The sum of two consecutive integers is 61. What are the integers?
Include a let statements and checks in your answer.

Answers

Answer 1

Answer:

30, and 31

Step-by-step explanation:

Let n=the smaller of the two integers

n+n+1=61

2n+1=61

2n=60

n=30

Answer 2

Answer:

30, and 31

Step-by-step explanation:

Let the "x" mean the smaller of the two integers

x+x+1=61

2x+1=61

2x=60

x=30

CHECK:

30+30+1=61

2(30)+1=61

60+1=61

61=61 ✓

HOPE THIS HELPS


Related Questions

What is the simplest form of 3/27a2b7?
3ab? (VD)
3abº (V3ab
O gab? (VD)
9ab33ab
Can someone help me plz?:)

Answers

Answer:

the solution is A

Step-by-step explanation:

[tex]\sqrt[3]{27a^{3}b^{7} } \\[/tex]

[tex]\sqrt[3]{(3)^3(a^3)(b^6)b}\\\\3ab^2\sqrt[3]{b}[/tex]

Answer:

3ab^2(3/b)

THE ANSWER A

Step-by-step explanation:

2020 HEHE

I need help with number 5

Answers

Answer:

B. BD = 9

Step-by-step explanation:

Simply set the 2 equations equal to each other (both are congruent due to perpendicular bisector):

6x + 3 = 3x = 6

3x + 3 = 6

3x = 3

x = 1

Then substitute 1 for x in BD

6(1) + 3

6 + 3

BD = 9

I think the answer is B

In an election 32 thousand people voted for Mayor Jackson . A total of 56 thousand people voted in the election . What is the ratio of number of votes that were not mayor Jackson to the total number of votes in simplest?

Answers

Answer:

3/7

Step-by-step explanation:

to find the ratio of the number of votes that weren’t mayor jackson you do 56-32. the ratio will be 24/56. now you just simplify to get 3/7

Answer:

3/7

Step-by-step explanation:

Subtract 32,000 from 56,000 and you will get 24,000

24,000/56,000 is simplified to 3/7

Based on the graph, what is the initial value of the linear relationship?

A coordinate plane is shown. A line passes through the x axis at negative 3 and the y axis at 5.

−4
−3
five over three
5

Answers

Answer:  The slope is five over three

Step-by-step explanation:

The equation for this graph would be:  y= 5x/3 +5

Answer:

5

Step-by-step explanation:

Initial value is basically another way to say the y intercept. I mean if you think about it, most word problem linear relations start the graph at the y intercept.

Hope this helps :)

the diagram shows a right angled triangle use pythagoras theorem to work out length of side ac

Answers

Answer:

Step-by-step explanation:

Using Pythagoras theorem,

AC^2 = AB^2 + BC^2

AC^2 = 4^2 + 15^2

AC^2 = 16 + 225

AC^2 = 241

AC = √241

Find the measure of the angel. n=_°

Answers

Answer:

n = 25°

Step-by-step explanation:

All interior angles of a triangle add up to 180°. We already know one of the angles is 90°, so we can build an equation:

90 + (n + 40) + n = 180.

Then we combine like-terms and subtract:

130 + 2n = 180,

2n = 50.

Then we divide by 2 to get our answer:

n = 25.

To double check, we insert 25 as our value:

90 + (40 + 25) + 25 = 180.

To fill up a car with 16 gallons cost $30.24. Which of the following is an equation that determines the
cost c for g gallons of gas?

Answers

Answer:

30.24/16= $1.89 per gallon = c/g

Step-by-step explanation:

c = $30.24

g = 16

Divide c/g

Answer:

g gallon = $1.89 g

Step-by-step explanation:

Gallon = g

16 gallons = 16 g

Cost = $30.24

So,

16 gallons = $30.24

1 gallon = $30.24/16

1 gallon = $1.89

g gallon = $1.89 g

Which graph or equation represents a no proportional relationship?

-A
-B
-C
-D

Answers

Answer:

Graph A is not proportional

Step-by-step explanation:

To have a proportional relationship, the line must go through (0,0)

Graph A does not go through (0,0) so it is not a proportional relationship

Please help! i will mark brainliest!​

Answers

Answer: A. one real solution

This solution is a double root (it repeats itself). An example would be x^2-8x+16 = 0 has the only solution x = 4.

given f(x) = 3/2x - 5 and g(x) = x^2 + 2x solve for g(-2)

Answers

Answer:

g(-2) = 0

Step-by-step explanation:

Since it is asking for g(-2), that means that we only have to worry about the equation g(x) = x^2+2x. When it asks for g(-2), that means you replace every "x" that shows up in the equation with -2.

So plugging in -2 for x we get g(-2)=(-2)^2+2(-2). Simplifying we get g(-2)=4+(-4). Now adding we finally get g(-2)=0

In the figure, O is the center, PT and PR are tangents, and
mZTOR = 150°. If OR = 6 cm, then what is the measure of
ZTPR?
a. 210°
b. 30°
c. 105°
d. 15°

Answers

Answer:

  b. 30°

Step-by-step explanation:

In quadrilateral OTPR, angles O and P are supplementary.

  angle P = 180° -angle O = 180° -150°

  angle P = 30° . . . . matches choice B

which expression is equivalent to 3 1/3?

Answers

Answer:

your answer is "A" 1/3

Step-by-step explanation:

Help please, Mathematics!

Answers

Answer:

B. 3,300

Divide 28,875 by 109,800,724.

Answer:

B

Step-by-step explanation: I divide 109,800,724 and 28,875. I used calculator and estimated

A triangle has sides with lengths 5, 6, and 7. Is the triangle right, acute, or obtuse? Question 2 options: A) Obtuse B) Right C) Can't be determined D) Acute

Answers

Answer:

D:  Acute triangle

Step-by-step explanation:

First check whether this could be a right triangle.  Using the Pythagorean Theorem, we get:

5^2 + 6^2 = ? = 7^2      This equation is not true, and therefore the triangle is not a right triangle.

The side lengths 5, 6 and 7 are very close to one another, and so the triangle must have essentially similar interior angles, which means that all three angles are acute.  Answer D is correct:  This is an acute triangle.

Answer: D) Acute

Step-by-step explanation:

SOMEONE PLEASE HELP ME ASAP PLEASE!!!​

Answers

You have to use point slope form for this equation and convert it to slope intercept form... the perpendicular slope will be the negative reciprocal of 1/6. So it will be -6. We have the point (-3,23) so we would have that as (x1,y1). So you can use point slope form. y-23=-6(x-(-3)). Remember to simplify the -(-3) part.

y-23=-6(x+3)

Use distributive property

y-23=-6x-18

Solve for y by adding 23 to each side giving you

y=-6x+5

So that’s your answer...

A sequence of transformations is described below.
A dilation about a point P
A rotation about another point Q
A vertical stretch about the horizontal line PQ
A reflection over a line PQ

Answers

Answer: Neither angle measures nor segment lengths

What number should replace the question mark?

Answers

Answer:

Just a guess but I think 5

Step-by-step explanation:

The top right square on all boxes is the difference of the second box and the first box which equals the third box. This rule is applied to all of the other boxes so if I'm not wrong the question mark should be 5

Answer:es el #5

Step-by-step explanation:

;)

Determine if EF || HL

Answers

Answer:

EF is not parallel to HL.

Step-by-step explanation:

They are not parallel because angle HLG is not equal to angle EFG. If the two lengths WERE parallel, those two angles would be equal. Angle GHL would be equal to angle GEF, but they are not equal, either.

Hope this helps!

Which statement is true about the following system of equations?
3x - 1/2y = 1
x + 2y = 7
Select one:
a. y<x
O b.y=x
O c.y>x
d. can not be determined​

Answers

Answer:

c. y>x

Step-by-step explanation:

When given a system of equations, one of many methods can be used to solve these types of systems. One of these includes substitution which involves solving for one variable that is included in another equation, and putting that equality in place of the variable.

Here is what I mean by this:

Given that 3x - 1/2y = 1, and x + 2y = 7, you can rearrange the x + 2y = 7 to solve for x by isolating it.

x + 2y = 7 → x = 2y - 2y = 7 - 2y [for an equation, what you do to one side, you must do to the other] → x = 7 - 2y.

Now that we have an expression which is equal to x.

We can directly replace that with the 3x in the other equation by multypling this by 3:

x = 7 - 2y → 3(x) - 1/2y = 1

3(7 - 2y) - 1/2y = 1

Now that we only have y's, we can simply the equation, and solve for y.

21 - 6y - 1/2y = 1

21 -13/2y = 1

(get rid of the constant on the left side by subtracting)

-21 -21

-13/2y = -20

(remove the denominator by Multiplying)

×2 ×2

-13y = -40

÷13 ÷13

(cancel out the coefficient by dividing)

-y = -40/13

(take the opposite of the other side to make y positive)

×-1 ×-1

y = 40/13.

Now that we have y just solve for x since we already have a term of x in the other equation:

y = 40/13 → x + 2y = 7

x + 2(40/13) = 7

x + 80/13 = 7

Then subtract both constants to find x:

x + 80/13 - 80/13 = 7 - 80/13

x = 7 - 80/13

(create like denominators, but Multipy

The question and pic is on the picture I took a picture of

Answers

Answer:

m<y = 155

Step-by-step explanation:

If m<x = 155, then m<y = 155 (Because vertically opposite angles are congruent)

Answer:

155°

Step-by-step explanation:

The two angles are a pair of vertically opposite angles.

Verticall opposite angles are opposite to each other and are equal.

Angle x = Angle y

155 = 155

The average of an electrician's hourly wage and a plumber's hourly wage is $33. One day a contractor hires an electrician for 9hr of work and the plumber for 6hr of work and pays a total of $468 in wages. Find the hourly wage for the electrician and for the plumber. Electrician makes $___ and Plumber makes $___

Answers

Answer:

Plumer : $198

Electrition : $270

Step-by-step explanation:

The Electrician makes $ 216 and Plumber makes $ 252

The hourly wage of the electrician = $ 24

The hourly wage of the plumber = $ 42

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the hourly wage of electrician be = $ x

Let the hourly wage of plumber be = $ y

The average of hourly wage of an electrician and plumber = $ 33

So , ( x + y ) / 2 = 33

Multiply by 2 on both sides , we get

x + y = 66   be equation (1)

And , One day a contractor hires an electrician for 9hr of work and the plumber for 6hr of work

So , total wages =
9 hours of work by electrician + 6 hours of work by plumber

9x + 6y = $ 468   be equation (2)

Now , we have 2 equations

Multiply equation (1) by 6 , we get

6x + 6y = 396   be equation (3)

And ,

equation (2) - equation (3) , we get

3x = 72

Divide by 3 on both sides , we get

x = 24

Substituting the value of x in equation (1) , we get

y + 24 = 66

Subtracting 24 on both sides, we get

y = 42

So , the hourly wage of electrician is $ 24 and the hourly wage of plumber is $ 42

Now , wage of electrician for 9 hours = 24 x 9

                                                              = $ 216

Wage of plumber for 6 hours = 42 x 6

                                                 = $ 252

So total wage = 216 + 252 = $ 468

Hence , the electrician makes $ 216 and plumber makes $ 252

To learn more about equations click :

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Seth started reading his book at 2:50 P.M. At 3:20 P.M. he finished his second chapter and decided to stop for a snack. How long did Seth read?

Answers

Answer:

30 mins

Step-by-step explanation:

if you add 10 mins to 2:50, it makes it 3:00, then you just add the 10 mins + the 20 mins (after 3pm) and you get 30

A 14-year old girl caught feelings too fast and/or fell too hard. She judged herself every single day. She felt as if people judged her as she walked past people. She wanted to loose weight. How can she loose 139 lbs if she ways 180 lbs without going on a diet or taking any medicine or pills? How much lbs would she loose? How much would she weigh after? What sizes would she wear in all clothing?

Answers

Answer:

She can loosen weight by exercising. If she exercises for about 6-8 months she can loosen about 139 pounds. After loosing that much weight, she will weigh 40 lbs/pounds. She will then wear clothes of S(Small) size.

Step-by-step explanation:

Tried my best

She can exercise more, if she wants to lose more weight she can exercise more. Then she can wear m or s size clothes

Consider functions f and g below. [tex]g(x) = -x^{2} + 2x + 4[/tex] Which of the following statements is true? A. As x approaches infinity, the values of f(x) and g(x) both approach infinity. B. As x approaches infinity, the values of f(x) and g(x) both approach negative infinity. C. As x approaches infinity, the value of f(x) approaches infinity and the value of g(x) approaches negative infinity. D. As x approaches infinity, the value of f(x) approaches negative infinity and the value of g(x) approaches infinity.

