(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)

Answer: Hi, the answer would be 150% or in decimal form 1.5 this is an increase. There fore your answere is 1.5 which makes it an increase.

How much hay does each horse and each cow get?

(a)The hay shared by 3 horses =  5 bales

So, the hay shared by 1 horse =  x

Rewriting the statements ,

3 h = 5 b  --(1)

1 h = x    -(2)

By applying cross multiplication method to (1) and (2)

3 (x) = 5

x = 5/3

The hay shared by 1 horse =  5/3

(b)The hay shared by 5 cows =  8 bales

So, the hay shared by 1 cow =  y

Rewriting the statements ,

5 c = 8 b  --(3)

1 c = y    -(4)

By applying cross multiplication method to (3) and (4)

5 (y) = 8

x = 8/5

The hay shared by 1 cow = 8/5

Which animal gets more, a horse of a cow?

Comparing the fractions,

The hay shared by 1 horse =  5/3  = 1.7

The hay shared by 1 cow = 8/5 = 1.6

1.7 > 1.6

So,  a horse gets more than a cow

How much more hay do they get?

Considering the difference of fractions,

Amount of more hay consumed = Hay shared by a horse - hay shared by a cow.

                                                     [tex]=\frac{5}{3} -\frac{8}{5} \\\\=\frac{25-24}{15} \\\\=\frac{1}{15}[/tex]

The horse share [tex]\frac{1}{15}[/tex] more hay than cows

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Given,

The area of the front yard is 60x^2 + 12x - 21 .

The grass area of the backyard is 81x^2 - 212x + 68.

The total are is the sum of the front yard and the back yard.

So, to obtain the total area adding the area of the front yard and back yard.

Hence, the total area is 141x^2-200x+47.

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

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.

To solve this exercise let's make a sketch of the rectangular field first:

The length, width, and diagonal of the rectangular field form a right triangle, to determine the width of the rectangle you can apply the Pythagorean theorem.

This theorem states that the square of the hypotenuse is equal to the sum of the square of the legs of the triangle.

The diagonal is the hypotenuse of the triangle, the length is one of the legs "a" and the width is the other leg "b".

Write the theorem for b:

Replace the expression with c=157 and a=135

The width of the field is 80.15 meters.

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

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

Hope this Helps!!!

The value of the function f'(g(x)) is -10

What is a function?

an expression or rule or law that describes a relationship between one variable  and another variable. i.e. between independent variable and dependent variable is known as function.

We are given f(-6)=-3, f'(-6)=-5, g(2)=-6, g'(2)=2

We are asked to find F'(2) where F(x)= f(g(x))

We will use the algebra of function to solve the given problem and find the required value

We have

[tex]F(x)=f(g(x))\\F'(x)= f'(g(x))*g'(x)[/tex]

Substituting x=2 in the above equation we get

[tex]F'(2)=f'(g(2))*g'(2)\\F'(2)=f'(-6)*2\\F'(2)=-5*2\\F'(2)=-10[/tex]

Hence the value of F'(2)= -10 as asked

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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.

Hope this Helps!!!

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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The given equation is

Square both sides to cancel the square root

Subtract 5 from both sides

Divide both sides by 7

The solution is t = 44/7 OR t = 6 2/7 (mixed number)

From the picture, we have the necessary information:

The supplementary angles.

The parallels being intersected by two secant lines. And alternate interior angles are congruent under this condition.

The other angle of the triangle is then:

As a result, the angles vertical angles, therefore

< BAC = 28 (it confirms the alternate interior angle Therefore, we can write all the angles in the following drawing:

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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Let price of 1 soup be "x" and 1 stew be "y".

4 soup and 4 stew is $31, thus we can write:

Also, given

2 soup and 1 stew costs $12.25, thus we can write:

Let' solve this for y and substitute it back to Equation 1. Then we will solve for x. The process is shown below:

Substituting,

Finding y:

Thus,

Answer:

Each order of Soup = $4.50

Each order of Stew = $3.25

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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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

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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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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first term a=32805

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

11th term:

So the 11th term is 0.555

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.

2 multiply by 700 is 1400

An easier trick to multipy numbers with zeros is;

Remove the zeros first, multiply the numbers, then add back the zeros

That is;

2 x 7 = 14

Then add back the zeros

That is;

1400

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

The side of the right triangle CD is 25.63 units

A right triangle is a triangle that has one of its angles as 90 degrees.

Base on the angles, the side of a right triangle can be named as follows:

Therefore, the side CD of the right triangle can be found as follows:

using Pythagoras theorem,

c² = a² + b²

Hence,

CD = √28.3² - 12²

CD = √800.89 - 144

CD = √656.89

CD = 25.6298653918

Therefore,

CD = 25.63 units

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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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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

Remember that

and

therefore

substitute given values

therefore

The answer is

The answer is the second option

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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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: