Ya sure.... What's your doubt?
Write the equation of the line perpendicular to y=5/6x+7/6 that passes through the point (-8,9) .
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{5}{6}}x+\cfrac{7}{6}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we can say that
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{5}{6}} ~\hfill \stackrel{reciprocal}{\cfrac{6}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{6}{5}}}[/tex]
so we're really looking for the equation of a line with a slope of -6/5 and that passes through (-8 , 9)
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{9})\qquad\qquad \stackrel{slope}{m}\implies -\cfrac{6}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{-\cfrac{6}{5}}(x-\stackrel{x_1}{(-8)})\implies y-9=-\cfrac{6}{5}(x+8) \\\\\\ y-9=-\cfrac{6}{5}x-\cfrac{48}{5}\implies y=-\cfrac{6}{5}x-\cfrac{48}{5}+9\implies y=-\cfrac{6}{5}x-\cfrac{3}{5}[/tex]
What is the area of this figure?
Answer:
20
Step-by-step explanation:
from the numbers i was seeing my answer is 20 i am so sorry if it not right.
h=-16t^2+320, how long will it take to hit the ground
Answer:
It will take 5 seconds
Jorge's math grade is calculated using a weighted average. Quizzes are worth 30%, homework is worth 10%, unit tests are worth 40%, and the final exam is worth 20%.
Jorge earned an average of 92% on his quizzes, 98% on his homework, 91% on his unit tests, and a score of 95% on his final exam.
What is Jorge's final math grade?
By rewriting the weights in decimal form and applying them to the correspondent percentages, we will see that the final grade is 92.8%.
What is Jore's final math grade?
The final grade will be given by:
G = a₁*x₁ + a₂*x₂ + ...
Where the values "a" are the weights, and the values "x" are the averages of Jeorge.
We know that the weights are:
30% on Quizzes.10% on homework40% on unit test.20% on the final exam.Then we can write the weights in decimal form:
a₁ = 0.3
a₂ = 0.1
a₃ = 0.4
a₄ = 0.2
And the scores are:
92% on quizzes.98% on homework91% on unit tests95% on final exam.So the final math grade will be:
G = 0.3*92 + 0.1*98 + 0.4*91 + 0.2*95 = 92.8%
If you want to learn more about percentages, you can read:
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Answer:
the answer is 92.8%
Step-by-step explanation:
What is the definition of a Pythagorean triple?
Answer:
a set of numbers that are used to find the hypotenuse
Step-by-step explanation:
brainliest
The integer solutions to the Pythagorean theorem, are called Pythagoras triples.
Definition of Pythagorean Triples:
The integer solutions to the Pythagorean theorem, [tex]a^{2} +b^{2} =c^{2}[/tex] are called Pythagorean triples which contains three positive integers a, b and c.
For example:
(3, 4, 5)
By evaluating we get
[tex]3^{2} +4^{2} =5^{2}[/tex]
⇒ 9 + 16 = 25
Hence, 3, 4 and 5 are Pythagorean triples.
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Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
20. You owe $1,568.00 on a credit card with a limit of $2,200.00 at an interest rate of 11.3% APR. You pay $300.00/month until it is paid off. How many months does it take you to pay it off?
- 6 months
- 9 months
- 4 months
- 7 months
Answer:
(a) 6 months
Step-by-step explanation:
The formula for figuring the monthly payment on an amortized loan can be used for finding the length of time it takes to pay off the loan.
That formula is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the number of years.
__
Using the given information, we can solve for t:
300 = 1568(0.113/12)/(1 -(1 +0.113/12)^(-12t))
1 -(1 +0.113/12)^(-12t) = 1568(0.113)/(12(300))
(1 +0.113/12)^(-12t) = 1 -(1568·0.113)/(12·300) ≈ 0.950782
Taking logs, we get ...
-12t·log(1 +0.113/12) = log(0.950782)
t = log(0.950782)/(-12·log(1 +0.113/12)) ≈ 0.448739 . . . . years
This fraction of a year is ...
(12 months/year)(0.448739 years) = 5.38 months
It will take you 6 months to pay off the loan.
