Mathematics College

Choose the point-slope form of the equation below that represents the line that passes through the points (−3, 2) and (2, 1).
A. y + 3 = −5(x − 2)
B. y − 2 = −5(x + 3)
C. y + 3 = −one fifth(x − 2)
D. y − 2 = −one fifth(x + 3)

Answers

Answer 1
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 2}})\quad % (c,d) &({{ 2}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{1-2}{2+3}[/tex]

[tex]\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=2\\ x_1=-3\\ m=\boxed{?} \end{cases} \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}[/tex]
Answer 2
the answer is C or y-2=-1/5(x+3)

Related Questions

If 3/2 divided by 1/4 =n, then n is between

Answers

3/2 / 1/4 = 3/2 * 4/1 
3*4= 12
2*1= 1
n= 12/1 or 12

Hope this helps! 

Find the measure of the angle and please explain step by step

Answers

angle 4 is the same as angle 8

 angle 7 & angle 8 has to equal 180 degree

 so angle 7 and angle 4 also have to equal 180

angle 4 is 3 times the size of 7

lets call 7  (x)

so 4(x) = 180

180/4  =45

x=45

angle 7 is 45 degrees

Question part points submissions used use a power series to approximate the definite integral, i, to six decimal places. 0.3 ln(1 + x4) dx 0

Answers

[tex]\ln(1+x)=\displaystyle-\sum_{n=1}^\infty\frac{(-x)^n}n[/tex]

[tex]\implies\ln(1+x^4)=\displaystyle-\sum_{n=1}^\infty\frac{(-x^4)^n}n[/tex]

[tex]\displaystyle-\int_0^{0.3}\sum_{n=1}^\infty\frac{(-x^4)^n}n\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\int_0^{0.3}x^{4n}\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\dfrac{x^{4n+1}}{4n+1}\bigg|_0^{0.3}[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}(0.3)^{4n+1}}{n(4n+1)}[/tex]
[tex]\approx0.000485[/tex]

Add (11a + 4b) + (a +4b - 2)


A) 12a + 8b - 2
B) 12a - 2
C) 11a - 2
D) 11a + 8b - 2

Answers

The answer to that question is A.

What is 6 increased by a number?

Answers

6 increased by a number in algebraic terms would be 6+x.

An employer interviews 10 people for 6 technical support positions in a company, and 5 of the 10 people are women. If all 10 are qualified, in how many ways can the employer fill the technical support positions if exactly 3 are women?

Answers

Let the people be {M1, M2, M3, M4, M5, W1, W2, W3, W4, W5}

where M1 is Man 1, W1 woman 1 and so on...


The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], gives the total numbers of ways of creating groups of r out of n.

r! means 1*2*3*...(r-1)*r.


The technical support group is going to have exactly 3 women, which will be chosen from 5 women, and 3 men which will be chosen from 5 men.

Each of the selections can be done in C(5, 3) many ways, and since the any selection of the men and women can be combined, in total there are:

C(5,3) *C(5, 3) many ways of creating the technical support group.

[tex]C(5,3) = \frac{5!}{3!2!}= \frac{5*4*3*2*1}{3*2*1*2*1}=10 [/tex]

10*10=100 many ways of forming the group.


Answer: 100

3x+17-5x=12-(6x+3) can someone help

Answers

3x+17-5x=12-(6x+3)

-2x+17=12-6x-3

-2x+17=9-6x

17=9-4x

8=-4x

x=-2
3x+17-5x=12-(6x+3)
-2x17=12-6x+3
-2x+17=9-6x
2x+6x=9-17
4x=-8
x=-2

How many license plates can be made using 3 digits and 3 letters of repeated digits and letters are not allowed?statistics?

Answers

[tex]10\cdot9\cdot8\cdot26\cdot25\cdot24=11,232,000[/tex]

Estimate then find the product 7×7956

Answers

Final answer:

To estimate the product of 7 and 7956, round 7956 to 8000 and then multiply by 7 to get 56,000. The exact product, calculated using the multiplication algorithm, is 55,692.

Explanation:

To estimate the product of 7×7956, we can round 7956 to the nearest thousand which gives us 8000. Then, we multiply 7×8000 to get an estimated product of 56,000. To find the exact product, we multiply 7 by 7956 to get 55,692.

When calculating such a product, we use the multiplication algorithm where we multiply each digit of the second number by the first number and then add up the resulting values.

