) * side b (16ft) * sin(67)

A = 80 ft * sin(67)

A = 73.64 ft

By graphing the system of equations, we can see that the solution is (4, -2)

Here we want to solve the system of equations:

y = (-3/2)*x + 4

y = (1/2)*x - 4

To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.

The graph can be seen on the image at the end.

We can see that the solution is (4, -2)

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Answer:

9

Step-by-step explanation:

The total amount of income Xander earns from selling y books algebraically is C = 25000 + xy + 0.08y.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenarios.

In this situation, Xander writes math textbooks that sell x dollars each, he received a bonus of $25,000 for signing a contract, and he receives 8% commission on each book sale.

c = total amount

y = number of books.

The total amount of income will be:

= 25000 + (x × y) + (8% × y)

= 25000 + xy + (0.08 × y)

C = 25000 + xy + 0.08y

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Answer:

1/6

Step-by-step explanation:

....................................

Answer: 16.7 percent.

Step-by-step explanation: So to get a 6 when rolling a six-sided die, probability = 1 ÷ 6 = 0.167, or 16.7 percent chance. So to get two 6s when rolling two dice, probability = 1/6 × 1/6 = 1/36 = 1 ÷ 36 = 0.0278, or 2.78 percent.

The actual distance between the houses is 32.9 miles

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Scaling is the increase or decrease in the size of a figure by a scale factor.

Given that:

1 inch equals 9.4 miles

Two houses are 3.5 inches apart on the map, therefore:

Actual distance = 3.5 inches * 9.4 miles per inch = 32.9 miles

The actual distance is 32.9 miles

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Answer:

165.065% increase

Step-by-step explanation:

Given:

2. (2, 4), slope 2

we will write the equation of the line that passes through the point (2, 4) and has slope = 2

We will write the equation of the line using the point-slope form which is:

where (m) is the slope and the point (h, k)

so,

m = 2

h = 2

k = 4

So, the equation will be:

so, the answer will be the equation of the line is:

Answer:

z=0

Step-by-step explanation:

Hope this helps and have a great day!

Intial position of the weight is at t = 0.

Looking at the graph, at t = 0, the initial position is at 40 cm.

Initial position is the starting of the sinusoidal curve shown.

It is at time 0, or the value of p(t) at t = 0.

This is at 40,

p(t) = 40

at

t = 0

Step-by-Step Explanation:

\(x + \frac{2}{5} = \frac{1}{3} \\ = > x = \frac{1}{3} - \frac{2}{5} \\ = > x = \frac{5 - 6}{15} \\ = > x = \frac{ - 1}{15} \)

Answer:

A) x = -1/15

According to the information, the Alton Company's total product costs amount to $156,500.

Explanation: To calculate the total product costs, we need to sum up the various cost components incurred by the company:

Adding all these costs together, we get:

$81,000 + $50,500 + $20,500 + $2,650 + $1,850 = $156,500

According to the above we can infer that the correct answer is $156,500.

Note: This question is incomplete. Here is the complete information:
Alton Company produces metal belts.

During the current month, the company incurred the following product costs: Raw materials $81,000; Direct labor $50,500; Electricity used in the Factory $20,500; Factory foreperson salary $2,650; and Maintenance of factory machinery $1,850. Alton Company's total product costs:

Note: This question is incomplete; here is the complete question:

Alton Company produces metal belts.

During the current month, the company incurred the following product costs: Raw materials $81,000; Direct labor $50,500; Electricity used in the Factory $20,500; Factory foreperson salary $2,650; and Maintenance of factory machinery $1,850. Alton Company's total product costs:

Multiple Choice

$23,150.

$131,500.

$25,000.

$156,500.

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Answer:

x = 1, x = -1

Step-by-step explanation:

Those bars mean absolute value, meaning that whatever's inside them is always positive.

We can now rewrite our equation as:

x + 1 + 2 = 4

Now solve:

x + 1 + 2 = 4

x + 3 = 4

x = 1

x can equal 1 or -1.

Hope this helps!

All the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

As given in the question,

Given inequality is given by :

x²< 4

Simplify the given inequality  x² < 4 to get all the real numbers x we have,

x² < 4

⇒ x² - 4 < 0

⇒ x² - 2² < 0

Apply a² - b² = ( a - b ) ( a + b ) we get,

⇒ ( x - 2 ) ( x + 2 ) < 0

⇒ x ∈ ( -2 , 2 ) as less than symbol represent open interval.

Therefore, all the real numbers x which satisfy the given inequality x²<4 , in  interval form is (-2, 2).

The complete question is :

Find all real numbers x such that x^2 < 4. Give your answer in interval notation.

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Answer:

50%

Step-by-step explanation:

We are given this set of data: Age of professors in years

47, 44, 48, 43, 35, 65, 56, 37, 73,51

We can firstly rearrange the years properly in ascending order.

