Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help

Answers

Answer 1

In the elimination method, we need to eliminate one of the variables using addition or subtraction.

In this case, if we add both equations, we have that:

Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.

In summary, using the elimination method, we add both equations. The result for that was a false r

Using Solving Systems Using Elimination Addition Method3x-7y=5-3x+7y=-9help

Related Questions

Martin earns $7.50 per hour proofreading ads per hour proofreading ads at a local newspaper. His weekly wage can. e found by multiplying his salary times the number of hours h he works.1. Write an equation.2. Find f(15)3. Find f (25)

Answers

If Martin earns 7.50 per hour (that is h), then the equation for his weekly wage can be expressed as;

[tex]\begin{gathered} (A)f(h)=7.5h \\ (B)f(15)=7.5(15) \\ f(15)=112.5 \\ (C)f(25)=7.5(25) \\ f(25)=187.5 \end{gathered}[/tex]

Therefore, answer number A shows the equation for his salary

Answer number 2 shows his salary at 15 hours ($112.5)

Answer number 3 shows his salary at 25 hours ($187.5)

Mrs. Williams estimates that she will spend $65 onschool supplies. She actually spends $73. What is thepercent error? Round to the nearest tenth ifnecessary.

Answers

We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.

This can be written as:

[tex]e=\frac{|p-a|}{a}\cdot100\%=\frac{|65-73|}{73}\cdot100\%=\frac{8}{73}\cdot100\%\approx11.0\%[/tex]

Answer: the percent error is approximately 11.0%

Lucky's Market purchased a new freezer for the store.When the freezer door stays open, the temperatureinside rises. The table shows how much thetemperature rises every 15 minutes. Find the unit rate.temperature (°F) =10number of minutes =15(answer) °F per minute

Answers

Notice that the information in the table can be modeled using a linear function. To find the slope (rate of change) given two points, use the formula below

[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]

Therefore, in our case,

[tex]\begin{gathered} (15,10),(30,20) \\ \Rightarrow slope=\frac{20-10}{30-15}=\frac{10}{15}=\frac{2}{3} \end{gathered}[/tex]

find x..in a right triangle ️ with a height of 10 and hypotenuse of 19

Answers

Since it is a right triangle we can apply the Pythagorean theorem:

c^2 = a^2 + b^2

Where:

c= hypotenuse (the longest side) = 19

a & b = the other 2 legs of the triangle

Replacing:

19^2 = 10^2 + x^2

Solve for x

361 = 100 + x^2

361 - 100 = x^2

261 = x^2

√261 =x

x= 16.16

Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation

Answers

For the given problem, we can observe that the image is bigger than the original diagram.

We can also observe that the image is rotated counterclockwise.

Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.

Answer: Option D

a. find a length of segment DF . use decimal rotation _______ unitsb. find the length of segment DF. use decimal rotation _______ units

Answers

[tex]\text{ Since the triangles are similar, we will use the Thales' theorem!}[/tex][tex]\begin{gathered} \text{ By thales' theorem, we have that } \\ \\ \frac{AB}{AC}=\frac{DE}{DF} \\ \frac{2}{4}=\frac{1.2}{DF} \\ \frac{DF}{4}=\frac{1.2}{2} \\ \frac{DF}{4}=0.6 \\ DF=0.6\cdot4 \\ DF=2.4 \end{gathered}[/tex][tex]\begin{gathered} \text{And again, by thales' theorem, we have} \\ \frac{AB}{BC}=\frac{DE}{EF} \\ \frac{2}{3}=\frac{1.2}{EF} \\ \frac{EF}{3}=\frac{1.2}{2} \\ \frac{EF}{3}=0.6 \\ EF=0.6\cdot3 \\ EF=1.8 \end{gathered}[/tex]

This is Calculus 1 Problem! MUST SHOW ALL THE JUSTIFICATION!!!

Answers

Given: A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 75.8 degrees.

Required: To determine how accurately the angle must be measured if the percent error in estimating the tree's height is less than 5%.

