Given:
y varies directly with x,
It is given that y = 7 when x = -9.
To find:
The value of y when x = 27 for the direct variation.
Solution:
It is given that y varies directly with x, so
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
It is given that y = 7 when x = -9. Putting these values in (i), we get
[tex]7=k(-9)[/tex]
[tex]-\dfrac{7}{9}=k[/tex]
Putting [tex]k=-\dfrac{7}{9}[/tex] in (i), we get
[tex]y=-\dfrac{7}{9}x[/tex]
Putting [tex]x=27[/tex], we get
[tex]y=-\dfrac{7}{9}(27)[/tex]
[tex]y=-21[/tex]
Therefore, the required value is [tex]y=-21[/tex].
if U= {1,2,3,4,5,6}, A ={1,2,3,}
B={2,3,5},and C ={4,5,6}
find (AUB)'n c
======================================================
Explanation:
A = {1,2,3}
B = {2,3,5}
A u B = {1,2,3,5}
The set A u B consists of anything in either set A or set B. This is a set union.
The complement of this is the complete opposite. So we only consider the items 4 & 6
(A u B)' = {4,6}
Note that sets AuB and (AuB)' can be unioned together to end up with the universal set U. Be sure not to mix up the universal set notation U with the union symbol 'u'
The last step is to see what sets (AuB)' and set C have in common. That would be 4 and 6 since both values are found in both sets
Therefore, (A u B)' n C = {4, 6}
The n refers to the intersection symbol.
x= -1/8 ,y= -2/5 ,z= 10/12 find the answer if x*( y* z ) = ( x* y ) * z
Answer:
a. x × (y + z) = -13/240
c. x × (y × z) = 1/24
Step-by-step explanation:
The given values of the variables are;
[tex]x = \dfrac{-1}{8} , y = \dfrac{-2}{5} \ and \ z = \dfrac{10}{12}[/tex]
a. x × (y + z) = (x × y) + (x × z), by distributive property
Plugging in the values gives;
[tex]\dfrac{-1}{8} \times \left (\dfrac{-2}{5} + \dfrac{10}{12} \right) = \left ( \dfrac{-1}{8} \times\dfrac{-2}{5} \right) + \left ( \dfrac{-1}{8} \times \dfrac{10}{12} \right)[/tex]
[tex]\dfrac{-1}{8} \times \left (\dfrac{-2}{5} + \dfrac{10}{12} \right) = \dfrac{-1}{8} \times \left (\dfrac{13}{30} \right) = \dfrac{-13}{240}[/tex]
[tex]\left ( \dfrac{-1}{8} \times\dfrac{-2}{5} \right) + \left ( \dfrac{-1}{8} \times \dfrac{10}{12} \right) = \dfrac{1}{20} + \dfrac{-5}{48} = \dfrac{-13}{240}[/tex]
Therefore;
[tex]\dfrac{-1}{8} \times \left (\dfrac{-2}{5} + \dfrac{10}{12} \right) = \left ( \dfrac{-1}{8} \times\dfrac{-2}{5} \right) + \left ( \dfrac{-1}{8} \times \dfrac{10}{12} \right) = \dfrac{-13}{240}[/tex]
c. x × (y × z) = (x × y) × z
Plugging in the values for 'x', 'y', and 'z' gives;
[tex]\dfrac{-1}{8} \times \left (\dfrac{-2}{5} \times \dfrac{10}{12} \right) = \left ( \dfrac{-1}{8} \times\dfrac{-2}{5} \right) \times \left ( \dfrac{10}{12} \right) = \dfrac{1}{24}[/tex]
YALLLL SOMEONE HELP A GIRL OUTTTT (ALSO NO LINKS I KNOW UR TRYING TO SCAM LOL)
Answer:
[tex]f(x) = {x}^{2} + 4x - 1 \\ f( - 1) = {( - 1)}^{2} + 4( - 1) - 1 \\ = - 4 \\ { \boxed{f( - 1) = - 4}} \\ \\ f(1) = {(1)}^{2} + 4(1) - 1 \\ = 4 \\ { \boxed{f(1) = 4}}[/tex]
624,612 rounded to the nearest hundred is
Answer:
624,600
Step-by-step explanation:
624,612
612 rounds to 600
624,600
Answer:
624,600
Step by step explanatiom:
cause math
pls help. will mark brainliest.
