write the equation if the line that passes through (4,5) and has a slope of m=3

Answer: There are four possible solutions

Step-by-step explanation:

I was unable to manipulate this system to develop solvable equations, so I made a table consisting of 7 rows with the following 5 columns:

Table 1

[tex]\begin{array}{c|c|c|c|c}{a&b&ab&c+d&cd\\1&7&7&16&\text{null}\\2&6&12&11&\text{null}\\3&5&15&8&2,6\\4&4&16&7&3,4\\5&3&15&8&6,2\\6&2&12&11&\text{null}\\7&1&7&16&\text{null}\\\end{array}[/tex]

I used the valid solutions (rows 3 thru 5) to determine which combinations satisfied ab + cd = 28.

Table 2

[tex]\begin{array}{c|c|c|c|c}a&b&c&d&ab+cd\\3&5&2&6&6+11=17\\3&5&6&2&18+10=28^*\\4&4&3&4&12+16=28^*\\4&4&4&3&16+12=28^*\\5&3&2&6&10+18=28^*\\5&3&6&2&30+6=36\\\end{array}[/tex]

* represent the valid solutions

Answer:

The probability of choosing an A student is 58% (0.58 or 29/50)

Step-by-step explanation:

The fact that 23 students are boys and 27 are girls is irrelevant to the question so we can ignore that.

There are 50 students in all and out of these students 15 boys and 14 girls made an A.

We can first add 15+14 which equals 29. So 29 students out of 50 made in A on the exam.

29/50 equals 0.58 or 58%.

Answer:

20-30 & 40-50

Step-by-step explanation:

To find which range of scores have a frequency of 1, let's break it all down into separate ranges.

20-30: 1

30-40: 2

40-50: 1

50-60: 2

60-70: 6

70-80: 9

80-90: 13

90-100: 5

We can see in our different ranges that the range 20-30 and 40-50 have a frequency of 1.

How did we find this?

Analyze the chart and find which area shows the range, the bars are the frequencies of the different ranges.

Answer:

x=5

Step-by-step explanation:

5x-6=19

first you add 6 to both sides now you have 5x=25 then you divide by 5 on both sides then you get x=5

Question

5x-6=19 what is the variable

Answer:

Step-by-step explanation:

5x - 6 = 19

5x = 19 + 6

5x = 25

x = 25 : 5

x = 5

Answer:

Step-by-step explanation:

Answer:

1.X= 8 or 1

2.X= 3 or -1

3. X = 5/14

Step-by-step explanation:

1. Expanding your original equation (x-6)(2x-6)=20) , you get 2x^2-18x+36=20. Then, subtract 20 from both sides. You  get 2x^2-18x+16=0. Now this is a standard Quadratic equation. Use the quadratic Formula to solve this, you get   X= 8 or 1.

2. 1. Expand : x²+6x+9-8x-12=0    2. Simplify : x^2-2x-3=0  3. Solve as a quadratic equation : x= 3 or -1.

3. Same thing as the first one!

Hope I helped! <3

Answer:

Step-by-step explanation:

The given congruent triangles △QXR and △NYC mean that corresponding sides and angles are equal. Hence, line segment QX equals NY and angle Y equals angle X.

The symbols △QXR and △NYC stand for two triangles which are mentioned to be congruent. Congruency in triangles means they have the same size and shape. This implies that the corresponding sides and angles of the two triangles are equal.

a) As per the congruency of the triangles, line segment QX in triangle △QXR would be congruent to corresponding segment in triangle △NYC, which is NY. Hence, line segment QX = NY.

b) Referring to the same principle, angle Y in triangle △NYC should be equal to its corresponding angle in triangle △QXR. Considering the order of the letters in triangles, angle Y would correspond to angle X. Hence, angle Y = angle X.

Learn more about Congruent Triangles here:

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Answer:

12

Step-by-step explanation:

So the ratio is 5:2, so we can set up a proportion! So there are 12 sweaters.

Answer:

(-2,6)

Step-by-step explanation:

The solution to a system of equations is where the two graphs intersection.  By looking at the graph we can see that they cross at an x coordinate of approximately -2.4 and  at a y coordinate of just above 6.  We do not have to be too specific since we just have to be to the nearest integer.

(-2,6)

Answer:

Five thousand- four hundred and nine.

Step-by-step explanation:

Answer:

27% of her net income is her rent payment

Step-by-step explanation:

Net earnings = $740

Lisa spend $200 for rent payment

We need to find out what percent of net earning is her rent payment

Let x be the percentage

x% of net income = rent

x% * 740 = 200

[tex]\frac{x}{100} * 740 = 200[/tex]

Multiply both sides by 1004

740x = 20000

divide both sides by 740

x=27.02702703

So its approximately 27%

Answer:

t = 0.35, t = 5.65

Step-by-step explanation:

You are given h = 30t - 5t^2. Put this in standard form order (ax^2 + bx + c) by switching the two terms.

h = -5t^2 + 30t

Now you want to find all the values of t for which the rocket's height is 10 meters, so your equation will be equal to 10 instead of h, because 10 is the height you are solving for.

10 = -5t^2 + 30t

Make the entire equation equal to 0 by subtracting 10 from both sides.

0 = -5t^2 + 30t - 10

To solve this quadratic equation, the easiest way would be to use the quadratic formula: [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Identify your a, b, and c values in the standard form equation (a = -5, b = 30, c = -10) and substitute these values into the quadratic formula.[tex]\frac{-(30)\pm\sqrt{(30)^2-4(-5)(-10)} }{2(-5)} \rightarrow \frac{-30\pm\sqrt{900-200=700} }{-10} \rightarrow \frac{-30\pm\sqrt{700} }{-10}[/tex]

We have (-30 ± sqrt 700)/-10.

Use a calculator to input the two solutions and solve for them; (-30 + sqrt 700)/-10 and (-30 - sqrt 700)/-10.

[tex]\frac{-30+\sqrt{700} }{-10} = 0.35[/tex]

[tex]\frac{-30- \sqrt{700} }{-10} =5.65[/tex]

The quadratic formula is used to solve the equation h = 30t - 5t^2 when h is set to 10 meters, yielding two times at which the rocket's height is 10 meters: approximately 0.59 seconds and 3.41 seconds.

10 = 30t - 5t2

Moving all terms to one side we get:

5t2 - 30t + 10 = 0

To simplify, we divide the entire equation by 5:

t2 - 6t + 2 = 0

Now we can apply the quadratic formula:

t = √ (62 - 4*1*2) )/ (2*1)

Calculating under the square root, we get:

t = (6 √ (36 - 8) )/ 2

t = (6 ± √28) / 2

Thus, the two solutions for t are:

t = (6 + √28) / 2 and t = (6 - √28) / 2

Rounded to the nearest hundredth, the values of t are approximately 0.59 s and 3.41 s. The rocket reaches a height of 10 meters at these two instances during its flight - once when ascending and once when descending.

Answer:

The answer would be 4 more hours.

Step-by-step explanation:

Since she can make 36 cupcakes in 1 hour,

144 divided by 36 is 4, so it would take four more hours to make the rest.

Hope I helped! God bless you :-)

Answer:

Maximum (250,125) Answer

Step-by-step explanation:

This is more of a graphing problem than it is anything else.

Begin by graphing all 4 given equations.

When you do that, mark the intersection points of at least 2 lines. In this case it is exactly 2 lines for each intersecting point.

6x + 4y <= 2000 and 2x + 4y <= 1000 intersect at (250,125)

x=>0 and y=>0 intersect at (0,0)

6x + 4y <=2000 and x => 0 intersect at 333.333

2x + 4y <=1000 and y>=0 intersect at  0,250.

Any other intersection points fall outside the range of the givens. The shaded part we are interested in is sort of a very dark green/blue. It is the interior of the quadrilateral determined by the 4 vertices that are marked.

Now all you have to do is determine the maximum point using P=15x + 12y

For 0,0                 P = 15*0 + 12,0 = 0

For 0,250            P = 15*0 + 12*250 = 3000

For 333.3333,0   P = 15*333.3333 + 12*0 = 5000 rounded.

For 250,125        P = 15*250 + 12*125 = 5250  Which is the maximum

Answer (250,125) produces the maximum value Answer

To determine the maximum value of the objective function P in a linear programming problem, one must graph the constraints to find the feasible region and then use the corner-point method to evaluate P at each vertex of this region.

The problem presented is a linear programming problem where we need to find the maximum value of the objective function P, given by P = 15x + 12y, subject to certain constraints involving x and y which must both be non-negative. To solve this problem, we will graph the constraints to find the feasible region and then use the corner-point method to evaluate the objective function at each vertex of this region to determine which gives the maximum value.

Step-by-step explanation:

Given speed of Charlotte in kilometer per hour = 9 km/h

We need to find the Charlotte's speed in meter per second.

We know 1 kilometer = 1000 meter

And 1 hour = 3600 seconds.

Plugging those values of km and hour in given speed in km/h, we get

[tex]9\ \frac{km}{h} = 9\times \ \frac{1000m}{3600 seconds}[/tex]

[tex]=\frac{10m}{4s}= 2.5\ m/s[/tex].

Therefore,

Answer:

Speed of Charlotte in a Unit which includes Km and hour [tex]=9 \frac{\text{Km}}{\text{hour}}[/tex]

1 Km=1000 meter

1 hour=60 minutes=3600 seconds

Speed of Charlotte in a Unit which includes meter and second is

                     [tex]=\frac{9 \times 1000}{3600}\frac{\text{meter}}{\text{seconds}}\\\\=\frac{90}{36}\frac{\text{meter}}{\text{seconds}}\\\\=\frac{5}{2}\frac{\text{meter}}{\text{seconds}}[/tex]  

[tex]A(n)=-3+(n-1)(-2.2)=-3+(n)(-2.2)+(-1)(-2.2)\\\\A(n)=-3-2.2n+2.2=-0.8-2.2n\\\\\text{Substitute n = 1, n = 4, n = 10}:\\\\A(1)=-0.8-2.2(1)=-0.8-2.2=-3\\\\A(4)=-0.8-2.2(4)=-0.8-2.2(4)=-0.8-8.8=-9.6\\\\A(10)=-0.8-2.2(10)=-0.8-22=-22.8[/tex]

Josh needs 3 and one-eighth feet of plywood to finish building his deck. This conclusion is derived from multiplying the amount of plywood he currently has (5/8 feet) by 5.

The problem stated tells us that Josh has five-eighths of a foot of plywood and he needs five times that amount to finish building the deck. We can solve this problem by performing a simple multiplication operation. The method to solve it would be: 5/8 (amount of plywood Josh has) * 5 (amount of plywood required) = 25/8 = 3 1/8 feet. Therefore, Josh needs 3 and one-eighth feet of plywood to finish building his deck.

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Answer:

<1 =33

<2 = 147

<4 = 147

Step-by-step explanation:

Angle 1 equals angle 3 because they are vertical angles.  Vertical angles are opposite angles made by two intersecting lines.

<1 = <3

<1 = 33

Angle 2 and <3 are supplementary angles because they form a straight line.  The add to 180 degrees

<2 + <3 = 180  

<2 + 33 = 180

Subtract 33 from each side

<2 +33-33 = 180-33

<2 = 147

Angle 2 equals angle 4 because they are vertical angles

<2 = <4

<4 = 147

Answer:

12.5 hours

Step-by-step explanation:

15/6 is 2.5. 2.5 is how many hours per worker. 5 times 2.5 is 12.5 hours

Answer:

1 1/3 feet per year

Step-by-step explanation:

Steps:

1. How many months per year? 12.

2. 12 divided by 3 (number of months) =4

3. multiply 1/3 and 4.

4. Your answer is 4/3 or 1 1/3 feet per year.

The shoreline is eroding at a rate of 4/3 feet per year, which is approximately 1.33 feet per year, calculated by multiplying the 3-month erosion rate of 1/3 foot by 4.

The question is about calculating the annual rate of shoreline erosion given the erosion rate for a specific shorter period. If a shoreline is eroding at a rate of 1/3 foot per 3 months, we can find the yearly erosion rate by multiplying that rate by the number of 3-month periods in a year, which is 4 (since there are 12 months in a year).

To calculate:

Multiply the 3-month erosion rate by 4:

(1/3 foot per 3 months) x 4 (3-month periods in a year) = 4/3 feet per year

Therefore, the shoreline is eroding at a rate of 4/3 feet, or approximately 1.33 feet, per year.

It's a linear function. We need only two points to the plotting of the graph.