Explanation: To estimate the angle, we will use the trigonometric ratio

[tex]tanx=\frac{h}{50}\text{ ...\lparen1\rparen}[/tex]

where h is the tree's height, and x is the angle of elevation to the top of the tree.

Hence we get

[tex]\begin{gathered} h=50\cdot(tan75.8\degree) \\ h=197.59\text{ feet} \end{gathered}[/tex]

Now differentiating equation 1, we get

[tex]sec^2xdx=\frac{1}{50}dh[/tex]

We can write the above equation as:

[tex]sec^2x\cdot\frac{xdx}{x}=\frac{h}{50}\cdot\frac{dh}{h}\text{ ...\lparen2\rparen}[/tex]

Also, it is given that the error in estimating the tree's height is less than 5%.

So

[tex]\frac{dh}{h}=0.05[/tex]

Also, we need to convert the angle x in radians:

[tex]x=1.32296\text{ rad}[/tex]

Putting these values in equation (2) gives:

[tex]\frac{dx}{x}=\frac{197.59}{50}\cdot\frac{cos^2(1.32296)}{1.32296}\cdot0.05[/tex]

Solving the above equation gives:

[tex]\begin{gathered} \frac{dx}{x}=3.9518\cdot0.04548551012\cdot0.05 \\ =0.008987\text{ radians} \end{gathered}[/tex]

Let

[tex]d\theta\text{ be the error in estimating the angle.}[/tex]

Then,

[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]

Final Answer:

[tex]\lvert{d\theta}\rvert\leq0.008987\text{ radians}[/tex]

Saltarecis a maker of high-end apparel for woman. For market research one afternoon, Saltare’s sales team surveyed adult women at a busy airport on the number of blouses they own. The histogram below summarizes the data. Use the histogram to answer each of the questions

Answers

(a)

The class width of the histogram is given by the range of each bar in the histogram, that is, the upper limit minus the lower limit of a bar (plus 1, since we need to include the boundary values of the range).

Looking at the first bar, the upper limit is 19 and the lower limit is 11, therefore the class width is 9 (because there are 9 elements between 11 and 19, so we need to add 1 to the subtraction of 19 and 11)

(b)

The most frequent class is the third one (third vertical bar).

The frequency of this bar (that is, the value in the y-axis) is equal to 8.

Therefore 8 women are in this class.

(c)

The number of women with 28 or fewer blouses is given by the frequency of the first two bars.

Adding the frequency of the first bar (1) and the frequency of the second bar (5), we have that 6 women have 28 or fewer blouses.

hello, while doing the question please don't put A decimal Answer ( ex: 1.5) because my teacher told me that's incorrect, you can add or subtract depending on the question, or check if you need to simplify! Thank you:)

Answers

Notice that the unit segment is divided in 8 parts. Then, each mark is equal to 1/8.

The kitten that weighs the most is placed over the 5ft mark. Then, its weight is:

[tex]\frac{5}{8}[/tex]

The kitten that weighs the least is placed over the third mark. Then, its weight is:

[tex]\frac{3}{8}[/tex]

Substract 3/8 from 5/8 to find the difference on their weights:

[tex]\frac{5}{8}-\frac{3}{8}[/tex]

Since both fractions have the same denominator, we can substract their numerators:

[tex]\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}=\frac{2}{8}=\frac{2/2}{8/2}=\frac{1}{4}[/tex]

Therefore, the difference in pounds between the heaviest and the lightest kittens, is:

[tex]\frac{1}{4}[/tex]

Write an equation of a circle with diameter AB.A(1,1), B(11,11)Choose the correct answer below.A. (X-6)2 + (y-6)2 = 11C. (x-6)2 – (y+6)2 = 50E. (X+6)2 + (y-6)2 = 50G. (X+6)2 – (y + 6)2 = 50

Answers

The question asks us to find the equation of a circle with diameter AB with coordinates:

A = (1, 1), B = (11, 11)

In order to solve this, we need to know the general form of the equation of a circle.

