Write an equation in slope-intercept form for the line with slope -3 and y-Intercept -2.

Answer:

Option D.

Step-by-step explanation:

We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.

A quadratic equation is prime if its factors can not possible. So, option A is incorrect.

In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.

For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.

The difference of 2 perfect squares is:

[tex]x^2-a^2=(x-a)(x+a)[/tex]

In this case factoring is the best method.

Therefore, the correct option is D.

Answer:

y= -207

Step-by-step explanation:

61 = 268 + y

Collect like terms

y= 61 - 268

Simplify

= -207

y= -207

Alternatively,

61 = 268 + y

Subtract 268 from both sides

61 - 268 = 268 + y - 268

-207 = y

Therefore,

y= -207

Step-by-step explanation:

a variable is a quantity that may change within the context of a mathematical problem or experiment

I hope this was helpful

Answer:

The matches are:

Feature: Increasing or decreasing interval (specifically, a decreasing interval)

Statement: As the input power's current grows beyond 1 ampere...

Feature: Relative minimum or maximum (specifically, relative maximum)

Statement: At its most efficient, the motor uses...

Feature: x-intercept

Statement: The motor loses all efficiency when the current...

Step-by-step explanation:

The first statement describes a decreasing interval, specifically the decreasing efficiency beyond 1 ampere of input current

The second statement describes a relative maximum, specifically the maximum efficiency at an input current of 1 ampere

The third statement describes an x-intercept, specifically the efficiency hitting 0% when the input current is ≥ 3 amperes

Answer:

(a) x -intercept with the last statement (the one at the bottom)

(b) Relative maximum with the second (middle) statement.

(c) Increasing or decreasing with the first (top) statement.

See details below:

Step-by-step explanation:

(a)  The x-intercept goes with the info on what happens when the graph crosses the horizontal axis, so it goes with the third statement given:

The motor loses all efficiency when the current hits 3 amps.

(b)  Relative max: agrees with what happens at the maximum the curve shows reaching approximately 50% value in the vertical scale:

At its most efficiency the motor uses about 50% of the  input power

(c)  Increasing or decreasing interval: The function clearly increases from values of the horizontal variable starting at around 0.4, up to a value of 1, and from then onwards it decreases. So it agrees with:

As the input grows more than 1 ampere, the motor becomes less efficient.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Total no. of outcomes = 1,2,3,4,5,6

No. of times 5 is on the cube =1

Therefore, probability of getting a 5 = [tex]\frac{1}{6}[/tex]

Answer:

c. 48 packages

d. Possibilities:

1 x 28 = 28

2 x 14 = 28

4 x 7 = 28

7 x 4 = 28

14 x 2 = 28

28 x 1 = 28

Possible combinations:

17, 1, 28

17, 2, 14

17, 4, 7

17, 7, 4

17, 14, 2

17, 28, 1

Step-by-step explanation:

c. 127 employees get 3 uniforms each, meaning a total of 127 * 3 = 381 uniforms

The uniforms come in packs of 8, so dividing 381 by 8, we get:

381/8 = 47.625

However, you probably can't order a portion of a package, so you must round up to 48 packages. There will be 3 uniforms left over.

d. The divisors of 28 are 1, 2, 4, 7, 14, and 28. All I did was enumerate the six possibilities.

The answer is any value that you put in for x would make the equation true. When you simplify the whole equation it looks like this: 2x - 6 = 2x - 6, therefor you could replace x with any value.

Answer:

[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]

Explanation-

As,

[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]

and

[tex]a^{-n}=1/a^n[/tex]

Answer:

RU = 9

ST = 3

Step-by-step explanation:

RT = 6

RS = ST = (1/2)RT = (1/2)(6) = 3

ST = 3

RU = 3ST = 3 * 3 = 9

Answer:

A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)

The diagonal of a triangle divides a two dimentional shape into two congruent shapes.

The congruent shapes are equally the same

Answer to part (a) is: 33 degrees

Answer to part (b) is: 5 meters

=============================================

Explanation:

Check out the diagram below.

