In this figure, lines a and B are intersected by Line T. Which of these statements proves that lines A and B are parallel

Given a right angle triangle

The hypotenuse of the triangle = x

The adjacent side to the angle 50 = 6

We will find x using the cosine function as follows:

Rounding to the nearest tenth

So, the answer will be x = 9.3

James used a scale factor of 4 to draw a scale representation of Triangle J and named it. Triangle K’s surface area is 10.

Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides.

Any one of a triangle’s three sides might serve as its foundation, although most frequently it is the bottom side.

Below, Triangle J is depicted. James used a scale factor of 4 to create a scale version of Triangle J that he dubbed Triangle K.

Area= 1/2 bh

=(1/2)*4*5

In such a case, K’s triangle’s area is 10.

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Note: The question is incomplete in the portal. Here is the total question,

Question: Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of  and labeled it Triangle K. What is the area of Triangle

The inicial number of jobs is 63.1 thousand, and each year this number will decrease by 1.7 thousand.

So the change from 2008 to 2018, that is, 10 years, will be:

To find the change in percentage, we need to divide the change (-17) by the inicial amount of jobs (63.1), then we have that:

So the change in this period is -27%, therefore the answer is B.

The 78th Percentile is 55.402

What is Percentile?

A Percentile (or centile) is a statistic measure that indicates the value below which a given percentage of observations in a group fall. The 20th percentile, for example, is the value (or score) below which 20% of the observations can be found.

The terms Percentile and Percentile rank are frequently used in the reporting of norm-referenced test scores. For example, a score in the 86th percentile, where 86 is the percentile rank, corresponds to a value below which 86% of the observations can be found. In contrast, a score in the 86th percentile indicates that it is at or below the value at which 86% of the observations can be found.

We know that,

μ = 50,

and σ = 7,

First, we need to find the z-score associated to this percentile.

We need to find the value [tex]Z_{p}[/tex] that solves the equation below.

[tex]Pr(Z < Z_{p}) = 0.78[/tex]

The value of [tex]Z_{p}[/tex] that solves the equation above cannot be made directly, it is solved either by looking at a standard normal distribution table or by approximation.

Based on this, we find that that the solution is [tex]Z_{p}[/tex] 0.772, because from the normal table we see that

Pr(Z<0.772)=0.78

Therefore, the percentile we are looking for is computed using the following formula:

[tex]P_{78}[/tex] = μ+ [tex]Z_{p}[/tex] × σ

= 50+0.772×7

= 55.405

Therefore, it is concluded that the corresponding 78-th percentile is found to be [tex]P_{78}[/tex] is 55.405.

​

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Let G be the cost os monthly game subscriptions, P the cost of a wekly phone bill, D = $30 the cost of a package of 42 diapers, F the cost of pizza on fridays and W the amount she receives each workday.

Then, for a initial amount I = $100, the money M she still have after the events in the text is given by:

If F + G = $65 and P = $150, we have:

If we are considering only how much she payed for the diapers and the phone bill, we have:

To convert the degree to radian use this rule

Substitute x by 489 and pi by 22/7

The answer is 8.53 radians the 3rd choice

Step 1: Name the equation

12y = 28x + 60 ....... equation 1

9y = 21x + 45 ........... equation 2

Step 2: Eliminate one of the variables (either x or y ) in the two equations

To do this,

(12y = 28x + 60) multiply by 9

=> 108y = 252x + 540 ........ equation 3

(9y = 21x + 45 ) multiply by 12

=> 108y =252x + 540....... equation 4

step 4

equate equations 3 and 4

252x + 540 = 252x + 540

step 5 :solve the equation

252 x -252x = 540

0 = 0

Hence, the Equations has no solution

option A i

Answer

First of, let us explain what congruent and supplementary mean.

Congruent angles are equal to each other.

Supplementary angles add up to give 180 degrees.

A) Alternate interior angles are congruent. Examples of alternate interior angles from the image include

- angles 3 and 6.

- angles 4 and 5.

