Determine whether each statement is always, sometimes, or never true. (Lesson 1-5 )
Two angles that form a linear pair are supplementary.

Interest is Rs.96  and Total amount payback is Rs.3096.

Principal (P) = Rs.3000

Rate of  interest (R) = 1.6%

Number of years (N) = 2 yrs

Simple interest = PNR/100

= (3000*1.6*2)/100

=(9600/100

=96Rs

Total Amount (A) = P+I

=3000+96

=3096Rs

The principal, or initial balance of your account, is where interest is calculated. This could be the initial sum of a loan or an investment. The simplest way to compute interest is as a percentage of the principal .Only relatively short-term loans frequently include one-time basic interest charges. Interest is frequently paid on a daily, monthly, quarterly, or annual basis for loans with longer terms. In that scenario, interest would be consistently earned.

Hence, the interest for the above principle is 96Rs and the total amount to be payback is 3096Rs.

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Answer:

9.81....

Step-by-step explanation:

x = 432/44

x = 9.81...

By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

Given,

The algebraic expression = 0.5x-x

Combine the like terms

0.5x-x=(0.5-1)x

= -0.5x

Simplified form is -0.5x

Hence, By combining the like terms, the simplified form of the expression 0.5x-x is -0.5x

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The relationship between the ∠1 and ∠5 is that both are corresponding angles

Given,

The angles = ∠1 and ∠5

Here,

∠1 and ∠5 are lies on the same side of the two lines and on the same side of the transversal

So, ∠1 and ∠5 are corresponding angles

Hence, The relationship between the ∠1 and ∠5 is that both are corresponding angles

The complete question is:

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠5

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Answer: 816

Step-by-step explanation:

h(3) = 1248 - 160(3) + 16(3)

h(3)= 1248 - 480 + 48

h(3)= 816

Answer:

25

Step-by-step explanation:

180 - 25 = 155

180 - 155 = 25

Power of a number 3⁶⁰ is the simplest form of math equation.

What is the power of a number?

What are power and exponent?

3^2*5*2*3 = 3⁶⁰

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Answer:

a. [tex]y=38x[/tex].

Step-by-step explanation:

Let y represent distance in miles and x represent gallons of gas.    

a. First of all, we will find mileage of Ann's car by dividing total distance traveled by total fuel consumed.

Since Ann's can travels 38 miles per gallon, so distance covered by using x gallons on gas would be [tex]38x[/tex] .

Therefore, our required equation would be [tex]y=38x[/tex].

The circumference of the children's ball to the nearest centimeter is 52 centimeters.

If a regulation volleyball has a circumference of about 66 centimeters, solve for its radius using the formula for the circumference of a circle given by:

C = 2πr

66 centimeters = 2πr

r = 33/π centimeters

Then, solve for the surface area of this regulation volleyball using the formula given by:

A = 4πr^2

A = 4π(33/π centimeters)^2

A = 4356/π square centimeters

If the ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6 : 1, then

surface area of regulation volleyball : surface area of a children's ball = 1.6 : 1

surface area of a children's ball = 4356/π square centimeters/1.6

surface area of a children's ball = 2722.5/π square centimeters

If  the children's ball has a surface area of 2722.5/π square centimeters, solve for its radius using the formula for the surface area given by:

A = 4πr^2

2722.5/π square centimeters = 4πr^2

r = 26.0887907/π centimeters

Solving for the circumference:

C = 2πr

C = 2π(26.0887907/π centimeters)

C = 52.17758139 centimeters

Rounding off to the nearest centimeter.

C = 52 centimeters

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Step-by-step explanation:

420x1800=756000

so 756k items in 30 minutes

In tape diagram, The number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

What is a tape diagram in math?

How a tape diagram appears?

represents the number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

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The density of the material is  0.4 kg/cubic cm.

Given that:-

Height of the cylinder = 54.5 mm

Diameter of the cylinder = 53.0 mm

Weight of the cylinder = 1 kg

We have to find the density of the cylinder.