[tex]5x-y=5\qquad\text{subtract 5x from both sides}\\\\-y=-5x+5\qquad\text{change the signs}\\\\y=5x-5\\\\for\ x=0\to y=5(0)-5=0-5=-5\to(0,\ -5)\\\\for\ x=1\to y=5(1)-5=5-5=0\to(1,\ 0)[/tex]

Answer:

176 km/88 liters = 2 km/liter

(250 km)(1 liter/2 km) = 125 liters

Answer:

24.7619048 %

Step-by-step explanation:

The percent spent on food

food/total

520/2100

.247619048

This is in decimal form

Multiply by 100 to change it to percent

24.7619048 %

[tex]f(x)=x^2-2x;\ g(x)=6x+4\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=0\Rightarrow(x^2-2x)+(6x+4)=0\\\\x^2+(-2x+6x)+4=0\\\\x^2-4x+4=0\\\\x^2-2x-2x+4=0\\\\x(x-2)-2(x-2)+0\\\\(x-2)(x-2)=0\iff x-2=0\\\\\boxed{x=2}[/tex]

Answer: The 6th term is 45

Step-by-step explanation:

for the 6th term you would substitute 6 for n

an = 8n - 3

an = 8 * 6 - 3

an = 48 - 3

an = 45

Answer:

[tex]4\sqrt{10}[/tex]

Step-by-step explanation:

We have been given that point A has the coordinates(2,5) point B has the coordinates (6,17).

To find the length of segment AB we will use distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Upon substituting coordinates of point A and point B in distance formula we will get,

[tex]\text{Distance between point A and point B}=\sqrt{(6-2)^2+(17-5)^2}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{(4)^2+(12)^2}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{16+144}[/tex]

[tex]\text{Distance between point A and point B}=\sqrt{160}[/tex]

[tex]\text{Distance between point A and point B}=4\sqrt{10}[/tex]

Therefore, the length of segment AB is [tex]4\sqrt{10}[/tex].

Answer:

The measure of angle C is 80 degree.

Step-by-step explanation:

Given information: In ΔABC, ∠A = 40° and ∠B = 60°.

Draw the auxiliary line BD parallel to the line segment AC.

If a transversal line intersects the pair of parallel line, then the alternate interior angles are same.

The angle 1 and 2 are alternate interior angles of angle A and B respectively. Therefore angle 1 is equal to angle A and angle 2 is equal to angle C.

Angle 1,2 and B are supplementary angles because they lie on a straight line, therefore their sum is 180 degree.

[tex]\angle 1+\angle B+\angle 3=180^{\circ}[/tex]

[tex]\angle A+\angle B+\angle =180^{\circ}[/tex]

[tex]40^{\circ}+60^{\circ}+\angle C=180^{\circ}[/tex]

[tex]\angle C=180^{\circ}-100^{\circ}[/tex]

[tex]\angle C=80^{\circ}[/tex]

The angle sum property is another way to solve this problem.

According to the angle sum property, the sum of interior angles of a triangle is 180 degree.

Therefore the measure of angle C is 80 degree.

Answer:

The probability will be 2/7.

Hope this helps :D

The probability that the event will fail to occur is 7:9 .

Given that the odds against an event is 2:7 or 2/7.

The meaning of odds against an event is the ratio of the number of times the respective event does not happen compared to the number of times the event occur .

So for the given problem, it refers that for every 2 occurrences that the event does not occur there will be 7 occurrences that it will happen.  

Thus the total number of occurrences of the event is (2 + 7) = 9

This means that the event will occur definitely 2 times in every 9 times total outcome.

The probability that the event will occur is 2/9 or 2:9 .  

Therefore the probability that the event will fail to occur is 1 - 2/9 = 7/9 or 7:9 .

To learn more about concepts of probability , refer -

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[tex]6x-14=2-10x\qquad\text{add 14 to both sides}\\\\6x=16-10x\qquad\text{add 10x to both sides}\\\\16x=16\qquad\text{divide both sides by 16}\\\\\boxed{x=1}[/tex]

[tex]Check:\\\\6x-14=6(1)-14=6-14=-8\\\\2-10x=2-10(1)=2-10=-8\\\\CORRECT[/tex]

Answer:

x=1

Step-by-step explanation:

6x-14=2-10x

First step is to add 10x to each side

6x+10x-14=2-10x+10x

16x-14=2

Now add 14 to each side

16x-14+14=2+14

16x=16

Divide each side by 16 to isolate x

16x/16 =16/16

x =1