Answer:
[tex]y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
Step-by-step explanation:
The genera slope-intercept equation of a line is
y = mx + 8 where m is the slope and b the y-interecept
A perpendicular line will have a slope = -1/m ie the negative of reciprocal of the first line such that m x (-1/m ) = -1
The equation of the tangent line is
3x + 2y = 28.
1. Convert to slope-intercept form:
Subtract 3x from both sidesSo slope = -3/2
Reciprocal of -3/2 = -2/3
Negative of reciprocal = +2/3
Slope of a perpendicular line should be -1/3 and the resultant equation of the line(the support arm) should be:
y = (2/3)x + b
To calculate b for the complete line equation plug in the point B(4, 8) and solve for B
y = 8 when x = 4
=> 8 = (2/3)(4) + b
Switch sides: (does not change any signs)
8/3 + b = 8
Subtract 8/3 on both sides
b = 8 - 8/3
b = 24/3 - 8/3
b = 16/3
So equation of the support arm is
[tex]\boxed{y = \dfrac{2}{3}x + \dfrac{16}{3}}[/tex]
solve using distributive property ASAP
8(x+2)
The equation 8(x+2) can be expressed using the distributive property as 8x + 16.
What is distributive property?The distributive property can be described as the as the multiplication system of solving a particular expressions easily through the process of distributing another number within the given brackets.
The expression that was given as 8(x+2) , if it so be solved using the distributive property the we will have 8x + 16 because this result means that it has been shared in to part, because the multiplication operation has been performed on the given expression.
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In exercises 11-14 ,find m<1,m<2, and m<3.explain your reasoning ?
The measure of angles 1, 2, and 3 in exercise 11. are 100°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 12. are 47°, 133°, and 47°.
The measure of angles 1, 2, and 3 in exercise 13. are 80°, 80°, and 100°.
The measure of angles 1, 2, and 3 in exercise 14. are 94°, 86°, and 94°.
For 11. part:
Considering a transversal p that cuts two parallel lines l and m,
Each pair of internal angles on the same side of a transversal that intersects two parallel lines are supplementary.
m∠1 + 80° = 180°
m∠1 = 180° - 80°
m∠1 = 100°
Similarly, m∠1 + m∠2 = 180°
⇒ 100° + m∠2 = 180°
⇒m∠2 = 180° - 100°
⇒m∠2 = 80°
and also, m∠2 + m∠3 = 180°
⇒ 80° + m∠3 = 180°
⇒m∠3 = 180° - 80°
⇒m∠3 = 100°
Therefore, m∠1 = 100°, m∠2 = 80° and m∠3 = 100°.
For 12. part:
m∠3 + 133° = 180°(interior angles are supplementary)
m∠3 = 180° - 133°
⇒m∠3 = 47°
m∠2 = 133°(alternate interior angles)
The angle vertically opposite to 133° would also be 133°.
So, 133° + m∠1 = 180°( interior angles are supplementary)
m∠1 = 47°
Therefore, m∠1 = 47°, m∠2 = 133° and m∠3 = 47°.
For 13. part:
m∠3 = 100° (vertically opposite angle)
Let's assume the angle adjacent to ∠3 is x.
m∠3 + m ∠x = 180° (Linear pair property)
100° + m ∠x = 180°
m ∠x = 180° - 100°
m ∠x = 80°
Therefore, m∠1 = m∠2 = m ∠x = 80°(Corresponding angles are equal.)
For 14. part:
m∠1 + 86° = 180°(co-interior angles are supplementary)
m∠1 = 180°- 86° = 94°
The angle vertically opposite to m∠1 is also equal to 94°.
94° + m∠1 = 180°(co-interior angles are supplementary)
m∠2 = 86°
Similarly, the angle vertically opposite to m∠2 is also equal to 86°.
86° + m∠3 = 180°(co-interior angles are supplementary)
m∠3 = 94°
Therefore, m∠1 = 94°, m∠2 = 86° and m∠3 = 94°.
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How many
inches are in 3.5 miles
Answer:
221 760 inches
Step-by-step explanation:
So, 3.5miles * 63360= 221760 inches.
Formula: multiply the value in miles by the conversation factor '63360'.
PLS ANSWER THIS MATH PROBLEM!!
Answer:
48[tex]units^{2}[/tex]
Step-by-step explanation:
(1 point) Find the slope of the line containing the points f(-3) = 9 and f(9) = -10.
The most appropriate choice for slope of a line will be given by-
Slope of the line = [tex]\frac{-19}{12}[/tex]
What is slope of a line?
At first it is important to know about line.
Line is a geometrical object that has only length but no breadth and no height.
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta\\[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by
m = [tex]tan\theta[/tex]
If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex]) , then
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]x_1 = -3, y_1 = 9. x_2 = 9, y_2 = -10[/tex]
Slope = [tex]\frac{-10 - 9}{9 - (-3))}[/tex]
= [tex]\frac{-19}{12}[/tex]
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Find the sample standard deviation.
15 42 53 7 9 12 14 28 47
The answer to your question is s. sqrt (316.9) = 17.8 when you take the square root of that number. As a result, the correct response is 17.8.
This is further explained below.
What is the sample standard deviation?Generally, Because you need to calculate the sample standard deviation to answer the question, use the following formula:
[tex]s = \sqrt {{ \sum of x - \bar x}{(n - 1} }[/tex]
There are 9 numbers, there, so n - 1 = 8
find the mean
[tex]\bar x[/tex]: 15 + 42 + 53 + . . . + 47 = 227. 227 / 9
x= 25.2
After that, deduct one from each number and then square the output, as seen here:
(15 - 25.2) = 104.0 (42 - 25.2)²
= 282.2 (53 - 25.2)²
= 772.8
After that, total up all of those values. The response to this, using this illustration as an example, is
[tex]x=\frac{ 2,535.2}{ 8}[/tex]
x= 316.9.
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The balance on a credit card, that charges a 15.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Enter
4
Finance charge = $93.00
What is finance charge of credit card?The interest you'll pay on a loan is defined as a finance charge, and it's most commonly used in the context of credit card debt. A financing fee is computed by taking your annual percentage rate, or APR, the amount you owe, and the time period into account.
Given that,
Interest rate = 15.5%
Date: 1-3 (3 days)
Average daily balance = amount paid × days
= $200 × 3 = $600
Date: 4-20 (17 days)
Average daily balance = amount paid × days
= $300 × 17 = $5100
Date: 21-30 (10 days)
Average daily balance = amount paid × days
= $150 × 10 = $1500
So, total average daily balance for the month
= $(600+5100+1500)
= $7200
Now, the finance charge = $7200 × (15.5÷12)
= $93.00
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equations with parenthesis
Answer:b=6
Step-by-step explanation:
A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 153 yellow peas.
a. Construct a 90% confidence interval to estimate of the percentage of yellow peas.
b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow?
a) The 90% confidence interval to estimate the percentage of yellow peas is (23.09%, 29.03%.)
b) Based on the confidence interval, the results of the experiment do not appear to contradict the expectation that 25% of the offspring peas would be yellow.
Given:
Confidence level,c = 90% = 0.90
Number of successes, x = 153
Sample size,n = 434 + 153 = 587
a) The sample proportion is the number of successes divided by the sample size is,
p = x/n
p = 153/587
p ≅ 0.2606
For confidence level 1 - α = 0.90, determine [tex]z_{\alpha /2} = z_{0.05}[/tex] utilizing the normal probability table in the appendix
[tex]z_{\alpha /2} = 1.64[/tex]
The margin of error is calculated as:
[tex]E = z_{\alpha /2} \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]E = 1.64\sqrt{\frac{0.2606(1 -0.2606)}{587} }[/tex]
E ≅ 0.0297
Therefore, the boundaries of the confidence interval are:
p - E = 0.2606 - 0.0297 = 0.2309 = 23.09%
p + E = 0.2606 + 0.0297 = 0.2903 = 29.03%
We are 90% confident that the true percentage of yellow peas is between 23.09% and 29.03%.
b) As 25% is between 23.09% and 29.03%, and 25% of the offspring are expected to be yellow peas and thus the results do not contradict expectations.
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What is the slope of the line represented by the equation 2x+3y=-12
Answer:
-2/3
Step-by-step explanation:
I graphed it
Write an equation in slope-intercept form for the line with slope -4/3 and y-intercept 3
I got that but I’m not sure if it’s right.
Answer:
[tex]y=-\frac{4}{3}x+3[/tex]
A set of average city temperatures in April are normally distributed with a mean of 19.7 Celsius in a standard deviation of two Celsius the average temperature of Kabul is 15 Celsius what proportion of the average city temperatures are lower than that of Kabul?
Answer:
There is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Step-by-step explanation:
In this question, we are to calculate the proportion of average city temperatures lower than that of Kabul.
Firstly, we shall calculate the z score
Mathematically;
z = (value - mean)/standard deviation = 15 - 19.7/2 = -4.7/2 = -2.35
so we are to calculate the probability of; P(z< -2.35) = 0.0094
This means there is a proportion of 0.94% cities with average city temperatures lower than that of Kabul
Pls help with number 20
The lengths 8 cm, 14 cm, 15 cm can form a triangle
Explanation:Given 8 cm, 14 cm, 15 cm
These can form a triangle if the sum of any two sides of the triangle is greater than the third side.
8 + 14 > 15
14 + 15 > 8
8 + 15 > 14
Since all the above are true, we conclude that they can form a triangle
f(x) = 8x + 1, g(x) = 4x - 2
Find (fg)(x).
f(g(x)) for the given equation f(x)=8x+1 and g(x)=4x-2 is 32x-15 using substitution method of solving the equation.
What is equation?An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. It is a formula that expresses the connection between two expressions on each side of a sign.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
given,
f(x)=8x+1
g(x)=4x-2
f(g(x))=8(4x-2)+1
=32x-16+1
f(g(x))=32x-15
Hence, this is required f(g(x)) for the given two equations.
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Multiply using the FOIL method.
(8z + 7)(9z-1)
Answer: [tex]72z^{2} +55z-7[/tex]
Step-by-step explanation:
We multiply each component with each other:
8z * 9z = 72z^2
8z * -1 = -8z
9z * 7 = 63z
7 * -1 = -7
We then add it all together, 63z + -8z = 55z and get
[tex]72z^{2} +55z-7[/tex]
May I please get help with this. For I have tried multiple times but still could not get the correct answers for them or even plot it on the graph 90 degrees clockwise
To rotate the figure 90 degrees clockwise about a point, every point (x, y) will rotate to (y, -x):
[tex](x,y)\to(y,-x)[/tex]The vertices of the triangle have the following coordinates:
[tex]\begin{gathered} 1=(-5,-1) \\ 2=(-1,-2) \\ 3=(-3,-4) \end{gathered}[/tex]Applying the transformation rule, we have the new coordinates to be:
[tex]\begin{gathered} 1\to(-1,-(-5))=(-1,5) \\ 2\to(-2,-(-1))=(-2,1) \\ 3\to(-4,-(-3))=(-4,3) \end{gathered}[/tex]The transformed image is shown below (the black triangle):
(-35) divided by 7 =?
Answer:
-5
Step-by-step explanation:
Answer: -5
Step-by-step explanation: -35 divided by 7 is -5
can someone help me on this
Answer:
The best estimate for the correlation coefficient is .85.
Find the area of a triangle bounded by the
y
axis, the line
f
(
x
)
=
4
−
1
5
x
, and the line perpendicular to
f
(
x
)
that passes through the origin.
The area of a triangle bounded by the region will be 11.95 sq. units.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
It is given that,
y = f(x) = 7- (4/5)x
Slope,m = -4/5
The slope of the perpendicular lines is,
[tex]\rm m_p = \frac{-1}{\dfrac{-4}{5}} \\\\ m_ p = \dfrc{5}{4}[/tex]
The equation of the perpendicular line passing through the origin is
[tex]\rm y = \frac{5}{4} x[/tex]
The equation can be written as,
[tex]\rm \frac{5}{4} x = 7 - \frac{4}{5} x \\\\ 25 x = 140 - 16 x \\\\ 41x = 140 \\\\ x = \dfrac{140}{41} \\\\ y = \frac{175}{41}[/tex]
As a result, the y-intercept of the line is,
[tex]\rm y =7- \dfrac{4}{5}x \\\\ y= 7[/tex]
The triangle is bounded by the points (0,0), (0,7), and (140/41, 175/41)
The area of the triangle is,
[tex]\rm A= \frac{1}{2} \times 7 \times \dfrac{140}{141} \\\\ A = 11.95 \ sq. unit[/tex]
Thus, the area of a triangle bounded by the region will be 11.95 sq. unit.
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Is 47/8 less then 23/4
Answer:
no
Step-by-step explanation:
Generally you can't really compare two functions with a different denomination, and you want to multiply the fractions by some fraction: [tex]\frac{a}{a}[/tex] which simplifies to one so we're not changing the value of the fraction at all but it helps so we have the same denominator.
You'll notice we can multiply 4 by 2 to get 8, which would give us the same denominator as 8.
[tex]\frac{23}{4}*\frac{2}{2}=\frac{46}{8}[/tex]
Now it's much easier to compare: [tex]\frac{47}{8}\text{ and }\frac{46}{8}[/tex] and here all we have to compare is the numerators, and obviously 47 is greater than 46 so the 47/8 is greater than the 23/4. This means 47/8 is not less than 23/4
Can somebody help me with this please ?
The correct answer is option d, output = 6 - input using coordinate geometry.
What is coordinate geometry?In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
From the graph, we can see that the coordinates have the values
For x = 1, y = 5
For x = 2, y = 4
For x = 3, y = 3
For x = 4, y = 2
Hence, we can conclude that the output (y) = 6 - input (x)
The correct option is (d) output = 6 - input.
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If the ratio of red objects to blue objects is 3 : 1, what precent of the objects are red?
Answer:
75%
Step-by-step explanation:
If the ratio of red:blue is 3:1, then there are 4 (some multiple of 4) in all.
The ratio of red:total is 3:4
3/4 is .75, times by 100 to convert to a percent.
.75 × 100 is 75%
Which value of xis in the domain of f(x) = √x – 7?
We are looking for values of x that will not make the equation undefined .Obviously the function has restrictions we have to make sure that x-7 is always ≥0 because it is under a square root
[tex]x-7\geq 0\\x\geq 7[/tex]
The domain of the function is all the real numbers greater or equal to 7 .
x≥7 ε R
A rental car agency charges $240.00 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $477.50
Answer: 950
Step-by-step explanation:
$477.50 - $240.00 = 237.50
$237.50 / $0.25 = 950
Kari wins 1,282 tickets at an arcade. For each group of 65 tickets, she will receive a prize. Kari solves the problem 1,282 ÷ 65 and determines that she has enough tickets right now for 19 prizes. What is the least number of additional tickets that Kari needs to win to have enough tickets for a 20th prize?and i need a step by step explanation.
Answer:
18 more tickets
Step-by-step explanation:
What we know:
We know that 65 Tickets is 1 Prize.
We know we have 1,282 tickets.
So if 65 tickets is one prize
then to figure out how many for twenty then we:
65 x 20 = 1300
Now to figure out how many more she needs at the least we:
1300 - 1282 = 18
So for 1 more prize she needs 18 more tickets.
If AC=19 and BC=7, find the length of AB.
what is the equation of a line that goes through the points 2, -2 and 0,2
it is vital that we first find the gradient/slope between the points .
⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{2-(-2)}{0-2} \\m=\frac{4}{-2} \\m=-2[/tex]
The general equation of a straight line is given by y=mx+c I will use the points (0,2) to find the value of y since the other variables are found already.
[tex]2=-2(0)+c\\\\c=2[/tex]
⇒This tells us that the equation of the line is y=-2x+2
What 2 2/4 x 3 5/6
I need an answer quick because i need this answer.
[tex] \frac{10}{4} \times \frac{23}{6} \\ = \frac{230}{24} \\ = \frac{115}{12} \\ = 9 \frac{7}{12} [/tex]
ATTACHED IS THE SOLUTION
The point Q lies on the segment PR.
Find the coordinates of Q so that PQ is
Check
17/0 of PR.
P(-3,4)
Coordinates of Q: D
Q (?, ?)
R (24,-32)
X
Save For Later
Submit
Answer:
Step-by-step explanation:
it would be 42,32 i know
help meeeeeeeeee
12 Answer:
Evaluate the expression: 8-6+4
13 Answer:
Evaluate the expression: 16÷(4-2)-3
14 Answer:
Check whether the given number is a solution of the equation:
3x + 5 = 17; x=2
a. solution is correct
b. solution is incorrect
15 Answer:
Check whether the given number is a solution of the equation:
4y - 7 = 3y - 4; y=3
a. solution is correct
b. solution is incorrect
16 Answer:
Check whether the given number is a solution of the inequality:
2m - 3 < 4; 2
a. number is a solution
b. number is not a solution
17 Answer:
Check whether the given number is a solution of the inequality:
5 + 2n ≥ 12; 0
a. number is a solution
b. number is not a solution
Answer:
Step-by-step explanation:
13) 8 - 6 + 4 = 2 + 4 = 6
14) 16÷(4-2)-3 = 16÷2 - 3 = 8 - 3 = 5
15) 3x + 5 = 17
3x = 17 - 5
3x = 12
x = 4 ≠ 2
b. solution is incorrect
16)4y - 7 = 3y - 4
4y - 3y = -4 + 7
y = 3
a. solution is correct
17) 2m - 3 < 4
2m < 4 + 3
2m < 7
m < 3.5
2 < 2.5, so a. number is a solution
18 ) 5 + 2n ≥ 12
2n ≥ 12 - 5
2n ≥ 7
n ≥ 3.5
0 is not greater than equal to 3.5, so b. number is not a solution