Question 21 of 25
What is the length of the x-component of the vector shown below?
8
71°
OA. 2.6
OB. 8.0
OC. 7.6
OD. 5.2

Applying the triangle midsegment theorem, the length of CD is: 8 units.

If the midpoints of two sides of a triangle are joined together by a line segment, that line segment is called the midsegment of the triangle. Every triangle has three of these.

According to the triangle midsegment theorem, the third side of a triangle is parallel to its midsegment, and also has a length that is twice of the length of the midsegment.

Given the image above, where points G, E, and F are the midpoints of the sides of the given triangle, thus:

EG is a midsegment that is parallel to a third side CD.

Therefore:

Length of CD = 2(EG)

Substitute

CD = 2(4)

CD = 8 units.

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An independent variable studied by using related samples in all conditions is called a within subjects factor.

An independent variable is defines as the variable that is modified or controlled in a scientific experiment. It reflects the rationale or cause for an outcome.

The variables that the experimenter adjusts to test their dependent variable are known as independent variables. A change in the independent variable has a direct effect on the dependent variable. The impact on the dependent variable is assessed and documented.

Examples of Independent Variables

A scientist is experimenting with the effect of light and dark on the behaviour of moths by turning on and off a light. The amount of light is the independent variable, while the moth's reaction is the dependent variable.

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Answer:

perimeter of a triangle is the total

Step-by-step explanation:

p=48cm

Length=3x

width=x

Now P= 2(L+W)

48 =2(3x+x)

48=2(4x)

48=8x

dividing both sides by 8

we have x=6

and so length=18 and width =6

on dividing the given term we get

12.2105.

A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

6. x = 28 degrees

7.  z = 1.6 cm

6.  Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

x = 56 / 2

x = 28 degrees

Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

z = 1.6 cm

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Answer:

Yes

Step-by-step explanation:

Answer:

£15 and £22

Step-by-step explanation:

let,the cost of one shirt be X and one jumper be y.Then according to question,

5x+4y=163-----(1)

also,

3x+2y=89------(2)

Now, multiplying eqn (2) by 2 and then subtracting from (1),we get

5x+4y=163

6x+4y=178

- - -

_________

-x=-15

:.x=15

Putting value of X in eqn (1),

5×15+4y=163

or,4y=163-75

or,y=88/4

:.y=22

Hence cost of one shirt is £15 and one jumper is £22.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

tan x= -3/1

So, H = √1 + 9 = √10

sin x= -3/ √10 and cos x= 1/ √10

So, sin 2x= 2 sin x cos x =2 ( -3/ √10 )(1/ √10) = -3/10

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 9/10)

                  = -8/10

and, tan 2x = sin 2x/ cos 2x =  -3/10 / ( -8/10) = 3/8

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If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.

We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.

Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:

L = 80

W = 80

The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.

The dimensions of the pen are 20 m × 40 m and the area will be 600 m².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given data in the question,

Let the length of the rectangle is x and,

Let the width of the rectangle is y.

So, the equation will be,

2x + y = 80              (1)

y = 80 - 2x              (2)

Use the formula of the area of a rectangle,

A = x × y

Substitute y = 80 - 2x in the above formula,

A = x × (80 - 2x)

= 80x - 2(x)²

= -2x² + 80x

dA/dx = -2x² + 80x

A' = -4x + 80

-4x = -80

x = 80/4

x = 20 m

Substitute x = 20 in equation (2)

y = 80 - 2(20)

y = 40 m  

So, the area should be,

A = 20 × 40

A = 600 m².

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the answer will be "all steps are correct"

The total cost of the topsoil needed to cover the layout will be

$(1.46 x 10⁻⁴)(15LB).

Given is that Joe must spread out topsoil to a depth of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and contains 10 cubic yards of topsoil.

In 10 yards³ = 466,560.1 in³

Assume the length and breadth to be [L] inches and [B] inches. The height is 15 inches.

Volume of the layout will be -

V = (15 x L x B) in³

466,560.1 in³ of the topsoil costs $67.89.

1 in³ of the topsoil will cost $(67.89/466560.1)

(15 x L x B) in³ of the topsoil will cost -

$(67.89/466560.1) x (15LB)

(1.46 x 10⁻⁴)(15LB)

Therefore, the total cost of the topsoil needed to cover the layout will be

$(1.46 x 10⁻⁴)(15LB)

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Answer:

HL

Step-by-step explanation:

to solve this we first must see what is congruent

we see that both triangles are right triangles

that means that we can use HL (hypotenuse length) to solve

we must first see if HL works though

we see that the hypotenuses are both equal

that means that we can use HL

that is your answer

The constant of proportionality of the image of actual height and height on set of the items is 20 / 11

Table

Stool

window

Bucket

Constant of proportionality are used to increase or decrease image. The situation of increment is usually called magnifying.

