Two sides of a triangle measure 10 cm and 15 cm. Which of the following is long enough to be the measure of the third side?
Group of answer choices

1

6

3

4

Answer:

C

Step-by-step explanation:

To reduce a fraction, you divide the numerator and denominator by the same number.

This number is the greatest common divisor (GCD) of the numerator and denominator. By dividing both the numerator and denominator by their GCD, you simplify the fraction to its simplest form. The GCD is the largest number that evenly divides both the numerator and denominator without leaving a remainder.

Dividing by the GCD ensures that the fraction is expressed in its lowest terms, where the numerator and denominator have no common factors other than 1. This process eliminates any common factors and reduces the fraction to its simplest representation.

Therefore, To reduce a fraction, you divide the numerator and denominator by the same number. Option c is correct.

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Answer with explanation:

Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.

The two expressions are

1. 7 x +4

2. 3 x +5 +4 x =1

Adding and subtracting Variables and constants

→7 x +5=1

→7 x +5-1

→7 x +4

→ When x=2,

7 x + 4 =7×2+4

=14 +4

=18

So, Both the expression has same value =18.

→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.

Correct options among the given statement about the expressions are:

1.When x = 2, both expressions have a value of 18.

2.The expressions have equivalent values for any value of x.

3.The expressions have equivalent values if x = 8.

The exponential regression equation for the set of data is given as follows: y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

4,281 bacteria.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For exponential regression, we must insert the points of a data-set into an exponential regression calculator.

The points for this problem are given as follows:

(0, 940), (1, 1034), (2, 1105), (3, 1223), (4, 1352), (5, 1520).

Inserting these points into a calculator, the equation is given as follows:

y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

y = 931.61 x (1.1)^16

y = 4,281 bacteria.

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Answer:

Step-by-step explanation:

The corresponding parts of the given triangles are ...

  vertical parts: tree, critter

  horizontal parts: tree's shadow, critter's shadow

The columns of A are linearly independent if and only if A has n pivot columns.

Fill in the blank:

If A is an m x n matrix, then the columns of A are linearly independent if and only if A has n pivot columns.

Explanation:

A pivot column of a matrix A is a column that contains a pivot element in the row echelon form of A.

In other words, a pivot column is a column that has a leading non-zero entry in the row echelon form of A.

Suppose A is an m x n matrix with columns. \(a1, a2, ..., an\).

If the columns of A are linearly independent, then there is no non-trivial solution to the equation. \(c1a1 + c2a2 + ... + cnan\) \(= 0\), where \(c1, c2, ..., cn\)are not all zero.

This implies that the coefficient matrix.\([a1, a2, ..., an]\)has full rank n, and so the row echelon form of A has n pivot columns.

Tthe row echelon form of A has n pivot columns, then the coefficient matrix [a1, a2, ..., an] has full rank n.

This implies that the columns of A are linearly independent, because if there were a non-trivial linear combination of the columns of A that gave the zero vector, then the coefficient matrix would not have full rank n.

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Answer:

x = 39

m ∠1 = 63°

m ∠2 = 117°

Step-by-step explanation:

m∠1 + m∠2 = 180° since they are adjacent linear angles lying on the same straight line

Therefore x + 24 + 3x = 180

4x + 24 = 180

4x = 180-24 = 156

x = 156/4 = 39

Therefore x = 39 (a)

FOr (b) substitute this value of x = 39 into each equation

m∠1 = x + 24 = 39 + 24 = 63°

m∠2 = 3x = 3(39) = 117°

Answer: \(\frac{5}{6}z+\frac{1}{2}\)

Step-by-step explanation:

\(\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}\)

Answer:

The two speeds are equal

Step-by-step explanation:

The speed is the distance divided by the time

100 meters / 9.75 seconds = 10.25641026 meters per second

Rounded to the nearest hundredth  10.26 meters per second

200 meters / 19.5 seconds = 10.25641026 meters per second

Rounded to the nearest hundredth  10.26 meters per second

The two speeds are equal

\(\sf{\bold{\blue{\underline{\underline{Given}}}}}\)

\(\sf{\bold{\red{\underline{\underline{To\:Find}}}}}\)

\(\sf{\bold{\purple{\underline{\underline{Solution}}}}}\)

⠀

we know that,

\(\boxed{\sf{speed=\dfrac{distance}{time}} }\)

In the 100-meter race in the 2012 Olympics he takes 9.75 sec

BUTTT,

he ran the 200-meter race in 19.5 seconds.

According to the question,

we have to compare the speed

⠀⠀⠀

\(\sf{\bold{\green{\underline{\underline{Answer}}}}}\)

The two speeds are equal of Yohan Blake.

Answer:

x² + 5x + 6

Step-by-step explanation:

Foil means first, outside, inside, last

First: (x+2)(x+3)

x × x = x²

Inside: (x+2)(x+3)

x × 3 = 3x

Ouside: (x+2)(x+3)

2 × x = 2x

Last: (x+2)(x+3)

2 × 3 = 6

adding them together:

x² + 3x + 2x + 6 = x² + 5x + 6

Answer:

-9n+8

Step-by-step explanation:

Total number sixth graders were surveyed is 600.

"percent" is Latin for "out of 100," so 5 % is literally 5 out of 100

Now--if it were 5 kids with birds, you would know that there were 100 total kids. But it's 30 kids, which is way more than 5; so your total number of kids is going to be way more than 100.

So what you need to do here is figure that "30 sixth graders own birds

i.e. 30 is 5% of some number."

How many times bigger than 5 is 30? (6 times, because 5 x 6 = 30, or you can think of it as 30 divided by 6 = 5)

So if you had to do 5 TIMES 6 to get to 30, you have to do 100 TIMES 6 to get the total number sixth graders were surveyed.

What's 100 x 6?

= 600.

So your total number sixth graders were surveyed is 600.

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If m + 1 is an even integer, then 2m + 1 is an odd integer.

Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.

Odd number: Odd numbers are those numbers that are not completely divisible by 2.

let us understand by addition on different combinations of odd numbers and even numbers.

Odd number + Odd number = Even number

Even number + Even number = Even number

Even number + Odd number = Odd number

Odd number + Even number = Odd number

In subtraction

Even number - Even number = Even number

Even number - Odd number = Odd number

Odd number - Even number = Odd number

Odd number - Odd number = Even number

In multiplication

Even number × Even number = Even number

Even number × Odd number = Even number

Odd number × Odd number = Odd number

Given:

m + 1 is an even integer.

since alternate numbers are even.

Therefore, m must be an odd number.

If m is odd, then m - 1 is even.

2m is divisible by 2, so it is always an even number.

So,

2m - 2 is even.

2m + 1 is odd.

2m + 2 is even.

Since 2m + 1 is an odd number.

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Answer:

i thinks it on a app

Step-by-step explanation:

yea the wedsite is

The dependent measures of the study were the number of parts produced and accuracy, which were used to assess the effects of the 1988 heat wave on worker productivity.

Based on the information provided, the study described represents a between-subjects design.

This is because the 48 machinists were randomly assigned to two different groups, with one group being tested at a cool room temperature and the other group being tested at a hot room temperature.

Each group was then measured using dependent measures of number of parts produced and accuracy.
A between-subjects design is a type of experimental design where different groups of participants are assigned to different conditions or treatments, and the outcomes are compared between these groups.

In this case, the two groups of machinists were assigned to different room temperatures and their productivity and accuracy were measured.

The use of dependent measures also suggests that this study was experimental in nature, meaning that the researchers were manipulating the independent variable (room temperature) in order to see how it affected the dependent variables (number of parts produced and accuracy).

Overall, this study used a between-subjects experimental design to test the effects of the 1988 heat wave on worker productivity, by randomly assigning machinists to different room temperatures and measuring their productivity and accuracy using dependent measures.

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Answer:

with the help of the theorems of triangles AAS ≅AAS

Step-by-step explanation:

We see from the figure that K and E are equidistant from T.  To be absolutely certain that KI, IE, ES, and KS are all the same lengths the diagonals must bisect each other perpendicularly at 90 degrees for the given figure to be a rhombus. A rhombus is a parallelogram in which all sides are equal.

If we look at the figure more carefully then we find that there are four triangles. Of the which the two sides KE and TE of the triangles are equal. Also the diagonal indicates that they both have a 90 degrees angle. Hence the two triangles KST and EST are equal.

To prove that triangle KEI is equal to Triangle KES.

Both have one line common which equal to both.

Both have a mid point T on the common line which divides the both bigger triangles into smaller triangles making 90 degrees angle. Hence the angles

KEI and KSE are of 90 degrees which are also opposite.

The angles SKT and IKT   and angles IET & SET are equal and opposite angles. Thus both the triangles KEI and triangle KES  are equal and opposite having equal and opposite sides.

Answer:

-18 in my opinion loss

Step-by-step explanation:

if they suck they suck depends on the team

The best measure of center for this data is the median, and its value is 3.

Option B is the correct answer.

We have,

From the line plot,

The median is the best measure of center for this type of data, as it is not affected by outliers.

To find the median, we need to arrange the data in order from least to greatest:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 10

Since there are 15 data points,

The median is the middle value, which is 3.

Therefore,

The best measure of center for this data is the median, and its value is 3.

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(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.

This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).

(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.

First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).

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Answer:

A,C

Step-by-step explanation:

i took the test

Answer:

y=2x-1

Step-by-step explanation:

Answer:

m=1.4285

Step-by-step explanation:

-7 (3m – 4) + 2

-7×3m+28+2

-21m+30

-21m=-30

m=30/21

m=1.4285

The equation that has only one solution is:

x2 - 6x + 9 = 0

Let's analyze each equation to determine the number of solutions:

1. x2 = 9

This equation represents a quadratic equation in which the variable x is squared. When we take the square root of both sides, we get x = ±3. Therefore, this equation has two solutions: x = 3 and x = -3.

2. x(x - 1) = 9:

Expanding the equation, we have

\(x^2 - x = 9.\)

Rearranging the terms, we get

\(x^2 - x - 9 = 0.\)

This is a quadratic equation in standard form. By applying the quadratic formula or factoring, we can determine its solutions. In this case, the solutions are not integers, and they are approximately

x ≈ 3.08 and x ≈ -2.08.

Thus, this equation has two solutions.

3. x2 - 6x + 9 = 0:

This equation is already in standard form, and we can attempt to solve it by factoring or applying the quadratic formula. However, upon closer inspection, we notice that the equation is a perfect square trinomial, which can be factored as \((x - 3)^2 = 0\). This equation has a repeated solution of x = 3.

Therefore, out of the given equations, only the equation x2 - 6x + 9 = 0 has a single solution, which is x = 3. The other equations have two solutions or approximate values for x.

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Answer:

y = 1/2x - 6

Step-by-step explanation:

y2 - y1 / x2 - x1

-2 - (-5) / 8 - 2

3 / 6

= 1/2

y = 1/2x + b

-5 = 1/2(2) + b

-5 = 1 + b

-6 = b

Answer:

\(inrease \: = 900 - 250 = 650 \\ persent = \frac{650}{250} \times 100 \\ = 65 \times 4 = 260\)