Solve the system of linear equations by graphing.
y = x +2
y = -x -4
The solution is

1. The coordinates are: START: (0,0) END: (6,-4), 2. The perimeter of rectangle YARD is 20 units,3. The lengths of YX and YZ are 4 units and 6 units, respectively, 4. The area of Mary's room is 24 square units,

1-To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Starting from the origin, his starting point is (0,0). From there, he moves 4 units down to the point (0,-4), and then 6 units right to reach his endpoint, which is at (6,-4).

2-The rectangle has two sides of length 4 and two sides of length 6. The perimeter is the sum of the lengths of all sides, so it is equal to 2(4) + 2(6) = 8 + 12 = 20 units.

3-The coordinates of points Y, X, and Z are not given, so we cannot calculate the lengths directly. However, we know that the sides of a rectangle are perpendicular, so we can use the Pythagorean theorem to find the lengths. Let Y be the origin (0,0), and let X be the point (0, -4). Then YX has length 4 units. Similarly, let Z be the point (6, 0), so YZ has length 6 units.

4.To find the area of a rectangle, we can multiply the lengths of its sides. From problem 3, we know that the lengths of the sides are 4 and 6 units, so the area is 4 x 6 = 24 square units.

5. The sides AB and AC form a right angle.

To determine which sides of the triangle form a right angle, we need to find the slope of each side. The slope of AB is (3-8)/(6-3) = -5/3, and the slope of AC is (3-3)/(6-3) = 0. Since the product of the slopes of two perpendicular lines is -1, we can see that AB is perpendicular to AC. Therefore, sides AB and AC form a right angle.

6. Tyler walks 9 blocks in all.

To find the distance Tyler walks, we need to calculate the length of sides AB and AC. Using the distance formula, we can find that the length of AB is sqrt[(6-3)² + (3-8)²] =√[(34) units, and the length of AC is 3 units. Therefore, Tyler walks 3 + √[34 units along the two sides that form the right angle. This is approximately 9.4 blocks, so he walks 9 blocks in all.

7. The distance between two points in a coordinate plane can be found using the distance formula:

d = √[(x₂-x₁)² + (y₂-y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them. The formula is derived from the Pythagorean theorem, which relates the sides of a right triangle.

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Hi! Hope this helps, and if it does, please mark brainliest!

Answer:

y = 43 and x = 90

Step-by-step explanation:

We know that a triangle is 180 degrees (each side equals 180 since they are their own triangles) We will focus on the left triangle. Since x is a right angle, it is 90 degrees. Since there is a slash across the two sides of the main triangle, that means both sides are equal. This means that the bottom left angle, the one above b, is equal to 47 degrees. That means we know two angles out of 3. For the sake of simplicity, the bottom left angle, the one above b, is point z. So point z is 47, and x is 90, added they are 137. Subtract that from 180, you will get 43. 43 is y.

Answer:

(2, 1 )

Step-by-step explanation:

Given the 2 equations

2x - y = 3 → (1)

x + y = 3 → (2)

Rearrange (2) expressing y in terms of x by subtracting x from both sides

y = 3 - x → (3)

Substitute y = 3 - x into (1)

2x - (3 - x) = 3

2x - 3 + x = 3

3x - 3 = 3 ( add 3 to both sides )

3x = 6 ( divide both sides by 3 )

x = 2

substitute x = 2 into (3) for corresponding value of y

y = 3 - 2 = 1

Solution is (2, 1 )

The angle D in ADC  of the trapezium ABCD is 61.93 degrees.

Since ABCD is a trapezium with right angles at B and C, we can draw perpendiculars from A and D to BC:

Let h be the height of the trapezium and let E and F be the feet of the perpendiculars from A and D to BC, respectively.

The area of the trapezium is given by the formula:

A = 1/2 × (AB + DC) × h

Substituting the given values, we get:

34 = 1/2 × (5 + 12) × h

= 8.5h

h = 4

Now, we can use the Pythagorean theorem in the right triangles ABE and DCF to find the lengths of AE and DF, respectively:

AE² = AB² - BE² = 5² - h² = 25 - 16 = 9

AE = 3

DF² = DC² - CF² = 12² - h² = 144 - 16 = 128

DF = √128 = 8√2

Finally, we can use the sine rule in the triangle ADC to find angle D:

sin(D) = DF/AC

AC = AE + EC = 5 + CF

CF = DC - BC = 12 - 5 = 7

AC = 5 + 7 = 12

sin(D) = 8√2/12

D = sin⁻¹(8√2/12) = 61.93° (rounded to two decimal places)

Therefore, angle D in ADC is 61.93 degrees.

