2(5/2x+8)=20x-14
Solve for x

The equation of the line that is parallel and perpendicular to y = -8x + 6 and passes through the point (7, 5) are y = -8x + 61 and  \(y = \frac{1}{8}x + \frac{33}{8}\) respectively.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

y = -8x + 6

Using the slope intercept:

Slope m = -8

Since the desired line is parallel, it will have the same slope.

Therefore, the slope of the parallel line is also -8.

Plug in the slope m = -8 and the poin (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

( y - 5) = -8( x - 7 )

Simplify

y - 5 = -8x + 56

y = -8x + 56 + 5

y = -8x + 61

The equation of the parallel line is y = -8x + 61.

For the perpendicular line:

The slope of the perpendicular line will be the negative reciprocal of -8, which is 1/8.

Hence, plug slope m = 1/8 and point (7,5) into the point-slope form:

( y - y₁ ) = m( x - x₁ )

\(y - 5 = \frac{1}{8} ( x + 7 )\\\\y - 5 = \frac{1}{8}x + \frac{7}{8} \\\\y = \frac{1}{8}x + \frac{7}{8} + 5\\\\y = \frac{1}{8}x + \frac{33}{8}\)

Therefore, the perpendicular line is \(y = \frac{1}{8}x + \frac{33}{8}\).

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Answer: 3.9

Step-by-step explanation:

Since the one hundredth digit is below 5 the higher digits will stay as they are.

Answer:

See below for answers and explanations (along with a graph for #3)

Step-by-step explanation:

Problem #1

Applying scalar multiplication, \(-4w=-4\langle-96,-180\rangle=\langle384,720\rangle\).

Its magnitude would be \(||-4w||=\sqrt{384^2+720^2}=816\).

Its direction would be \(\displaystyle\theta=tan^{-1}\biggr(\frac{720}{384}\biggr)\approx61.927^\circ\approx62^\circ\).

Thus, B) 816; 62° is the correct answer

Problem #2

Find the time it takes for the ball to cover 13ft:

\(x=(24\cos48^\circ)t\\13=(24\cos48^\circ)t\\t\approx0.8095\)

Find the height of the ball at the time it takes for the ball to cover 13ft:

\(y=6.1+(24\sin48^\circ)t-16t^2\\y=6.1+(24\sin48^\circ)(0.8095)-16(0.8095)^2\\y\approx10.053\)

Thus, A) 10.053 is the correct answer

Problem #3

We have \(u=\langle0,-8\rangle\) and \(v=\langle6,0\rangle\) as our vectors. Thus, \(u+v=\langle0+6,-8+0\rangle=\langle6,-8\rangle\). Attached below is the correct graph. You can also solve the problem visually by using the parallelogram method where the resultant vector is the diagonal of the parallelogram.

Problem 4 (#7)

\(\displaystyle t \cdot v=(7)(-10)+(-3)(-8)=-70+24=-46\)

Thus, C) -46 is the correct answer

Problem 5 (#8)

Find \(r\) and \(\theta\):

\(r=\sqrt{x^2+y^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}\approx8.246\)

\(\displaystyle\theta=tan^{-1}\biggr(\frac{y}{x}\biggr)=tan^{-1}\biggr(\frac{-8}{2}\biggr)\approx-75.964^\circ\)

Find the true direction angle accounting for Quadrant IV:

\(\theta=360^\circ-75.964^\circ=284.036^\circ\)

Write the complex number in polar/trigonometric form:

\(z=8.246(\cos284.036^\circ+i\sin284.036^\circ)\)

Thus, C) 8.246(cos 284.036° + i sin 284.036°) is the correct answer

Problem 6 (#12)

Eliminate the parameter and find the rectangular equation:

\(x=3t\\\frac{x}{3}=t\\ \\y=t^2+5\\y=(\frac{x}{3})^2+5\\y=\frac{x^2}{9}+5\\9y=x^2+45\\0=x^2-9y+45\\x^2-9y+45=0\)

Thus, D) x^2-9y+45=0 is the correct answer

Problem 7 (#13)

Find the magnitude of the vector:

\(||v||=\sqrt{(-77)^2+36^2}=85\)

Find the true direction of the vector accounting for Quadrant II:

\(\displaystyle \theta=tan^{-1}\biggr(\frac{36}{-77}\biggr)\approx-25^\circ=180^\circ-25^\circ=155^\circ\)

Write the vector in trigonometric form:

\(w=85\cos155^\circ i+85\sin155^\circ j\)

Thus, D) w=85cos155°i+85sin155°j is the corrwect answer

Problem 8 (#15)

\(\frac{z_1+z_2}{2}=\frac{(3-7i)+(-9-19i)}{2}=\frac{-6-26i}{2}=-3-13i=(-3,-13)\)