For now, focus only on triangle ABC. The ladder is segment AC = 10. We first need to find the length of [tex]AB = h_1[/tex] which is the initial height of the ladder.

sin(angle) = opposite/hypotenuse

sin(70) = h/10

h = 10*sin(70)

h = 9.396926 approximately

Subtract off 4 since the ladder slips 4 meters down the wall

h-4 = 9.396926-4

h-4 = 5.396926

which is the new height the ladder reaches. The hypotenuse stays the same

sin(angle) = opposite/hypotenuse

sin(theta) = 5.396926/10

theta = arcsin(5.396926/10)

theta = 32.662715

theta = 33 degrees when rounding to 2 significant figures

This is the value of [tex]\theta_2[/tex] in the diagram below.

---------------------------------

We'll use the cosine rule with the old theta value [tex]\theta_1[/tex]

cos(angle) = adjacent/hypotenuse

cos(70) = x/10

x = 10*cos(70)

x = 3.420201 is the approximate distance the foot of the ladder is from the wall. This is before the ladder slips.

After the ladder slips, we use the new angle value [tex]\theta_2[/tex]

cos(angle) = adjacent/hypotenuse

cos(32.662715) = x/10

x = 10*cos(32.662715)

x = 8.418622

Subtract the two x values

8.418622-3.420201 =  4.998421

which gives the approximate distance the foot of the ladder moved (the distance from point C to point E in the diagram)

This rounds to 5.0 or simply 5 when rounding to 2 significant figures.

Answer:

when we put an exponent on a number which already has an exponent, the exponents are multiplied

we have: [tex]3^{6^{18} }[/tex]

= [tex]3^{108}[/tex]

(3)^6×18

(3)^108

now if you want to further simplify it then just simply calculate 3^108 on the calculator

to make it clear (3^6)^18 and 3^6^8 are two different situations

in the first one the power will be multiplied by the second power

and in the second one 6 will be multiplied by itself 8 times

Answer:

A)82.02 mi

B) 18.7° SE

Step-by-step explanation:

From the image attached, we can see the angles and distance depicted as given in the question. Using parallel angles, we have been able to establish that the internal angle at egg island is 100°.

A) Thus, we can find the distance between the home port and forrest island using law of cosines which is that;

a² = b² + c² - 2bc Cos A

Thus, let the distance between the home port and forrest island be x.

So,

x² = 40² + 65² - 2(40 × 65)cos 100

x² = 1600 + 4225 - (2 × 2600 × -0.1736)

x² = 6727.72

x = √6727.72

x = 82.02 mi

B) To find the bearing from Forrest Island back to his home port, we will make use of law of sines which is that;

A/sinA = b/sinB = c/sinC

82.02/sin 100 = 40/sinθ

Cross multiply to get;

sinθ = (40 × sin 100)/82.02

sin θ = 0.4803

θ = sin^(-1) 0.4803

θ = 28.7°

From the diagram we can see that from parallel angles, 10° is part of the total angle θ.

Thus, the bearing from Forrest Island back to his home port is;

28.7 - 10 = 18.7° SE

Answer:

No

Step-by-step explanation:

Factors of 289 are = 1, 7, 289

answer

no

explanation

the factor of 289= 1 , 17

Answer:

14.74%

Step-by-step explanation:

The formula for ANNUAL PERCENTAGE YIELD (APY) for an account that is COMPOUNDED CONTINUOUSLY is given as

APY = Pe^rt - 1

Where P = Principal

e = exponential

r = rate

t = time

Since Principal and Time was not given in the question,

APY = e^r - 1

r = 13.75% = 0.1375

APY = e^0.1375 - 1

APY = 1.147401706 - 1

APY = 0.147401706

Converting to percentage

= 0.147401706 × 100

= 14.7401706%

Approximately to 2 decimal places: 14.74%

Therefore, the annual percentage yield is 14.74%

*Correct Question:

Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 3/2. Is Theodore correct?