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Me ayudas por favor

:-/ es para Hoy

The solution is : D. XY,  is of the segments below is a secant.

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.

here, we have,

we know that,

A secant is a line which intersects a circle at exactly two different points and leaves a chord on joining those two points.

again, we know,

A chord is a line which which terminates on the two different points on the circle.

and, we have,

Radius is the line joining the center to any of the point on the  circle.

we know,

Tangent is a line which crosses from the outer periphery of the circle touching at any of its one point.

we get,

Thus the secant in the given diagram is clearly none other than XY.

Hence, The solution is : D. XY,  is of the segments below is a secant.

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Answer:

The minimum value is 2.5.

Step-by-step explanation:

This is a sine wave that is parallel to the x axis.  It will never go below 2.5, as shown on the graph.

The equation of the tangent line can be found by the point slope form,

y - y1 = m(x - x1)

To find an equation of a function given the tangent line, you will need to use the point-slope form of a linear equation, which is

y - y1 = m(x - x1)

where,(x1, y1) are the coordinates of the point where the tangent line touches the curve.

m is the slope of the tangent line.

Here are the steps to follow:

1) Differentiate the function to find the derivative (slope) of the curve at the point where the tangent line touches the curve.

2)Plug in the x-coordinate of the point of tangency into the derivative to find the slope of the tangent line.

3) Use the slope you found in step 2 and the coordinates of the point of tangency (x1, y1) to write the equation of the tangent line using the point-slope form.

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The common ratio of the geometric sequence is 5/2.

To find the common ratio, we need to determine the ratio between consecutive terms. Let's examine the given sequence step by step:

The first term is 6.

To get to the second term, we multiply the first term by 15/6 = 2.5.

To get to the third term, we multiply the second term by (75/2) / 15 = 2.5.

To get to the fourth term, we multiply the third term by (375/4) / (75/2) = 2.5.

We can see that each term is obtained by multiplying the previous term by 2.5. Therefore, the common ratio of the geometric sequence is 5/2.

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Their hourly wage in 9 more years is $23.60 per hour.

To find the hourly wage in 9 more years, we can use the formula for exponential growth:

A = \(P * (1 + r)^t\)

Where:

To find the annual growth rate, we can use the formula:

r = \((A/P)^(^1^/^t^)\) - 1

Substituting the given values, we get:

r = \((\$16.09 / \$6.90)^(^1^/^1^1^)\) - 1

r = 0.0883 or 8.83%

Now we can use this growth rate to find the hourly wage in 9 more years:

A = $6.90 * \((1 + 0.0883)^9\)

A = $23.60 (rounded to the nearest cent)

Therefore, the hourly wage of the automobile plant workers in 9 more years, if their wages continue to grow exponentially at the same rate, would be $23.60 per hour.

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Answer:

4

Step-by-step explanation:

they all equal to 4

4 x 12 = 48

4 x 7 = 28

4 x 11= 44

therefor its 4

The greatest common factor of 48, 28, and 44 is 4.

The greatest common factor for 42, 28, and 44 is to be determined.

Factors can be defined by splitting the value into multipliable values.

Here,
Factor of 42 = 2,4,6,7
Factor of 28 = 2,4,7
Factor for 44 = 2,4,11
So, the greatest common factor is 4

Thus, the greatest common factor of 48, 28, and 44 is 4.  

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Answer:

a ≥ -4

Step-by-step explanation:

a/2 +1 ≥ -1

Answer:

16.1%

Step-by-step explanation:

Answer:

15.0

Step-by-step explanation:

Answer:

x > 9

Step-by-step explanation:

Let's take this problem step-by-step:

Let's first set up some variables:

Let's examine the information given:

          ⇒ average child is 75 pounds

          ⇒ average adult is 150 pounds

                 ⇒ therefore: \(75c + 150a\leq 1500\)

          ⇒ therefore: \(c + a \leq 14\)

Let's graph the equations:

 \(75c+150a\leq 1500\\c+a\leq 14\)

    ⇒ look at the image attached

The point at which the two graphs intersect:

  ⇒ is the solution that represents the amount of children and adults and

      their combine weight

With the horizontal axis being the # of children and vertical axis being the # of adults:

 ⇒ the solution is 8 children and 6 adults

Answer: 8 children and 6 adults

Hope that helped!

Answer:

Total earnings = $80,425

Step-by-step explanation:

Commission = Sale Price × Commission %

Commission = $950,000 × .0275                         2.75% as a decimal is .0275

Commission = $26,125

Total earnings = Base salary + Amount of Commission

Total earnings = $54,300 + $26,125

Total earnings = $80,425

Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer:

n equals 4

Step-by-step explanation:

Answer:

D)35. Hope it hepls

Step-by-step explanation:

because 35 is between 30 and 40

We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Answer:

The position of the equipment elevator is 180 feet deep

The position of the miner's elevator is 156 feet deep

The equipment elevator is deeper.

