Which equation can be used to calculate the area of the shaded triangle in the figure below?

A rectangle with a length of 18 feet and width of 4 feet. A diagonal cuts the rectangle into two halves. One of the triangular halves is shaded.
(1 point)


2(18 + 4) = 44

fraction 1 over 2 (18 + 4) = 11

2(18 × 4) = 144

fraction 1 over 2 (18 × 4) = 36

The slope of the line that contains the points (1,-1) and (-2,8) is calculated using the change in y-values over the change in x-values, which results in a slope of -3.

To find the slope of the line that contains the points (1,-1) and (-2,8), we use the formula:

slope (m) = (Change in y) / (Change in x) = (y2 - y1) / (x2 - x1)

Substitute the given points into the formula:

m = (8 - (-1)) / (-2 - 1)
= (8 + 1) / (-2 - 1)
= 9 / (-3)
= -3

So, the slope of the line is -3.

To find the value of x for which WXYZ must be a parallelogram, set up an equation by equating the lengths of opposite sides. Solve the equation to find the value of x.

To find the value of x for which WXYZ must be a parallelogram, we first need to understand the properties of parallelograms. One important property is that opposite sides are equal in length. Given that WZ = XY, we can set up an equation: 4x + 20 = x + 26. By solving this equation, we can find the value of x.

4x + 20 = x + 26

Subtracting x from both sides, we get:

3x + 20 = 26

Subtracting 20 from both sides, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

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Answer: The answer is 34 and 17

Step-by-step explanation: 34+17= 51

and 34-17=17

Answer:

y=9

y=1

y= -7

y= -15

Step-by-step explanation:

You have to use the number in the x colum and fill in itnot te equation

y= -4x+1

Start with the first number, -2

y= -4(-2)+1          multiply -4 and -2 because of PEMDAS

y=8+1                         simplify

y=9

Now do the next number, 0

y= -4(0)+1        Multiple -4 and 0  because of PEMDAS (Anything times 0 is 0)

y=1

Now do the next number, 2

y= -4(2) + 1      Multiply -4 and 2 because of PEMDAS

y= -8 + 1       Simplify

y=-7

Now do the next number, 4

y= -4(4) +1         Multiply -4 and 4 because of Pemdas

y = -16 +1

y= -15

The maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.

In Mathematics and Geometry, the x-intercept of any function is the point at which the graph of a function crosses or touches the x-axis and the y-value or value of "y" is equal to zero (0).

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following x-intercept:

x-intercept = (200, 0)

In this context, we can logically conclude that the maximum number of half-day passes that the pool can sell and make exactly $1000 is 200 half-day passes.

Complete Question:

A city pool sells full-day and half-day passes during the summer. The goal is to make $1000 each day from pool pass sales. The graph shows the number of full-day and half-day passes they need to sell to make $1000.

What is the maximum number of half-day passes the pool can sell and make exactly $1000?

Answer:

Part A = 90

Part B = 145

Step-by-step explanation:

For part A, we know that a triangle has a sum of 180 degrees. So we just add the angles we already know and then subtract them from 180. For part B, we know that angle ACB and angle ACD are supplementary angles, meaning they add up to 180 degrees. So just take 180 and subtract 35 to find the measure of angle ACD.

Answer:

Pound of Apples = 2$

Pound of Banana = 2.75$

Step-by-step explanation:

Data

Yesterday Christopher sold 35 pounds of apples (35A) and 34 pounds of bananas (34B) for a total revenue of $163.5 (=163.50)

Today he sold 15 pounds of apples (15A) and 17 pounds of bananas (17B) for a total revenue of $76.75. (=76.75)

Now well, we have a system of the equation

35A+34B=163.50

15A+17B=76.75

we must eliminate A or B,  As you can see 34 is twice 17, so we multiply on both sides of the equation so as not to alter it

35A+34B=163.50                35A+34B=163.50                            

15A+17B=76.75 (-2) ⇒        -30A-34B=-153.50

                                              5A-0B = 10

5A=10 ⇒ A=10/5 ⇒ A=2

and B:

35(2)+34B=163.5 ⇒ 70+34B=163.5 ⇒ 34B=163.5-70

34B=93.5 = 93.5/34

B=2.75

Let x represent the price of each pound of apples and y represent the price of each pound of bananas.

Since 35 pounds of apples and 34 pounds of bananas for a total revenue of $163.50. Hence:

35x + 34y = 163.50      (1)

Also, 15 pounds of apples and 17 pounds of bananas for a total revenue of $76.75. Hence:

15x + 17y = 76.75        (2)

Solving equations 1 and 2 simultaneously gives x = 2, y = 2.75

The price of each pound of apples is $2 while price of each pound of banana is $2.75

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Answer:

r = -4/5

Step-by-step explanation:

Divide both sides by 15 so you have r

-12/15        simplify (both by 3)

-4/5

Answer: x=-9

Step-by-step explanation:

First, we want to isolate x by subtracting ten from both sides

4x=-36

Then divide by four to get:

X=-9

Answer:-6

Step-by-step explanation:

you'd want to subtract the ten and move it under the 26, adding to make a negative 36 then divide by 4 on both sides

