Find x .

Please help I’m begging

1.  (a)The  vertex of the  function \(y=x^{2} +5x-7\)  is \((-\frac{5}{2} ,-\frac{53}{4} )\)

How is the vertex calculated?

In function \(y=x^{2} +5x-7\),

a= 1 ,b= 5, c= -7

For a function   \(y=ax^{2} +bx+c\)  , where (a≠0),

The vertex is \((-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )\)

\(x_v=-\frac{b}{2a}\\\\ =-\frac{5}{2*1} \\\\=-\frac{5}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*1*(-7)-(5^{2} )}{4*1}\\\\ =-\frac{53}{4}\)

So, vertex  \((-\frac{5}{2} ,-\frac{53}{4} )\) is minimum because a>0

(b)The solutions are \((\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)\)

How is the solution calculated?

When a function \(y=ax^{2} +bx+c =0\)  where (a≠0),

\(x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-5\pm\sqrt{5^{2} -4(1)(-7)} }{2(1)} \\\\x=\frac{-5\pm\sqrt{53} }{2} \\\\x=\frac{\sqrt{53} -5}{2} , x=\frac{-5-\sqrt{53} }{2} \\\\\text{The solutions are } (\frac{\sqrt{53} -5}{2},0) (\frac{-5-\sqrt{53} }{2},0)\)

2. (a)The  vertex of the  function \(y=-x^{2} +3x+8\)  is \((\frac{3}{2} ,\frac{41}{4} )\)

How is the vertex calculated?

In function \(y=-x^{2} +3x +8\)

a= -1 ,b= 3, c= 8

For a function   \(y=ax^{2} +bx+c\)  , where (a≠0),

The vertex is \((-\frac{b}{2a} ,\frac{4ac-b^{2} }{4a} )\)

\(x_v=-\frac{b}{2a}\\\\ =-\frac{3}{2*(-1)} \\\\=\frac{3}{2} \\\\\\y_v=\frac{4ac-b^{2} }{4a} \\\\=\frac{4*(-1)*(8)-(3^{2} )}{4*(-1)}\\\\ =\frac{41}{4}\)

So, vertex  \((\frac{3}{2} ,\frac{41}{4} )\) is maximum because a<0

(b)The solutions are \((\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)\)

How is the solution calculated?

When a function \(y=ax^{2} +bx+c =0\)  where (a≠0),

\(x=\frac{-b\pm\sqrt{b^{2} -4ac} }{2a} \\\\x=\frac{-3\pm\sqrt{3^{2} -4(-1)(8)} }{2(-1)} \\\\x=\frac{-3\pm\sqrt{41} }{-2} \\\\x=\frac{3\pm\sqrt{41} }{2}\\\\x=\frac{3-\sqrt{41}}{2} , x=\frac{3+\sqrt{41} }{2} \\\\\text{The solutions are } (\frac{3+\sqrt{41} }{2},0) (\frac{3-\sqrt{41} }{2},0)\)

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The law of conservation of energy and momentum can be used to construct the equation that connects the initial release height of block x (hx) and the speed of the two-block system following the collision (v s).

Block x's initial kinetic energy (0.5 * m x * v x2) and potential energy (m x * g * hx) are both equal to the total kinetic energy of both blocks after the collision (0.5 * (m x + m y) * v s).

Combining everything, we get the following equation:

m x * g * hx + 0.5 * m x * v x2 = 0.5 * (m x + m y) * v s2.

where g is the acceleration brought on by gravity, v x is the starting speed of block x, and m x and m y are the masses of blocks x and y.

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Answer:

multiply by

Convert from Convert to

US gpd US gpm cfm IMP gpd IMP gpm

m3/s 22800000 15852 2119 19000000 13200

m3/min 380000 264.2 35.32 316667 220

m3/h 6333.3 4.403 0.589 5277.8 3.67

liter/sec 22800 15.852 2.119 19000 13.20

liter/min 380 0.2642 0.0353 316.7 0.22

liter/h 6.33 0.0044 0.00059 5.28 0.0037

US gpd 1 0.000695 0.000093 0.833 0.000579

US gpm 1438.3 1 0.1337 1198.6 0.833

cfm 10760.3 7.48 1 8966.9 6.23

Imp gpd 1.2 0.00083 0.00011 1

Step-by-step explanation:

googled it

The domain and the range of the provided graph of a square root function include the following:

Domain = (-∞, 0).

