(BRAINLYEST TO RIGHT ANSWER) pls i need help!

Considering the definition of parallel and perpendicular line, the parallel line has a slope of -54 and the perpendicular line has a slope of 1/54.

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope.

Perpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, the line is y= -54x -4.

where:

Since two lines are parallel if they have the same slope, the parallel line has a slope of -54.

If you multiply the slopes of two perpendicular lines, you get –1. So:

-54 × slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-54)

slope perpendicular line= 1/54

The perpendicular line has a slope of 1/54.

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Answer:

a) If the diameter is 400 feet wide, then the radius is half that, which is 200 feet wide.

b) The circumfernce is π times the diameter, which is 400 feet. 400×π≈1256.64

c) She is not correct. She squared 400, which is 160000, when she should have squared 200, which is 40000. Then, multiply by π.

40000 × π ≈ 125663.7

The error involved in approximating the sum of the given series by the sum of the first five terms of the series is `R5 = 1/6³ + 1/7³ + ...`.

To estimate the error that is made by approximating the sum of the given series by the series the first 5 terms 1/k³, we can use the remainder term of a convergent series.

The given series is ∑ 1/k³ from k = 1 to infinity.We have to find the error involved in approximating the sum of the given series by the sum of the first five terms of the series.

That is, we need to find the difference between the actual sum of the series and the sum of the first five terms of the series.

The sum of the series is given by: `S = 1/1³ + 1/2³ + 1/3³ + 1/4³ + ... + 1/n³ + ...` We can use the remainder term of the series to find the error in approximation.

The remainder term `Rn` is given by: `Rn = Sn - S` where `Sn` is the sum of the first `n` terms of the series. Thus, we have to find the remainder term for `n = 5`.

The remainder term `Rn` is given by: `Rn = S - Sn = 1/6³ + 1/7³ + ...` Since the given series is convergent, the remainder term `Rn` tends to zero as `n` tends to infinity.

So, if we take the sum of the first five terms of the series, the error involved in approximation is given by the remainder term `R5`.

The error involved in this approximation is very small and can be neglected.

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Answer:

smaller x = -5

larger x = 5

Step-by-step explanation:

-x^2 - 8 = -33

Add 8 to each side

-x^2 - 8+8 = -33+8

-x^2 = -25

divide each side by -1

x^2 = 25

Take the square root of each side

sqrt(x^2) = ±sqrt(25)

x = ±5

x = -5, x = 5

Answer:

\(lesser \: \: \: x =( - 5 )\\ greater \: \: \: x =( 5)\)

Step-by-step explanation:

\( - {x}^{2} - 8 = - 33 \\ - {x}^{2} = - 33 + 8 \\ - {x}^{2} = - 25 \\ {x}^{2} = 25 \\ x = \sqrt{25} \\ x = + 5 \\ x = - 5\)

hope this helps

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Answer:

The base salary was £21,500.

Step-by-step explanation:

Giving the following information:

Increase rate (g)= 12%

New salary= £24,080

To calculate the base salary, we need to use the following formula:

Base salary= new salary / (1 + increase rate)

Base salary= 24,080 / (1.12)

Base salary= £21,500

The base salary was £21,500.

Inaccurate density values can result from various factors such as measurement errors, impurities in the sample, incorrect calculations, or inconsistent experimental conditions.

Density is a physical property that represents the mass of a substance per unit volume. When obtaining density values, it is crucial to ensure accurate measurements of both mass and volume. Any errors in measuring the mass or volume of the sample can lead to inaccurate density calculations. Common sources of measurement errors include using imprecise or faulty measuring instruments, incorrect reading of values, or not properly accounting for the presence of air bubbles or moisture.

Impurities present in the sample can also affect density measurements. If the sample contains contaminants or substances with different densities, the overall density value may be skewed. It is important to ensure that the sample being tested is pure and does not contain any foreign substances that could alter the density.

Moreover, inconsistent experimental conditions such as variations in temperature or pressure can influence the density of a substance. Density is temperature-dependent, and fluctuations in temperature can lead to variations in the density values obtained. It is essential to conduct experiments under controlled conditions to minimize the impact of such variables.

In the case of the cube of butter or margarine in water, the density of butter is lower than that of water. Due to its lower density, the cube of butter will float in water. The density of water is approximately 1 g/cm³, while the density of butter is around 0.9 g/cm³. Since the density of the cube of butter is less than the density of water, it will experience an upward buoyant force greater than its weight, causing it to float.

When drops of a saturated salt solution are added to pure water, the salt solution is denser than water. This is consistent with the fact that a saturated salt solution has a higher density than pure water. The addition of the salt solution increases the overall density of the water, causing the drops to sink. This observation aligns with the principle that objects with higher density than the surrounding medium will sink.

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Answer:

35.88

Step-by-step explanation:

92/100 = x/39. 100x = 3588. x = 35.88

Answer:

54 - 37.5 = 16.5     16.5/3 = 5.5

Step-by-step explanation:

Hope I helped.

The statement suggesting that larger groups are more effective than smaller groups is false. Smaller groups tend to have better communication, efficiency, and individual participation.

The statement suggests that larger groups, specifically groups of twenty to thirty people with representatives from multiple subgroups, are more effective than smaller groups of six to eight people. However, this statement is generally considered false for several reasons:

Larger groups can face challenges in communication and coordination. With more members, it becomes more difficult to ensure effective information sharing, active participation, and clear decision-making. Small groups often have better communication and coordination due to fewer individuals involved.

Smaller groups tend to be more efficient and productive. In larger groups, there can be increased time spent on managing diverse opinions and reaching consensus, which can slow down the decision-making process and hinder productivity. Smaller groups can often make quicker decisions and accomplish tasks more efficiently.

Larger groups may result in reduced individual participation. Some members may feel less inclined to contribute or may be overshadowed by more dominant personalities. In smaller groups, each member can have a more significant impact and be actively engaged in the group's work.

Smaller groups tend to foster better group dynamics and cohesion. It is easier for members to develop strong relationships, trust, and a shared sense of purpose in smaller groups. Larger groups can struggle with maintaining cohesiveness and a sense of belonging.

While larger groups may have certain advantages, such as a broader range of perspectives and resources, the statement disregards the potential drawbacks of managing larger groups effectively. Overall, smaller groups often exhibit better communication, efficiency, and individual participation, making the statement false in general.

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The bearing of how far east of point G is point H is 51.68 m

Bearing is the number of degrees in the angle measured in a clockwise direction from the north line to the line joining the centre of the compass. It is used to describe a particular direction in which an object is traveling.

How to determine this

When point G and point H are 58 m apart

Point H is at a bearing of 63 degrees

i.e At point H = 63°

To calculate how far east of point G is to point H

When North to East is 90°

So, 90° - 63°

= 27°

x meter away from point H to the East

= cos 27° * 58 m

= 0.9114 * 58 m

= 52.86 m

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To find the slant asymptote of the function y = x^2 + 4x + 4, we need to perform polynomial long division. In this case, we will divide the function by y = x.


1. Divide the function y = x^2 + 4x + 4 by y = x using polynomial long division.
2. x goes into x^2 x times. Write x on top.
3. Multiply x by x, which is x^2. Write x^2 under x^2 in the dividend and subtract it.
4. Bring down 4x from the dividend.
5. x goes into 4x, 4 times. Write 4 next to x on top.
6. Multiply 4 by x, which is 4x. Write 4x under 4x in the dividend and subtract it.
7. Bring down the constant term 4 from the dividend.
8. Since the degree of the remaining dividend (constant term) is lower than the divisor's degree (x), we stop dividing.


After performing polynomial long division, we get the quotient y = x + 4, which is the equation of the slant asymptote for the given function.

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Answer:

Non-linear and decreasing so B

Step-by-step explanation:

It is non-linear as it is not a straight line

It's also going down so its decreasing

The best approximation of the number of yellow markers in the box is 30.

The first step is to express the sample of markers picked as a fraction of the total markers in the box.

Sample of markers picked = markers in the sample / total number of markers in the box

= 50 / 300 = 1/6

The second step is to divide the number of yellow markers by the fraction gotten in the previous step

Number of yellow markers in the box = 5 ÷ 1/6

= 5 x 6 = 30 markers

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Answer:

Below

Step-by-step explanation:

A) The derivative of the position function is the velocity function

    derivative =  19 - 3.72 t      at t = 1   this = 15.28 m/s

B)  unclear:    19 - 3.72a

C)    H= 0 when at surface

            0 = 19t - 1.86 t^2

                  Quadratic Formula shows t = 10.2 s

D )  it will come down at the same speed it went up (but opposite direction)         =       -19 m/s

Answer: Use a variable

w

to represent the width of the room.

From the given information find that

10

w

=

80

, hence

w

=

8

.

So the room is

8

meters by

32

meters.

Explanation:

Let

w

represent the width of the room in meters.

Then the length of the room is

4

w

.

So the perimeter of the room is

w

+

4

w

+

w

+

4

w

=

10

w

.

Given that the perimeter is

80

meters, that translates as:

10

w

=

80

Divide both sides by

10

to get

w

=

8

.

Hence the width of the room is

8

meters and the length is

4

w

=

32

meters.

Step-by-step explanation:

The dimensions of the room are 5 meters long and 5 meters wide.

The perimeter of a rectangular room is equal to twice the sum of its length and width. In this case, the perimeter of the rectangular room is equal to 2 x (length + width) =  10 meters.

Therefore, we can write:
2 x (L + W) = 10

To find the dimensions of the room, we need to solve the equation for L and W.
L + W = 5
L = 5 - W

Substitute this equation for L in the original equation:
2 x (5 - W + W) = 10
2 x (5) = 10
10 = 10

Therefore, L = 5 and W = 5, so the dimensions of the room are 5 meters long and 5 meters wide.

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Answer:

-9 and -2

Step-by-step explanation:

-9 and -2

two negatives multiply to make a positive (18)

and -9 add -2 is -11

Answer:

c = 5cm

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

do the square root of 25 and c to solve for c

the square root of c^2 is c

therefore, c= 5cm

Answer:

Options B, C and D

Step-by-step explanation:

Linear pair of angles means sum of the angles of the pair is 180° which are formed at a point of a line.

In other words, pair of supplementary angles is the linear pair.

From the figure attached,

Pair of the linear angles are,

1). ∠BAC and ∠CAD

2). ∠BAE and ∠EAD

3). ∠EAD and ∠DAC

Therefore, Options B, C and D are correct.

Answer:

B, C, and D

Step-by-step explanation:

The equations of the tangents to the curve are y = 3x - 6 and y = -3x + 30.

To find the equations of the tangents to the curve, we need to determine the slope of the tangent line at the given point of tangency.

The given curve is defined by the parametric equations x = 6t^2 - 2 and y = 4t^3 - 2.

We can eliminate the parameter t by expressing t in terms of x.

Rearranging the first equation, we have t^2 = (x + 2) / 6, and taking the square root of both sides, we get t = ±√((x + 2) / 6).

Substituting this value of t into the equation for y, we have y = 4(±√((x + 2) / 6))^3 - 2.

Simplifying this expression, we obtain y = ±(4/3)√((x + 2)^3 / 6) - 2.

Now, let's find the slopes of the tangents at the point (8, 6). We take the derivative of y with respect to x and evaluate it at x = 8.

Differentiating y with respect to x, we get dy/dx = ±(4/3)√(2(x + 2)^3 / 3)(1 / 2) = ±(2/3)√((x + 2)^3 / 3).

Evaluating the derivative at x = 8, we have dy/dx = ±(2/3)√((8 + 2)^3 / 3) = ±(2/3)√(10^3 / 3) = ±(2/3)√(1000/3) = ±20√10/3.

Since the slopes of the tangents are given by the derivative, the two possible slopes are ±20√10/3.

Now we can find the equations of the tangents using the point-slope form. Using the point (8, 6), we have:

y - 6 = (±20√10/3)(x - 8).

Simplifying these equations, we get:

y = 3x - 6 and y = -3x + 30.

Therefore, the equations of the tangents to the curve that pass through the point (8, 6) are y = 3x - 6 (the smaller slope) and y = -3x + 30 (the larger slope).

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Given:

Bob owns a hardware store he sells hammers for 15$

On Saturday he sold 36 hammers.

The total cost of the hammers =

So, the answer will be $540

The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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Answer:

\(y = - \frac{6}{5} x - 3\)

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the gradient and c is the y-intercept.

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

\(m = \frac{3 - ( - 3)}{ - 5 - 0} \)

\(m = \frac{3 + 3}{ - 5} \)

\(m = - \frac{6}{5} \)

Substitute the value of m into the equation:

\(y = - \frac{6}{5} x + c\)

To find the value of c, substitute a pair of coordinates.

When x= 0, y= -3,

\( - 3 = - \frac{6}{5} (0) + c\)

c= -3

Thus, the equation of the line is \(y = - \frac{6}{5} x - 3\).

Answer:

x = 12

x = 9

Step-by-step explanation:

See picture below :)

Answer:

0.009

Step-by-step explanation:

1. 9/25

2.  x/40

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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The additive identity property, we know that for any vector v, v + 0 = v. Applying this property, we get:

0 = 0u

To prove theorem 6.1(a), which states that 0u = 0, where 0 represents the zero vector and u is any vector, we will use the axioms and properties of vector addition and scalar multiplication.

Proof:

Let 0 be the zero vector and u be any vector.

By definition of scalar multiplication, we have:

0u = (0 + 0)u

Using the distributive property of scalar multiplication over vector addition, we can write:

0u = 0u + 0u

Now, we can add the additive inverse of 0u to both sides of the equation:

0u + (-0u) = (0u + 0u) + (-0u)

By the additive inverse property, we know that for any vector v, v + (-v) = 0. Applying this property, we get:

0 = 0u + 0

Now, let's subtract 0 from both sides of the equation:

0 - 0 = (0u + 0) - 0

By the additive identity property, we know that for any vector v, v + 0 = v. Applying this property, we get:

0 = 0u

Hence, we have proved that 0u = 0.

Therefore, theorem 6.1(a) holds true.

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