Thus, C) (-3,-13) is the correct answer

Problem 9 (#16)

Treat the golf ball and wind as vectors:

\(u=\langle1.3\cos140^\circ,1.3\sin140^\circ\rangle\) <-- Golf Ball

\(v=\langle1.2\cos50^\circ,1.2\sin50^\circ\rangle\) <-- Wind

Add the vectors:

\(u+v=\langle1.3\cos140^\circ+1.2\cos50^\circ,1.3\sin140^\circ+1.2\sin50^\circ\rangle\approx\langle-0.225,1.755\rangle\)

Find the magnitude of the resultant vector:

\(||u+v||=\sqrt{(-0.225)^2+1.755^2}\approx1.769\)

Find the true direction of the resultant vector accounting for Quadrant II:

\(\displaystyle \theta=\tan^{-1}\biggr(\frac{1.755}{-0.225}\biggr)\approx-82.694^\circ\approx-83^\circ=180^\circ-83^\circ=97^\circ\)

Thus, B) 1.769 m/s; 97° is the correct answer

Problem 10 (#17)

Identify the vectors and add them:

\(u+v+w=\langle50\cos20^\circ,50\sin20^\circ\rangle+\langle13\cos90^\circ,13\sin90^\circ\rangle+\langle35\cos280^\circ,35\sin280^\circ\rangle=\langle50\cos20^\circ+13\cos90^\circ+35\cos280^\circ,50\sin20^\circ+13\sin90^\circ+35\sin280^\circ\rangle=\langle53.062,-4.367\rangle\)

Find the magnitude of the resultant vector:

\(||u+v+w||=\sqrt{53.062^2+(-4.367)^2}\approx53.241\)

Find the true direction of the resultant vector accounting for Quadrant IV:

\(\displaystyle \theta=\tan^{-1}\biggr(\frac{-4.367}{53.062}\biggr)\approx-4.705^\circ\approx-5^\circ=360^\circ-5^\circ=355^\circ\)

Thus, A) 53.241, 355° is the correct answer

Problem 11 (#18)

We observe that \(z_1=-8-6i\) and \(z_2=4-4i\), hence, \(z_1+z_2=(-8-6i)+(4-4i)=-4-10i\)

Thus, Q is the correct answer

Problem 12 (#19)

Find the dot product of the vectors:

\(F_1\cdot F_2=(12000*14500)+(7000*-5000)=174000000+(-35000000)=139000000\)

Find the magnitude of each vector:

\(||F_1||=\sqrt{12000^2+7000^2}=1000\sqrt{193}\\||F_2||=\sqrt{14500^2+(-5000)^2}=500\sqrt{941}\)

Find the angle between the two vectors:

\(\displaystyle \theta=\cos^{-1}\biggr(\frac{F_1\cdot F_2}{||F_1||||F_2||}\biggr)\\ \theta=\cos^{-1}\biggr(\frac{139000000}{(1000\sqrt{193})(500\sqrt{941})}\biggr)\\\theta\approx49.282^\circ\approx49^\circ\)

Thus, C) 49° is the correct answer

Problem 13 (#20)

Using scalar multiplication, \(7v-2w=7\langle8,-3\rangle-2\langle-12,4\rangle=\langle56,-21\rangle-\langle-24,8\rangle=\langle56-(-24),-21-8\rangle=\langle80,-29\rangle=80i-29j\)

Thus, A) -80i - 29j is the correct answer

Answer:

3.75 in decimal form and 3 3/4 in fraction form

Step-by-step explanation:

Answer:

x=0.7

Step-by-step explanation:

Answer:

\(\sqrt[9]{x^{7} }\)

Step-by-step explanation:

Hope this helps

Answer:

(3 x - 5)^{2}

Step-by-step explanation:

Rewrite the expression into the form of a^2\pm 2ab+b^2:(3 x)^{2} - 2 \times 3 x \times 5 + 5^{2}

Factor the expression using a^{2}\pm 2ab+b^{2}=(a\pm b)^{2}:(3 x - 5)^{2}

Answer: (3 x - 5)^{2}

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer:

There is only one solution to the equation

Step-by-step explanation:

Let's begin by solving the equation

4z + 2(z-4) = 3z + 11

4z + 2z - 8 = 3z + 11

6z - 3z = 11 + 8

3z = 19

z = 19/3

Answer:

a = 127 kg

b = 55 kg

Step-by-step explanation:

a + b = 182

a - 36 = b + 36

   + 36      + 36

a = b + 72

(a) + b = 182

(b + 72) + b = 182

2b + 72 = 182

      -72    -72

2b = 110

÷2    ÷2

b = 55

a + (b) = 182

a + (55) = 182

   - 55      - 55

a = 127

{127 - 36 = 91}

{55 + 36 = 91}

{91 + 91 = 182}

The estimated value of 2/3 is roughly 0.67, of 1 it is 1 and for 0 it is 0.

