ABC is isosceles with AB=AC=8 units and BC=6 units. D and E are midpoints of AB and BC respectively. Calculate the length of DE?

Final answer:

You can make 19 cheese sandwiches with 38 bread slices and 28 cheese slices.

Explanation:

In this scenario, you have 38 bread slices and 28 cheese slices. The equation for a cheese sandwich is 1 sandwich = 2 slices of bread + 1 slice of cheese. So, if you set the number of bread slices to '2' and the number of cheese slices to '1', you can calculate how many cheese sandwiches you can make.

First, divide the number of bread slices (38) by 2 to get the number of sandwiches that can be made with the bread: 38 / 2 = 19 sandwiches.

Next, divide the number of cheese slices (28) by 1 to get the number of sandwiches that can be made with the cheese: 28 / 1 = 28 sandwiches.

Since you can only make 19 sandwiches with the available bread, the limiting factor is the bread. Therefore, you can make 19 cheese sandwiches with the given amounts of bread and cheese.

The value obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The given expression is,

(4×2⁵) ÷ (2³ × 1/16 )

Keep the base constant and add the exponents when multiplying similar bases. Maintaining the same base while multiplying the exponents will raise a base with power to another power. When dividing two bases with similar exponents, keep the exponents of the numerator and denominator constant.

= (2² × 2⁵) ÷ (2³ × 2⁻⁴ )

= (2⁷) ÷ (2⁻¹)

= 2⁸

Thus, the values obtained as the power of 2 after solving the expression, (4×2⁵) ÷ (2³ × 1/16 ) will be 2⁸.

Learn more about the integer exponent here:

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The snowfall in Milwaukee last year was 39.75 inches above the normal amount, calculated by subtracting the normal annual snowfall from last year's total.

The student's question is related to subtraction of two amounts to find the difference between the actual snowfall and the normal snowfall in Milwaukee.

To determine how much above normal last year's snowfall was, we subtract the normal snowfall amount from last year's total snowfall.

Last year's snowfall in Milwaukee = 92 inches
Normal annual snowfall = 52 1/4 inches

To find how much above normal the snowfall was, we calculate:

92 inches - 52 1/4 inches = 92 inches - 52.25 inches

This equals 39.75 inches above normal snowfall.

Answer:

n = 2

Step-by-step explanation:

As per statement of the question we will form the equation first.

[tex](\frac{3}{5})n-\frac{4}{5}=(\frac{1}{5})n[/tex]

Now we will solve the given equation to get the solution of n.

[tex](\frac{3}{5})n=\frac{4}{5}+(\frac{1}{5})n[/tex]

[tex](\frac{3}{5})n-(\frac{1}{5})n=\frac{4}{5}[/tex]

[tex](\frac{3-1}{5})n=\frac{4}{5}[/tex]

[tex](\frac{2}{5})n= \frac{4}{5}[/tex]

Now we cross multiply the fractions

(2×5)×n = 4×5

10.n = 20

[tex]n=\frac{10}{5}=2[/tex]

Therefore answer is n = 2

The 50th shape in the repeating sequence of shapes (triangle, square, circle) is a square. This conclusion is reached by dividing 50 by the 3 shapes in the sequence and noting that the remainder indicates the position in the sequence.

The problem presented is one of patterns and sequences, a common topic explored in middle school mathematics. The repeating pattern here consists of three shapes: a triangle, a square, and a circle. This sequence of three shapes continues indefinitely.

To find the 50th shape in the sequence, divide 50 by 3. You'll get 16 remainder 2. This indicates that after 16 complete cycles of the pattern (each consisting of a triangle, square, or circle), the 50th shape is the 2nd shape in the next cycle - the square. Hence the 50th shape according to Jessica's rule is a square.

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The 50th shape in the repeating pattern of Triangle, Square, Circle is a Square.

To find the 50th shape, we need to understand the cyclical nature of this pattern, which repeats every 3 shapes.

Step-by-Step Solution:

Therefore, the 50th shape is a Square.

I substitute 1 in 2

AD²=2*[(17-AD)²+(AD/2)²]----> AD²=2*[289-34AD+AD²+0.25AD²]

AD²=578-68AD+2.50AD²--------> 1.50AD²-68AD+578

1.50AD²-68AD+578=0

 using a graph tool to solve the quadratic equation

see the attached figure

AD1=11.33 in

AD2=34 in----------is not solution because (AB+AD=17)

Solution is AD=11.33 in

AB=17-11.33--------> 17-11.33-----> AB=5.67 in

 the answer is

AD=11.33 in

AB=5.67 in

Final answer:

The business woman invested $17,000 in the 3.5% interest account and $21,000 in the 6.5% interest account.

Explanation:

To find how much she invested in each account:

Let x be the amount invested at 3.5% interest and y be the amount at 6.5%.

We can set up a system of equations like this: x + y = $38,000 and 0.035x + 0.065y = $1,960.

Solving this system, we get x = $17,000 and y = $21,000.

Therefore, investment is $17,000 in the 3.5% interest account, $21,000 in the 6.5% interest account

Final answer:

The sums for the given pairs of binary integers are: a. 10101111 + 11011011 equals 110001010, b. 10010111 + 11111111 equals 110010110, c. 01110101 + 10101100 equals 100100001.

Explanation:

The sum of each pair of binary integers is calculated using binary addition rules, which are similar to decimal addition, but instead, you only have two digits, 0 and 1, and carry over whenever you add two 1's. Let's perform the calculations for each given pair:

a. 10101111 + 11011011 = 110001010
b. 10010111 + 11111111 = 110010110

c. 01110101 + 10101100 = 100100001

Remember to start adding from the rightmost digit (least significant bit) and move left, carrying over as necessary when the sum of two bits is 2 (binary 10).

⇒Plotting the Quadrilateral on two Dimensional Plane

 And finding the diagonal of Quadrilateral bisect each other.

If you will look at the Quadrilateral, none of the interior angle is of 90°, so it can't be Square or Rectangle.

Finding the length of two Adjacent Sides

[tex]TO=\sqrt{(18-9)^2+(10-10)^2}\\\\TO=9 \text{Unit}\\\\OA=\sqrt{(18-14)^2+(10-5)^2}\\\\OA=\sqrt{4^2+5^2}\\\\OA=\sqrt{41}[/tex]

As, the Length of Adjacent sides are not equal,so it can't be a Rhombus.

The Given Quadrilateral ,"TOAD" is a Parallelogram.

⇒The Point of Intersection of both Diagonal can be Obtained by

       [tex]=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\\text{Point P}=(\frac{14+9}{2},\frac{5+10}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})\\\\\text{Point P}=(\frac{18+5}{2},\frac{10+5}{2})\\\\\text{Point P}=(\frac{23}{2},\frac{15}{2})[/tex]

Intersection of both diagonals is same, diagonals bisect each other.    

Point of Intersection of Diagonal is Point P

     [tex]=(\frac{23}{2},\frac{15}{2})[/tex]

Part C      

Distance formula

   [tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2)}\\\\TP=\sqrt{(\frac{23}{2}-9)^2+(\frac{15}{2}-10)^2}\\\\TP=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PA=\sqrt{(\frac{23}{2}-14)^2+(\frac{15}{2}-5)^2}\\\\PA=\sqrt{\frac{25}{4}+\frac{25}{4}}\\\\TP=\frac{5}{\sqrt{2}}\\\\PD=\sqrt{(\frac{23}{2}-5)^2+(\frac{15}{2}-5)^2}\\\\PD=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PD=\frac{\sqrt{169+25}}{2}\\\\PD=\frac{\sqrt{194}}{2}\\\\PO=\sqrt{(\frac{23}{2}-18)^2+(\frac{15}{2}-10)^2}\\\\PO=\sqrt{\frac{169}{4}+\frac{25}{4}}\\\\PO=\frac{\sqrt{169+25}}{2}\\\\PO=\frac{\sqrt{194}}{2}[/tex]

→DP=PO

→PT=PA

Length of Segments from point of intersection of two diagonal is same.So,  Diagonal are bisector of each other.