We know that,

Density  = mass/volume

Here, mass = 1 kg

We know that,

Volume of a cylinder = [tex]\frac{1}{3} \pi r^2 h[/tex]

Where,

r is the radius of the cylinder, and

h is the height of the cylinder

Here, h = 54.5 mm, and

r = 53/2 = 26.5 mm

Hence,

Volume of cylinder = (1/3)*(22/7)*(26.5)(26.5)*54.5 ≈ 2566.088 ≈ 2566 cubic mm. = 2566/(10*10*10) cubic cm = 2.566 cubic cm

Density of cylinder = 1kg/2.566 cubic cm  ≈ 0.3897  ≈ 0.4 kg/cubic cm.

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The solution of the differential equation as given in the task content is; ln(5p +a)/5 + C = t

It follows from the task content that the solution of the differential equation is required.

Given;

dp/dt=5p +a

To find; solution to the differential equation;

By variable separation; the resulting equation is;

dp/(5p +a) = dt

By integrating both sides of the equation; we have;

ln(5p +a)/5 + C = t

Ultimately, although both sides of the equation integrated yield a constant of integration as the integral is indefinite, the two constants have been combined into constant, C as in the equation above.

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Calculating the likelihood of experiments happening is one of the branches of mathematics named as probability. The probability that none of the 2 vials have hairline cracks is 0.0565.

The study of probabilities, which exists defined by the ratio of favorable occurrences to probable cases, exists comprehended as probability.

The probability that there won't be any hairline cracks = 13/53

If you choose two vials at random from the delivery

Probability (avoiding hairline cracks) = 13 - 1/53 - 1

Probability (avoiding hairline cracks) = 12/52

To find the chance that neither of the two vials has a hairline crack is

(13/53) × (12/52) = 0.2452 × 0.2307

= 0.0565

The probability that none of the 2 vials have hairline cracks is 0.0565

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An equiangular triangle is also an example of an acute triangle is a True statement.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An equiangular triangle is a triangle whose all angles are the same and since all angles are the same so by geometrical constraint all sides must be the same so it will also be an equilateral triangle.

In an equilateral triangle, all interior angles are 60°, and since an acute angle triangle is a triangle in which all angles must be less than 90°.

So an equiangular triangle will be an acute triangle.

Hence "An equiangular triangle is also an example of an acute triangle is a True statement".

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|x-5| + 7 = 13 is equal to x= -11 and x = 1.

[tex]|x-5|+7=13[/tex]

Subtract 7 from both sides

[tex]|x-5|+7-7=13-7[/tex]

Simplify

[tex]|x-5|=6[/tex]

Apply absolute rule: If [tex]$|u|=a, a > 0$[/tex] then [tex]$u=a$[/tex] or [tex]$u=-a$[/tex] [tex]$x-5=-6$[/tex] or [tex]$x-5=6$[/tex]

[tex]$$x-5=-6 \text { or } x-5=6$$[/tex]

[tex]$$x=-1 \text { or } x=11$$[/tex]

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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Answer:

23 dollars.

Step-by-step explanation:

She spent a total of 174 - 13 = 161 dollars.

So, the cost of each book = 161/7

= 23 dollars.

A(0,-3), B(3,-2), C(1, -1) (B) is  the coordinates of ΔA'' B'' C'' after a reflection in the x -axis and a rotation of 180.

What does the term "coordinates" mean?

A 180 degree clockwise rotation will change the coordinates as follows (x,y) --> (-x,-y)

A(-3, 0), B(-2, 3), C(-1, 0) -->

A(3, 0), B(2, -3), C(1, -1)

Reflection across the line y=-x will change the coordinates as follows (x,y) --> (-y,-x)

A(3, 0), B(2, -3), C(1, -1) -->

A(0,-3), B(3,-2), C(1, -1) (B)

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Answer:

x [tex]\leq[/tex] 28

Step-by-step explanation:

lets say you chose 27 . 27 - 13 = 14 . thats not enough . but everything 28 and above would work for x . so x would be equal to or greater than 28 . hope this helps :)

Answer: <LMO and <LMJ

Step-by-step explanation:

Supplementary angles add up to a straight line, a 180 degree angle is called a straight angle. Supplementary angles add up to 180 degrees.

Answer: <LMO and <LMJ since they add up to the line OMJ

The width of the message as shown in the image attached is 3 inches.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the width of the message. The area of the postcard is 24 square inches, hence:

(b + 3)4 = 24

4b + 12 = 24

b = 3

The width of the message as shown in the image attached is 3 inches.

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Answer:   w > 50

This is because we are focusing on weights (w) that are larger than 50

We won't have an "or equal to" as part of this.

An inequality for the given scenario is;

⇒ w > 50

Here,

The given scenario is;

For safety, all dogs at a dog park who weigh, w, more than 50 pounds must play in Area 2.

We have to find the inequality.

What is Inequality?

An inequality compares two values, showing if one is less than, greater than.

Now,

Weight of all dogs = w

And, Weight of all dogs w is more than 50 pounds.

Hence, An inequality for the given scenario is;

⇒ w > 50

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The discriminant of the quadratic equation is q · (q + 8) < 0. The solution set of this inequality is (0, - 8).

The nature of the roots of quadratic equations of the form a · x² + b · x + c = 0 can be inferred by the understading of its discriminant under the following condition:

b² - 4 · a · c < 0

Where a, b, c are the coefficients of the polynomial.

If we know that a = 2 · q, b = q and c = - 1, then the equation of the discriminant is:

q² - 4 · (2 · q) · (- 1) < 0

q² + 8 · q < 0

And by algebraic handling, we find the set of possible values of q:

q · (q + 8) < 0

The solution set of this inequality is (0, - 8).

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Step-by-step explanation:

f(x) = 5|x - 1| - 5

f(x) will be positive that means >= 0, if

5|x - 1| - 5 >= 0

5|x - 1| >= 5

|x - 1| >= 1

that will be true for x <= 0 or x >= 2

f(x) will be negative for the other cases.

so, 0 < x < 2

f(x) is increasing in

[1, infinity)

the value "1" is for sure included, as it starts the increasing part.

f(x) is decreasing in

(-infinity, 1]

"1" is again included, because it ends the decreasing part.

end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.

Answer:

2

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \large{\frac{5}{8}} \: \div \large{\frac{5}{16}} \\ \\ = \frac{5}{8} \times \frac{16}{5} \\ \\ = \green 2 \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

2

Step-by-step explanation:

(5/8) ÷ (5/16)

= (5*16) ÷ (8*5)

= 80 ÷ 40

= 2

Answer:

21 seconds

Step-by-step explanation:

First let's find out how long it would take for them to have the same score.

160 + 5s = 100 + 8s

160 = 100 + 3s

60 = 3s

20 = s

Since it takes 20 seconds to get the same score and Raul get's more points every second, it would take 21 seconds for Raul to take the lead.

Answer:

graph B would be the answer.

Step-by-step explanation:

-

A scatter plot is a series of points plotted on horizontal and vertical axes. If there is no correlation between variables, the points appear randomly scattered on the coordinate plane. The points will be clustered around a straight line if the correlation is high. A scatter chart is a data visualization tool that helps show trends.

The scatter plot shows not only the magnitude of the correlation but also the direction of the correlation.

As the vertical (or Y-axis) variable increases, the correlation is positive as the horizontal (or X-axis) variable increases.

The correlation is negative if the y-axis variable decreases and the x-axis variable increases, or vice versa.

The correlation is zero if none of the above criteria can be established.

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Answer:

314.0063694

Step-by-step explanation:

You will have to use the pythogoras. triple to solve the equation

Answer:

Step-by-step explanation:

the diagonal is the hypotenuse of the two triangles that form the rectangle (see figure) we solve with Pythagoras

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

a² = b²+ c²

a² = 250² + 190²

a² = 62500 + 36100

a² = 98600

a = √98600

a = 314 m