The general form of the equation of a circle is given by:

[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ \text{where,} \\ (a,b)=\text{ coordinates of the center of the circle} \\ r=\text{radius of the circle} \end{gathered}[/tex]

We have been given the coordinates of the diameter. This means that finding the midpoint of the diameter

will give us the center coordinates of the circle, which is (a, b).

The formula for finding the midpoint of a line is given below:

[tex]\begin{gathered} (x,y)=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ \text{where,} \\ x_2,y_2=\text{ second coordinate} \\ x_1,y_1=\text{first coordinate} \end{gathered}[/tex]

For better understanding, a sketch is made below:

Therefore, let us find the coordinates of the center of the circle using the midpoint formula given above:

[tex]\begin{gathered} a,b=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2} \\ x_2=11,y_2=11 \\ x_1=1,y_1=1 \\ \\ \therefore(a,b)=\frac{11+1}{2},\frac{11+1}{2} \\ \\ (a,b)=6,6 \\ Thus, \\ a=6,b=6 \end{gathered}[/tex]

Now that we have the coordinates of the center, we now need to find the value of the radius of the circle.

This is done by finding the length from the center of the circle to any side of the diameter.

Let us use from point (6,6) which is the center to the point (11, 11) which is one side of the diameter.

The formula for finding the distance between two points is given by:

[tex]\begin{gathered} |\text{distance}|^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ \text{where,} \\ x_2,y_2=\text{second point} \\ x_1,y_1=\text{first point} \end{gathered}[/tex]

hence, we can now find the square of the radius as:

[tex]\begin{gathered} r^2=(y_2-y^{}_1)^2+(x_2-x_1)^2_{} \\ x_2,y_2=11,11_{} \\ x_1,y_1=6,6 \\ \\ \therefore r^2=(11-6)^2+(11-6)^2 \\ r^2=5^2+5^2 \\ r^2=25+25 \\ \therefore r^2=50 \end{gathered}[/tex]

Now that we have the radius, we can now compute the equation of the circle as:

[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2 \\ a=6,b=6,r^2=50 \\ \\ \therefore(x-6)^2+(y-6)^2=50\text{ (Option B)} \end{gathered}[/tex]

A graph of the circle is given below:

What is 9207 /10 equivalent to?

Answers

Answer:

9207/10 is equivalent to 920.7

Simplify the following equations in ax^2+bx+c=0 or ay^2+c=0 2x+y=6 4x^2+5y+y+1=0

Answers

Given the equation;

[tex]4x^2+5y^2+y+1=0[/tex]

We shall begin by Subtracting 5y^2 + y from both sides;

[tex]\begin{gathered} 4x^2+5y^2+y+1-5y^2-y=0-5y^2-y \\ 4x^2+1=-5y^2-y \\ \text{Factor out -1 from the right hand side;} \\ 4x^2+1=-1(5y^2+y) \end{gathered}[/tex]

Next step we subtract 1 from both sides;

[tex]\begin{gathered} 4x^2+1-1=-1(5y^2+y)-1 \\ 4x^2=-(5y^2+y)-1 \\ \end{gathered}[/tex]

Next step we take the square root of both sides;

[tex]\begin{gathered} \sqrt[]{4x^2}=\pm\sqrt[]{-(5y^2+y)-1} \\ 2x=\pm\sqrt[]{-(5y^2+y)-1} \end{gathered}[/tex]

We can now open the parenthesis on the right hand side;

[tex]\begin{gathered} 2x=\pm\sqrt[]{-5y^2-y-1} \\ \text{Divide both sides by 2;} \\ x=\frac{\pm\sqrt[]{-5y^2-y-1}}{2} \end{gathered}[/tex][tex]undefined[/tex]

the first yr a community college offered a Certificate in data management , 12 people earned the certificate. the next year 17 people earned the certificate. what was the percent increase in the # of people earning the certificate?

Answers

we make an expression

[tex]12\times x=17[/tex]

we know that if we multiply to twelve by the ratio of increase we will obtain 17

now solve for x that is the ratio

[tex]x=\frac{17}{12}=1.42[/tex]

multiply by 100 to obtain a percentage

[tex]1.42\times100=142[/tex]

the percentage is 142%

Find the volume of a cone with a height of 8 m and a base diameter of 12 mUse the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit in your answer.

Answers

The volume V of a cone with radius r and height h is:

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

And the radius is half the diameter. Since this cone has a diameter of 12 m, the radius is:

[tex]r=\frac{12m}{2}=6m[/tex]

And the height is 8m. Thus, the volume V is:

[tex]\begin{gathered} V=\frac{1}{3}\pi(6m)^28m \\ \\ V=\frac{\pi}{3}(36m^2)8m \\ \\ V=\frac{\pi}{3}(288)(m^2\cdot m) \\ \\ V=\pi\cdot\frac{288}{3}m^3 \\ \\ V=96\pi m^{3} \end{gathered}[/tex]

Now, using 3.14 for π, we obtain:

[tex]\begin{gathered} V=96\cdot3.14m^3 \\ \\ V=301.44m^{3} \end{gathered}[/tex]

Therefore, the volume of that cone is 301.44m³.

A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00.? (The new function is shown by the dotted line.)

Answers

Given the function with a graph that shows the cost of belonging to the club as a function of CDs purchased

linear function with the form

[tex]y=x[/tex]

since the new graph has a new cd cost up by $1.00

then the new line is

Correct answer

Option C

how do I find the perimeter of a quadrilateral on a graph?

Answers

The perimeter of a figure is always the sum of the lengths of the sides.

If we have the coordinates of the vertices of the quadrilateral, we can calculate the length of each side as the distance between the vertices.

For example, the length of a side AB will be the distance between the points A and B:

[tex]d=\sqrt[]{(x_b-x_a)^2+\mleft(y_b-y_a\mright)^2}[/tex]

Adding the length of the four sides will give the perimeter of the quadrilateral.

Writing a equation of a circle centers at the origin

Answers

ANSWER

[tex]x^2+y^2=100[/tex]

EXPLANATION

The general equation of a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where (h, k) = the center of the circle

r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)

The center of the circle is the origin, that is:

[tex](h,k)=(0,0)[/tex]

To find the radius, apply the formula for distance between two points:

[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]

where (x1, y1) is the point the circle passes through

Hence, the radius is:

[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]

Hence, the equation of the circle is:

[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]

Find the length of the segment indicated. Round to the nearest tenth if necessary. Note: One segment of each triangle is a tangent line

Answers

Given

A circle with a tangent drawn to it forming one side of a triangle

Required

we need to find the diameter of the circle

Explanation

clearly it is a right angled triangle as radius through point of contact is perpendicular to the tangent. let the lenght of missing side be d

Therefore

[tex]d^2+12^2=20^2[/tex]

or

[tex]d^2=400-144[/tex]

or

[tex]d^2=256[/tex]

or d=16

Maya bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $400 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 7.5 % per year and for the laptop it was 8% per year. The total finance charges for one year were $371. How much did each computer cost before finance charges? Desktop: $Laptop: $

Answers

1. Let D be price of desktop

let L be price of a Laptop

• we know that the laptop cost $400 less than the desktop

L = D -400

• for desktop D, Maya paid interest of 7.5% per year: 7.5/100 = 0.075

,

• For Laptop L , Maya paid interest of 8 % per year : 8/100 = 0.08

,

• We know that total charges for finance was $ 371,

therefore :

0.075 D + 0.08L = 371, (remember from the above , L = D-400 , lets substitute this value for L)

0.075 D + 0.08( D-400) = 371

0.075D + 0.08 D -32 = 371

0.155D = (371 +32)=403

D = 403/0.0155

D = $26 000

and L = D-400

= 26000-400

= $25600

• This means that Desktopcost $26000 and Laptop cost $25600,

Identify the key features of the graph, including the x - intercepts. Y-intercept, axis of symmetry, and vertex. (3)

Answers

The graph of the given finction is:

Here, the x-intercept is at -1 and -6

The y-intercept is at 6

The axis of symmetry is x=-3.5

The vertex is (-3.5,-6.2)

If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.

Answers

Radius of the circle : Radius is the distance from the center outwards.

With the help of radius we can determine the following terms:

1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :

[tex]\text{ Diameter= 2}\times Radius[/tex]

2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:

[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]

3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:

[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]

4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :

[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]

5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :

[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]

In the given figure the radius is AO & BO

Question 10 of 11 Step 1 of 1CorrectThcorrectOne group (A) contains 390 people. Three fifths of the people in group A will be selected to win $100 fuel cards. There is another group (B) in a nearby town that willreceive the same number of fuel cards, but there are 553 people in that group. What will be the ratio of nonwinners in group Ato nonwinners in group B after theselections are made? Express your ratio as a fraction or with a colon.AnswerkeypadRestore Your Guth2019 Hawkes Learning

Answers

Given : Two groups

Group A: contains 390 people.

Three fifths of the people in group A will be selected to win $100 fuel cards.

So, the number of people who will win = 3/5 * 390 = 234

Group B : contains 553 people

the group will receive the same number of fuel cards

so, the group will receive 234 cards

The non-winners of group A = 390 - 234 = 156

The non-winners of group B = 553 - 234 = 319

The ratio between them = 156 : 319

Which of the following expressions is equivalent to 2^4x − 5? the quantity 8 to the power of x end quantity over 10 the quantity 4 to the power of x end quantity over 5 the quantity 16 to the power of x end quantity over 32 the quantity 1 to the power of x end quantity over 32

Answers

The equivalent expression for the given exponent equation is 16^x/32

Given,

The exponent equation; 2^4x - 5

We have to find the expressions which is equivalent to 2^4x - 5

Exponential equations are inverse of logarithmic equations.

This can also be expressed as;

2^(4x-5) = 2^4x/2^5

2^4x-5 =16^x/2^5

2^4x-4 = 16^x/32

Hence the equivalent expression is 16^x/32

Learn more about equivalent expressions here;

https://brainly.com/question/28292075

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Answer:it's not 4^x/5

Step-by-step explanation:

F(x) = -3x,x<0 4,x=0 x^2, x>0 given the piece wide functions shown below select all of the statements that are true

Answers

The correct statements regarding the numeric values of the piece-wise function are given as follows:

B. f(3) = 9.

D. f(2) = 4.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

A piece-wise function means that the definition of the input is different based on the input of the function. In this problem, all the numeric values we are calculating are for positive numbers, hence the definition of the function is given by:

f(x) = x².

Then the numeric values of the function are given as follows:

f(1) = 1² = 1.f(2) = 2² = 4.f(3) = 3² = 9.f(4) = 4² = 16.

Meaning that options B and D are correct.

Missing information

The options are given by the image at the end of the answer.

Learn more about the numeric values of a function at brainly.com/question/28367050

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I need help figuring out if what I got is rigjt

Answers

The figure in the picture shows 3 squares that form a right triangle. Each side of the triangle is determined by one side of the squares.

The only information we know is the area of two of the squares. The area of a square is calculated as the square of one of its sides

[tex]A=a^2[/tex]

So to determine the side lengths of the squares, we can calculate the square root of the given areas:

[tex]\begin{gathered} A=a^2 \\ a=\sqrt[]{A} \end{gathered}[/tex]

For one of the squares, the area is 64m², you can determine the side length as follows:

[tex]\begin{gathered} a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]

For the square with an area 225m², the side length can be calculated as follows:

[tex]\begin{gathered} a=\sqrt[]{225} \\ a=15 \end{gathered}[/tex]

Now, to determine the third side of the triangle, we have to apply the Pythagorean theorem. This theorem states that the square of the hypothenuse (c) of a right triangle is equal to the sum of the squares of its sides (a and b), it can be expressed as follows:

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

If we know two sides of the triangle, we can determine the length of the third one. In this case, the missing side is the hypothenuse (c), to calculate it you have to add the squares of the sides and then apply the square root:

[tex]\begin{gathered} c^2=225+64 \\ c=\sqrt[]{225+64} \\ c=\sqrt[]{289} \\ c=17 \end{gathered}[/tex]

So the triangle's sides have the following lengths: 8, 15 and, 17

Now that we know the side lengths we can calculate the perimeter of the triangle. The perimeter of any shape is calculated by adding its sides:

[tex]\begin{gathered} P=8+15+17 \\ P=40m \end{gathered}[/tex]

yes you did get it right

In the picture below, angle 2 = 130 degrees, what is the measurement of angle 8?

Answers

Answer:

130°

Step-by-step explanation:

Alternate interior angles are equal in measure.

20. Write the slope-intercept form of the line described in the followingPerpendicular to -2+3y=-15and passing through (2, -8)

Answers

The equation of a line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Solve for "y" from the equation given in the exercise in order to write it in Slope-Intercept form:

[tex]\begin{gathered} -2+3y=-15 \\ 3y=-15+2 \\ y=-\frac{13}{2} \end{gathered}[/tex]

You can notice that the equation has this form:

[tex]y=b[/tex]

Where "b" is the y-intercept.

Then, it's a horizontal line, which means that its slope is:

[tex]m=0[/tex]

Since it is a horizontal line, the lines perpendicular to that line is a vertical line, whose slope is undefined and whose equation is:

[tex]x=k[/tex]

Where "k" is the x-intercept.

Knowing that the x-coordinate of any point on a vertical line is always the same, and knowing that this line passes through this point:

[tex]\mleft(2,-8\mright)[/tex]

You can determine that the equation of the line is:

[tex]x=2[/tex]

points E,D and H are the midpoints of the sides of TUV, UV=100,TV=126,and HD=100, find HE.

Answers

Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:

[tex]\begin{gathered} \frac{VD}{VU}=\frac{HD}{TU} \\ \end{gathered}[/tex]

Since D is the midpoint of VU, VD=50

[tex]\begin{gathered} \frac{50}{100}=\frac{100}{TU} \\ 50\times TU=100\times100 \\ TU=200 \end{gathered}[/tex]

then

[tex]\begin{gathered} \frac{HE}{UV}=\frac{HD}{TU} \\ \frac{HE}{100}=\frac{100}{200} \\ HE=\frac{100}{200}\times100 \\ HE=50 \end{gathered}[/tex]

A diesel train left Abuja and traveled west. One hour later a freight train left traveling 50 mph faster in an effort to catch up to it. After three hours of freight train finally caught up. Find the diesel train’s average speed.

Answers

The speed at which diesel train was moving is = 150mph

In the above question, it is given that,

Let the speed of the diesel train which left Abuja be x mph

then, speed of freight train which is moving 50 mph faster than diesel train = (50 + x)mph

Further, the freight train finally caught up the diesel train after three hours

So time taken by freight train = 3 hours

While time taken by diesel train would 1 hour more than freight train as its moving slower = 3 + 1 = 4 hours

Now, it is given that both the trains finally catch up, it means the distance travelled by both the trains would be equal

We know that,

Speed = [tex]\frac{Distance}{Time}[/tex]

Distance = Speed x Time

Distance travelled by Diesel train = distance travelled by Freight train

4x = 3(50 + x)

4x = 150 + 3x

x = 150 mph

Hence, the speed at which diesel train was moving is = 150mph

While, the speed at which freight train was moving is = (150 + x)mph = (150 + 50)= 200mph

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What is 120 percent of 118?

Answers

120 percent of 118 is expressed mathematically as;

120% of 118

120/100 * 118

= 12/10 * 118

= 6/5 * 118

= 708/5

= 141.6%

Hence 120 percent of 118 is 141.6%

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