Determine the solution of the equation 4y - 5= 7.
A) 4
B) 3
C)

Let the original fraction be

[tex]\dfrac{n-1}{n}[/tex]

Now let's increase both numerator and denominator by 2:

[tex]\dfrac{n+1}{n+2}[/tex]

This produces a 1/12 increase:

[tex]\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}[/tex]

The left hand side can be rearranged as

[tex]\dfrac{2}{n^2+2n}=\dfrac{1}{12}[/tex]

Invert both sides:

[tex]\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24[/tex]

Solve the quadratic equation:

[tex]n^2+2n-24=0 \iff n=-6 \lor n=4[/tex]

So, in the first case, the original fraction is

[tex]\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}[/tex]

In the second case, we have

[tex]\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}[/tex]

Answer:

The values of k will be:

[tex]k=-1,\:k=3[/tex]

Step-by-step explanation:

Let the expression of polynomial P be

[tex]P\left(x\right)=3x^2-4kx-4k^2[/tex]

Let the expression if the polynomial Q be

[tex]\:Q\left(x\right)=\:\left(x+2\right)\:[/tex]

Plug in Q(x) = 0

0 = x+2

x = -2

As (x+2) is a factor of 3x²-4kx-4k²

substitute x = -2 in the the polynomial

3x²-4kx-4k² = 0

[tex]3\left(-2\right)^2-4k\left(-2\right)-4k^2\:=0[/tex]

[tex]12+8k-4k^2=0[/tex]

Write in the standard form ax²+bx+c = 0

[tex]-4k^2+8k+12=0[/tex]

Factor out common term -4

[tex]-4\left(k^2-2k-3\right)=0[/tex]

Factor k²-2k-3: (k+1)(k-3)

[tex]-4\left(k+1\right)\left(k-3\right)=0[/tex]

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

[tex]k+1=0\quad \mathrm{or}\quad \:k-3=0[/tex]

solving k+1=0

k+1 = 0

k = -1

solving k-3=0

k-3=0

k = 3

Thus, the values of k will be:

[tex]k=-1,\:k=3[/tex]

Answer:

The solution for your question is X=6

Answer:

3.07×10^8

Step-by-step explanation:

:)

hope this helps

Answer: 307,000,000 in scientific notation is 3.07 × 10^8.

Answer:

2 13/20 cm

Step-by-step explanation:

The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?

From the above question, we are converting, from decimal to mixed number , hence:

2.65 has 2 decimal places

Hence:

2.65 cm = (265/100)cm

= ( 2 + 65/100) cm

= ( 2 13/20 )cm

The mixed number that represents the length of the phone screen is 2 13/20 cm

Answer:

0.95t

Step-by-step explanation:

Given expression:

t − 0.05t

The equivalent expression could be found by factorizing the expression

t − 0.05t

= t ( 1 - 0.05)

= t (0.95)

= 0.95t

Check

When t = 2

t − 0.05t

= 2 - 0.05(2)

= 2 - 0.1

= 1.9

When t = 2

0.95t

= 0.95(2)

= 1.9

Therefore, the equivalent expression to t − 0.05t is 0.95t

Answer:

12 songs

Step-by-step explanation:

Brenda's band plays songs in sets of 4

Melissa's band plays songs in sets of 6.

After performing together, both bands realize that they have played the same number of songs.

What is the smallest number of songs each band could have performed?

The smallest number of songs each band could have performed can be calculated by finding the lowest common multiple of 4 and 6

4 = 8, 12, 16, 20, 24, 28, 32, 36, 40

6 = 12, 18, 24, 30, 36, 42

The lowest common multiple of 4 and 6 is 12

The smallest number of songs each band could have performed is 12 dongs

Answer:

Since it's a parallelogram, the length of AD and BC are the same.

Hence, [tex]x + 21 = 12x - 1[/tex].

[tex]x + 21 = 12x - 1[/tex]

[tex]12x - x = 21 + 1[/tex]

[tex]11x = 22[/tex]

[tex]x = 2[/tex]

Therefore, x = 2.

Step-by-step explanation:

Hope this helped!

Answer:

BC = 5

Step-by-step explanation:

Since it is an isosceles, it is the base angles that are equal

Since the base angles are equal, then the sides facing these angles are equal

Mathematically, what we are supposed to have as equals should be AB and BC since they are the sides facing the base angles

Thus, BC should be 5

Answer:

0.13 and 0.1 hope it will help you..

