Mathematics High School

write an equation of the line that is parallel to the line y = -x + 4 and passes through the points 0, 10.

Please help me!

Answers

Answer 1
Line parallel to y = -x+4 will have the same gradient.
Gradient = -1
Equation of line: y = -x + c
Point : (0,10) replace in the above equation
y = -x + c
10 = -0 + c
c = 10
Equation is: y = -x + 10


Hope it helped!

Related Questions

You and your friend are standing back-to-back. Your friend runs 10 feet forward and then 8 feet right. At the same time, you run 11 feet forward and then 12 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?

Answers

Approximately about (20.71 ft)

Will mark brainliest!!

The histogram shows the ages of cars sold at a car auction.

What percent of the cars was less than 20 years old or more than 40 years old?

Answers

.96% (?)

I know not the correctness of my answer due to:
The Total was 8 to fit the criteria, the others older than 20 but younger than 40 are 12
(However I do not know how to calculate percentage, went to Google and got a percentage calculator to find what percentage 8 is to 12)
40% I hoped me helped

Set operations including cardinality of power sets and listing the elements of a power set and finding the number of subsets of a given size. let u = {-1, 0, 1, 2, 3, 4, 6} , a = {-1, 1, 2, 3, 4} and b = {0, 2, 4, 6}. find
a.a u b,
b.a ∩ b,
c.b – a,
d.the power set of b and its cardinality

Answers

a. a [tex]\cup[/tex] b
a [tex]\cup[/tex] b means the resulting set when a and b are merged, less duplicates.
a [tex]\cup[/tex] b={-1, 1, 2, 3, 4} [tex]\cup[/tex]  {0, 2, 4, 6}
={-1,0,1,2,3,4,6}

b. a [tex]\cap[/tex] b
a [tex]\cap[/tex] b means the set of members which are common to both a and b.
a [tex]\cap[/tex] b={-1, 1, 2, 3, 4} [tex]\cap[/tex]  {0, 2, 4, 6}
={2,4}

c. b-a
b-a is the set of members present in b but not in a.
{0, 2, 4, 6}-{-1, 1, 2, 3, 4}
={0,6}

d. Power set of b, its cardinality
Power set is the set of all possible combinations of elements.
There are 2^n members in the power set of x where n is the number of elements in the set x.
For example, power set of S={1,2} is {[tex]\phi[/tex],{1},{2},{1,2}}
The cardinality of S above is the number of elements in the set, therefore 2^2=4.

For b={0,2,4,6}
The power set is
{[tex]\phi[/tex],{0},{2},{4},{6},{0,2},{0,4},{0,6},{2,4},{2,6},{4,6},{0,2,4},{0,2,6},{0,4,6},{2,4,6},{0,2,4,6}}
for a total of 2^4=16 members in the power set.
Therefore the cardinality of the power set is 16.

 

The union of A and B is {-1, 0, 1, 2, 3, 4, 6}, the intersection is {2, 4}, and the difference B - A is {0, 6}. The power set of B contains 16 subsets.

Set Operations: Union, Intersection, Difference, and Power Sets

Let's solve the given problems step by step:

a. The union of sets A and B (A ∪ B)

A ∪ B represents all unique elements that are in either set A or set B.

Given: A = {-1, 1, 2, 3, 4} and B = {0, 2, 4, 6}

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

b. The intersection of sets A and B (A ∩ B)

A ∩ B represents all elements that are present in both sets A and B.

A ∩ B = {2, 4}

c. The difference of sets B and A (B - A)

B - A represents all elements that are in set B but not in set A.

B - A = {0, 6}

d. The power set of B and its cardinality

The power set of a set is the set of all its subsets, including the empty set and the set itself. If a set has n elements, its power set will contain 2^n subsets.

B = {0, 2, 4, 6}

The power set of B is: { {}, {0}, {2}, {4}, {6}, {0, 2}, {0, 4}, {0, 6}, {2, 4}, {2, 6}, {4, 6}, {0, 2, 4}, {0, 2, 6}, {0, 4, 6}, {2, 4, 6}, {0, 2, 4, 6} }

The cardinality of the power set of B is 2^4 = 16.

