A bookstore sells 1 book for $14.75. Which table represents the relationship between number of books and the total price?

ABCD is a parallelogram. E is the point where the diagonals AC and BD meet. Prove that triangle ABE is congruent to triangle CDE

Darina [25.2K]

ABCD is a parallelogram Given
AE=CE, BE=DE The diagonals of a parallelogram are bisect each other
∠AEB=∠CED Vertical angles are congruent
ΔABE is congruent to ΔCDE SAS theorem

5 0

1 year ago

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What is another way to write 9x200?

pashok25 [27]

9×2=18. add the tow zeros like this 9×2=18+00=1,800

7 0

1 year ago

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A homemade lip balm consists of coconut oil and beeswax. Coconut oil costs $0.50 per ounce and beeswax costs $2.00 per ounce. If

Alika [10]

Let

a--------> the total cost in dollars of $6$ ounces of coconut oil

b--------> the total cost in dollars of $5$ ounces of beeswax

we know that

$a=0.50 \frac{\$}{ounce}*6=\$3$

$b=2.00 \frac{\$}{ounce}*5=\$10$

therefore

the answer is

the total cost in dollars of $6$ ounces of coconut oil is $a=\$3$

the total cost in dollars of $5$ ounces ofbeeswax is $b=\$10$

7 0

2 years ago

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Using the extended Euclidean algorithm, find the multiplicative inverse of a. 135 mod 61 b. 7465 mod 2464 c. 42828 mod 6407

rodikova [14]

Answer:

(a)1≡47 mod 61

(b)1≡2329 mod 2464

(c)Does not exist

Step-by-step explanation:

The operation a(mod b) has an inverse if the the two integers (a,b)

are co-prime. i.e. their g.c.d is 1.

(a)Given 135 mod 61

We first reduce it to its lowest form.

135 mod 61=13 mod 61

61=13(4)+9 ==> 9=61-13(4)

13=9(1)+4 ==> 4=13-9(1)

9=4(2)+1 ==> 1=9-4(2)

4=1(4)

Next we rewrite 1 as a linear combination of 13 and 61.

1=9-4(2)

=9-(13-9(1))2

=9(3)-13(2)

=(61-13(4))(3)-13(2)

=61(3)-13(12)-13(2)

1=61(3)-13(14)

1=61(3)+13(-14)

1≡-14 mod 61≡(-14+61)mod 61

1≡47 mod 61

(b)7465 mod 2464

Reducing it to its lowest form

7465 mod 2464=73 mod 2464

2464=73(33)+55 ==>55=2464-73(33)

73= 55(1)+18 ==> 18=73-55(1)

55=18(3)+1 ==>1=55-18(3)

18=1(18)

Rewriting 1 as a linear combination of 73 and 2464.

1=55-18(3)

=2464-73(33)-(73-55(1))(3)

=2464-73(33)-73(3)+55(3)

=2464-73(36)+55(3)

=2464-73(36)+(2464-73(33))(3)

=2464-73(36)+2464(3)-73(99)

=2464(4)-73(135)

1=2464(4)+73(-135)

Therefore:

1≡-135 mod 2464

1≡(-135+2464)mod 2464

1≡2329 mod 2464

(c)42828 mod 6407

The two numbers are not co-prime. In fact their g.c.d is 43.

Therefore their inverse does not exist.

4 0

1 year ago

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Henry is asked to find the exact value of cos 10pi/3. His steps are shown below.

nata0808 [166]

Answer:

A) The reference angle should be $\frac{\pi }{3}$ , and the sign of the value should be negative.

Step-by-step explanation:

cos( $\frac{10\pi }{3}$ )

Remove full rotations of 2π until the angle is between 0 and 2 $\pi$ .

cos( $\frac{4\pi }{3}$ )

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

-cos( $\frac{\pi }{3}$ )

The exact value of cos( $\frac{\pi }{3}$ ) is $\frac{1}{2}$ .

− $\frac{1}{2}$

8 0

2 years ago

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