See the figure below for a better understanding of the problem. Since we have a 45-45-90 triangle, this is an isosceles triangle, so both the adjacent and opposite sides measure the same value, say, x. Then the hypotenuse would be:

[tex]H=\sqrt{x^2+x^2} \\ \\ H=2\sqrt{2}[/tex]

Then. the ratio of the length of the hypotenuse to the length of a side is:

[tex]\boxed{r=\frac{2\sqrt{x}}{x}}[/tex]

In a 45-45-90 triangle, the ratio of the length of the hypotenuse to the length of a side is √2:1. This means that if one of the legs (the sides opposite the 45-degree angles) has a length of "x" units, then the hypotenuse (the side opposite the 90-degree angle) will have a length of "x√2" units.

A central angle has the same measure as its arc.

Answer:

0.0000052 kg

Step-by-step explanation:

Per one kilogram, there are one thousand grams. By dividing 0.0052 grams by 1000, we can find kilograms.

0.0052/1000 = 0.0000052 kg

(This could also be written as 5.2 x 10^-6 kg)

Hope this helps!

The range of a set of values is the lowest and highest number of that data set.

First, lets put the numbers from least to greatest.

138, 142, 155, 165, 172, 193

Second, find the lowest and greatest number in the data set.

138 is the lowest and 193 is the highest number in the data set.

Therefore, 138 and 193 is the range.

Best of Luck!

Chuck Mallory deposited $179.33 in currency and $358.66 in checks at an ATM. This total transaction totaled $538.00.

The question references a deposit made at an ATM. We'll analyze this transaction with the given facts.

Let's declare two variables to solve this problem. Let C represent the Currency and Ch represent the Checks. Based on the facts, we can establish the following equations:

We can solve for C by replacing Ch in the first equation with 2C from the second equation. Doing this, we get C + 2C = $538, or 3C = $538.

By dividing both sides of the equation by 3, We get C = $179.33. He deposited $179.33 in currency.

We can then find how much in checks he deposited by substituting C=$179.33 in the second equation. Ch = 2* $179.33, so Ch = $358.66. He deposited $358.66 in checks.

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Answer:

Isosceles Triangle

Step-by-step explanation:

Since, sides of triangle measures 10 cm, 10 cm & 6 cm.

Therefore, two sides of triangle have equal measurement.

Hence, it is an ISOSCELES triangle.

Problem setup:

The shape is way too complicated by itself, so I cut the shape into 5 different parts.

Please refer to the attached image or my answer will not make much sense.

Shape 1:

This is a triangle. The base is 3 and the height is 2. Thus, the area is:

[tex]A=\dfrac{1}{2}*3*2[/tex]

[tex]=3[/tex]

Shape 1 has an area of 3 square units.

Shape 2:

This shape is also a triangle. The base is 4 and the height is 2. Thus, the area is:

[tex]A=\dfrac{1}{2}*4*2[/tex]

[tex]=4[/tex]

Shape 2 has an area of 4 square units.

Shape 3:

This a unit square (the side lengths are 1).

Thus, Shape 3 has an area of 1 square unit.

Shape 4:

This shape is a rectangle. The base is 3 and the height is 4. Thus, the area is:

[tex]A=3*4[/tex]

[tex]=12[/tex]

Shape 4 has an area of 12 square units.

Shape 5:

This shape is also a rectangle. The base is 4 and the height is 2. Thus, the area is:

[tex]A=4*2[/tex]

[tex]=8[/tex]

Shape 5 has an area of 8 square units.

Total shape:

Add the areas of all 5 shapes to find the area of the shaded figure.

[tex]A=3+4+1+12+8[/tex]

[tex]=26[/tex]

The figure has a total area of 26 square units.

Side notes:

There is a way to solve this problem by only dividing this into only 3 different shapes, can you figure it out?

Let me know if you need a hint or any clarifications, thanks!

~ Padoru

Answer:

B. [tex]x\leq 8[/tex]

Step-by-step explanation:

[tex]3(x+4)\leq 36[/tex]

[tex]3x+12\leq 36[/tex]  use distributive property to multiply 3 by (x + 4)

[tex]3x+12\leq 36\\-12\leq -12\\3x\leq 24[/tex]  subtract 12 on both sides (cancel out 12)

[tex]3x\leq 24[/tex]

[tex]\frac{3x}{3} \leq \frac{24}{3}[/tex]  divide 3 on both sides (cancel out 3)

[tex]x\leq 8[/tex]

Answer:

80cm^2/s

Step-by-step explanation:

This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.

So lets consider the area of a square:

A = s^2 (where s represents the length of one side of the square)

Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:

[tex]\frac{dA}{dt} = 2s(\frac{ds}{dt})[/tex]

The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:

[tex]\frac{dA}{dt} = 16s[/tex]

Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.

25 = s^2

s = +/- 5 (since side lengths are only positive we only consider +5)

s = 5

Now we can plug this back in for s:

[tex]\frac{dA}{dt} = 80[/tex]

Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.

