Mathematics High School

## Answers

**Answer 1**

Sum of **angles** in triangle = 180°

Sum of two side lengths > **Length** of the Third side

**Congruency** of triangles.

What is a triangle:

A polygon that has three sides, three **vertices**, and three **angles** is known as a triangle. Based on the **dimensions** of the sides and angles, triangles can be divided into many categories.

The sides and** angles** of a triangle determine its attributes; the following list of triangle** properties** will help you understand this:

Properties of the triangle:The measure of a triangle's three angles adds up to 180° or two right angles. This property of the triangle is known as the triangle's **angle sum property.**In the triangle, the sum of the** lengths** of the two sides is **greater than** the length of the third side. In all three sides of a triangle, the side **opposite** the larger angle is the **longest** side. A triangle's **exterior angle** is always equal to the sum of its inner opposing angles. If the corresponding angles of two triangles are the same and the lengths of their sides are proportionate, then the two triangles are said to be **congruent**.Any **two sides** of a triangle can be added together to have a length larger than the **third side**. Similar to this, any two triangle sides have length differences between them that are **smaller than** the length of the third side.

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## Related Questions

How do you solve a nonlinear system?

### Answers

A set of equations that contain at least one **nonlinear equation** is referred to as a system of nonlinear equations and steps to** solve** are mentioned below.

What is non-linear equation and method to solve?

A nonlinear system's solution is an ordered pair that solves both equations, much like with systems of linear equations. A nonlinear system could have several **solutions**. This will become clear as we use **graphing** to solve a set of nonlinear equations. The** point of intersection** of the two lines served as the system's solution when linear equations were being solved. Systems of nonlinear equations can have graphs that are circles, parabolas, or hyperbolas, as well as a number of locations where their lines cross, resulting in a number of solutions. **Visualize** the various ways the graphs might connect once you've determined which ones they are.

**Steps to solve non linear equation **are:

Identify the graph of each equation. **Sketch** the possible options for intersection. Graph the first **equation**. Graph the second equation on the same rectangular **coordinate** system. Determine whether the graphs intersect. Identify the points of intersection. Check that each** ordered pair** is a solution to both original equations.

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2) There are 750 spectators in the stadium, of which 420 are women

and the rest are men.

a) What percent of the spectators are women?

b) What percent of the spectators are men?

### Answers

The **percentage** of **spectators** that are **women** is 56% and the percentage of **spectators** that are men is 44%

What is a percent example?

Since one **percent** (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount** specified**. As an** illustration**, 1% of 1,000 chickens is equivalent to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

What is a percent in math?

In essence, percentages are** fractions **with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a **percentage.** For instance, you would have received a 75% grade if you answered 75 out of 100 **questions** correctly on a test (75/100).

In the above question

The **percentage **of **spectators** that are women is 56% and the percentage of spectators that are men is 44%

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A system of linear equations is shown in the graph. How many solutions does the system have?

a coordinate plane with one line that passes through the points 0 comma 1 and 3 comma 2 and another line that passes through the points 0 comma negative 4 and 3 comma negative 3

One solution at (0, −4)

One solution at (−3, 0)

No solution

Infinitely many solutions

### Answers

**Answer:**

Answer = no solution

**Step-by-step explanation:**

Explanation:

Because the two given lines are parallel, we can conclude that they will never intersect. Hence, there will never be a solution (a point at which two lines intersect)

Hope this helps you out :)

1. Write the first five terms of the arithmetic sequence.

a₁ = 6; d = 4

### Answers

The first five terms of the **arithmetic sequence** with a₁ = 6 and d = 4 are:

a₁ = 6

a₂ = 6 + 4 = 10

a₃ = 10 + 4 = 14

a₄ = 14 + 4 = 18

a₅ = 18 + 4 = 22

How do you determine the arithmetic sequence order?

The formula for determining the nth term is used to locate a specific term in an **arithmetic sequence**. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. As a result, enter the given values for a and d into the formula to determine the nth term.

