The area of a rectangle is (x^2 – 12x + 35). If the length is (x – 5), find the width. (hint: “x - 5” times “something” will give you “x^2 – 12x + 35.”)

The measure of the height of an equilateral triangle with a side length of 6 is 3√3.

We have,

In an equilateral triangle, all three sides are equal, and all three angles are also equal.

To calculate the height of an equilateral triangle, we can use the formula:

Height = (√3 / 2) x side

Given that the side length of the equilateral triangle is 6, we can substitute this value into the formula to find the height:

Height = (√3 / 2) x 6

Height = (√3) x 3

Simplifying, we have:

Height = 3√3

Therefore,

The measure of the height of an equilateral triangle with a side length of 6 is 3√3.

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The complete question.

Calculate the measure of the height of an equilateral triangle of side 6

Answer:

Let s be the number of squares and t be the number of triangles.

s + t = 17---->4s + 4t = 68

4s + 3t = 64---->4s + 3t = 64

----------------- -----------------

t = 4, s = 13

4 triangles, 13 squares

A pyramid is a solid figure with a base that is a polygon and sides that are triangles that meet at the top.

Answer: A solid figure with a base that is a polygon and sides that are triangles that meet at the top.

Step-by-step explanation: A pyramid consists of a polygonal base and sides that are triangles. A polygon is a 2D shape that only has straight lines that enclose an area.

To solve this problem, we need to first convert the distance on the map to actual distance using the map scale.

1 cm on the map represents 50,000 cm (or 500m) in actual distance.

So, 8.5 cm on the map represents 8.5 x 500m = 4,250m in actual distance.

Now, we can use the formula: time = distance ÷ speed

Here, distance = 4,250m and speed = 10km/h = 10,000m/h

So, time = 4,250m ÷ 10,000m/h = 0.425 hours

To convert hours to minutes, we can multiply by 60:

time = 0.425 x 60 = 25.5 minutes

Therefore, it will take Myra 25.5 minutes to run from the park entrance to the beach.

The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]

The row echelon form of a matrix contains the entire matrix except the last column in the format of an identity matrix, with the last column containing the solution to the system of equations represented by the matrix.

Considering the matrix, the system of equations is given as follows:

Multiplying the last equation by 2 and adding with the second equation, the value of y is obtained as follows:

-4y = -8

4y = 8

y = 2.

The value of z is given as follows:

z = 6 - y

z = 4.

The value of x is given as follows:

7x = -63 + y + 3z

7x = -63 + 2 + 14

7x = -49

x = -7.

Hence the row-echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&-7\\0&1&0&2\\0&0&1&4\end{array}\right][/tex]

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The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

Given that;

A circle is shown.

Now, We can formulate;

16|) The value of m QT is,

m QT = 2 ∠QST

         = 2 × 71

         = 142 degree

17) The value of m ∠STR is,

m ∠STR = 1/2 m ∠SXR

             = 1/2 × 46

             = 23 deg

17) Since,  ∠ RST = 90°

Then, We get;

m ∠RSQ = 90 - ∠QST

              = 90 - 71

              = 19 degree

Thus, The values of all the solutions are,

16) m QT = 142 deg

17) m ∠STR = 23 deg

18) m ∠RSQ = 19 deg

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The area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. It states that for any triangle ABC, the ratio of the length of a side to the sine of the angle opposite that side is constant, that is;

a/sinA = b/sinB = c/sinC

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.

angle m∠O = 180 - (83 + 88) {sum of interior angles of a triangle}

angle m∠O = 9°

Using the sine rule;

6.5/sin9 = ON/sin88

ON = (6.5 × sin88°)/sin9 {cross multiplication}

ON = 41.5

Area of the triangle = 1/2 × 6.5cm × 41.5cm × sin83

Area of the triangle = 133.9

Therefore, the area of the triangle ∆NOP is derived to be 133.9 square centimeter to the nearest tenth using the sine rule.

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Answer:

216 in. 3

Step-by-step explanation:

math ...

The measurement that is the same for Charles and Jermod is the median

The dot plots show the distribution of the number of minutes that Charles and Jermod spent on homework per day for three weeks. To determine which measurement is the same for both of them, we need to compare the dot plots.

Looking at the dot plots, we can see that both Charles and Jermod have a dot at 35 minutes, indicating that they both spent 35 minutes on homework on at least one day.

Therefore, the measurement that is the same for Charles and Jermod is the median, since it is the middle value of the data when arranged in order. In this case, the median is not clearly identifiable from the dot plots

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Answer: The ratio is 4:1

The interval in which both functions are positive is the one in option C.

(3, ∞)

First, when we have a graph, to identify when the function is positive we need to see when the graph of the function is above the horizontal axis.

So here we just need to see in which interval are both curves (orange one and blue one) are above the horizontal axis.

We can see that from x = 3 and above, both of the curves are above the horizontal axis, then the interval in which both functions are positive is:

(3, ∞)

So the correct option is C.

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Step-by-step explanation:

Cost of house = Birr ( 200 000    + 400 x )    where x is square meters

  for 80 m^2    cost = Birr ( 200 000 + 400(80)) = Birr  232000

The domain of the piecewise function is the set of all real numbers.

(-∞, ∞)

For a function y = f(x), we define the domain as the set of the possible inputs of the function (this is the possible values that x can take)

Here we can see the graph of a piecewise function. To find the domain, we need to look at the horizontal axis of the graph.

We can see that the function covers the whole horizontal axis, then the domain is the set of all real numbers, which means that we can write this as:

D = (-∞, ∞)

Then the correct option is the last one.

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Answer: The angle is 105 degrees

Step-by-step explanation:

In a triangle, there is 180 degrees total. To find x, we can do....

x = 180 - 41 - 34

x = 105

The temperature difference between Rome and Munich is [tex]2[/tex]°C in the first case.

a) To find the difference in temperature between Rome and Munich, we compare their respective temperatures on the bar chart. Let's assume the temperatures on the chart are represented by the heights of the bars. From the chart, the temperature in Rome is [tex]10[/tex]°C, and the temperature in Munich is [tex]8[/tex]°C.

The difference in temperature between Rome and Munich can be calculated as the absolute difference between their values:

[tex]\[ \text{Difference in temperature} = |10 - 8| = 2°C \][/tex]

Therefore, the temperature difference between Rome and Munich is [tex]2[/tex]°C.

b) If the temperature in Oslo rises by [tex]5[/tex]°C over the next [tex]6[/tex] hours, we can add this increase to the current temperature in Oslo to determine the temperature at [tex]6[/tex] pm. However, the initial temperature in Oslo is not provided in the information given.

Without the initial temperature, we cannot calculate the specific temperature at [tex]6[/tex] pm.

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1. The table of at least 4 values of the function is

x 0   -6   6  3

y  36  0  0 27

2. The domain is All set of real values and the range: y ≤ 36

3. The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)

Given that we have

y = -x² + 36

From the graph, we have the following values

x      y

0    36

-6    0

6    0

Set x  = 3

So, we have

y = -3² + 36

Evaluate

y = 27

So, we have

x      y

0    36

-6    0

6    0

3    27

From the graph, we have

These values mean that;

For the x and y intercepts of the rainbow, we have

x = (-6, 0) and (6, 0)

y = (0, 36)

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The value of x + y = 70 when 2 lines AB and CD intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.

Given that,

AB and CD 2 lines intersect each other at O. If angle ∠AOD = 120 degree, ∠BOC=3y and ∠BOD = 2x.

We have to determine the value of (x + y)​.

We know that,

In the picture we can see the two lines AB and CD intersect each other at O.

So,

From line AB a straight line has 180°.