A. Yes, the triangles are similar with a scale factor of 3/2.

B. No, the triangles are similar with a scale factor of 2/1.

C. No, the triangles are similar with a scale factor of 2/3.

D. No, the triangles are similar with a scale factor of 4/3.

Answer:

C. No, the triangles are similar with a scale factor of 2/3.

Step-by-step explanation:

∆TUV is the original triangle. After transformation, the size reduced to give us ∆WXY. This means ∆TUV was reduced by a scale factor to give ∆WXY. The scale factor should be a fraction, suggesting, the original size of the ∆ was reduced upon transformation.

Thus, the ratio of their corresponding sides = the scale factor.

This is: [tex] \frac{8}{12} = \frac{16}{24} = \frac{12}{18} = \frac{2}{3} [/tex]

If you multiply the side length of ∆TUV by ⅔, you'd get side length of ∆WXY.

So, Theodore is wrong.

Answer:

6:8 and 9:12

Step-by-step explanation:

The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

When compared to one another, equivalent ratios are defined as having the same values.

For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

Given:

The table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, then

ratio = 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

so,

6/8 = 3/4

9/12 = 3/4

Thus, 6/8 = 9/12 = 3/4, which is equivalent.

Hence, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

Learn more about equivalent ratios here:

brainly.com/question/13513438

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Answer: Find answer in the attached file

Answer:

a: -2f(x+4)

Step-by-step explanation:

Took the quiz, got 100%.

The function f(x) = ∛x is transformed to obtain g(x) = -2f(x + 4). Option A is correct.

The function f(x) = ∛x is shifted horizontally to the left by 4 units.

This means that every point on the graph of f(x) is moved 4 units to the left.

After the horizontal shift, the function is reflected vertically and stretched vertically by a factor of 2.

The reflection indicates that the graph is flipped upside down, and the stretching means that the graph is elongated vertically by a factor of 2.

By applying these transformations to the function f(x) = ∛x, we obtain the function g(x) = -2f(x + 4).

The negative sign indicates the vertical reflection, and the factor of 2 represents the vertical stretching.

The horizontal shift of 4 units is applied to the argument of the function, which is (x + 4)

To learn more on Graph transformations click:

https://brainly.com/question/19040905

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Answer:

B. 0.58 + 1.48h

Step-by-step explanation:

h+0.48h+0.58

=(1h+0.48h)+0.58

=1.48h +0.58

Answer:

Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.

Step-by-step explanation:

Parametric tests are used for interval and ratio data and Non parametric tests are used for ordinal and nominal data.

The interval data shows data with differences or intervals.

The ratio data is the one in which statistical inferences is used and can be added ,subtracted , multiplied, or divided.

Ordinal data is one in which we measure quantitative data such as height , weight  but is in order.

Nominal data  is one in which we measure quantitative data such as hair color eye color  without order or which does not require order or sequence.

Answer:

C

Step-by-step explanation:

Note that the right triangle has two tick marks.

This means that the sides are equivalent.

Therefore, this is a 45-45-90 triangle.

In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2

Since n is 5√2, then the hypotenuse x is n√2. Thus:

[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]

Simplify:

[tex]x=5(2)=10[/tex]

The answer is C :)

Answer:

tan (thita) = 35/13

Step-by-step explanation:

Tan( angle) = opposite/ adjacent

Tan( angle) = 35/13

Angle = arc tan 35/13

Angle = 69.624 degrees

Round the answer as needed.

Answer:

the probability that a randomly chosen test-taker will score 142 or lower = 0.8643

Step-by-step explanation:

We are given;

Data point; x = 142

Mean; μ = 153

Standard deviation; σ = 10

So,let's find the z-score using;

z = (x - μ)/σ

z = (142 - 153)/10

z = -1.1

From the z-distribution table attached, the probability is;

P(z < -1.1) = 1 - 0.13567 ≈ 0.8643

Answer:

Two integers are relatively primes if and only if their only common positive integer factor is 1.

Step-by-step explanation:

The prime number is one whose only divisor is 1 and itself.

The prime factors of a whole number are the exact prime divisors of that whole number. In other words, every composite number can be written as a multiplication of two or more prime factors.

So, two integers are relative primes if they have no prime factor in common, or, put another way, if they have no common divisor other than 1.

So, two integers are relatively primes if and only if their only common positive integer factor is 1.

Answer: Amounts

Step-by-step explanation:

Time series analysis are the method which are used by researchers to analyze the time series data so as to get the features of the data and to also derive meaningful statistics.

A linear trend equation is used to represent time series values when the data are changing by equal amounts.

Answer:

3.04

Step-by-step explanation:

Given the prediction equation:

y_hat = 145.5 -5.5*x

- - - - x - - - - - - - - - у

1 - - 10.36 - - - - 87.87

2 - - 9.96 - - - - 89.83

3 - - 12.50 - - - - 71.61

1) y_hat = 145.5 -5.5*(10.36)

y_hat = 145.5 - 56.98 = 88.58

2) y_hat = 145.5 -5.5*(9.96)

y_hat = 145.5 - 54.78 = 90.72

3) y_hat = 145.5 -5.5*(12.50)

y_hat = 145.5 - 68.75 = 76.75

Root mean squared error (RMSE) :

Number of observations (n) = 3

√(Σ(y_hat - y)^2) / n

y_hat = predicted value

y = actual value

Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]

Σ(0.71^2) + (0.89^2) + (5.14^2)

27.7158 / 3 = 9.2386

√9.2386

= 3.0395065

= 3.04

Answer:

The  value  is   [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]

Step-by-step explanation:

From the question we are told that

    The  total number of cars is  [tex]n = 35[/tex]

     The  number cars considered is  [tex]r = 3[/tex]

Generally the number of different top three finishes possible for this race of 35 cars  is mathematically represented as

       [tex]\left n } \atop }} \right. P_r = \frac{n!}{(n - r) !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = \frac{35! }{(35 - 3) !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = \frac{35 * 34 * 33 * 32! }{32 !}[/tex]

       [tex]\left 35 } \atop }} \right. P_3 = 39270[/tex]

Answer:

[tex]\mathbf{ - \dfrac{3 \pi^2}{2}}[/tex]

Step-by-step explanation:

Given that:

F(x, y, z) = 5xi - 5yj - 3zk

The objective is to evaluate the [tex]\int _c F \ dr .C[/tex]

and C is given by the vector function  r(t) = (sin t, cost, t) where  0 ≤ t ≤ π

[tex]F(r(t)) = 5 \ sint \ i - 5 \ cost \ j - 3t \ k[/tex]

∴

[tex]\int_c F . \ dr = \int ^{\pi}_{0} ( 5 \ sint \ i - 5 cos t \ j - 3 t \ k ) ( cos \ t , - sin \ t , 1 ) \ dt[/tex]

[tex]=\int ^{\pi}_{0} ( 5 \ sint \ cost+ 5 cos t \ sin t - 3 t) dt[/tex]

[tex]=\int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt -3 \int ^{\pi}_{0} \ dt[/tex]

[tex]= \int ^{\pi}_{0} ( 10 \ sint \ cost) \ dt - 3 [\dfrac {t^2}{2}]^{\pi}_{0} \ \ dt[/tex]

[tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0} - \dfrac{3}{2}(\pi)^2[/tex]

By dividing 2 with 10 and integrating [tex]= 10 [\dfrac{sin^2 \ t}{2}]^{\pi}_{0}[/tex]; we have:

[tex]=5(sin^2t -sin^2 0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]=5(0) -\dfrac{3 \pi^2}{2}[/tex]

[tex]= 0 - \dfrac{3 \pi^2}{2}[/tex]

[tex]\mathbf{= - \dfrac{3 \pi^2}{2}}[/tex]