Answer:
(-4,17)
Step-by-step explanation:
y = f(x)
f(-4) = (-4)^2+1 = 17
y-coordinate = 17
Answer:
D). (-4, 17)
Step-by-step explanation:
Plug in -4 for x.
[tex]f(-4)=(-4)^2}+1[/tex]
Solve.
[tex]f(-4)=16+1[/tex]
[tex]f(-4)=17[/tex]
We already know that the x-coordinate is -4. (-4, y)
f(x) stands for y, so y=17.
(-4, 17)
I hope this helps!
Which equation represents a line which is perpendicular to the line y = -4x - 5
A) x + 4y = -32
B) 4x - y = -4
C) 4x + y = 3
D) 4y - x = 4
What is the length of
each leg of the triangle below?
Answer:
11 sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin 45 = x /22
22 sin 45 = x
22 ( sqrt(2)/2) =x
11 sqrt(2)
The legs are equal since the base angles are equal
A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet. What is the height of the ladder?
Answer:
17.89 ft
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
8^2 +16^2 = c^2
64+ 256 = c^2
320 =c^2
Taking the square root of each side
sqrt(320) = sqrt(c^2)
sqrt(64*5) = c
sqrt(64) sqrt(5) =c
8 sqrt(5) = c
17.88854382=c
17.89 ft
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet. Find:-What is the height of the ladder?solution:-A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet.
so it is a right angle triangle
we know that,in a right angle triangle, According to the Pythagorean theorom,
[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]
where
l= legs b=baseh=hypotenuse According to the question, [tex]\sf{8^2+16^2=h^2 }[/tex] [tex]\sf{64+256=h^2 }[/tex] [tex]\sf{ h^2=320 }[/tex] [tex]\sf{h=\sqrt{320} }[/tex] [tex]\sf{h=8\sqrt{5} }[/tex] Therefore:-The height of the ladder is [tex]\sf{8\sqrt{5} }[/tex]
The battery standby duration (in hours) of a new model of cell phone is known to be normally distributed. Ten pieces of such new model of cell phone supplied from the manufacturer are randomly chosen and the actual standby durations are recorded as below:
48.2 47.8 45.6 47.2 49.3
51.2 44.2 45.4 49.2 43.6
(a) Calculate the unbiased estimates of population mean and standard deviation of battery standby duration (in hours) of the new cell phone.
Answer:
[tex]\mu = 47.17[/tex]
[tex]\sigma = 2.31[/tex]
Step-by-step explanation:
Solving (a): The population mean
This is calculated as:
[tex]\mu = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\mu = \frac{48.2+ 47.8 +45.6 +47.2 +49.3+51.2 +44.2 +45.4 +49.2 +43.6}{10}[/tex]
[tex]\mu = \frac{471.7}{10}[/tex]
[tex]\mu = 47.17[/tex]
Solving (b): The population standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(48.2-47.17)^2 + (47.8-47.17)^2 +.........+(43.6-47.17)^2}{10}}[/tex]
[tex]\sigma = \sqrt{\frac{53.521}{10}}[/tex]
[tex]\sigma = \sqrt{5.3521[/tex]
[tex]\sigma = 2.31[/tex]
2. What are the last 2 digits of 1 + 2 + 3 + + 2005 2006
Let S be the sum. So you have
S = 1 + 2 + 3 + … + 2004 + 2005 + 2006
as well as
S = 2006 + 2005 + 2004 + … + 3 + 2 + 1
Then
2S = (1 + 2006) + (2 + 2005) + … + (2005 + 2) + (2006 + 1)
2S = 2007 + 2007 + … + 2007 + 2007
2S = 2006 × 2007
S = (2006 × 2007)/2
S = 2,013,021
which makes the last two digits 21.
I NEED JUSTIFICATION AND WORK ON PART A AND B
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds? (5 points)
Part B: Which is the more reasonable measurement of the diameter of a human hair:
1.8 ⋅ 10−2 mm or 1.8 ⋅ 102 mm? Justify your answer. (5 points)
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Answer:
6.045 * 10 ^40 ergs
1.8 * 10^-2 mm
Step-by-step explanation:
3.9 ⋅ 10^33 erg per second * 1.55 * 10 ^7 seconds
3.9 * 1.55 * 10^(33+7)
6.045 * 10 ^40 ergs
Human hair is around .1 mm thick
.1 = 1 * 10 ^ -1
This is closer to 1.8 * 10^-2
1.8 *10^2 = 180 mm which is too thick This is approximately 18 cm
Step-by-step explanation:
A rectangle has an area of 72 swaure units. The width of the rectangle is 9 units. The length of the rectangle is 2x + 4. What is the rectangle's length?
Answer:
8 units
Step-by-step explanation:
Area of a rectangle = Width multiplied by Length
Substitute in all the known numbers into this formula to get
72 = (9) × [tex](2x+4)[/tex]
Solve the equation for x, to find out the length
[tex]9(2x+4)=72[/tex]
[tex]2x+4=72/9[/tex]
[tex]2x+4=8[/tex]
[tex]2x=8-4[/tex]
[tex]2x=4[/tex]
[tex]x=4/2[/tex]
[tex]x=2[/tex]
Length of the rectangle = [tex](2x+4)[/tex]
[tex]2(2)+4[/tex]
[tex]4+4=8[/tex]
limx²-9x+20
x->4 x-4?
Answer:
-1
Step-by-step explanation:
lim x tends to 4 (x^2-9x+20)/(x-4). (x^2-9x+20)(x-4)=x-5.
So the limit is 4-5=-1
I need help on this question 5=7+x/5
Answer:
-10 = x
Step-by-step explanation:
5=7+x/5
Subtract 7 from each side
5-7=7-7+x/5
-2 = x/5
Multiply each side by 5
-2 *5 = x/5 *5
-10 = x
Help Please!!!
Find volume of the sphere
Answer:
Step-by-step explanation:
Hey GurpTheDestoyer! Find the volume of the sphere. Round to the nearest whole number. Radius= 8 what is the volume? The Volume = 2,144.660585 cm3. Hope this helped! <3
the graph of a linear function is given below
Answer:
The "zero" is where it crosses the x axis which is -2 in this graph
Step-by-step explanation:
Can someone help me with this task please? !!
Answer:
we need to get your brain thinking in this way. that you begin to understand how to do these things.
airways to say that your brain is not working that way, is not a valid excuse. we need to change that. your brain needs to get used to this way of thinking.
so, please, please, PLEASE go through the explanations below and tell me, where exactly in these explanations you stopped understanding what I was saying. so that I can better explain to you what is happening.
1. (0, -2)
2. 4
3. a geometric sequence. the common ratio is -2.0
4. the third option
5. the fourth option
Step-by-step explanation:
1. as x increases, y decreases. until, suddenly after x=0, this tendency reverses, and with increasing x also y increases. so, this is a turning point.
2. look at the line. it only starts with x>0 (it looks like x is around 1).
"input" is all the values of x the function has a defined result for (y = result values).
so, as there is no line for negative x, we can eliminate the first 2 answers.
x=0 is no valid answer either (as mentioned above, the line only starts well after x=0).
in the answer options the only x value having an y value above or below this x value is x=4.
3. look at the difference between 2 numbers next to each other in the sequence.
2.4 to -4.8
-4.8 to 9.6
and so on.
what do we need to do to get from the left to the right ?
we need to multiply by -2.
so, the relationship between "sequence item n" (an) to "sequence item n-1" (an-1) is a ratio, a multiplication factor :
an/an-1 = -2
4. it is completely simple. a function can be many things. on an x/y coordinate grid it can have gaps, it can have sharp direction changes,...
but there us one thing a function can never have : multiple different y values for one x value.
in the first graph x=2 has two different y values (-1 and -3). so, it is not clear what the result for x=2 would be. and that means, it is not a function.
in the second graph x=4 has two different y values.
in the third graph all is OK.
in the fourth graph x=-2 has two different y values.
so, only the third option is a function.
5. this function calculates the height of the thrown rock after t seconds of flight.
therefore, only the fourth answer makes sense.
Can someone please just help me fill in those three boxes I’ve been struggling
Use the graph, the equations, or a table of values to support a logical argument that the linear functions
are inverses.
(please help)
Step-by-step explanation:
one line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).
and this line has the offset of y=-5 for x=0
so, the line equation is
y = -3x - 5
inverse means that we exchange x and y and then solve for y again :
x = -3y - 5
3y = -x - 5
y = -x/3 - 5/3
when we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).
and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.
for example (-2, -1)
-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1
correct.
so, the equation we got for the inverse function fits exactly with the second line in the graph.
therefore, yes, they are both inverse functions to each other.
