Answer:
The equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
Step-by-step explanation:
Given point is [tex](4,-1)[/tex] and equation of line is [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex]
Let the slope of line that passes through point [tex](4,-1)[/tex] is [tex]m_1[/tex]
And slope of line [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]m_2=\frac{7}{2}[/tex] . As it is in the form of [tex]y=mx+c[/tex]
We know the relation between slope of perpendicular line are given by
[tex]m_1\times m_2=-1\\And\ m_1=\frac{-1}{m_2}[/tex]
So, the slope [tex]m_1=\frac{-1}{\frac{7}{2}}=\frac{-2}{7}[/tex]
Now, we can write the equation of line having point [tex](4,-1)[/tex] and slope [tex]\frac{-2}{7}[/tex]
[tex](y-y_1)=m(x-x_1)\\\\(y-(-1))=\frac{-2}{7}(x-4)\\\\y+1=\frac{-2x}{7}-(\frac{2\times -4}{7})\\ \\y+1=\frac{-2x}{7}+\frac{8}{7}\\\\y=\frac{-2x}{7}+\frac{8}{7}-1\\\\y=\frac{-2x}{7}+\frac{8-7}{7}\\\\y=\frac{-2x}{7}+\frac{1}{7}[/tex]
So, the equation of line passes through [tex](4,-1)[/tex] and perpendicular to the graph [tex]y=\frac{7}{2}x-\frac{3}{2}[/tex] is [tex]y=\frac{-2x}{7}+\frac{1}{7}[/tex]
LaTeX: \angle∠J and LaTeX: \angle∠K are supplementary angles. If mLaTeX: \angle∠K is 84LaTeX: ^\circ∘, what is the measure of LaTeX: \angle∠J?
Group of answer choices
The length of a rectangle is 3 1/6 cm longer than the width. The perimeter of the rectangle is 15 1/3 cm. What are the width and length of this rectangle?
The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]
Step-by-step explanation:
Let,
Width of rectangle = w
Length of rectangle = w+[tex]3\frac{1}{6}=w+\frac{19}{6}[/tex]
Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}\ cm[/tex]
Perimeter of rectangle = 2(Length + Width)
[tex]2(w+\frac{19}{6}+w)=\frac{46}{3}\\2(2w+\frac{19}{6})=\frac{46}{3}\\4w+\frac{19}{3}=\frac{46}{3}[/tex]
Subtracting [tex]\frac{19}{3}[/tex] from both sides
[tex]4w+\frac{19}{3}-\frac{19}{3}=\frac{46}{3}-\frac{19}{3}\\4w=\frac{46-19}{3}\\4w=\frac{27}{3}\\4w=9[/tex]
Dividing both sides by 4
[tex]\frac{4w}{4}=\frac{9}{4}\\w=\frac{9}{4}[/tex]
Therefore,
Width of rectangle = w = [tex]\frac{9}{4}=2\frac{1}{4}[/tex] cm
Length of rectangle = [tex]w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}=\frac{27+38}{12}=\frac{65}{12}=5\frac{5}{12}\ cm[/tex]
The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]
Keywords: perimeter, addition
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What is the quotient?
StartFraction 2 y squared minus 6 y minus 20 Over 4 y + 12 EndFraction divided by StartFraction y squared + 5 y + 6 Over 3 y squared + 18 y + 27 EndFraction
The quotient is [tex]\frac{3(y-5)}{2}[/tex]
Explanation:
The expression is [tex]\frac{2 y^{2}-6 y-20}{4 y+12} \div \frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex]
Now, reciprocal the term [tex]\frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex] and convert ÷ to ×
[tex]\frac{2 y^{2}-6 y-20}{4 y+12} \times \frac{3 y^{2}+18 y+27}{y^{2}+5 y+6}[/tex]
Taking the common terms out, we get,
[tex]\frac{2\left(y^{2}-3 y-10\right)}{4(y+3)} \times \frac{3\left(y^{2}+6 y+9\right)}{y^{2}+5 y+6}[/tex]
Factorizing each numerator and denominator, we get,
[tex]\frac{2(y-5)(y+2)}{4(y+3)} \times \frac{3(y+3)(y+3)}{(y+3)(y+2)}[/tex]
Multiplying the terms, we have,
[tex]\frac{6(y-5)(y+2)(y+3)^{2}}{4(y+3)^{2}(y+2)}[/tex]
Cancelling the common factors, we get,
[tex]\frac{3(y-5)}{2}[/tex]
Thus, the quotient is [tex]\frac{3(y-5)}{2}[/tex]
Answer:
B
Step-by-step explanation:
On edge 2021
16)
Use the triangle inequality theorem to determine the smallest angle in the figure.
ZSCI
ZCIS
ZCSI
Lisc
Answer:
∠CIS.
Step-by-step explanation:
This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.
The smallest angle that the angular momentum vector can make with the z-axis for an electron with quantum number l=2 is found using the magnetic quantum numbers. For m₁=+2, the angle would be the smallest, approaching 0 degrees.
Explanation:The question pertains to the calculation of the smallest angle that the angular momentum vector ℓ can make with the z-axis given the quantum number l for an electron. To find this, we use the concept of quantized angular momentum in quantum mechanics.
For an electron with a quantum number l=2, it can have multiple magnetic quantum numbers m₁, ranging from -l to +l. Therefore, for l=2, m₁ can be -2, -1, 0, 1, or 2. Each of these values corresponds to a different angle with the z-axis.
The smallest angle corresponds to the maximum value of m₁, which is 2 in this case. The formula cos 0 = Lz/L uses the magnetic quantum number m₁ and the total angular momentum to calculate the cosine of the angle. For m₁=+1, the value of cos 0 would be 0.707, using the provided ratios and simplifying the formulas given. This corresponds to an angle whose cosine is 0.707, which through the inverse cosine function can be determined to be approximately 45 degrees. However, for m₁=+2, the angle would be even smaller, approaching 0 degrees as the z-component of angular momentum becomes maximally aligned with the z-axis.
click on the value for m that makes this inequality true
Answer:
To solve this inequality you need to get m by itself
3m+10<30 (First subtract 10 from each side)
3m<20 (10-10=0, 30-10=20) (Then divide each side by 3)
m< 20/3 or 6.666666
So your answer is any that is less than 6.66666
Your answer would be 5
5
Hope this helps ;)
Evaluate a + (-b) where a = 4 and b =2
Answer:
The answer is 2
Step-by-step explanation:
4 + (-2) = 2
Answer:
2
Step-by-step explanation:
Given the expression : a + (-b)
where a = 4 and b = 2
Therefore: a + (-b) = 4 + (-2)
=4 - 2
= 2
what is the value of g divided 4, if g=20
Answer:
5
Step-by-step explanation:
G=20
20÷4=5
Hope this helps!
What is a formula for the nth term of the given sequence?
-17, -8, 1...
−17,−8,1...
a_{n}=-8+9(n-1)a
n
=−8+9(n−1)
a_{n}=-17(9)^{n}a
n
=−17(9)
n
a_{n}=9n-26a
n
=9n−26
a_{n}=-17-9(n-1)a
n
=−17−9(n−1)
Answer:
The nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]
Step-by-step explanation:
Given sequence is -17,-8,1,...
To find the nth term of the given sequence :
Let [tex]a_1=-17,a_2=-8,a_3=1,...[/tex]
To find the common difference d :
[tex]d=a_2-a_1[/tex]
[tex]=-8-(-17)[/tex]
[tex]=-8+17[/tex]
Therefore d=9
[tex]d=a_3-a_2[/tex]
[tex]=1-(-8)[/tex]
[tex]=1+8[/tex]
Therefore d=9
The common difference d is 9
Therefore the given sequence is an arithmetic sequence
The nth term of an arithmetic sequence is given below
[tex]a_n=a_1+(n-1)d[/tex]
Substitute [tex]a_1=-17[/tex] and d=9 in the above equation we get
[tex]a_n=-17+(n-1)9[/tex]
Therefore the nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]
The formula for the nth term of the sequence -17, -8, 1 is a_n = 9n - 26, where n is the position of the term in the sequence.
Explanation:The sequence provided is -17, -8, 1, which suggests that there is a common difference between terms since it is an arithmetic sequence. To find the nth term of an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference. In this case, the common difference is 9 (since -8 - (-17) = 9).
So, using the formula for the nth term of an arithmetic sequence:
a_1 = -17 (the first term)d = 9 (the common difference)Our formula becomes a_n = -17 + (n - 1) × 9. Simplifying this:
a_n = -17 + 9n - 9
a_n = 9n - 26
Therefore, the formula for the nth term of the given sequence is a_n = 9n - 26.
the consecutive odd integers have a sum of 36. find the integers
how many consecutive odd integers are there, or else I can't help you
==================================================
Work Shown:
x = some integer
2x = even integer
2x+1 = odd integer
(2x+1)+2 = 2x+3 = odd integer just after 2x+1
The integers 2x+1 and 2x+3 add to 36
(2x+1)+(2x+3) = 36
2x+2x+1+3 = 36
4x+4 = 36
4x+4-4 = 36-4 ... subtract 4 from both sides
4x = 32
4x/4 = 32/4 .... divide both sides by 4
x = 8
With x = 8, we can say
2x+1 = 2*8+1 = 17 is the first odd integer
2x+3 = 2*8+3 = 19 is the next odd integer
17+19 = 36, so the answer is confirmed
--------------------
A non-algebraic way to get the answer is to divide 36 in half to get 18
Then try odd integers around 18, so 19+21 = 40 but thats too high
then maybe try 15+17 = 32, thats too low
17+19 = 36 is right on the money
please help asap I also need it in my own words
Step-by-step explanation:
so to find out how long you would first do 60-30 as this is how many extra minutes they workout. the answer is 30.
then you would divide 30 by 2 that makes 15 as there is 2 people then you would add 15 to 30 and you get 45
45mins on treadmill
freehand=60-45=15
60-30=30
30÷2=15
15+30=45
60-45=15
part A:
freehand=f
treadmill=t
x=y+30
that is what i believe the eqation is
Solve the system of linear equations by substitution.
5x+2y=9
x+y= -3
Answer:
Step-by-step explanation:
5x+2y=9.......(1)
x+y= -3.........(2)
Making y as subject bin (2)
y = -3 - x
Substituting in (1)
5x + 2(-3 - x) = 9
5x - 6 - 2x = 9
3x = 9 + 6
3x = 15
x = 15/3
x = 5
And y = -3 - x
y = -3 - 5
y = -8
Answer:
The solution for the system of linear equations is x = 5, y = -8
Step-by-step explanation:
Let's solve the system of linear equations by substitution:
5x + 2y = 9
x + y = -3
Solving for x in the 1st equation, this way:
5x + 2y = 9
5x = 9 - 2y
x = (9 - 2y)/5
Substituting x in the 2nd equation:
x + y = -3
(9 - 2y)/5 + y = -3
9 - 2y + 5y = - 15 (Multiplying by 5 at both sides)
3y = - 15 - 9
y = -24/3
y = - 8
Substituting y in the 1st equation:
5x + 2y = 9
5x + 2 * - 8 = 9
5x - 16 = 9
5x = 25
x = 25/5 = 5
The solution for the system of linear equations is x = 5, y = -8
jackie can spell 83% of her words correctly. if she attempted 23 words, about how many did she make
The following table shows the consumer price index(CPI) for a fictional country from 1992-2000.during which of these time periods was there a period deflation?
A.1992-1994
B.1994-1996
C.1996-1998
D.1998-2000
D.1998-2000
Step-by-step explanation:
Deflation describes the drop of prices for goods and services leading to slowing down of economic growth.During economic uncertainty, prices of goods and services can get very low causing the inflation rate to go lower than zero.CPI index shows inflation when it rises over a short period of time.CPI declines to mean deflation where there is a steady decrease in prices of goods and services.
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Keywords : table, CPI, country, period, deflation
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PLEASEE I’m failing math with a 57 I need help
4. take 110-80/4-2, this gives you 30/2, which is then 15. Therefore it is 15 dollars per hour
26,208/42 find the quotient?
The quotient of 26,208 divided by 42 is 624. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.
Explanation:To find the quotient of 26,208 divided by 42, you need to perform a division operation. When you divide 26,208 by 42, you'll find that the answer is 624 without any remainder. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.
