Answer:
11) D. y=5/2x+5/2 , 12) B. y=8/5x+69/5, 14) A. y=-9/5x-67/5
Step-by-step explanation:
11) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\perp}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\perp}[/tex] - Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
Where [tex]m[/tex] is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:
[tex]-2\cdot x - 5\cdot y = -19[/tex]
[tex]2\cdot x +5\cdot y = 19[/tex]
[tex]5\cdot y = 19 - 2\cdot x[/tex]
[tex]y = \frac{19}{5} -\frac{2}{5}\cdot x[/tex]
The original slope is [tex]-\frac{2}{5}[/tex], and the slope of the perpendicular line is:
[tex]m_{\perp} = -\frac{1}{\left(-\frac{2}{5}\right) }[/tex]
[tex]m_{\perp} = \frac{5}{2}[/tex]
If [tex]x_{o} = -3[/tex], [tex]y_{o} = -5[/tex] and [tex]m_{\perp} = \frac{5}{2}[/tex], then:
[tex]y-(-5) = \frac{5}{2}\cdot [x-(-3)][/tex]
[tex]y + 5 = \frac{5}{2}\cdot x +\frac{15}{2}[/tex]
[tex]y = \frac{5}{2}\cdot x +\frac{5}{2}[/tex]
The right answer is D.
12) The function of the parallel line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\parallel}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\parallel}[/tex] - Slope, dimensionless.
Its slope is the slope of the given, which must be transformed into its explicitive form:
[tex]-8\cdot x + 5\cdot y = 89[/tex]
[tex]5\cdot y = 89 +8\cdot x[/tex]
[tex]y = \frac{89}{5}+\frac{8}{5} \cdot x[/tex]
The slope of the parallel line is [tex]\frac{8}{5}[/tex].
If [tex]x_{o} = -8[/tex], [tex]y_{o} = 1[/tex] and [tex]m_{\parallel} = \frac{8}{5}[/tex], then:
[tex]y-1 = \frac{8}{5}\cdot [x-(-8)][/tex]
[tex]y-1 = \frac{8}{5}\cdot x +\frac{64}{5}[/tex]
[tex]y = \frac{8}{5}\cdot x +\frac{69}{5}[/tex]
The correct answer is B.
14) The function of the perpendicular line can be found in terms of its slope and a given point by this formula:
[tex]y-y_{o} = m_{\perp}\cdot (x-x_{o})[/tex]
Where:
[tex]x_{o}[/tex], [tex]y_{o}[/tex] - Components of the given point, dimensionless.
[tex]m_{\perp}[/tex] - Slope, dimensionless.
Besides, a slope that is perpendicular to original line can be calculated by this expression:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
Where [tex]m[/tex] is the slope of the original line, dimensionless.
The original slope is determined from the explicitive form of the given line:
[tex]-5\cdot x +9\cdot y = 49[/tex]
[tex]9\cdot y = 49+5\cdot x[/tex]
[tex]y = \frac{49}{9} +\frac{5}{9}\cdot x[/tex]
The original slope is [tex]\frac{5}{9}[/tex], and the slope of the perpendicular line is:
[tex]m_{\perp} = -\frac{1}{m}[/tex]
[tex]m_{\perp} = -\frac{1}{\frac{5}{9} }[/tex]
[tex]m_{\perp} = -\frac{9}{5}[/tex]
If [tex]x_{o} = -8[/tex], [tex]y_{o} = 1[/tex] and [tex]m_{\perp} = -\frac{9}{5}[/tex], then:
[tex]y-1 = -\frac{9}{5}\cdot [x-(-8)][/tex]
[tex]y-1 = -\frac{9}{5}\cdot x-\frac{72}{5}[/tex]
[tex]y = -\frac{9}{5}\cdot x -\frac{67}{5}[/tex]
The correct answer is A.
Triangle ABC has vertices A(4,8) B(-3,2) and C(-1,6). Triangle ABC is dilated so that the new vertices are A'(12,24) B'(-9,6) and C'(-3,18). What is the scale factor?
Name one pair of rays that are not opposite rays.
Answer:
ED and EC
Step-by-step explanation:
If the two rays which extend in the opposite direction having same endpoint is said to be opposite rays.
From the picture attached,
Rays having same endpoint E but not in the opposite directions are ED and EC.
This pair of rays meet at point E having different directions.
Similarly EA and EB is the other pair of rays having same end point (at E) but not in opposite directions.
Figure A was translated 5 units left to create Figure B.
Figure B was reflected over the line y=1 to create Figure
C. Figure C was rotated 90 degrees clockwise around
the origin to create Figure D. Are Figure A and Figure D
congruent?
А A
Prove your answer using any tools and explain
reasoning in the box below:
10
Answer:
a
Step-by-step explanation:
Please Help Brainliest to whoever can give a clear explanation for this problem!
In triangle ABC, [tex] \angle A = 90 [/tex], AC = 1, and AB = 5. Point D lies on ray AC such that [tex]\angle DBC = 2\angle CBA[/tex]. Compute AD.
See the attached sketch. Let [tex]\beta[/tex] denote angle ABC and [tex]\beta'[/tex] denote angle CBD. Then [tex]\beta'=2\beta[/tex].
From the sketch, we see that
[tex]\tan\beta=\dfrac15[/tex]
[tex]\tan(\beta+\beta')=\tan(3\beta)=\dfrac{AD}5[/tex]
Write [tex]\tan(3\beta)[/tex] in terms of [tex]\tan\beta[/tex]. Recall the angle sum identity for tangent:
[tex]\tan(x+y)=\dfrac{\tan x+\tan y}{1-\tan x\tan y}[/tex]
This gives us
[tex]\tan(3\beta)=\dfrac{\tan\beta+\frac{2\tan\beta}{1-\tan^2\beta}}{1-\tan\beta\cdot\frac{2\tan\beta}{1-\tan^2\beta}}=\dfrac{\tan\beta(\tan^2\beta-3)}{3\tan^2\beta-1}[/tex]
and plugging in [tex]\tan\beta=\frac15[/tex] leaves us with
[tex]\tan(3\beta)=\dfrac{37}{55}[/tex]
and so AD = 5 * 37/55 = 37/11.
What are the roots of the equation? x² + 3x - 18 = 0
Answer:
[tex]x[/tex] = -6
[tex]x[/tex] = 3
Step-by-step explain
[tex]x^{2}[/tex] = 3[tex]x[/tex] - 18 =0
[tex]x^{2}[/tex] =6[tex]x[/tex] - 3[tex]x[/tex] - 18 = 0
[tex]x[/tex] x ([tex]x[/tex] + 6) -3[tex]x[/tex] - 18 = 0
[tex]x[/tex] x ([tex]x[/tex] + 6) - 3([tex]x[/tex] = 6)=0
([tex]x[/tex] = 6) x ([tex]x[/tex] 3) = 0
[tex]x[/tex] +6 = 0
[tex]x[/tex] - 3 = 0
[tex]x[/tex] = -6
[tex]x[/tex] = 3
Square root of 9610 by division method
Answer:98.03060747
Step-by-step explanation:
Square root 9610
What is the value of the expression below when y = 7?
y2+ 5y + 6
90
Plug in 7 for x and solve.
[tex]{y}^{2} + 5y + 6[/tex]
[tex]{(7)}^{2} + 5(7) + 6[/tex]
[tex]49 + 35 + 6[/tex]
[tex]90[/tex]
What is the equation for g, which is f(x) = 2x2 + 3x − 1 reflected across the y-axis? Group of answer choices g(x) = −2x2 − 3x − 1 g(x) = 2x2 + 3x − 1 g(x) = −2x2 − 3x + 1 g(x) = 2x2 − 3x − 1
Answer:
[tex]g(x) = 2x^2 - 3x - 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x^2 + 3x - 1[/tex]
Required
Determine g(x), if f(x) is reflected across the y axis
When a function (x,y) is reflected across the y axis, the new function becomes (−x,y).
In other words,
[tex]g(x) = f(-x)[/tex]
Calculating f(-x)
[tex]f(-x) = 2(-x)^2 + 3(-x) - 1[/tex]
[tex]f(-x) = 2x^2 - 3x - 1[/tex]
Substitute g(x) for f(-x)
[tex]g(x) = 2x^2 - 3x - 1[/tex]
Hence;
[tex]g(x) = 2x^2 - 3x - 1[/tex]
what is the decimal that is greater than 3/10 and less than 2/5
Answer:
0.31 - 0.39
Step-by-step explanation:
3/10 = 0.3
2/5 = 0.4
All the values between 0.3 and 0.4 excluding 0.3 and 0.4 (can't be 0.3 or 0.4)
The decimal number that is greater than 3/10 and less than 2/5 will be;
⇒ 0.35
What is Decimal number?A decimal number is a number that consists of a whole and a fractional part.
Given that;
A decimal number is greater than 3/10 and less than 2/5.
Now,
Let a decimal number = x
So, We get;
⇒ 3/10 < x < 2/5
Since, We have;
⇒ 3/10 = 0.3
⇒ 2/5 = 0.4
Thus, The decimal number that is greater than 3/10 and less than 2/5 is 0.35.
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What’s 13/19 as a decimal rounded to the nearest hundredth?
Answer:
0.68
Step-by-step explanation:
We can use long division to find the decimal equivalent of [tex]\frac{13}{19}[/tex] since a fraction is just another way of writing a division statement.
[tex]19\overline{\smash{)}#13}\\\\0.\\19\overline{\smash{)}#130}\\\\0.6\\19\overline{\smash{)}#130-114=16}\\\\0.6\\19\overline{\smash{)}#160}\\\\0.68\\19\overline{\smash{)}#160-152 = 8}\\\\0.68\\19\overline{\smash{)}#80}\\\\0.684\\19\overline{\smash{)}#80}[/tex]
0.684 to the nearest hundredth is 0.68.
Hope this helped!
Write an equation in slope-intercept form of the line with slope 3 that contains the point (1, 2).
Answer:
Step-by-step explanation:
y - 2 = 3(x - 1)
y - 2 = 3x - 3
y = 3x - 1
Tim has a bag of 36 orange-flavored sweets and Peter has a bag of 44 grape-flavored sweets. They have to divide up the sweets into small trays with equal number of sweets; each tray containing either orange-flavored or grape-flavored sweets only. If there is no remainder, find the largest possible number of sweets in each tray.
Answer:
Largest possible number of sweets in each tray[tex]=4[/tex]
Step-by-step explanation:
Given:
Number of orange-flavored sweets = 36
Number of grape-flavored sweets = 44
To find: largest possible number of sweets in each tray
Solution:
HCF(highest common factor) of two or more numbers refers to the greatest number which can divide the given numbers
To find largest possible number of sweets in each tray, find the HCF(highest common factor) of 36 and 44.
[tex]36=2^{2}\times 3^{2}\\44=2^{2}\times 11[/tex]
So,
[tex]HCF(36,44)=2^{2}=4[/tex]
So,
Largest possible number of sweets in each tray[tex]=4[/tex]
The largest possible number of sweets in each tray is 4.
In order to determine the largest possible sweets in each tray, the highest common factor of the number of sweets have to determined. The highest common factor is the highest factor that is common to two or more numbers.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 44 = 1, 2, 4, 11, 22, 44.
Common factors = 1, 2, 4
Highest common factor - 4
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If you add two negative integers, what will the sign on the sum be? Explain.
Answer:
Negative
Step-by-step explanation:
If both are negative, they can't grow when you add them. If I owe someone 3 dollars, then I owe them 3 more, I don't owe them 0, I owe them 6. The equation would be My amount of money-3-3
Which of the following measures of central tendency are resistant to outliers? (May be more than one correct answer) Group of answer choices Median Mode Mean Range Inter-quartile Range (IQR) Standard Deviation
Answer
Median
Step-by-step explanation:
It should be noted that medians are resistant to outliers.
Outliers simply means the data records which are different from every other record. It escapes normality. The outlier affects mean, inter-quartile range, mode and the range.
It should be noted that the median isn't affected by outliers. The reason for this is that the median depends on the arrangement and the order of the data. For example, when one changes the lowest score in a given set of numbers, the order won't be affected.
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you deposit $3000 into an account that pays 8% compounded quarterly. how much will you have in 10 years?
Answer:
$5400 USD
Step-by-step explanation:
Investment=3,000
Interest=8% = .08
Time=10 years
([3000 x .08 x 10] + 3,000
[240 x 10] + 3,000
2,400 + 3,000= 5,400
Manny is participating in a Bike-a-thon and travels at a constant rate of 6 miles in 20 minutes.
Manny rode his bike for 3 hours. How far did he travel?
Manny rode his bike for 1.5 hours. How far did he travel?
I will give 20 extra points for you <3
Answer:
1. 54
2.?
Step-by-step explanation:
:) Have a nice day
whats the answer 5(x-y+2)
whats the answer 5(x-y+2)
Answer :
5x - 5y + 10
Step-by-step explanation:
5(x - y + 2)
5(x) + 5( - y) + 5(2)
5x - 5y + 10
[tex]\boxed{\boxed{\bold{THANKS}}} [/tex]
I need help asap please! <3
please help ill give 10 points and a brainly to who ever who can answer this. thanks!!!
Answer:
Step-by-step explanation:
Express 0.1 as a fraction.
Step-by-step explanation:
Write 0.1 as
0.1
1
Multiply both numerator and denominator by 10 for every number after the decimal point
0.1 × 10
1 × 10
=
1
10
Reducing the fraction gives
1
10
In fraction form the number 0.1 can be written as 1/10.
Use the concept of fraction defined as:
A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p/q.
The given number is: 0.1
Since the given number is a decimal number,
And it has only in digit after decimal.
Therefore,
Divide and multiply by 10 with this number,
[tex]0.1 \times \dfrac{10}{10} = \dfrac{1}{10}[/tex]
Hence,
The fraction from of the number 0.1 is 1/10
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A triangle has side lengths of (5.3p+ 7.6) centimeters, (3.8p – 4.3) centimeters,
and (2.4q - 7.4) centimeters. Which expression represents the perimeter, in
centimeters, of the triangle?
Answer:
The perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres
Step-by-step explanation:
Let a, b and c be the sides off a triangle. Its perimeter P = a + b + c.
Now, the triangle has side lengths (5.3p+ 7.6) centimetres, (3.8p – 4.3) centimetres, and (2.4q - 7.4) centimetres.
Let a = (5.3p+ 7.6) cm , b = (3.8p – 4.3) cm and c = (2.4q - 7.4) cm
So the perimeter of the triangle is P = a + b + c
substituting the values of a, b and c, we have
P = (5.3p + 7.6) cm + (3.8p – 4.3) cm + (2.4q - 7.4) cm
opening the brackets and collecting like terms, we have
P = (5.3p + 3.8p + 2.4q + 7.6 - 4.3 - 7.4) cm
P = (9.1p + 2.4q - 4.1) centimetres
So the perimeter of the triangle in centimetres is (9.1p + 2.4q - 4.1) centimetres
I know it’s a lot but I’m pretty stupid and could use help online class ain’t easy when you’re internet sucks thanks!
Problem 5
There are 2 answers and they are choice B and choice C
We can tell by looking at the factors. For something like choice B, the factor (x+6) shows up twice, so that means x = -6 is a double root. Something like choice A has roots x = -6 and x = 6 which aren't the same.
========================================
Problem 6
Ted is correct. He set each factor equal to 0 and solved each equation that resulted from doing so.
Note how 3x-2 = 0 turns into 3x = 2 after adding 2 to both sides. Then he divided both sides by 3 to get x = 2/3. That's the first solution. The second solution x = -5 results from solving x+5 = 0. You subtract 5 from both sides.
To fix Maggie's mistake, you just need to correct her steps to mirror Ted's steps.
20=v−7 what does v equal?
Answer:
27
Step-by-step explanation:
20=v-7
v=20+7
v=27
Hence, v equals to 27
[tex]\huge\mathbb\purple{EXPLAIN}[/tex]
[tex]20 = v - 7[/tex]
[tex]v = 20 + 7 = 27[/tex]
PLZ HELP 235 people are at RSM summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answer:
number of girls = 90
Number of boys = 125
Number of adults = 20
Step-by-step explanation:
Total people at the summer camp= 235
Let
number of girls=x
Number of boys = x + 35
Number of adults = x - 70
Total people at the summer camp= number of girls + Number of boys + Number of adults
235 = x + (x+35) + (x - 70)
235 = x + x + 35 + x - 70
235 = 3x - 35
Add 35 to both sides
235 + 35 = 3x
270 = 3x
Divide both sides by 3
x= 270/3
= 90
x = 90
number of girls= x = 90
Number of boys = x + 35
= 90 + 35
= 125
Number of adults = x - 70
= 90 - 70
= 20
Total = 90 + 125 + 20
= 235
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20
Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter. They bought 7 loaves of bread. Each loaf had 18 slices of bread. The boys used up all the bread to make the sandwiches. They used 2 slices to make each sandwich. How many sandwiches did they make for the shelter?