Then ∠AOD + ∠DOB = 180°

120° + 2x = 180°

2x = 180° - 120°

2x = 60

x = [tex]\frac{60}{2}[/tex]

x = 30°

Then ∠DOB = 2x = 2(30) = 60°

And by vertically opposite angles ∠AOD = ∠COB

120° = 3y

3y = 120°

y = [tex]\frac{120}{3}[/tex]

y = 40°

Then ∠COB = 120°

So,

Now, x + y = 30 + 40 = 70

Therefore, The value of x + y = 70

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The Exponential equation is 8x = 64. the correct answer is option A: log8 64 = x.

The exponential equation is 8x = 64.

To rewrite the exponential equation in logarithmic form, we use the following format:

log base a of b = c if and only if ac = b

Here, the base is 8 and the result is 64.

So, we can rewrite the equation as:

log8 64 = x

Therefore, the correct answer is option A: log8 64 = x.

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The value of x, considering the rectangle given at the end of the answer, is given as follows:

x = 8.

From the rectangle given at the end of the answer, the bases are given as follows:

For a rectangle, the bases are congruent, meaning that they have the same measure.

Considering that the bases are congruent, the value of x is obtained as follows:

4(x - 7) = 2(10 - x)

4x - 28 = 20 - 2x

6x = 48

x = 48/6.

x = 8.

The rectangle is given by the image presented at the end of the answer.

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The probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.

Using the binomial probability formula:

P(X = 14) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials,

p is the probability of success, and

k is the number of successes.

Plugging in the given values, we have:

P(X = 14) = (19 choose 14) * 0.8^14 * (1-0.8)^(19-14)

P(X = 14) = 0.1025 (rounded to four decimal places)

Therefore, the probability of obtaining 14 successes in 19 trials with a probability of success of 0.8 is approximately 0.1025.

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Answer:

This line passes through (0, -9)

Slope = 2

y = 2x-9

Step-by-step explanation:

Slope intercept form is : y=mx+b (m = slope, b= y-intercept)

First, let's distribute the 2 to the (x-6).

y-3 = 2x-12

Second, set it into slope intercept form (y = mx+b) by adding 3 to both sides.

y = 2x-9

This will be the equation in slope intercept form.

After looking at the the slope intercept form, we know that m = the slope. So the since the 2 is in the place of m when in slope intercept form, m=2. this would mean that the slope = 2.

Y-intercept is the point when the line touches the y-axis. To find the y-intercept, x would have to equal 0. This would mean that the point would have to be (0, y). After looking at the slope intercept form, and comparing it with our equation in slope intercept form, we know that -9 is in the place of b. This would mean that b = -9. This would also mean that the y-intercept is equal to -9. Therefore, the point would be (0, -9).

Answer:

To find the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7), we first need to find the center and radius of the circle.

The center of the circle is the midpoint of the diameter, which can be found using the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.

Using (4,-7) and (-12,-7) as the endpoint coordinates, we get:

Midpoint = ((4 + (-12))/2, (-7 + (-7))/2) = (-4, -7)

So the center of the circle is (-4, -7).

The radius of the circle is half the length of the diameter, which is:

Radius = 1/2 × distance between (4,-7) and (-12,-7)

Radius = 1/2 × (4 - (-12)) = 8

So the radius of the circle is 8.

Now we can write the equation of the circle in standard form:

(x - h)² + (y - k)² = r²

Where (h,k) is the center of the circle and r is the radius.

Substituting the values we found, we get:

(x - (-4))² + (y - (-7))² = 8²

Simplifying this equation, we get:

(x + 4)² + (y + 7)² = 64

Therefore, the equation in standard form for the circle that has a diameter with endpoints (4,-7) and (-12,-7) is (x + 4)² + (y + 7)² = 64.

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Answer:

34.1

Step-by-step explanation:

In this case we have supplementary information that is not required to find the length of [tex]x[/tex].
A screenshot is provided below with the other values.

[tex]x^2-12x+36=0\\(x-6)^2=0\\x-6=0\\x=6[/tex]

Answer:

Step-by-step explanation:here it is. you did not say which grade ...

but hoping ok method .