solving for the constant of proportionality, assuming the factor is k

height on set * k = actual height

44 * k = 80

k = 80 / 44

k = 20/11

Height on set for other items

Table

= 28 ÷ 20/11

= 15.4 inches

Stool

= 18 ÷ 20/11

=  9.9 inches

window

= 80/11 ÷ 20/11

= 4 inches

Bucket

= 40/11 ÷ 20/11

= 2 inches

The Constant of proportionality is calculated to be 20/11

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Answer:

see explanation

Step-by-step explanation:

the mistake is that a zero should be inserted to indicate the x - term

the standard form of a polynomial of degree 3 is

ax³ + bx² + cx + d

given

[tex]\frac{3m^3-2m^2-150}{m-4}[/tex]

there is no m- term in the numerator so a zero has to be inserted in its place, that is

4 | 3   - 2   0  - 150

     ↓    12   40  160

   ---------------------------

     3   10  40    10

The equation of vertical line passing through the point (4,-3) will be x = 4

And, The equation of horizontal line passing through the point (4,-3) will be y = - 3.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The horizontal and vertical lines passing through the point (4,-3).

Now,

Since, The horizontal and vertical lines passing through the point (4,-3).

Hence, The equation of vertical line passing through the point (4,-3) is the value of x.

So, We get;

The equation of vertical line is,

⇒ x = 4

And, The equation of horizontal line passing through the point (4,-3) is the value of y coordinate.

So, We get;

The equation of horizontal line is,

⇒ y = - 3

Thus, The equation of horizontal line is , y = - 3

And, The equation of vertical line is, x = 4

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The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 9 / 10

Now,

Since, The fraction is,

⇒ 9 / 10

Hence, The fraction with denominator 100 is;

⇒ 9 / 10 = 9×10 / 10×10

             = 90/100

Thus, The equivalent fraction with a denominator of 100 will be;

⇒ 90 / 100

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5 x 3²⁴  bacteria will there be after one day.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Consider what is actually happening in the question.

You begin with 5 bacteria, and after 1 hour it has tripled so you now have

5x 3=15.

Next hour, it triples again so you now have 5 x 3 x 3=45

You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴  means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).

Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:

n x 324 where n is the number of bacteria you begin with.

Since you begin with 1 bacteria, the solution is 5 x 3²⁴.

Hence 5 x 3²⁴  bacteria will there be after one day.

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Adam have 4 / 9  fraction of the 18 counters. A fraction is a number that is stated as a quotient by dividing the numerator and the denominator.

Fraction a number that is stated as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. A fractional equation is one that contains one or more terms that are fractions. The first step in solving a fractional equation is to eliminate the fractions by multiplying both sides of the equation by the LCD of each term.

Adam has 18 counters

Lesley get 10 counters

Adam have 18 - 10 = 8

8 / 18 = 4 /9

Adam have 4 /9 fraction of the counters.

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Answer

150000 after 4 years

Step-by-step explanation:

Answer: $1000 = 12x + 112

Step-by-step explanation:

let x be the amount of hours worked

It takes 11.55 years for money to double if invested at 6% compound interest.

What is compound interest?

Calculating the answer exactly:  P⁰°⁰⁶ⁿ=A .

We don’t know the initial value of the principal but we do know that the accumulated value is double (twice) the principal.

P⁰°⁰⁶ⁿ = 2P

We divide both sides by  P

e⁰°⁰⁶ⁿ = 2

Using natural logarithm:

0.06 n = ln(2)

n = ln(2)/0.06

n = 11.55 years

Hence, It takes 11.55 years for money to double if invested at 6% compound interest.

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Answer:

D. Slope is 1

Step-by-step explanation:

Start at any point on the line. Go up 1 (rise of 1). Go right 1 (run of 1). You're on the line again.

slope = rise/run = 1/1 = 1

An inequality that expresses the mean number of steps that Diego needs to walk during the last 3 days of this week to more than 70,000 steps is  32076+3x>70000.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Diego's goal is to walk more than 70,000 steps this week.

a) The mean number of steps that Diego walked during the first 4 days of this week is 8019.

So, the number of steps =4×8019

= 32076

Let x be the mean number of steps that Diego needs to walk during the last 3 days of this week to walk more than 70,000 steps.

Now, the inequality is 32076+3x>70000

b) The mean number of steps that Diego needs to walk during the last 3 days of this week is 12642

Substitute x=12642 in the inequality 32076+3x>70000, we get

32076+37926>70000

70002>70000

Yes, Diego will reach his goal of walking more than 70,000 steps this week.

Therefore, the inequality to represent the given situation is 32076+3x>70000.

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Answer: hope it helps

Step-by-step explanation:

2^6=64≡ -1 ( mod 13)

So 2^70=16*(2^6)^11=16*(-)^11(mod 13)

2^70 ≡-16 ( mod 13)

2^70 ≡10 ( mod 13)

Now 3^3=27≡1 ( mod 13)

So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)

≡ 3 ( mod 13)

Thus 2^70+3^70 ≡ 10+3 (mod 13)

≡ 0 ( mod 13)

Answer: 1058000 tickets

Step-by-step explanation:

23000 x 46 = 1058000

1058000 tickets

Answer:4.05

Step-by-step explanation: Walnut divided by 2 is 0.9 and Oak is 0.9. Maple is 0.45 and Spruce. All that is added up to 4.05