∠1 and ∠2 form a linear pair. If m ∠1 is eight more than m ∠2 find the measures of both angles

Step-by-step explanation:

simple interest formula is I = p × r × t / 100

$32 = p × 8 × 3 / 100

$32 = 24p / 100

32 × 100 = 24p

3200 / 24 = $133.33

Answer:

slope = \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, - 9 ) and (x₂, y₂ ) = (12, 6 )

m = \(\frac{6-(-9)}{12-2}\) = \(\frac{6+9}{10}\) = \(\frac{15}{10}\) = \(\frac{3}{2}\)

The completed statement with regards to the area of the square and the rectangle are;

The estimated value of the length of the shaded square is 5·√5 inches. The estimated value of the area of the unshaded rectangle is 175 square inches.

The area of a square is the product of the side lengths which are congruent, therefore;

Area of a square = Side length, s × Side length, s = s²

The possible figure in the question includes;

A shaded square that is 125 square inches

An adjacent unshaded rectangle, that share a side with the square that has a side length of 7·√5 inches

Please find attached the possible drawing of the figure in the question, (not drawn to scale) obtained from a similar question posted online, created with MS Word.

Therefore;

The side length of the square = √(125) inches =  5·√5 inches

The estimated value of the side length of the square is; 5·√5 inches

The area of a rectangle = Length × Width

The length of the rectangle = 7·√5 inches

The width of the rectangle = 5·√5 inches

Therefore;

The area of the unshaded rectangle, therefore is; 5·√5 × 7·√5 = 175

The estimated area of the unshaded rectangle is 175 square inches

Learn more on the area of a rectangle here: https://brainly.com/question/26303775

#SPJ1

Answer: y=1

Step-by-step explanation:

1. Subtract 4y from both sides to get y + 4 = 5.

2. Then subtract 4 from both sides to get y = 1.

Therefore, you get your answer, y = 1. Hope this helps!

The characteristic of the researcher having direct control over at least one variable to both surveys and Observational .

The option that is not a characteristic of both surveys and observational studies is:

a. The researcher has direct control over at least one variable.

Surveys and observational studies have several characteristics in common, such as collecting data about a population and not proving cause and effect. However, the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies.

In a survey, the researcher collects data by asking questions to individuals or groups. They do not have direct control over the variables being studied but rather collect information based on participants' responses. The researcher's role is primarily in designing the survey, selecting the sample, and analyzing the data.

In an observational study, the researcher observes and records data without intervening or manipulating any variables. The researcher does not have control over the variables being observed; instead, they observe and document the existing conditions or behaviors.

the characteristic of the researcher having direct control over at least one variable is not applicable to both surveys and observational studies. Both methods involve data collection about a population and do not establish cause and effect relationships, but control over variables is not a shared characteristic.

To know more about Observational .

https://brainly.com/question/14354714

#SPJ11

The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

For more such questions on frequency, click on:

https://brainly.com/question/254161

#SPJ8

If we write a quadratic in vertex form:

\(y=a(x-h)^2+k\)

Then:

\(\bold{a}\)   \(\longrightarrow\)    is the coefficient of \(x^2\)

\(\bold{h}\)   \(\longrightarrow\)    is the axis of symmetry.

\(\bold{k}\)   \(\longrightarrow\)    is the max/min value of the function.

Also:

If \(a > 0\) then the parabola will be of the form \(\cup\) and will have a minimum value.

\(a < 0\) then the parabola will be of the form \(\cap\) and will have a minimum value.

For the given functions:

\(a < 0\)

\(f(x)=-(x-1)^2+5\)        this has a maximum value of \(\bold{5}\)

\(a > 0\)

\(f(x)=(x+2)^2-3\)           this has a minimum value of \(\bold{-3}\)

Answer:

Step-by-step explanation:

The expression 2x - 11x - 6 can be simplified as follows:

2x - 11x - 6 = -9x - 6

So, the equivalent expression is -9x - 6.

The answer is:

-9x - 6

Work/explanation:

To simplify this expression, we combine the like terms :

\(\huge\text{2x - 11x - 6} \\ \\ \\ \text{-9x - 6}\)

There's nothing that we can do for this expression. It's been simplified as much as possible.

Answer:

A) 50

Step-by-step explanation:

X = 5

15 * 5 + 75 = 150

150 / 3 = 50

y = 50

From the given sets we get A’∩ (B∪C’) = {2,8,9}.

Given the universal set U= {1,2,3,4,5,6,7,8,9}

A = {1,5,6,7}

B = {1,2,7}

C= {2,3,4,6,7}

A’ (A not) means to remove all the elements of set A from the universal set U

A∪B (union of A and B) means to write all the elements of both the sets but to not repeat the single element

A∩B (intersection of A and B) means to write only the common elements of both the sets

A’ = {2,3,4,8,9}

C’ = {1,5,8,9}

First we need to find out B∪C’ which means the union of B and C’

B∪C’ = {1,2,5,7,8,9}

Now we need to find A’ (B∪C’) = {2,8,9}

To know more about sets - https://brainly.com/question/4801204

#SPJ9

Answer:A

Step-by-step explanation:

Step-by-step explanation:

Given

-30 = - 0.4 k

30 = 0.4k

k = 30 / 0.4

k = 75

hope it helps :)

Answer:

Simplifying

-38 = -0.4k

Solving

-38 = -0.4k

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '0.4k' to each side of the equation.

-38 + 0.4k = -0.4k + 0.4k

Combine like terms: -0.4k + 0.4k = 0.0

-38 + 0.4k = 0.0

Add '38' to each side of the equation.

-38 + 38 + 0.4k = 0.0 + 38

Combine like terms: -38 + 38 = 0

0 + 0.4k = 0.0 + 38

0.4k = 0.0 + 38

Combine like terms: 0.0 + 38 = 38

0.4k = 38

Divide each side by '0.4'.

k = 95

Simplifying

k = 95

In the triangle , The value of x is, 3√7

The value of y is, 12

The value of z is, 4√7

Now, By definition of cosines of angle we get;

⇒ y/ (7 + 9) = 9 / y

Solve for y as;

⇒ y² = 144

⇒ y = 12

And, WE can formulate;

z / (9 + 7) = 7 / z

z / 16 = 7 / z

z² = 112

z = 4√7

And, By Pythagoras theorem we get;

⇒ 7² + x² = (4√7)²

⇒ 49 + x² = 112

⇒ x = 3√7

Thus, The value of x is, 3√7

The value of y is, 12

The value of z is, 4√7

Learn more about the Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ1

Answer:

Step-by-step explanation:

Given that:

the differential equations:

\(\dfrac{dx}{dt}= x+y = 1 \\ \\ \dfrac{dy}{dt}= 1-x^2+y^2\)

For x-nullcline;

\(\implies \dfrac{dx}{dt} =0 \\ \\ \implies x+y-1\)

From the image attached below, the sketch of the x-nullcline was carefully drawn and the regions were identified.

So, x-increases at the time when \(\dfrac{dx}{dt}>0\)

\(\implies x+y -1 >0\)

Thus, the solution move towards the right for  x+y>1

The balance in the account after the given period is \(\$6,872.74\)  

we know that

The compound interest formula is equal to  

\(\text{A}=\text{P}(1+\frac{\text{r}}{\text{n}})^{\text{nt}}\)

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

\(\text{t}= 8 \ \text{years}\)

\(\text{P}=\$4,000\)

\(\text{r}=0.07\)

\(\text{n}=1\)

substitute in the formula above

\(\text{A}=\$4,000(1+\frac{0.07}{1})^{1\times8}=\$6,872.74\)  

The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

For more such questions on square

https://brainly.com/question/27307830

#SPJ8

Answer:

4x - 3 - 2x + 5 = 6 - 3x + 2 + 5x

2x + 2 = 2x + 8

2 ≠ 8, so this equation has no solutions.

Answer:

No solution

Step-by-step explanation:

Given:

\(4x-3-2x+5=6-3x+2+5x\)

rearrange terms so like terms are together

\(4x-2x-3+5=6+2-3x+5x\)

combine like terms

\(2x+2=8+2x\)

subtract 2x to both sides

\(2\neq 8\)

2 doesn't equal 8, meaning that there are 0 solutions to this problem.

Hope this helps! :)

Answer:

7.85 in³

Step-by-step explanation:

π · r² · h

3.14  · 0.5² · 10

7.85 in³

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

for such more question on values

https://brainly.com/question/11546044

#SPJ8

Answer:

24.554

Your answer is correct

Answer:

Probability of owning one dog;

12/100 = 0.12

Probability of owning 2 dogs;

0.12 x 0.12 = 0.0144, but we make it a percent so:-

1.44%, there is a 1.44% probability that they both own a dog.

Answer:

19, 20, 21, and 22

Step-by-step explanation:

19+20+21+22 = 82

Answer:The Fahrenheit (symbol: °F) is a unit of temperature that was widely used prior to metrication. It is currently defined by two fixed points: the temperature at which water freezes, 32°F, and the boiling point of water, 212°F, both at sea level and standard atmospheric pressure. The interval between the freezing and boiling point is divided into 180 equal parts.

Step-by-step explanation: HOPE THIS HELPS :)

You'll have three copies of the red "-x" rectangles to represent -3x

Next, you'll need five copies of the blue squares with the label "1". This represents 5 since 1*5 = 5.

Lastly, you'll need one copy of the purple rectangle that has "y" on it.

All of this forms the expression -3x+5+y

All of these figures will be above the dashed line to be in the positive region.

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

Learn more on a Ferris wheel here;

https://brainly.com/question/30524034

#SPJ1