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3 years ago

In the right triangle ΔABC, ∠A=36°. Find the measure of the other acute angle: ∠B.

Mathematics

1 answer:

Sever21 [200]3 years ago

4 0

Answer:

A. 54

Step-by-step explanation:

A right angle = 90 degrees

They provided one acute angle which is 36

Add 90 + 36 = 126

A triangle = 180

So 180-126=54

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Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

3 0

3 years ago

A part time seamstress made $8881.93 last year. If she claimed herself as an exemption for $3650 and had a $5700 standard deduct

Rainbow [258]

Answer:

Step-by-step explanation:

3 0

3 years ago

at a country concert,the ratio of number of the Boys to the number of girls is 2:7 if there are 250 more girls than boys how man

sergey [27]

Answer:

100

Step-by-step explanation:

Ratio is a fraction, so ratio of boys to girls would be written as [let boys be "b" and girls be "g"]:

$\frac{b}{g}=\frac{2}{7}$

Also, there are 250 more girls than boys, so we can write:

g = 250 + b

Lets substitute this into "g" of the ratio we wrote and cross mulitply and solve for b:

$\frac{b}{g}=\frac{2}{7}\\\frac{b}{250+b}=\frac{2}{7}\\7b=2(250+b)\\7b=500+2b\\5b=500\\b=\frac{500}{5}=100$

The number of boys = 100

3 0

4 years ago

Help please this is for inequality math!! n + 7 < - 3

stealth61 [152]

Answer:

n < -10

Step-by-step explanation:

n+7 < -3

subtract 7 from both sides

n+7-7 < -3-7

n < -10

4 0

3 years ago

Andrew believes the honor roll students at his school have an unfair advantage in being assigned to the math class they request.

Artist 52 [7]

<span>   Honor roll Not on honor roll Total
Received math class requested 315   64   379
Did not get math class requested 41   80   121
Total 356 144   500

Honor roll: request granted: 315/356 = 0.88 x 100% = 88%
Not Honor roll request granted: 64/144 = 0.44 x 100% = 44%

Honor roll students were given preference in granting request than those not in the honor roll.</span>

5 0

3 years ago