Range = (-2, ∞).

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, 0}

Range = {-2, ∞}

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Answer:

y=2(100-x)

Step-by-step explanation:

Given the expression, knowing also that the expression has two unknowns x and y

2,000 = 20x + 10y

step one:

we can reduce all coefficients by dividing through  by a common multiple

i.e dividing through by 10 we have

2,000/10 = 20x/10 + 10y/10

200=2x+y

step two:

we can either solve in terms of x or y

let us solve in terms of y

y=200-2x

step three:

we can factor 2 on the left-hand side we have

y=2(100-x)

Answer:

SAS

Step-by-step explanation:

In triangle ABC and triangle EFD

1. BC = CD (S) Given

2. < BCD = < EFD (A) being vertically opposite. angles.

3. AC = CE (S) Given

Hence

By SAS postulate Triangle ABC and triangle EFD are congruent.

HOPE IT HELPS :)❤

Answer:

the slope of the line would be 3/4

Step-by-step explanation:

to find this use your equation for slope: y2-y1/x2-x1

this will give you 5-2/4-0

simplified it is 3/4

another way to know the slope is that the slope will be rise/run, so since the line is going up 3 places and over 4 places, your slope would be 3/4

Answer:

4x-36

Step-by-step explanation:

Put together like terms

X plus 3x = 4x

Mr. Jones bought approximately 13 pamphlets.

In this problem, we have two types of items: books and pamphlets. Books cost 50¢ and pamphlets cost 15¢ at the book sale.

Let's use variables to represent the quantities we don't know. Let's say Mr. Jones bought x books and y pamphlets.

We are given two pieces of information:
1. Mr. Jones spent $90 on his purchases.
2. He bought 15 more pamphlets than books.

Now, let's set up the equations based on the given information.

First, let's consider the cost equation. The total cost of the books and pamphlets should equal $90.

The cost of x books is 50¢ * x, and the cost of y pamphlets is 15¢ * y. So, the equation becomes:
50x + 15y = 90

Next, let's consider the second piece of information. Mr. Jones bought 15 more pamphlets than books, which means y = x + 15.

Now, we have a system of two equations:
50x + 15y = 90
y = x + 15

To solve this system, we can use substitution or elimination method. Let's use substitution:

Substitute the value of y from the second equation into the first equation:
50x + 15(x + 15) = 90

Simplify the equation:
50x + 15x + 225 = 90
65x + 225 = 90

Subtract 225 from both sides:
65x = 90 - 225
65x = -135

Divide both sides by 65:
x = -135 / 65
x ≈ -2.08

Since we cannot have a negative number of books, we know that x must be a positive whole number. So, let's round x to the nearest whole number:
x ≈ -2

Now, substitute this value of x back into the second equation to find y:
y = x + 15
y ≈ -2 + 15
y ≈ 13

Therefore, Mr. Jones bought approximately 13 pamphlets.

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Answer:

8

Step-by-step explanation:

\(5^{2}\)−17

=25−17

=8

Answer:

$20.78

Step-by-step explanation:

10.52 - (-10.26)

10.52 + 10.26

20.78

The number of sales a promoter can expect if he spends $10,000 in advertising is $80,000 that is option B.

While going through a word problem like this, read it a few times to comprehend the context without focusing too much on the numbers..... Something along the lines of....

"If a promoter spends money on advertising, he will get more customers."

Short sentences should be used to summarise the content.

$10,000 is spent by the promoter.

"For every $100 spent, 20 new customers are drawn."

"Tickets are $40."

In one calculation this would be:

Using ratio of,

income/expenditure = 800/100 = income/10,000

= 10000 x 20 x 40 / 100

= 80,000

Therefore, the value of sale increase should be $80,000.

