Question 1b Identify the amount in this statement. 6 is 30% of 20. The amount = The solution is
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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Answer:228m

Step-by-step explanation: 19m x 12m = 228m

Answer: 228m

Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.

Answer:

0

Step-by-step explanation:

because 6 plus 8 eqaul 14

The likely population of the infected elk in the wildlife preserve is 840.

A sample is a smaller group of the population. A sample is a representation of the population.

The fraction of infected elks in the sample to the total sample would be the same of the infected elks in the population to the total population of the elks.

Population of the infected elk = (infected elks in the sample / total sample) x number of elks in the preserve

(8/50) x 5250

= 0.16 x 5250 = 840

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The required exact value of sin(585 degrees) is -0.707

The sine function is periodic with a period of 360 degrees.
Therefore,
= sin(585 degrees)
= sin(585 degrees - 360 degrees)
= sin(225 degrees).

The sine function has a negative value in the third quadrant, and 225 degrees is in the third quadrant.
Therefore,
sin(225 degrees) = -sin(45 degrees)
                             = -(1/sqrt(2)) = -0.7071.

Therefore, the exact value of sin(585 degrees) is -0.7071.

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The solution is :

After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]

Here, we have,

The designated sum can replace either row. Consult your curriculum materials for the intent.

Here, we'll replace row 2 with the sum.

 3(2, -2, 5) +(-6, 3, -4) = (3(2)-6, 3(-2)+3, 3(5)-4) = (0, -3, 11)

After the row operation replaces the second row, the augmented matrix is ... [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]

Hence, The solution is :

After the row operation replaces the second row, the augmented matrix is : [tex]\left[\begin{array}{ccc}-6 &3& -4 \\0&-3&11\end{array}\right][/tex]

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The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. This is because a horizontal line has a slope of zero

The slope of a line of best fit is undefined when the slope is of the line of best fit is horizontal. A line of best fit is a straight line that is used to represent the data on a scatter plot. It is the line that best fits the data points in a scatter plot.

The slope of a line of best fit is the rate of change of the y-coordinate relative to the x-coordinate.. In other words, there is no rate of change of the y-coordinate relative to the x-coordinate when the line is horizontal.

The x values of the data set increase at an unspecified rate as the y values decrease. This means that the line of best fit has a negative slope. A negative slope means that the y-coordinate decreases as the x-coordinate increases.

In other words, there is a rate of change of the y-coordinate relative to the x-coordinate. The slope of the line of best fit is the value of this rate of change.

The slope of a line of best fit is used to determine the direction and strength of the relationship between two variables.

A positive slope means that the variables are directly proportional, while a negative slope means that they are inversely proportional. The slope of a line of best fit can be calculated using the formula y2 - y1 / x2 - x1.

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You would need to purchase 6 gallons of primer.

The points (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

From the question, we have the following parameters that can be used in our computation:

The graph

Also, we have the following ordered pairs

(1,0) (8,0). (0,4). (3,0)

From the graph, we have the following ordered pairs in the shaded region

(0, 4)

Other points (1,0) (8,0). and. (3,0) are not in the shaded region

This means that (1,0) (8,0). and. (3,0) are not the solution of system of inqualities

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The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

Given the equation:

15(2x - 10) + 4x = -3(15x + 4)

Solving the parenthesis:

30x - 150 + 4x = -45x - 12

Collect like terms:

30x + 4x + 45x = -12 + 150

79x = 138

Dividing both sides by 79:

x = 1.7

The value of x is 1.7

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The ridgeline will be 18.67 feet above the house.

Generally, a height refers to the measurement of someone or something from head to foot or from base to top.

To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span

Given data:

Pitch = 7

Span = 32 feet

Inputting the values, we have:

Height = (7 / 12) * 32

Height = 0.5833 * 32

Height = 18.6656

Height = 18.67 feet.

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Answer:

B. More streetlights are installed on one street and people are then asked if they like the change.

Step-by-step explanation:

An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.

The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

We have,

The vertex form of a parabola is given by the equation y = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

Now,

Given that the parabola passes through (-2, 4) and has a vertex (0, 8), we can substitute these values into the equation to find the value of 'a'.

Using the vertex (0, 8):

8 = a(0 - 0)² + 8

8 = a(0) + 8

8 = 8

Since the coefficient of the squared term is 'a', which remains unchanged, we can conclude that a = 1.

Therefore,

The equation of the parabola in vertex form is y = (x - 0)² + 8, which simplifies to y = x² + 8.

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The diameter of the second pile of phosphate is 53.5 ft.

We have,

Conveyor belt:

Cone shape:

Diameter = 48.6 ft

Radius = D/2 = 24.3 ft

Height = 15.3 ft

Volume.

= 1/3 x π x r² x h

= 1/3 x 3.14 x 24.3 x 24.3 x 15.3______(1)

Shorter conveyor belt:

Cone shape:

Diameter = D

Height = (15.3 - 2.7) = 12.6 ft

Volume.

= 1/3 x π x (D/2)² x h

= 1/3 x 3.14 x (D/2)² x 12.6_______(2)

Since (1) and (2) are equal.

24.3 x 24.3 x 15.3 = (D/2)² x 12.6

(D/2)² = 717.02

D²/4 = 717.02

D² = 717.02 x 4

D² = 2868.09

D = 53.55

D = 53.5 ft

Thus,

The diameter of the second pile of phosphate is 53.5 ft.

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Answer:

Step-by-step explanation:

To determine the value of t if the three points A(7, 4), B(-1, -2), and C(3t, 5-4t) are collinear, we can use the concept of slope. If the points are collinear, the slopes between any two pairs of points should be equal.

The slope between points A and B is given by:

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (-2 - 4) / (-1 - 7)

= (-6) / (-8)

= 3/4

Now, let's calculate the slope between points B and C:

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (5 - (-2)) / (3t - (-1))

= (7) / (3t + 1)

Since the points are collinear, the slopes m₁ and m₂ should be equal. Therefore, we can set up the equation:

3/4 = 7 / (3t + 1)

To solve for t, we can cross-multiply and solve the resulting equation:

4(7) = 3(3t + 1)

28 = 9t + 3

25 = 9t

t = 25 / 9

Therefore, the value of t that makes the points A(7, 4), B(-1, -2), and C(3t, 5-4t) collinear is t = 25/9.

Answer:

6/7

Step-by-step explanation:

If the three points are collinear, then the slope of the line passing through any two of the points should be the same as the slope of the line passing through the other two points.

Let's find the slope of the line passing through points A and B:

slope AB = (y2-y1)/(x2-x1)

= (-2-4)/(-1-7)

= -6/-8

= 3/4

Now let's find the slope of the line passing through points B and C:

slope BC = (y2-y1)/(x2-x1)

= (5-4t-(-2))/(3t-(-1))

= (7-4t)/(3t+1)

Since the three points are collinear, slope AB = slope BC:

3/4 = (7-4t)/(3t+1)

Cross-multiplying and simplifying:

12t + 4 = 28-16t

28t = 24

t = 24/28

t = 6/7

Therefore, the value of t is 6/7 if the three points A, B, and C are collinear.

Answer:

6 * (5 - x)

Step-by-step explanation:

This expression calculates the difference between 5 and x, and then multiplies it by 6. The difference is obtained by subtracting x from 5, and then the entire result is multiplied by 6.

The coordinates of the vertices after a dilation of the scale factor would be:

To perform a dilation with a scale factor of 1/2 centered at the origin, we multiply the coordinates of each vertex by the scale factor.

Given the vertices:

W = (5, 10)

V = (0, -10)

U = (5, -10)

After applying the dilation with a scale factor of 1/2, the new coordinates of the vertices would be:

W' = (5 * 1/2, 10 x 1/2) = (2.5, 5)

V' = (0 * 1/2, -10 x 1/2) = (0, -5)

U' = (5 * 1/2, -10 x 1/2) = (2.5, -5)

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Answer: 626 yd^2

Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.

Answer:

50) Midpoint: (5.5, 0)

51) Midpoint:  (6, -8)

Step-by-step explanation:

We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where

50) We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (10, 10) and (1, -10):

(10 + 1) / 2

11 / 2

5.5

y-coordinate of midpoint of (10, 10) and (1, -10):

(10 + (-10)) / 2

(10 - 10) / 2

0 / 2

0

Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).

51) We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:

x-coordinate of midpoint of (3, -6) and (9, -10):

(3 + 9) / 2

12 / 2

6

y-coordinate of midpoint of (3, -6) and (9, -10):

(-6 + -10) / 2

(-16) / 2

-8

Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).

Answer: 3x² - 27y² = (3x²) - (27)(y²) = 3(x² - 9y²) = 3(x - 3y)(x + 3y), and 2014² - 2013² = (2014 + 2013)(2014 - 2013) = (3127)(1) = 3127

Im not 100% sure of this answer cause I'm not that good at stuff like this but I still think this is right fr fr

A simplification of the given expression is 1/m¹⁶.

In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.

Mathematically, an exponent can be represented or modeled by this mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:

[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]

1/m¹⁶

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Answer: E. 25%

Step-by-step explanation: There are 12 circles in total. 3 out of those twelve are shaded in, making it in fraction form 3/12. dividing both the numerator in the denominator by 3 simplifies it into 1/4. which is subsequently, 25%

In the given data, current and voltage are directly proportional, while the resistance is constant.

The relationship between the voltage, current, and resistance in an electric circuit is described by Ohm's Law.

The law states that the voltage across a circuit is directly proportional to the current flowing in the circuit.

V ∝ I

V = IR

where;

From the given data set we can see that for each division of current by voltage we have almost a constant value of 30 ohms.

Thus, if we observe the values given in the data set, we can conclude that;

current and voltage are directly proportional, while the resistance is constant.

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The set of 3 lengths that make a right triangle is {8, 15, 17}

Remember that for any right triangle, the sum of the squares of the two shorter sides must be equal to the square of the longer side.

So if the 3 sides are A, B, and C, such that:

A < B < C

We will have:

A² + B² = C²

Now you only need to try sets of 3 values in that equation, if we use: 8, 15, and 17 we will have:

8² + 15² = 17²

289 = 289

That equationis true, thus, these 3 lengths make a right triangle.

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Answer:

2=a

7=b

Step-by-step explanation:

a+14=6a+4

-a  

14=5a+4

-4

10=5a

/5

2=a

9b+8=10b+1

-1

9b+7=10b

-9b

7=1b

/1

7=b

Answer:

WZ=7

XY=7

WX=2

ZY=2

Step-by-step explanation:

9b+8=10b+1

Take 9b to 10b and 1 to 8 to form the equation

8 - 1 =10b - 9b

7 = b

a + 14 =6a + 4

Take a to 6a and 4 to 14 to form the equation

14 - 4 =6a - a

10 =5a

Simplify the answer

10/5 =5a/5

Five divide by five 1 and 10 divided by 5 is 2

Answer is therfore

2 = a

If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.

Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².

So, we have:

lw = 114

Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.

So, we have:

2l + 2w = 50

We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:

l = 114/w

We can then substitute this expression for l in the second equation:

2(114/w) + 2w = 50

Multiplying both sides by w to eliminate the fraction, we get:

228 + 2w² = 50w

Rearranging and simplifying, we get a quadratic equation:

2w² - 50w + 228 = 0

We can solve for w using the quadratic formula:

w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5

Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:

l(5) = 114

l ≈ 22.8

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