Hence we have:

35, 37, 43, 44, 48, 51, 53 56, 65, 73

The number of the professor given = 10 professors

The number of professors younger 50 years = 5

Therefore, the percentage of these professors who are younger than 50

Is:

5/10 × 100 = 50%

Therefore, 50% of the professors are younger than 50

The annual growth rate is 4.73 %

The continuous growth rate is 4.62 %

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

Let us assume:

The initial amount of 1, so results are 2.

Let x be the  percent in decimal form

Growth rate per year:

\(1(1+x)^{15} = 2\)

Take ln on both the sides

\(ln((1+x)^{15}) = ln(2)\)

15*ln(1+x) =0 .693

ln(x+1) = 0.693/15

ln(x+1) = 0.04621

Take anti ln on both the sides

x+1 = 1.0473

x = 1.0473 - 1

x = .0473

x =4.73 % annual growth rate

Continuous growth rate:

\(1*e^{15x} = 2\)

\(ln(e^{15x}) = ln(2)\)

15x*ln(e) = ln(2)

ln(e) = 1

15x =0.693

x =0 .693/15

x = .0462

x = 4.62 %

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Answer:

roots are 5, -2

Step-by-step explanation:

set each factor equal to zero and solve:

x - 5 = 0

x = 5

x + 2 = 0

x = -2

Answer:

x = 5, -2

Step-by-step explanation:

(x - 5)(x + 2) = 0

Using the 0 product property:

Case 1

Case 2

The roots are \(\boxed{5, -2}\)

-Chetan K

A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.

A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.

Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.

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Answer:

0.036

Step-by-step explanation:

0.9 x 0.04 = 0.036

Answer:

0.04

Step-by-step explanation:

you just divide to get the answer :)

Answer:

2 times

Step-by-step explanation:

The probability of 1/3 means that the spinner will land on a 2, 1/3 of the time:

We can predict how many times it will land on a 2 by finding 1/3 of 6:

6/3

= 2

So, the spinner will land on a 2, two times

Number of times probability of landing on a 2 is 2, when you spin the spinner 6 times.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, in a game, the probability that a spinner will land on a 2 is 1/3.

If you spin the spinner 6 times, probability of landing on a 2 is

1/3 ×6

= 2

Therefore, number of times probability of landing on a 2 is 2.

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Answer:

16.8

Step-by-step explanation:

the one above would the y

The values of function being changed according to the recursive formulae  a) f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96, b)  f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576, c) f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

Let's find the values of f(1), f(2), f(3), f(4), and f(5) for each of the given recursive definitions:

(a) f(n+1) = -2f(n)

Using this recursive formula, we can calculate the values as follows:

f(1) = -2f(0) = -2(3) = -6

f(2) = -2f(1) = -2(-6) = 12

f(3) = -2f(2) = -2(12) = -24

f(4) = -2f(3) = -2(-24) = 48

f(5) = -2f(4) = -2(48) = -96

Therefore, f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96.

(b) f(n+1) = 3f(n) + 7

Using this recursive formula, we can calculate the values as follows:

f(1) = 3f(0) + 7 = 3(3) + 7 = 9 + 7 = 16

f(2) = 3f(1) + 7 = 3(16) + 7 = 48 + 7 = 55

f(3) = 3f(2) + 7 = 3(55) + 7 = 165 + 7 = 172

f(4) = 3f(3) + 7 = 3(172) + 7 = 516 + 7 = 523

f(5) = 3f(4) + 7 = 3(523) + 7 = 1569 + 7 = 1576

Therefore, f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576.

(c) f(n+1) = f(n)² – 2f(n) – 2

Using this recursive formula, we can calculate the values as follows:

f(1) = f(0)²  - 2f(0) - 2 = 3²  - 2(3) - 2 = 9 - 6 - 2 = 1

f(2) = f(1)²  - 2f(1) - 2 = 1²  - 2(1) - 2 = 1 - 2 - 2 = -3

f(3) = f(2)²  - 2f(2) - 2 = (-3)²  - 2(-3) - 2 = 9 + 6 - 2 = 13

f(4) = f(3)²  - 2f(3) - 2 = 13²  - 2(13) - 2 = 169 - 26 - 2 = 141

f(5) = f(4)²  - 2f(4) - 2 = 141²  - 2(141) - 2 = 19881 - 282 - 2 = 19597

Therefore, f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

Therefore, The values of function being changed according to thr recursive formulae a) f(1) = -6, f(2) = 12, f(3) = -24, f(4) = 48, and f(5) = -96, b)  f(1) = 16, f(2) = 55, f(3) = 172, f(4) = 523, and f(5) = 1576, c) f(1) = 1, f(2) = -3, f(3) = 13, f(4) = 141, and f(5) = 19597.

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Answer:

They have equal slopes.

Step-by-step explanation:

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching.

Answer:

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

We see x - 2 is the common factor in the given expression.

Simplify as:

Answer:

10x - 20

Step-by-step explanation:

distribute the 3 and the 7 into the parentheses, getting you to (3x - 6) + (7x - 14), from there you should be able to just combine the like terms getting you to 10x - 20.