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At a birthday party, five people are sharing 3/4 of a pan of lasagna. What equal-sized portion of the whole pan will each of the five people receive?

a. Draw a visual model to represent the situation and the solution.

b. Write an equation to represent the situation. Explain your reasoning.

Answer:

6.1 cm

Step-by-step explanation:

it depends on what your teacher told you and wants to see.

because, theoretically, it would be 6.0 cm. but that would render the whole triangle into a flat line, as the 2 equal sides together (2×6 = 12) would be exactly as long as the baseline (12) of the triangle.

which is again a theoretically possible construct (counting as extreme triangle).

but it is more likely that your teacher wants the definition applied that for each combination of 2 sides this combination has to be larger (and not larger or equal) than the third side.

so, the 2 equal sides have to be larger than 6 cm.

the smallest number in your answer options to fit that criteria is 6.1 cm

just FYI - your teacher was not very precise in the phrasing, because there are many numbers smaller than 6.1 that would still be correct.

like 6.01, or 6.005, ...

Rounded to the nearest tenth, the smallest possible length is 6.1 cm.Thus, the answer is B) 6.1 cm.

In an acute isosceles triangle, the longest side is opposite the largest angle. Since the triangle is isosceles, the two congruent sides are equal in length.

In an acute triangle, the largest angle is less than 90 degrees. In an isosceles triangle, the two base angles are congruent. Therefore, each base angle must be less than 45 degrees.

Now, let's apply the triangle inequality theorem to determine the smallest possible length of one of the congruent sides. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the longest side is 12 centimeters. Let's assume each of the congruent sides has a length of x centimeters.

Based on the triangle inequality theorem, we have the following inequality:

2x > 12

To find the smallest possible length, we divide both sides of the inequality by 2:

x > 6

Therefore, the smallest possible length of one of the two congruent sides is greater than 6 centimeters.

Rounded to the nearest tenth, the smallest possible length is 6.1 cm.

Thus, the answer is B) 6.1 cm.

To know more about  congruent sides , here

https://brainly.com/question/29789999

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Step-by-step explanation:

55 > 4u + 15

40 > 4u

10 > u

so, this is true for all u < 10

Answer:

D [tex]\sqrt{43}[/tex] is the right answer

Step-by-step explanation:

I. If Number is devided by 4 or 25%

                    25% + 25% is 50%

                    50% = [tex]\frac{50}{100}[/tex] is 0.5

II. When 6 + 0.5 = 6.5

                 Use calculator the nearlest value is [tex]\sqrt{43}[/tex]

                 [tex]\sqrt{43}[/tex] = 6.557

So we'll pick D.choice

Hope that help :D

Answer:

999

Step-by-step explanation:

Step-by-step explanation:

Distributive Property

Answer:

The number is 5

Step-by-step explanation:

A number is multiplied by 8 = 8x

8x + 2

8x + 2 = 42         Subtract 2 from both sides

    - 2      -2

8x = 40                Divide by 8

x = 40/8

x = 5

Answer:

10

Step-by-step explanation:

we know that y=sqrt(7), so just plug it into the expression y^2 +3. now we have (sqrt(7))^2 +3, (sqrt(x))^2=x, so (sqrt(7))^2 +3= 7+3=10

Answer:

Step-by-step explanation:

increased means add.

5 + 2*t

Answer:

2x(2x-9)

Step-by-step explanation:

2x is the factor.

Answer:

B. [tex]\frac{3+\sqrt{29} }{2}[/tex]

Step-by-step explanation:

[tex]\frac{-(-3)\sqrt{(-3^2-4(1)(5)} }{(2)(1)}[/tex]

[tex]=\frac{-(-3)+\sqrt{29} }{2}[/tex]

Answer:  The total interest is 656.25.

Step-by-step explanation:

T = 3yrs

P = 3500

R = 6.25%

I = PTR/100

 = 3500*3*6.25/100

 = 65625/100

= 656.25

Answer:

It is B

Step-by-step explanation:

[tex] ln(x) + ln(y) - ln(z) [/tex]

from law of logarithms:

[tex]{ \bf{ ln(a) + ln(b) = ln(ab) }} \\ and \\ { \bf{ ln(a) - ln(b) = ln( \frac{a}{b} ) }}[/tex]

so, in the question:

[tex] ln(x) + ln(y) - ln(z) \\ \\ = \{ ln(xy) - ln(z) \} \\ \\ = ln( \frac{xy}{z} ) [/tex]

The required logarithmic expression is ln(xy/z). Option B is correct.

Given that
To simplify ln x + ln y + ln z

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

A logarithmic function can be defined as the function inverse of the exponential function is a logarithmic function.

In the question, an algebraic expression of the log function is given a simplified form of the expression to be determined using the logarithmic property.

Simplification,
= ln x +ln y + ln z
Since log A  + log B = log(A.B)
and log A - logB = log(A/B)

From above properties
= ln (x . y) - ln z
= ln [(x. y )/z]

Thus, the required logarithmic expression is ln(xy/z). Option B is correct.

Learn more about logarithmic function here:
https://brainly.com/question/24211708
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Answer:

6

Step-by-step explanation:

1/2 of 12

1/2×12

6

i hope this will help

Answer:

compostion

Step-by-step explanation:

comPOSTION

9514 1404 393

Answer:

  10,000

Step-by-step explanation:

5(9·8·7·4 -2(6 +3 -1)) = 10,000 . . . . a 5-digit even number

Answer:

9

Step-by-step explanation:

since the side that was originally 2 is now six, it means that it tripled, and 3x3 is 9.

the answer would be d !

−5 + 11i

Answer:d

Step-by-step explanation:

the answer would be d !

−5 + 11i

The perpendicular bisector on a line segment AB is in the attached image.

Given:

To Construct:

Solution:

A segment is a line with two ends with a specific length.

A perpendicular bisector is a line intersecting the other line segment into two equal lengtsh at an angle of 90 degrees.

Steps of construction:

The perpendicular bisector to a segment AB is in the image attached.

Learn more about: Segments and perpendicular bisectors here:

https://brainly.in/question/3957?tbs_match=3

#learnwithbrainly

Answer:

Step-by-step explanation:

To create a perpendicular bisector, you need a compass, a straightedge, and a pencil. As well as the line segment AB drew down.

1> You start by opening the compass and stretching it to a width greater than half the length of AB.

2> Then you simply place one point of the compass on the line segments A. From here, you move the compass and draw arcs above and below the line AB.

3> Without moving the compass measure, remove it from point A and place it onto point B. You basically repeat step 2 by drawing arcs above and below the line again.

4> If you've done it right, the arcs should be in the middle, X and Y, and using a straightedge/ruler you draw a line that goes vertically through where they connect.

and that should be your perpendicular bisector using segment AB.

Answer:

I think c = 5,sorry if im wrong

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = 25 and the square root of 25 is 5

Answer:

The hypotenuse is 5 meters.

Step-by-step explanation:

According to the Pythagorean Theorem, the sum of the squares or, in this case, triangles, of the lengths of the legs of a right triangle equals the square or triangle equals the square or triangle of the hypotenuse.

A= 4m

B= 3m

4 with exponent of 2 plus 3 with exponent of 2 will help you get your answer. 4 times 4 is 16 and 3 times 3 is 9. 16 plus 9 equals to 25 and find the square root of 25 which is 5 because 5 times 5 equals to 25. I hope this helps!

Answer:

1,246,193 rounded to the nearest thousands is 1,246,000

Because the digit next to the thousands place (The hundreds place) is less that 5, it is 1 therefore you keep the digit the same in the thousands place and make the rest a 0.

Answer:

1,246,000

Step-by-step explanation:

1,246,193

The 6 is in the thousands place

We look at the hundreds place

1 is in the hundreds place,  Since it is 4 or less, we leave the thousands place alone.

1,246,000

Answer:

x = -8

Step-by-step explanation:

-23 + 7 = -16

-16 ÷ 2 = -8

2 × -8 =-16 - 7 = -23

Answer:

No... provided no other information or no graph is provided.

Step-by-step explanation:

You can find the x-coordinate of the vertex which can be calculated using the two given x-intercepts. Using the symmetry of the parabola, it would just mean the vertex should lay midway between the x's. So the x-coordinate of the vertex is (12+35)/2=47/2.

However, we do not have enough information about the relationship between x and y to find the y-coordinate of the vertex.

All we are given is y=a(x-12)(x-35) (where a is real number) since we know the relationship is quadratic, and the zeros are 12 & 35.

So we could have many possible y-coordinates for our vertex since we don't know the value of a in our equation and we can plug in our x-coordinate for our vertex to find them all.

y=a(47/2-12)(47/2-35)

I'm just going to put everything to right of a in calculator:

y=-529/4 ×a

So that's all the possible y-coordinates for the vertex.

Answer:

Exact form: - 125/3

Decimal form: - 41.6

Mixed number form: - 41 ⅔

I hope I've helped

Answer:

A

Step-by-step explanation:

Six hundred seventy-two thousandths = 0.672

0.672 < 0.8

Answer:

A: rectangle

B: still a rectangle

Step-by-step explanation:

Basically, if you cut it in half starting from the top straight down it would make it a rectangle because it can't be a square because all sides are not equal. And if you go from the far right top edge to the bottom left edge it will still be a rectangle but long.

Hope this helps love <3

9514 1404 393

Answer:

  x = 605π/12 ≈ 158.4

Step-by-step explanation:

To eliminate the denominator under the variable, multiply both sides of the equation by that value.

  [tex]\dfrac{x}{\pi\cdot11^2}=\dfrac{15}{36}\\\\x\cdot\dfrac{\pi\cdot11^2}{\pi\cdot11^2}=\dfrac{5}{12}\cdot\pi\cdot11^2\\\\\boxed{x=\dfrac{605\pi}{12}\approx158.38863}[/tex]

Hi there!  

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I believe your answer is:  

-15

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Here’s why:  

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

3.75

Step-by-step explanation:

8 fl x 60 ( minutes )= 48 fl oz

48 fl oz divided by 128= 3.75 gallons.