Look at pic for directions and the triangle


9) What is the area of the triangle?

10) what is the area of the rectangular shaded (lavender) area that lies behind the triangle

11) explain how to find the area of the triangle without using a formula

We could calculate the weight of individual balloons from given density and empty mass. From that calculate the total weight of balloons and added to the weight of fixings. So the weight of archway becomes 111.33g.

Volume of helium each balloon is holding = 1.2L

Density of helium = 0.1785

Density = mass/volume

Mass = density/volume

So mass of helium in each balloon = 1.2×0.1785 = 0.2142 g =  214.2 mg

Mass of empty balloon = 27 mg

So the total mass of a balloon after filled with helium = 214.2 + 27 = 241.2 mg

Mass of 275 such balloons = Mass of 1 balloon × 275

                                             = 241.2 ×275 = 66330 mg = 66.33 g

Mass of all strings and fixings = 45 g

Total mass of archway = mass of 275 balloons + mass of fixings and strings = 66.33 + 45 = 111.33 g

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Probability that the event can happen = 1/2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Given,

Total outcomes of event = 14

Outcomes, event can happen = 7

Probability

= Favorable Outcomes/Total Outcomes

= 7/14 = 1/2

Hence, 1/2 is Probability that the event occurs.

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Answer:

0.43 cup of water

Step-by-step explanation:

We know

For every 1 1/8 cups of water, she uses 2 5/8 of flour.

1 1/8 = 9/8 = 1.125

2 5/8 = 21/8 = 2.625

How much water does Cindy need for each cup of flour?

1.125 divided by 2.625 = 0.43 cup of water

So, Cindy needs 0.43 cup of eater for each cup of flour

The musical frequency of notes is decreasing between beat number 6 and 7.

Beats refer to the periodic variations in the loudness of a sound resulting from the interference between two waves of slightly different frequencies. When two waves of different frequencies overlap, they create an interference pattern that results in a waveform that varies in amplitude (loudness) over time. The resulting pattern of loud and soft sounds is known as beats.

The musical note frequency is in the given question is measured in Hz and it started decreasing from a frequency of 444 Hz to frequency of 392 Hz.

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Correlation is to "measurement of variables", as experimentation is to "manipulation of variables".

Correlation refers to the statistical relationship between two or more variables, where changes in one variable are related to changes in the other variable(s). It measures the strength and direction of the relationship, but it does not establish cause and effect.

Experimentation, on the other hand, involves the manipulation of variables to determine the cause-and-effect relationship between variables. The experimenter changes the independent variable and measures the effect it has on the dependent variable.

This method allows the experimenter to establish cause and effect and to control extraneous variables that might interfere with the relationship between the independent and dependent variables.

Therefore, the correct answer is D.

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--The given question is incomplete; the complete question is

"Correlation is to___as experimentation is to___.

A. manipulation of variables; measurement of variables

B. unobtrusiveness: correlation

C. single variables; multiple variables

D. measurement of variables; manipulation of variables"--

To use the linear combination method to solve the system of equations:

2x – 3y = 13

3x + y = -8

We can multiply the second equation by 3 to get:

9x + 3y = -24

Now we can add this equation to the first equation to eliminate the y term:

2x – 3y + 9x + 3y = 13 - 24

Simplifying the left-hand side and the right-hand side of the equation:

11x = -11

Finally, we can solve for x:

x = -1

Substitute x = -1 in either of the original equations:

2x – 3y = 13

2(-1) - 3y = 13

-2 - 3y = 13

-3y = 15

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Explanation: We used the linear combination method to eliminate one of the variables by adding the two equations together. Then, we solved for the remaining variable and substituted the value back into one of the original equations to solve for the other variable.

Answer:

3404.9(1dp)

Step-by-step explanation:

The volume of the cylinder is 162πx, the volume of the cone (1/3)πx^3 and the volume of the hemisphere is (162πx + (1/3)πx^3)/2

Volume of the cylinder:

The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height of the cylinder.

In this case, the height of the cylinder is equal to the diameter of the paperweight hemisphere, which is twice the radius of the cone.

Let's call the radius of the cone "x". The diameter of the paperweight hemisphere is equal to 2x, so the height of the cylinder is equal to 2x. The radius of the cylinder is 9 cm, so we can calculate the volume of the cylinder as follows:

V = πr^2h = π * 9^2 * 2x = 162πx

Volume of the cone:

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone. In this case, the height of the cone is equal to the radius of the cone, so we can calculate the volume of the cone as follows:

V = (1/3)πr^2h = (1/3)π * x^2 * x = (1/3)πx^3

Volume of the hemisphere:

The volume of a hemisphere can be calculated using the formula V = (2/3)πr^3, where r is the radius of the hemisphere. To estimate the volume of the hemisphere, we can calculate the average of the volumes of the cylinder and cone.

V_hemisphere = (V_cylinder + V_cone)/2 = (162πx + (1/3)πx^3)/2

This expression represents the estimated volume of the hemisphere in terms of x, the radius of the cone.

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Noah, Preston, and Zach work for 26 hours, 24 hours and 44 hours respectively

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

Let N, P and Z represent the number of hours Noah, Preston, and Zach work respectively. Thus, we can write:

N = P + 2  ---- (1)

Z = 2P - 4  ---- (2)

N + P + Z = 94  ---- (3)

Put (1) and (2) in (3):

N + P + Z = 94

P+2 + P + 2P-4 = 94

4P -2 = 94

4P = 94 + 2

4P = 96

P = 96/4

P = 24

Since N = P + 2,

N = 24 + 2 = 26

Since Z = 2P - 4,

Z = 2(24) - 4 = 44

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The values in the parallelogram figure are as follows

angle B = 74 degrees

x = 4

angle BCA = 49 degrees

Remembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees

The property that the two opposite sides of parallelogram is used to find x

4x = 16

x = 4

Applying alternate interior angles postulate, we can see that

angle BCA = angle DAC = 49 degrees

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Answer:

y = -2x + 7

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals.

That means that their product is -1.

If the slope of a line is m, then a perpendicular line has slope -1/m.

Given line slope: 1/2

Perpendicular slope: -2

Perpendicular line:

y = -2x + b

Point on new line: (0, 7)

7 = -2(0) + b

b = 7

Perpendicular line:

y = -2x + 7

Perpendicular lines have slopes that are negative reciprocals of each other.

We're given:

First, we must find the slope.

The y-intercept occurs when x=0. Therefore, given the point (0,7), we know that the y-intercept is 7:

[tex]y=-2x+7[/tex]

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

Use the simple formula "a / b" to create a group of linked variables "a" and "b," where "b" may also be higher than zero. One ratio is created by combining two equation ratios. If there were only one man and three ladies, the ratio would be 1:1. There are 1/4 males and 3/4 girls in the group. A division between two or more objects, a number, or even a portion of a component's volume are all examples of parts.

Here,

Ratio 1: AB:BC = 2:1

Let's use the midpoint formula to find the coordinates of point C, which is the midpoint of line segment AB:

C = ((5+x)/2, (0+y)/2) = ((5+x)/2, y/2)

Since AB:BC = 2:1, we know that the distance from A to B is twice the distance from B to C. Using the distance formula, we can write:

2 * BC = AB

2 * √((x+1)² + y²) = √((x-5)^2 + y^2)

Simplifying this equation, we get:

4 * (x+1)² + 4y² = x² - 10x + 25 + y²

Simplifying further, we get:

3x²+ 8x - 16y² - 75 = 0

Ratio 2: CD:DE = 1:2

Let's use the midpoint formula to find the coordinates of point E, which is the midpoint of line segment CD:

E = ((p-1)/2, (q-4)/2)

Since CD:DE = 1:2.

Therefore , the solution of the given problem of ratio comes out to be

CD:DE = 1:2. and AB:BC = 2:1 .

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Answer:

(-4, 6) (-1, 0)

Source:

Took test. ✌

Part A: By comparing B and L, L has greater rate of change.

Part B: By comparing B and L, B has greater y-intercept.

This can be solved using the concept of equation of function.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

Part B:

Let, the equation of function B is,

Y = mx+c

Where m is slope and C is intercept

At (-3,-7)

-7 = -3m+c

C = 3m-7

At (-1,-1)

-1 = -m+3m-7

-1 = 2m -7

2m = 6

m = 3

C = 3m-7

C = 3×3 - 7

C =2

So, equation of line B is

Y = mx+c

Y = 3x+2

Where intercept is 2, note y intercept can also be found by putting x = 0, slope = 3

Part A:

Rate of change is slope for B can also be found by -1-(-7)/-1-(-3)=6/2=3

For equation L.

Y=6x+4

Slope=6, intercept =4

For L: when x=0, y=4,x=1,y=10

Rate of change=slope=(10 - 4)/ (1 - 0)=6

Line            Equation              Rate of change(slope(m)      Y intercept (c)

B                    y = 3x+2                      3                                         2

L                     y = 6x- 4                     6                                         - 4

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The values of x and y​ are x = 5 and y = 5.

The subtraction of vectors a and b can be represented as the vector sum of a and the negative of b:

a - b = a + (-b)

To find the negative of b, simply multiply each component by -1:

-b = (-1) × (1, 2) = (-1, -2)

So,

a - b = a + (-b) = (6, 7) + (-1, -2) = (5, 5)

Therefore, the values of x and y are 5 and 5 respectively.

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Constant: Mug price = $8.95, Refill price = $1.50, Rate: Refill rate = $1.50, Equation: 8.95 + 1.50x = 26.95, Solve: x = 15 refills​. Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

To calculate the number of refills Jalissa purchased last month, we must first define the constants of the equation. The cost of the mug is $8.95 and the cost of the refill is $1.50. After establishing these constants, we can create an equation using the rate of refills ($1.50) and the total amount that Jalissa spent ($26.95). The equation is 8.95 + 1.50x = 26.95. This equation can then be solved to find the value of x, which is the number of refills Jalissa purchased. To solve the equation, subtract 8.95 from both sides to get 1.50x = 18. This equation can then be divided by 1.50 to find the value of x, which is 15. This means that Jalissa purchased 15 refills last month, paying $26.95 for the mug and refills combined.

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Answer:

Ecuación: 59.53 - 6.49 = 53.04

53.04 / 8 = X

X = 6.63

Respuesta: X=6.63

Answer:

5.6km

Step-by-step explanation:

1km = 1000 meters

5,600 meters = 5.6km

5600 divided by 1000 = 5.6km

So, Chen walked 5.6km today.

The distance between D(-5, -6) and E(5,2) is 12.8, and the slope is 0.8. The distance between E(5,2) and F(4, -4) is 6.08, and the slope is 6. The distance between F(4, -4) and G(-6, -12) is 12.8, and the slope is 0.8.

Distance Formula:

The distance between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:

d = √((x2-x1)² + (y2-y1)²)

Slope Formula:

The slope of the line between two points A(x1, y1) and B(x2, y2) is calculated using the following formula:

m = (y2-y1)/(x2-x1)

Distance between D(-5, -6) and E(5,2):

d = √((5-(-5))² + (2-(-6))²)

d = √((10)² + (8)²)

d = √(100 + 64)

d = √164

d = 12.8

Slope between D(-5, -6) and E(5,2):

m = (2-(-6))/(5-(-5))

m = (8)/(10)

m = 0.8

Distance between E(5,2) and F(4, -4):

d = √((4-5)² + (-4-2)²)

d = √((-1)² + (-6)²)

d = √(1 + 36)

d = √37

d = 6.08

Slope between E(5,2) and F(4, -4):

m = (-4-2)/(4-5)

m = (-6)/(-1)

m = 6

Distance between F(4, -4) and G(-6, -12):

d = √((-6-4)² + (-12-(-4))²)

d = √((-10)² + (-8)²)

d = √(100 + 64) …

d = √164

d = 12.8

Slope between F(4, -4) and G(-6, -12):

m = (-12-(-4))/(-6-4)

m = (-8)/(-10)

m = 0.8

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The slope is 0.8 and the distance between D(-5, -6) and E(5,2) is 12.8.

The slope is 6 and the distance between E(5,2) and F(4, -4) is 6.08.

The slope is 0.8 and the distance between F(4, -4) and G(6, -12) is 12.8.

The formula for Distance:

The following formula is used to determine the distance that separates points A (x1, y1) and B (x2, y2) from one another:

d = √((x2-x1)² + (y2-y1)²)

Slope Method:

The following formula can be used to determine the slope of the line that connects the two points A (x1, y1) and B (x2, y2):

m = (y2-y1)/(x2-x1)

The distance that separates D(-5, -6) from E(5,2):

d = √((5-(-5))² + (2-(-6))²)

d = √((10)² + (8)²)

d = √(100 + 64)

d = √164

d = 12.8

Slope from D(-5, -6) to E(5,2):

m = (2-(-6))/(5-(-5))

m = (8)/(10)

m = 0.8

Between E(5, 2) and F(4, -4):

d = √((4-5)² + (-4-2)²)

d = √((-1)² + (-6)²)

d = √(1 + 36)

d = √37

d = 6.08

Slope between E(5,2) and F(4, -4):

m = (-4-2)/(4-5)

m = (-6)/(-1)

m = 6

Distance between F(4, -4) and G(-6, -12):

d = √((-6-4)² + (-12-(-4))²)

d = √((-10)² + (-8)²)

d = √(100 + 64) …

d = √164

d = 12.8

Slope between F(4, -4) and G(-6, -12):

m = (-12-(-4))/(-6-4)

m = (-8)/(-10)

m = 0.8

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The transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

The vertices of the triangle are L (-7, 4), M(-3, 0) and N(-8, 1).

a. Translation: (x,y) → (x + 5, y-6) is as follows:

L' = (-7 + 5, 4 - 6) = (-2, -2)

M' = (-3 + 5, 0 - 6) = (2, -6)

N' = (-8 + 5, 1 - 6) = (-3, -5)

b. Reflection in line y = -x is as follows:

Here, the value of y coordinate is negative x coordinate and x coordinate is negative y coordinate.

