Can someone PLEASE help me with 4 and 5??? I’m legitimately struggling.

Mathematics

2 answers:

puteri [66]3 years ago

4 0

4) The key here is recognizing that the diagonals of a rectangle are congruent, and that they bisect each other. Therefore, AE = BE, and AE + BE = BD. Substituting, you get $(2x+3)+(12-x)=BD \\ x+15=BD$ .
BD=x+7

5) The sides of a rectangle are parallel to each other. When you draw lines extending the sides, the implications of this become obvious. Suddenly, you have two parallel lines intersected by a transversal, and you probably know those angle relationships. BAC = ACD, so $3x+5=40-2x$ . $x=7$ .

To find AED (I believe there's an easier way, but I'm not sure), see that AED is the supplement of AEB, and AEB is 180° $- 2(BAC) = 180-6x-10 = 170-6(7)=128$ . Therefore, AED is $180-128=52$ .
AED=52°

zzz [600]3 years ago

3 0

Problem 4.

In a rectangle, the diagonals are congruent and bisect each other.
You have AC = BD, and AE = CE = BE = DE.
Also each segment of a diagonal is half the length of the diagonal.

AE = BE

2x + 3 = 12 - x

3x = 9

x = 3

AE = 2x + 3 = 2(3) + 3 = 6 + 3 = 9

BD = 2(AE) = 2(9) = 18

Problem 5.

Sides AB and CD are parallel.
Angles BAC and ACD are alternate interior angles of parallel lines, so they are congruent.

m<BAC = m<ACD

3x + 5 = 40 - 2x

5x = 35

x = 7

m<ACD = 40 - 2x = 40 - 2(7) = 40 - 14 = 26

m<BDC = m<ACD = 26

<AED is a remote exterior angle to angles BDC and ACD.

m<AED = m<BCD + m<ACD = 26 + 26 = 52

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Carys is checking her tax bill for the last year .the tax rates were as follows: no tax on the first 11000 of earnings .earnings

faust18 [17]

Answer:

$7,440.

Step-by-step explanation:

We have been given the tax rates as follows:

$0-$11,000 = No tax.

$11,000-$43,000 = 20%.

$43,000-$150,000 = 40%.

Earnings over $150,000 = 45%.

Since last year Carys earned $45,600, so we will have to find the tax paid by her for 11,000-43,000 at rate of 20%, then the tax for amount over 43,000 at the rate of 40%.

$\text{The amount of tax paid by Carys for 11000-43000}=\frac{20}{100}\times (43,000-11,000)$