Line A has equation y = -4x + 1 and line B contains the points (-2,1) and (1,-11). Select any statement(s) below that are true.

Line B has a slope of -5.


Line A has a slope of -4.


Line A and line B have the same slope.


Line B has a flatter slope than line A.


Line A has a flatter slope than line B.

Answer:

plot the point at 1

Step-by-step explanation:

If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .

The force exerted by the screen door spring can be calculated using Hooke's law,

The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.

The formula for "Hooke's-law" is ⇒ F = kx

Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.

In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;

Substituting the values,

We get,

⇒ F = (188 N/m)(0.292 m)

⇒ F = 54.896 N

⇒ F ≈ 54.9N

Therefore, The force exerted by the screen door spring is approximately 54.9 N.

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Answer:

P(0,2), Q(3,5), R(3,0)

Step-by-step explanation:

Answer:

the slope-intercept form of the line which is perpendicular bisector to the segment with endpoints A(5,9), B(7,13) is y = (-1/2)x + 14

Answer:

It depends on the values of x and y. If x is positive and y is negative, then option A (x + y) would have a negative value. If y is greater than x, then option B (x - y) would have a negative value. If either x or y (or both) is negative, then option C (x*y) could have a negative value. Option D (x/y) could also have a negative value if x is negative and y is positive, or if both x and y are negative.

Answer:

Step-by-step explanation:

B because it has subtraction

16. The base side y = 10.565 and altitude x = 22.657

17. The hypotenuse c = 49.70 and base y = 46.70.

18. The value of AB = 30√3 and AC = 45

19. The value of AB = 36√3 and BC = 18√3.

In geοmetry, a hypοtenuse is the lοngest side οf a right-angled triangle, the side οppοsite the right angle. The length οf the hypοtenuse can be fοund using the Pythagοrean theοrem, which states that the square οf the length οf the hypοtenuse equals the sum οf the squares οf the lengths οf the οther twο sides.

16. Given hypotenuse = 25

θ = 25°

Sin θ = opposite/hypotenuse

Sin 25° = y/25

y = Sin 25° × 25

y = 10.565

Given hypotenuse = 25

θ = 25°

Cos θ = adjacent/hypotenuse

Cos 25° = x/25

x = Cos 25° × 25

x = 22.657

17. Given Side = 17

θ = 20°

Sin 20° = 17/c

c = 17/Sin 20°

c = 49.70

Cos θ = adjacent/hypotenuse

Cos 20° = y/49.70

y = Cos 20° × 49.70

y = 46.70

18. Given BC = 15√3

In a 30°−60°−90°  triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.

Thus, BC = 15√3

AB = 2(15√3)

= 30√3

and

AC = √3(15√3)

= 15 × 3

= 45

Thus, when BC = 15√3, then AB = 30√3 and AC = 45

19. Given AC = 54

In a 30°−60°−90°  triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is 3√ times the length of the shorter leg.

Thus, BC = x and AC = x√3

54 = x√3

54 = x√3

x = 54/√3

x = 18√3

BC = 18√3

AB = 2x = 2(BC) = 2(18√3)

= 36(√3)

Thus, when AC = 54, then AB = 36√3 and BC = 18√3.

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Answer:

Step-by-step explanation:

The domain is found by setting the denominator equal to 0 and solving for y. This value of y gives you the values that cause the denominator to go to 0, which is a problem. In this rational expression, there are no real numbers that cause the denominator to go to 0, so the domain is all real numbers.

Absolutely, Jada's response is right. A square is a quadrilateral with four equal-length sides. A quadrilateral is a square if all four sides measure 5 cm.

Unfortunately, there is no alternative form Jada could have drawn that meets the requirement of all four sides measuring 5 cm. Every other quadrilateral with four equal-length sides is likewise a square. If Jada had drawn a quadrilateral with one or more sides of varying lengths, the specified criterion would not have been met. As a result, the only design Jada could have sketched that meets the requirement of having all four sides measure 5 cm is a square. It is worthwhile to investigate the properties of quadrilaterals and how they connect to the conditions presented in the problem. A quadrilateral is a four-sided polygon. Quadrilaterals come in a variety of shapes, including squares, rectangles, parallelograms, trapezoids, and kites. Certain quadrilaterals have unique qualities, such as opposing sides that are parallel or all angles that are right angles. The criterion in the provided problem is that all four sides of the quadrilateral measure 5 cm.

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a) 1/2, b) 1/4, c) 3/13, d) 7/26 (fraction of black and face cards) in a traditional Western pack of playing cards.

A traditional Western pack of playing cards consists of four suits: Hearts (colored red), Diamonds (colored red), Spades (colored black), and Clubs (colored black). Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.

a) To find the fraction of the playing cards that are red, we need to add up the number of red cards and divide by the total number of cards in the deck. There are two red suits, Hearts and Diamonds, and each has 13 cards. So there are 26 red cards in total. Since there are 52 cards in a deck, the fraction of red cards is 26/52 or 1/2.

b) To find the fraction of cards that are Diamonds, we simply divide the number of Diamonds (13) by the total number of cards (52). This gives us a fraction of 13/52 or 1/4.

c) To find the fraction of face cards, we need to add up the number of face cards and divide by the total number of cards in the deck. In each suit, there are three face cards: King, Queen, and Jack. So there are 12 face cards in each deck (4 suits x 3 face cards per suit). Therefore, there are 12/52 or 3/13 face cards in the deck.

d) To find the fraction of black and face cards, we need to count the number of black cards and the number of face cards that are also black. There are two black suits, Spades and Clubs, and each has 13 cards. So there are total 26 black cards. Of these 26 cards, there are 12 face cards (King, Queen, and Jack) which are not black, leaving 14 black cards which are face cards. Therefore, the fraction of black and face cards is 14/52 or 7/26.

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For the given elementary chemical reaction, the solution to the question is: C = a^2 * (1-t^2/400(1-a))

The question asks about calculating the concentration of C in a chemical reaction. Given that the reaction equation is as follows: A + B → C The rate of reaction can be expressed as: dc/dt = k[A][B] Where, k is the rate constant[A] is the concentration of reactant A in moles/L[B] is the concentration of reactant B in moles/L, c is the concentration of product C in moles/L

The initial concentration of A and B is [A] = a moles/L, [B] = b moles/L Let r be the rate of reaction, i.e. r = dc/dt Thus, using the equation r = k[A][B], we get r = k(a)(b)Now, we can write a differential equation for the concentration of C as follows: dc/dt = r, with initial concentration of C as 0 moles/L∴ dc/dt = kab

Substituting r = k(a)(b) in the equation, we get dc/dt = kabdc/db = kab*dt Differentiating both sides, we get, ln(C) = kab*t + C where C is a constant, ln(C) = ln(a^2) = 2ln(a) = C When a = b, the concentration of C will be maximum at t = (1/k)(ln(a)).

Thus the concentration of C as a function of time (when a = b) is given by C = a^2 * (1-t^2/2)If [C] = a after 20 seconds, then using the equation, we get a = a^2 * (1 - 20^2 * k^2/2)Therefore, 1 = a * (1 - 200k^2) Solving this equation for k, we get, k = ± sqrt[(1-a)/200a^2] For the positive value of k, the concentration of C as a function of time is given by C = a^2 * (1-t^2/400(1-a)).

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Answer:

y = - [tex]\frac{5}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table

m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then

c = - 1

y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line

Step-by-step explanation:

I do not believe you are given enough info to prove they are congruent....you only have ONE angle and one side that are equal ....you need another side or another angle to prove congruency....

I've added an illustration to show how the two triangles would not be congruent without changing the  info given in the pic

.

Answer:

-25

Step-by-step explanation:

simplification using BODMAS

[tex]-5 * 4 + -5[/tex]
-20 - 5
= -25

The equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex], the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].

What are equivalent expressions?

Equivalent expressions are different algebraic expressions that have the same value when evaluated for a particular set of variables.

The equivalent expressions  [tex]x^3[/tex] are:

[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex]

= [tex]\frac{(x ^ 8)}{(x ^ 2) }[/tex]

=[tex]x^{8-2}[/tex]

= [tex]x^6[/tex]

[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]

= [tex]x^{6-3}[/tex]

=[tex]x^3[/tex]

[tex]\frac{(x^{30}) }{(x^{10})}[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x^{30}) }{(x^{10})}[/tex]

=[tex]x^{30-10}[/tex]

=[tex]x^{20}[/tex]

[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] : This expression can be simplified as follows:

=[tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex]

=[tex]x^{-3-(-6)}[/tex]

=[tex]x^{-3+6}[/tex]

=[tex]x^{3}[/tex]

Therefore, the equivalent expressions of [tex]x^3[/tex] are[tex]\frac{(x ^ 6)}{(x ^ 3)}[/tex]and [tex]\frac{(x^{-3}) }{(x^{-6}) }[/tex] , the expressions [tex]\frac{(x^{30}) }{(x^{10})}[/tex] and [tex]\frac{(x ^ 4) ^ 2)}{x ^ 2}[/tex] are not equivalent to [tex]x^3[/tex].

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

A = 16 is the equation that accurately depicts how to calculate the sector's area.

Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.

Here,

The formula for calculating a circle's sector's area is:

=> A = (θ/360) x πr²

where A is the sector's area, is its central angle measurement, and r is the circle's radius.

Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:

=> A = (90/360) x π(8²)

=>  A = (1/4) x π(64)

=>  A = π(16)

=>  A = 16π

A = 16 is the equation that accurately depicts how to calculate the sector's area.

The answer will be given in radius squared units, in this case, cm2.

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Option D. The correct calculation of the area of the sector is      [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:

[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]

or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

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Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:

x - 3 = x² + 2x - 4

This is option B.

Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.

Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.

Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.

Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.

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Complete question:

What is result of substituting for y in the bottom equation?

y = x – 3,

y = x² + 2x – 4

A. y=(x-3)²+2(x-3)-4

B. x-3=x²+2x-4

C. y=x²+2x-4-(x-3)

D. (x-3)=x²

The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.

The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:

[tex]F(x) = P(X ≤ x)[/tex]

The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,

[tex]F(x) = ∫-∞ x f(u) du[/tex]

Where f(u) is the probability density function.

For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]

Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.

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Complete question:

What is the cumulative distribution function for a continuous random variable x?

Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.

Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.

Here,

For a group of n = 4, the standard error of the mean (SEM) is as follows:

=> SEM = α/√(n)

=> 24/√(4) = 12

Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.

b. The SEM for a group of n = 9 is:

=> α/√(n) = 24/√(9)

=> 8; SEM = α

Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.

c. The SEM for a sample of 16 is as follows:

=> α / √(n) = 24 / √(16) = 6;

=>  SEM =α

Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.

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Find CD:

Let,

[tex]r_1[/tex] be a radius of Circle A

[tex]r_2[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_1=30[/tex]

[tex]r_1=\dfrac{15}{\pi }[/tex]

[tex]CD=D_1+D_2[/tex]

[tex]=2r_1+2rx_2[/tex]

[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]

[tex]CD=17.55cm.[/tex]

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Based on the principle of Inequality, Attached image is a graph of the inequality for  |x| < 5. The red region is the solution set.

A mathematical statement known as an equation demonstrates the relationship between two or more numbers and variables by utilizing mathematical operations such as addition, subtraction, multiplication, division, exponents, and so forth.

Therefore, An expression that demonstrates a non-equal comparison of numbers and variables is called an inequality. So, the graph that best represents this solution set is a number line with open circles at x = -5 and x = 5 and a shaded region in between, indicating that all values of x within this range satisfy the inequality.

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The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.

The new value of the stock in Company A is:

[tex]4500 + (5 \times 4500) = $4725[/tex]

The new value of the stock in Company B is:

[tex]3900 + (11 \times 3900) = 4339[/tex]

The total value of the investor's stock account after the increase is:

$4725 + $4339 = $9064

To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:

($9064 - $8400) / $8400 = 0.0795

We then multiply this decimal by 100 to get the percentage increase:

0.0795 x 100 = 7.95%

Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

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