Answer:

Volume of the cylinder = [tex]7686.72\,inches^3[/tex]

Step-by-step explanation:

Radius(r) of the cylinder= [tex]12\,inches[/tex]

Height(h) of the cylinder= [tex]17\,inches[/tex]

Volume of a cylinder is :

                   [tex]\pi \times r^2\times h[/tex]

As,

          [tex]\pi =\dfrac{22}{7}=3.14[/tex]

Volume is:  

            [tex]=3.14\times (12\times 12)\times 17\\\\=3.14\times 144 \times 17\\\\=3.14\times 2448\\\\=7686.72\,inches^3[/tex]

The volume of the cylinder is: [tex]7686.72\,inches^3[/tex]                    

The difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.

Solution:

Length of Monarch butterfly = [tex]3\frac{1}{2}[/tex] in

Length of Bumble bee = [tex]\frac{5}{8}[/tex] in

Difference between their lengths

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

To convert mixed fraction into improper fraction.

                                    [tex]=\frac{7}{2}-\frac{5}{8}[/tex]

To make the denominator same, multiply and divide the first term by 4.

                                    [tex]=\frac{28}{8}-\frac{5}{8}[/tex]

                                   [tex]=\frac{23}{8}[/tex]

Difference between length of Monarchy and Bumble bee is [tex]\frac{23}{8}[/tex] in.

Length of Walking stick = 4 in

Length of Grasshopper = [tex]1\frac{3}{4}[/tex] in

Difference between their lengths

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

To convert mixed fraction into improper fraction.

                                    [tex]=\frac{4}{1}-\frac{7}{4}[/tex]

To make the denominator same, multiply and divide the first term by 4.

                                    [tex]=\frac{16}{4}-\frac{7}{4}[/tex]

                                   [tex]=\frac{9}{4}[/tex]

Difference between length of Walking stick and Grasshopper is [tex]\frac{9}{4}[/tex] in.

Compare: [tex]\frac{23}{8}[/tex] and [tex]\frac{9}{4}[/tex]

To compare the fractions, make the denominator same.

So multiply and divide [tex]\frac{9}{4}[/tex] by 2, we get

[tex]\frac{23}{8}[/tex] and [tex]\frac{18}{8}[/tex]

[tex]$\frac{23}{8}>\frac{18}{8}[/tex]

Hence the difference in length between a monarch butterfly and a bumblebee greater than the difference in length between a walking stick and grasshopper.

Factors of 12 : 1, 2, 3, 4, 6, 12

Factors of 20: 1, 2, 4, 5, 10, 20

In both lists of factors, 4 is in common. Therefore, the value of K is 4 because it can divide into both 12 and 20 without a remainder. 2 is also another possible value of K.

Answer:

4

Step-by-step explanation:

1*12=12   1*20=20

2*6=12   2*10=20

3*4=12   4*5=20

both have a similar multiple of 4, so k must be 4.

Answer:

7(60+3)

Step-by-step explanation:

The distributive property is a(b+c) = ab+ac

7 x 63 = (7x60) + (7x3) = 7(60+3)

So in distributive form it would be 7(60+3)

Answer:

7(1·9)

Hope this helps

Answer:

(5 x + 2) (x + 2)

Step-by-step explanation:

Factor the following:

5 x^2 + 10 x + 2 x + 4

10 x + 2 x = 12 x:

5 x^2 + 12 x + 4

Factor the quadratic 5 x^2 + 12 x + 4. The coefficient of x^2 is 5 and the constant term is 4. The product of 5 and 4 is 20. The factors of 20 which sum to 12 are 2 and 10. So 5 x^2 + 12 x + 4 = 5 x^2 + 10 x + 2 x + 4 = 2 (5 x + 2) + x (5 x + 2):

2 (5 x + 2) + x (5 x + 2)

Factor 5 x + 2 from 2 (5 x + 2) + x (5 x + 2):

Answer: (5 x + 2) (x + 2)

Answer:

95.25 calories

Step-by-step explanation:

127  x 0.25 = 31.75

127 -31.75 = 95.25

Answer:

0

Step-by-step explanation:

19z-19z=0

this is because z is always equivalent to itself, and therefore 19z is equivalent to 19z

When you subtract two numbers that are equivalent, you will always get 0

Answer:

Of two numbers, The largest whole number which is a factor of both.

Step-by-step explanation:

The diameter of the base of the tower is approximately 15m.

The height of the leaning tower = 56 m

The leaning tower is cylindrical in shape.

Suppose the diameter of the base of the tower is d

The volume of a cylinder with a diameter d and height h is [tex]\frac{\pi }{4} d^{2} h[/tex].

Given that the volume of the tower is about 9,891 cubic meters.

This means [tex]\frac{\pi }{4} d^{2} h=9891[/tex]

[tex]\frac{\pi }{4} d^{2} *56=9891[/tex]

[tex]d=15m[/tex]

Hence, the diameter of the base of the tower is approximately 15m.

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Answer:n=-1

Step-by-step explanation:n=-6+5

n=-1

Answer:

n = -1

Step-by-step explanation:

Given

n - 5 = -6

Add 5 to both sides in order to isolate the unknown

n - 5 + 5 = -6 + 5

n = -1