Answers

As x approaches infinity, the value of f(x) approaches infinity and the value of g(x) approaches negative infinity. Then the correct option is C.

What is the parabola?

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

Where a is the leading coefficient.

Consider functions f and g below.  

g(x) = –x² + 2x + 4

The function can be written as

g(x) = –(x – 1)² + 5

As x approaches infinity, the value of f(x) approaches infinity and the value of g(x) approaches negative infinity.

Then the correct option is C.

More about the parabola link is given below.

https://brainly.com/question/8495504

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С
Use the geometric mean (leg) theorem. What is the
value of a?
b
A
0 72
h
02770
6
a
O 2015
705
14
B
Intro
Done

Answers

Answer: it is a

Step-by-step explanation:

HELP NEEDED,THANK YOU find all real zeros and complex of each function f(x)=x(4x-6)(x+1)(3x+5).SHOW WORK!!!

Answers

Answer:

x=0, 3/2, -1, -5/3

Step-by-step explanation:

The x-axis interception points of x(4x-6)(x+1)(3x+5): (0, 0), (3/2, 0), (-1, 0), (-5/3, 0)

The y-axis interception points of x(4x-6)(x+1)(3x+5): (0,0)

So the answer is 0, 3/2, -1, and -5/3.

if the domain of a coordinate transformation that is reflected over the y-axis is (-1,3),(2,1),(5,-1)and(-1,-2) what is the range

Answers

Answer:

Range remains the same.

Step-by-step explanation:

(1,3),(-2,1),(-5,-1) and (1,-2)

The range is { -2 ≤ y≤ 3 } .

What is Transformation?

Transformation is changing the graph to a new one by Rotation, Reflection, Translation, and Dilation.

Reflection is to create a mirror image of the coordinate or the figure.

After reflection along any axis, the coordinate of the other axis changes to its additive inverse.

(x,y) ----> when reflected along y axis ----> ( -x , y)

The domain is all the values a function can have as input and the range is all the values that a function can have.

The original coordinate changes to  (-1,3),(2,1),(5,-1)and(-1,-2).

When reflected along the y-axis, the coordinates of the x-axis change and there is no change in the y-axis.

So the value of the domain changes while the range remains the same.

The range is { -2 ≤y≤3}

To know more about Transformation

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The points plotted below satisfy a polynomial. In what ranges of x-values must there be a root of the graph? Check all that apply. I will mark brainliest!​

Answers

Answer:

not sure,but I think the answer is 3 to 4

The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm.
Approximately how much space is in between the two spheres?
A. 61 cm³
B. 113.1cm³
C. 255.5 cm³
D. 766.6 cm³​

Answers

Answer:

Step-by-step explanation:

reqd. space=difference of volumes=4/3 πR³-4/3πr³=4/3π(R³-r³)

=4/3 π(5³-4³)

=4/3 π(125-64)

=4/3π(61)

≈255.5 cm³

i’m pretty sure the answer would be C

literally a free 50 points, just need the answer, What is the solution to the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n?

Answers

Answer:

n = 1/2

Step-by-step explanation:

So the equation is 4/5n - 1/5 = 2/5n.

So, the first thing that we need to do is get the variable on one side.

So, to do that we need to subtract 4/5n on both sides.

Now our equation is -1/5 = -2/5n

Now the last step is to simplify.

To do that, we need to multiply by the reciprocal of 2/5 on both sides.

That leaves us with 1/2 = n

Answer:

n = 2

Step-by-step explanation:

=> [tex]\frac{4}{5n} - \frac{1}{5} = \frac{2}{5n}[/tex]

Combining like terms

=> [tex]\frac{4}{5n } - \frac{2}{5n} = \frac{1}{5}[/tex]

=> [tex]\frac{4-2}{5n} = \frac{1}{5}[/tex]

=> [tex]\frac{2}{5n}= \frac{1}{5}[/tex]

Cross Multiplying

=> 5n = 2*5

=> 5n = 10

Dividing both sides by 5

=> n = 2

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