Two times the sum of three consecutive odd integers is fifteen more than three times the largest of the integers. Find the integers?

Answer: x=2 or x=-12

Step-by-step explanation: Subtract 12 to both sides of the equation: x² + 10x = 24. Subtract 24 to both sides of the equation: x² + 10x -24. Next, find out which two numbers multiply to -24 and add up to 10: 12 and -2.

X² + 12x + -2x -24.

X(x - 2) and 12(x - 2)

Solve for x: (x+12) and (x-2) = 0

X = -12 or x=2

Answer:  The correct option is

(A) x = -12 or x = 2.

Step-by-step explanation:  We are given to solve the following quadratic equation for x :

[tex]x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

From equation (i), we have

[tex]x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0~~~~~~~[\textup{the sum of 12 and -2 is 10 and product is -24}]\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x+12)(x-2)=0\\\\\Rightarrow x+12=0,~~~~x-2=0\\\\\Rightarrow x=-12,2.[/tex]

Thus, the required solution of the given equation is x = -12 or x = 2.

Option (A) is CORRECT.

Answer:

0.0064 is your answer

Step-by-step explanation:

because 4÷25 = 0.16 and 4÷100=0.04 and of course 4÷4=1

When the 0.16 and 0.04 that gets 0.0064

Answer:

Tim read for 42 minutes

Step-by-step explanation:

You have to subtract 6:47 by 6:05 to find how long he read for.

   6:47

-   6:05

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

   0:42

Answer:

Tim read for 42 minutes

Step-by-step explanation:

Since the hours are the same, we only need to subtract the minutes.

47-5 = 42 minutes

Answer:

Step-by-step explanation:  Pru, Piper, Phoebe their ratio 5:3:4 added = 12

What this would mean is that Pru has 5/12 of the total amount, Piper has 3/12 of the total, and Phoebe has 4/12 of the total amount of spices all together.

pru = piper + 24

5/12x = 3/12x + 24

5/12x - 3/12x = 24

2/12x = 24

x = 24 / (1/6)

x = 24 * 6

x = 144 spices in all.

Pru has : 5/12(144) = 720/12 = 60 spices

Piper has : 3/12(144) = 432/12 = 36 spices

Phoebe has : 4/12(144) = 576/12 = 48 spices <====

Answer:

48 spices

Step-by-step explanation:

The number of spices each has is a multiple of 5, 3, and 4.

The number of spices each has is 5x, 3x, and 4x.

Pru has 5x spices.

Piper has 3x spices.

Pru has 24 more spices than Piper, so

5x = 3x + 24

2x = 24

x = 12

Phoebe has 4x spices, so Phoebe has

4(12) = 48

Answer:

y = 3x - 18

Step-by-step explanation:

The given line, y = -3x + 9, has slope -3.  Any new line perpendicular to this has slope +3/1, or just 3.

Start with the general slope-intercept form of the equation of a straight line:

y = mx + b.  Now substitute 9 for y, 9 for x and 3 for m:

9 = 3(9) + b.  Then b = -18, and the desired equation is y = 3x - 18.

The equation of the line perpendicular to y = -3x + 9 that passes through the point (9,9) is y = ([tex]\frac{1}{3}[/tex])x + 6.

The question is asking to find the equation of a line in slope-intercept form that is perpendicular to the given line y = -3x + 9 and passes through the point (9,9). To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the new line. The slope of any line perpendicular to a line with a slope of m is [tex]-\frac{1}{m}[/tex]. Since the given line has a slope of -3, the slope of the perpendicular line will be [tex]\frac{1}{3}[/tex]. Now using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can write the equation of the new line through the point (9,9) as y - 9 = ([tex]\frac{1}{3}[/tex])(x - 9). Simplifying this equation gives us y = ([tex]\frac{1}{3}[/tex])x + 6, which is in slope-intercept form y = mx + b where m is the slope and b is the y-intercept of the line.

Answer:

31 and 28

Step-by-step explanation:

Let x represent the first number.

Let y represent the second number.

x + y = 59

x - y = 3

Use substitution method to solve.

x = y + 3

y + 3 + y = 59

2y + 3 = 59

Subtract both sides by 3.

2y = 56

Divide both sides by 2.

y = 28

Let's find the second number.

59 - 28 = 31

Check

31 -28 = 3

Answer The two numbers are 28 and 31.

The numbers are 31 and 28.

To find the two numbers where the sum is 59 and the difference is 3, we can set up two equations based on the information given.

Let the two numbers be x and y, where x > y. The equations would be:

Adding these two equations eliminates y, giving us:

2x = 62

Divide both sides by 2 to find x:

x = 31

Now substitute x back into one of the original equations to find y:

31 + y = 59

Subtract 31 from both sides:

y = 59 - 31

y = 28

Therefore, the two numbers are 31 and 28.

Answer:

2/3

Step-by-step explanation:

You flip the second fraction and multiply the fractions.

When we divide (1/2) by (3/4) we have 2/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The fraction (1/2) is divided by another fraction (3/4).

Now, we know (a/b)/(c/d) = (a/b)×(d/c).

Therefore, (1/2) is divided by (3/4) is,

= (1/2)×(4/3).

= 4/6.

= 2/3.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ5

The pair of points on the inverse function g, given that (-3,4) and (5,-2) are on function f, are (4,-3) and (-2,5), obtained by swapping the x and y coordinates of the original points.

To determine which pair of points are on function g, which is the inverse of function f, we swap the x and y coordinates of the given points on function f. The points (-3,4) and (5,-2) are on function f, so the corresponding points on the inverse function g would be (4,-3) and (-2,5), respectively. In the context of functions and their inverses, the dependence of y on x in one function becomes the dependence of x on y in the inverse function. This flipping of coordinates is an essential property of inverse functions and can be visualized by reflecting across the line y = x on a graph.

Answer:

Step-by-step explanation:

Y=cos(x+r/2)

Answer:

[tex]y=cos(x+\pi )[/tex]

Step-by-step explanation:

From the graph, we can see that y = -1 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = cos(x + pi/2) = cos(0 + pi/2) = 0

2. y = cos(x+2pi) = cos(0+2pi) = 1

3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5

4. y = cos(x+pi) = cos(0+pi) = -1

Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.

Answer:

Boys : girls

5:6

Step-by-step explanation:

Boys : girls

20:24

We can divide each  of these numbers by 4

20/4 =5

24/4 =6

Boys : girls

5:6

Answer:

For every 5 boys there are 6 girls

Step-by-step explanation:

because 20 and 24 both go into the same number and thats four.

20 divided by 4 = 5

24 divided by 4= 6

so for every 5 boys there are 6 girls

Look at the picture.

∠2 and ∠3 are Corresponding Angles. j || k, thereofre m∠2 = m∠3.

∠1 and ∠3 are supplementary angles, therefore m∠1 + m∠3 = 108°.

m∠1 = 10x + 4, m∠2 = m∠3 = 4x - 6. Therefore we have the equation:

(10x + 4) + (4x - 6) = 180

(10x + 4x) + (4 - 6) = 180

14x - 2 = 180     add 2 to both sides

14x = 182     divide both sides by 14

x = 13

10x + 4 = 10(13) + 4 = 130 + 4 = 134

4x - 6 = 4(13) - 6 = 52 - 6 = 46

Answer:$7.50

Step-by-step explanation: make 4 boxes on a paper and put two lines in each box and you see that it is 8 in the boxes all to heather so that equals $8.00 so you can’t put a dollar in each box because if you do it will equal twelve dollars and you have to make ten dollars so you put $0.50 in each box so in each box it will be $2.50 in each box so you have to add $2.50 for times so it equals $10.00 so I added it it does  add up to ten dollars  so to see how much 3 bottles of water count you have to add up $2.50 3 timer and it equal $7.50

3 bottles of water costs $ 7.50

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the problem,

4 bottles of water costs $ 10

1 bottle of water costs $ (10 / 4) = $ 2.50

3 bottles of water costs $ (2.50 x 3) = $ 7.50

∴Cost of 3 bottles is $7.50

Find more details about "Unitary method" here: https://brainly.com/question/24587372

#SPJ2

[tex]\left\{\begin{array}{ccc}2x+2y=8\\3x+2y=12&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+2y=8\\-3x-2y=-12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\to\boxed{x=4}\\\\\text{Put the value of x to the first equation:}\\\\2(4)+2y=8\\8+2y=8\qquad\text{subtract 8 from both sides}\\2y=0\qquad\text{divide both sides by 2}\\\boxed{y=0}\\\\Answer:\ \boxed{x=4\ and\ y=0\to(4,\ 0)}[/tex]

Answer:

YES

Step-by-step explanation:

First, let's find the total number of seats int he airplane.

14 + 64 + 4 * 108 = 510

The airplane has a total or 510 seats.

Half of the number of seats is 510/2 = 255.

Now let's calculate the number of seats being used and compare with 255.

5/7 * 14 + 5/16 * 64 + 5/9 * 4 * 108 =

= 2 * 5 + 4 * 5 + 12 * 4 * 5

= 10 + 20 + 240

= 270

270 seats are being used.

270 is greater than 255, so more than half of the seats are being used.

Answer: YES

multiply. your answer is 11894.217.

this could be a cross multiply problem, so [tex]\frac{25.7}{x} =\frac{1}{462.81} =11894.217[/tex]

Answer:

Carr University has 1000 times more students than Whitestone College

Step-by-step explanation:

Whitestone College has a student population of 4 x 10 students

Carr University has a student population of 40,000 students.

To find out how big the number of students at Carr is compared to Whitestone College students.

Students of Carr University / Students of Whitestone.

40,000 / 4 x 10 = 1000

Carr University has 1000 times more students than Whitestone College

Answer:

9. x=10

10. x=8

11. x=9/4=2.25

12. x=28

13. x=14

14. x=35

15. x=66

16. x=77/6

Step-by-step explanation:

9. x/20=18/36

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 18:

x/20=(18/18) / (36/18)

x/20=1/2

Solving for x: Multiplying both sides of the equation by 20:

20(x/20)=20(1/2)

x=10

10. x/12=6/9

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 3:

x/12=(6/3) / (9/3)

x/12=2/3

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(2/3)

x=4(2)

x=8

11. x/3=3/4

Solving for x: Multiplying both sides of the equation by 3:

3(x/3)=3(3/4)

x=9/4=2.25

12. x/42=30/45

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 15:

x/42=(30/15) / (45/15)

x/42=2/3

Solving for x: Multiplying both sides of the equation by 42:

42(x/42)=42(2/3)

x=14(2)

x=28

13. x/12=14/12

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 2:

x/12=(14/2) / (12/2)

x/12=7/6

Solving for x: Multiplying both sides of the equation by 12:

12(x/12)=12(7/6)

x=2(7)

x=14

14. x/25=28/20

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 4:

x/25=(28/4) / (20/4)

x/25=7/5

Solving for x: Multiplying both sides of the equation by 25:

25(x/25)=25(7/5)

x=5(7)

x=35

15. x/110=(160-100)/100

x/110=60/100

Simplifying the fraction on the right side of the equation, dividing the numerator and denominator by 20:

x/110=(60/20) / (100/20)

x/110=3/5

Solving for x: Multiplying both sides of the equation by 110:

110(x/110)=110(3/5)

x=22(3)

x=66

16. x/11=(x+7)/17

Solving for x: Cross Multiplication:

17x=11(x+7)

Eliminating the parentheses on the right side of the equation:

17x=11(x)+11(7)

Multiplying:

17x=11x+77

Grouping the x's on the left side of the equation: Subtracting 11x both sides of the equation:

17x-11x=11x+77-11x

Subtracting:

6x=77

Dividing both sides of the equation by 6:

6x/6=77/6

Dividing:

x=77/6

Answer:

A. 8x - 9y = -23

Step-by-step explanation:

(-4,-1) and (1/2,3)

We write the equation in slope intercept form y=mx+b

then we convert it into standard form

m is the slope and b is the y intercept

[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

(-4,-1) and (1/2,3)

[tex]slope = \frac{3-(-1)}{\frac{1}{2}-(-4)}[/tex]

[tex]slope = \frac{4}{\frac{1}{2}+4}[/tex]

[tex]slope = \frac{4}{\frac{9}{2}}[/tex]

[tex]slope = 4*\frac{2}{9}[/tex]

[tex]slope m =\frac{8}{9}[/tex]

To find out b we plug in (-4,-1)  and slope m value in y = mx+b

-1 = (8/9) (-4) + b

[tex]-1 = -\frac{32}{9} +b[/tex]

Add 32/9 on both sides

[tex]-1+\frac{32}{9} = b[/tex]

Take common denominator 9

[tex]\frac{-9+32}{9} = b[/tex]

[tex]\frac{23}{9} = b[/tex]

So equation y = mx + b becomes

[tex]y= \frac{8x}{9} + \frac{23}{9}[/tex]

Standard form is Ax + By = C

To get standard form , multiply the whole equation by 9

9y = 8x + 23

Subtract 8x on both sides

-8x + 9y = 23

Multiply the whole equation by -1

8x - 9y = -23

Answer:

16.5 inches

Step-by-step explanation:

WE have arc length formula for a circle as

Arc length = [tex]\frac{x}{360} (2\pi r)[/tex]

where x is the central angle the arc subtends at the centre.

Here x = 135

r= 7 inches

Hence arc length

=[tex]\frac{135}{360} (2\pi )(7) =16.5"[/tex]

Hence option B

16.5 inches is right answer for arc length for a circle of radius 7 inches.

The measure of length of arc AB is 16.5 inches. Therefore, option B is the correct answer.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Given that, the radius of the circle is 7 inches and measure of arc AB is 135°.

Let O be the center of circle.

So, ∠AOB=135°

We know that, arc length of circle is θ/360° ×2πr

= 135°/360° ×2×3.14×7

= 0.375×2×3.14×7

= 16.485

≈ 16.5 inches

Therefore, the approximate length of AB is 16.5 inches.

To learn more about the circle theorems visit:

https://brainly.com/question/19906313.

#SPJ5

Answer:

8

Step-by-step explanation:

Substitute the equation and values into the average rate of change formula.

Answer:

Her average was 86%

Answer:

86%

Step-by-step explanation:

Multiply by the inverse of 3/4 which is 4/3. -6 times 4/3 (or 1 1/3) which is -8 because 1/3 of -6 is -2 and -2 plus -6 is -8.

x=-8

Answer:

Multiply by 4/3

Step-by-step explanation:

To solve for x, we need to isolate x.

We can isolate x in one step by multiplying by the reciprocal of 3/4, which is 4/3

3/4x = -6

Multiplying by 4/3

4/3* 3/4 x = -6 * 4/3

x = -8

Answer:

Add your entire question here to receive help from users and Brainly teachers. Pictures are great when things are difficult to type.

Step-by-step explanation:

Type your complete question or upload a picture to receive help on those tough questions. Your question is difficult to read or decipher. Try adding a picture next time to make it clearer to understand.

Final answer:

A formula to determine Seth's weekly lunch expense is Weekly Spending = n × 5, where n represents the new price of lunch and the multiplication by 5 accounts for each day of the school week.

Explanation:

To help Seth determine how much he'll now spend on lunch every week, we need to create a formula that takes into account the new price of a lunch and the frequency of his purchases. Let's assume the new price of a lunch is represented by the variable n. Since Seth buys lunch 5 days a week, the formula to calculate his weekly spending will be Weekly Spending = n × 5. This formula can be used to multiply the new price of a lunch (n) by 5, giving Seth the total amount he will spend each week on school lunches.

Let us simplify each Expression Separately :

✿  [tex]\mathsf{(\frac{cot\theta.cos\theta}{sin\theta}).tan\theta}[/tex]

[tex]\mathsf{\implies (\frac{cot\theta.tan\theta.cos\theta}{sin\theta})}[/tex]

[tex]\mathsf{We\;know\;that : tan\theta.cot\theta = 1}[/tex]

[tex]\mathsf{\implies (\frac{cos\theta}{sin\theta})}[/tex]

[tex]\mathsf{We\;know\;that : cot\theta = \frac{cos\theta}{sin\theta} }[/tex]

[tex]\mathsf{\implies (\frac{cot\theta.cos\theta}{sin\theta}).tan\theta = cot\theta }[/tex]

✿  [tex]\mathsf{(\frac{sin\theta}{cos\theta.tan\theta})}[/tex]

[tex]\implies \mathsf{(\frac{\frac{sin\theta}{cos\theta}}{tan\theta})}[/tex]

[tex]\mathsf{We\;know\;that : tan\theta = \frac{sin\theta}{cos\theta} }[/tex]

[tex]\implies \mathsf{(\frac{tan\theta}{tan\theta})}[/tex]

[tex]\implies \mathsf{1}[/tex]

[tex]\mathsf{\implies (\frac{sin\theta}{cos\theta.tan\theta}) = 1}[/tex]

[tex]\mathsf{The\;Simplest\;form\;of\;the\;Given\;Expression\;is : cot\theta}[/tex]

The simplifying form of expression by using the trigonometry formula is,

⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex] = cot θ

The used formula is,

[tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex]

And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex]

Given that,

The expression is,

[tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]

Now, by using the trigonometry formula, simplify the expression as,

⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]

Substitute [tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex] And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex],

⇒ [tex]\frac{cot(\theta)}{tan\theta} \times tan\theta \div \frac{tan\theta}{tan\theta}[/tex]

⇒ [tex]cot \theta \div 1[/tex]

Therefore, the solution of expression is,

⇒ cot θ

To learn more about trigonometry visit:

brainly.com/question/13729598

#SPJ4

Answer:

y = 4.5 x

Step-by-step explanation:

If this is a proportional relationship, we can find the slope

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

m = (27-0)/(6-0)

m = 27/6

m=9/2

The slope is 9/2

The y intercept, where it crosses the y axis is 0

Using the slope intercept form of the equation y=mx+b

y = 9/2 x+0

y =9/2x

It wants the decimal form

y = 4.5 x

Answer:

31

Step-by-step explanation:

(24/3)+(7x2)-(15/5)+(6*2)

8+(7x2)-(15/5)+(6*2)

8+14-(15/5)+(6*2)

8+14-3+(6*2)

8+14-3+12

22-3+12

19+12

31

Sorry if I did my math wrong :)