Answer:
b = -4
Step-by-step explanation:
multiply both sides by 3 to get:
4b-8 = 6b
-8 = 6b-4b
-8 = 2b
-8/2 = b
-4 = b
can someone help me? i really don’t understand
Answer:
Step-by-step explanation:
This question is from the similarity chapter. It would be really kind of you if you would answer this question.
Answer:
a) 1650 m
b) 1677.05 m
Step-by-step explanation:
Hi there!
1) Determine what is required for the answers
For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.
For part B, we're asked to solve for the length of the road, or the length of AB.
2) Prove similarity
In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).
How do we know they're similar?
Angles AYX and ACB are corresponding and they both measure 90 degreesBoth triangles share angle ATherefore, the two triangles are similar because of AA~ (angle-angle similarity).
3) Solve for part A
Recall that we need to find the length of AC.
First, set up a proportion. XY corresponds to BC and AY corresponds to AC:
[tex]\frac{XY}{BC}=\frac{AY}{AC}[/tex]
Plug in known values
[tex]\frac{2}{300}=\frac{11}{AC}[/tex]
Cross-multiply
[tex]2AC=11*300\\2AC=3300\\AC=1650[/tex]
Therefore, the road will rise 300 m over a horizontal distance of 1650 m.
4) Solve for part B
To find the length of AB, we can use the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex] where c is the hypotenuse of a right triangle and a and b are the other sides
Plug in 300 and 1650 as the legs (we are solving for the longest side)
[tex]300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c[/tex]
Therefore, the length of the road is approximately 1677.05 m.
I hope this helps!
Answer the question.
Answer:
$19.53
Step-by-step explanation:
$20 - 0.1(20) = 20 - 2 = 18
18 + 0.085(18) = 18 + 1.53 = 19.53
Kim bought a pair of jeans for $48 and 5 t-shirts. She spent a total of $158.00. How much did each t-shirt cost?
How do you write the equation?
Answer:
each t-shirt costed 22 dollars
48+ 5(x)=158
Step-by-step explanation:
158-48=110
110 divided by 5= 22
hope this helps!
please give brainist or give me a follow if you can<3
Today is Leilas birthday. She is 5 years old. How old is leila in months
Answer:
60
Step-by-step explanation:
There are 12 months in a year, so 5 years×12 months=60 months.
**You may wish to revise multiplication or the calendar year. I'm always happy to help
Answer:
60
Step-by-step explanation:
PLZ HURRY will give BRAIN-LY-EST and 20 points if correct
Answer:
[tex]{ \boxed{ \tt{4x + 4x \: → \: 8x}}} \\ \\ { \boxed{ \tt{3x + 5x + 8 \:→ \: 8x + 8 }}} \\ \\ { \boxed{ \tt{ - 7x + 4 + 3x \: → \: - 4x + 4}}} \\ \\ { \boxed{ \tt{4x + 4x + 4x + 4x \: → \: 16x}}}[/tex]
Answer:
4x + 4x → 8x
3x + 5x + 8 → 8x + 8
-7x + 4 + 3x → -4x + 4
4x + 4x + 4x + 4x → 16x
Step-by-step explanation:
The left side consists of a series of expressions and the right side is the list of choices to match to. This is simple math if you already know how to combine like terms. Combining like terms is combining numbers that represent the same value. Take a look at 4x + 4x for example, 4x and 4x are two numbers with the same value. Not that they both have the number 4, but that they have the same special variable. If there are two or more numbers with the same variable like x for example, combine the two, meaning you add the numbers. Just don't add the variables because clearly, the variable is an unknown number so you can't add variables. Instead, you can apply the same variable to the sum of two or more numbers. So 4x + 4x equals 8x. Do the same process again to the other 3 expressions. Also, you can't add a number with a variable to a number alone. They don't represent the same value.
3x and 5x are the same value so combine them. Now you only have 8x + 8 left as the simplified version of the expression.
-7x and 3x are the same value so combine them. Don't forget that the 7 is negative. Use a calculator if needed. Now you only have -4x + 4 as the simplified version of the expression.
Similar to 4x + 4x in the first expression, just add all of the numbers up. There isn't a number alone in this expression. 16x should be your final answer.
I hope this helps! Let me know if I am wrong. :D
The graph below shows four sections: A, B, C, and D.
Which section of the graph represents the solution set of the system of inequalities below?
Identify the word form of this number: 316,758
Answer:
it is Three hundred and sixteen thousand,seven hundred and fifty eight.
Hey there!
316,758
3 is in the HUNDRED THOUSANDS place
1 is in the TEN THOUSANDS place
6 is in the THOUSANDS place
7 is in the HUNDREDS place
5 is in the TENS place
8 is in the ONES place
Expanded form
300,000 + 10,000 + 6,000 + 700 + 50 + 8
Answer:
Three hundred sixteen thousand seven hundred fifty-eight
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
9x4 + 24x3 - 27x2 + 12x
Answer:
3x(3x³ + 8x² – 9x + 4)
Step-by-step explanation:
9x4 + 24x3 - 27x2 + 12x =
9x⁴ + 24x³ – 27x² + 12x =
3(3x⁴ + 24x³ – 27x² + 12x) =
3x(3x³ + 24x² – 27x + 12).
3x³ + 24x² – 27x + 12 cannot be factored
[rational numbers].
make x subject of the formula in y=2x+p
Answer:
(y-p)/2
Step-by-step explanation:
take p to the left side. + p becomes - p. Now divide the whole thing by 2
Answer:
[tex] x = \frac{y - p}{2} [/tex]
Step-by-step explanation:
[tex]y = 2x + p \\ y - p = 2x \\ x = \frac{y - p}{2} [/tex]
passes through (-2, 1) and (2, -5)
Answer:
The equation of the line is:
[tex]y = -\frac{3}{2}x - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Slope:
We have two points, (-2,1) and (2,-5). The slope is given by the change in y divied by the change in x. So
Change in y: -5 - 1 = -6
Change in x: 2 - (-2) = 2 + 4 = 4
Slope: [tex]m = \frac{-6}{4} = -\frac{3}{2}[/tex]
So
[tex]y = -\frac{3}{2}x + b[/tex]
Passes through (-2, 1)
This means that when [tex]x = -2, y = 1[/tex]. We use this to find the y-intercept. So
[tex]y = -\frac{3}{2}x + b[/tex]
[tex]1 = -\frac{3}{2}(-2) + b[/tex]
[tex]1 = 3 + b[/tex]
[tex]b = -2[/tex]
So, the equation of the line is:
[tex]y = -\frac{3}{2}x - 2[/tex]
.Divide the sum of 13/5 and -12/7 by the product of -31/7 and -(1/2)
Answer:
hello u so cool i admire you <3
PLEASE HELP ASAP
the graphs below have the same shape. what is the equation of the red graph?
Answer:
D
Step-by-step explanation:
I checked it on desmos and also the shift is 1 up that means subtracting from a larger number
Answer: d
Step-by-step explanation:
Given that abc and def are similar find fd
Answer:
FD = 8
Step-by-step explanation:
since they are similar triangle .use these ratios to find FD
AB/DE = AC/FD
now substitute the values
6/x-3 = 12/x+1
do cross multiplication
12(x-3) = 6(x+1)
12x - 36 = 6x + 6
12x - 6x = 6 + 36
6x = 42
x = 42/6
x = 7
now substitute x
FD = x + 1
=7 + 1
=8
Trevor had 3/4 pound of peanut she wants to split them evenly among 4 people. How many pounds of peanuts would each person get?
cari nilai k dengan keaadaan h^2(2k/5)=32
Answer:
[tex] {h}^{2} ( \frac{2k}{5} ) = 32 \\ 2k. {h}^{2} = 160 \\ k {h}^{2} = 80[/tex]
[tex]k=\frac{80}{h²}[/tex]
Which of the diagrams below represents the statement "If it is an triangle,
then it has three vertices"?
three
vertices
triangle
triangle
three
vertices
Figure A
Figure B
A. Figure A
B. Figure B
SUBMIT
HELP PLZ
Answer:
I think it's A, because all triangles have 3 vertices.
