Answer:
A. 10
Step-by-step explanation:
As we know that
The length of the major axis of the ellipse is 10
i.e
2 a = 10
Also, the ellipse is the curve that consists of 2 focal points in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve
Now we assume that P is the curve point
So,
PF1 + PF2
i.e
2 a (blue line) + (red line)
2 a = 10
Therefore the sum of the length is 10
Answer:
10
Step-by-step explanation:
please help me with this
Answer:
a) 10
b) 2.5
Step-by-step explanation:
2^n = 1024
2^n = 2^10
n = 10
4^(2n-3) = 16
4^(2n-3) = 4^2
2n-3 = 2
2n = 5
n = 2.5
Solution:-1:-
[tex]\\ \sf\longmapsto 2^n=1024[/tex]
Equal the bases[tex]\\ \sf\longmapsto 2^n=2^10[/tex]
[tex]\\ \sf\longmapsto n=10[/tex]
Solution:-2:-
[tex]\\ \sf\longmapsto 4^{2n-3}=16[/tex]
[tex]\\ \sf\longmapsto 4^{2n-3}=4^2[/tex]
[tex]\\ \sf\longmapsto 2n-3=2[/tex]
[tex]\\ \sf\longmapsto 2n=2+3[/tex]
[tex]\\ \sf\longmapsto 2n=5[/tex]
[tex]\\ \sf\longmapsto n=\dfrac{5}{2}[/tex]
[tex]\\ \sf\longmapsto n=2.5[/tex]
help me with guys plzzzzz
Answer:
C
Step-by-step explanation:
So the lion weighs more than the ant right?
And we wish to figure out how much greater the lion's weight is compared to the ant's weight.
So only thing we have to do is divide.
[tex]\frac{1 * 10^5}{2*10^-3} = \frac{10^5}{2*10^-3} = \frac{10^8}{2} = 50000000 = 5 * 10^7[/tex]
Answer:
5×10^7
Step-by-step explanation:
2×10^-3 1×10^5
(1×10^5)/(2×10^-3)=
5×10^7
to scheck :(2*10^-3)(5*10^7)=(1*10^5)
shannon is paid £1150 a month after deductions.what is her net annual salary?(a year=12 months )
Answer:
£13800
Step-by-step explanation:
1150*12=£13800
Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$. [tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]
Answer:
[tex]x =-5\ - \sqrt{8}[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 10x + 25 = 8[/tex]
Required
Find the smallest value of x
[tex]x^2 + 10x + 25 = 8[/tex]
Expand the expression on the right hand side
[tex]x^2 + 5x + 5x + 25 = 8[/tex]
Factorize
[tex]x(x+5)+5(x+5) = 8[/tex]
[tex](x+5)(x+5) = 8[/tex]
[tex](x+5)^2 = 8[/tex]
Take Square root of both sides
[tex]\sqrt{(x+5)^2} = \±\sqrt{8}[/tex]
[tex](x+5) = \±\sqrt{8}[/tex]
Remove bracket
[tex]x+5 = \±\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5 =-5\± \sqrt{8}[/tex]
[tex]x =-5\± \sqrt{8}[/tex]
[tex]x =-5\ + \sqrt{8}[/tex] or [tex]x =-5\ - \sqrt{8}[/tex]
Comparing both values of x;
The smallest value of x is
[tex]x =-5\ - \sqrt{8}[/tex]
An insect crawls up 5cm every second on a 6cm vertical rod and then falls down 2cm over the next second. How many seconds will it take to climb the rod?
Answer:
3 seconds
Step-by-step explanation:
It's quite simple. First, add 5cm to the progress of the insect, counting it as 1 second. Then subtract 2cm because it falls over the next second, thus taking another second. Then finally, plus 5cm, making it 3 seconds. It's not 4 seconds because at 3 seconds it had already reached the top.
If I didn't clear everything or messed up, please comment.
561
Worksheet
1. Assume that your kidneys can filter out 25% of medicine in your blood every 4 hours. You take one
1000-milligram dose of the medicine. Fill in the table showing the amount of the medicine in your
blood as a function of time. The first three data points are already completed.
At first you will have decimals. Round each value to the nearest milligram so there are no
decimals in your answers.
Time since taking the medicine (in hours)
Amount of medicine in blood (in milligrams)
0
1000
4
1000 - (1000 x 0.25) = 750
8
750 - (750 x 0.25) = 562.5 563
12
16
20
24
28
32
36
40 44 48 52 56
Answer:
12
563 - (563x0.25) = 422.25 -> 422
16
422 -(422x0.25) = 316.5 -> 317
20
317 - (317x0.25) = 237.75 -> 238
24
238 - (238x0.25) = 178.5 -> 179
28 (continue the step by step process)
134.25 -> 134
32
100.5 -> 101
36
75.75 -> 76
40
57
44
42.75 -> 43
48
32.25 -> 32
52
24
56
18
Step-by-step explanation:
the time interval has to keep skipping by four hours because the medicine is filtered in that amount of time.
The multiplying by 0.25 part must be done first in order to show how much the kidney has filtered.
after this, you need to subtract that from how many milligrams of medicine are left in your system
note that if you do not subtract, you will only be showing how much the kidney has filtered. the question asks for how much is left in the SYSTEM overall, so subtracting is quite necessary to completely answer the question.
I hope this helped.
x^2+4xy+4y^2-8x-16y-20
Answer:
Step-by-step explanation:
x²+4xy+4y²-8x-16y-20=(x+2y)²-8(x+2y)-20
put x+y=t
t²-8t-20=t²-10t+2t-20=t(t-10)+2(t-10)=(t-10)(t+2)
substitute the value of t
x²-4xy+4y²-8x-16y-20=(x+2y-10)(x+2y+2)
i don't know what else you want.
The opposite angles of a parallelogram are (3x + 5)° and (61 – x)°. Find the measure of four angles.
Answer:
47°;47°;113°;113°
Step-by-step explanation:
3x+5=61-x
4x=56
X=14
What is x
I dont get it
Answer:
x = 35
Step-by-step explanation:
The angles of a triangle add to 180 degrees
103+ 42 + BCA = 180
BCA = 180 -103 -42
BCA =35
BCA and x are corresponding angles and corresponding angles are equal if the lines are parallel
What transformation of the parent function f(x) is made to get f(3x)?
Answer: Vertically shifting it by 3
The transformation of a function is horizontally shrink by a factor of 3 .
What is a horizontal shrink?We can apply horizontal shrink to a function by multiplying its input values by a scale factor, a, where 0 < 1/a < 1.Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.
Below is a graph of the data.As we have expected, the graph stretches by a factor of 2 and 3. This is true for all horizontal stretches. The graph only stretches away from the y-axis when we horizontally stretch a graph.Horizontal stretch on other functions will exhibit similar properties. Let’s say we have f(x) = |x|, if this function’s graph is to be stretched horizontally to attain g(x), the new function’s expression can be expressed as |1/3 ∙ x| = |x/3|.How do you horizontally shrink by a factor of 3 ?
If g(x) = 3f (x): For any given input, the output of g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.Learn more about Transformation on :
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find the area of parallelogram and round to the nearest tenth.
Answer:
A = 152.9 ~ 153
Step-by-step explanation:
A = bh
= 13.9 * 11
= 152.9 ~ 153
solving polinomial(2x+8)(2x-1)
Answer:
4x²+14x-8 ( multiplying)
x=-4 , x=1/2 ( find solution)
Step-by-step explanation:
(2x+8)(2x-1)
start :
2x*2x=4x²
2x*-1 = -2x
8*2x=16x
8*-1=-8
add the results : 4x²-2x+16x-8 = 4x²+14x-8
If you mean find the solution :(2x+8)(2x-1)=0
2x+8=0
x=-8/2=-4
OR 2x-1=0
then x=1/2
Answer:
=4x2+14x−8
Step-by-step explanation:
(2x+8)(2x−1)
=(2x+8)(2x+−1)
=(2x)(2x)+(2x)(−1)+(8)(2x)+(8)(−1)
=4x2−2x+16x−8
=4x2+14x−8
I hope this helps! :]
Drag each label to the correct location on the table. Each label can be used more than once. A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team. mean mean interquartile range interquartile range standard deviation standard deviation median median
Answer:
a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.