Here's how you would perform the multiplication step by step:

7×7 = 49, add the carried over 6 to get 55, write down 5 and carry over the 5.

After placing the digits in their correct positions, we get the final answer: 55,692. Therefore, the exact product of 7×7956 is 55,692.

A triangle has an area of 56 square units its height is 14 units what is the length of its base

Answers

the length of the base is 8
area=56
height= 14
A=1/2 bh
56=1/2 b(14)
56=b(14)/2
8=b

Txt me quicky i need help

Answers

your chances of getting a even number is 

P(even) = 4/8

simplified is 1/2


hope this helps

If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?

Answers

Final answer:

The commutative property allows you to rearrange the factors of a multiplication problem.

Explanation:

The property that allows you to rearrange the factors of a multiplication problem is the commutative property. This property states that the order of the factors can be changed without changing the product. In this case, if cba represents three numbers multiplied together, you can rearrange the factors to read abc because multiplying in any order will give you the same product.

For example, if c = 2, b = 3, and a = 4, then cba = 2 * 3 * 4 = 24. Rearranging the factors to abc gives abc = 4 * 3 * 2 = 24, which is the same product.

Simplify 2(f^4)^2 f^3 divided by 6f^9

Answers

((2f^4)^2*f^3)/(6f^9)

pertinent rules of exponents:

(a^b)^c=a^(b*c),  (a^b)(a^c)=a^(b+c), and (a^b)/(a^c)=a^(b-c) so

(2f^(4*2)*f^3)/(6f^9)

(2f^8*f^3)/(6f^9)

(2f^(8+3))/(6f^9)

(2f^11)/(6f^9)

(2/6)(f^11/f^9)

(1/3)(f^(11-9)

(1/3)(f^2)

(f^2)/3

Final answer:

The expression 2(f^4)^2 f^3 divided by 6f^9 simplifies to 1/3 f^2, after applying the properties of exponents and dividing coefficients.

Explanation:

To simplify the expression 2(f^4)^2 f^3 divided by 6f^9, we need to use the properties of exponents. First, we simplify (f^4)^2 by multiplying the exponents, which gives us f^8.

Then, we multiply f^8 by f^3 to get f^11. Next, we divide our new expression 2f^11 by 6f^9. This can be done by dividing the coefficients (2 divided by 6) and subtracting the exponents of f (11 minus 9), resulting in f^2 over 3, or 1/3 f^2.

For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations.



f(x):

(a, f(a) and (b,f(b)

1.) f(x)=x - 3 (0,f(0)) and (6,f(6))
2.) f(x) = -x (-4,f(-4)) and(2,f(2))
3.) f(x)=x2 (-2,f(-2)) and (0,f(0))
4.) f(x)=x3 (-1,f(-1)) and (1,f(1))
5.) f(x)=2x (0,f(0)) and (4,f(4))

Answers

Function 1: 

f(x) = x - 3
f(0) = 0 - 3 = -3
f(6) = 6 - 3 = 3

Slope = [tex] \frac{-3-3}{6-0} = \frac{-6}{6} =-1[/tex]

Function 2:

f(x) = -x
f(-4) = 4
f(2) = -2

Slope = [tex] \frac{4--2}{-4-2}= \frac{6}{-6}=-1 [/tex]

Function 3:

f(x) = x²
f(-2) = (-2)² = 4
f(0) = (0)² = 0

Slope = [tex] \frac{4-0}{-2-0}= \frac{4}{-2}=-2 [/tex]

Function 4:

f(x) = x³
f(-1) = (-1)³ = -1
f(1) = (1)³ = 1

Slope = [tex] \frac{-1-1}{-1-1}= \frac{-2}{-2}=1 [/tex]

Function 5:

f(x) = 2ˣ
f(0) = 2⁰ = 1
f(4) = 2⁴ = 16

Slope = [tex] \frac{1-16}{0-4}= \frac{-15}{-4}=3.75 [/tex]

Write the event as a set of outcomes. We flip three coins and obtain more tails than heads.

Answers

We start by listing the outcome of flipping two coins. The first table shows the outcomes HH, HT, TH, and TT. These outcomes then become the input combined with the third coins, as shown in the second table.

We have 8 outcomes in total: HHH, HHT, HHT, TTH, HHT, HTT, TTH, and TTT

The probability that we obtain more tails than heads is 4/8

A parachutist's rate during a free fall reaches 165 feet per second. What is this rate in meters per second? At this rate, how many meters will the parachutist fall during 5 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answers.

Answers

Answer: [tex]250\ m[/tex]

Step-by-step explanation:

Assuming that:

[tex]1\ m=3.3\ ft[/tex]

We can make the conversion from feet per second to meters per second with this procedure:

[tex](165\ \frac{ft}{s})(\frac{1\ m}{3.3\ ft})=50\ \frac{m}{s}[/tex]

Let be "x" the amount of meters the parachutist will fall during 5 seconds of free fall

Knowing that in 1 second the parachutist falls 50 meters, we can calculate "x" by solving the following multiplication:

[tex]x=(50\ \frac{m}{s})(5\ s)\\\\x=250\ m[/tex]

Final answer:

The parachutist's rate of free fall is 165 feet per second, which is equivalent to 50 meters per second. The parachutist will fall approximately 250 meters during 5 seconds of free fall.

Explanation:

To convert the rate of 165 feet per second to meters per second, we need to use the conversion factor of 1 meter equals 3.3 feet. So, the rate in meters per second is 165 feet per second divided by 3.3 feet per meter, which equals 50 meters per second.

To find how many meters the parachutist will fall during 5 seconds of free fall, we can multiply the rate of 50 meters per second by the time of 5 seconds. This gives us 250 meters of free fall during 5 seconds.

There are 12 more toy cars than toy trucks in a toy box. With a total of 38 toy cars and trucks.How many toy trucks are in the toy box?

Answers

based on my calculation its 31 toy trucks.
i just simply do like this

38÷2
=19-12
=7

38-7
=31#

Answer:

Hui

Step-by-step explanation:

Can you help me solve this 2/3 (5 x 4) ÷ 3 + 6/7 =

Answers

[tex]\frac{2}{3}(5 *4)/3+\frac{6}{7}\\\\\frac{2*5*4}{3}*\frac{1}{3}+\frac{6}{7}\\\\\frac{2*5*4}{3*3}+\frac{6}{7}\\\\\frac{40}{9}+\frac{6}{7}\\\\\frac{40}{9}*1+\frac{6}{7}*1\\\\\frac{40}{9}(\frac{7}{7})+\frac{6}{7}(\frac{9}{9})\\\\\frac{280}{63}+\frac{54}{63}\\\\\frac{334}{63}=5\ \frac{19}{63}[/tex]
(pemdas)
this is the order you do the math
parenthesis
exponents
multiplication or division which ever is first
Addition or subtraction which ever is first

2/3 (5 x 4) ÷ 3 + 6/7
2/3 (20)÷3+6/7
40/3÷3+6/7
40/9+6/7
find common denominator
280/63+54/63
334/63 or 5.301

EASY 5 POINTS REALLY NEED HELP RN!!!! Which expression finds the length of side x in this right triangle?

Answers

Use Pythagoras:


x² = (8.5)² + (5)²


x = √[(8.5)² + (5)²]

Answer:

Top right one

Step-by-step explanation:

Add me on instagram at skyy.thatdancer

Look at the radian measure for every 30 degrees and 45 degrees in the Unit Circle. Explain how finding the exact measure in quadrant one can help you determine the remaining exact radian measures.

Answers

Google radian measures on the unit circle for lots of images of completed unit circles with these radian measurements. But the core idea is that if you can find the 30° and 45° radian measures (π/6 and π/4 respectively) to move to the corresponding angle in quadrant 2, you'd just need to add π/2 (90°) to that value, to find the values in quadrant 3 add π (180°), quadrant 4 add 3π/4 or you could also just minus π/2 to move 90° in the opposite direction. Say I wanted to find the 45° angle in quadrant 3, measured from the 0° line on the unit circle, in radians. I could say I know 45° is π/4 in quadrant 1, so to move it to quadrant 3, I need to add π or 180° to it. π/4 + π = π/4 + 4π/4 = 5π/4 which is the angle we need in radians.

Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.

Answers

tan42°=x/35

x=35tan42°  units

x≈31.51 units (to nearest hundredth of a unit)

Answer:

[tex]x=31.51\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle

[tex]tan(42\°)=x/35[/tex]

isolate the variable x

[tex]x=35tan(42\°)=31.51\ units[/tex]

What is the length of a diagonal of a square with a side length of 6?

Answers

By the Pythagorean Theorem:

d^2=x^2+y^2, where x and y are the dimensions of the rectangle, however this is just a square, so x=y=s so

d^2=s^2+s^2

d^2=2s^2, and we are told that s=6 so

d^2=2(6^2)

d^2=2(36)

d=√(2(36))

d=6√2  units

d≈8.49 units (to nearest hundredth of a unit)
d = 8.49 

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I                          I
I            d            I a
I                          I 
I                          I
I- - - - - - - - - - - - I

what number is 115% of 73.8?

Answers

To find this, multiply 73.8 by the decimal form of the percent (1.15) to get 84.87
115% of 73.8 is about 84.8

Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What is the total amount of material she needs? A. 3 1/2 yards B. 3 2/3 yards C. 4 yards D. 4 3/8 yards Mark for review (Will be highlighted on the review page)

Answers

In order to calculate this, We need to make sure that both measurements have the same denominator, so we need to transform 3/4 into a fraction with denominator of 8

1  3/4  >>>     1   6/8     ( the 6 comes from 8/4  x 3)

The total material that jane need would be:

2  5/8 + 1  6/8

= 3    11/8    

= 4    3/8

The answer is option D,



3.   Solve z2 – 15z + 56 = 0 using the zero product property.      A. z = 8, 7 B. z = –5, –2 C. z = 8, –4 D. z = –4, 7

Answers

We are tasked to solve for the values of z using and applying the zero product property which means that we need to get the factors and equate it to be equal to zero. Such that the given expression z² - 15z + 56 = 0 will have a solution shown below:
z² - 15z + 56 = 0
The expression will have a and b values such as a = - 7 and b = -8.
z² - 15z + 56 = 0
(z -7) (z-8) = 0
solving for the first value of z, we have it:
z - 7 = 0
z = 7
Solving for the second value of z, we have it:
z - 8 = 0
z = 8

Therefore, the answer to this problem is the letter "A" which is 7 and 8.

Will someone please answer this question?

Answers

surface area = 5ab +5bh

a = 4

b=7

h=18

5*4*7 = 140

5*7*18 = 630

630+140 = 770 square meters

How can you use place value and period names to read and write 324,904 in word form.

Answers

three hundred twenty-four thousand, nine hundred and four
yes you can. you would read that as:
three hundred twenty four thousand, nine hundred four.

no ands were in between the numbers because there are no decimals.
hope this helped, xx

box contains 15 items,4 of which are defective and 11 are good. Two items are selected. What is probability that the first is good and the second defective?

Answers

The probability of the first item being good is 11/15.
Since we have taken 1 item out the remaining total is now 14, so the probability of getting a defective item is now 4/14.
Now you multiply the probabilities together to get (11/15)(2/7)=22/105

Final answer:

The probability that the first item selected is good and the second item is defective is 22/105.

Explanation:

To find the probability that the first item selected is good and the second item is defective, we need to consider the total number of items, the number of good items, and the number of defective items.

The total number of items is 15, with 11 being good and 4 being defective. When we select the first item, there are 15 options, out of which 11 are good. Therefore, the probability of selecting a good item first is 11/15.

After selecting the first item, there are now 14 items left in the box, with 10 being good and 4 being defective. When we select the second item, there are 14 options, out of which 4 are defective. Therefore, the probability of selecting a defective item second is 4/14, which simplifies to 2/7.

To find the probability that both events occur, we multiply the probabilities: (11/15) * (2/7) = 22/105.

From September 1981 to September 1984 the enrollment at a particular school declined to 11%. If the number of students enrolled at that school in September 1984 was 712 what was the enrollment in September 1981?

a) 78 b) 634 c) 701
d) 790 e)800

Answers

634, you have to multiply it by 89% of the original number, 712, to deduct 11%


The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for pi .

Answers

volume = pi x r^2 x h

3.14 x 4 x 14^2 = 2461.76 cubic feet

Fixed the typo I had in my answer.

Answer:

So volume of the swimming pool is 2461.76 feet³.

Step-by-step explanation:

The Darnells are having a swimming pool installed.

The pool has a radius of 14 feet and height of 4 feet.

Since pool is in the form of a cylinder so volume of cylinder

= πr²h

= π (14)² × 4

= (3.14) (196) × 4

= 2461.76 cubic feet.

So volume of the swimming pool is 2461.76 feet³.

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