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Answer:

The quadratic equation is: \(y=x^2-36\)

Step-by-step explanation:

If the roots of the quadratic equation are "-6" and "6", then it must have the following factors:  \((x+6)\,\, and \,\,(x-6)\)

Therefore, we can write the equation in factor form as:

\(y=a\,(x+6)\,(x-6)\)

where a is a real number constant factor. Now, this equation in standard form will look like:

\(y=a\,(x^2+6x-6x-6^2)=a\,(x^2-36)=ax^2-36\,a\)

Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant  factor \(a\) must be "1". The final expression for the quadratic becomes:

\(y=x^2-36\)

Answer:

14.85

Step-by-step explanation:

P₁V₁ = P₂V₂

13 x 8 = P₂ x 7

P₂ = (13 x 8)/7

  = 104/7

P₂ = 14.85 atm

Answer:

6

Step-by-step explanation:

1. 5-4=1

2. 1×8=8

3. 8-2=6

Answer: 56 + 12 = 68

y + 12 = x

x = 68

Step-by-step explanation:

The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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Answer:

the answer is C

you have to use horner Division because its so easily to use

just search horner divission in polonium and you will find it

The expression f(x)/g(x) defines function h(x)=3x^2+12x.The answer is C.

We have given that,

\(f(x)=3x^2+9x^2-12x\)

\(g(x)=x-1\)

and,    \(h(x)=3x^2+12x\)

Suppose f(x) and g(x) are function,

\((\frac{f}{g}) (x)=\frac{f(x)}{g(x)}\)

So we have given function us

\(f(x)=3x^2+9x^2-12x\)

\(g(x)=x-1\)

We have divide f(x) by g(x)

\(=\frac{3x^3+9x^2-12x}{x-1}\)

\(=3x\left(x+4\right)\)

\(=3x^2+12x\)

Therefore we get the expression f(x)/g(x) defines function h.

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The solution is Option C.

The equation of line is given by y = -2x + 58

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 2 , 54 )

Let the second point be Q ( 5 , 48 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 48 ) / ( 2 - 5 )

On simplifying the equation , we get

Slope m = 6 / -3

Slope m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 54 = -2 ( x - 2 )

On simplifying the equation , we get

y - 54 = 2x + 4

Adding 54 on both sides of the equation , we get

y = -2x + 58

Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )

Hence , the equation of line is y = -2x + 58

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The false statement is: "The researchers would come to the conclusion that the programme was successful if they used a significance level of 1%."

What is significance level?

A significance level, denoted by α, is the threshold chosen by researchers to determine the level of evidence required to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error (incorrectly rejecting the null hypothesis when it is true).

In this case, the given p-value is 0.003. If the null hypothesis is true, the p-value represents the likelihood of obtaining a test statistic that is equally extreme to or more extreme than the one that was observed. It offers proof that the null hypothesis is false.

We can conclude that there is strong evidence to reject the null hypothesis in favour of the alternative hypothesis because the p-value is 0.003, which is lower than any often used significance level like 0.05 or 0.01. Thus, if the researchers apply a 5% level of significance, they would draw the conclusion that the programme was successful.

However, if the researchers use a significance level of 1%, they would require even stronger evidence to reject the null hypothesis. Since the p-value of 0.003 is greater than 0.01, they would not be able to reject the null hypothesis at the 1% significance level and would not conclude that the program was effective.

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Answer:

  20.5 years

Step-by-step explanation:

The population is given by the exponential function ...

  p = 16000·(1 +0.022)^t

When p = 25000, we can find the value of t by taking logarithms.

  log(25000/16000) = t·log(1.022) . . . . . divide by 16000, take the log

  t = log(25/16)/log(1.022) ≈ 20.5 . . . . . . divide by the coefficient of t

It will take about 20.5 years for the population to reach 25000.

Hello!

Here we are given a long division question.

The first thing I would do is see how many times the term of the highest degree in the divisor could go into the term of the highest degree in the dividend, which would be 3.

Then, we could already see that the divisor's degree would be higher than that of the dividend, so the rest would go in the remainder over the divisor.

\(\frac{18x^2+5x+5}{6x^2-4x+1}\)

\(3+\frac{17x+2}{6x^2-4x+1}\)

Hope this helps!

Answer:

This is it trust me

Step-by-step explanation:

I just took it and got a 100

Answer:

160 square inches

Step-by-step explanation:

You can split the irregular figure up into regular shapes:

the top 4x6 inch rectangle

the middle section can be a 18x6 rectangle (added 7+11 for the length)

the bottom 4x7 rectangle (sibtracted 10-6 for the width)

Then, find the area of each section with the equation A = lw.

A= 4(6) = 24 square inches

A = 18(6) = 108 square inches

A = 4(7) = 28 square inches

Add these areas up to get the total area of the irregular figure.

24 + 108 + 28 = 160 square inches

Using the definition of continuity and the properties of limits to show that the function is continuous at the given number  f(x)=-5

continuity of a real function is provided generally in a calculus’s introductory course in terms of a limit’s idea.

First, a function f with variable x is continuous at the point “a” on the real line, if the limit of f(x), when x approaches the point “a”, is equal to the value of f(x) at “a”, i.e., f(a).

Second, the function (as a whole) is continuous, if it is continuous at every point in its domain.

We know that the value of f near x to the left of a, i.e. left-hand limit of f at a and the value of f near x to the right f a,

i.e. right-hand limit are equal, then that common value is called the limit of f(x) at x = a. Also,

a function f is said to be continuous at a if limit of f(x) as x approaches a is equal to f(a).

A function f is continuous at a number a if

\(\lim_{x \to\n} f( x) = f(a)\)

f(x) = \(x ^3x^4 5\)

     = \(\lim_{x \to \ a} x^3 * \lim_{x \to \ a} x^4 *5\\= (-1)^3 * (-1)^4 *5\\= -1 * 1* 5\\= -5\)

Using the definition of continuity and the properties of limits to show that the function is continuous at the given number  f(x)=-5

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Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

The events are mutually exclusive events, so P(A|B) is 0.

In this question,

If two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then

⇒ A ∩ B = 0

Now the conditional probability, P(A|B) = \(\frac{P(A \cap B )}{P(B)}\)

⇒ \(\frac{0}{0.10}\)

⇒ 0.

Hence we can conclude that the events are mutually exclusive events, so P(A|B) is 0.

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Answer:

Step-by-step explanation:

In the given question, it is given that

ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.

And we have to find the value of tan B.

And tangent of any angle is equal to the ratio of vertical by horizontal. That is

\(tanB=\frac{8}{15}\)

And that's the required missing ratio for tan B .

The value of the trigonometric function sin B, cos B, and sin A is 8/17, 15/17, and 15/17 respectively.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

A ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.

Then we have

\(\sin B = \dfrac{8}{17}\\\\\\\cos B = \dfrac{15}{17}\\\\\\\sin A = \dfrac{15}{17}\)

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The 95% confidence interval on the true proportion of underweight rats from this experiment is (0.189, 0.611), the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02 is 576 and,  the sample size required to be 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p, is 9604.

1. Calculation of a 95% confidence interval on the true proportion of underweight rats:

Here, n = 30, and p = 12/30 = 0.4 (12 rats out of 30 were underweight).

We will use the following formula to calculate the 95% confidence interval on the true proportion of underweight rats: (p - E, p + E),

where E = zα/2 * √[p (1 - p) / n]We know that α = 0.05 (since the confidence level is 95%).

Therefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 1.96 * √[(0.4)(0.6) / 30] = 0.211(p - E, p + E) = (0.4 - 0.211, 0.4 + 0.211) = (0.189, 0.611)

Therefore, a 95% confidence interval on the true proportion of underweight rats from this experiment is (0.189, 0.611).

2. Calculation of the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02:

Here, we will use the following formula to calculate the minimum sample size required:n = [zα/2 / E]² * p * (1 - p)

We know that α = 0.05 (since the confidence level is 95%). T

herefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 0.02 (since we want the error to be less than 0.02).p = 0.4 (using the point estimate of p obtained from the preliminary sample).n = [1.96 / 0.02]² * 0.4 * 0.6 = 576

Therefore, the minimum sample size required to be 95% confident that the error in estimating the true value of p is less than 0.02 is 576.

3. Calculation of the sample size required to be 95% confidence that the error in estimating p is less than 0.02, regardless of the true value of p:

We will use the following formula to calculate the sample size required:

n = [zα/2 / E]²We know that α = 0.05 (since the confidence level is 95%).

Therefore, zα/2 = z0.025 = 1.96 (from the standard normal table).

E = 0.02 (since we want the error to be less than 0.02).n = [1.96 / 0.02]² = 9604

Therefore, the sample size required to be 95% confident that the error in estimating p is less than 0.02, regardless of the true value of p, is 9604.

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