Two consecutive positive integers have a product of 156. Find the integers.
The integers are ___

Answers

Answer 1
Explaination :

So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!

So let us assume the unknown positive integers as a and (a + 1).

Product of both integers :-

a (a + 1) = 156 [Equation formed]

Solving the equation :-

[tex]: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}[/tex]

Therefore,

First positive integer is 12

Second positive integer :-

2nd positive integer = a + 1 2nd positive integer = 12 + 1 2nd positive integer = 13


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Answer:

1 and a half hours < 100 mins

Step-by-step explanation:

1 and a half hours is equal to :

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Using pi as 3.14. what is the circumference of a circle with a radius of 3mm.

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Answer:

18.84

Step-by-step explanation:

Circumference = 2 * PI * R

2 * 3.14 * 3 = 18.84

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Answer:

What type of question is this

Answer:

The area of a rectangle is given by A = l × w, where l is the length and w is the width.

The length (l) and width (w) of the small rectangle are 14 feet and 6 feet, respectively, so the area of the small rectangle (As) is:

AS  =  14 ft. × 6 ft.

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The length (l) and width (w) of the large rectangle are 20 feet and 7 feet, respectively, so the area of the large rectangle (Al) is:

Al  =  20 ft. × 7 ft.

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Answer:

a=14/50 or 28%/0.28

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

AC and BD are perpendicular bisectors of each other. Find the perimeter of ADB.

A. 60
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C. 30
D. 50

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I think it is C. 30
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Step-by-step explanation:

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The graph shows the population of a city n months after the establishment of a new automobile plant in the city.

Answers

Answer: for sure the answer is increased rapidly

Step-by-step explanation:

The population of the city increased rapidly for the first four months and then slowly approached 7000 people.

What is Graph?

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

WE have given the  graph shows the population of a city n months after the establishment of a new automobile plant in the city.

We can see that at 4000 people, the graph increases and then become constant at the rate of 7000 people.

So we can conclude that the population of the city increases rapidly for the first four months and then slowly approached 7000 people.

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Which graph represents the solution of the system
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Answer:

its b

Step-by-step explanation:

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Answer:

Its C

Step-by-step explanation:

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What is the distance, in units, between point D and point E?
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Answer:

4(5+8)

Step-by-step explanation:

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Answer: perimeter = sum of all side lengths

Step-by-step explanation:

To measure the amount of tape needed to section off a crime scene.

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The graph shown is the second derivative

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c: represents the initial position

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Simplify the given polynomial expressions as much as possible


(12a2 + 6a - 8) - (-22a2 + 12 - 15a)

Answers

Answer:

34a^2 + 21a - 20

Step-by-step explanation:

(12a^2 + 6a -8) - (-22a + 12 - 15a)

12a^2 + 6a - 8 + 22a + 12 - 15a

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Answers

Answer:

its A

Step-by-step explanation:

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Answer:

A. 5 1/2

Step-by-step explanation:

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Find the Circumference.​

Answers

Answer:

1.

r = 12 m.

d = 24 m.

circumference: 75.36 m² or 24π m²

2.

r = 10 cm.

d = 20 cm.

circumference: 62.8 cm² or 20π cm²

3.

r = 4 dm.

d = 24 dm.

circumference: 25.12 dm² or 8π dm²

Step-by-step explanation:

Circumference of a circle: 2πrπ (pi) = 3.14r (radius) = d/2d (diamater) = 2r

Substitute the the values of the table into the formula:

1.

r = 12 m.

d = 24 m.

circumference: 75.36 m² or 24π m²

2πr

2 * 3.14 * 12

3.14 * 24

75.36 m² or 24π m² <== circumference

12 * 2 = 24 m <== diameter

2.

r = 10 cm.

d = 20 cm.

circumference: 62.8 cm² or 20π cm²

r = 20/2 = 10 cm <== radius

2πr

2 * 3.14 * 10

3.14 * 20

62.8 cm² or 20π cm² <== circumference

3.

r = 4 dm.

d = 24 dm.

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Answers

Answer: 32c-1 is one of them

Step-by-step explanation:

What is the product of the polynomials below?
(3x2 - 2x - 3)(5x2 + 4x + 5)
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B. 15X442x 8X2 - 2x + 2
C. 15x4 + 2x3 - 8x2 - 2x -15
D. 15X4+2x8x422x42

Answers

A. 15x4+2x3-8x-22-15

The product of the polynomials is [tex]15x^4 - 8x^3 - 6x^2 - 22x - 15.[/tex]

What is a polynomial?

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

To find the product of the polynomials (3x² - 2x - 3) (5x² + 4x + 5), we can use the distributive property of multiplication to multiply each term in the first polynomial by each term in the second polynomial, and then combine like terms.

We can start by multiplying the first term in the first polynomial, 3x^2, by each term in the second polynomial:

3x² (5x² + 4x + 5)

= [tex]15x^4 + 12x^3 + 15x^2[/tex]

Next, we multiply the second term in the first polynomial, -2x, by each term in the second polynomial:

-2x(5x² + 4x + 5) = -10x³ - 8x² - 10x

Finally, we multiply the third term in the first polynomial, -3, by each term in the second polynomial:

-3(5x² + 4x + 5) = -15x² - 12x - 15

Putting these three results together, we have:

(3x² - 2x - 3) (5x² + 4x + 5)

= [tex]15x^4 + 2x^3 - 3x^2 + 12x^2 - 10x^3 - 10x - 15x^2 - 12x - 15[/tex]

Simplifying and collecting like terms, we get:

(3x² - 2x - 3)(5x² + 4x + 5)

[tex]15x^4 - 8x^3 - 6x^2 - 22x - 15[/tex]

Therefore,

The product of the polynomials is [tex]15x^4 - 8x^3 - 6x^2 - 22x - 15.[/tex]

Learn more about polynomials here:

https://brainly.com/question/2284746

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Find the area of the circle shown.

Use 3.14
3
.
14
as an approximation for π
π
. Round your answer to the nearest tenth.

Answers

Answer: Area = pie multiplied by radius multiplied by radius (pie × square of radius)

Step-by-step explanation: If you are given diameter, radius will be half of the diameter.

Simply multiply 3.14 by radius squared

For problem 8, find the area of the shaded region. The polygon is a regular polygon. please show work.​​

Answers

Answer:

34.86 unit²

Step-by-step explanation:

[tex]A_{triangle}[/tex] = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] , where s = [tex]\frac{P}{2}[/tex] ; P = a + b + c

[tex]A_{hexagon}[/tex] = 6 × [tex]A_{triangle}[/tex]

[tex]A_{circle}[/tex] = [tex]\pi r^2[/tex]

[tex]\pi[/tex] ≈ [tex]\frac{22}{7}[/tex]

~~~~~~~~~~~~~~~~~~~

The vertices of a right triangle are p(-3,4), q(-3,-4) and r (7,-4). Explain algebratically whether or not (2,0) is on the side of the triangle.

Answers

Algebraically, it was possible to show that the point (2,0) is on the side (PR) of the given triangle.

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  In this triangle from the trigonometric ratios or the Pythagoras Theorem ([tex](hypotenuse)^2=(side_1)^2+(side_2)^2[/tex]), it is possible finding angles or sides.

The question gives the points for a right triangle, you can draw the triangle, see the attached image. From the figure, it is possible to see the lengths for the sides PQ=8 and QR=10.

Linear Equation

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

a= the slope. If

a> 0 , the function is increasing; a< 0 , the function is decreasing;

b=the constant term that represents the y-intercept.

The slope for the line PR can be calculated from the ratio between the side PQ and QR.

[tex]a=\frac{PQ}{QR}=\frac{4-(-4)}{(-3-7)}=\frac{8}{-10} =-0.8[/tex]

From the attached figure, it is possible to see that the y-intercept is (2,0). Therefore, the given point is on the side PR, but the question asks to show this algebraically.

From the Standard form (ax+b), the equation for the line PR will be:                      y=- 0.8x+b. After that, you should replace the coordinates of the given point P (-3,4) in the equation line:  y=-0.8x+b for finding b.

4=-0.8*(-3)+b

4=2.4+b

b=4-2.4= 1.6

Then, the equation line y=-0.8x+1.6.

Now you should replace the x-coordinate for the point (2,0) in the equation  y=-0.8x+1.6.

y=-0.8*2+1.6

y=-1.6+1.6

y=0

The calculated y-coordinate is the same the y-coordinate for the point (2,0), thus the point (2,0) is on the side of the triangle.

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brainly.com/question/12242745                                        

Which equation is the inverse of 5 y 4 = (x 3) squared one-half? y = one-fifth x squared six-fifths x eleven-tenths y = 3 plus-or-minus startroot 5 x seven-halves endroot negative 5 y minus 4 = negative (x 3) squared minus one-half y = negative 3 plus-or-minus startroot 5 x seven-halves endroot

Answers

The inverse function of the function 5y + 4 = (x + 3)² + 0.5 is shown below. Then the correct option is D.

[tex]\rm y= \pm \sqrt{5x + \dfrac{7}{2}} - 3[/tex]

What is the inverse of a function?

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means, the inverse of 'f' is a reverse operator, that takes back the effect of 'f'

The equation is given below.

[tex]\rm 5y + 4 = (x+3)^2 + \dfrac{1}{2}[/tex]

Then y will be

[tex]\rm 5y = (x+3)^2 + \dfrac{1}{2} - 4\\\\\rm y \ \ = \dfrac{(x+3)^2}{5} - \dfrac{7}{10}[/tex]

The replace y by x and x by y, then we have

[tex]\begin{aligned} x &= \dfrac{2(y+3)^2}{10} - \dfrac{7}{10}\\\\\dfrac{10x + 7}{2} &= (y + 3)^2 \\\\\sqrt{5x + \dfrac{7}{2}} &= y + 3\\\\y &= \pm \sqrt{5x + \dfrac{7}{2}} - 3 \end{aligned}[/tex]

More about the inverse function link is given below.

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Answer: D

Step-by-step explanation:

The 2022 Russian Invasion of Ukraine began due to the cause of the collapse of the Soviet Union, which was sped along by the independence of the baltic states in 1990. When Ukraine left the USSR in 1991 and gave it's nuclear weapons to Russia in 2006, it began clear that Ukraine needed to be returned back into the hands of Moscow, before becoming another frontline for the NATO Army to invade the Russian Federation from the west, with more support from Japan in the east. Oh and I did the Edge test in 2022 so thats how I know it's D.

The length of a rectangle is 4 cm longer than its width.
If the perimeter of the rectangle is 52 cm, find its length and width.

Answers

Answer: L is 15 and w is 11

Step by step
2(w+4)+2w=52
2w +8 +2w=52
4w +8=52
4w=52-8
4w=44
W=11
L=11+4=15

Solve for X question number 15

Answers

You have to do the square root of 144.
X=12.
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