B) Alternate exterior angles are congruent. Examples of alternate exterior angles from this image include

- angles 1 and 8.

- angles 2 and 7.

C) Same-side interior angles are supplemetary. Examples of same-side interior angles from the image include

- angles 3 and 5.

- angles 4 and 6.

D) Same-side corresponding angles are also supplementary. Examples of same-side exterior angles from the image include

- angles 1 and 7.

- angles 2 and 8.

E) Corresponding angles for two parallel lines are congruent. Examples of corresponding angles from the image include

- angles 1 and 5.

- angles 2 and 6.

- angles 3 and 7.

- angles 4 and 8.

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Using the addition rule with different signs, we know that the resultant answer will have the same sign.

A general example to help you recognize patterns:

Adding Integers:

Subtracting Integers:

Therefore, using the addition rule with different signs, we know that the resultant answer will have the same sign.

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The trigonometry expression is cos Ф = 3√5/7 , sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2

sin Ф = perpendicular(p) / hypotenuse(h)

         = 2/7

base(b) = √(h²-p²)

            =[tex]\sqrt{7^{2} - 2^{2} }[/tex]

            = √45

            = 3√5

cosФ = b/h

         = 3√5/7

sec Ф = h/b

          = 7/3√5

cosec Ф = h/ p

             = 7/2

tan Ф = p/b

          = 2/3√5

cot Ф = b/p

          =3√5/ 2

Therefore cos Ф = 3√5/7, sec Ф = 7/3√5, cosec Ф = 7/2, tan Ф = 2/3√5, cot Ф = 3√5/ 2.

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Tommie will earn $12.65 per hour after his 10% raise after 4 weeks.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Given is tommie who earns $11.50 per hour and he will get a 10% raise after working 4 weeks.

The amount tommy will earn after 10% raise can be calculated as follows-

10% of 11.50

10/100 x 11.5

1.15

Earnings per hour after raise = 11.5 + 1.15 = $12.65

Therefore, tommie will earn $12.65 per hour after his 10% raise after 4 weeks.

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The volume of a cube = Side³

The length of one edge of Julie's Jewelry box is 6 cm.

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices, and 12 edges. 

The volume of a cube = Side³

We have,

The volume of the Jewelry box = 216 cm³

The length of one edge of the box = L

The volume of a cube is given as:

V = L³

216 = L³

[ 6 x 6 x 6 = 216 ]

L = ∛216

L = ∛6³

L = 6

Thus,

The length of one edge of Julie's Jewelry box is 6 cm.

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When a line is steeper than other one it means it has a greater slope. In this case the slope represents the speed of Melinda and Paul. As shown in the picture, the line that represents Paul's movement has a greater slope than the one that represents Melinda's, it means Paul ran at a faster constant speed than Melinda.

If Melinda ran at a constant velocity of 5mph and Paul ran faster than her, an equation that could represent the relationship between Paul's distance an his time has to have a greater slope than 5, which is 7.

Answer:

5.0 km.

Step-by-step explanation:

Answer: 4.25 Km

Step-by-step explanation:

First you're going to consider the first number given as the main one to start with. (1.5 km)

The question told you that the hiker first went north so you can consider north positive, then he walked back south 0.45 km.

So far your calculation should be 1.5 - 0.45 = 1.05

Then the hiker walks again north with a distance of 3.2 km

so now add that to your value (1.05) as 1.5 and 3.2 are going to the same direction and 0.45 is only opposing them

Final calculation: 1.05 + 3.2 = 4.25 (1.5 - 0.45 + 3.2)

Another way of explaination if you didn't get this one:

The two values 1.5 and 3.2 are mentioned to be in the same direction (north), while 0.45 is mentioned to be opposing them going south, so you can either consider it as
(+)1.5 + 3.2 - 0.45  (But this one would make more sense)

        Or

- 1.5 - 3.2 + 0.45

Hope you understood and good luck with your studies :D

The line which is passing through the point on the graph (2,7) and with vertex (0,3) having equation is    [tex]x^{2}[/tex] -y +3 = 0

The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c are R and a [tex]\neq[/tex] 0,  are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).

