2x + y = 3


x - 2y = -1



If equation two is multiplied by -2 and then the equations are added, the result is


3y = 5

5y = 5

-3y = 3

Answer:

55.8

Step-by-step explanation:

cos(x)=9/16

x=55.8

The angle of elevation of the ladder is approximately 60.5 degrees.

To find the angle of elevation (x) of the ladder, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house is one of the legs.

Using the tangent function:

tan(x) = opposite/adjacent

tan(x) = 16 ft / 9 ft

Now, solve for x:

x = arctan(16/9)

Using a calculator, we find

x ≈ 60.5 degrees

So, the angle of elevation of the ladder is approximately 60.5 degrees.

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Answer:

-8+2i and -8+2i

Step-by-step explanation:

here simply we'll use general formula

x= (-b +or - √ b^2-4ac)/2a

Answer:

equation 1or 2 divide

3x+y=7

2x+5y=22

or, equation 1 multiple 5

15x+5y=35

2x+5y=22

or,13x=13

therefore x=1 again

value of x put the y in equation 2

2.1 + 5y=22

5y=11

therefore y=11/5

Answer:

2.6 2.6 2.8 2.9 2.9

Step-by-step explanation:

used median for the five numbers.

Answer:

(a) [tex]f(2) = 81[/tex]

(b) [tex]g(2) = 83[/tex]

(c) Test average for maths class after test 2 is greater

Step-by-step explanation:

Given

[tex]f(x) = 0.5x + 80[/tex]

[tex]x \to g(x)[/tex]

[tex]1 \to 81[/tex]

[tex]2 \to 83[/tex]

[tex]3 \to 85[/tex]

Solving (a): f(2)

We have:

[tex]f(x) = 0.5x + 80[/tex]

[tex]f(2) = 0.5*2+80[/tex]

[tex]f(2) = 1 + 80[/tex]

[tex]f(2) = 81[/tex]

Solving (b): g(2)

From the table:

[tex]g(x) = 83[/tex] when [tex]x = 2[/tex]

So:

[tex]g(2) = 83[/tex]

Solving (c): Which is greater f(2) or g(2)

In (a) and (b),

[tex]f(2) = 81[/tex]

[tex]g(2) = 83[/tex]

Hence, test average for maths class is greater

Answer:

Step-by-step explanation:

12. To find the carpet needed. Find the area :

   The figure is combination of semi circle and a rectangle.

   So Area = Area of semi circle + Area of rectangle

      [tex]Area \ of \ semi \ circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 25 = 39.25 \ ft^2 \\\\Area \ of \ rectangle = Length \times Breadth = 15 \times 10 =150 \ ft^2[/tex]

     Area = 150 + 39.25 = 189.25 sq ft

13.   Cost per square feet = $$9.95

     Therefore cost for 189.25 square feet = 9.95 x 189.25 = $1883.04

a diameter is a line that starts from the circumference to the other part of the circumference

Answer:

They are not in the same location

Step-by-step explanation:

Well because we have x axis and y axis, x always has to go first. In (2, 5) 2 is first and has to start from the x axis and 5 is the y axis. And the (5,2) is the opposite and the places would be in totally different places on the coordinate plane.

Answer: No

Step-by-step explanation: The order of coordinates for a given point is very important. For example, (2, 5) and (5, 2) represent two very different points on a coordinate system, as shown in the picture below.

A given point, such as (2, 5), is often reffered to as

an ordered pair because the order of coordinates is very important.

9514 1404 393

Answer:

  C.  Rhombus

Step-by-step explanation:

The symmetry of the coordinates tells you the figure has equal-length sides, but the angles are not right angles. Such a figure is a rhombus.

Answer:

4equal to plus 5 eul is to be 9

Answer:

92 dB

Step-by-step explanation:

Use the mean formula, mean = sum of elements / number of elements.

Since it is a 8 hour work day, there are 8 elements.

mean = sum of elements / number of elements

mean = (98 + 98 + 98 + 98 + 98 + 82 + 82 + 82) / 8

mean = 736 / 8

mean = 92

So, the average noise level is 92 dB

Answer:

77.5% probability that this ball traveled fewer than 216 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 247 feet and a standard deviation of 41 feet.

This means that [tex]\mu = 247, \sigma = 41[/tex]

What is the probability that this ball traveled fewer than 216 feet?

The probability as a decimal is the p-value of Z when X = 216. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{216 - 247}{41}[/tex]

[tex]Z = 0.756[/tex]

[tex]Z = 0.756[/tex] has a p-value of 0.775

0.775*100% = 77.5%

77.5% probability that this ball traveled fewer than 216 feet.

Answer:

Step-by-step explanation:

divide the cost to the students.

use x

x+15= 17250

move 15 other side. which becomes negative

Answer: it is 1,150 per student

Step-by-step explanation: simple 17,250 divided by 15 = 1,150 now double check by 1,150 times 15 =17,250 so I am correct it is 1,150 per student

Answer:

A = 30 units²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = 12 and h = 5 , then

A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²

Answer:

The plumber worked 50 hours, and his assistant worked 25 hours.

Step-by-step explanation:

Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:

40 x 30 + 20 x 20 = 1200 + 400 = 1600

50 x 30 + 25 x 20 = 1500 + 500 = 2000

Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.

Answer:

Vertex: (3,16)

Axis of symmetry: x = 3

Step-by-step explanation:

The vertex is the minimum or maximum of the graph.

The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.

Answer:

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Step-by-step explanation:

Given

See attachment for question

Required

Solve

We have:

[tex]\frac{11}{12} - \frac{1}{3}[/tex]

Take LCM and solve

[tex]\frac{11}{12} - \frac{1}{3} = \frac{11 - 4}{12}[/tex]

[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]

Answer:

1

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Find the sum. Write your answer in simplest form.

Step-by-step explanation:

Answer:

4! = 24

Step-by-step explanation:

4! = 4 * 3 * 2 * 1

4! = 24

Answer:

11. (a) 3/4+1/2=5/4

   (b) 4/5= 8/10 , 16/20

12. 8 children don't like choc ice cream

Step-by-step explanation:

11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)

12. 3/5 of 20 = 12

     20-12=8

18.9% is the answer

Step-by-step explanation:

volume of a cylinder = πd²/4 x h

where d is diameter and h is height of cylinder.

thus

vol of A is

[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]

and

[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]

difference in vol of a and b is

[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]

this volume will remain empty after container A is pumped into container B.

this volume as a percentage of total volume of B is

[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]

Answer:

53 1/3

Step-by-step explanation:

200×4/5=160

160×2/3=106 2/3

106 2/3×1/2=53 1/3

Step-by-step explanation:

200×1/2=100

100×2/3=66.6666666667

so, the question is wrong

b and c will be reduced

Step-by-step explanation:

exterior angle= sum of other two angles

in the pic the sum is 152 so the exterior angle should've been 152 but it has been decreased so b and c will also decrease........

Answer:

B) this line has zero slope.

Step-by-step explanation:

it doesn't increase or decrease. it is a constant; zero

Answer:

This line has zero slope.

Step-by-step explanation:

The slope of the line doesn't change it just stays straight.

Answer:

T = k * (A/W)

Step-by-step explanation: