Write the statement as a conditional statement, then tell which part is the hypothesis and which is the conclusion. Write the inverse, converse, and contrapositive of your conditional statement:


People who reduce their time in the shower will save money on water.

Answers

Answer 1

Conditional Statement: If people reduce their time in the shower then they will save money on water.

Hypothesis: "If people reduce their time in the shower"

Conclusion: "they will save money on water"

What is the conditional statement?

A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).

Conditional Statement: If people reduce their time in the shower then they will save money on water.

Hypothesis: "If people reduce their time in the shower"

Conclusion: "they will save money on water"

Inverse Statement: If people did not reduce their time in the shower, then they will not save money on water.

Converse Statement: If they will save money on water then people reduce their time in the shower.

Contrapositive Statement: If they will not save money on water then people do not reduce their time in the shower.

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Related Questions


Adding: If the two values have the same sign, then?
And use the same sign.
and use the same sign

Answers

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

What is Addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.Same Sign - When adding absolute values, use the same sign for the result.Different Signs - Denote the result with the same sign as the number with the bigger absolute value after subtracting the smaller absolute value from the larger absolute value.Subtracting signs - The opposite of an integer number is added when subtracting an integer.

A general example to help you recognize patterns:

Adding Integers:

(−3)+2=−121+(−28)=−79+(−9)=0

Subtracting Integers:

−3−(−9)=−3+9=6−7−8=−7+(−8)=−15

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

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If Volume = 216 cm^3, what is the length of one edge of Julie's jewelry box?

Answers

The volume of a cube = Side³

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

What is a cube?

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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Use the vertex (0,3) and a point on the graph (2,7) to find the general form of the equation of the quadratic function.

Answers

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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Which graph represents this equation?y = 3:2 - 61ОА.+X-4No26-24-6B.24N- 2C.

Answers

To determine which one is the graph of the equation:

[tex]y=\frac{3}{2}x^2-6x[/tex]

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

[tex]\frac{3}{2}x^2-6x=0[/tex]

Solving for x we have:

[tex]\begin{gathered} \frac{3}{2}x^2-6x=0 \\ x(\frac{3}{2}x-6)=0 \\ \text{then} \\ x=0 \\ or \\ \frac{3}{2}x-6=0 \\ \frac{3}{2}x=6 \\ x=\frac{2}{3}\cdot6 \\ x=4 \end{gathered}[/tex]

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.

Assume the random variable X is normally distributed with mean μ = 50 and standard deviation o=7. Find the 78th percentile

Answers

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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The diagonal of a rectangular filed 135m long is 157m. What is the Width of the field?

Answers

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.

[tex]a^2+b^2=c^2[/tex]

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:

[tex]\begin{gathered} a^2-a^2+b^2=c^2-a^2 \\ b^2=c^2-a^2 \\ \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]

Replace the expression with c=157 and a=135

[tex]\begin{gathered} b=\sqrt[]{157^2-135^2} \\ b=\sqrt[]{24649-18225} \\ b=\sqrt[]{6424} \\ b=80.149\approx80.15 \end{gathered}[/tex]

The width of the field is 80.15 meters.

The area of the front yard for question number 1 is 60x^2 + 12x - 21 The grass area of the backyard for question number 2 is 81x^2 - 212x + 68

Answers

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.

[tex]\begin{gathered} \text{Total area= area of front yard+area of back yard} \\ =60x^2+12x-21+81x^2-212x+68 \\ =60x^2+81x^2+12x-212x-21+68 \\ =x^2(60+81)+x(12-212)-21+68 \\ =141x^2-200x+47 \end{gathered}[/tex]

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

x + y = 5 17x + 4y = 46 ) Find the solution to the system of equations. Write it as an ordered pair below.

Answers

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

thereforethe solution is the ordered pair (2,3)

Build Understanding ACTIVITY When two lines are cut by a third line, the third line is called a transversal. The intersections of the lines form eight angles, including five special types of angle pairs. When the two lines cut by a transversal are parallel, as shown, the angles in any of the special pairs will be either congruent or supplementary. 1/2 3/4 5/6 7/8 1 The term alternate means that two angles are on opposite sides of the transversal. A. Alternate interior angles are angles on opposite sides of the transversal inside the parallel lines. Measure a pair of alternate interior angles with a protractor. Name the angles you found. Are they congruent or supplementary?

Answers

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!!!

Simplify completely: cos/1−sin

Answers

What is Trigonometry?

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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what is 2×700 please tell me

Answers

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

The answer is 1,400

2x700=1,400

for the first week of January,Patricia Morgan worked 46 hours. Patricia earns $9.70 an hour. her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours. calculate the following for the first week of January ( round your responses to the nearest cent if necessary) regular pay amount, overtime pay, gross pay

Answers

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!!!

Three horse share five bales of hay equally. Five cows share eight bales of hay equally.

How much hay does each horse and each cow get?
Which animal gets more, a horse of a cow? How much more hay do they get?

Answers

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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i only need the answer THANK YOU!

Answers

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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Triangle J is shown below. James drew a scale version of Triangle J using a scale factor of 4 and labeled it Triangle K. What is the area of triangle K

Answers

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.

What are the triangle’s three main components?

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.

How big is triangle K’s surface area?

Area= 1/2 bh

=(1/2)*4*5

=10

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

How do I turn the contents of the passage into an equation?Her phone bill, the cost of diapers, and the subscriptions and pizza for her son. I guess I have to give her an amount to start with, so I’ll go with she started with $100.What if the subscriptions and pizza were 65. The diapers were 30. And her phone bill is 150. Can you show how much she paid toward the diapers and phone bill?

Answers

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:

[tex]\begin{gathered} M=(W+I)-(G+P+D+F) \\ M=(W+100)-(G+P+30+F) \\ M=W+70-G-P-F \end{gathered}[/tex]

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

[tex]\begin{gathered} M=W+70-65-150 \\ M=W-145 \end{gathered}[/tex]

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

[tex]D+P=30+150=\text{ \$}180[/tex]

Pls help I’m close finishing this assignment

A. No, Alexandra made a mistake going from the given expression to Step 1. Alexandra should have added 18 and 3 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate exponents.

B. No, Alexandra made a mistake going from Step 1 to Step 2. Alexandra should have divided 9 by 9 before adding. The order of operations says to divide before you add.

C. Yes, Alexandra's work is correct.

Answers

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

What is an expression?

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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In the diagram below, AB || DEF, AE and BD intersect at C, m2B = 43°, and mZCEF = 152°.

Answers

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:

Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at arate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this induchange from 2008 to 2018?a. 70%b. -27%C. -17%d. -75%

Answers

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:

[tex]10\cdot(-1.7)=-17[/tex]

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:

[tex]\frac{-17}{63.1}=-0.27=-27\text{\%}[/tex]

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

Answer the image below

Answers

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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A line passes through the point (4,-7) and has a slope of -6 write an equation in slope intercept form for this line

Answers

Best way to do this: point slope form

y-y1=m(x-x1)

Sub point/slope in to point slope equation

y-(-7)= -6(x-4)

Distribute and make appropriate signs

y+7=-6x+24

Rearrange into slope intercept form

**y=-6x+17**

1) Our baseball team last year had 10 boys. This year there are 15 boys. Find the percent of
change including whether it is an increase and decrease.

Answers

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.

1
Suppose Vanessa can clean her bedroom in 30
minutes. Steven can clean the same room in only
15 minutes. If they work together, how long
will it take them to clean the bedroom ?

Answers

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 ?

Time and work is concerned with the amount of time it takes a person or a group of people to complete a task and the effectiveness of the work performed by each of them. The rate of work and the amount of time required are inversely proportional. Time taken = 1 / The rate of work.

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Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.

Answers

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

Convert 489 degrees into radians.10.54 radians9 radians8.53 radians15.73 radians

Answers

To convert the degree to radian use this rule

[tex]x(radian)=\frac{x^{\circ}}{180}\times\pi[/tex]

Substitute x by 489 and pi by 22/7

[tex]\begin{gathered} x(radian)=\frac{489}{180}\times\frac{22}{7} \\ \\ x(radian)=8.53 \end{gathered}[/tex]

The answer is 8.53 radians the 3rd choice

Find the 11th term of the sequence: 32805, 10935, 3645...

Answers

first term a=32805

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

11th term:

[tex]\begin{gathered} a_{11}=32805(\frac{1}{3})^{11-1} \\ a_{11}=32805(\frac{1}{3})^{10} \\ a_{11}=32805(\frac{1}{59049}) \\ a_{11}=0.555 \end{gathered}[/tex]

So the 11th term is 0.555

What is the exact value of tan 7pi/12? Thank you!

Answers

Remember that

[tex]tan(\frac{7\pi}{12})=tan(105^o)=-tan(75^o)=-tan(45^o+30^o)[/tex]

and

[tex]tan(A+B)=\frac{tanA+tanB}{1-tanA*tanB}[/tex]

therefore

[tex]tan(45^o+30^o)=\frac{tan45^o+tan30^o}{1-tan45^o*tan30^o}[/tex]

substitute given values

[tex]tan(45^o+30^o)=\frac{1+\frac{\sqrt{3}}{3}}{1-(1)(\frac{\sqrt{3}}{3})}=\frac{\frac{3+\sqrt{3}}{3}}{\frac{3-\sqrt{3}}{3}}=\frac{3+\sqrt{3}}{3-\sqrt{3}}*\frac{3+\sqrt{3}}{3+\sqrt{3}}=\frac{9+6\sqrt{3}+3}{6}=\frac{12+6\sqrt{3}}{6}=2+\sqrt{3}[/tex]

therefore

The answer is

[tex]tan(\frac{7\pi}{12})=-(2+\sqrt{3})[/tex]

The answer is the second option

In right triangle ABC, CD¯¯¯¯¯ is the altitude to hypotenuse AB¯¯¯¯¯. If AB = 28.3¯ and DB = 12, find CD.

Answers

The side of the right triangle CD is 25.63 units

How to find side of a right triangle?

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:

opposite sidehypotenuse sideadjacent side

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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Four people ordered total bill for soup and four people ordered stew is $31 .If only 2 people had ordered soup and one person ordered stew ,the bill would have been $12.25 .How much is each order of soup and stew ?

Answers

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

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

[tex]4x+4y=31[/tex]

Also, given

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

[tex]2x+y=12.25[/tex]

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

[tex]y=12.25-2x[/tex]

Substituting,

[tex]\begin{gathered} 4x+4y=31 \\ 4x+4(12.25-2x)=31 \\ 4x+49-8x=31 \\ 49-31=8x-4x \\ 18=4x \\ x=\frac{18}{4} \\ x=4.5 \end{gathered}[/tex]

Finding y:

[tex]\begin{gathered} y=12.25-2x \\ y=12.25-2(4.5) \\ y=3.25 \end{gathered}[/tex]

Thus,

Answer:

Each order of Soup = $4.50

Each order of Stew = $3.25

12y=28x+609y=21x+45A.) no solution B.) many solutions C.) one solution

Answers

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

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