The general equation of the quadratic equation if (h, k) is the vertex and (x, y) is a point on the curve is given by  

y = [tex]a(x-h)^{2} + k[/tex] ......eqn 1

In the situation where a must be determined at position (h, k) and (x, y)

In the above question, it is given that,

vertex is (h,k) = (0,3) and the point on the graph is (x,y) = (2,7)

Now we'll put the points in the general equation of the quadratic equation to get the desired equation

y = [tex]a(x-h)^{2} + k[/tex]

y = [tex]a(x-0)^{2}[/tex] + 3 .....eqn 1

Now putting the value of (x,y)

7 = [tex]a(2-0)^{2}[/tex] + 3

7 = 4a + 3

4a = 4

a = 1

putting the value of a in the equation 1, we get

y = [tex]1(x-0)^{2}[/tex] + 3

y = [tex]x^{2}[/tex] + 3

[tex]x^{2}[/tex] -y +3 = 0

Hence, the equation of the line passing through a point on the graph (2,7) with the vertex (0,3) is  [tex]x^{2}[/tex]  -y +3 = 0

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first term a=32805

common ration: r=10935/32805=1/3

11th term:

So the 11th term is 0.555

The expression illustrates that C. Yes, Alexandra's work is correct.

The expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The expression is given as:

= (18 + 3²) ÷ 3²

= (18 + 9) ÷ 9

= 27 ÷ 9

= 3

In this case, the work is correct.

Therefore, the correct option is C.

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Options E and F are the correct options

Here, we need to get the equation of the line that passes through the two points given

Mathematically, the equation of a line can be generally expressed as ;

y = mx + c

where m is the slope of the line and c is the y-intercept of the lien ( where it crosses the y-axis)

To get the slope m , we are goint to use the formula below;

Substituting these values into the slope equation , we have

m = (-1-(6))/(-1-(-5)) = -7/4

The equation is now in the form;

y = -7x/4 + c

what is left is to get the y-intercept

We can get the value of the y-intercept by substituting for x and y using any of the points

Let us use the second point

Here, x = -1 and y = -1

Thus;

-1 = -7(-1)/4 + c

-1 = 7/4 + c

c = -1-7/4 = -11/4

So the complete equation of the line is;

y = -7x/4 - 11/4

To properly answer the questions, we need the forms in the options that looks like or can be manipulated arithmetically to look like what we have as our answer

We proceed with each of the options one after the other to see if they can be written in the form of our answer

Option A

y - 5 = -7/4 ( x + 6)

Opening the bracket and evaluating;

y - 5 = -7x/4 - 42/4

y = -7x/4 -42/4 + 5

y = -7x/4 -22/4

we can see this is not a correct option

Option B

y - 6 = -4/7 (x + 5)

Multiply through by 7

7y - 42 = -4x - 20

7y = -4x - 20 + 42

7y = -4x + 22

divide through by 7

y = -4x/7 + 22/7

We can see this is incorrect also

Option C

y - 1 = -4/7(x-1)

Multiply through by 7

7y - 7 = -4x + 4

7y = -4x + 4 + 7

7y = -4x + 11

divide through by 7

y = -4x/7 + 11/7

This is incorrect too

Option D

y + 1 = -4/7 ( x + 1)

Multiply through by 7

7y + 7 = -4x - 4

7y = -4x -4 -7

7y = -4x - 11

y = -4x/7 - 11/7

This is incorrect also

Option E

y - 6 = -7/4 (x + 5)

Multiply through by 4

4y - 24 = -7x - 35

4y = -7x - 35 + 24

4y = -7x -11

y = -7x/4 - 11/4

This is a correct option

Option F

y + 1 = -7/4 ( x + 1)

Multiply through by 4

4y + 4 = -7x - 7

4y = -7x - 7-4

4y = -7x - 11

y = -7x/4 - 11/4

This is a correct option too

To determine which one is the graph of the equation:

We can finc the x-intercepts of the equations, we know that this happens when y=0, then we have:

Solving for x we have:

This means that the the graph have to cross the x axis in the values x=0 and x=4.

Looking at the options we notice that the only graph that do this is option B, therefore the gaprh of the equation is shown on B.

The value of the composite function (fog)(2) is equivalent to 0

A mathematical procedure called "function composition" combines two functions, f and g, to produce a third function, h, where g is the sum of f and

Given the functions below;

f(x) = x^2-3x+5

g(x) = -2x

Determine the composite function (gof)(2)

(fog) = f(g(x))

f(g(x)) = g(x^2-3x+5)

f(g(x)) = -2(x^2-3x+5)

f(g(2)) = -2(2^2-3(2)+2)

f(g(2)) = -2(0) = 0

This gives the equivalent composite value

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In the given figure we have that

AC=AD -----> by the radius of the circle

Δ ACO -------> is a right triangle

Δ ADO -------> is a right triangle

Applying the Pythagorean Theorem in both triangles

AC^2=CO^2+AO^2

AD^2=DO^2+AO^2

Remember that

AC=AD ----> radius of the circle

so

CO=DO

Δ ACO≅Δ ADO -----> by SSS

therefore

is proved that the radius that bisects the chord is a perpendicular bisector

There are basic six ratios in trigonometry that help in establishing a relationship between the ratio of sides of a right triangle with the angle. If θ is the angle in a right-angled triangle, formed between the base and hypotenuse, then

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

The value of the other three functions: cot, sec, and cosec depend on tan, cos, and sin respectively as given below.

cot θ = 1/tan θ = Base/Perpendicular

sec θ = 1/cos θ = Hypotenuse/Base

cosec θ = 1/sin θ = Hypotenuse/Perpendicular

Given:

cos x/ 1- sin x

Using Trigonometric identities

1-sin²x = cos²x

So, on rationalizing

= (cos x) /(1-sinx) x (1+sinx)/(1+sinx)

= (cos x)  (1+sinx) /(1²-sin²x)

=  (cos x)  (1+sinx) /(1-sin²x)

=  (cos x)(1+sinx)/(cos²x)

= (1+sinx)/(cos x)

=1/ cos x + sin x / cos x

=sec x + tan x

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we have

x + y = 5 -----> equation A

17x + 4y = 46 ------> equation B

Solve the system by substitution

step 1

isolate the variable x in equation A

x=5-y ------> equation C

step 2

substitute equation C in equation B

17(5-y)+4y=46

solve for y

85-17y+4y=46

17y-4y=85-46

13y=39

y=3

Find the value of x

x=5-y

x=5-3=2

Answer

Regular pay = $388

Overtime pay = $87.3

Gross pay = $388 + $87.3

= $475.3

Explanation

During the first week of January, Patricia Morgan worked 46 hours at a rate of $9.70 per hour for regular hours.

For overtime, the pay is 1.5 times the normal rate. That is, 1.5 × $9.70 = $14.55

So, working for 46 hours, that is, 40 hours regular pay rate, and 6 hours overtime pay rate.

Regular pay = 40 × $9.70 = $388

Overtime pay = 6 × $14.55 = $87.3

Gross pay = Regular pay + Overtime pay

= $388 + $87.3

= $475.3

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Answer: she does an average of -0.07

Step-by-step explanation:

add the all up which equals -0.35 divide that by how many there are which equals -0.07

How long will it take them to clean the bedroom? 10 minutes

How to calculate the time of the work done together?

Given:

Vanessa  (A)= 30 minutes

Steven (B) = 15 minutes

The total time taken if both work together is given by,

             [tex]A+B=\frac{AB}{A+B} \\\\=\frac{30*15}{30+15}\\\\=\frac{450}{45}\\\\= 10[/tex]

So, it would take 10 minutes to clean the bedroom, if they work together

What is the time - work concept ?

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