What exactly is an arithmetic sequence example?

An **arithmetic sequence** is created by adding a group of integers together to create a sequence. Because each number is the sum of the two numbers before it, the sequence 2, 4, 6, 8, and 10 is an example of an **arithmetic sequence**.

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somerset key 8.1 a landscape architect wants to plant a circle of flowers around a triangular garden. she has sketched the triangle on a coordinate grid with vertices at a(0, 0), b(8, 12), and c(18, 0). explain how the architect can find the center of the circle that will circ*mscribe triangle abc. then find the radius of the circ*mscribed circle.

### Answers

As per the** linear equation** concept, the **radius **of the circ*mscribed circle is **√793/3**

Here we have given that a landscape architect wants to plant a circle of flowers around a triangular garden. she has sketched the triangle on a coordinate grid with vertices at a(0, 0), b(8, 12), and c(18, 0).

And we need to find the center of the circle that will circ*mscribe triangle ABC and then find the radius of the circ*mscribed circle.

In order to find the radius of the circle , we have to find the equation of the given point,

For that we have to calculate the slope and the y intercept,

The value of **slope **is calculated as,

=> m = (12 - 0)/(8 - 0)

=> m = 12/8

=> m = 3/2

Here the slope is the perpendicular line is calculated as,

=> m = -2/3

Now, the value of **intercept **is calculated as,

=> 12 = -2/3(8) + c

=> 3/2 = -2/3 + c

=> c = (9 + 6)/6

=> c = 15/6

=> c = 5/2

Then the equation of the **line **is,

=> y = -2/3x + 5/2

Then the **center **point is calculated as x = 9,

=> y = -2/3 (9) + 5/2

=> y = -6 + 5/2

=> y = 8/3

Therefore, the center of the circle is (9, 8/3)

And the **radius **is calculated as,

=> (9)² + (8/3)² = r²

=> 81 + 64/9 = r²

=> r = √793/3

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{ (1,2), ( 3, 4), ( 5,5) } determine whether each relation i a function. Give the domain and range for each relation

### Answers

If the **ordered pair** of the relation is {(1,2), (3, 4), (5,5)}, then {1, 3, 5} and **range** {2, 4, 5}

The ordered pairs of the relation is

{(1,2), (3, 4), (5,5)}

**The relation** is the defined as the mathematical statement that shows the relationship between the x values and y values in the ordered pair.

**The domain **is the set of all input of the relation, and domain is also known as x values of the relation

The range is the set of all outputs of the relation, and range is also known as the** y values** of the relation

The ordered pair = {(1,2), (3, 4), (5,5)}

The domain = {1, 3, 5}

The range = {2, 4, 5}

Therefore, the domain is {1, 3, 5} and range {2, 4, 5}

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If mand n average i 50

p and q average i 70

then what will be the average of m,n,p,q

### Answers

we know that average of two number are

AV= (m+n)/2

we are given that

(m+n)/2 = 50

m+n= 50×2

m+n=100

similarly

Arithmetic average of p and q = 7

(p+q)/2

=70

p+q= 70×2

p+q= 140.

Now, arthemetic mean of

(m+n+p+q)/4=

(140+100)/4

= 240/4

= 60

so average of m, n, p, q is 60

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What is the result when the number 90 is decreased by 10%?

### Answers

**Answer:**

81

**Step-by-step explanation:**

First find the amount decrease

90 * 10 %

90 * .10

9

90 decreased by 9

90 -9

81

Please help!

Find the value of X

### Answers

**Answer:**

x=68º

**Step-by-step explanation:**

The dashes on the lines show they are equal in length making it an isosceles triangle. this makes the degrees equal as well so:

68º=x and vise versa

**Answer:**

x = 68°

**Step-by-step explanation:**

68° = x° [ being Isosceles triangle ]

Quetion content area top left

Part 1

The rectangle hown ha a perimeter of 78 cm and the given area. It length i 3 more than twice it width. Write and olve a ytem of equation to find the dimenion of the rectangle

### Answers

The** length** of the **triangle** is 39 cm and the **width** of the triangle is 13 cm.

**Triangle:**

A** triangle **is a **polygon** with three sides and **three vertices**. It is one of the basic shapes in **geometry**. A triangle with angles A, B, and C is represented by Δ ABC.

Now,

Let, width of **rectangle** = x cm

So, the **length** of rectangle = 3x

Given that,

** perimeter **of the rectangle = 78 cm

2 (length + breadth ) = 78

2(3x+x) = 78

Now,

2(3x + x) = 78

⇒ 2(4x) = 78

⇒ 4x = 78/2

⇒ 3x = 39

⇒ x = 39/3

⇒ x = 13

Thus, **breadth/width** of **rectangle** = 13 cm

So, length of rectangle =3x

=3 × 13

=39 cm

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if mark uses the normal approximation of the binomial distribution to model the number of home runs, what is the standard deviation for a total of 200 games? answer choices are rounded to the hundredths place.

### Answers

The **standard deviation** for a total of 200 games is 5.3735.

How to calculate the standard deviation?

Let X = **number** of home runs of this player in 200 games played by him.

p = **probability** that a this player hits a home run in a single game and this is given to be 0.175.

Where np = Mean of X and √{np(1 - p)} is the standard deviation of X.

Here n = 200 and p = 0.175. So, the **standard deviation** for a total of 200 **games** is the standard deviation for a total of X

= √(200 x 0.175 x 0.825) / 2

= 5.3735

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Is a dilation in which the scale factor is less than 1?

### Answers

Yes, it is a **dilation** in which the scale factor is less than 1. If the **scale factor** is between 0 and 1, then the image shrinks.

Dilation

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

An example of dilation math is a square of side 5 units can be dilated to a square of side 15 units, but the shape of the square remains the same.

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Rewrite the expression you developed in Part B as a single term with a fractional coefficient

### Answers

It is either 1 1/4c or 5/4c when the **expression **created in Part B with a fractional coefficient.

**What are the types of coefficients?**

In mathematics, **numerical **coefficients and literal coefficients are the two main types of coefficients that are used. Both a numerical and literal coefficient: The number being multiplied by the variable is the numerical coefficient (s).

Can we have fractions as coefficients?

It is not advisable to utilize fractions as stoichiometric coefficients. Every stoichiometric coefficient must be multiplied by the denominator whenever there is a fraction in order to get whole values and keep the mole ratio constant.

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(Using Algebra)

Find the value of X

### Answers

On solving the provided question we can say that - since angle are equal of a **triangle**, so x = 2

What is triangles?

Three sides and **three vertices **make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. Three triangle **angles **added together equal 180 degrees. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

since two angle are equal, then then corresponding sides will be equal,

therefore,

using algebra

12=6x

x=2

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How do you write 0.99 as a percentage

### Answers

99% is .99 as a percent. i need 20 words so don't worry about the rest of these words

Answer:

99%

Step-by-step explanation:

you move the decimal over to the right 2 times to make a percentage.

suppose that a brand of lightbulb lasts on average 2872 hours with a standard deviation of 108 hours. assume the life of the lightbulb is normally distributed. calculate the probability that a particular bulb will last from 2638 to 2949 hours?

### Answers

The **probability **that a **lightbulb **will last between 2638 and 2949 hours is approximately 0.8084.

To solve this problem, you can use the normal distribution formula to calculate the **probability **that a **lightbulb **will last between 2638 and 2949 hours:

P(2638 < x < 2949) = P(z1 < (x - mean)/standard deviation < z2)

Where x is the number of hours that the lightbulb lasts, mean is the **average number **of hours that the lightbulb lasts (2872 hours in this case), and the **standard deviation **is the standard deviation of the number of hours that the lightbulb lasts (108 hours in this case), z1 is the standard normal deviate corresponding to the lower bound of the interval (2638 hours in this case), and z2 is the standard normal deviate corresponding to the upper bound of the interval (2949 hours in this case).