How many distinct 3 digit code can i create such that this code is divisible by 4.
For example these codes are rejected since they have repeating numbers/less than 3 digits:
024/100/112/996/444
The other answer is just wrong.
There are 9•9•8 = 648 distinct 3-digit codes. The first digit can be any numeral from 1-9, the next digit can be any from 0-9 minus the one used in the first position, and the last digit can be any from 0-9 minus both the numerals used in the first two positions.
But that doesn't even account for the divisibility constraint.
Let the code be [tex]abc[/tex]. We can expand this as
[tex]100a + 10b + c[/tex]
In order for this to be divisible by 4, we observe that
[tex]100a + 8b + 2b + c = 4 (25a + 2b) + (2b+c)[/tex]
so we only need [tex]2b+c[/tex] to be divisible by 4.
The last digit must be even, so there are only 5 choices for the last digit. I list the possibilities and outcomes below. For some integer [tex]k[/tex], we need
[tex]c=0 \implies 2b=4k \implies b=2k[/tex]
[tex]c=2 \implies 2b+2=4k \implies b = 2k-1[/tex]
[tex]c=4 \implies 2b+4 = 4k \implies b = 2(k-1)[/tex]
[tex]c=6 \implies 2b+6 = 4k \implies b = 2k-3[/tex]
[tex]c=8 \implies 2b+8=4k \implies b = 2(k-2)[/tex]
Ignoring [tex]a[/tex] for the moment, in the cases of [tex]c\in\{0,4,8\}[/tex], [tex]b[/tex] is also even. This leaves 3 choices for [tex]c[/tex] and 2 choices for [tex]b[/tex].
Likewise, in the cases of [tex]c\in\{2,6\}[/tex], [tex]b[/tex] is odd. This leaves 2 choices for [tex]c[/tex] and 5 choices for [tex]b[/tex].
Now taking into account the choice for [tex]a[/tex], we have the following decision tree.
• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•3•3 = 18 codes.
• If [tex]a\in\{4,8\}[/tex] and [tex]c\in\{0,4,8\}\setminus\{a\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{a,c\}[/tex] - a total of 2•2•3 = 12 codes.
• If [tex]a\in\{2,6\}[/tex] and [tex]c\in\{2,6\}\setminus\{a\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a,c\}[/tex] - a total of 2•1•5 = 10 codes.
• If [tex]a\in\{4,8\}[/tex] and [tex]c \in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}[/tex] - a total of 2•2•5 = 20 codes.
• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{0,4,8\}[/tex], then [tex]b\in\{0,2,4,6,8\}\setminus\{c\}[/tex] - a total of 5•3•4 = 60 codes.
• If [tex]a\in\{1,3,5,7,9\}[/tex] and [tex]c\in\{2,6\}[/tex], then [tex]b\in\{1,3,5,7,9\}\setminus\{a\}[/tex] - a total of 5•2•4 = 40 codes.
Hence there are a total of 18 + 12 + 10 + 20 + 60 + 40 = 160 codes.
Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?
Answer:
it’s C. 2.5
Step-by-step explanation:
I will give the brainiest if you get it right.
Answer:
1 ≤ x < 7/4
Step-by-step explanation:
The function f(x) is defined as increasing on the domain (-8, 4), so the ordering of the arguments is not changed by the function. We can solve the inequality as though f(x) = x, which is increasing everywhere.
Inequality solutionsf(4x -3) ≥ f(2 -x²)
4x -3 ≥ 2 -x² . . . . . . using our assumed definition of f(x)
x² +4x -5 ≥ 0 . . . . . subtract 2-x²
(x -1)(x +4) ≥ 0 . . . . factored form; zeros at -4, +1
The values of x that make this true are ones that make the factors have the same signs: x ≤ -4 or x ≥ 1.
Domain restrictionsThe domain of f(x) is -8 < x < 4, so we require the arguments of f be restricted to those values
Left side
-8 < 4x -3 < 4
-5 < 4x < 7
-5/4 < x < 7/4
Right side
-8 < 2 -x² < 4 . . . . . right side is always true
x² < 10 . . . . . . . . . . . add x² +8
|x| < √10 . . . . . . . . . . less restrictive than the the left-side restriction
SolutionWith the given domain restrictions on f(x), the inequality will be true on the interval ...
1 ≤ x < 7/4
__
Additional comment
The attached graph shows the left-side function argument (dashed blue) and the right-side function argument (dashed green) with the given domain restrictions. The red curve is the difference in function values for the function defined as above. It is only non-negative between 1 and 1.75 as we found above.
This general behavior is applicable for any f(x) that can be described as in the problem statement. For example, f(x) = √(x+8) also gives an increasing curve for the difference f(4x-3)-f(2-x²) on the interval (-5/4, 7/4) with an x-intercept of +1.
<95141404393>
Find the quotient of 36 and -4.
The quotient of 36 and -4 is -9.
36/-4 = -9
calvin and susie baked some cookies in the ratio of 3 : 7. calvin baked 60 fewer cookies than susie. how many cookies did they bake altogether?
Answer:
Acc to ques
7x-3x = 60
x = 15
so they made total of 10x = 150
Pls show work thank you!!!
[tex]|-16-x|=0\\\\\implies -16-x = 0\\\\\implies x = -16[/tex]
True or False: In an exponential regression, the data points tend to increase in one direction and flatten out in the other direction.
Answer:
T
Step-by-step explanation:
The regression line is flat when there is no ability to predict whatsoever. The regression line is sloped at an angle when there is a relationship. The extent to which the regression line is sloped, however, represents the degree to which we are able to predict the y scores with the x scores
i need helps pls
The net of a square pyramid and its dimensions are shown in the diagram. What is the total surface area in square feet?
5,760 ft²
976 ft²
1,120 ft²
1,040 ft²
The net square pyramid and its given dimension as shown has a total surface area of 1040 ft².
How to calculate surface area of a square pyramidSurface area of a square pyramid = A + 1 / 2 ps
where
A = area of the basep = perimeter of bases = slant heightTherefore,
A = l²
where
l = length = 20 ftA = 20² = 400 ft²
p = 4l = 4 × 20 = 80 ft
s = 16 ft
Therefore,
Surface area = 400 + 1 / 2 × 80 × 16
Surface area = 400 + 1280 / 2
Surface area = 400 + 640
Surface area = 1040 ft²
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Find the average of this set of numbers.1, 9, 11, 13, 26
A) 12
B) 13
C) 14
D) none of the above
[tex]\green{ \underline { \boxed{ \sf{Average = \frac{Sum \:of \: observation}{Number \:of \: observation}}}}}[/tex]
[tex]\longrightarrow[/tex]Here, no of observation are 5
Now,
[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{1+9+11+13+26}{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf Average = \frac{60}{5} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf Average = 12 \\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]The Average of given set of numbers is 12 .
[tex]\therefore\: [/tex] Option A) is correct ✔️
Solve for b. -36 + 2.5 = 4
Answer:
False
Step-by-step explanation:
The sides are not equal
If f(x) = 2x² - 5, f(5) =
Answer:
45
Step-by-step explanation:
Put in '5' where 'x' is
2 (5)^2 - 5 = 45
What is the equation: [tex]2x^2-5[/tex]
What do we want to find: f(5)
To find f(5), we must plug the value '5'
⇒ into the 'x' position
⇒ f(x)
So: [tex]f(5) = 2(5^2)-5 = 2 * 25 - 5 = 50 -5 = 45[/tex]
Thus f(5) = 45
Hope that helps!
write the following numbers in words (1) 396 624 (2) 5 200 090 (3) 4 606 220
Answer:
1. three hundred ninety six thousand twenty four
2. five million two hundred thousand ninety
3. four million six hundred six thousand two hundred twenty
The sales tax on a table saw is $8.25.
a. What is the purchase price of the table saw (before tax) if the sales tax rate is 5.5%?
b. Find the total price of the table saw.
Answer:
a. $150
b. $158.25
Step-by-step explanation:
a.The amount of tax is the product of the tax rate and the price being taxed. This relation can let us solve for the price.
tax = tax rate × price
price = tax/(tax rate) = $8.25/0.055 = $150.00
The purchase price of the table saw is $150.00.
__
b.The total price is the sum of the purchase price and the tax.
total price = price + tax
total price = $150.00 +8.25 = $158.25
The total price of the table saw is $158.25.
Express the set using interval notation.
x≥1
Answer:
[1,∞)
Step-by-step explanation:
Brackets indicate equal to while parentheses indicate not equal to this bound.
Solve the following equation:
3 x one half
==========================================================
Let's simplify the expression:-
[tex]\bigstar{\boxed{\frac{3}{1} *\frac{1}{2}}[/tex]
Multiply 3 times 1 and 1 times 2:-
[tex]\bigstar{\boxed{\pmb{\frac{3}{2} }}[/tex]
======================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Y varies inversely as x: y=13, when x=3
Answer:
I'm not to sure of this answer
Z
77°
P
W
X
What is the measure of arc XWZ?
OA
257°
O B. 1039
O C. 206°
O D. 1543
Show that 9.1 is not a solution of the equation n-6.4 = 2.61. Then find
the solution
Answer:
The solution is 9.01.
Step-by-step explanation:
To prove that 9.1 isn't the solution we have to plug 9.1 into the equation. By replacing n with 9.1 we get 2.7 which isn't equal to 2.61.
To find the solution we must add 6.4 to both sides of the equation.
ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️
the answer is b if i remeber
Help me the question 1 in my picture
Answer:
Number 1 is b
I found the answer on a website
A wire is first bent into the shape of a triangle. Each side of the triangle is 16 long. Then the wire is unbent and reshaped into a rectangle. If the length of the rectangle is 15 in, what is its width?
Answer:
the width is 9in
Step-by-step explanation:
perimeter of triangle =3×16 = 48
let w= width of rectangle
perimeter of triangle = perimeter of rectangle
48= 2(15 +w)
24= 15 + w
w= 9
What is the value of X?
Answer:
x=7
Step-by-step explanation:
In a 45 45 90 triangle the two legs are equal so you set 33=5x-2 and then solve the equation.
A farmer wants to know how many of his cows have no spots. He has 200 cows total. He takes a random sample of 40 cows. Of these, 11 of the cows have no spots. What can the farmer predict about the entire population?
The farmer can predict that 11 cows in the entire population have no spots
The farmer can predict that 55 cows in the entire population have no spots
The farmer can predict that 40 cows in the entire population have no spots
The farmer can predict that all of the cows have no spots
Answer:
The farmer can predict that 55 cows in the entire population have no spots.
Step-by-step explanation:
The farmer can predict that 40 cows in the entire population have no spots, the correct option is C.
How to find the confidence interval for population proportion from large sample?Suppose we're given that:
Favourable Cases X (in count, in sample)
Sample Size N
Level of significance =[tex]\alpha[/tex]
Then, the sample proportion of favorable cases is:
[tex]\hat{p} = \dfrac{X}{N}[/tex]
The critical value at the level of significance[tex]\alpha is Z_{1- \alpha/2}[/tex]
The corresponding confidence interval is:
[tex]CI = & \displaystyle \left( \hat p - z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}, \hat p + z_c \sqrt{\frac{\hat p (1-\hat p)}{n}} \right)[/tex]
The given information;
The farmer took a random sample of 40 cows out of 200 total cows and found that 11 of those cows have no spots. We can use this sample data to make a prediction about the entire population using statistical inference.
Now,
Plugging in the values, we get:
CI = 0.275 ± 1.96sqrt((0.275(1-0.275))/40)
CI = 0.275 ± 0.139
CI = (0.136, 0.414)
This means that we can be 95% confident that the true proportion of cows with no spots in the entire population lies between 0.136 and 0.414.
the farmer can predict that between 13.6% and 41.4%
Therefore, by confidence interval the answer will be farmer can predict that 40 cows in the entire population have no spots
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