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3 years ago

Please help me with questions 23, 24, and 25

Mathematics

1 answer:

alekssr [168]3 years ago

6 0

Problem 23
A = 40
B = 3x+1
C = 3x+1
B and C are congruent, so they have the same angle measure

The three angles of any triangle add to 180 degrees
A+B+C = 180
40+(3x+1)+(3x+1) = 180
6x+42 = 180
6x = 180-42
6x = 138
x = 138/6
x = 23

Answer: B) 23

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Problem 24

AB is the midsegment parallel to XY
So AB is half that of XY
AB = (1/2)*XY
AB = (1/2)*28
AB = 14

Answer: B) 14

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Problem 25

Note the ratio of the given rectangle's sides: 7/12 = 0.583 roughly

Divide the answer choices in a similar fashion
A) 5/7 = 0.714
B) 14/36 = 0.389
C) 21/36 = 0.583
D) 21/48 = 0.4375

We get the same result in choice C as we did in the original rectangle

Answer: C) 21 ft x 36 ft

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Just number 23 super confused

vodka [1.7K]

Answer:

x = -7

Step-by-step explanation:

This is an exponential equation.

$\frac{1}{2}^x=128$

We need to take log(or ln) of both sides and use logarithm property to solve this.

So, let's take ln of both sides, so we have:

$ln(\frac{1}{2}^x)=ln(128)$

Now, we will use this property shown below to further simplify:

$ln(a^b)=bln(a)$

So, we now have:

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The value of x is -7

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We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

Step-by-step explanation:

Given

Principle P = $2500

Interest rate r = 5% = 0.05

Time period t = 8 years

To determine

Accrue Amount A = ?

Using the compound interest equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

where:

A represents the Accrue Amount

P represents the Principal Amount

r represents the interest rate

t represents the time period in years

n represents the number of compounding periods per unit t

Important tip:

Given that the interest is compounded 6 times each year, therefore, the value of n = 6.

now substituting P = 2500, r = 0.05, t = 8 and n = 6 in the equation

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

$A=2500\left(1+\frac{0.05}{6}\right)^{\left(6\right)\left(8\right)}$

$\:A=2500\left(1+\frac{0.05}{6}\right)^{48}$

$A=2500\times 1.48935$ ∵ $\left(1+\frac{0.05}{6}\right)^{48\:\:}=1.48935$

$A=\:3723.38$ $

Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $2500 at a rate of 5% per year compounded 6 times per year over 8 years is $3723.38.

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