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3 years ago

Find the equation of a line through (4,-5) perpendicular to 6x-2y=7

Mathematics

1 answer:

blondinia [14]3 years ago

8 0

Answer: y=-1/3+2/3

Step-by-step explanation:

1. 6x-2y=7 subtract 6x from both sides.

2. -2y=-6x+7 divide both sides by -2 to isolate y

3. y=3x+7 that’s the y=Mx+b format, now we must find the negative inverse of the slope (m) which is -1/3.

4. Plug in variables.

-5=-1/3(4)+b

5. Solve:

-5=-4/3+b

add 4/3 to both sides to get -3 2/3=b

6. Make y=mx+b equation.

y=-1/3x+2/3

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In abc above,what is the length of ad

Nezavi [6.7K]

Answer:

Step-by-step explanation:

First calculate BD using sine ratio in Δ BCD and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , thus

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{BD}{BC}$ = $\frac{BD}{12}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2BD = 12 $\sqrt{3}$ ( divide both sides by 2 )

BD = 6 $\sqrt{3}$

-----------------------------------------------------------

Calculate AD using the tangent ratio in Δ ABD and the exact value

tan30° = $\frac{1}{\sqrt{3} }$ , thus

tan30° = $\frac{opposite}{adjacent}$ = $\frac{AD}{BD}$ = $\frac{AD}{6\sqrt{3} }$ = $\frac{1}{\sqrt{3} }$ ( cross- multiply )

$\sqrt{3}$ AD = 6 $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

AD = 6 → B

4 0

2 years ago

What is the value of the expression ? (243^2)^1/10 A.9 B.81 C.3 D.27

podryga [215]

$(243^2)^{\tfrac 1{10}}\\\\=243^{\tfrac 2{10}}\\\\=243^{\tfrac 15}\\\\=(3^5)^{\tfrac 15}\\\\=3^{\tfrac 55}\\\\=3^1\\ \\=3\\\\\text{Hence the the answer is C.}$

7 0

2 years ago

Question 4 (1 point)

mrs_skeptik [129]

Answer:

(C)y=0

Step-by-step explanation:

An exponential function of the form $f(x) = a (b^x) + c$ always has a horizontal asymptote at y = c.

Given our function $y=4^x$

Comparing with the form, $f(x) = a (b^x) + c$ , we observe that c=0.

Therefore, the exponential function has an asymptote at y=0.

The correct option is C.

7 0

3 years ago

am • an = am + n, where a is a real number and m and n are integers Use the product of powers property to simplify the expressio

Maru [420]

1. Take out the constants
-(2 x 3 x 4 x 2)xxyy^3
2. Simplify 2 x 3 x 4 x 2 to 48
-48xxyy^3
3. Use Product Rule: x^ax^b = x^a+b
-48x^1+1y^1+3
4. Simplify 1 + 1 to 2
-48x^2y^1+3
5. Simplify 1 + 3 to 4
-48x^2y^4

9 0

2 years ago

Read 2 more answers

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1479 and a standard devi

kotykmax [81]

Answer:

0.35% of students from this school earn scores that satisfy the admission requirement.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1479 and a standard deviation of 302.

This means that $\mu = 1479, \sigma = 302$

The local college includes a minimum score of 2294 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement?

The proportion is 1 subtracted by the pvalue of Z when X = 2294. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2294 - 1479}{302}$

$Z = 2.7$

$Z = 2.7$ has a pvalue of 0.9965

1 - 0.9965 = 0.0035

0.0035*100% = 0.35%

0.35% of students from this school earn scores that satisfy the admission requirement.

6 0

2 years ago