The two given graphs are inverse functions of each other.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
One line has the slope of -3 (-3/1 meaning that when x increases by 1 unit, y decreases by 3 units).and this line has the offset of y=-5 for x=0
The line equation is
y = -3x - 5
Inverse means that we exchange x and y and then solve for y again :
x = -3y - 5
3y = -x - 5
y = -x/3 - 5/3
When we look at the second line, we see its slope is -1/3 (when x increases by 3 units, y decreases by 1 unit).and while we cannot read the offset on the y-axis precisely, we can use a clearly readable point to prove or disprove the equation above.
for example (-2, -1)
-1 = -(-2/3) - 5/3 = 2/3 - 5/3 = -3/3 = -1
The equation we got for the inverse function fits exactly with the second line in the graph.
Therefore the two given graphs are inverse functions of each other.
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Can someone help me with this math homework please!
2.The school chess club is selling T-shirts for a profit of $4 each and baseball caps for a profit of $5 eac The club wants to sell 50 items and make a profit of $230. Calculate how many of each item the chess club needs
Step-by-step explanation
They sold $480 of tshirts, the ratio is 480;20, simplified to 24:1.
One shirt is $20, but $4 is the amount taken from 20 for the equipment.
Multiply $24 by the $4 taken for the equipment. (Equals $96)
They make 4/20 (1/5) of the the sales as a profit for equipment.
Multiply 1/5 by 480 and you will get $96 as the club's profits.
I hope this helped ya
The chess club needs 20 T-shirts and 30 baseball caps.
What is Profit?Profit is a term that often refers to the financial gain that a company receives when revenue exceeds costs and expenses. A child at a lemonade stand, for example, spends one quarter to make one cup of lemonade. She then charges $2 for the drink. Her profit on a cup of lemonade is $1.75.
Given :
Total no. of items to be sold = 50
Total profit to be made = $230
Profit on each T-shirt = $4
Profit on each Baseball cap = $5
Let no. of t-shirts be x
Let no. of t-shirts be y
Forming equations according to given problem :
Eq 1 : x + y = 50
Eq 2 : 4x + 5y = 230
Multiplying Eq 1 with 4 we get : 4x + 4y = 200
Subtracting Eq 1 from Eq 2
Solving Eq1 and Eq2 we get x = 20 and y = 30.
Therefore, The chess club needs 20 T- shirts and 30 baseball caps.
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Given m
n, find the value of x.
הון
n
.
80°
Answer: =
Submit Answer
PLS HELP
Answer:
x + 80°= 180° ( angles made in straight line)
x = 180°-80°
x = 100°
hope it is helpful to you
Answer:
check ur Answer in the attachment .
Express 0.00506 in standard form
Answer:
[tex]5.06 x 10^{-3}[/tex]
Step-by-step explanation:
Move decimal 3 place to right.
Because the decimal was moved to right, the exponent is negative.
In an A.P the term is -10 and the 15th term is 11 and the last term is 41. Find the sum of all terms in this progression.
This is equivalent to the fraction 1085/2
===============================================================
Explanation:
AP stands for "arithmetic progression", which is another name for "arithmetic sequence"
a1 = -10 is the first term
the 15th term happens when n = 15, so
an = a1 + d*(n-1)
a15 = -10 + d(15-1)
a15 = 14d-10
Set this equal to 11 (the stated 15th term) and solve for d
a15 = 11
14d-10 = 11
14d = 11+10
14d = 21
d = 21/14
d = 3/2
d = 1.5 is the common difference
Let's find the nth term
an = a1 + d(n-1)
an = -10 + 1.5(n-1)
an = -10 + 1.5n - 1.5
an = 1.5n - 11.5
-------------------------------
The last term is 41, so we'll replace the 'an' with that and solve for n
an = 1.5n - 11.5
41 = 1.5n - 11.5
41+11.5 = 1.5n
52.5 = 1.5n
1.5n = 52.5
n = (52.5)/(1.5)
n = 35
So the 35th term is 41.
-------------------------------
We're summing n = 35 terms from a1 = -10 to an = 41
S = sum of the first n terms of arithmetic progression
S = (n/2)*(a1 + an)
S = (35/2)*(-10+41)
S = 542.5
The 35 terms add up to 542.5 which is the final answer
As an improper fraction, this converts to 1085/2
Given a cylinder with a height of 15 and a radius of 13, find the surface area.
The surface area of this cylinder is ___π
**Read the Fill in the Blank area carefully**
Divisibility rules with algebra
Answer:
D=8
Step-by-step explanation:
normal division rules
33 goes into 47 1 time
then it leaves 17D
if we divide 170 by 33, we get 5 and if we divide 179 by 33, we still get 5. So we have 17D-165. That leaves us with something that you multiply 33 with to have a 2 in the ones place so that you get a remainder of 2. (In order to get 2 in the remainder, we need a 2 in the ones place because 4-2=2. In order to get that we need to see which number multiplied with 33 would get us a number smaller than 179 but also has a 2 in the ones place. Theres only one number and thats 4. 33*4=132. So in order to get only 2 in the remainder, we need the rest to be subtracted. This means that 17D-165=134. This way we can see that D=8
cos 39 degrees =57/x
Answer:
x = 73.35
Step-by-step explanation:
Here, we want to find the value of x
We can get this by simply re-arranging the equation
we have this as follows;
x = 57/cos 39 degrees
x = 73.35
Can someone help me with this math homework please!
Answer:
4
Step-by-step explanation:
A line with 0 slope is parallel to x axis and it must have the same y coordinates
Answer:
4
Step-by-step explanation:
( 3, b ) and ( - 2, 4 )
x1 y1 x2 y2
Here,
x1 = y1 = 0
x2 = - 2
y2 = 4
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope = ( 4 - b ) / ( - 2 - 3 )
0 = ( 4 - b ) / - 5
4 - b = - 5 x 0
4 - b = 0
4 = b
b = 4
How do I simplify this? With steps please :)
Answer:
[tex]{ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}[/tex]
Calculate the length b to two decimal places
b
22
1100
B
14
A
A. 36.99
B. 890.68
C. 29.84
D. 36
HELPPPPPPP ASAPPPPPPPPPPP
The length of the side CA is 29.84. Therefore, option C is the correct answer.
We need to calculate the length b to two decimal places.
AB=14, BC=22 and ∠B=110°.
What is the cosine rule to find the length of the side of the triangle?The cosine rule to find the length of the side of the triangle is a²=b²+c²-2bc cos A.
b²=14²+22²-2×14×22×cos110°
⇒b²=680-616×(-0.342)
⇒b²=680+210.672
⇒b=29.84
The length of the side CA is 29.84. Therefore, option C is the correct answer.
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At what x-value are the equations equal?
Answer:
x=2 is the answer to your question
A number is equal to three times the smaller number also the sum of the smaller number and four is the larger number situation is graft on the coordinate plane below where X represents the smaller number and Y represents the larger number which two equations represent the situation
Answer:
this question is missing needed information
The angle between the top of a building and a point 80 feet away from the base (on level ground) is 70° . To the nearest foot, how tall is the building?
Answer: 220 feet tall
Step-by-step explanation:
1. Draw!
2. Use trigonometric ratios to solve for the height (Remember SOH CAH TOA)
Answer:
The building is 220 ft tall
Step-by-step explanation:
△ABCis reflected to form △A′B′C′. The vertices of △ABC are A(3, 1), B(1, 5), and C(6, 9). The vertices of △A′B′C′ are A′(−1, −3), B′(−5, −1), and C′(−9, −6). Which reflection results in the transformation of △ABC to △A′B′C′? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x I NEED HELP PLS The answer choies are: A. Reflection across the x-axis B. Reflection across the y-axis C. Reflection across y = x D. Reflection across y=−x
Answer: D) reflection across y = -x
Explanation:
When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).
When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]
So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).
Similarly, B(1,5) moves to B ' (-5, -1)
Finally, C(6,9) becomes C ' (-9, -6)
If the discriminant of an equation is zero, which of the following is true of the equation?
[tex]\sf Your \: question \: is \: incomplete. \: [/tex]
______________________
[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹
[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]
[tex]\boxed{ \sf{Explanation}} [/tex]
[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]
Answer:
see explanation
Step-by-step explanation:
If b² - 4ac = 0
Then the roots are real and equal