In summary:

A ∪ B = {-1, 0, 1, 2, 3, 4, 6}

A ∩ B = {2, 4}

B - A = {0, 6}

The power set of B has 16 elements.

What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –(x – 6) and passes through the point (−2, −2)?

Answers

That line is in point-slope form:

[tex]\sf y-y_1=m(x-x_1)[/tex]

Where 'm' is the slope and (x1, y1) is a point on the line.

Perpendicular lines have opposite slopes. To get the opposite, we take the reciprocal and multiply it by -1.

[tex]\sf -1[/tex]

Reciprocal:

[tex]\sf -\dfrac{1}{1}\rightarrow -\dfrac{1}{1}\rightarrow -1[/tex]

Multiply by -1:

[tex]\sf 1[/tex]

We can plug this slope and the point into point-slope form, and then convert it to slope-intercept form.

[tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\sf y-(-2)=1(x-(-2))[/tex]

Negatives cancel out:

[tex]\sf y+2=1(x+2)[/tex]

Distribute 1 into the parenthesis:

[tex]\sf y+2=x+2[/tex]

Subtract 2 to both sides:

[tex]\boxed{\sf y=x}[/tex]

Kail Ryans 10 laps around the track each day each lap around the track is 400 m meters how many times around the track will she need to run a total of 12 kilometers

Answers

hello

1 km = 1000 m

12 km = 12,000 m

Each day, she runs 10 * 400 m = 4000 m

12,000 m / 4000 m = 3

It will take 3 days.

Have a nice day

Use the quadratic formula to determine the exact solutions to the equation. 6x2+4x−3=0

Answers

Using the quadratic formula this is the solution i found for you

The correct answer is [tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

To find the exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex]using the quadratic formula, we can follow these steps:

Given quadratic equation: [tex]6x^2 + 4x - 3 = 0[/tex]

[tex]a = 6, b = 4, c = -3[/tex]

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4(6)(-3)}}{2(6)}[/tex]

[tex]x = \frac{-4 \pm \sqrt{16 + 72}}{12}[/tex]

[tex]x = \frac{-4 \pm \sqrt{88}}{12}[/tex]

[tex]x = \frac{-4 \pm \sqrt{4 \cdot 22}}{12}[/tex]

[tex]x = \frac{-4 \pm 2\sqrt{22}}{12}[/tex]

Solution 1: [tex]x = \frac{-4 + 2\sqrt{22}}{12}[/tex]

Solution 2: [tex]x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

Therefore, the two exact solutions to the equation [tex]6x^2 + 4x - 3 = 0[/tex] are:

[tex]x = \frac{-4 + 2\sqrt{22}}{12}$ and $x = \frac{-4 - 2\sqrt{22}}{12}[/tex]

what is the 8th term in the following sequence 28,33,38,43.....

Answers

To solve this, you have to figure out how they created the sequence, i.e., how did they get from 28 to 33 and then from 33 to 38 (etc.). If you subtract 28 from 33 the answer is 5, and the same is true for all the consecutive numbers in the sequence, so you have to add five to 43 to figure out the next term. You already have four terms, so we only need 4 more:
28, 33, 38, 43, 48, 53, 58, 63   63 is the 8th term. 










































You and your friend are standing back-to-back. Your friend runs 16 feet forward and then 12 feet right. At the same time, you run 12 feet forward and then 9 feet right. You stop and throw a baseball to your friend, who catches it. How far did you throw the baseball?

Answers

You would throw a baseball 9 feet and your friend would catch the baseball. Hope this helps!
Let's assume that you stared at the origin.  So your friend moved 16 units along the x-axis and 12 down the y-axis landing him at (16, -12), while you on the other hand run 12 feet forward along the x-axis, and 9 units into the negative y area.  This makes you at (-12, -9).  So solve graph these points.  Use the graph to count the difference between the 2 x coordinates, you should get 28, the solution for the y distance (ignore the negatives) is 3.  So we can use the Palagorien Theorem to solve.  (28)2 + (3)2 = x2.  Solve for x.

784+9=x2
793=x2
28.1602556807=x

A poker hand consist of 5 cards?
a.find the total number of possible five card poker card hands.
b.find the number of ways in which one can king can be selected? c)find the number of ways in which four aces can be selected .
d.find the number of ways of getting four aces and one king.

Answers

c) it is answer in four acres can be selected.

In poker probability calculations, there are 2,598,960 possible five-card hands, various specific hand combinations such as those containing a king or four aces have their own probability, which can be determined using the formulas for combinations.

Calculations for Poker Probabilities

The subject of probability in a poker hand involves various combinations and permutations. Here's how the calculations are made:

Total number of five-card poker hands: The total number is calculated using combinations, as the order in which cards are drawn does not matter. This is given by the combination formula C(n, r) = n! / (r!(n-r)!), where n is the total number of available cards (52), and r is the number of cards drawn (5). Thus, there are 52! / (5!(52-5)!)= 2,598,960 possible hands.

Number of ways one king can be selected: There are four kings in a deck, so there are C(52, 5) - C(48, 5) ways to choose a hand with at least one king, as you subtract the number of hands without any kings from the total number of hands.

Number of ways four aces can be selected: There is only one way to choose all four aces, and then there are 48 remaining cards to choose the fifth card from, which gives 48 combinations.

Number of ways of getting four aces and one king: There are four kings to choose from and one specific combination of aces, so there are 4 ways to have a hand with four aces and one king.

In triangle XYZ, the length of side XY is 24 mm and the length of side YZ is 34 mm. Which of the following could be the length side XZ?

A. 8 mm
B. 63 mm
C. 42 mm
D. 60 mm

Answers

In a triangle, the length of any side is greater than the difference of the lengths of the other two sides and less than the sum of the lengths of the other two sides.

34 mm - 24 mm = 10 mm

The length of side XZ must be greater than 10 mm.

24 mm + 34 mm = 58 mm

The length of side XZ must be less than 58 mm.

The only choice between 10 mm and 58 mm is 42 mm.

Determine the equation for the parabola graphed below.

Answers

The general equation for a parabola is: y = a(x - b)^2 + c
So given the vertex is at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then we substitute a point from the graph (aside from the vertex). The easiest is the y-intercept of (0, 5):
5 = a(1)^2 + 7
a = -2
Therefore the equation is: y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5

The equation for the parabola graphed below is  [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]

A parabola's general equation is: y = a(x - b)2 + c

Given that the vertex is located at (-1, 7), this means that b = -1 and c = 7:

y = a(x + 1)^2 + 7

Then, instead of the vertex, we replace a point from the graph. The y-intercept of (0, 5) is the simplest:

5 = a(1)^2 + 7

a = -2

As a result, the equation is as follows: [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]

What is the lateral area of this regular octagonal pyramid?(PICTURE ONE)




114.8 cm²

162.4 cm²

229.7 cm²

281.3 cm²

2.What is the slant height x of the square pyramid?(PICTURE 2)

The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge and is labeled as x. The length of the lateral edge is 8 meters. The lateral edge makes a 60 degree angle with the base edge

Express your answer in radical form.

3.What is the surface area of this square pyramid? (pICTURE 3)

Round your answer to the nearest tenth, if necessary.


43.8 yd²

66.6 yd²

105 yd²

171.6 yd²

Answers

Q1)
the lateral area of the pyramid is the total area of all the lateral faces excluding the base.
In this regular octagonal pyramid, the lateral sides are triangles. As there are 8 triangles we need to find the area of all 8 sides.
Area of one lateral triangle face = 1/2 * base * slant height 
slant height is the hypotenuse of the right angled triangle formed from the base of the pyramid with the perpendicular height.
slant height - l
l² = 7² + 7² = 49 *2
 l²  = 98 
l = √98
l = 9.9
Area = 1/2 * 5.8 cm * 9.9 cm 
         = 28.71 cm²
There are 8 sides 
total lateral area = 8 * 28.71 = 229.68 rounded off is 229.7 cm²
third option is correct - 229.7 cm²

Q2)
in the triangular face, the lateral edge makes a 60° angle with the base edge. Therefore 2 of the angles are 60° each, since the sum of the interior angles of a triangle is 180°, the third angle too is 60°. this makes the triangle an equilateral triangle with equal angles, hence equal sides. 
since lateral edge is 8 cm,base edge too is 8 cm. 
since this is an equilateral triangle, the perpendicular line cuts the base edge at its midpoint, bisecting the line forming 2 right angled triangles.
in the right angled triangle, height of triangle is x slant height ,
base = 8 /2 = 4 cm
hypotenuse = 8 cm
We need to find x, use Pythogoras' theorem 
4² + x² = 8²
16 + x² = 64
x² = 62 - 16
x = √48
x = √4x√4x√3
  = 2x2√3
  = 4√3 cm

Q3)
surface area of the square pyramid 
surface area of the base + surface area of triangular faces 
square area = length x length 
                    = 6.2 x 6.2 
                    = 38.44 yd²
triangular face area = 1/2 * length * height 
since the angle between lateral edge and base edge is 60°, its an equilateral triangle where all sides are equal. in this case each side is 6.2 yd. 
to find the perpendicular height, use pythogoras' theorem
the perpendicular line(slant height ) cuts the base edge at its midpoint, therefore length of the right angled triangle is = 6.2/2 = 3.1 yd

slant height - l
l² + 3.1² = 6.2²
l² = 38.44 -9.61
l²  = 28.83 
l = 5.37
area = 1/2 *length *height 
        = 1/2 * 6.2 * 5.37
        = 16.64 yd²
there are 4 triangles = 4 * 16.64 = 66.58 yd²
total area = 38.44 + 66.58 = 105 yd²
correct answer is 3rd option - 105 yd²

Answer:

1.  229.7cm^2

2.  4 (square root) 3 cm

3.  16.64yd^2

Step-by-step explanation:

I just took th test, and came to confirm the other guys' answers ;)

Can someone please help me solve this problem????

Weston is buying a house for $215,000. He is financing $185,000 and obtained a 30-year, fixed-rate mortgage with a 6.525% interest rate. How much are his monthly payments?

$1,005.94

$1,362.48

$1,614.09

$1,172.37,

Answers

$1,172.37 The formula for calculating the payment on a loan is P = r(PV)/(1 - (1 + r)^(-n)) where P = Payment PV = Present value r = interest per period n = number of periods Since there's 12 months per year and the loan is for 30 years, there will be 12 * 30 = 360 periods. The interest rate per month will be 0.06525 / 12 = 0.0054375, and finally, the present value is the size of the loan at 185000. Now let's substitute and solve. P = r(PV)/(1 - (1 + r)^(-n)) P = 0.0054375(185000)/(1 - (1 + 0.0054375)^(-360)) P = 1005.9375/(1 - (1.0054375)^(-360)) P = 1005.9375/(1 - 0.141961802) P = 1005.9375/0.858038198 P = 1172.369134 P = 1172.37 So the monthly interest and principle payments are $1,172.37 Note: The actual payments will be higher since the above figure doesn't include insurance and taxes.
For this problem, we will be using the formula for loan:

PMT=P[(r/n)/1-(1+r/n)^-ny]
where: 
P=Principal Value
r=rate
n=number of compoundings/year
y=year

To solve:
*Weston is only financing $185,000.

P=$185,000
r=6.525% or 0.06525
n=12 (monthly)
year=30

PMT=185000[(0.06525/12)/1-(1+0.6525/12)^-12*30
        = 185000[(.0054375)/1-(1+.0054375)^-360
        = 185000[(.0054375)/1-(1.0054375)^-360
        = 185000[(.0054375)/1-(0.142)
        = 185000[(.0054375)/(.858)
        = 185000(0.00634)
        = 1,172.37

Answer: $1,172.37

How do you do this? It's so confusing! Please help!

Answers

check the picture below.

notice AB ⟂ BC , whilst ∡B = 30°.

now, if we run a perpendicular line from C to AB, it'll be a 90° angle at M, however ∡AMC has to be 105°, so it has to be slanted more towards A, like in the picture, and surely you already know which one is the shortest.

PLEASE HELP ME ON THIS
THANK U
PLZ SHOW UR WORK

Answers

2012
50,000 records

2013
50,000 × 1.1
55,000 records

2014
55,000 × 1.1
60,500 records

2015
60,500 × 1.1
66,550 records

2016
66,550 × 1.1
73,205 records 

Please Help!!!

The figure shows a line graph and two shaded triangles that are similar:



Which statement about the slope of the line is true? (5 points)
Select one:
a. It is fraction 1 over 2 throughout the line.

b. It is 2 throughout the line.

c. The slope from point O to point A is fraction 1 over 2 time the slope of the line from
point A to point B.

d. The slope from point O to point A is two times the slope of the line from point A to point B.

Answers

The slope is 1/2 throughout the entire line.

Looking at the first triangle, the rise is 2 and the run is 4.  That gives us a slope of 2/4 = 1/2.

For the second triangle, the rise is 1 and the slope is 2.  This gives us a slope of 1/2.

Any linear function will have the same slope throughout the entire line.

Place the indicated product in the proper location on the grid.

(5c +2/3 )(5c -2/3 )

Answers

Answer
25c^2-4/9



Explanation
In this question you are expected to expand (5c+2/3)(5c-2/3)
(5c+2/3)(5c-2/3)=(5c×5c)-(5c×2/3)+(5c×2/3)-(2/3×2/3)
=25c^2-10c/3+10c/3-4/9
25c^2-4/9
The expanded form of (5c+2/3)(5c-2/3) is 25c^2-4/9 and this is what the question requires of you to do.

Answer:

The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]    

Step-by-step explanation:

given : The polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]

We have to place the indicated product in the proper location o the grid.

Consider the given polynomial  [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)[/tex]

Apply identity of difference of square

[tex]\left(a+b\right)\left(a-b\right)=a^2-b^2[/tex]

We have,

[tex]=\left(5c\right)^2-\left(\frac{2}{3}\right)^2[/tex]

Simplify, we have,

[tex]=25c^2-\frac{4}{9}[/tex]

Thus, The product of the polynomial [tex]\left(5c+\frac{2}{3}\right)\left(5c-\frac{2}{3}\right)=25c^2-\frac{4}{9}[/tex]

Location on gris shown below.

Exponential Growth/Decay Function

Hint/Tip:

Remember, the basic general exponential function form is: y = Abx In detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = A(1-r)x

Always work with the rate as a decimal number, not as percentage. If the rate is given as percent (%), you will need to divide it by 100 to have the decimal form.

The value of a car is $21,500. It loses 12% of its value every year.

(a) Write a function that represents the value y (in dollars) of the car after x years.

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answers

(a) Write a function that represents the value and (in dollars) of the car after x years.
 For this case what we should do is write the equation of exponential type.
 We have then:
 y = A (b) ^ x
 Substituting the values:
 y = 21500 (0.88) ^ x
 Answer:
 y = 21500 (0.88) ^ x

 (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
 We use the function found in part (a) and evaluate for x = 6.
 We have then:
 y = 21500 (0.88) ^ 6
 y = 9985 $
 Answer: 
 the value of the car after 6 years is: 
 y = 9985 $

A warranty identification number for a certain product consists of a letter of the alphabet followed by four-digit number. How many possible identification numbers are there if the first digit of the four-digit number must be nonzero?,

Answers

A warranty identification number has the format: A0000 There are 26 letters in the alphabet. If the identification number has the first digit being 0 then for each letter the number can only go up to A0999. Including A0000, this means there is 1000 combinations per letter. So there is 26,000 possible identification numbers.

John says the transformation rule (x, y) es002-1.jpg (x + 4, y + 7) can be used to describe the slide of the pre-image (4, 5) to the image (0, –2). What was his error?

Answers

John didn't check his work.

The appropriate transformation rule is (x -4, y-7).

_____
John's signs were in error.

Sample Response: The pre-image is the point you start with. To check the transformation rule, substitute the values of the coordinates (4, 5) into the rule. You get (4, 5) → (4+4, 5+7). Simplify to get (4, 5) → (8, 12). This is the image. Instead the rule was applied to the image. This is the source of the error.


Determine 10th term : 5,-25,125

Answers

Every time, the previous term is multiplied by -5. 
Keep doing this until you reach the tenth term. 
You will get -9,765,625. 
Hope this helps!

What is the volume of a square pyramid with a base length of 6 cm and a height of 9 cm?



Enter your answer in the box.


cm³

Answers

Just took the test, it’s 108

Answer:

1/3 x base squared x  height

Step-by-step explanation:

so yes 108 is correct.

A globe in a brass stand has a diameter of 40 in . what is the volume of the globe to the nearest cubic inch?

Answers

You take half of the diameter to find the radius. 40 divided by 2 = 20 

2* 3.14* 20 = 125.6in cubed 

Don't forget to put 2 above inches for volume.
The Globe is in the shape of a sphere, so we will use the volume of the sphere formula.


--------------------------------------------------------------------
Formula: Volume of a sphere
--------------------------------------------------------------------
[tex]Volume \ of \ a \ sphere = \frac{4}{3} \pi r^3[/tex]

--------------------------------------------------------------------
Given Diameter, Find Radius
--------------------------------------------------------------------
Diameter = 40 in
Radius = 40 ÷ 2 = 20 in

--------------------------------------------------------------------
Apply Formula
--------------------------------------------------------------------
[tex]Volume \ of \ the \ sphere = \frac{4}{3} \pi (20)^3[/tex]
[tex]Volume \ of \ the \ sphere = 33510 in^3[/tex]

--------------------------------------------------------------------
Ans: Volume of the Globe is 33510 in³
--------------------------------------------------------------------

Write the equation of a line that includes the point (1, 5) and has a slope of 3 in standard form. 3x + y = 5 –3x + y = 5 3x + y = 2 –3x + y = 2

Answers

-10 is the answer lah bro . 

Jenna's parents required her to put $10 of her $50 monthly allowance into a savings account for what percent of her monthly allowance did this represent?

Answers

$10 is 20% of $50 dollars therefore the answer is it represented 20% of her monthly allowance

Final answer:

To determine the initial amount needed in a bank account to reach $10,000 in ten years with 10% compound interest, use the compound interest formula.

Explanation:

To find out how much money you need to put in a bank account to have $10,000 in ten years with 10% interest compounded annually:

Use the formula for compound interest: A = P(1 + r/n)^(nt)

Plug in the values: $10,000 = P(1 + 0.10/1)^(1*10)

Solve for P: P = $10,000 / (1.10^10)

Calculation:

PV = FV / (1 + r/n)^(n*t)

Inserting the known values:

PV = $10,000 / (1 + 0.10/1)^(1*10)

PV = $10,000 / (1.10)^10

Calculating the exponent:

PV = $10,000 / 2.59374

Finally:

PV = $3,855.43 (approximately)

Therefore, you need to put approximately $3,855.53 into the bank account initially.

What does -3.4 E + 38 mean? (In normal number terms).

Answers

"E" stands for exponent, specifically 10. If something says "E+38" (like in Microsoft Excel), that means 10^38 in scientific notation.  
Therefore, "-3.4 E + 38" means -3.4x10^38.  
The "+38" means there are 38 zeros following a 1 as the exponent. It also works with negative numbers. For example, E-3 equals 10^-3

find the positive value of x in the geometric sequence 7x-2,4x+4,3x

Answers

Hello,


Let's assume k the ratio.