For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .
What is median?Median represents the middle value of the given data when arranged in a particular order.
Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.
The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.
We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.
Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.
Learn more about the Varsity team here
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A classroom has 14 boys and 18 girls. What is the ratio of boys to girls?
Answer:
7:9
Step-by-step explanation:
boys:girls
14:18
simplify -- divide by 2
7:9
Answer:
7:9
Step-by-step explanation:
so we start of with 14 boys to 18 girls, but we need to simplify it.
so we half both numbers to get to 7:9.
this is the most simplified form of this ratio.
the answer is 7:9
Find the product of 0.3×0.23
Answer:
0.069
Step-by-step explanation:
0.3*0.23=0.069
which is odd one out 4:10 12:25 20:50 8:20
Answer:
All of them except 12:25 simply to 2:5. So 12:25 is the odd one out.
Find the decimal number exactly halfway between 1.01 and 1.02.
please help
Answer:
1.015
Step-by-step explanation:
just find their average, which is adding them up and dividing by 2
(1.01 + 1.02)/2 = 1.015
The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
What are decimals?A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.
The given numbers are,
1.01 and 1.02
Now to find the halfway between the number we need to find their sum first and then the half of the sum.
So, the sum of number,
1.01 + 1.02 = 1.03
Now for half way divide the sum by 2
1.03/2 = 1.015
Hence, The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
More about decimal :
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On a piece of paper graph
f(x) = {-1 if -1 <= x < 0}
{ -2 if 0 <= x < 0}
{ -3 if 1 <= x < 2
In this question, a piece-wise function is asked to be graphed.
Piece-wise function:
A piece-wise function is a function that has different definitions, depending on the input.
In this question, the function has three different definitions:
For x between -1(inclusive) and 0, y takes a constant value of -1.
For x between 0(inclusive) and 1, y takes a constant value of -2.
For x between 1(inclusive) and 2, y takes a constant value of -3.
Additionally:
At the inclusive points, the interval is circled, and thus, the graphic is given at the end of this answer.
For another example of the graphic of a piece-wise function, you can check https://brainly.com/question/16855064
Answer:
Step-by-step explanation:
1. (1, 3); (2, 3)
2. (0, 0) (1, 0)
3. (-1, 1) (0,0)
Determine algebraically whether the function is even, odd, or neither even nor odd.
A. Neither
B. Even
C. Odd
9514 1404 393
Answer:
B. even
Step-by-step explanation:
Functions are classed according to what happens when x is replaced by -x.
f(-x) = f(x) . . . even
f(-x) = -f(x) . . . odd
__
Here, we have ...
f(-x) = 2/(-x)^2 = 2/x^2 = f(x) . . . . an even function
Yivgeny's gymnastics scores were 1.5, 1.7, 5.5, and 9.1. In order to calculate his total score, you pick the two top scores and add them. What is his total score?
Answer:
14.6
Step-by-step explanation:
In the question, we are told that:
Yivgeny's gymnastics scores were 1.5, 1.7, 5.5, and 9.1.
In the question, we are also told that to calculate his total score, we add his top two scores.
Yivgeny's top two gymnastics scores are:
5.5 and 9.1.
Hence, his total scores = 5.5 + 9.1
= 14.6
Yivgeny's total scores = 14.7
5×12÷[-12÷{15+(4-3)}]
Answer: -80
Step-by-step explanation:
Which of the binomials below is a factor of this trinomial?
X^2 + 5x + 6
Answer:
(x + 2) , (x + 3) are factors
Step-by-step explanation:
Given
x² + 5x + 6
Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (+ 5)
The factors are + 2 and + 3, since
2 × 3 = 6 and 2 + 3 = 5 , thus
x² + 5x + 6 = (x + 2)(x + 3)
WORKED EXAMPLES
Try Vertical Angle Problems
ZC and Dare vertical angles.
m_C=° and mZD=(-3x +80)°
What is mZC
Enter your answer in the box.
Answer:
20
Step-by-step explanation:
Vertical angles are equal to each other
x = -3x + 80
x + 3x = 80
4x = 80 divide both sides by 4
x = 20
If ABC - AZXY, mZA = 50, and mZC = 30,
what is mZX?
