Hannah is the oldest of four siblings whose ages are consecutive integers the sum of their ages is 86 fine Hannah's age

Answers

Answer 1

Answer:

20, 21,22,23

Step-by-step explanation:

Consecutive means in order.  Integers are the set of whole numbers and their opposites: ...-3,-2,-1,0 ,1,2,3...

Let x = the one sibling

Let x + 1 = the second sibling

Let x + 2 = the third sibling

Let x+4 = the fourth sibling.

If you add the four siblings together they equal 86

(x) + (x +1) + (x + 2) + (x+3) = 86  I put the parentheses in so that you can see each sibling, but it is not needed.

x + x+ 1 +x + 2 + x+ 3 = 86  Combine like terms

4x + 6 = 86  Subtract 6 from both sides

4x = 80  Divide both sides by 4

x = 20

The first sibling is 20, then 21, then 22 and finally 23

Check:

20 + 21 + 22 + 23 = 86


Related Questions

JK = 5x-8, KL = 7x-12, JL = 52. Find x.

Answers

The value of x is 6

What is a line segment?

A line segment can be defined as the partition formed by end points of a line.

From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L

This can be represented as;

JK + KL = JL

Where;

JK = 5x-8KL = 7x-12JL = 52

Substitute the values into the formula, we have;

5x -8 + 7x - 12 = 52

Now, collect like terms

12x = 52 + 20

Add like terms

12x = 72

Make 'x' the subject of formula

x = 72/12

x = 6

Thus, the value of x is 6

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532÷46
Also give remainder

Answers

Answer:

11 with a remainder of 26

Step-by-step explanation:

Check out the attached photo

A plane travels 600 mph for the first three hours of the trip. Then, the plane travels at a constant speed of 300 mph for two hours. Calculate the plane's average speed.

Answers

Answer: 480.mph

Explanation:

The top numbers for 8 and 20

Answers

Answer:

Step-by-step explanation:

2/4 is equal to 0.5

4/8 is equal to 0.5

10/20 is equal to 0.5

Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.

Answers

Answer:

Domain: [-2, 2]Range: [-2, 2]Not a function

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

For the relation to the function, each value of x must map onto no more than one value of y.

Answer:

Domain: -2≥x≥2

Range: -2≥x≥2

Not a function

Step-by-step explanation:

Write the property that justifies each mathematical statement. Look carefully!!
1. a(cd) = ac - ad
2. 2x + y = y + 2x
3. — 3(4c) = (- 3 * 4)c
4. 3(4ab) = (4ab)3
5. - 9(3 + 2x) = -9(3) - 9(2x)
6. 3+ (2 + n) = (3 + 2) + n

Answers

The properties of algebra used here are

For first point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For Second point the algebraic properties used is  Associative Property of Addition

For third point the algebraic properties used is Associative Property of Multiplication.

For fourth point the algebraic properties used is  Commutative Property of Multiplication

For fifth point the algebraic properties used is  Distributive Properties of Addition Over Multiplication.

For sixth point the algebraic properties used is Associative Property of Addition

The correct question is Write the property that justifies each mathematical statement. Look carefully!!

1. a(c-d) = ac - ad

2. 2x + y = y + 2x

3. — 3(4c) = (- 3 * 4)c

4. 3(4ab) = (4ab)3

5. - 9(3 + 2x) = -9(3) - 9(2x)

6. 3+ (2 + n) = (3 + 2) + n

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1 a) A restaurant is open 24 hours a day. The manager wants to divide the day into work shifts of equal length. The shifts w=should not overlap. All shifts durations should be a whole number of hours. Describe the different ways this can be done.



b) The manager turns on the restaurant's two neon signs at the same time. Both signs blink as they are turned o. One blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again?

Answers

The possible answers for the restaurants are Three 8-hour shifts; four 6-hour shifts; six 4-hour shifts.

2. The seconds that they will blink together again is 45 seconds.

How to illustrate the information?

Here we have to determine the factors of 24 for the shifts i.e.  1, 2, 3, 4, 6, 8, 12, 24 .

A 1-hour shift does not make much sense; most employers will also not use a 2-hour or 3-hour shift.

Restaurants typically do not use 12-hour shifts either, and employers do not use 24-hour shifts either.

Since both signs blink as they are turned on and one blinks every 9 seconds. The other sign blinks every 15 seconds. The least common multiple is 45.

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Sasha has 520cm of rope she uses 2m 72mm of the rope how many millimeters of rope does Sasha have left?

Answers

Accoding to the given statements;

Sasha have left 2480 mm of rope.

According to the given values;

Sasha has 520 cm of rope

She used 2m 72 mm of rope

So, 1 cm = 10mm

And 1m = 1000mm

So, 520 × 10 = 5200mm

2.72× 1000 = 2720mm

5200 - 2720 = 2480mm

Sasha have left 2480 mm of rope.

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A piece of wood is 7 1/4 feet long. How many 2-foot long pieces can Sue cut from the wood?
A. 1
B. 2
C. 3
D. 4

Answers

The answer would be C. 3

Answer:

7.25 feet/2 feet = 3.625 pieces so you can have 3 pieces of 2 feet each and 1 piece left over that is less than 2 feet.

Round to the nearest whole number, if necessary.

Answers

16.5 is 30% of 55

1650/55 = 30

Please help!!!!
The equation for the line parallel to the graph of y = 6x + -2 with the same y- intercept as the graph of y = 36x + 2 is written as y = mx + b. Determine the values of m and b. What is the value of m + b?​

Answers

The values of m and b are 6 and 2 respectively and the value of m + b is 8.

The slope intercept of the straight line is used to find the equation of the straight line. The slope intercept formula requires knowing the slope of the line and the point of intersection of the line with the y-axis. Consider a  line with slope "m" and y-intercept "b". The slope-intercept shape formula for a straight line with slopes 'm' and 'b' as y-intercept is given as y = mx + b.

It is given that the equation y = mx + b   ....(1) for the line parallel to the graph of  y = 6x + -2    ...(2) means that slope of the equation y = mx + b which is parallel to the graph y = 6x + -2  is same i. e on comparing equation (1) and (2) , we get m = 6

On the other hand , the equation y = mx + b has the same y- intercept as the graph of y = 36x + 2   .....(3)

On  comparing equation (1) and (3) , we get b = 2

Therefore , m + b = 6 + 2

                             = 8

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Calculate the size of angle ABC in each of these triangles. X B b A a 570 A 95⁰ 55⁰ 60% 5 Calculate the size of angle BCD in each of these diagrams. B b A C 110⁰ C 49⁰ 63° C 9⁰ D A B B 125% 30° 40° 62⁰ 289 b C 6 Three angles of a quadrilateral are 60°, 80° and 110°. How big is the fourth angle? 7 Calculate the sizes of the lettered angles in these quadrilaterals. 35° D 25 C Q 35° 71% D B 172 38° B 132 100⁰ A​

Answers

Answer:

4.

∠ABC + ∠BCA + ∠CAB = 180

therefore, ∠ABC = 180 - ∠BCA - ∠CAB

using this formula to solve 4a, 4b and 4c:

4a. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 49 -57 = 26

∠ABC = 26

4b. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 28 -90 = 62

∠ABC = 62

4c. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 38 - 25 = 117

∠ABC = 117

5a. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 55 - 60 = 65

∠BCA = 65

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 65 = 115

∠BCD =115

5b. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180

∠BCA = 180 - ∠CAB - ∠ABC = 180 - 125 - 30 = 25

∠BCA = 25

∠BCD + ∠BCA = 180

therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 25 = 155

∠BCD = 155

5c. ∠ABD + ∠CBD = 180

therefore ∠CBD = 180 - ∠ABD = 180 - 132 = 48

∠CBD = 48

In the Triangle BCD, ∠CBD + ∠BDC + ∠BCD = 180

therefore ∠BCD = 180 - ∠CBD - ∠BDC = 180 - 48 - 71 = 61

∠BCD =61

6. 4 angles of a quadrilateral = 360

∠a+110+60+80=360

∠a=360-110-60-80=110

∠a = 110

7. four angles of a quadrilateral = 360

using his formula to solve for ∠a, ∠b and ∠c.

for angle a: ∠a+110+95+63=360

∠a=360-110-95-63=92

∠a = 92

for angle b: ∠b+40+62+35=360

∠b=360-40-62-35=223

∠b=223

for angle c: ∠c+100+172+35=360

∠c=360-100-172-35=53

∠c=53

A frequency table of grades has five classes A B C D F with frequencies of 4,11,14,5 and 3 using percentages what are the relative frequencies

Answers

Answer:

A frequency table of grades has five classes A B C D F

Step-by-step explanation:

A frequency table of grades has five classes A B C D F

Margo borrows $1100, agreeing to pay it back with 3% annual interest after 11 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.