Answer:

Ordinal

Step-by-step explanation:

The ordinal measurement level means the arrangement of the number so that it could tell the position of something in the list

Since in the question it is mentioned that the day care center ask the children for listing their five favorite toys and the arrangement could be done from most favorite to least favorite

So this represent the ordinal measurement level

Answer:

it will take her  [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House

Step-by-step explanation:

It took Sheldon [tex]17 \frac{5}{6}[/tex]  minutes to walk to Raj's house

It also took Sheldon [tex]4\frac{5}{8}[/tex] minutes to use the bus.

To get the time difference between the two transport mechanisms, we subtract their different time durations.

This will be

[tex]17\frac{5}{6} - 4\frac{5}{8}=317/24[/tex]

We can convert this to Mixed fractions as shown [tex]13\frac{5}{24}[/tex] minutes.

Therefore, it will take her  [tex]13\frac{5}{24}[/tex] minutes more to walk down to Raj's House

Answer:

$48

Step-by-step explanation:

Because he has 3/4 you would divide 36 by 3 whick is 12 then multiply by 4 to get the total of $48

Answer:

$48 :)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

I think it is C.

Step-by-step explanation:

Answer:

[tex]\mathbf{a}\cdot \mathbf{b}=-3[/tex]

Step-by-step explanation:

The dot product of vectors.

Given two vectors a and b in their rectangular form:

[tex]\mathbf{a}= a_x\mathbf{i}+a_y\mathbf{j}[/tex]

[tex]\mathbf{b}= b_x\mathbf{i}+b_y\mathbf{j}[/tex]

The dot product of the vectors is a scalar with value:

[tex]\mathbf{a}\cdot \mathbf{b}=a_x.a_y+b_x.b_y[/tex]

The given vectors are:

[tex]\mathbf{u}= -5\mathbf{i}+3\mathbf{j}[/tex]

[tex]\mathbf{v}= 3\mathbf{i}+4\mathbf{j}[/tex]

Calculating the dot product:

[tex]\mathbf{a}\cdot \mathbf{b}=(-5)(3)+(3)(4)=-15+12=-3[/tex]

[tex]\mathbf{a}\cdot \mathbf{b}=-3[/tex]

Answer:

NQ=15

Step-by-step explanation:

To solve this we can use the side-splitter theorem.

NS/SR=NP/PQ

PQ=x since we do not know it's value

now to subsitute the given/known values.

12/78=2/x

solve for x using cross multiplication.

12x=156

x=13

PQ=13

NQ= PQ+NP

NP=2

NQ=13+2

NQ=15

The length of NQ is 15.

Answer:

2, 5

Step-by-step explanation:

hope this helps

please mark me brainliest

Answer:30

Step-by-step explanation:

Steps below. I formed an equation out of the word problem.

Answer:

-7/-9 pretty sure

Step-by-step explanation:

x2-x1

y2-y1

3-10= -7

1-10= -9

Answer:

F. 10

Step-by-step explanation:

6d - 2c

6 * 3 - 2 * 4

18 - 8

10

Answer:

Step-by-step explanation:

Write all the equations in standard form cleared of decimals or fractions.

Choose a variable to eliminate; then choose any two of the three equations and eliminate the chosen variable.

Select a different set of two equations and eliminate the same variable as in Step 2.

Solve the two equations from steps 2 and 3 for the two variables they contain.

Answer:

60

Step-by-step explanation:

divide 400 by 40 you get the answer 10

now multiply 6 by 10 you get the answer 60 thats is the total pear fruit

Answer:

D. 16

Step-by-step explanation:

32/2 = 16

Answer:

C) Multiplication

Step-by-step explanation:

You would want to remember PEMDAS. you would want to multiply the the parentheses first.

Answer:

[tex]y = \frac{3}{2}x +2[/tex]

Step-by-step explanation:

Required:

Write an equation to represent this  situation

Let x represents the number of weeks and y represents the growth.

When he planted it:

[tex](x_1,y_1) = (0,2)[/tex]

Two weeks later:

[tex](x_2,y_2) = (2,5)[/tex]

At 6 weeks:

[tex](x_3,y_3) = (6,11)[/tex]

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{5-2}{2-0}[/tex]

[tex]m = \frac{3}{2}[/tex]

Then calculate the equation using:

[tex]y - y_3 = m(x - x_3)[/tex]

[tex]y - 11 = \frac{3}{2}(x - 6)[/tex]

[tex]y - 11 = \frac{3}{2}x - 9[/tex]

Solve for y

[tex]y = \frac{3}{2}x - 9+11[/tex]

[tex]y = \frac{3}{2}x +2[/tex]

Answer:

B

Step-by-step explanation:

3+5+7=3+7+5