What does a estimate mean?

A number given to a demographic parameter that was taken from the a statistical sample. A pricing estimate for the job that needs to be done. 3. an assessment or view of the essence, character, or trait of an object or a person.

What is an illustration of an estimate?

To make computations simpler, an estimate is an approximate estimation of the real value, amount, or quantity.

For 2/3, on dividing we get the value as 0.67.

Since 1 is a number and doesn't need to be rounded or approximated, the guess is 1.

Since it is a number without a fractional component, the approximation of 0 also is 0.

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Answer:

52

Step-by-step explanation:

78 divided by 3 is 26

26 times 2 is 52

Given:

The triangles  ΔKRO and ΔKCO are right triangles with common leg and congruent hypotenuse. It is sufficient for HL (Hypotenuse - leg) congruence. RK and KC are hypotenuse and OK is common leg.

     Statement                                       Reason                

Given:

To prove FG ≅ AG, we'll first prove the triangles are congruent by AAS as we have one congruent angle pair, one side is common to both triangles, another pair of congruent angles is formed by the angle bisector. The common side is adjacent to one of the congruent angles but not included.

     Statement                                       Reason                

Answer:

Step-by-step explanation:

An appropriate inequality would be w ≤ 1.6 tons

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

The value of x = 109°

angle PQS = 24°

Step-by-step explanation:

24° + 47° + x = 180° { angles on straight line }

=> 71 ° + x = 180°

=> x = 180° - 71°

=> x = 109°

Now,

Angle PQS = 24°

angle PQS = angle QSR { alternative angle }

Step-by-step explanation:

a)(i) x=109°

(ii)It's given that PST is straight line then PST=180°,and

PST=QSP+QSR+x

180° =47°+24°+x

180°=71°+x

180°-71°=x

109°=x

b)(i)PQS=71°

(ii)we know opposite angles are equal in parallelogram

so PSR=PQR=71°

The location which is in the region for plants receiving the maximum amount of water is "(-3,-1)". The Option A is correct.

Water flows into the open pore spaces in the soil by gravity, and the size and spacing of the soil particles determine how much water can flow in. Because coarse soils have larger pore spacing at the soil surface, they have a higher infiltration rate than fine soils.

Based on the graph, we observed that the point of location in which is in the region for plants receiving the maximum amount of water is the point (-3,-1). Therefore, we agree that Option A is correct.

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Answer: 2 seconds

Step-by-step explanation:

i got it right on plato/edmentum

Answer:

x > 5 or x < -9

Pls mark brainliest. Thanks!

Answer:

\(x =i\\\\x =-i\\\\x=\sqrt 5\\\\x=-\sqrt 5\)

Step-by-step explanation:

\(~~~~~~~~x^4-4x^2 -5 = 0\\\\\implies x^4-5x^2+x^2 -5 = 0\\ \\\implies x^2(x^2 -5)+(x^2-5) =0\\ \\\implies (x^2 +1)(x^2 -5) - 0\\\\\implies x^2+1 = 0~~~~~~~~~ \text{Or}~~~~~~~~~ x^2 -5 = 0\\\\\implies x^2 = -1~~~~~~~~~~~~ \text{Or}~~~~~~~~~x^2 = 5\\\\\implies x= \pm\sqrt{-1}~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\\\\implies x = \pm i~~~~~~~~~~~~~~\text{Or}~~~~~~~~~x=\pm\sqrt 5\\\)

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Answer:

it is called an irrational number

Step-by-step explanation:

I think that this is a fact answer, so I don't know how to explain it

Answer:

-4x

Step-by-step explanation:

((-3x-4+y) + (4x-y)) - (5x-4)
= (-3x-4+y+4x-y) - 5x+4
= (x-4) -5x+4
=x-4-5x+4
=-4x

The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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Answer:

-x²³ - 5xy² + y² + 5x²y/3 -X 3 (x-y) (x² - y²)

Step-by-step explanation:

cuz of my handy calculator

Answer:

20.25

Step-by-step explanation:

7.5x 2.7

break it down 7.5x2=15

7.5x 0.7=5.25 add all together and when multiplying don't forget to move decimals over

Answer:

x^2+y^2=25

Step-by-step explanation:

bc x-0=x and ect.

Answer:

u= 55/17

Step-by-step explanation:

Answer:

Step-by-step explanation:

u/11=5/17 so cross multiplication, 17u=5*11, 17u=55, so u =55/17

Answer: SAS

Step-by-step explanation:

Answer:

there's no angle z theres only x but the answer for x is 133

Step-by-step explanation: