1 2 3 4 5 6 7 8 9 10
TIME REMAINING
48:54
What number should be added to both sides of the equation to complete the square?

x2 + 3x = 6



3
62

Answers

Answer 1
Answer:

2.25

Explanation:

Consider the square ...

... (x+a)² = x² +2ax +a²

The constant term (a²) is the square of half the x-coefficient: a² = (2a/2)².

The x-coefficient in your expression is 3. The square of half that is ...

... (3/2)² = 9/4 = 2.25

Adding 2.25 to both sides gives ...

... x² +3x + 2.25 = 6 + 2.25

... (x +1.5)² = 8.25 . . . . completed square

Answer 2

(3/2)^2

I believe it is (3/2)^2 because I tried working it out and got something like it. I did get an answer of x = ±[tex]\sqrt{33}[/tex] over 2.

Most sources appear to give 2.25, which is equal to 3/2 squared.

Attached some work.

1 2 3 4 5 6 7 8 9 10TIME REMAINING48:54What Number Should Be Added To Both Sides Of The Equation To Complete

Related Questions

Give the quotient and remainder 348 divided by 9

Answers

38 is quotient and 6 is remainder
Hi. This is a simple division problem.  You divide 9 into 348 which goes 38 times (9x3=27 which you subtract from the 34 leaving 7. Now bring the 8 down and divide 9 into 78, which goes in 8 (9x8=72) leaving you with a remainder of 6.

348/9 = 38 R6

I hope this helps.
Take care,
Diana

Which Equation best represents the line graphed above?
Y=-3x-1 Y=-3x+1 Y=3x+1 Y=3x-1

Answers

C. y=3x+1 is the answer.

Answer:

[tex]y=3x+1[/tex]

Step-by-step explanation:

The line has positive slope, therefore the variable in the equation must be positive ([tex]y=-3x+1[/tex] and [tex]y=-3x-1[/tex] must be discarded)

Now, in the graph we can see that the line passes over the following points:

[tex](0,1) \rightarrow x=0, y=1\\(1,4) \rightarrow x=1, y=4[/tex]

With the point [tex](0,1)[/tex], we can discard [tex]y=3x-1[/tex] because:

in the equation  [tex]y=3x-1[/tex], we have: [tex]x=0 \rightarrow y=3(0)-1=0-1=-1\rightarrow y=-1[/tex]

The line doesn't pass over the point [tex](0,-1)[/tex]

Therefore, the equation is [tex]y=3x+1[/tex].

We can verify the answer with the points [tex](0,1)[/tex] and [tex](1,4)[/tex], replacing values in the equation:

[tex](0,1):\\x=0\rightarrow y=3(0)+1=0+1=1\rightarrow y=1\\\\(1,4):\\x=1\rightarrow y=3(1)+1=3+1=4\rightarrow y=4[/tex]

Explain how you would use addition to find the product of –2 and 5 using the integer tiles and the number line.

Answers

Sent a picture of the solution to the problem (s).

Answer:

Sample Response: With integer tiles, you would add 5 groups of negative 2 tiles or remove 2 groups of 5 positive tiles. On the number line, you would bounce by 5 to the left 2 times.

What uses numbers, variables and operations symbol?

Answers

Final answer:

Mathematics uses numbers, variables, and operations, particularly in algebraic expressions. An example of this is the equation 5x + 2 = 12, where '5' and '2' are numbers, 'x' is variable, and '+' and '=' are operation symbols.

Explanation:

The subject that uses numbers, variables, and operations is Mathematics. This combination is commonly seen in algebraic expressions. For example, in the equation 5x + 2 = 12, '5' and '2' are numbers, 'x' is a variable, and '+' and '=' are operation symbols. The numbers are used as constants or coefficients, the variable represents an unknown value, and the operations symbols dictate how these elements should interact. Through algebra, we can solve this equation and find the value of the variable 'x'.

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Final answer:

In Mathematics, particularly Algebra, numbers, variables and operation symbols are frequently used. This language is evident in forms like scientific and exponential notation, which are methods to represent large quantities using powers of ten.

Explanation:

The system of using numbers, variables, and operation symbols is commonly seen in Mathematics. In particular, this is prominent in Algebra, where numbers are often represented by variables, and operations like multiplication, division, addition, or subtraction involve these variables. One form of this language includes scientific notation. Scientific notation is a mathematical expression used to represent very large numbers using powers of ten. For instance, 500,000,000 can be written as 5 × 10^8 in scientific notation. Another way to express large quantities is through exponential notation, where the number is represented as a product of two numbers, one of which is a power of ten. Learning and practicing how to use these forms becomes essential for further scientific studies.

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The diagram represents a triangle that is reduced by a scale factor of 0.4.

What is the height of the original triangle?
0.8 inches
2.4 inches
5 inches
8 inches

Answers

x = height of original triangle

0.4x = 2
x = 2 / 0.4
x = 5 <==

Answer:

The height of the original triangle is [tex]5\ inches[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to divide the length of the corresponding side of the reduced triangle by the length of the corresponding side of the original triangle

Let

z-----> the scale factor

x----->  the length of the corresponding side of the reduced triangle

y-----> the length of the corresponding side of the original triangle

so

[tex]z=\frac{x}{y}[/tex]

in this problem we have

[tex]z=0.4[/tex]

[tex]x=2\ in[/tex] -----> the height of the reduced triangle

substitute and solve for y

[tex]0.4=\frac{2}{y}[/tex]

[tex]y=2/0.4=5\ in[/tex]

A superhero recently asked his nemesis how many cats she has. She answered with a​ riddle: ​"Seven dash eighths of my cats plus four​." How many cats does the nemesis​ have?

Answers

The answer is 4.875

-3(x+4)+15=-12
plz show all work

Answers

-3(x + 4) + 15 = -12

-3(x + 4) = -12 - 15

-3(x + 4) = -27

x + 4 = -27/-3

x + 4 = 9

x = 9 - 4

x = 5

hope that helps, God bless!

Ten less than three times the sum of a number and five is equal to twenty-nine. What is the number ?

Answers

Hello!
So the following would be your equation.
3(x+5)-10= 29
Your first step would be to use the Distributive Property based upon PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction). Since we have Parenthesis, we distribute first.
3(x+5)-10=29
^ ^
——————
So, your new equation would be—
3x+15-10=29
Now, you need to combine like terms—
15-10=29
3x+5=29
——————
Therefore your new equation is—
3x+5=29.
Now you need to move the constants (5,29) to one side of the equal sign. To do this, you would use the Subtraction Property of Equality and rid the 5–
3x+5=29
-5 -5
——————
Your equation is now—
3x=24.
Finally, you need to remove the 3 from x. This means you must use the Division Property of Equality, and rid the 3.
3x=24
— —
3 3
Your solved equation is—
X=8

Hope this helped!
~KayEmQue

The number to attended art museum symphony concert rock concerts in events of 1990 compared to the number of words in the same events this year will graph do you use

Answers

where is the graph to use? unsolvable question

A single die is rolled twice. the set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}. find the probability of getting two numbers whose sum is greater than 10.

Answers

We need to find the rolls whose sum is greater than 10. By looking at the outcomes, we see that (5,6), (6,5), and (6,6) all have a sum greater than 10. Therefore, there are 3 chances to get a sum greater than 10. Since there are 36 chances overall, the probability of rolling greater than 10 are 3/36 = 1/12.

Answer:

Step-by-step explanation:

1/12

Find all the points where the tangent plane to this ellipsoid is parallel to the plane

Answers

neeed moldes plz would help a lot
Final answer:

To find points where the tangent plane to an ellipsoid is parallel to a plane, calculate the gradient vector of the ellipsoid and set it proportional to the normal vector of the given plane, then solve the resulting system for  (x, y, z).

Explanation:

To find all the points where the tangent plane to an ellipsoid is parallel to a given plane, you first need to consider the equation of the ellipsoid and the equation of the tangent plane.

The ellipsoid can be described by the general equation  f(x, y, z) = 0, while the tangent plane at a point on the ellipsoid can be described by the gradient of f at that point, given as  ∇f.

The gradient, which is a vector, gives us the normal to the tangent plane at the given point.

For a tangent plane to be parallel to another plane, their normal vectors must be proportional.

So, if we have the normal vector of the given plane, we can set up an equation with the gradient of the ellipsoid, and solve for the points (x, y, z) that satisfy this condition.

It requires solving a system of equations where the coefficients of the normals to both planes are proportional.

These points  (x, y, z) will be the points of tangency where the ellipsoid's tangent plane is parallel to the given plane.

We use the calculus concepts of partial derivatives to find the gradient vector and algebra to solve for the unknowns corresponding to the points of tangency.

Find the sum of the infinite series tan2 θ − tan4 θ + tan6 θ + . . . + (−1)n−1 tan2n θ + . . . whenever the series converges.

Answers

[tex]\displaystyle\sum_{n=1}^\infty(-1)^{n-1}\tan^{2n}\theta=1-\sum_{n=0}^\infty(-\tan^2\theta)^n=1-\dfrac1{1+\tan^2\theta}[/tex]

where [tex]|-\tan^2\theta|=\tan^2\theta<1[/tex] in order that the series converges, which is to say the series converges for

[tex]\tan^2\theta<1\implies|\tan\theta|<1\implies|\theta|<\dfrac\pi4[/tex]

We can simplify the sum a bit further, noting that [tex]1+\tan^2\theta=\sec^2\theta[/tex], giving

[tex]\displaystyle\sum_{n=1}^\infty(-1)^{n-1}\tan^{2n}\theta=1-\cos^2\theta=\sin^2\theta[/tex]

Find the volume of the solid that lies under the hyperbolic paraboloid z = 4 + x 2 − y 2 and and above the square r = [−1, 1] × [0, 2].

Answers

[tex]\displaystyle\int_{x=-1}^{x=1}\int_{y=0}^{y=2}(4+x^2-y^2)\,\mathrm dy\,\mathrm dx=12[/tex]

The volume of the solid under the hyperbolic paraboloid [tex]z = 4 + x^2-y^2[/tex] and above the square r = [−1, 1] × [0, 2] is [tex]20\text{ cubic units}[/tex]

The question is asking us to find the volume bounded by the following surfaces

The plane [tex]z=0[/tex] and the surface [tex]z = 4 + x^2 - y^2[/tex]The planes [tex]x=-1[/tex] and [tex]x=1[/tex]The planes [tex]y=0[/tex] and [tex]y=2[/tex]

To do this, we have to evaluate the triple integral

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz[/tex]

Evaluating the triple integral

First, we integrate with respect to [tex]z[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz\\\\=\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)[/tex]

Next, we integrate with respect to [tex]y[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)\\\\=\displaystyle \int\limit_0^2\,dx \left[4y+x^2y-\dfrac{y^3}{3} \right]_{-1}^1\\\\=\displaystyle \int\limit_0^2\,dx \left[ \left(4(1)+x^2(1)-\dfrac{(1)^3}{3} \right)- \left(4(-1)+x^2(-1)-\dfrac{(-1)^3}{3} \right)\right]\\\\=\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\[/tex]

Finally, we integrate with respect to [tex]x[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\=\left[\dfrac{22}{3}x+\dfrac{2x^3}{3}\right]_0^2\\\\=\left(\dfrac{22}{3}(2)+\dfrac{2(2)^3}{3}\right) - \left(\dfrac{22}{3}(0)+\dfrac{2(0)^3}{3}\right)\\\\=20 \text{ cubic units}[/tex]

The volume of the solid is [tex]20\text{ cubic units}[/tex]

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At a certain school, 72% of the students play one or more sports. the percentage of students who play one or more sports and who graduate is 67%. find the probability that a student graduates given that the student plays one or more sports.

Answers

The probability that a student graduates given that the student plays one or more sports = probability that students play one or more sports and who graduate/probability that students play one or more sports

  = 0.67 / 0.72

  = 0.9306 (Answer)

circle theorem - easy work

Answers

angle in a semi circle is 90°
<a = 180-90-<b = 90-28 = 62°

opposite angles of a cyclic quadrilateral sums up to 180°
<b + <a = 180
<b = 180-62
<b = 118°

The cartesian coordinates of the point are (−1,3√). hence, polar coordinates of the point are

Answers

wages wages wages wages wages wages wages wages wages vwages wages wages wages wages wages wages wages wages wages wages wages wages 

Assume the least squares equation is ŷ = 10 + 20x. what does the value of 10 in the equation indicate?

Answers

10 is the initial value, found when x=0.  I don't know what you are measuring by "0" and "10" here, so can't be more specific.

The random variable x is said to have the yule simon distribution if

Answers

a. Yule-Simons PMF is valid due to non-negativity and sum 1 proof.

b. E[X] = 2 calculated through partial fraction and cancellation.

c. E[X^2] = ∞ shown using comparison test with p-series.


a. Proving it's a Probability Mass Function (PMF):

Condition 1: Non-negativity: P{X = n} = 4/(n(n + 1)(n + 2)) is always positive for n ≥ 1, as all factors in the denominator are positive.

Condition 2: Sums to 1:

We need to show ∑_(n=1)^∞ P{X = n} = 1.

Use partial fraction decomposition:

4/(n(n + 1)(n + 2)) = 1/(n) - 1/(n + 1) + 1/(2(n + 2))

Expand the infinite series:

∑_(n=1)^∞ P{X = n} = (1/1 - 1/2 + 1/6) + (1/2 - 1/3 + 1/8) + ...

Notice terms cancel out:

= 1 + (1/6 - 1/6) + (1/8 - 1/8) + ... = 1

Therefore, P{X = n} is a valid PMF.

b. Expectation E[X] = 2:

E[X] = ∑_(n=1)^∞ n * P{X = n}

Substitute P{X = n} with its expression:

E[X] = ∑_(n=1)^∞ n * (4/(n(n + 1)(n + 2)))

Apply partial fraction decomposition (as in a) and simplify:

E[X] = ∑_(n=1)^∞ (1/(n + 1) - 2/(n + 2))

Expand the series and observe cancellations:

E[X] = (1/2 - 2/3) + (1/3 - 2/4) + ... = 1 - 1/2 = 1/2

Multiply by 4 to account for the 4 in the original PMF:

E[X] = 4 * (1/2) = 2

Therefore, E[X] = 2.

c. Expectation E[X^2] = ∞:

E[X^2] = ∑_(n=1)^∞ n^2 * P{X = n}

Substitute P{X = n} and simplify:

E[X^2] = ∑_(n=1)^∞ (4n/(n + 1)(n + 2))

Use the comparison test:

4n/(n + 1)(n + 2) > 4n/(n^3) = 4/(n^2) for n ≥ 1

Since ∑_(n=1)^∞ 4/(n^2) (p-series with p = 2) converges, so does E[X^2].

Therefore, E[X^2] = ∞.

The probable question is in the image attached.

1.33*10^6 m/s is equal to how many years

Answers

1,330,000 is the answer.

Probably late lol

Show how to make a ten to solve 13-7. Write the number sentence

Answers

To subtract 7 from 13 you use the fact that 13 is one ten plus three units, i.e. 13 = 10 + 3. then you can subtract 7 from 10 which is 3, and then add the 3 other 3 units to get 3 + 3 = 6. In this way, you have subtracted 7 from 13 using the fact that 13 is one ten plus 3 units.

You purchased a five pack of new light bulbs that were recalled because 6% of the lights did not work. what is the probability that at least one of your lights is defective

Answers

The probability that at least one of the five light bulbs is defective is approximately 26.61%. This is found by calculating the probability that all bulbs work ([tex]0.94^5[/tex]) and subtracting that from 1.

The student is asking about the probability of having at least one defective light bulb in a pack of five, given a defect rate of 6%. To calculate this, we will use the complement rule, which states that the probability of at least one success is equal to 1 minus the probability of zero successes (no defective bulbs).

First, we calculate the probability that a bulb is not defective, which is 94% or 0.94 (since 100% - 6% = 94%). Since the bulbs are independent, the probability that all five bulbs are not defective is:

[tex](0.94)^5[/tex]

The probability that at least one bulb is defective is thus:

1 - [tex](0.94)^5[/tex]

Using a calculator, this gives us:

[tex]1 - (0.94^5) \approx 1 - 0.7339 \approx 0.2661 or 26.61%[/tex]

So, there is approximately a 26.61% chance that at least one of the five light bulbs is defective.

The probability that at least one of the light bulbs is defective is approximately 0.264909 or 26.49%.

To find the probability that at least one of the light bulbs is defective, we can use the complement rule.

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

In this case, the event of interest is that at least one light bulb is defective. The complement of this event is that none of the light bulbs are defective.

Given that 6% of the light bulbs are defective, the probability that any one light bulb is not defective is 1 - 0.06 = 0.94.

Since each light bulb operates independently of the others, the probability that none of the five light bulbs are defective is [tex]\((0.94)^5\)[/tex].

Therefore, the probability that at least one of the light bulbs is defective is [tex]\(1 - (0.94)^5\)[/tex].

Let's calculate it:

P(at least one defective) = 1 - (0.94)^5

P(at least one defective) = 1 - 0.735091 = 0.264909

So, the probability that at least one of the light bulbs is defective is approximately 0.264909 or 26.49%.

a bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands how far is the bird from its starting point

Answers

check the picture below.

The distance of the bird from its starting point will be 29.15 miles.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

A bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands.

Now,

Since, A bird flies 25 miles Due West then turns due south and flies for another 15 miles and lands.

Let the distance of the bird from its starting point = x

So, By using Pythagoras theorem, we get;

⇒ x² = 15² + 25²

⇒ x² = 225 + 625

⇒ x² = 850

⇒ x = √850

⇒ x = 29.15 miles

Thus, The distance of the bird from its starting point = 29.15 miles.

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Please help me with this question on algebra

Answers

The solution is option D.

  0     4
- 6     1
  3    -4
 
Rember rows times columns.

=>
a11 = 4*0 + 0*(-3) = 0

a12 = 4*1 + 0*1 = 4 + 0 = 4

a21 = -1*0 + 2*(-3) = 0 - 6 = -6

a22 = -1*1 + 2*1 = -1 + 2 = 1

a31 = -3*0 + (-1)*(-3) = 0 + 3 = 3

a32 = -3*1 + (-1)*1 = -3 - 1 = -4

you are converting 68km to meters and your answer is 0.068 m explain why the answer is incorrect

Answers

The answer is incorrect because there are 1000 meters in 1 kilometer, not 1000 kilometers in a meter, the answer should've been 68 times 10^3 which makes it 6,800 meters.
Final answer:

The conversion of 68 kilometers into meters gives 68000 meters, not 0.068 meters. The error arises due to dividing instead of multiplying the kilometers by 1000 (because 1 km equals 1000m).

Explanation:

When you are converting from kilometers to meters, you need to understand that 1 kilometer is equal to 1000 meters. Therefore, to convert 68 kilometers to meters, you should multiply 68 by 1000, not dividing it. You calculate 68km * 1000 = 68000m. So, 68 kilometers is equal to 68,000 meters, not 0.068 meters. The response 0.068 meters is incorrect because it is vastly smaller than the actual conversion result.

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Last year, a janitorial supervisor had a gross income of $34,100, of which he contributed 8% to his 401(k) plan. If he got paid bimonthly, how much was deducted from each paycheck for his 401(k) plan?

A.389.71
B.227.31
C.52.46
D.113.67

Answers

there was a gross income of 34,100....8% goes to 401K plan..
8% of 34,100 = 0.08(34,100) = 2728

he gets paid bimonthly...so he gets paid twice a month...and being that there is 12 months in a year, he gets paid (12 * 2) = 24 times

2728/24 = 113.666 rounds to 113.67 each paycheck <==

If the gross income is $34,100,113.67 was deducted from each paycheck for his 401(k) plan.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that last year, a janitorial supervisor had a gross income of $34,100 of which he contributed 8% to his 401(k) plan.

As a result,

=8% of 34,100

=0.08(34,100)

=2728

Given that there are 12 months in a year and he is paid every two months, or twice a month, for a total of 24 payments,

=2728/24

= 113.666

Thus, if the gross income is $34,100,113.67 was deducted from each paycheck for his 401(k) plan.

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All real numbers more than 4 units from 6

Answers

2 and 10 are 4 units from 6.

Two sets of real numbers are more than 4 units from 6:  (-inf., 2) and (10, inf.)

Round your answer to this problem to the nearest degree.

In triangle ABC, if ∠A = 120°, a = 8, and b = 3, then ∠B =
°.a0

Answers

Use the sine law: sinB/b = sinA/a

SinB = b*sinA/a

sinB = 3*sin120° /8

∠ B = 18.94° ≈ 19°

Answer:

∠B = 19°

Step-by-step explanation:

Given : In triangle ABC, if ∠A = 120°, a = 8, and b = 3

We have to find the measure of B that is ∠B

Consider the given triangle ABC,

Using Sine rule ,

For a triangle with measure of angle A, B and C and side  a faces angle A,  

side b faces angle B and  side c faces angle C

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]

we have, a = 8 , b = 3 and ∠A = 120°

Consider first two ratios,

[tex]\frac{8}{\sin 120^{\circ}}=\frac{3}{\sin B}[/tex]

Solve for B, we have,

[tex]\sin \left(120^{\circ \:}\right)=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{8}{\frac{\sqrt{3}}{2}}=\frac{3}{\sin \left(B\right)}[/tex]

[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c[/tex]

[tex]8\sin \left(B\right)=\frac{\sqrt{3}}{2}\cdot \:3[/tex]

Simplify, we have,

[tex]\sin \left(B\right)=\frac{3\sqrt{3}}{16}[/tex]

Taking sine inverse both side, we have,

[tex]B=\sin^{-1}\left(\frac{3\sqrt{3}}{16}\right)[/tex]

We have, [tex]B=18.95^{\circ \:}[/tex]

Thus, ∠B = 19°

Solve the absolute value equation. |3x| = 12

Answers

The answer to this is |x| = 4

Find the median of the following data set. 1 1/4,5/8 ,3/5 ,1/2 ,1 1/2, 1 3/4
5/6
7/8
15/16

Answers

first we have to put the numbers in order

1/2, 3/5, (5/8, 1 1/4), 1 1/2, 1 3/4

the median is the middle number. when there is an odd number of numbers, u will have 1 middle number. But when there is an even number of numbers, like this one, there will be 2 middle numbers. So u have to take ur 2 middle numbers, add them, then divide them by 2 to get the average median.

are 2 middle numbers are : 5/8 and 1 1/4..

(5/8 + 1 1/4) / 2 = (5/8 + 5/4) / 2 = (5/8 + 10/8) / 2 = 
(15/8) / 2 = 15/8 * 1/2 = 15/16 <==

Answer:

Step-by-step explanation:

answer is 15/16

Henery cut a 7 foot board into 4 equal pieces. What mixed number represents the length of each piece

Answers

1 and 3/4 would be the mixed number that represents the length of each piece. You would get this number by dividing 7 by 4 :)
Final answer:

When a 7-foot board is divided into 4 equal pieces, each piece will be 1.75 feet, or, as a mixed number, 1 3/4 feet.

Explanation:

To figure out the length of each piece when a 7-foot board is divided into 4 equal parts, we perform division. We divide the total length of the board by the number of pieces. That is, 7 ÷ 4 = 1.75.

This is a decimal number. To express it as a mixed number, we remember that '.75' is the same as '75/100', and this fraction can be simplified to '3/4'. So, 1.75 feet is the same as 1 3/4 feet. Therefore, each piece of board will be 1 3/4 feet long.

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