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2 years ago

Which is the simplified form of p Superscript 0? p StartFraction 1 Over p EndFraction 0 1.

Mathematics

1 answer:

Oksi-84 [34.3K]2 years ago

5 0

The simplified form of p superscript 0 is equal to the zero power of p, which is 1.

<h3>What is simplified form of a term?</h3>

Simplified form of a term is the simplest way of expression the term, by applying the required operations of mathematics.

Given information-

The term given in the problem is p superscript 0.

The term superscript is used for the number which is written above the given number which means power of the number.

Thus the term p superscript 0 can be written as,

$p^0$

Let the simplest form of the given term is $x$ . Thus,

$x=p^0$

In the given number the power of unknown number <em>p </em>is 0. It means the number <em>p</em> has to be multiplied by itself with 0 times.

It can be simply said that the number $p^0$ is the product of no number. When we multiplied with any number with no number, the result should be unity.

Therefore it can be said that, when the power of any number is equal to the zero. Then the result of it equal to the one.

As for the given number, the power is equal to the zero. Thus the result of it should be equal to the one. Therefore,

$x=p^0=1$

Hence, the simplified form of p superscript 0 is 1.

Learn more about the simplified form here;

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Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

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<em>i hope this helps, good luck :)</em>

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2 years ago

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A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice. A. How much sparkling w

cluponka [151]

Answer: We need to mix 18 quarts of sparkling water with 9 quarts of grape juice.

We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.

Step-by-step explanation:

Given: A recipe for sparkling grape juice calls for 1.5 quarts of sparkling water and .75 quart of grape juice.

Since, for recipe of sparkling grape juice , they should be used in same proportion.

Let x be the amount of sparkling water need to mix with 9 quarts of grape juice, then

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Let y be the amount of grape juice need to mix with 3.75 quarts of sparkling water, then

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We need to mix 1.875 quarts of grape juice with 3.75 quarts of sparkling water.

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