Let it be x
Using angle sum theory
[tex]\\ \sf\longmapsto 50+30+x=180[/tex]
[tex]\\ \sf\longmapsto 80+x=180[/tex]
[tex]\\ \sf\longmapsto x=180-80[/tex]
[tex]\\ \sf\longmapsto x=100[/tex]
The weights of cars passing over a bridge have a mean of 3,550 pounds and standard deviation of 870 pounds. Assume that the weights of the cars passing over the bridge are normally distributed. Use a calculator to find the probability that the weight of a randomly-selected car passing over the bridge is less than 3,000 pounds.
Answer:
0.24315
Step-by-step explanation:
Using the z score formula to solve this question
z = (x - μ) / σ,
Such that:
x = raw score
μ = population mean
σ = population standard deviation.
From the question:
x = 3000
μ = 3550
σ = 870
z = (3000 - 3550) / 870
z = -550/870
z = -0.6962
Using the z score table as well as probability calculator(as requested in the question to find the z score)
The probability of having less than 3000 is obtained as:
P(x<3000) = 0.24315
how many are 2 raised to 3 ???
Answer:
8
Step-by-step explanation:
2^3
It is two multiplied by itself 3 times
2*2*2
8
this graph shows the solution to which inequality (3 3) (-3 -1)
Answer:
B
Step-by-step explanation:
since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer
y>2/3 x +1 is your answer (B)
Answer:
[tex] \boxed{y > \frac{2}{3} x + 1}[/tex]Option B is the correct option.
Step-by-step explanation:
point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1
point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3
Now, let's find the slope:
Slope ( m ) = [tex] = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{3 - ( - 1)}{3 - ( - 3)} [/tex]
[tex] = \frac{3 + 1}{3 + 3} [/tex]
[tex] = \frac{4}{6} [/tex]
[tex] = \frac{2}{3} [/tex]
At ( 3 , - 1 )
y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis
[tex] - 1 = \frac{2}{3} \times ( - 3) + c[/tex]
Solve for c
[tex] - 1 + 2 = c[/tex]
[tex]c = 1[/tex]
Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.
The answer would be:
[tex]y > \frac{2}{3} x + 1[/tex]
Hope I helped!
Best regards!
Jess receives a $15000 salary for working as an engineer. If Jess has to spend $6000 of her salary on expenses each year, then what percent of Jess's money does she have to spend? Round your answer to the nearest whole number if necessary.
Answer:
Jess will have to spend 40% of her salary
Step-by-step explanation:
Jess salary = $15,000
Jess expenses = $6,000
what percent of Jess's money does she have to spend
Percentage of Jess expenses = Jess expenses / Total salary × 100
= 6,000 / 15,000 × 100
= 0.4 × 100
= 40%
Jess will have to spend 40% of her salary
For a company picnic, Jacob ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 68 cookies, and 75% of them were gingerbread. How many gingerbread cookies did Jacob get?
Answer:
51 gingerbread cookies
Step-by-step explanation:
Find how many gingerbread cookies he got by finding 75% of 68:
68(0.75)
= 51
So, Jacob got 51 gingerbread cookies.
simplify3³×9²×125³÷9³
Answer:
Step-by-step explanation:
Prime factorize 9 and 125
9 = 3* 3 = 3²
125 = 5 * 5 * 5 = 5³
3³ * 9² * 125³ ÷ 9³ = [tex]\frac{3^{3}*(3^{2})^{2}*(5^{3})^{3}}{(3^{2})^{3}}\\[/tex]
[tex]= \frac{3^{3}*3^{4}*5^{9}}{3^{6}}\\\\=\frac{3^{3+4}*5^{9}}{3^{6}}\\\\= \frac{3^{7}*5^{9}}{3^{6}}\\\\=3^{7-6}*5^{9}\\=3*5^{9}[/tex]
Exponent laws:
[tex](a^{m})^{n}=a^{m*n}\\\\\\a^{m}*a^{n} = a^{m +n}\\\\\\\frac{a^{m}}{a^{n}}=a^{m-n} \ ; \ m > n[/tex]