[tex] \left \{ {{3x=k*(4x+4)} \atop {4x+4=k*(7x-2)}} \right. \\\\ \left \{ {{3x-4kx=4k} \atop {4x-7kx=-2k-4}} \right. \\\\ \left \{ {{x(3-4k)=4k} \atop {x(4-7k)=-2k-4}} \right. \\\\ \left \{ {{x=\dfrac{4k}{3-4k} \atop {x=\dfrac{-2k-4}{4-7k} \right. \\\\ \dfrac{4k}{3-4k}=\dfrac{-2k-4}{4-7k}\\\\ 36k^2-6k-12=0\\ 6k^2-k-2=0\\ \boxed{k= \dfrac{2}{3} \ or\ k= -\dfrac{1}{2}}\\\\ x=\dfrac{4*\dfrac{2}{3} }{3-4*\dfrac{2}{3} }=8\\ x=\dfrac{4*\dfrac{-1}{2} }{3-4*\dfrac{-1}{2} }=-\dfrac{2}{5}\\ [/tex]

[tex] \boxed{x= 8 \ or\ x= -\dfrac{2}{5}}\\\\ [/tex]





The value of x = 8.

We have a geometric sequence.

We have to determine the positive value of x.

Define Geometric Sequence.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio.

According to the question -

The Geometric sequence is -

7x - 2, 4x + 4, 3x

According to the concept of Geometric sequence -

[tex]$\frac{a(2)}{a(1)} =\frac{a(3)}{a(2)}[/tex]

[tex]$\frac{4x+4}{7x-2} =\frac{3x}{4x +4}[/tex]

(4x + 4)(4x + 4) = 3x(7x - 2)

16[tex]x^{2}[/tex] + 16x + 16x + 16 = 21[tex]x^{2}[/tex] - 6x

16[tex]x^{2}[/tex] + 32x + 16 = 21[tex]x^{2}[/tex] - 6x

38x + 16 = 5[tex]x^{2}[/tex]

5[tex]x^{2}[/tex] - 38x - 16 = 0

Solve the above quadratic equation, you will get two roots -

x = 8    and     x = 0.4

Since, we need positive value, therefore -

x = 8.

Hence, the value of x = 8.

To solve more questions on Geometric sequence, visit the link below -

https://brainly.com/question/19201330

#SPJ2

A rectangle is 1/2 feet long and 3/4 wide what is the area of rectangle

Answers

The rectangle is 1/2 ft long.
I assume you left out "ft" from the width, so the width is 3/4 ft.

A = LW = 1/2 ft * 3/4 ft = 3/8 ft^2


The area of rectangle is L×W.

A = 1/2 × 3/4
A = 0.375 or 3/8

hElP!
A carpenter designs two cabinets: one in the shape of an oblique rectangular prism and one in the shape of a right rectangular prism. The volume of each cabinet is 4,608 cubic inches. The oblique rectangular prism is 48 inches tall and has an edge length of 64 inches. The right rectangular prism has a height of 48 inches. Which statements about the cabinets are true? CHECK ALL THAT APPLY
a. The cabinets have the same base area.
b.The base area of the oblique prism is smaller than the base area of the right prism.
c.The cabinets may have the same base dimensions.
(MORE DOWN BELOW),

Answers

Answer:

A- The cabinets have the same base area.

C- The cabinets may have the same base dimensions.

D- The cabinets may have different base dimensions

Step-by-step explanation:

Answer:

A. C. D.

Step-by-step explanation:

for the final answer do i add the 5 to (x+1) making it 5x+5 or do i leave it how it is? Also how do i find the domain

Answers

You don't "add the 5" in any event. Multiplication is very different from addition, and precision of vocabulary is important.

It depends on what your teacher or answer key expect. You can take a hint from the fact that the given polynomials are all multiplied out.

(5x^2 +5)/(x -1)

_____
The domain of polynomials in general is "all real numbers." However, you must exclude any specific numbers that make the rational expression be undefined. This includes numbers that make the denominator of the numerator zero, as well as those that make either the numerator or the denominator of the denominator zero. In other words, you must exclude from the domain
.. x ∈ {-5, 1, 2}
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