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Finger [1]
3 years ago
6

The quadrilateral ABCD is a rhombus with diagonals AC = 12 ft and BD = 4 ft. The points M and N divide diagonal AC on three equa

l parts. Prove that BMDN is a square and find its area.
Mathematics
1 answer:
victus00 [196]3 years ago
8 0

Answer:

area of BMDN 8 ft²

Step-by-step explanation:

In BMDN the diagonals are BD and MN.

MN is 12/3 = 4 ft long, and BD = 4 ft.

A rhombus with equal diagonals is a square, so BMDN is a square.

In the right triangle BDN, the diagonal BD is the hypotenuse, then:

DN² + NB² = BD²

but DN = NB, then:

2*DN² = 16 ft²

DN² = 8 ft²

The area of BMDN is computed as one of its sides squared. Then, DN² is its area

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Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o
AlekseyPX

Answer : 96

x – y = 16 --------> equation 1

\frac{1}{8} x +\frac{1}{2} y = 52

x is the higher grade and y is the lower grade

We solve the first equation for y

x - y = 16

-y = 16 -x ( divide each term by -1)

y = -16 + x

Now substitute y in second equation

\frac{1}{8} x +\frac{1}{2} ( -16 + x ) = 52

\frac{1}{8} x - 8 +   \frac{1}{2} x = 52

\frac{1}{8} x  +   \frac{1}{2} x - 8 = 52

Take common denominator to combine fractions

\frac{1}{8} x  +   \frac{4}{8} x  -8 = 52

\frac{5}{8} x - 8  = 52

Add 8 on both sides

\frac{5}{8} x   = 60

Multiply both sides by \frac{8}{5}

x = 96

We know x is the higher grade

96 is the higher grade of Jose’s two tests.

6 0
3 years ago
Read 2 more answers
(8^3 + 2^2 + 1) - (7 - 7^3+3^2)
Andreyy89

Answer:

844 is the ans

Step-by-step explanation:

512+4+1 -7 +343+9= 844

3 0
3 years ago
How many unit cubes would you need to make a model of a rectangular prism that is 6 units long, 2 units wide, and 5 units high?
Zina [86]

Answer:

60

Step-by-step explanation:

Volume = 6*2*5 = 60

6 0
3 years ago
Read 2 more answers
The sum of a number and 8 is inore than 4.
marta [7]

Hey there!

Guide:

• The word “sum” means “add”

• The word “difference” means “subtract”

• The word “product” means “multiply”

• The word “quotient” means “divide”

• The word “is” means “equal”

• The word “more-than” can either mean “add” or “bigger than”. It is a number that is bigger than the number compared to (like 6 is bigger than 5)

• The word “less-than” can either mean “subtract” or “smaller than”. It is a number that is being is smaller than the number that it is being compared to (like 5 is smaller than 6)

Guide 2:

• > is greater than / more than

• < is less than

• + is sum

• - is difference

• × is product or “of”

• ÷ is quotient

• ≥ is greater than or equal to whereas it is either greater than or equivalent to the numbers that are being compared

• ≤ is less than or equal to where is either less than or equivalent to the numbers that are equivalent to each other

Now that we have that information out of the way, we can answer you question.

We have the words: “sum” and “is” in your mathematical word expression, we know that we’re ADDing and trying to figure out what is GREATER than 4.

Your “number” that is being compared to “8” is unknown so we will label it as “z” as it’s variable.

Anyways let’s answer your question

“The sum of a number and 8”

z + 8

“Is more than 4”

> 4

YOUR EQUATION: “z + 8 > 4” (POSSIBLE ANSWER #1)

SOLVING FOR YOUR EQUATION:

z + 8 > 4

SUBTRACT 8 to BOTH SIDES

z + 8 - 8 > 4 - 8

CANCEL out: 8 - 8 because it gives you 0

KEEP: 4 - 8 because it helps you figure out what is being compared to the z-value.

z > 4 - 8

SIMPLIFY IT!

z > -2 (POSSIBLE ANSWER #2)

It is an OPEN circle shaded to the RIGHT side of the number line starting at -4. (Factoid for POSSIBILITY #2)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

4 0
2 years ago
The pool already has 12 gallons of water, and he wants to fill it to at least 27 gallons. The water flows at a rate of 6 gallons
bearhunter [10]

Answer:

6x + 12 = 27

x = minutes

x = 2.5 minutes to fill the pool

5 0
2 years ago
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