L' = (-7, 4) = (-4, 7)

M' = (-3, 0) = (0, 3)

N' = (-8, 1) = (-1, 8)

Hence, the transformation of the vertices of the triangle is a. L' = (-7 + 5, 4 - 6) = (-2, -2), M' = (-3 + 5, 0 - 6) = (2, -6), N' = (-8 + 5, 1 - 6) = (-3, -5). b. L' = (-7, 4) = (-4, 7), M' = (-3, 0) = (0, 3), and N' = (-8, 1) = (-1, 8).

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Answer:

its A. x² + 3x + 2/5x because it's the right answer

Answer:

Step-by-step explanation:

Sorry did you already finish?

1. B. 2/3 = 8/12 b/c 2x4 = 8 and 3x4 = 12

2. D. 5/6 = 10/12 b/c 5x2 = 10 and 6x2 = 12

3. 2

4. A. simplified is 2/3 C. self-explanatory D. simplified is 3/4

Answer:

y = 125°

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540°

y + 86° + 142° + 72° + 115° = 540°

y + 415° = 540° ( subtract 415° from both sides )

y = 125°

Answer:

125°

Step-by-step explanation:

First you find the value of total interior angles

Since it's a Pentagon

[tex](5- 2) \times 180[/tex]

Then you arrive at 540°

When you sum all the angles in the Pentagon together they should be equal to 540

[tex]540 = 86 + 142 + 72 + 115 + y[/tex]

[tex]540 = 415 + y[/tex]

[tex]540 - 415 = y[/tex]

[tex]y = 125[/tex]

Answer: 398 + 399 + 400 equals 1197 

Step-by-step explanation: The sum of three consecutive natural numbers is 1197, find the numbers X) + (X + 1) + (X + 2) = 1197 To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:X + X + 1 + X + 2 = 11973X + 3 = 11973X + 3 - 3 = 1197 - 33X = 11943X/3 = 1194/3X = 398Which means that the first number is 398, the second number is 398 + 1 and the third number is 398 + 2. Therefore, three consecutive integers that add up to 1197 are 398, 399, and 400. 

The solution is given below.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

the reflection is with respect to y=x line,

so, the transformation will be,

(x,y)⇒(y,x)

so, we get,

X = (-3,8 ) ⇒ X' = (8,-3)

Y(2,5)⇒Y(5,2)

Z(-4,-1)⇒Z'(-1,-4)

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Answer:

B

Step-by-step explanation:

[tex]1. \: 5.1 \div - 2 \\ 2. \: - 2.55[/tex]

The area of the triangle in the diagram is one square foot.

We know that the area of a triangle of base B and height H is given by the formula:

Area = B*H/2

On the diagram we can se that the measure of the base is 3 ft, and the height is 2/3 ft, then the area of that triangle will be:

Area = (3 ft)*(2/3 ft)/2 = 1 ft²

The area of the triangle is one square foot.

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The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

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Consecuencia de 5^3 - 3 √(375 ÷ 3) + (7 + 2)^2 - 9^11 ÷ 9^9 es 91.46.

Potencias es una operación matemática para la multiplicación repetida de un número tanto como el rango. El rango de un número es un número que se escribe más pequeño y se ubica ligeramente hacia arriba. Basado en la semántica de escribir letras se llama superíndice, por ejemplo: 2², 3², 4³ y otros. En inglés, el exponencial se llama "potencia" o "exponente".

5³=125

3√(375:3) =3√125=3√5³= 3.5^3/2

(7+2) ²=9²=81

9¹¹÷9^9=9²=81

5³ - 3 √(375 ÷ 3) + (7 + 2)² - 9¹¹ ÷ 9^9= 5³-3.5^3/2+81-81 =125-3√125=125-(3(11.18) = 125- 33.54=91.46

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The equivalent expressions to t(-7.4s+3.8-4.5)-t are:

This expression can be simplified as follows:

t(-7.4s + 3.8 - 4.5) - t

= t(-7.4s - 0.7) - t

= -7.4st - 1.7t.

t(-7.4s+3.8-4.5)-t

= t(-3.6s-4.5)-t

-7.4s + 3.8 - 4.5t - t

= t(7.4s+3.8)-5.5t

Therefore the correct options are A, B, E.

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