Use the zero-product property to solve the equation.
(x + 3)^2 = 0

first of all, let's find the common ratio in this geometric sequence, by simply dividing a any of the terms by the term right behind it, hmmm say -12 and 16

[tex]16~~,~~-12~~,~~9~~,~~-\cfrac{27}{4}~\hfill \stackrel{\textit{\LARGE common ratio}}{\cfrac{-12}{16}\implies -\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\textit{first term}\\ r=\textit{common ratio}\\ \qquad -1 < r < 1\\[-0.5em] \hrulefill\\ a_1=16\\[1em] r=-\frac{3}{4} \end{cases}[/tex]

[tex]S=\cfrac{16}{ ~~ 1-\left( -\frac{3}{4} \right) ~~ }\implies S=\cfrac{16}{ ~~ 1 + \frac{3}{4} ~~ }\implies S=\cfrac{16}{~~ \frac{ 7}{ 4} ~~}\implies S=\cfrac{64}{7}[/tex]

The equation -7(8x + 5) = 5x+10 has one solution of x which satisfies the equation. The solution is x = -45/61.

What is solution of system of equation?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system.

According to the given question:

Given equations is -7(8x + 5) = 5x+10

Simplifying both sides to get value of x

-7(8x + 5) = 5x+10

-56x - 35 = 5x + 10

-61x = 45

x = -45/61

Therefore x has one solution which is -45/61

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Answer:

2

Step-by-step explanation:

The y-intercept is the point at which the graph crosses the y-axis.

(I have marked it in blue on the attached graph).

From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.

The two true statements about these are,

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.

So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.

The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

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The total number of people at the stadium was 6800 people .

A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .

For Example : 2% is = 2/100   .

In the question ,

it is given that ,

percent of teenagers fans in the stadium is = 5%

number of teenagers present at the football stadium is = 340

which means 5% represents 340 people ,

So , 1% will be 340/5 = 68 people .

the total percent of people present in the stadium is = 100% ,

multiplying both sides by 100 ,

we get ,

So , 100%  = 68 × 100 = 6800 people

Therefore , The total attendance at the football stadium was 6800 people .

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The Trigonometric ratios are:

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

H/P = Cosecθ

H/B = Secθ

B/P = Cotθ

Where,

'P' represents the perpendicular

'B' represents the base

'H' = represents the hypotenuse

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

A. As the values of p, b or h are not given.

Pythagoras Theorem states that:

h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]

Altitude of a triangle is usually given by the perpendicular,

So,

h² = p² + b²

h² - b² = p²

p² = h² - b²

p  = [tex]\sqrt{h^2 - b^2}[/tex]

B. The trigonometric ratios for θ = 60°

Sin 60 = √3/2

Cos 60 = 1/2

Tan 60 = √3

C. The trigonometric ratios for θ = 30°

Sin 30 = 1/2

Cos 30 = √3/2

Tan 30 = 1/√3

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Answer:

Step-by-step explanation:

4,505 tickets were sold 219 times.

4,505 x 219

The answer is 986,595

The value of [y] will be 1.

Given is the following expression -

y = 2 x (2/4)

We can write the value of [y] as -

y = 4/4 = 1

y = 1

Therefore, the value of [y] will be 1.

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Answer:

200*1-0.95-0.95+0.9025

200*1-1.9+0.9025

200*0.0025

0.5

Answers in bold

Median of car 1:  249

Median of car 2:  251

====================================================

Explanation:

This is the data set for car 1

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5}202 & 247 & 241 & 223 & 246\\\cline{1-5}253 & 271 & 241 & 291 & 249\\\cline{1-5}259 & 257 & 261 & 246 & 268\\\cline{1-5}\end{array}[/tex]

Which when written out as a single long line, we have this:

202, 247, 241, 223, 246, 253, 271, 241, 291, 249, 259, 257, 261, 246, 268

Sort those values from smallest to largest to get this set

202, 223, 241, 241, 246, 246, 247, 249, 253, 257, 259, 261, 268, 271, 291

There are n = 15 items in that set.

n/2 = 15/2 = 7.5 which rounds to 8

The middle-most item, aka median, is in slot 8.

There are 7 items below the median, and 7 items above it. Giving us 7+1+7 = 15 items total.

Start at "202" and count 8 slots to the right until you arrive at 249 which is the median of the car 1 data set. Make sure you are looking at the sorted data set.

Follow similar steps for the car 2 data set. You should get 251 as the median of the car 2 data set.

Answer:

slope = -4

Step-by-step explanation:

A (-2,5)

B (0, -3)

slope = (-3-5)/(0-(-2)

-8/2

-4

The point F lies on 4.5 in the number line.

What is the number line?

The number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on

= (my+nx)/(m+n) in the number line.

Here in the given problem that,

Point D lies on -6 in the number lin

Point E lies on 8 in the number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence, the point F lies on 4.5 in the number line.

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Answer:

The answer is A

Step-by-step explanation: I'm so smart

Answer: $7

Step-by-step explanation:

We know that $28 for four people.

So we take 28 divided by 4 and we get $7 per people

At the end of the sale, there were a total of 196 customers in the store for the given function.

The earliest known attempt to the notion of function may be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity.

The total number of shoppers in the store is the number of shoppers present at the start of the sale Plus the number of shoppers who entered the store minus the number of shoppers who left.

Given that there were no shoppers in the store before the sale began, the number of shoppers in the store at the start of the sale is 0.

It is assumed that the number of customers who have entered the store is represented by S(t)=0.5t⁴-16t³+144t².

So, at t=12, the number of shoppers in the store is S(12)=

0.5(12)⁴-16(12)³+144(12)²

S(12)=3456 shoppers.

L(t)= -80+(4400/t²-14t+55)

At t=12,

[tex]\int\limits^{12}_0 {L(t)} \, dt[/tex]=[tex]\int\limits^{12}_0[/tex]( -80+(4400/t²-14t+55))dt

At the end of the sale, there were a total of 196 customers in the store.

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Answer:

-3

Step-by-step explanation:

we just fill in x to see if it is true

5(-3)+12>2(-3)+6

-15+12>-6+6

-3>0
false

5(3)+12>2(3)+6

15+12>6+6

27>12
true

5(-1)+12>2(-1)+6

-5+12>-2+6

7>4
true

5(1)+12>2(1)+6

5+12>2+6

17>8
true

Hopes this helps please mark brainliest

Answer:

x = 9

Step-by-step explanation:

(7x + 7) + 60 = 13x + 13 (exterior angle)

7x + 67 = 13x + 13

6x = 54

x = 9

Answer: True

Step-by-step explanation:

-The f-distribution curve is positively skewed towards the right with a range of 0 and ∞

The value of F is always positive or zero. It never has negative values.

Answer:

x < 11

Step-by-step explanation:

there you go :)

4300 workers are there in all.

What is algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Here, we have

In a company, 90% of the workers are women.

430 people work for the company who aren’t women.

% of male = 10%

Now,

10% of x = 430

10÷100 × x = 430

x = 4300

Hence, 4300 workers are there in all.

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Answer:

the answer is no

Step-by-step explanation:

The best treatment for this patient's acute blood pressure control is to administer an intravenous (IV) antihypertensive medication such as labetalol or nitroprusside. Additionally, it is important to assess for underlying causes of her elevated blood pressure such as infection, kidney disease, or heart failure.

What is blood pressure?
Blood pressure (BP) is indeed the force exerted by moving blood against blood vessel walls. The heart's action of trying to pump blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) just above atmospheric pressure in the immediate vicinity. Along with respiratory rate, pulse rate, oxygen levels, and body temperature, blood pressure is among the vital signs that medical professionals consider when assessing a patient's health.

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Serena's company implemented the process of Delayering.

To improve operational efficiency, delayering is the act of removing levels of hierarchy between the top and bottom levels of staff.

Delayering often involves the removal of intermediate managers, giving top managers better access to the business as a whole and fostering the necessary openness.

The delayering process has benefits and drawbacks of its own. Although the employer can lower pay costs, the company's ability to make decisions may suffer as a result of top managers' diminished visibility.  

Delayering is helpful for reducing bureaucracy and increasing flexibility in the organizational structure. Additionally, it enhances internal communication and participation. Other advantages include increased drive and empowerment.

Given that

Serena's company decided to reduce the number of levels within the job structure and as a result, she has 20 more people who report to her. her company implemented.

By the given observation about Delayering, we can conclude that the company implemented the process of Delayering.

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T|=|S|⟹ there is bijection F:S→T.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

According to our question-

The function f:ST |S||T| has an injective and not a surjective nature.

Assume an injective function exists: g:TS|T||S|. |T|=|S|

(this follow from the Cantor-Bernstein theorem).

|T|=|S|⟹ F:S:T has a bijection.

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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.

The expressions that are simplified are:

[tex]n^{4}[/tex]

[tex]\frac{1}{n^{-5}}[/tex]

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

Options A, B, and E are the correct answer.

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,

[tex]n^{4}[/tex]

This is already simplified.

[tex]\frac{1}{n^{-5}}[/tex]

This is already simplified.

[tex]n^6 . n^{-8}[/tex]

= [tex]n^{6 - 8}[/tex]

= [tex]n^{-2}[/tex]

[tex]n^7 . p^8[/tex]

= [tex]n^{7 + 8}[/tex]

= [tex]n^{15}[/tex]

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

This is already in simplified form.

Thus,

The expressions that are simplified are:

[tex]n^{4}[/tex]

[tex]\frac{1}{n^{-5}}[/tex]

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

Options A, B, and E are the correct answer.

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Answer:

------------------

RHS and HL refer to same thing.

A right angled triangle has one hypotenuse and two sides.

If the hypotenuse and one side of one triangle is congruent to hypotenuse and one side of another triangle, then the two triangles are congruent.

We know sides of a right triangle are also called the hypotenuse and legs. RHS is also called HL because they both refer to hypotenuse and one side or leg.

The tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

We have,

First car price is  =  $13,500

and tax of the first car is = $910

Second car price is  =  $16,500

and tax of the second car is = ?

so,

 $13,500 -----    100,

  $910      -----    x

x = 910 * 100 / 13500

x =  6.7

therefore, the rate of tax is 6.7%

so, we will calculate the tax for the second car,

$16,500 -----    100,

    y        -----    6.7

y = 6.7 * 16,500 / 100

y = $1105.5

difference of tax price between two cars = $1105.5 - $910 = $195.5

Hence, the tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

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The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.

An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠,  <, or ≤ symbols.

The specified inequality is; h < 3·h < 3

When h < 3·h, we get;

h is a positive number larger than 0, such that we get;

When h < 0, 3·h < h

Therefore; h > 0

The inequality, 3·h < 3, indicates;

3·h < 3

h < 3/3 = 1

h < 1

Which indicates that we get;

0 < h < 1

Therefore, non of the values make the inequality, h < 3·h < 3

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The production level that a maximum profit is   186000 and the maximum profit will at the points of (200, -4000) , under the concept of absolute maximum value.

The  P(x, y) = 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000, the first partial differentiate  of the  given equation with respect to x and  y,

Px= ( 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000) = 8-0.001(2x-y) ....2

Py= 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000)  = 10-0.001(x-2y) ... 3

Considering the above  equation to  be equal to  zero  :

=>8-0.001(2x-y) =0 =>0.001(2x-y) =8 .....4

=>10-0.001(x-2y) =0 =>0.001(x-2y) =  10 ...5

Solving the equations 4 and 5 we get the lues of x and  y  we get are :

x= 2000, and y = -4000 , Now the partial differentiate for the equations 2  ad 3  are with respect to x and y :

pxx(x,y)=-0.002

pyy(x,y)=  0.002

pxy(x,y) =-1

The discriminant of the function wil  be  at (2000,-4000):

D = 0.002*-0.002 -(-1)^2 =-1.0004 ,here D <0,  so the  critical values (200, -4000) reaches the maximum value .So the  production level will be :

P(2000, -4000) = 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000 = 186000

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The sum of decimals 4.2 and 466.99​ evaluates to 471.19

Decimals are numbers that consist of two parts namely, a whole number part and a fractional part separated by a decimal point e.g 2.35

Given:  4.2 and 466.99​

To evaluate the sum of 4.2 and 466.99​, you simply need to add the two numbers. Arrange the numbers as shown below and add as you would add other numbers.

    4.2

466.99

.................

  471.19

................

Therefore, the sum 4.2 and 466.99​ is  471.19

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