Step-by-step explanation:
find the length of arc AB help plz
Which polynomial is a monomial?
O A. 2p-P
O B. 6 - 2x2 - 4x2 +45
O c. 5r283A
O D. 1 - 2x + 5x
Answer:
Which polynomial is a monomial?
O A. 2p-P
O B. 6 - 2x2 - 4x2 +45
O c. 5r283A
O D. 1 - 2x + 5x
. 5r283A
The relative frequency table below summarizes a survey about support for candidate X in an upcoming
national election. In this survey, 210 randomly selected Virginians opposed candidate X.
How many people in this survey were Californians who opposed candidate X?
Does the table show evidence of an association between being from Virginia and opposing candidate X?
Choose all answers that apply:
Answer:
D.
Step-by-step explanation:
a) no, because 50% of people who support candidate x are from California, but only 62.5% of all people in the study are from California.
b) yes, because 50% of people who support candidate x are from California, but only 62.5% of all people in the study are from California.
c) no, because 62.5% of people who support candidate x are from California, but only 50% of all people in the study are from California.
d) yes, because 62.5% of people who support candidate x are from California, but only 50% of all people in the study are from California.
The answer is D.
Step-by-step explanation:
Answer:
How many people in the survey were Californians?
- 250
Yes, because 50% of Californians support candidate X, but only 40% of all people support him.
Yes, because 62.5% of people who support candidate X and 50% of Californians do not support candidate X.
Simplify -62 ÷ 12 - 2(-7).
Answer:
53/6 = 8.83
Step-by-step explanation:
2 x -7 = -14
-62 / 12 = -5.16667
-5.16667 - (-14) = 8.83333
Final answer: 8.83
I hope this helps you! :D
Answer:
use pamdas
Step-by-step explanation:
the answer I got using pemdas was 8.83
A staff member at UF's Wellness Center is interested in seeing if a new stress reduction program will lower employees systolic blood pressure levels. Twenty people are selected and have their blood pressure measured. Each person then participates in the stress reduction program. One month after the stress reduction program, the systolic blood pressure levels of the employees were measured again. Did the program reduce the average systolic blood pressure level? Note: Differences were taken by taking "before systolic blood pressure" minus "After blood pressure"
The 95% confidence interval was (5.6, 10.2).
A. On average, the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at the 95% confidence level
B. We are 95% confident that there is no difference in average systolic blood pressure levels before and after the stress reduction program.
C. On average, the systolic blood pressure levels after the stress reduction program were significantly higher than the systolic blood pressure levels before the stress reduction program, at the 95% confidence level.
Answer:
A. On average the blood pressure levels before the stress reduction program were significantly higher than the systolic blood pressure levels after the stress reduction program, at 95% confidence level
Step-by-step explanation:
The confidence interval parameters is intended to detect if the new stress reduction program will lower the systolic blood pressure levels of employees
The difference between the the mean systolic blood pressure levels taken = The before systolic pressure - The after systolic blood pressure
The 95% confidence interval obtained = (5.6, 10.2)
Therefore, given that the values of the difference between the means are both positive, then there a difference as the confidence interval does not include zero (0), and at the 95% confidence level, the average systolic blood pressure levels before the stress reduction program are higher than the average systolic blood pressure levels after the program
How many vertices does this three-dimensional shape have?
Answer:
6
Step-by-step explanation:
I may be wrong.
If I am, delete this answer.
If it's right, please mark it as the Brainliest. I would really appreciate it.
The total number of vertices that this three-dimensional shape will be 6. Then the correct option is D.
What is Geometry?Geometry is one of the earliest areas of mathematics, along with algebra. It is concerned with spatial qualities such as figure proximity, form, size, and relative location. A geometer is a mathematics who works in the discipline of geometry.
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
In the given diagram, the upper part of the triangular pyramid has 3 corners and the lower part of the triangular pyramid has 3 corners.
Then the total number of vertices that this three-dimensional shape will be 6. Then the correct option is D.
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ2
t = 4k + 9
k = 2
Work out the value of t.
A)17
B)18
C)25
(Working not needed)
(3.21 × 103)(1.13 × 105)
Answer:
39229.25
Step-by-step explanation:
Answer:
39229.25
Step-by-step explanation:
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