To calculate z1 and z2, you can use the following formulas:

z1 = (2638 - 2872)/108 = -1.22

z2 = (2949 - 2872)/108 = 0.85

To calculate the probability, you can use a normal distribution calculator or table to find the probability that a standard normal random variable is between -1.22 and 0.85.

Using a normal distribution calculator or table, you can find that the probability that a lightbulb will last between 2638 and 2949 hours is approximately 0.8084.

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Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2. 9% interest compounded quarterly, how much interest will she earn in 10 years?.

### Answers

**The amount of interest **that she earned in 10 years is $1005.09

The principal amount = $3000

The **interest rate** = 2.9%

Time period = 10 years

The interest is **compounded quarterly**

The equation of compound interest

A = P(1 + r/n)^(t×n)

Where A is the final amount

P is the** principal amount **

r is the interest rate

n is the number of time interest is elapsed

t is the time period

Substitute the values in the equation of** compound interest **

A = 3000( 1 + (2.9/100)/4)^(10×4)

= 3000(1.00725)^40

= 3000(1.335)

= $4005.09

The interest that she earned = 4005.09 - 3000

= $1005.09

Therefore, she earned $1005.09 interest

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What's the least number of bits that you'll need to represent 59 in binary?

### Answers

The least **number **of bits that you'll need to represent 59 in **binary **is **(111011)₂**

**Binary:**

In math, binary refers a **numbering **scheme in which there are only two possible values for each **digit **-- 0 or 1

Given,

Here we need to find the binary equivalent to 59.

In order to solve this one, we have to divide 59 by 2. Use the **integer quotient **obtained in this step as the **dividend **for the next step. Repeat the process until the quotient becomes 0.

When 59 is **divided **by 2, the quotient is 29 and the remainder is 1.

When 29 is divided by 2, the quotient is 14 and the remainder is 1.

When 14 is divided by 2, the quotient is 7 and the **remainder **is 0.

When 7 is divided by 2, the quotient is 3 and the remainder is 1.

When 3 is divided by 2, the **quotient **is 1 and the remainder is 1.

When 1 is divided by 2, the quotient is 0 and the remainder is 1.

Now, we have to write the **remainders **from **bottom **to top.

=> (59)₁₀ = (111011)₂

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what do imaginary solutions tell you about the quadratic function?

please help asap

### Answers

**Answer:**

**Imaginary **solutions **means **there is **no real solutions**.If no real solutions then the graph **doesn't intersect the x-axis**.It means **the graph is either above or below the x-axis**.

Are the two rectangular prisms similar?

### Answers

The rectangular **prisms **cannot be compared because they do not have similar **ratios**.

Given that,

We have to find are two **rectangular **prisms similar.

We know that,

What is rectangular prism?

A rectangular prism is a solid three-dimensional shape having six faces, including rectangular **bases**. An alternative term for a rectangular prism is a cuboid. The cross-section of a **cuboid **is identical to that of a rectangular prism.

A rectangular prism is a prism with rectangle-shaped bases (the top face and bottom face).

Therefore, The rectangular prisms cannot be compared because they do not have **similar **ratios.

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How do I calculate the distance between two latitude longitude points in Excel?

### Answers

We convert **latitude and longitude** points in **decimal form** and apply **nautical formula**.

What is **latitude** points?

Latitude is used to calculate **how far north or south** of the **Equator** you are. It is calculated using 180 fictitious lines that are drawn in circles east-west of the equator. Parallels are the names for these lines. An imaginary ring connecting all points sharing a parallel is known as a circle of latitude.

What is **longitude** points?

The distance east or west of the prime meridian is known as longitude. Imaginary lines that circle the globe vertically (up and down) and converge at the North and South Poles are used to calculate longitude. The term "**meridians**" refers to **these lines**. **One arc degree** of longitude is the length of each meridian.

We are given **Latitude and Longitude** of **origin point**

(Lat_place_1, Lon_place_1).

and also we are given **Latitude and Longitude** of **Destination point**

(Lat_place_2,Lon_place_2).

Now we have to find distance begtween origin point and Destination Point.

Convert Latitude and Longitude to **Decimal Degrees**

Total Degrees (in the decimal form) = Deg + [Mins / 60] + [Seconds / 3600]

Now that you have the latitude and longitude **values** in decimals, you just face the equation for the nautical miles between Timbuktu and Casablanca, noted underneath.

Nautical Miles= ACOS [(sin(Lat_place_1*PI()/180)*sin(Lat_place_2*PI()/180)+

cos(Lat_place_1*PI()/180)*cos(Lat_place_2*PI()/180)*

cos(Lon_place_2*PI()/180-Lon_place_1*PI()/180)) ] *3443.8985

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Does AAS prove triangles congruent?

### Answers

**Yes, AAS or Angle-Angle-Side **proves the triangle is **congruent**.

What is **AAS **or **Angle-Angle-Side congruence**?

According to the **AAS congruence rule**, any two **angles** and the excluded **side **of one triangle must be identical to the corresponding **angles **and excluded **side **of the other triangle.

The **sides **are not included between the **angles **but rather run in either direction of the **angles**, whilst the **angles **are sequential and matching in nature.

The two adjacent or consecutive **angles **of one triangle are identical to the corresponding **angles** of another triangle, as seen in the illustration below. Because the **sides** of both triangles after the **angles **rather than included between them, they are also equal.

According to the **AAS** or **Angle Angle** **Side congruence** **rule**, two triangles are said to be congruent if two sets of comparable **angles **and the opposing or non-included **sides **are equal.

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if you answer all correctly i'll make you brainliest, but it has to be within the next thirty minutes

to differentiate them, answer using the words fraction, decimal, and integer

FIFTY POINTS AND BRAINLIEST CMON PEOPLE

### Answers

The **solution **for the inequality 4.8 - 9x < -(4x - 8) - 1 is x > -0.44.

The solution for the **inequality **4x - 1 > 18 is x > 4.75.

And the **solution **for the inequality -2 > -x - (-1/2x + 1) is x > 2.

What is inequality?

**Inequality **shows relation between two expression which are **not equal **to each others.

The given **inequality **in decimal,

4.8 - 9x < -(4x - 8) - 1

Simplify the **inequality **to find the value of x,

4.8 - 9x < -4x + 8 - 1

4.8 - 9x < -4x + 7

4.8 - 7 < 9x - 4x

-2.2 < 5x

x > -2.2 / 5

x > -0.44

The given **inequality **in integer,

4x - 1 > 18

4x > 19

x > 19 / 4

x > 4.75

The given **inequality **in fraction,

-2 > -x - (-1/2x + 1)

-2 > -x + 1/2x - 1

x - 1/2 x > 2 - 1

1/2 x > 1

x > 2

The **solutions **for the **inequalities **x > -0.44, x > 4.75 and x > 2.

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If rt biect angle qr , the meaure of angle qrt = 5x-9 and the meaure of angle rt = 2x33, find the meaure of angle rt

### Answers

The **measure **of **∡SRT** is 61.

**What is angle bisector?**

**Angle bisector** is the line which **divides **the given **angle **into two **equal parts**.

**According to the given question:**

Segment RT bisects ∡QRS.

m ∡QRT = 5x – 9 and m ∡SRT = 2x + 33

Therefore,

m∡QRT=m∡SRT

5x – 9=2x + 33

3x=42

x=14

Now, we can find ∡SRT using x

∡SRT=2x+33

∡SRT=2(14)+33

∡SRT=28+33

∡SRT = 61

Therefore, the measure of ∡SRT is 61

Complete question:

If segment RT bisects ∡QRS, m∡QRT = 5x – 9 and m∡SRT = 2x + 33, find m∡SRT.

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the following argument is valid: p1) if it is raining then then your car will get wet. p2) it is not raining. c) your car will not get wet.

### Answers

Yes, the **argument is valid.** If the** two premises** (p1 and p2) are true, then the conclusion (c) must also be true.

The argument is valid because the conclusion is logically entailed by the two premises. If it is raining then the car will get wet, and if it is not raining then the car will not get wet. This follows from the logical law of noncontradiction, which states that for any statement, either it is true or its negation is true, but not both. Since the first premise states that it is raining, and the second premise states that** it is not raining**, the logical conclusion is that the car will not get wet.

The argument is based on a logical principle known as noncontradiction, which states that for any statement, either it is true or its negation is true, but not both. In this case, the two premises (p1 and p2) both concern the same statement: that it is raining. The** first premise **states that if it is raining then the car will get wet, and the second premise states that it is not raining. Therefore, the **logical conclusion** is that the car will not get wet. This conclusion follows logically from the two premises, so the **argument is valid.**

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10. Jordan and Jake are saving money from their newspaper route earnings. Their savings s, in dollars, are related to the time t, in weeks, after they start working. Jordan’s savings are given by the equation. s = 60t + 25, and Jake’s are given by the equation s = 100 + 45t. What is the meaning of the solution of the system of equations?

### Answers

Using** substitution method** to solve the **system of linear equation**, they will save $325 after 5 weeks

System of Linear Equation

**System** of** linear equations** is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of** variables**.

In the question given, the system of **linear equation**s are;

s = 60t + 25 ...eq(i)

s = 100 + 45t ...eq(ii)

s = Amount savedt = number of weeks

From equation (i)

s = 60t + 25

Put eq(i) into eq(ii)

60t + 25 = 100 + 45t

60t - 45t = 100 - 25

15t = 75

t = 5

Put t = 5 into equ (i)

s = 60(5) + 25

s = 325

The meaning is that at week 5, they will saved $325

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Which situation can be represented by the equation 40x + 0 = 200 ?

### Answers

40 divided by 200 is x

**Answer:**

40 divided by 200 is x.

x = 5

Hope this helped!

Which of the following describes the transformation from Figure 1 to Figure 2?

### Answers

A statement which best describe the **transformation** from Figure 1 to **Figure 2** is: C. reflection over the **y-axis**.

What is a reflection?

In Mathematics, a **reflection** can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a **reflection **over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a **reflection** over the y-axis to the **coordinates** of figure 1, the coordinates of figure 2 include the following:

(x, y) → (-x, y)

Coordinate A = (-6, 5) → **Coordinate** A' = (-(-6), 5) = (6, 5).

Coordinate B = (-4, 5) → Coordinate B' = (-(-4), 5) = (4, 5).

Coordinate C = (-3, 5) → Coordinate C' = (-(-3), 5) = (3, 5).

**Coordinate** D = (-5, 4) → Coordinate D' = (-(-5), 4) = (5, 4).

Coordinate E = (-5, 3) → Coordinate E' = (-(-5), 3) = (5, 3).

Coordinate F = (-7, 3) → **Coordinate** F' = (-(-7), 3) = (7, 3).

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Find the measure of angle 1

### Answers

The required **measure **of **angle **1 is 120°. Option D is correct.

A figure of an isosceles triangle is shown, and a measure of the angle 1 is to be deteremined.

What is the triangle?

The **triangle **is a **geometric** **shape **that includes 3 **sides **and the sum of the interior **angle **should not be greater than 180°

here,

For a triangle, the sum of the interior angle should be equal to 180°,

So,

30 + 30 + ∠1 = 180

∠1 = 180 - 60

∠1 = 120°

Thus, the required **measure **of **angle **1 is 120°. Option D is correct.

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help please I heed some

### Answers

The two **pairs** of parallel lines form a **quadrilateral **whose internal angles are **right** **angles **so the value of x is 90°.

What is a transversal?

We know when a transversal **intersects **two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

Given, line a **|| **line b and line c **|| **d.

These four lines form a **quadrilateral **whose internal angles are all right angles.

Hence the value of **x **is 90°.

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