If x−y=3 and x+y=5, what is the value of y?

Answer:

y = 2x + 3

Step-by-step explanation:

The y-intercept is clearly marked:  it's b = 3 (or 0, 3).

Going from the point (-3, -3) to the point (0, 3),

x increases by 3 and y increases by 6.  Thus, the slope of the line through these two points is m = rise / run = 6 / 3, or m = 2.

Starting with the slope-intercept form of the equation of a straight line:

y = mx + b, we substitute 2 for m and 3 for b, obtaining:

y = 2x + 3

Answer:

y = 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 3) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3+3}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = 2x + 3 ← equation of line

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have the diameter d = 16ft.

d = 2r, therefore r = (16 ft) : 2 = 8 ft.

Substitute:

[tex]A=\pi(8^2)=64\pi\ ft^2[/tex]

[tex]\pi\approx3.14\to A\approx(64)(3.14)=200.96\ ft^2[/tex]

Answer:

C) 200.96 ft²

Step-by-step explanation:

Area formula of a circle: A = πr²

radius = circumference/2 = 8 ft

Plug in: A = π(8)²

Multiply: A = 64π

Approximate+ Multiply: π ≈ 3.14 --> A ≈ 200.96 ft²

Answer:

-2/3

Step-by-step explanation:

3x=sqrt4-4

3 times a number is 4 less than the square of that number. The negative solution is  -1

What are quadratic equations?

Quadratic equations are of the form ax² + bx + c where a ≠ 0.

Factorization, often known as factoring, is the process of expressing a number or another mathematical object or mathematical equations as a product of several factors.

Now, In the given question let's first assume that the unknown number is a variable x.

So, 3 times that number is (3 × x)

And then, 4 less than the square of that number is (x² - 4)

Now, as the question states that 3 times a number is 4 less than the square of that number,

So we can write,

3x = x² - 4

Now, we have to solve this quadratic equation with the help of factorization.

To solve the quadratic equation we first bring all the terms to any of the sides and after rearranging a little the equation is as follows:

x² - 3x - 4 = 0

Now, if we want to find the factors in the form ax² + bx + c we need to multiply a and c and then we have to identify what two numbers sum up to b and multiply to ac.

Here, a = 1, b = -3 and c = -4

Now, ac = -4

So, we have to identify what two numbers sum up to b and multiply to ac. The numbers are -4 and 1 and we can check that they sum up to -3 and multiply to -4.

So first we have to split the equation: x² - 3x - 4 = 0

x² - 4x + 1x - 4 = 0

Now, we have to group the above equation,

(x² - 4x) + (1x - 4) = 0

Taking x common from the first group and taking 1 common from the second group we get,

(x)(x - 4) + (1)(x - 4) = 0

Now, again taking (x - 4) common from the equation we get,

(x - 4) × (x + 1) = 0

So, we set each factor to zero now,

(x - 4) = 0

Adding 4 to each side of the equation we get,

x - 4 + 4 = 4

Simplifying we get,

x = 4

(x + 1) = 0

Adding -1 to each side of the equation we get,

x + 1 - 1 = -1

Simplifying we get,

x = -1

So, we now have two solutions of x that is 4 and -1

But according to the question we only need the negative one.

Therefore, the negative solution is  -1

To know more about how to solve quadratic equations by factorization

use this - brainly.com/question/544930

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Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

2 divided by 6 is [tex]\frac{1}{3}[/tex]

To confirm it,

[tex]6 * \frac{1}{3} =2[/tex]

Answer:

Rosie now has c+3 charms

Explanation:

We are given that the original number of charms that Rosie has is c

We know that Ray gave Rosie 3 new charms

This means that the number of charms that Rosie originally had increased by 3

To express this increase, we use addition where we add 3 to the original number of charms that she had

New number of charms = original number of charms + 3

New number of charms = c + 3

Hope this helps :)

Answer:

c+3

Step-by-step explanation: she already had c charms, since we do not know what c is equal to, we can only simplify the question down to c(what she had) +3(what ray gave her)

Answer:

26 feet

Step-by-step explanation:

Perimeter of the Square = 4 x 6.5 = 26

Answer:

after one month = 100*.05=

$5 earned + $100 already there= $105

after 2 months = $105*.05=

$5.25 earned + $105 already there= $110.25

after 3 months = $110.25*.05=

$5.51 earned + $110.25 already there=

$115.76 is how much she'll have in the account after 3 mos.

Answer:

[tex]\large\boxed{-8\sqrt9=-24}[/tex]

Step-by-step explanation:

[tex]\sqrt{a}=b\iff b^2=a\\\\\sqrt9=3\ \text{because}\ 3^2=9\\\\-8\sqrt9=-8(3)=-24[/tex]

addition since inverse means opposite

To isolate p in this equation you have to add 20 to both sides, since addition is the inverse operation of subtraction and vise versa. Adding 20 to both sides will cancel it out of the left side since -20 + 20 = 0.

Hope this helped!

Answer:

4) 0, -1, 1, 1, 1

5) correct

6) [tex]x = -2 \pm 2\sqrt5[/tex]

Step-by-step explanation:

4) fill in the previous sequence element in the next. This sequence gets "stuck" at 1.

6) use the quadratic formula.

Answer:

y-7=-(4/3)(x-5)  (point slope form)

y=-(4/3)x+(41/3) (slope intercept form)

4x+3y-41=0 (general form)

Step-by-step explanation:

step 1

Find the slope of the perpendicular line to 4y-3x+9=0

If two lines are perpendicular, then the product of their slopes is equal to -1

4y-3x+9=0

4y=3x-9

y=(3/4)x-9/4 -----> the slope is m=3/4

The perpendicular slope is

m*(3/4)=-1

m=-4/3

step 2

Find the equation of the line into slope point form

y-y1=m(x-x1)

we have

(x1,y1)=(5,7)

m=-4/3

substitute

y-7=-(4/3)(x-5) ----> equation of the line into point slope form

Convert to slope intercept form ----> y=mx+b

y-7=-(4/3)(x-5)

y-7=-(4/3)x+(20/3)

y=-(4/3)x+(20/3)+7

y=-(4/3)x+(41/3) -----> equation of the line into slope intercept form

Convert to general form ----> Ax+By+C=0

y=-(4/3)x+(41/3)

Multiply by 3 both sides

3y=-4x+41

4x+3y-41=0 -----> equation of the line in general form

Answer:

1. 15in^2

2. 3421.19in^3

3. 11494.04cm^3

4. Radius is 3.1

Hope this helps!

Step-by-step explanation:

The area of the base of first cylinder is 47.05 in², volume of a cone is 3421.2 in³, the  volume of a sphere is 11494.04 cm³ and the radius of last sphere is 3.102 cm.

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

Volume of cylinder can be given as,

V=πr²h

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

The area of the base of a cylinder with a volume of 240π in³ and a height of 16 inches has to be find out. The radius of this cylinder is,

V=πr²h

240π=πr²(16)

r=√(240/16)

r=3.87 in

Thus, the surface area of the base is

A=πr²

A=π(3.87)²

A=47.05 in²

The volume of a cone with a height of 27 inches and a radius of 11 inches is,

V=(πr²h)/3

V=(π(11)²(27))/3

V=3421.2 in³

The volume of a sphere with a radius of 14 cm is;

V=(4πr³)/3

V=(4π(14)³)/3

V=11494.04 cm³

The volume of a sphere is 125 π cm³. The radius of it is,

V=(4πr³)/3

125=(4πr³)/3

r=∛(93.75/π)

r=3.102 cm.

Thus, the area of the base of first cylinder is 47.05 in², volume of a cone is 3421.2 in³, the  volume of a sphere is 11494.04 cm³ and the radius of last sphere is 3.102 cm.

Learn more about the volume of cylinder here;

https://brainly.com/question/12748872

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Answer:

[tex]f\left(x\right)=x^2-3x-54[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^2-3x-54[/tex].

Now we need to rewrite that equation in standard form.

Given equation is a polynomial function. So to write that in standard form, we need to rearrange terms in descending order of exponents of the variable (x).

We see that exponents of variable x are 2, 1  and 0.

Terms are already written in descending order of exponents.

Hence final answer is given function itself. [tex]f\left(x\right)=x^2-3x-54[/tex]

Answer:

ASA

Step-by-step explanation:

You are given 2 equal sets of angles.

<ABD and <ACD    (right angles)

<BAD and <CDA    (bisected angle)

You can get <ADB = <ADC because every triangle has 180 degrees. You know two of the angles: you can show that  the 3 rd set are equal a subtraction postulate.

AD = AD              (Reflexive property)

The triangles are congruent by ASA

If AAS is acceptable then it is correct in this case.

AD = AD

The two right angles are equal

The two angles created by the angle bisector are equal.

These three facts give AAS, but please see my comment below.

Answer:

The correct answer is AAS.

Step-by-step explanation:

Answer:  [tex]y=-7[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

Find the slope with this formula:

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

Given the points (-10,-7) (3,-7), substitute values into the formula. Then:

[tex]m=\frac{-7-(-7)}{-10-3}\\\\m=\frac{0}{-13}\\\\m=0[/tex]

Substitute the slope and any point into  [tex]y=mx+b[/tex] and solve for "b":

[tex]-7=0x+b\\b=-7[/tex]

Then, substituting "m" and "b" into the equation  [tex]y=mx+b[/tex], you get that the equation of this line is:

 [tex]y=0x-7[/tex]

 [tex]y=-7[/tex]

Answer:

Step-by-step explanation:

the answer is y=-7

Answer:

862.75 meters^3

Step-by-step explanation:

(17)(14.5)(3.5)=862.75

Answer:

862.75

Explanation:

17multiply by 14.5 multiply by 3.5

Tessellation is possible only for equilateral triangles, squares and regular hexagons. Therefore, there are only three regular polygons that tessellate.

Tessellation is possible, if each interior angle of a polygon is a factor of 360 degrees.

Now, in the given image, pentagon and octagon cannot tessellate.

And the triangle does not seem to be an equilateral triangle. But in general we can say that triangle tessellates.

So, the answer might be triangle (if its equilateral)

Answer:

The answer is D

Step-by-step explanation:

(12 + 6) x ( 11 - 7) = 72

18 x 4 = 72

72 = 72

Answer:

The answer is D.

Step-by-step explanation:

The only equation that equals 72 is letter D. if you add 12 + 6 you get 18 so now the equation is 18 * (11 - 7) = 72 then you do 11 - 7 and get 4 so now the equation is 18 * 4 = 72 and 18 * 4 equals 72 so your answer is correct.

Answer:

x = 1.36

Step-by-step explanation:

We are given the following equation;

7^x = 14

we are required to determine the value of x;

the first step is to introduce natural logs on both sides of the equation;

[tex]ln(7^{x})=ln(14)\\\\xln(7)=ln(14)\\\\x=\frac{ln(14)}{ln(7)}\\\\x=1.3562[/tex]

Answer:

a.  [tex]\frac{1}{6}[/tex]

b.  [tex]\frac{67}{450}[/tex]

Step-by-step explanation:

Theoretical probability is what we expect to happen and experimental probability is what actually happens.

a. In theoretical probability, it doesn't matter what happened in the past. So basically we want to know the probability of rolling a 3 when a number cube is rolled.

There are 6 faces (from 1 to 6) in a number cube. And there is 1 "3". So the probabilty of rolling a 3 is:

1/6

b. In experimental probability, we need to know what happened before. When the cube was rolled 450 times, it came up "3", 67 times.

Hence the experimental probabilty of rolling a "3" is:

67/450

Answer:

its an obtuse

Step-by-step explanation:

The triangle is:

               A.   Scalene.

               E.  Acute

Scalene triangle--

A triangle is said to be scalene if the length of all the three sides of a triangle are different.

Right triangle--

A triangle is said to be a right triangle if one of the angle is right angle i.e. measure of one of the angle is: 90 degrees.

Equilateral triangle--

A triangle is said to be equilateral if all of the sides of a triangle are equal.

Obtuse triangle--

A triangle is said to be obtuse if measure of one of the angle is more than 90 degrees but less than 180 degrees.

Acute triangle--

A triangle is said to be acute triangle if the measure of all the three angles of a triangle are less than 90 degrees.

Based on the diagram we observe that all the sides of a triangle are different and all the three angles of a triangle are less than 90 degrees.

Hence, the triangle is scalene and it is a acute triangle.

Answer:

3544

Step-by-step explanation:

This is a problem of compound growth. The formula is

[tex]F=P(1+r)^t[/tex]

Where F is the value in the future (in this case, the population after 13 years)

P is the intial amount (here, the initial population of 2000, so P = 2000)

r is the rate of growth (here, it is 4.5%, in decimal, 0.045)

t is the time frame (here, it is 13 years, so t = 13)

we can plug the numbers into the formula and solve for F:

[tex]F=P(1+r)^t\\F=2000(1+0.045)^{13}\\F=2000(1.045)^{13}\\F=3544.4[/tex]

rounded to the nearest whole number, the population after 13 years would be 3544

Answer:

The  population after 13 years = 3544

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t -   number of years

n - number of times compounded yearly

Here we have to consider compounded growth.

To find the population

Here P = 2000 , R = 4.5% = 0.045% and n = 13 years

A =  P[1 +R/n]^nt

 = 2000[1 + 0.045/1]^(1 * 13)

 = 2000 * 1.77

 = 3544

Therefore the  population after 13 years = 3544

Answer:

-288

Step-by-step explanation:

n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.

The sum of the  infinite geometric series is:

                                 -288

We know that the sum of the infinite geometric series:

[tex]\sum_{n=1}^{\infty} ar^{n-1}[/tex]

is given by the formula:

[tex]Sum=\dfrac{a}{1-r}[/tex]

The series is given by:

     [tex]\sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}[/tex]

By looking at the series we observe that the first term of the series is:

            [tex]a=-144[/tex]

and the common ratio of the series is:

[tex]r=\dfrac{1}{2}[/tex]

Hence, the sum of the series is:

[tex]Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288[/tex]

Answer:

They intersect but not perpendicular.

Answer:

17 4/5

Step-by-step explanation:

Fist, add the whole numbers.

5 + 6 + 5 = 16

Now add the fractions.

2/3 and 1/3 have the same denominator so you can add easily.

2/3 + 1/3 = 3/3 = 1

Now 16 + 1 = 17

Then what's left is Mr. Caswall's 4/5 and then we add that to 17.

So it's 17 4/5

Hope this helps!

Answer:

17 4/5 miles.

Step-by-step explanation:

First add the integer parts of the mixed numbers:

5 + 5 + 6 = 16 miles.

Now add the fractions:

2/3 + 1/3 + 4/5

LCD of 3 and 5 is 15 so we have:

10/15 + 5/15 + 12/15

= 27/15

= 9/5

= 1 4/5 miles.

So our answer is 16 + 1 4/5

= 17 4/5 miles.

Answer:

40/3

Step-by-step explanation:

Here you're dividing the fraction -5/3 by the fraction -1/8.

Right off, we can simplify this by recalling that (-)(-) = (+), and so we have:

Divide 5/3 by 1/8.

There's a rule for dividing by a fraction:  Invert the fraction and multiply.  So, applying that rule here, we get:

5      8

---- * ---- = 40/3

 3      1

Answer: false

Step-by-step explanation:

Final answer:

The probability of any number from 0 to 4 appearing in a randomly generated list is 1/5, not 1/4. The false notion might come from misinterpreting randomness or falling prey to the gambler's fallacy.

Explanation:

Your question pertains to the concept of probability in a random distribution of numbers. Specifically, you are asking whether the probability of each number occurring in a randomly generated list of numbers from 0 to 4 is 1/4. This statement is false. Since there are five possible outcomes (0, 1, 2, 3, and 4), and assuming that each number has an equal chance of being selected, the correct probability of each number occurring would be 1/5, not 1/4.

The misconception that the probability is 1/4 likely arises from a misunderstanding of randomness and probability. People often have a preconceived notion of what randomness looks like, influenced by incidents of the gambler's fallacy, where they believe past events affect the likelihood of future events. Which is not mathematically accurate. For example, the gambler's fallacy is when someone thinks that after flipping a coin and getting heads multiple times, tails is 'due' to occur. However, each flip is independent, and the probability remains at 50% for heads or tails, regardless of past flips.

Understanding true randomness means recognizing that each outcome in a set of distinct outcomes has an equal chance of occurring, and that chance is determined by dividing 1 by the total number of possible outcomes. In the scenario with the list of numbers from 0 to 4, since there are 5 possible outcomes, the correct probability should be calculated as 1/5.

Answer:

log(M/N) = 4, log(P/N) = 5

log M - log N = 4

log P - log N = 5

log P - log M = log(P/M) = 1

P/M = 10

P = 10M

The correct answer is C.

Since it is evident that P is in fact ten times larger than M, the right response is P = 10M Option C is correct.

To solve this problem

Given that log(M/N) = 4, log(P/N) = 5 and both logarithms have the same base, let's consider the relationship between M and P

Since Log (M) = 4 this implies that M =[tex]10^4[/tex]

Similarly, Log ( P) = 5 this implies that P = [tex]10^ 5[/tex]

Now, we can compare P and M :

[tex]P = 10^5[/tex]

[tex]M = 10^4[/tex]

Since it is evident that P is in fact ten times larger than M, the right response is:

C . P = 10M

Therefore, This reflects the relationship that P is 10 times M.

Answer:

4

Step-by-step explanation:

8x + 4 = 27 + 6x - 15

Combine Like Terms:

8x + 4 = 12 + 6x

Combine Like Terms:

2x = 8

Combine Like Terms:

X = 4