Answer:
63 sandwiches
Step-by-step explanation:
Pete and his friend Danny volunteered to bring sandwiches for lunch at a homeless shelter
They brought 7 loaves of bread
Each loaves have 18 slices
They used 2 slices each to make the sandwich
The first step is to calculate the total number of slices
Sinces 7 loaves of bread are used and each of them contain 18 slices then, the total number of slices can be calculated as follows
= 7 ×18
= 126 slices
Therefore since 2 slices of bread is used to make one sandwich then, the number of sandwiches that was made can be calculated as follows
= 126/2
= 63
Hence 63 sandwiches were made for the shelter
What is Uche's pumping rate in \dfrac{\text{mL}}{\text{s}} s mL start fraction, start text, m, L, end text, divided by, start text, s, end text, end fraction?
Step-by-step explanation:
Pumping rate my be defined as the the rate ta which a liquid is pumped through a system. It is measured as the flow of the liquid at a unit time. It may be referred to as the capacity of the pump which defines how much liquid is being passed through the pump in a certain given time.
The pumping rate in mL/s refers to the amount of liquid passed in one second of time.
a2+ 12a− 7 − 3a2− 5a+ 8
Using four or more complete sentences, contrast race and ethnicity and provide an example of each.
Answer:
Race and Ethnicity are considered to be social constructs that enable humans to be grouped or categorized. They are sometimes used interchangeably but most argue that they are different and give them different definitions.
Race is generally used to refer to people that have the same physical characteristics such as skin color or the same texture of hair for instance Black and White/Caucasian.
Ethnicity on the other hand relates to people sharing a common culture, language, nation, and/ or tribal heritage for instance, the English, the Irish and the Igbo.
Answer:
The terms race and ethnicity are often used interchangeably throughout society. However, there is a distinct difference between the two. Race refers to a classification system based on inherited physical or biological traits, such as eye, hair, or skin color. In contrast, ethnicity refers to a group of people that can be linked together by common characteristics such as shared experiences, history, culture, or beliefs. Examples of ethnic groups include Native Americans, French Canadians, and Kongos.
Step-by-step explanation:
(edg2020)
Given the polynomial 21x^4+3y-6x^2+34 1. What polynomial must be subtracted from it to obtain 29x^2-7? 2. What polynomial must be added to it to obtain a first degree polynomial?
Answer:
[tex]21x^4+3y-35x^2+41[/tex] must be subtracted
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)
Step-by-step explanation:
We have the following polynomial
[tex]21x^4+3y-6x^2+34[/tex]
And need to find a polynomial to subtract from it to get
[tex]29x^2-7[/tex]
This means that if we subtract these two polynomials, we will get our desired polynomial
[tex]21x^4+3y-6x^2+34-(29x^2-7)\\\\21x^4+3y-6x^2+34-29x^2+7\\\\21x^4+3y-35x^2+41[/tex]
Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found
[tex]21x^4+3y-6x^2+34-(21x^4+3y-35x^2+41)\\\\21x^4+3y-6x^2+34-21x^4-3y+35x^2-41\\\\-6x^2+34+35x^2-41\\\\29x^2-7[/tex]
As we got the desired result, we know that this answer is correct.
And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?
Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.
This means that our desired polynomial needs to only have some amount of x's and constants.
We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2
[tex]21x^4+3y-6x^2+34-(x-2)\\\\21x^4+3y-6x^2+34-x+2\\\\21x^4+3y-6x^2-x+36[/tex]
As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)
(-2, 8) (9, 10) (1,7) (3, 9) (10, 12)
Function
Not a Function
Answer: function
Step-by-step explanation: To determine whether the relation shown here
is a function, remember that a relation is a function if each x term
corresponds to exactly one y term.
In the data set show, each x term, -2, 9, 1, 3, and 10 appears only once.
This means that each x term corresponds to exactly one y term.
So yes, the relation is a function.