Answers

Answer:

$30.25

Step-by-step explanation:

1100 (.03) [tex](\frac{11}{12})[/tex]

What is the scale for 3 cm on the map correspond to 120 km in the actual distance?

how do i express the answer in the box. see attachment.

Answers

The scale of the map is 1:4000000

Scale of a map

From the question, we are to determine the scale of the map

From the given information,

3cm on the map correspond to 120 km

First, we will convert 120 km to cm

120 km = 120000 m

120000 m = 12000000 cm

Thus,

3cm on the map correspond to 12000000 cm

Then,

The scale of the map is

3:12000000

Reducing to the lowest term

1:4000000

Hence, the scale of the map is 1:4000000

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An account is opened with an initial deposit of $1100 and earns 3.7% interest compounded monthly.

What will the account be worth in 15 years?

Round your answer to the nearest cent.

Answers

In 15 years, the account will be worth $1896 if the 3.7% interest is compounded monthly on initial deposit of $1100.

What is compound interest?

It is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Given Data

A =  [tex]P(1+\frac{r}{100} )^{t}[/tex]

P=$1100

r =3.7%

t = 15years

Substitute the values in formula, A = [tex]P(1+\frac{r}{100} )^{t}[/tex]

A= 1100(1+{3.7/100})¹⁵

A = 1100(1+0.037)¹⁵

A = 1100(1.037)¹⁵

A= 1100(1.724)

A= 1896.4

Round off to nearest cent - $1896

Hence, $1896 will the account be worth in 15 years

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What is the range of possible sizes for side x? (Khan)

Answers

The range of possible sizes for side x is 2.3 < x < 8.7.

What are the possible sizes for the missing side of a triangle?

Herein we have a triangle, of which two of its sides are known and we can now the set of all possible values by using the law of the cosine:

x² = 3.2² + 5.5² - 2 · 3.2 · 5.5 · cos θ

x = √(40.49 - 35.2 · cos θ)

The cosine is bounded between - 1 and 1, then the possible sizes for the side x are:

2.3 < x < 8.7

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The price of one ounce of gold is approximately $1750 US dollars. If the exchange rate is $1 US dollar = $0.85 Euro, how much will gold cost in Euro per gram?

Answers

Step-by-step explanation:

mm/kyc-kbiy-rvk come.

Answer:

Step-by-step explanation: Gold will cost €2.06 per gram.

Jaspar deposits £2,500 into a savings account at 7% per annum compound interest.
How much does he have in his account after 2 years?

Answers

Jasper had 362.25 in his account after two years, per the given statement.

What exactly is compound interest?

The interest you earn upon interest is known as compound interest. This may be demonstrated with simple math: if you have $100 and that it earns 5% interest every year, you will have $105 at the end of the first year. You'll have $110.25 by the end of the second year.

According to the given data:

Given:

Jaspar deposits £2,500

interest rate = 7

Time = 2 year

Compound interest is interest calculated on the aggregate amount rather than the principle amount alone.

Amount = P(1+r/100)^n

=2500(1+7/100)²

=2500(100+7/100)²

= 2500(107/100)²

= 2862.25

C.I.= Amount - Principal

= 2862.25-2500

= 362.25

According to the given statement jasper have 362.25 in his account after 2 years.

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Which rational number equals 0.5?
A. 1/50
B. 1/5
C. 5/10
D. 5/9

Answers

C
Why?
Because 5 divided by 10 = 0.5

Answer:

C. 5/10

Step-by-step explanation:

Using a calculator:

Divide each numerator by each denominator. The answer must be 0.5

A. 1/50 = 0.02

B. 1/5 = 0.2

C. 5/10 = 0.5

D. 5/9 = 0.555...

Answer: C. 5/10

Without a calculator.

0.5 as a fraction is 1/2. Notice the denominator, 2, is twice the numerator, 1.

The answer also must have a denominator that is twice the numerator.

A. 1/50      2 × 1 = 2, not 50

B. 1/5         2 × 1 = 2, not 5

C. 5/10      2 × 5 = 10; this is it.

D. 5/9       2 × 5 = 10, not 9

Answer: C. 5/10

Evaluate −y when y=6.

Answers

Answer:

-6

Step-by-step explanation:

y=6

-y=-6

Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Can someone pls help me with this question

Answers

Domain: (-infinity, 5)

Range: [-3, infinity)

The table shows the total distance of four trails. You want to complete a trail in 1 1/2 hours with an absolute deviation of at most 15 minutes. you hike at a rate of 3 miles per hour. CREATE AN ABSOLUTE VALUE INEQUALITY

Answers

Answer:

The answer would be: A = 5 1/4

What is ratio in mathematics?

Answers

Answer:

Ratio is a comparison between 2 numbers.

Hope this helps :)

50 points help show your work and I’m giving brainliest

Answers

The values of the expressions in the table following their evaluation are;

1. 73

2. 97

3. x = 108

4. -13/6

5. 1 and 97

6. 1 and 41

7. The graph of the number line

8. She needs to add 5/36 cup of sugar

The length of the actual is 6 miles

How can the expressions be evaluated?

1. The given expression is 5•x + 14 - 6

The value of x at which the expression is evaluated is x = 13

Which gives;

5×13 + 14 - 6 = 73

2. Twelve times six plus 25 can be expressed as 12 × 6 + 25

12 × 6 + 25 = 97

3. x/9 = 12

Multiplying across gives;

x × 1 = 9 × 12 = 108

x = 108

4. The expression is 3/16 - 3/8

= (3 - 2× 3)/16

3/16 - 3/8 = (3 - 2× 3)/16 = -3/16

(3 - 2× 3)/16 = -3/16

5. The prime factors of 97 are; 1 and 97

6. 41 is a prime number.

The factors of 41 are; 1 and 41

7. The graph of x = -1/3

8. Quantity of sugar required = 3¼

Quantity added = 3⅑

Quantity needed = 3¼ - 3⅑ = 5/36

9. 4 inches is equivalent to 2 miles

Therefore;

12 inches = 3 × 4 inches is equivalent to 3 × 2 mi = 6 mi

The length of the actual trail is 6 miles

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The diameter of Jupiter at its equator is approximately 1.43 x 10 to the 5th power kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.000439 meters. Write this number in scientific notation.

Answers

The number in standard notation is 143,000.

The number in scientific notation is 4.39 x 10^-4

What is scientific and standard notation?

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

For example:

• The number : 1 x 10² is equivalent to 100

• The number 5 x 10³ is equivalent to 500

When changing a number that is less than 1 to scientific notation, there would be a negative sign before the power.

0.000439 = 4.39 x 10^-4

In order to convert a number from scientific notation to standard notation, multiply the number by its power.

1.43 x 10^5

= 1.43 x 100,000 = 143,000

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Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2). What are the coordinates of the vertices of the image after a reflection in the y-axis?
A) P' (3,-8)
B) P (-3,8)
□C) Q' (5,7)
□D) Q' (5-7)
□E) R¹ (-2,0)
OF) R¹ (0,2)

Answers

Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:

P'' (-3,-8)

P' (3,8)

Q'' (-5,7)

Q'' (-5,-7)

R'' (2,0)

R'' (0,2).

A reflection around the axis and is given by the following rule:

(x, y) ----> (-x, y)

Applying the rule to each vertices of the reflection y - axis we have:

A) P' (3,-8) ----> P'' (-3,-8)

B) P (-3,8)  ----> P' (3,8)

C) Q' (5,7)  ----> Q'' (-5,7)

D) Q' (5,-7)  ----> Q'' (-5,-7)

E) R¹ (-2,0) ----> R'' (2,0)

F) R¹ (0,2) ----> R'' (0,2)

Therefore,

Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:

P'' (-3,-8)

P' (3,8)

Q'' (-5,7)

Q'' (-5,-7)

R'' (2,0)

R'' (0,2).

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Select the correct answer. Find the inverse of function f. 1/2x+7

Answers

Answer: y=2x-14

Step-by-step explanation:

Solve for x

x/2+7 = y

x/2+7-7=y-7

x/2=y-7

2x/2=2(y-7)

x=2y-14

y=2x-14  ==> switch the x and y variables

what are the answers for the table

Answers

Answer:
X-intercepts: -1 and 3

Y-intercepts: 3
Vertex: (1, 4)
Axis of Symmetry: y= -1x + 3x + 4 (I think this is right it might not be and im sorry if it isnt).

Step-by-step explanation: Hope this helps even a little bit <33

AB=20
A and B are integers; they may or may not be distinct.
Which of the following could be equal to A-B?
A. 9
B.7
C.6
D.8
Please show me how you figured this out.

Answers

How you figure it out is you do 17+3
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