Step-by-step explanation:

From the question,

For the equipment elevator

Velocity (v) = 4 feet/second

and for the miner's elevator,

Velocity (v) = 13 feet/second

To determine the position of each elevator, the position can be related to the distance covered.

From

Velocity = Distance / Time

Distance = Velocity × Time

Now, from the question,

The equipment elevator first descends for 33 seconds, after which the miner's elevator then start to descend both elevators descend for another 12 seconds. That is, the equipment elevator descends for a total of (33+12) seconds while the miner's elevator descends for 12 seconds.

Now, for the equipment elevator

Velocity = 4 feet/second

Time = (33 + 12 seconds) = 45 seconds

From

Distance = Velocity × Time

Distance = 4 × 45

Distance = 180 feet

The position of the equipment elevator is 180 feet deep

For the miner's elevator,

Velocity = 13 feet/second

Time = 12 seconds

Also, from

Distance = Velocity × Time

Distance = 13 × 12

Distance = 156 feet

The position of the miner's elevator is 156 feet deep

Hence, the equipment elevator is deeper.

Answer:

\( = 2x - 2 + 3x < 2 \\ 5x < 2 + 2 \\ 5x < 4 \\ x < \frac{4}{5} < 0.8 \\ 0 \: is \: answer\)

To determine the time it will take for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously, we can use the continuous compound interest formula:It will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

A = P * e^(rt),

where A is the final amount, P is the principal amount, e is the base of the natural logarithm (approximately 2.71828), r is the interest rate, and t is the time in years.

In this case, we have:

A = $17,100,

P = $10,000,

r = 5.50% = 0.055 (expressed as a decimal).

Substituting these values into the formula, we get:

$17,100 = $10,000 * e^(0.055t).

Dividing both sides of the equation by $10,000, we have:

1.71 = e^(0.055t).

To solve for t, we can take the natural logarithm (ln) of both sides:

ln(1.71) = 0.055t.

Now, divide both sides by 0.055:

t = ln(1.71) / 0.055.

Using a calculator, we find:

t ≈ 9.22 years.

Therefore, it will take approximately 9.22 years for $10,000 to grow to $17,100 when invested at 5.50% compounded continuously.

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Answer:

9=18 divided by 2

Step-by-step explanation:

Answer:

9=18÷2

Step-by-step explanation:

because 18÷2=9 youre just reversing it

Answer:

36%

Step-by-step explanation:

9÷25

Answer:

36%

Step-by-step explanation:

Good luck kiddos :)

Answer:

y = 4x - 2

y = -x + 3

Step-by-step explanation:

Answer:

1/a^2

Step-by-step explanation:

The probability that a student plays either baseball or soccer is 0.4296 (or 42.96%).This is the long answer.

Percentage of students that play baseball = 18%Percentage of students that play soccer = 32%Probability of a student playing baseball given that the student plays soccer = 22%We need to find the probability that a student plays either baseball or soccer (or both).Let the probability of a student playing baseball be P(B)Let the probability of a student playing soccer be P(S)Using the formula of conditional probability:P(B|S) = P(B ∩ S) / P(S)Where P(B ∩ S) is the probability that a student plays both baseball and soccerP(B ∩ S) = P(B) + P(S) - P(B ∪ S) (Using the formula of probability of the union of two events)Where P(B ∪ S) is the probability that a student plays either baseball or soccer or bothP(B ∪ S) = P(B) + P(S) - P(B ∩ S)Now substituting the values in the formula:P(B|S) = P(B ∩ S) / P(S) => 0.22 = P(B) + P(S) - P(B ∪ S) / 0.32

Now we need to calculate the probability that a student plays either baseball or soccer or both. Using the formula of probability of the union of two events. P(B ∪ S) = P(B) + P(S) - P(B ∩ S)We know :P(B) = 0.18P(S) = 0.32We need to calculate P(B ∩ S) which can be calculated as follows :P(B|S) = P(B ∩ S) / P(S)0.22 = P(B ∩ S) / 0.32 => P(B ∩ S) = 0.22 x 0.32 = 0.0704Now substituting the values in the formula :P(B ∪ S) = P(B) + P(S) - P(B ∩ S)P(B ∪ S) = 0.18 + 0.32 - 0.0704 = 0.4296

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Answer:

\( 41 - ( - 7) = 41 + 7 = 48\)