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3 years ago

1.Which statement about the equation is true? x + 2 = x + 4 2. 5(w−1)−2=5w+7

Mathematics

1 answer:

Marysya12 [62]3 years ago

7 0

Answer:

Both equations have no solution.

Step-by-step explanation:

The first equation is:

$x + 2 = x + 4$

Group the similar terms to get:

$x - x = 4 - 2$

$0 = - 2$

This equation has no solution because

$0 \ne - 2$

The second equation is

$5(w - 1) - 2 = 5w + 7$

We expand the parenthesis to obtain:

$5w - 5 - 2 = 5w + 7$

$5w - 7= 5w + 7$

Group similar terms:

$5w -5w = 7 + 7$

$0 = 14$

This equation does not also have solution because

$0 \ne14$

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PLEASE HELP ASAP ILL GIVE BRAINLIEST!!!!!<br><br>find measure of arc MK

Gwar [14]

Answer:

Arc length MK = 15.45 units (nearest hundredth)

Arc measure = 58.24°

Step-by-step explanation:

Calculate the measure of the angle KLN (as this equals m∠KLM which is the measure of arc MK)

ΔKNL is a right triangle, so we can use the cos trig ratio to find ∠KLM:

$\sf \cos(\theta)=\dfrac{A}{H}$

where:

$\theta$ is the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Given:

$\theta$ = ∠KLM
A = LN = 8
H = KL = 15.2

$\implies \sf \cos(KLM)=\dfrac{8}{15.2}$

$\implies \sf \angle KLM=\cos^{-1}\left(\dfrac{8}{15.2}\right)$

$\implies \sf \angle KLM=58.24313614^{\circ}$

Therefore, the measure of arc MK = 58.24° (nearest hundredth)

$\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right) \quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle)}$

Given:

r = 15.2
∠KLM = 58.24313614°

$\implies \textsf{Arc length MK}=2 \pi (15.2)\left(\dfrac{\sf \angle KLM}{360^{\circ}}\right)$

$\implies \textsf{Arc length MK}=\sf 15.45132428\:units$

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2 years ago

In which of the options below will the number 3 correctly fill in the blank. Select all that apply. A) ___ : 4 = 12 : 16 B) 1 :

aniked [119]

Answer:

A and B

Step-by-step explanation:

Given

List of given options

Required

Which will correctly take 3 to fill the blank

Represent the blanks with x

Option A:

$x : 4 = 12 : 16$

Convert to fractions

$\frac{x}{4} = \frac{12}{16}$

Multiply through by 4

$4 * \frac{x}{4} = 4 * \frac{12}{16}$

$x = \frac{48}{16}$

$x = 3$

Option B:

$1 : 5= x : 15$

Convert to fraction;

$\frac{1}{5} = \frac{x}{15}$

Multiply through by 15

$15 * \frac{1}{5} = \frac{x}{15} * 15$

$15 * \frac{1}{5} = x$

$3 = x$

$x = 3$

Option C:

$x : 1 = 12 : 3$

Convert to fraction

$\frac{x}{1} = \frac{12}{3}$

$x = 4$

Option D

$15:x = 3:1$

Convert to fraction

$\frac{15}{x} = \frac{3}{1}$

Cross Multiply

$3 * x = 15 * 1$

$3 * x = 15$

Divide through by 3

$x = 5$

From the above calculations.

<em>Option A and B can be filled with 3</em>

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3 years ago

Ava opens an account with $400. She deposits $200/month for 20 years. The interest rate is 2.15%. How much interest will she hav

artcher [175]

Answer:

d. None of the above

Step-by-step explanation:

We assume the sequence of deposits is ...

month 0: $400

month 1: $200

month 2: $200

...

month 240: $200 . . . . accumulated interest is determined at this point

That is, no interest is earned on the last deposit.

_____

The value of the initial $400 deposit after 20 years at 2.15% interest compounded monthly is ...

$400×(1 +.0215/12)^(12×20) = $400×1.536666 ≈ $614.67

The value of the $200 annuity at the same interest rate is ...

$200((1 +.0215/12)^(12×20) -1)/(.0215/12) = $200×299.534612 ≈ $59,906.92

So, the total account value is ...

$614.67 +59,906.92 = $60521.59

The total amount deposited was ...

$400 +$200×240 = $48,400

The interest earned is the difference between the account value and the total of deposits:

$60,521.59 -48,400 = $12,121.59 . . . . interest earned

This value does not match any numerical answer choice, so we conclude the appropriate answer is ...

None of the above

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3 years ago

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Aleks04 [339]

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