Write an equation in slope intercept form for the line perpendicular to y= -2x +9 and containing the point (4,-3)

Answer: Angle I is congruent to angle L

Step-by-step explanation:

Did da test

To prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

"Two or more triangles are similar if and only if the corresponding angle measures same and their corresponding side lengths are in proportion.."

For given example,

ΔGHI is dilated to form new ΔJKL.

Also, angle H is congruent to angle K.

To prove ΔGHI and ΔJKL are similar.

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

Therefore, to prove ΔGHI and ΔJKL are similar following statements must be true,

i) angle I and angle L are congruent.

ii) angle G and angle J are congruent

iii) sides of the triangles are in proportion

⇒\(\frac{GH}{JK}= \frac{HI}{KL}= \frac{IG}{LJ}\)

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Answer:100,000

Step-by-step explanation:

Answer:

see attached

Step-by-step explanation:

Recall that

\(\dfrac{d}{dx}\left[\cot(x)\right] = -\csc^2(x)\)

so that

\(\displaystyle \int \frac{dx}{\sin^2\left(\frac{x-2}3\right)} = \int \csc^2\left(\frac{x-2}3\right) \, dx = \boxed{-3 \cot\left(\frac{x-2}3\right) + C}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{Your \ exercise \ is \to\int\limits \frac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx } \end{gathered}$}\)

             \(\boldsymbol{Replaces \ u=\dfrac{x-2}{3} \longmapsto \dfrac{du}{dx}=\dfrac{1}{3} \longmapsto \ dx=3 \ du }\)

                                               \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}\)

                                                    \(\boldsymbol{\sf{Simplify }}\)

                                              \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=3\int\limits csc^2(u)du } \end{gathered}$}\)

                                                    \(\boldsymbol{\sf{Solving \ now }}\)

                                                    \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\int\limits csc^2(u)du } \end{gathered}$}\)

                                            \(\boldsymbol{\sf{This\:is\:a\:standard\:integral. }}\)

                                                     \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}\)

                                       \(\boldsymbol{\sf{We\:replace\:the\:integrals\:already\:solved. }}\)

                                                   \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}\)

                                                      \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}\)

                                      \(\boldsymbol{The\:substitution\:is\:undone\: u=\dfrac{x-2}{3} ;}\)

                                                      \(\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-3cot\left(\frac{x-2}{3}\right) } \end{gathered}$}\)

       \(\boxed{\large\displaystyle\text{$\begin{gathered}\sf Answer \longmapsto \bf{\int\limits \dfrac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx }=\boldsymbol{ -3cot\left(\frac{x-2}{3}\right)+C } \end{gathered}$}}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \underline{\bf{\green{I\:hope \ it \ helps \ you..... Regards }}} \end{gathered}$}\)

let's convert those $1.60 to pennies, that's 160 pennies, now, let's divide those 160 by (5 + 3) and distribute between the girls accordingly

\(\stackrel{Girl1}{5}~~ : ~~\stackrel{Girl2}{3} ~~ \implies ~~ \stackrel{Girl1}{5\cdot \frac{160}{5+3}}~~ : ~~\stackrel{Girl2}{3\cdot \frac{160}{5+3}} ~~ \implies ~~ \stackrel{Girl1}{5\cdot 20}~~ : ~~\stackrel{Girl2}{3\cdot 20} \\\\\\ \stackrel{Girl1}{100}~~ : ~~\stackrel{Girl2}{60}\qquad \textit{one girl got \underline{40 more cents } than the other girl}\)

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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The change in y between x = 5 and x = 9 is 2572.

What is a function?

An assignment of a Y element to every X element constitutes a function from X to Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Here, the function is given as y(x) = 4x ^ 3 + 3x ^ 2 - 3x.

we'll find the value of given function i.e. y when x = 5 and 9.

when x = 5,   y(5) = 4(5) ^ 3 + 3(5) ^ 2 - 3(5)

                            = 4(125) + 3(25) - 15

                            = 500 + 75 - 15

                            = 560.

when x = 9,   y(9) = 4(9) ^ 3 + 3(9) ^ 2 - 3(9)

                            = 4(729) + 3(81) - 27

                            = 2916 + 243 - 27

                            = 3132.

So, the change in y is  2572 (3132 - 560).

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Answer:

21

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define expression

3 × 3 + 3 + 3 × 3

Step 2: Evaluate

Answer:

21

Step-by-step explanation:

3 x 3 = 9

9 + 3 = 12

3 x 3 = 6

12 + 6 = 18

18 + 3 = 21

The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.

To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.

Given:

∠A = 50°

∠C = 90°

CB = 16

We can start by finding the measure of ∠B:

∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)

50° + ∠B + 90° = 180°

∠B + 140° = 180°

∠B = 180° - 140°

∠B = 40°

Now, using Sine law

CB/ sin A = AB / sin C

16 / sin 50 = AB / sin 90

16 / 0.766044 = AB

AB = 12.25

Again 12.25 = AC/ sin B

12.25 = AC / sin 40

AC = 19.068

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Answer:

Kindly check explanation

Step-by-step explanation:

An appropriate research design which may be employed is to perform a random assignment of the 150 students into two groups whereby a certain group is made to perform the jumping exercise and the other group sitting still for 5 minutes, after this concentration level is measured in both groups in other to evaluate if there are differences in concentration levels between the two groups.

Given the hypothesis :

H0: There is no difference in the mean improvement of long-term concentration for either treatment.

Ha: The mean improvement of long-term concentration is greater for the jumping jacks treatment.

A type 1 error occurs when a true null is rejected ; this means that we conclude that The mean improvement of long-term concentration is greater for the jumping jacks treatment when this is actually not true. Hence, students will be allowed to do jumping jack in class but there won't be any improvement.

A type 11 error occurs when we fail to reject a false null hypothesis ; Hence, we conclude that There is no difference in the mean improvement of long-term concentration for either treatment when the jumping Jacks treatment actually does improve concentration level. Hence, the school will fail to allow students do jumping jack in class.

In my opinion, type 11 error is more serious in this scenario because, the school would have failed to identify and ignored a treatment which makes it's students attain a better level of concentration.

Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

Answer:

Six Million Seven Hundred Eighty Two Thousand one hundred sixty three

Step-by-step explanation:

Hope it helps...Pls Mark as Brainliest!!

Answer:

Six Million Seven Hundred Eighty Two Thousand One Hundred and Sixty Three.

Step-by-step explanation:

6, 782, 163

(a) If x = 25 and dy/dt = 3, then dx/dt = 150

(b) If x = 9 and dx/dt = 9, then dy/dt = 3/2

As we have,

y=\(\sqrt{x}\)

So, x=y^2

Now differentiating the above expression with respect to t by using the chain rule

As, \(\frac{dx}{dt}=\frac{dx}{dy} \times \frac{dy}{dt}\)

So, differentiating y^2 with respect to y first.

\(\frac{dx}{dy}=\frac{d}{dy}(y^2)=\frac{1}{2{\sqrt{y}}}\)

Now when we differentiate y with respect to t, then the terms of y will be considered as constant.

We will get it as:

\(\frac{dx}{dt}=\frac{1}{2 \sqrt{9}} \frac{\mathrm{dx}}{\mathrm{dt}} \\\\\Rightarrow\frac{\mathrm{dx}}{\mathrm{dt}} =\frac{1}{2 \times 3} \times 9\\\Rightarrow \frac{\mathrm{dx}}{\mathrm{dt}} =\frac{3}{2}(a)\)

Calculating dx/dt

\(\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dy}}(y^2) \cdot \frac{\mathrm{dy}}{\mathrm{dt}}\\\\\frac{\mathrm{dx}}{\mathrm{dt}}=2y \cdot \frac{\mathrm{dy}}{\mathrm{dt}}\)

As the value of x = 25 and dy/dt = 3.

So, dx/dt = 2*25 *3 = 150

(b)

\(\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dx}}(\sqrt{\mathrm{x}}) \cdot \frac{\mathrm{dx}}{\mathrm{dt}}\\\\\frac{\mathrm{dy}}{\mathrm{dt}} =\frac{1}{2 \sqrt{\mathrm{x}}} \frac{\mathrm{dx}}{\mathrm{dt}}\)

As x = 9 and dx/dt = 9.

So, value of dy/dt will be \(\frac{dy}{dt}=\frac{1}{2{\sqrt{9}}}\times 9=\frac{9}{6}=\frac{3}{2}\)

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Answer:

The amount to be raised at the fund raiser is $3,333.33

Step-by-step explanation:

Here, we want to know the amount of money needed to be raised for the fundraiser

Let the amount raised be $x

Thus;

15% of $x = $500

$500 is the cost of the fund raiser

15/100 * x = 500

15x/100 = 500

15x = (100 * 500)

x = (100 * 500)/15

x = 3,333.33

For the given expression, the variable is p, coefficient is 17 and the exponent is 5.

Expression:

Expression refer the algebraic expression that consists of variables, numbers and math operators.

Given,

Here we have the expression 17p⁵

Now, we have to find the exponent, coefficient and variable.

As per the definition of exponent, the term exponent refers the power value of the expression.

So, the exponent is 5.

And the definition of coefficient is an integer that is written along with a variable or it is multiplied by the variable.

So, the coefficient is 17.

And the variable of this expression is p.

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The bushels Camden already picked is 2 and The slope is 6.

An equation is an expression that shows the relationship between some timeers and variables.

Given that equation that represents the number of bushels of guavas he picked over a period of time, in hours, is y = 6x + 2.

Here m = 6 which is the slope of the line.

The bushels Camden already picked are 2

The bushels can Camden harvest per hour is 6 which is the slope of the equation.

The graph of the equation is attached below.

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9514 1404 393

Answer:

  150

Step-by-step explanation:

Each banjo sold contributes $100 toward profit. Then $15000/$100 = 150 banjos need to be sold to cover the $15,000 in start-up costs. A properly extended graph shows this.

The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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The most appropriate choice of percentage will be given by-

343011 copies of book have been sold to date.

What is Percentage?

Percentage is a ratio expressed as a percentage of 100.

Let the total number of copies sold be x

Number of copies sold in the first month or release = \(\frac{9.3}{100} x\)

By the problem,

                         \(\frac{9.3}{100}x = 31900\)

                         \(9.3 x = 31900\) * \(100\)

                             \(x = \frac{31900 * 100}{9.3}\)

                             \(x = 343011\) (rounded off to nearest integer)

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Answer: Copyright protects original work, whereas a trademark protects items that distinguish or identify a particular business from another.

The trademark laws protect the product or service name and any slogans used in the advertising, while the copyright laws protect the additional creative written expression contained in the ad. Hope this helps!

Step-by-step explanation:

Answer: 166.72 \(ft^{2}\)

Step-by-step explanation: math

Step-by-step explanation:

All you have to do here is use the surface area, or SA, equation.

Sa=2lw+2lh+2hw
sa=2(8.5)(3.2)+2(8.5)(4.8)+2(4.8)(3.2)

Sa=54.4+81.6+30.72

Sa=166.72

Hope this helped!

Answer: 25,67%

Step-by-step explanation:

We have 11 girls and 14 boys, this is a total of 11 + 14 = 25 students.

If all the students have the same probability of being infected, the probability that a girl will get infected first is equal to the number of girls dividedthe total number of students:

p1 = 11/25

Now we get a boy infected, the number of boys is 14, and the total number of students is now 24 (because we already have a girl infected)

this probability is p2 = 14/24

The probability for both events is equal to the product of the probabilities:

P = p1*p2 = (11/25)*(14/24) = 0.2567

or 25,67%

The equivalent equation to find the ordered pair will be y=0.3x where x represents the number of days the book is late and y represents the total fine fee.

A linear equation is an equation where the highest degree in the equation is 1.

for example, y=mx,

where y and x is the variable and m, is the constant.

Given, that the librarian charges $0.30 per each day that the book is late to submit

for estimating the relation between the number of days the book is late and the total fine fee

Let's assume the number of days the book is late is x,

and the total fine is y

the librarian charges $0.30 per one day

so for x days, the total charge will be =0.30x

so from above, it is clear that the linear equation will be

y=0.3x

applying all the order pairs in this equation we can decide.

The equivalent equation to find the ordered pair will be y=0.3x

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The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

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Solution

For this case since the probability is almost the 50% we can conclude that the best answer is:

.C. Neither likely nor unlikely

We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.

Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.

The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:

Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%

Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%

We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:

Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)

Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185

We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.

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Answer:

f = 4/3

f = 1.3

f = 1 1/3

Step-by-step explanation:

Move all terms that don't contain f to the right side and solve.