Slope criteria for Parallel and Perpendicular Lines: Mastery Test
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Given: A B || CD
If the coordinates of point A are (8.0) and the coordinates of point Bare (3.7), the y-intercept of AB is
. If the coordinates of
point Dare (5,5). the equation of line CD is y=
X +
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Answer:

[tex]\frac{7}{2}\sqrt{3}[/tex]

Step-by-step explanation:

the ratio of hypotenuse to longer leg of 30-60-90 triangle is 1 to sqrt(3)/2, and multiply by 7 to obtain answer

Answer:

4 cups of flour is needed and 4/3 cups of sugar

Step-by-step explanation:

Given

2 dozen Muffins; 3 cups of flour and 1 cup of sugar

Required

Determine the cups of flour if 18 muffins is used

First, we have to determine the proportion of the number of muffins used previously and now;

Represent this with p;

[tex]p = \frac{2\ dozen}{18}[/tex]

[tex]p = \frac{2 * 12}{18}[/tex]

[tex]p = \frac{24}{18}[/tex]

[tex]p = \frac{4}{3}[/tex]

Multiply this to the previous cups of flours and sugars;

Cups of flour = p * previous cups of flour

[tex]Cups\ of\ flour = \frac{4}{3} * 3[/tex]

[tex]Cups\ of\ flour = 4[/tex]

Cups of Sugar = p * previous cups of sugar

[tex]Cups\ of\ sugar= \frac{4}{3} * 1[/tex]

[tex]Cups\ of\ sugar= \frac{4}{3}[/tex]

Hence, 4 cups of flour is needed and 4/3 cups of sugar

1 gallon = 4 quarts

4 quarts = 8 pints

8 pints = 16 cups

16 cups = 128 fluid ounces

He bought 128 ounces

Answer:

D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)

(4, 0)

[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)

(0,-16)

[tex]c = -16[/tex] (Eq. 3)

Then,

[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)

[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)

[tex]a = 4 + 0.5\cdot b[/tex]

Then,

[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)

[tex]64 + 12\cdot b = 16[/tex]

[tex]12\cdot b = -48[/tex]

[tex]b = -4[/tex]

The remaining coeffcient is:

[tex]a = 4 + 0.5\cdot b[/tex]

[tex]a = 4 + 0.5\cdot (-4)[/tex]

[tex]a = 2[/tex]

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.

Answer:

D ƒ(x) = 2x2 – 4x – 16

Step-by-step explanation:

The measures of the angles between the peaks are;

m∠BSC = 22.5°

m∠ASB = 67.5°

The reason for arriving at the above angles is as follows:

The known values are;

The location of the surveyor = Point S

The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC

The measure of angle m∠ASC = A right angle = 90°

Required:

To find m∠ASB and m∠BSC

From the given diagram, we have;

m∠ASC = 90°

m∠ASC = m∠ASB + m∠BSC (angle addition postulate)

m∠ASB = 3 × m∠BSC

∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC

m∠ASC = 4 × m∠BSC = 90°

m∠BSC = 90°/4 = 22.5°

m∠BSC = 22.5°

m∠ASB = 3 × m∠BSC

∴ m∠ASB = 3 × 22.5° = 67.5°

m∠ASB = 67.5°

Learn more about angle addition postulate here:

https://brainly.com/question/4208193

Answer:

342 m

Step-by-step explanation:

SIn(20) * 1000 = RS

342 = RS

Answer:

Yes, it is invertible

Step-by-step explanation:

We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.

Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!

Then the determinant of this matrix becomes:

[tex]4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0[/tex]

And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:

[tex]Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3[/tex]

Therefore, the Det of the initial matrix is : 4 * 3 = 12

and then the matrix is invertible

Answer:

1). m° = 56.1°

2). X= 91.8 mm

Step-by-step explanation:

For angle m°

Using the sine rule

15.1/sin m= 18.2/sin 90

But Sin 90= 1

15.1/sin m= 18.2

15.1= 18.2*sin m

Sin m = 15.1/18.2

Sin m=0.8297

m= sin^-1(0.8297)

m= 56.06°

m° = 56.1°

For length of side x

Using sine rule

X/sin 61= 105/sin 90

But sin 90= 1

X/sin 61= 105

X = sin61 *105

X=0.8746*105

X= 91.833 mm

X= 91.8 mm

Answer:

(3, 0)

Step-by-step explanation:

x-intercept is where the line touches the x-axis

It is the point on the line where y=0

Answer:

3,0

Step-by-step explanation:

the point where the line cuts the x axis is the x-intecept

Answer:

See below.

Step-by-step explanation:

From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.

In set-builder notation, this is:

[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]

In interval notation, this is:

[tex][3,5)[/tex]

Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.

Answer:

[tex]log_{10}[/tex] 10000 = 4

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Here b = 10, n = 4 and x = 10000, thus

[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form

that is [tex]10^{4}[/tex] = 10000 ← in exponential form

Answer:

[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]

Step-by-step explanation:

Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:

[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]

9514 1404 393

Answer:

  A

Step-by-step explanation:

Vertical multiplication of polynomials is virtually identical to vertical multiplication of integers. The "place value" associated with a column is the power of the variable. When adding within a column, there is no "carry" to the next column the way there is with integers.

Here, the correct answer choice can be found by looking at the coefficients of x^2 and of x.

Answer:

Step-by-step explanation:

Hello, please consider the following.

Question 1.

[tex]\dfrac{3^{2x+1}}{3^{3x-4}\cdot 3^{6-7x}}=27^x\\\\<=> 3^{2x+1}\cdot 3^{-3x+4}\cdot 3^{-6+7x}=3^{2x+1-3x+4-6+7x}=(3^3)^x=3^{3x}\\\\<=> 2x+1-3x+4-6+7x=3x\\\\<=> 6x-1=3x\\\\<=> 3x=1\\\\<=> \boxed{x=\dfrac{1}{3}}[/tex]

Question2.

[tex]2^{x+y}=8=2^3 <=>x+y=3\\\\3^{x-y}=1=3^0<=>x-y=0[/tex]

So, it gives (by adding the two equations) 2x = 3

[tex]\boxed{x=\dfrac{3}{2} \ \ and \ \ y = x = \dfrac{3}{2} }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Sphere Volume = 4/3 * PI * radius^3

Sphere Volume = 4/3 * PI * 8^3

Sphere Volume = 4/3 * PI * 512

Sphere Volume = 2,144.7 cubic inches

Step-by-step explanation:

Answer:

x=3, multiplicity of 2

x=-5, multiplicity of 1

Step-by-step explanation:

f(x) = (x - 3)(x - 3)(x + 5)

Rewriting

f(x) = (x - 3)^2(x + 5)

Setting equal to zero

0 =  (x - 3)^2(x + 5)

Using the zero product property

(x-3)^2  = 0   x+5 = 0

x-3 = 0         x= -5

x=3             x-5

Since x-3 was squared, the multiplicity is 2

Answer:

x=3, multiplicity of 2

x=-5, multiplicity of 1

Step-by-step explanation

Step-by-step explanation:

what is the criteria for success ? how many questions must be right ? and how many must be wrong for failure ?

if success means all answers right, then she has 4 choices on the first question to pick one right answer. and then for each of those again 4 choices on the second question and so on.

so, all possible outcomes are 4²⁰.

that means the probability to guess all 20 right is

1/4²⁰

a tiny, tiny number.

and the probabilty to have all wrong ?

she has 4 choices to pick 1 of 3 wrong answers.

so, the probability is 3/4 to answer the first question wrong.

for that she has again then the same chance to get the second question wrong too.

so, it is 3/4 × 3/4 = 9/16

and so on.

the probability to guess all 20 wrong is then

(3/4)²⁰ ≈ 0.0032

that is still a small number but much, much larger than the probability to get everything right.

still, even the goal to truly get everything wrong is highly unlikely.

Answer:

72

Step-by-step explanation:

The formula for surface area is SA = 2lw + 2wh + 2lh

W = width

L= length

H = height

A = 2(wl + hl + hw)

2·(6·3+2·3+2·6)

Simplify that down to get the answer 72

9514 1404 393

Answer:

  990 square inches

Step-by-step explanation:

The area is the half the product of length and height.

  A = (1/2)(18 in)(110 in) = 990 in²

The area of the triangle is 990 square inches.

9514 1404 393

Answer:

Step-by-step explanation:

-2 is 2 units in the negative direction (left on a number line). When that is added to 3, the result is 2 units from 3 in the negative direction.

Answer:

The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.

If it was just a number and no x then it would still be the coefficient.

The degree is 9 as it is the highest power shown.

Step-by-step explanation:

See attachment for examples

Answer:

x = 18

Step-by-step explanation:

To solve this problem, we can use the exterior angle theorem, which means the measure of an exterior angle is the sum of its remote interior angles. In this case, this would mean:

x + 72 = 5x

Since this gives us an equation, we can just solve for x:

x + 72 = 5x

72 = 4x

x = 18

Answer:

failure to correctly define the problem

Step-by-step explanation:

He changes the menu without identify that the real problem was the service.

Answer:

3 and 2

Step-by-step explanation:

I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.

Answer:

Washer $735

Dryer $245

Step-by-step explanation:

If x is the cost of the washer, and y is the cost of the dryer, then:

x + y = 980

x = 3y

Solve with substitution.

3y + y = 980

4y = 980

y = 245

x = 735

Answer:

Macroeconomics is a study that deals with the whole economy and everything pertaining to it.

Step-by-step explanation:

when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.

Answer:

A

Step-by-step explanation: