If y= 2x+3, find the value of y when x= 2.

[tex]3^{2c} + 1 = 28\times3^c - 9 \implies 3^{2c} - 28\times3^c = -10[/tex]

Complete the square on the left side:

[tex]3^{2c} - 28\times3^c = \left(3^{2c}-28\times3^c+14^2\right)-14^2 = \left(3^c-14\right)^2 - 196[/tex]

Then the equation becomes

[tex]\left(3^c-14\right)^2 - 196 = -10 \\\\ \left(3^c-14\right)^2 = 186 \\\\ 3^c - 14 = \pm\sqrt{186} \\\\ 3^c = 14\pm\sqrt{186}[/tex]

Both 14 + √186 and 14 - √186 are positive numbers, so we can take the logarithm (base 3) of both sides without issue:

[tex]\log_3\left(3^c) = c = \log_3\left(14\pm\sqrt{186}\right)[/tex]

Then in increasing order, the solutions are

c = log₃(14 - √186), c = log₃(14 + √186)

Answer:

-1/2  ,  3

Step-by-step explanation:

In order to find the roots of the function 2x² - 5x - 3  

We have to solve the quadratic equation :

2x² - 5x - 3 = 0

Calculating the discriminant Δ :

Δ = b² - 4ac

  = (-5)² - 4(2)(-3)

  = 25 + 24

  = 49

Then

√Δ = √49 = 7

Determining the Zeros :

[tex]x=\frac{-b+\sqrt{b^{2}-4ac} }{2a} = \frac{5+7} {2 \times (2)} =\frac{12}{4} =3[/tex]

or

[tex]x=\frac{-b-\sqrt{b^{2}-4ac} }{2a} = \frac{5-7} {2 \times (2)} =\frac{-2}{4} =\frac{-1}{2}[/tex]

Answer:

[tex]\displaystyle \cos(\theta) = \frac{\sqrt{7}}{4}[/tex].

[tex]\displaystyle \tan(\theta) = \frac{3\sqrt{7}}{7}[/tex].

Step-by-step explanation:

By the Pythagorean identity, for any given angle [tex]\theta[/tex], [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Given that [tex]\displaystyle \sin(\theta) = 3/4[/tex], solve this equation for [tex]\cos(\theta)[/tex].

[tex](\sin(\theta))^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\displaystyle \left(\frac{3}{4}\right)^{2} + (\cos(\theta))^{2} = 1[/tex].

[tex]\begin{aligned} \cos(\theta) &= \sqrt{1 - \frac{9}{16}} \\ &= \sqrt{\frac{7}{16}} \\ &= \frac{\sqrt{7}}{4} \end{aligned}[/tex].

The tangent of an angle is equal to the ratio between the sine and cosine of that angle. In this question:

[tex]\begin{aligned} \tan(\theta) &= \frac{\sin(\theta)}{\cos(\theta)} \\ &= \frac{3/4}{\sqrt{7}/4} \\ &= \frac{3}{\sqrt{7}} \\ &= \frac{3\sqrt{7}}{7}\end{aligned}[/tex].

Answer:

100

Step-by-step explanation:

anything lower then 4 stays anythiing 5 or higher is rounded

so this also works with 40 50 400 500 4000 5000, you gte the point

oodluck on your test or homework! :)

Answer:

1/4

Step-by-step explanation:

Answer:

-4/21

Step-by-step explanation:

-3/5×20/63

-3×4/63

-4/21

Johannesburg's sister is 54cm tall

Explanation:

3/5 = 0.6

0.6 * 90 = 54

54 is 3/5 of 90, therefore Johannesburg's sister is 54cm tall

Answer:

[tex]take \: the \: number = x \\ thenx \times 6 = 2 \times 19 \\ \\ 6x = 38 \\ x = \frac{38}{6} \\ x = 6.33 \\ thank \: you[/tex]

Answer:

38.75

Step-by-step explanation:

perimeter = 2(15.6+3.8) =38.8

lower bound = the smallest value that would round up to the estimated value =38.75

Step-by-step explanation:

No of Student in Debre Berhan University - 80 students

No of students good in mathematics and English -15

no of student good in mathematics -45+15+13

therefore no of student good in math is 75 .

pls mark me branilest

Answer:

7/60 acres

Step-by-step explanation:

60 pounds of seed = 7 acres

We want to find acres per pound of seed, so we want to make one side of the equation equal to 1 pound of seed. To do this, we can divide both sides by 60, as anything divided by itself equals 1. We thus have

60/60 pounds of seed = 7/60 acres

1 pound of seed = 7/60 acres

Answer:

» B. 3- (+22) and C. 3 + (-22)

» A. 3- (-22) and E. 22 + 3

» D. 22 - 3 and H. 22 +(-3)

Step-by-step explanation:

[tex].[/tex]

Answer:

3 - (+22)

3 + (-22)

-22 + 3

Step-by-step explanation:

9514 1404 393

Answer:

  T, T, F, F, T

Step-by-step explanation:

First of all, it is helpful to know ...

  √8 ≈ 2.8284

  √7 ≈ 2.6458

Now you can check the inequalities:

0, 1, 2, and √7 are left of √8 on a number line, so are all less than √8.

3 and 8 are right of √8 on a number line, so are greater than √8.

Answer:

T, T, F, F, T.

Step-by-step explanation:

Person above is correct!!

The fraction that represents the total number of seats occupied during the three days is 1.

The total number of seats in the auditorium is 200.

On day 1, 40% of the seats were occupied. So, 40/100 * 200 = 80 seats were occupied on day 1.

On day 2, 35% of the seats were occupied. So, 35/100 * 200 = 70 seats were occupied on day 2.

On day 3, 25% of the seats were occupied. So, 25/100 * 200 = 50 seats were occupied on day 3.

The total number of seats occupied during the three days is 80 + 70 + 50 = 200 seats.

The fraction that represents the total number of seats occupied during the three days is 200/200 = 1.

Here is the solution in mathematical form:

Let x be the fraction that represents the total number of seats occupied during the three days.

Then, x * 200 = 80 + 70 + 50

x = (80 + 70 + 50) / 200

x = 1

Therefore, the answer is 1.

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Answer:

tero bau ko tauko got it sjdhhrurjrbr

Answer:

LHS=6x/12x=6/12=1/2

RHS=1/2

LHS=RHS

Step-by-step explanation:

since < 5 = < 8, so,

< 7 = < 6 = 29°

and < 5 = 90° - 29° = 61°

Answer:

The perimeter of it is going to be 50

Step-by-step explanation:

This is because when finding the perimeter you add up all the sides so

14 + 12 + 18 + 6 = 50

Answer:

50 m

Step-by-step explanation:

Perimeter

= Sum of the length of all sides

= 14 m + 12 m + 6 m + 18 m

= 50 m

[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]

Explanation:

The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).

Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.

Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.

Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.

Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.

The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}

If X is a subset of Y then all the elements of A also contained in B.

According to the given statement we have o determine which of the following collections of subsets of the plane R2.

R2 defines a two dimension plane.

x+y = c where c is a real number.

Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.

Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.

B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.

C. is false as well

D. Is ruled out because the notation should be (x,y) in R2 and not simply R.

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I'll get 32 jelly beans

Amount of jelly beans shared = 56

My fraction = 4/(4+3) = 4/7

My sister's fraction = 3/(4+3) = 3/7

The number of jelly beans that I'll get will then be:

= My fraction × Number of jelly beans

= 4/7 × 56

= 4 × 8

= 32

Therefore, I'll get 32 jelly beans

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475,805 rounded to the nearest ten thousand would be 476,000.

Step-by-step explanation:

Using the properties of logarithms, the left side of the equation becomes

[tex]\log{3x^3} - \log{x^2} = \log{3x}[/tex]

while the right hand side becomes

[tex]\log{27} - \log{x} = \log{\frac{27}{x}}[/tex]

so we end up with

[tex]3x^2 =27 \Rightarrow x = 3[/tex]

Answer:

$8,000

Step-by-step explanation:

8,375.79 < 8,500 so it will round to 8,000

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

4.3

Step-by-step explanation:

Answer:

[tex]29[/tex]

Step-by-step explanation:

Let x be the original price.

( 1 - 20% ) x = 23.2

[tex] 0.8x = 23.2[/tex]

[tex] \frac{0.8x}{0.8} = \frac{23.2}{0.8} [/tex]

[tex] x = 29[/tex]

Answer:

it's A or C

Step-by-step explanation:

because if it was be it would round to .19 but c and a round to .18

Answer:

Think of two or three jobs with which you are familiar, perhaps a teacher, a retail worker, a nurse, or a police officer.

In each case, indicate why the employment contract is necessarily incomplete. What important parts of the person’s job—things that the employer would like to see the employee do or not do—cannot be covered in a contract, or if they are, cannot be enforced?

Step-by-step explanation:

Answer:

g^-1(x)=x/2+3/2

Step-by-step explanation: