Solve for y: 2x - y = 3

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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Answer:

A

Step-by-step explanation:

Here's a graph too. Make sure you pay attention to the lines, if they are dotted or not.

I hope this helps!!

1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.

Total number of people in the club = 12

total number of positions = (president, vice president, secretary) = 3

From 12 people 3 people are taken at a time.

That is, using the formula for permutation we get,

ⁿPₓ = \(\frac{n!}{(n-x)!}\)

Here n = 12 and x = 3

P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320

Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.

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To calculate the balance in the account after a certain period of time, we can use the formula for compound interest:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Time in years

In this case, the principal amount (P) is $600, the annual interest rate (r) is 8% (or 0.08 in decimal form), and the interest is compounded monthly, so the number of times compounded per year (n) is 12.

Let's calculate the balance after one year:

\(A = 600(1 + \frac{0.08}{12})^{12 \cdot 1}\\\\= 600(1.00666666667)^{12}\\\\\approx 600(1.08328706767)\\\\\approx 649.97\)

Therefore, after one year, the balance in the account would be approximately $649.97.

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The following are the rules of monomials and exponents that are used:

Monomials: It is a polynomial with one term, where each term consists of a coefficient and a variable.

The coefficients and variables are multiplied together and each of the products that is obtained is known as monomial.

For example, 4x, 3x², 5x²y, 10, 2x³, etc.

Exponent: The exponent of a number says how many times to use the number in multiplication.

For example, in ³⁴, 3 is the base, 4 is the exponent, and ³⁴ means 3 multiplied by itself 4 times. 3 x 3 x 3 x 3 = 81.Rules:Product rule:

When multiplying monomials that have the same base, add the exponents.

For example, a³ x a² = a³+² = a⁵. Anything to the zero power equals 1.

For example, x⁰ = 1.

Answer key: The answer key will include solutions for all the given questions that are present in the worksheet. Each problem in the worksheet has to be answered using the above rules of monomials and exponents.

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Answer:

80+16h≥256

Step-by-step explanation:

the 80 represents the $80 that Corinna already has

the 16h represents the amount of money made at the museum, with h being the number of hours worked

the inequality symbol is a greater than or equal sign because Corinna must have at least $256 to get the plane ticket, which means you either have to have the exact amount amount or more than the exact amount needed

The allowance time, if the standard time is 234.15 minutes and the basic time is 233.4 minutes is 0.75 minute

To calculate the allowance time, we can use the following formula:

Allowance time = Standard time - Basic time

Thus, Allowance time = 234.15 minutes - 233.4 minute = 0.75 minutes

Therefore, the allowance time is 0.75 minutes.

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The critical value of 2.576. If |z| > 2.576, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To test the manufacturer's claim at a 1% significance level, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The medicine is 90% effective in relieving backache.

H₀: p = 0.9

Alternative hypothesis (H₁): The medicine is not 90% effective in relieving backache.

H₁: p ≠ 0.9

Where p represents the true proportion of people who experience relief from backache after taking the medicine.

To conduct the hypothesis test, we will use the sample proportion and perform a z-test.

Calculate the sample proportion:

p = x/n

where x is the number of people who experienced relief (160) and n is the sample size (200).

p= 160/200 = 0.8

Calculate the standard error:

SE = √(p(1 - p)/n)

SE = √((0.8 * (1 - 0.8))/200)

Calculate the test statistic (z-score):

z = (p - p₀) / SE

where p₀ is the hypothesized proportion (0.9 in this case).

z = (0.8 - 0.9) / SE

Determine the critical value for a two-tailed test at a 1% significance level.

Since we have a two-tailed test at a 1% significance level, the critical value will be z* = ±2.576 (obtained from a standard normal distribution table or calculator).

Compare the absolute value of the test statistic to the critical value to make a decision:

If the absolute value of the test statistic is greater than the critical value (|z| > z*), we reject the null hypothesis.

If the absolute value of the test statistic is less than or equal to the critical value (|z| ≤ z*), we fail to reject the null hypothesis.

Substituting the values into the equation, we can determine the test statistic and compare it to the critical value.

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60.5 is mean

61 is median

65 is interquartile range

14 is range

Answer:

60.5 is mean.

_________________

61 is median.

_________________

65 is interquartile range.

_________________

14 is range.

Considering the route as a curve of a quadratic function, the information should be completed as follows;

In Mathematics and Geometry, the vertex form of a quadratic function is represented by the following mathematical equation (formula):

y = a(x - h)² + k

Where:

Based on the information provided about this quadratic function, we can logically deduce that a mathematical equation which quickly reveals the vertex of the quadratic function is given by:

y = a(x - h)² + k

0 = a(2.9 - (-1))² + 4

3.9a = -4

a = -4/3.9

a = -1.03

Therefore, the required quadratic function is given by:

y = a(x - h)² + k

y = -1.03(x - (-1))² + 4

y = -1.03(x + 1)² + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

63

Step-by-step explanation:

John's percentage:

36 and 48 have a common factor of 12 so divide both of them by 12.

36/12= 3 and 48/12=4 therefore

so 36/48= 3/4 which is 75% but we don't need to focus on the percent.

Don's no. of shirts:

we know Don has 84 shirts so we say

3/4 of 84= no. of shirts that Don put in his closet

84/4=21 21x3=63

Don put 63 shirts in his closet.

Hope that helped! Anymore questions just ask! :)

Answer:

−6x+18

Step-by-step explanation:

-6(x-3)

(−6)(x+−3)

=(−6)(x)+(−6)(−3)

=−6x+18

Answer:

18 - 6x

Step-by-step explanation:

According to the distributive property:

-6(x-3) =

-6*x + -6*-3 =

-6x + 18

Answer:

It is B

Step-by-step explanation:

B:3=b

bx3=B

Kindly, check below

1) As we can see, this is a piecewise function. So, let's plot that accordingly to each interval.

2) So, we can represent that this way:

Note that the open dot does not include the endpoint. And closed dots include the endpoints.

Thus, this is the answer.

Answer:

2 Evaluate Take this to prepare for the final quiz in the Evaluate module of this ... Choose all of the numbers below which are common denominators of the 5 7 ... by using the distributive property and combining like terms: x (3 + y ) (5x x ) + 6x y . 5. ... Use the FOIL method to find: (x + 3xy)(3x 3 y ). Use a pattern to find: (x 3y) 3 .

Answer:

y = 1

Step-by-step explanation:

\(\frac{6}{2}=\frac{2(y+2)}{2}\\ \Leftrightarrow 3-2=y=2-2\\\Leftrightarrow y=1\)

The solution to the given equation 6 = 2(y+2) is y = 1, which is determined by distribution and arithmetic operations.

The equation is given as follows:

6 = 2(y+2)

To solve the equation 6 = 2(y + 2) for y, we need to isolate y on one side of the equation.

First, distribute the 2 on the left side by multiplying it with y and 2:

6 = 2y + 4.

Next, move the constant term (4) to the other side of the equation by subtracting it from both sides:

6 - 4 = 2y

2 = 2y

y = 2/2

Apply division operation to get:

y = 1

Therefore, the solution to the given equation is y = 1.

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The total number of defective iphones from a batch of 16,530 iphones is equal to 513 .

Total  number of iphones examined by quality-control inspector =290

Total number of iphones in a batch = 16,530

Number of iphones defective out of 290 = 9

Let us consider x be the number of defective iPhones in the batch of 16,530 iPhones.

Use proportions to find out how many defective iPhones there will be in a batch of 16,530 iPhones.

The proportion of defective iPhones in the sample of 290 iPhones is,

= 9/290

Proportion of defective iPhones in a batch of 16,530 iPhones,

Set up a proportion,

9/290 = x/16530

To solve for x, we can cross-multiply,

⇒ 9 x 16530 = 290 x

⇒ 148,770 = 290 x

⇒ x = 513

Therefore, there will be approximately 513 defective iPhones in a batch of 16,530 iPhones.

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18^9 * 1839467234728348^28332 is approximately equal to 4.2198316658586158100166848710232 × 10^172409.

To solve this problem, we can use the properties of exponents, specifically the product rule:

(a^m)(a^n) = a^(m+n)

We can apply this rule to simplify the expression:

18^9 * 1839467234728348^28332

= (23^2)^9 * (1839467234728348)^28332

= 2^9 * 3^(29) * (1839467234728348)^28332

= 512 * 3^18 * (1839467234728348)^28332

Now, we can use a calculator or a computer to compute the value of the expression. The result is a very large number:

4.2198316658586158100166848710232 × 10^172409

Therefore, 18^9 * 1839467234728348^28332 is approximately equal to 4.2198316658586158100166848710232 × 10^172409.

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The final value of the given expressions are:

1) 12√(33)c

2) 8√5 (3√2 + 8√3)

3) 3

4) -12√6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1)

√99c . √48c

√(9 x 11)x . √(16 x 3)c

3√11c . 4√3c

12√(11 x 3)c²

12√(33)c

2)

2√(80) ( √18 + 4√12 )

2 √(16 x 5) ( √(9 x 2) + 4√(4 x 3) )

2 x 4√5 ( 3√2 + 8√3 )

8√5 (3√2 + 8√3)

3)

(√2 - √5) . (-√2 - √5)

= -2 - √10 + √10 + 5

= 3

4)

√(48) x -√18

= √(16 x 3) x -√(2 x 9)

= 4√3 x -3√2

= -12√6

Thus,

The value of each of the expresssion is given above.

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The correct option is b. 9.7 meters/second².

The magnitude of the acceleration of the falling ball is 9.7 meters/second².

Acceleration is the rate for which velocity changes over time, both in terms of speed and direction. A point or object travelling in a straight path gets accelerated if it accelerates or decelerates.

The final velocity of a falling ball, v = 33 m/s

The ball's initial velocity, u= 0 m/s

The time it required for the ball to arrive at the ground, t = 3.4 seconds

The ball's acceleration during the fall Equals 'a'.

The formula for acceleration is;

acceleration = (final velocity - initial velocity)/time

Substituting the values in the formula;

a = (33 - 0)/3.4

a = 9.7

Therefore, the rate of acceleration of the falling ball is 9.7 m/s².

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Answer:

The answer would be C. Inference

Answer:

\(6x^2+8x\)

Step-by-step explanation:

Hey there!

In order to find the answer to this question, what you need to do is first find the area of the whole grey box as a whole (including the white box to)

The dimensions for this is 3x+2 and 4x

Now we know that to find area, we need to multiply length by height

So (3x+2)(4x) is what we have to solve to get the area

Now we simplify:

1. Distribute

2. \(12x^2+8x\)

So now we know that the total area is \(12x^2+8x\)

Now what we do is take out the area of the white box from the area of the grey box

Lets find the area of the white box:

l=3x   (l - length)

h=2x (h - height)

\(3x*2x=6x^2\)

Now we have the area of both shapes

Since we have all the information we need to find the final answer, the following steps below will be using the information we found to find the final answer:

In order to find the final answer which is the area of the shaded region, we take out the area of the white region from the total area of the grey region (including the white region)

So now we can formulate this new equation:

\(12x^2+8x-6x^2= ta\)

(ta= total area)

Now we simplify:

\(6x^2+8x\\\) is going to be our final answer

So our final answer is \(6x^2+8x\)

Answer: 3x + 6

Step-by-step explanation: PLEASE MARK ME AS BRAINLISTI AND HAVE A GREAT DAY!!!

Answer:

3x+6

Step-by-step explanation:

\( \frac{y}{4} = - 3\)

\(y = - 3 \times 4\)

\(y = - 12\)

Multiplication would be used.

Answer:

17

Step-by-step explanation:

The image is not too clear. Let us assume we need the base AB

AB  = opposite

BC = hypotenuse

Sin theta = opp/hyp

Sin 37 = AB/BC

Sin 37 = AB/28

AB = 28sin37

AB = 28(0.6018)

AB = 16.85

AB ≈ 17

Hence the length of AB is 17

The smallest positive integer Joelle could have multiplied 756 by

15876

This is further explained below.

What is a perfect square?

Generally, A perfect square number is a number in mathematics that, when its square root is calculated, yields a natural number.

To solve this problem we can do:

By properties of roots

So, so that the multiplication of 756 by an integer becomes a perfect square, you have to multiply it by 21 to make $21^2$ and thus "eliminate" the root.

756 * 21=15876

In conclusion,  You can verify that 15876is a perfect square since root (15876)=132 and 132 is a natural number

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The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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Answer:

  2150 people

Step-by-step explanation:

You want the number of people in a town after 10 years if the initial population of 1600 is growing at 3% per year.

Exponential growth can be modeled by the equation ...

  p(t) = a·b^t

where a = p(0) = the initial population, and

b = annual growth factor = (1 + annual growth rate)

The problem statement tells you p(0) = 1600, and the growth rate is 3%. This means the equation modeling the population is ...

  p(t) = 1600·1.03^t

The population in 10 years is modeled as ...

  p(10) = 1600·1.03^10 ≈ 2150

The population of the town after 10 years is expected to be about 2150 people.

Answer:

he will score 10 goals in 5 games

__________

\( \: \)

\( \sqrt{1,69} = ...\)

\( = {1,69}^{ \frac{1}{2} } \)

\( = \bold{1,3}\)

Soo, asnwer for Question \(\sqrt{1,69} = 1,3\)