State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The ₋component form of a vector describes the vector in terms of change in x and change in y .

Based on the linear pair postulate, the statements and the reasons for the proof are explained below.

The linear pair postulate states that if two angles form a linear pair, then both angles are supplementary, and therefore have a sum of 180 degrees.

The proof that states that angle 1 and angle 3 are congruent angles is shown below:

Statement 1. ∠1 and ∠2 are a linear pair

Reason: Given

Statement 2: ∠1 and ∠2 are supplementary      

Reason: Linear Pair Postulate  

Statement 3: m∠1 + m∠2 = 180°  

Reason: Definition of Supplementary Angles  

Statement 4: ∠2 = ∠4      

Reason: Given  

Statement 5: ∠3 = ∠4

Reason: Vertical Angles Theorem

Statement 6: ∠2 = ∠3

Reason: Corresponding angles theorem  

Statement 7: m∠2 = m∠3

Reason: Corresponding angles are congruent  

Statement 8: m∠1 + m∠3 = 180

Reason: Supplementary angle theorem

Statement 9: <1 and <3 are supplementary

Reason: Definition of supplementary angles

Learn more about linear pair on:

https://brainly.com/question/13218054

#SPJ1

Answer:

13

Step-by-step explanation:

first use PEMDAS= P= Parentheses E= Exponents M= Multiplication D= Division A= Addiction S= Subtraction.

(3+6)+6-2=

9+6-2=

15-2=

13

Add 3+6 which is 9

Add 3+6 which is 9then add 9+6 equal to 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15boom that's how you do it

Answer:

22

Step-by-step explanation:

Use Pemdas

P means parenthesis so add the numbers in the parenthesis

3 + 6 = 9

2(9) + 6 - 2 =

Next is E, but there are no exponents so now there is M

multiply 2 times 9, you will get 18.

18 + 6 - 2 =

So next is A which is addition, add 18 + 6

18 + 6 = 24.

24 - 2

And lastly, S which is subtraction.

24 - 2 = 22

So the answer is 22

Answer:

A:12.898

B:7.999

Step-by-step explanation:

A: 4.361+8.537

B:2.704+5.295

The coordinate of the midpoint of JP is -1

On the number line, we have the following coordinates

J = -7

P = 5

The coordinate of the midpoint of JP is calculated using

Midpoint = 1/2 * (J + P)

This gives

Midpoint = 1/2 * (-7 + 5)

Evaluate the sum

Midpoint = 1/2 * -2

Evaluate the product

Midpoint = -1

Hence, the coordinate of the midpoint of JP is -1

Read more about coordinate at

https://brainly.com/question/17206319

#SPJ1

Answer:

-0.595

Step-by-step explanation:

..

By the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

From the question, we are to prove that ΔBXA ≅ ΔBYA

From the Hypotenuse Leg theorem which states that "two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side".

From the given information,

BX ⊥ XA.

ΔBXA is right triangle with hypotenuse AB

Also,

BY ⊥ YA.

ΔBYA is right triangle with hypotenuse AB

∴ The hypotenuses of the triangles are congruent

Also, from the given information,

XA is congruent to YA

XA and YA are the legs of the right triangles.

Hence, by the Hypotenuse Leg theorem, the two triangles are congruent. That is, ΔBXA ≅ ΔBYA

Learn more on Congruent triangles here: https://brainly.com/question/27983954

#SPJ1

The probabilities from the binomial probability mass function P(x ≤ 2) will be 0.9298.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

q = 1 - p = 1 - 0.10 = 0.90

Let x be a binomial random variable with p = 0.1 and n = 10.

The probabilities from the binomial probability mass function P(x ≤ 2) will be

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x ≤ 2) = ¹⁰C₀ × (0.1)⁰ × (0.9)¹⁰ + ¹⁰C₁ × (0.1) × (0.9)⁹ + ¹⁰C₂ × (0.1)² × (0.9)⁸

P(x ≤ 2) = 0.3487 + 0.3874 + 0.1937

P(x ≤ 2) = 0.9298

Your question was incomplete but the complete question is given below.

Let x be a binomial random variable with p = 0.1 and n = 10. Calculate the probability from the binomial probability mass function less than or equal to 2.

More about the binomial distribution link is given below.

https://brainly.com/question/14565246

#SPJ1

Answer:

1. x < 4

2. x > 1

3. x < 5

Step-by-step explanation:

Athlete swam at a constant rate, his speed in m/s is 2.343 m/s

The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.

The formula for speed is as straightforward as dividing a distance by a time. We may define speed as the rate of change of position of an item in any direction by taking the distance traveled and dividing it by the time.

Given,

the distance covered = 50m

total time taken = 21.34s

Speed = distance / Time

speed = 50/ 21.34

speed = 2.343 m/s

To learn more about speed from given link

https://brainly.com/question/26046491

#SPJ9

What is the sum of the finite geometric series?

a. -15+30-60+120-240+480= 315

Given:

a=-15

r= -2

n=6

[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{-15(1-(-2)^{6})}{1+2}\\\\S_6=\frac{-15(1-64)}{3}\\\\S_6=\frac{-15(-63)}{3}\\\\S_6=5*63=315[/tex]

What is a finite geometric series?

To learn more about finite geometric series, refer:

brainly.com/question/4520322

#SPJ4

The solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is a = -1

In this question, we have been given an equation.

[tex]\frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}[/tex]

We need to find the solution of given equation.

[tex]\Rightarrow \frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}\\\\\Rightarrow \frac{2(2a+1)+6a}{12}=\frac{a-1}{3}\\\\\Rightarrow \frac{4a+2+6a}{12}=\frac{a-1}{3}\\\\ \Rightarrow \frac{10a+2}{4}=a-1\\\\\Rightarrow 10a+2=4a-4\\\\\Rightarrow 6a=-6\\\\\Rightarrow a=-1[/tex]

We need to check above solution.

Substitute a = -1 in LHS of given equation.

2a + 1 / 6 + a/2

= [2(-1) + 1 / 6] + [-1/2]

= (-1/6 - 1/2)

= -(4/6)

= -2/3

Substitute a = -1 in RHS of given equation.

a-1/3

= (-1 - 1)/3

= - 2/3

So, LHS = RHS

Therefore, the solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is      a = -1

Learn more about an equation here:

brainly.com/question/649785

#SPJ4

Answer:

$3,985.00

Step-by-step explanation:

The formula for the amount accrued, A if you invest an amount P at r% compounded annually for n years is given by the formula

[tex]A = P\left(1 + \dfrac{r}{100}\right)^n[/tex][tex]A = P\left(1 + \dfrac{2}{100}\right)^{30} \\\\= P\left(1 + 0.02\right)^{30} \\\\= P\left(1 .02\right)^{30} \\\\= \; \$3,985.00[/tex]

The division by 100 is necessary to allow r% to be reduced to a decimal

So using this formula directly by substituting values gives

By using distributive property 15(3 + 8) 15 11 = 165 both approaches yield the same conclusion.

Distrubutive Property Formula : a(b+c)=a b+a c

The distributive property is also known as the distributive law of multiplication over addition and subtraction. By its very name, the procedure implies that something will be divided or distributed.  According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC. Subtraction also belongs to the scope of this distributive law, which is expressed as A (B - C) = AB - AC. The distribution of operand A among the other two operands is seen from this.

A (B + C) = AB + AC represents the distributive property of multiplication over addition.

15(3+8) = (15.3) + (15.8)

15.11 = 45 + 120

165 = 165

Using the law of BODMAS, we can now attempt to solve the expression. The solution is as follows. We will first add the figures in brackets, and then we will multiply this total by the figure outside of the brackets.

Hence, using distributive property, it follows that 15(3 + 8) x 15 = 165. As a result, both approaches yield the same conclusion.

To learn more about BODMAS visit:

https://brainly.com/question/16738857

#SPJ1

Answer:

-41

Step-by-step explanation:

h(x) = | 1-7x

First, calculate the value for the function for x = -9

h(-9) = |1--7x|

h(-9) = |1+63|

h(-9) = |64|

h(-9) = 64

23-h(-9) = 23-64 = -41

Hope this helps ;0

The result of multiplying the numbers 234 x 0.35 is 81.9

The numbers are given as:

234 and 0.35

Express the numbers in a product expression

So, we have

234 x 0.35

Express 234 as 200 + 34

So, we have

234 x 0.35 = (200 + 34) x 0.35

Expand the bracket

So, we have

234 x 0.35 = 200 x 0.35 + 34 x 0.35

Evaluate the product

So, we have

234 x 0.35 = 70 + 11.9

Evaluate the sum

So, we have

234 x 0.35 = 81.9

Hence, the result of multiplying the numbers 234 x 0.35 is 81.9

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

Answer: 1000

Step-by-step explanation:

4000/4

Answer:

1000

Step-by-step explanation:

blank can be written as x. since this is a multiplication problem we need to the opposite of multiplying, which is dividing. rewrite the problem as 4000/4=x

solve by dividing 4000 by 4 to get 1000

Answer:

Step-by-step explanation:

Differences are 3 less then 2 less.

So, the next term would be 4-1 = 3.

Answer:

[tex]4x\left(x-3\right)[/tex]

Step-by-step explanation:

[tex]x^{y+z}=x^yx^z\\x^2=xx\\=4xx-12x\\=4xx-4\cdot \:3x\\=4x\left(x-3\right)[/tex]

The value of f(-4) is 18 because

3(2+4)

6+12=18

Answer: 6,7,8

Step-by-step explanation:

Answer:

Solution on Screen

Step-by-step explanation:

It's okay don't worry

The function g(3)'s expression is 8, which is

The supplied function is defined by a single expression, as per the query. Calculate the value of the other function using the provided expression.

In light of this, g(r) = -5 + 13 = 8

Additionally, the computed value can also be used as the value of the function expression g(3).

Consequently, the value of the function provided is 8.

The relationship between the dependent and independent variables is explained by the function. For the functions, it has a collection of values that may be connected using the domain technique.

To learn more about the function from the given link:

https://brainly.com/question/25638609

#SPJ9

The components of the two vectors are added and subtracted to produce the addition and subtraction vector PQ. i.e. →PQ = →Q + →P and →PQ = →Q - →P

A vector, which denotes the mathematical and geometrical direction of the provided quantity, is a quantity with both magnitude and direction.

For example : Velocity, Displacement etc.  

Let's start by assuming that,

P(x,y,z) and Q(u,v,w)

Now, we need to find the vector addition and subtraction

Addition of vectors to give →PQ

→PQ = →Q + →P

= (ui + vj + wk ) + (xi + yj + zk)

= (ui + xi ) +(vj  + yj) + (wk +zk)

= (u+x) i + (v + y) j + (w + z)k

= →PQ

Similarly, Subtraction of vectors to give →PQ

→PQ = →Q - →P

= (ui + vj + wk ) - (xi + yj + zk)

= (ui + vj + wk  - xi - yj - zk)

= (ui - xi ) +(vj  - yj) + (wk -zk)

= (u-x) i + (v - y) j + (w - z)k

= →PQ

For example : Let P(1,2,1) and Q ( -1, -2,4)

Then, Addition →PQ = →Q + →P

= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)

=  (1-1) i + (2 -2) j + (1 + 4)k

= oi+0j +5j

= 5j

Subtraction →PQ = →Q - →P

= (1i + 2j + 1k ) - (-1i + (-2)j + 4k)

=  (1+1) i + (2 +2) j + (1 - 4)k

= 2i+4j -3j

Hence, the vector PQ addition and subtraction is given by the addition & subtraction of the components of the two vectors.

To learn more about Vectors, here

brainly.com/question/24256726

#SPJ4

A quadrilateral (square) may always be used to create a square in a circle. Because squares have right angles at each vertex, every pair of opposing angles in a square is complementary and inscribed in a circle. This is an unavoidable characteristic of squares.

If the form in question is a square, each pair of adjoining angles is supplementary and inscribed in a circle. This is owing to the presence of right angles at each vertex of the square. This means that the assertion can never be proven false.

Learn more about quadrilaterals and squares - https://brainly.com/question/23935806

When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.

For example :

How many different triangles may be formed with side lengths of 5m,9m and 6 m ?

Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.

We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.

This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed

To learn more about, Triangles here

brainly.com/question/2773823

#SPJ4

Solving for y in terms of x gives y = 31 - 5x

The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.

It is also described as the variable that is being worked out in a given equation.

Given the equation;

5x +y = 31

Let's make 'y' the subject

We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have

y = 31 - 5x

Thus, solving for y in terms of x gives y = 31 - 5x

Learn more about subject of formula here:

https://brainly.com/question/10643782

#SPJ1

Answer:

20

Step-by-step explanation:

We know that two vertical angles are equal to each other.

Then

First, We have to solve the equation 5y + 10 = 2y + 16  for y.

After that ,we can easily find the measure of the angles by substituting y by its value in their expression.

SOLVING THE EQUATION :

5y + 10 = 2y + 16

⇔ 5y - 2y = 16 - 10

⇔ 3y = 6

⇔ y = 2

Determining the measure of the angles :

angle 1 → 5(2) + 10 = 20

angle 2 → 2(2) + 16 = 20

According to the given data  the property justifies statement is: Multiplication Property of Equality.

According to the Multiplication Property for Equations, an equation can be multiplied as well as divided by the exact number upon every of the equation's sides without changing the solution.

If a = b, then a/c = b/c where c is greater than zero. In other words, if two expressions are equal and subsequently multiply or divide (except for 0) the same constant by both, the two sides will remain equal.

x/2=7

x = 14

Multiplication Property of Equality is :

If a = b,

Multiply constant on both sides.

a * c = b * c

so ,

in the given sum x/2 = 7

multiplying this equation by 2 * x/2 = 7 * 2

                                                                                       = x = 14

According to the given data  the property justifies statement is: Multiplication Property of Equality.

To know more about Multiplication Property of Equality visit:

https://brainly.com/question/9070018

#SPJ4

A geometric series exist as the totality of an infinite number of terms that contain a constant ratio between consecutive terms.

The infinite geometric series 1/64 + 1/32 +1/16 + . . . . diverges.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Let the sequence be 1/64 + 1/32 + 1/16 + . . . .

a(first  term) = 1/6

r(common ratio) = a2/a1 = (1/32) / (1/64)

= (64/32) = 2

Since, | r | > 1, the infinite geometric series diverges.

To learn more about infinite geometric series, refer to:

brainly.com/question/27350852

#SPJ4