In ΔDEF,{EF}\cong{DE} EF ≅ DE and m∠E = 104°. Find m∠D.
The 3 inside angles need to equal 180.
Subtract E from 180 to find the sum of the other two angles:
180 - 104 = 76
Now because EF ≅ DE , angle D and F would be the same so divide 76 by 2
Angle D = 38
A cat weighs 3.5 ounces when born. The cat grows 0.5 ounces each week. After
how many weeks does the cat way 16.5 ounces?
Answer:
10 weeks
Step-by-step explanation:
Answer: 26 weeks
Step-by-step explanation:
This is an example of an arithmetic sequence.
The first term = 3.5
common difference = 0.5
Using the formula for calculating the nth term of an arithmetic sequence :
[tex]t_{n}[/tex] = a + (n - 1 ) d
Therefore :
16.5 = 3.5 + ( n - 1 ) x 0.5
16. 5 = 3.5 + 0.5n - 0.5
16.5 = 3 + 0.5n
16.5 - 3 = 0.5n
13.5 = 0.5n
n = 13.5/0.5
n = 27
Therefore , it will take the cat (n-1) weeks to weigh 16.5 ounce, which will be 27 - 1 = 26
check:
3.5 + 26 ( 0.5)
= 3.5 + 13
= 16.5
Math question please help :)
Question 3
Answer: Choice A) {(3,4) (3,5)}-----------
Explanation:
Note how in choice A we have repeated x values
x = 3 pairs up with y = 4 and y = 5 at the same time.
The input x = 3 must only pair up with one output only if we want a function to happen.
If you plotted the points (3,4) and (3,5), it is possible to draw a vertical line through them. So this fails the vertical line test.
The other answer choices do not have repeated x values, so they are all functions.
==========================================
Question 4
Answer: choice A) 2x+3y = 10 and choice D) y = 18-----------
If you plotted choice A and choice D on an xy coordinate system, you should see straight lines forming.
2x+3y = 10 turns into y = (-2/3)x+10/3 which is y = mx+b form.
Choice D's equation is equivalent to y = 0x+18, so its slope here is 0, making it a flat horizontal line.
Choice B does not count as an answer because while it is a linear vertical line, it is not a function for similar reasons back in question 3. The fact that x = 16 pairs up with infinitely many y values is what makes this not be a function.
Choice C is not a linear equation. Instead it is a quadratic equation because the largest exponent is 2.
Simplify the expression:
(-2q+5)(-7)
How can u solve 40x16 by breaking apart the numbers
Answer: 640
Step-by-step explanation:
You can break 16 up into 10 and 6: 40(10+6)
40(10)+40(6)
400+240
640
Final answer:
To solve 40x16, break apart the numbers into tens and use the distributive property to calculate the partial products, then sum up these products to get the final result of 640.
Explanation:
To solve 40x16 by breaking apart the numbers, you can use a strategy known as decomposing or partial products. Here's a step-by-step explanation:
Break apart the number 40 into 10s: 40 = 30 + 10.
Break apart the number 16 into 10s: 16 = 10 + 6.
Now use the distributive property to multiply each part:
(30 + 10) × (10 + 6)
Multiply each part individually: 30 x 10, 30 x 6, 10 x 10, and 10 x 6.
Calculate the partial products: 300, 180, 100, and 60.
Finally, add all the partial products: 300 + 180 + 100 + 60 = 640.
So, 40x16 equals 640 when you apply the breaking apart method.
How do you write the difference of a number and eight, divided by ten
Answer:
(x-8)/10
Step-by-step explanation:
-------
(X - 8)/10 or (8 -X)/10
The unknown number can be given as X
The difference between the number and 8 can be given as 8 -X or X - 8
The dividing it by 10 will give (x-8)/10 or (8-x)/10 depending on the value of the unknown number X
The hypotenuse of a 45°-45°-90° triangle measures 7 StartRoot 2 EndRoot units.
A right triangle is shown. The hypotenuse has a length of 7 StartRoot 2 EndRoot and the lengths of the other 2 sides are congruent.
What is the length of one leg of the triangle?
Answer:
A. 7
Step-by-step explanation:
my unit test review said the other persons answer was wrong and it said this was right so ya.
The length of one leg of the given triangle is 1 unit.
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the squares of other two sides.
Given the following parameters;
Hypotenuse = √2
If the lengths of the other two sides are congruent, thus;
x² + x² = (√2)²
2x² = 2
x² = 2/2
x² = 1
x = 1
Hence, the length of one leg of the triangle is 1 unit.
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please help!! brainliest!!
Identify the sets of lines to which the given line is a transversal.
line a
Answer:
I think the answer is C
Step-by-step explanation:
from looking at the graph and how the lins intercept
Answer:
C is the correct answer.
Step-by-step explanation:
Complete the statement using always, sometimes, or never.
A quadrilateral is
a trapezoid.
a.) always
b.) sometimes
c.) never
it had to be b cuz now all quadrilateral have straight sides
which expressions are equivalent?
Answer:
C none of the above
Step-by-step explanation:
x + z + y
is not going to be equal to x + y - z
Its like saying 10 + 5 - 4 = 11
To 10 + 5 + 4, they are not going to be equal
Answer:
C none of the above
Step-by-step explanation:
7. The sun is at an angle of elevation of 58º. A tree casts a shadow 20 meters long on
the ground. How tall is the tree?
The height of tree is 32 meter
Solution:
Given that, The sun is at an angle of elevation of 58 degree
A tree casts a shadow 20 meters long on the ground
The sun, tree and shadow forms a right angled triangle
The figure is attached below
ABC is a right angled triangle
AC is the height of tree
AB is the length of shadow
AB = 20 meters
Angle of elevation, angle B = 58 degree
By definition of tan,
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
In this right angled triangle ABC,
opposite = AC and adjacent = AB
Therefore,
[tex]tan\ 58 = \frac{AC}{AB}\\\\tan\ 58 = \frac{AC}{20}\\\\1.6 = \frac{AC}{20}\\\\AC = 1.6 \times 20\\\\AC = 32[/tex]
Thus height of tree is 32 meter
Final answer:
To determine the height of the tree using the angle of elevation of the sun and the shadow length, apply the tangent function. With an elevation of 58º and a shadow of 20 meters, the tree’s height is calculated to be approximately 33.94 meters.
Explanation:
To find the height of the tree given the angle of elevation of the sun and the length of the shadow it casts, we can make use of trigonometry. Specifically, we will use the tangent function, which relates the angle of elevation with the opposite side (the height of the tree) and the adjacent side (the length of the shadow).
Step-by-step solution:
Let's denote the height of the tree as H and the length of the shadow as 20 meters.The angle of elevation of the sun is given as 58º.Using the tangent function: tan(θ) = opposite/adjacent, where θ is the angle of elevation.Plugging in the values, we get tan(58º) = H / 20 meters.Solve for H by multiplying both sides by 20 meters: H = 20 meters · tan(58º).Use a calculator to find tan(58º), and then compute H.After calculating, we find that the height of the tree is approximately 33.94 meters.Thus, the height of the tree is approximately 33.94 meters.
How to write 21 less than n equal 31 in a equation promblem
Answer:
n-21=31
Step-by-step explanation:
Just read it carefully, it is worded weirdly, but just think about it.
Answer:
52
Step-by-step explanation:
n-21=31
n=31+21
n=52
List all of the elements of set A if A = {x|x is an integer and -6 ≤ x <0}
{-5, -4, -3, -2, -1}
{-6, -5, -4, -3, -2, -1, 0}
{-6, -5, -4, -3, -2, -1}
Answer:
{-6, -5, -4, -3, -2, -1}.
Step-by-step explanation:
The set contains the integer -6 ( because of the ≤ ) but not 0 because of the < 0.
How would the following triangle be classified?
Step-by-step explanation:
All sides are congruent, therefore is an equilateral triangle.
It's also an isosceles acute triangle because two sides are congruent and all angles are acute.
It's also an isosceles triangle because two sides are congruent.
What is it equivalent expression for 3(x+9)-2
========================================
Work Shown:
3(x+9)-2
3*x+3*9 - 2 ..... distribute
3x+27-2 .... multiply
3x+25 .... combine like terms
Answer:3x+25
Step-by-step explanation: