Answer:
The graph of f(x) = |x| is shifted to the right 8 units, up 3 units.Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
We have g(x) = |x - 8| + 3
f(x) = |x| → f(x - 8) = |x - 8| shift the graph 8 units to the right
f(x - 8) + 3 → |x - 8| + 3 shift the graph 3 unit up
An experiment consists of rolling a die, flipping a coin, and spinning a spinner divided into 4 equal regions. The number of elements in the sample space of this experiment is
12
3
6
48
Answer:
48
Step-by-step explanation:
There are 3 events that are taking place.
Rolling a die which has 6 possible outcomes.
Flipping a coin which has 2 possible outcomes.
Spinning a spinner which has 4 possible outcomes.
Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.
i.e.
Total outcomes = 6 x 2 x 4 = 48
The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48
Answer:
The correct answer option is 48.
Step-by-step explanation:
Here in this experiment, three events are taking place that include rolling a die, flipping a coin and spinning a spinner.
The possible outcomes of each of these events are:
Rolling a die - 6
Flipping a coin - 2
Spinning a spinner - 4
Therefore, we can find the number of elements in the sample space of this environment by multiplying their possible outcomes.
Number of elements = 6 × 2 × 4 = 48
Write the augmented matrix for each system of equations.
9x-4y-5z=9
7x+4y-4z=-1
6x-6y+z=5
Answer:
a. [tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
Step-by-step explanation:
The given system of equation is
[tex]9x-4y-5z=9[/tex]
[tex]7x+4y-4z=-1[/tex]
[tex]6x-6y+z=-5[/tex]
The coefficient matrix is :
[tex]\left[\begin{array}{ccc}9&-4&-5\\7&4&-4\\6&-6&1\end{array}\right][/tex]
The constant matrix is
[tex]\left[\begin{array}{c}9\\-1\\-5\end{array}\right][/tex]
The augmented matrix is obtained by combining the coefficient matrix and the constant matrix.
[tex]\left[\begin{array}{cccc}9&-4&-5&|9\\7&4&-4&|-1\\6&-6&1&|-5\end{array}\right][/tex]
The correct choice is A
Find three consecutive even integers that sum up to -72.
Answer:
-26, -24 and -22Step-by-step explanation:
[tex]n,\ n+2,\ n+4-\text{three consecutive even integers}\\\\\text{The equation:}\\\\n+(n+2)+(n+4)=-72\\\\n+n+2+n+4=-72\qquad\text{combine like terms}\\\\3n+6=-72\qquad\text{subtract 6 from both sides}\\\\3n+6-6=-72-6\\\\3n=-78\qquad\text{divide both sides by 3}\\\\\dfrac{3n}{3}=-\dfrac{78}{3}\\\\n=-26\\\\n+2=-26+2=-24\\\\n+4=-26+4=-22[/tex]
Elmer body skateboard ramp for his son he wants to surprise him with it so he wants to wrap the ramp with special paper what is the minimum amount of wrapping paper he will need to wrap the ramp.
Answer:
480 feet
Step-by-step explanation:
A cab charges $1.75 for the flat fee and $0.25 for each mile. Write and solve an inequality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
I think it's 53 miles
Step-by-step explanation:
After flat fee of $1.75 leaves him $13.25. Then use the remainder to calculate miles. Each dollar allows 4 miles × 13 = 52+1=53
The inequality is:
[tex]1.75+0.25x\leq 15[/tex]
The solution of the inequality is:
[tex]x\leq 53[/tex]
Step-by-step explanation:Let Eddie could travel x miles.
It is given that:
A cab charges $1.75 for the flat fee and $0.25 for each mile.
This means that the fee charged by Eddie if he travels x miles excluding the flat fee is:
$ 0.25x
Total amount the cab will charge Eddie is:
1.75+0.25x
Also, it is given that:
He has only $ 15 to spend this means that he can spend no more than 15 on riding in a cab.
Hence, the inequality is given by:
[tex]1.75+0.25x\leq 15[/tex]
Now on solving the inequality i.e. finding the possible values of x from the inequality.
We subtract both side of the inequality by 1.75 to obtain:
[tex]0.25x\leq 13.25[/tex]
Now on dividing both side of the inequality by 0.25 we get:
[tex]x\leq 53[/tex]
Hence, Eddie could travel less than or equal to 53 miles .
Algebra !! Please help, I have been stuck on this for a long time.
Answer:
x+3
Step-by-step explanation:
Factor x² + 6x + 9 = (x+3)(x+3)
Factor x² + 5x + 6 = (x+3)(x+2)
We can see that (x+3) is the LCM since it goes into x² + 6x + 9 and
x² + 5x + 6
10+(2x3)2/4x1/2 3 zzzzzzzzzzzzzzzzz
Answer: 233/23
Step-by-step explanation:
An airplane's altitude changes -378 feet over 7 minutes. What was the mean change of altitude in feet per minute?
The mean altitude will be -54 per minute
Step-by-step explanation:We are given with altitude change as -378 feet over 7 minutes
Now
We need feet per minute
So -378 / 7 will give us the altitude change per minute
-378 / 7 = -54
Therefore the mean change of altitude in feet per minute is -54 per minute
write an explicit formula formula for the sequence 2, 8, 14, 20, 26,...
a. a_n= 2n-2
b. a_n= 2n+2
c. a_n=4n+2
d. a_n = 6n-4
Answer:
d. a_n = 6n - 4.
Step-by-step explanation:
The common difference (d) is 8-2 = 14-8 = 20-14 = 26-20 = 6.
This is an Arithmetic Sequence with the first term (a1) is 2.
The general form of the explicit formula is a_n = a1 + d(n - 1) so this sequence has the formula:
a_n = 2 + 6(n - 1)
a_n = 2 + 6n - 6
a_n = 6n - 4.
The sequence is an illustration of an arithmetic sequence.
The explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
We have:
[tex]a_1 = 2[/tex] -- the first term
Next, we calculate the common difference (d)
[tex]d = a_2 - a_1[/tex]
So, we have:
[tex]d = 8 -2[/tex]
[tex]d = 6[/tex]
The explicit formula is calculated using:
[tex]a_n = a_1 + (n - 1)d[/tex]
So, we have:
[tex]a_n =2 + (n - 1) \times 6[/tex]
Open bracket
[tex]a_n = 2 + 6n - 6[/tex]
Collect like terms
[tex]a_n = 6n - 6 + 2[/tex]
[tex]a_n = 6n - 4[/tex]
Hence, the explicit formula is: (d) [tex]a_n = 6n - 4[/tex]
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There are two brands of Corn Flakes, Post and Kellogs. Each brand has the same size box. However, because of each brand’s filling procedure, they have different mean weights. The weights of a box of Post Corn Flakes is approximately normal with μ = 64.1 oz and σ = .5 oz while the weight of a box of Kellogs, which is also normally distributed, has μ = 63.9 oz and σ = .4 oz.
A box is selected from each brand and weighed. What is the probability that the Post box will outweigh the Kellogs box?
Probability of an event is the measure of its chance of occurrence. The probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] standard deviation [tex]\sigma[/tex])
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z-tables, the p-value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
What is the distribution of random variable which is sum of normal distributions?Suppose that a random variable X is formed by [tex]n[/tex] mutually independent and normally distributed random variables such that:
[tex]X_i = N(\mu_i , \sigma^2_i) ; \: i = 1,2, \cdots, n[/tex]
And if
[tex]X = X_1 + X_2 + \cdots + X_n[/tex]
Then, its distribution is given as:
[tex]X \sim N(\mu_1 + \mu_2 + \cdots + \mu_n, \: \: \sigma^2_1 + \sigma^2_2 + \cdots + \sigma^2_n)[/tex]
If, for the given case, we assume two normally distributed random variables as:
X = variable assuming weights of boxes of Post Corn Flakes
Y = variable assuming weights of boxes of Kellogs
Then, as per the given data, we get:
[tex]X \sim N(\mu = 64.1, \sigma = 0.5)\\Y \sim N(\mu = 63.9, \sigma = 0.4)[/tex]
Then, the probability that the Post box will outweigh the Kellogs box can be written as:
[tex]P(X > Y)[/tex]
Or,
[tex]P(X -Y > 0)[/tex]
We need to know about the properties of X-Y.
Also, since [tex]E(aX) = aE(X), Var(aX) = a^2Var(X)[/tex], thus,
[tex]-Y \sim N(-63.9, 0.4)[/tex]
As both are independent(assuming), thus,
[tex]X - Y \sim N(\mu = 64.1 - 63.9, \sigma = 0.5 + 0.4) = N(0.2, 0.9)[/tex]
Using the standard normal distribution, we get the needed probability as:
[tex]P(X -Y > 0) = 1 - P(X - Y \leq 0) \\P(X -Y > 0)= 1- P(Z = \dfrac{(X-Y) - \mu}{\sigma} \leq \dfrac{0 - 0.2}{0.9})\\P(X -Y > 0) \approx 1 - P(Z \leq -0.22)[/tex]
Using the z-tables, the p-value for Z = -0.22 is 0.4129
Thus, [tex]P(X > Y) = P(X - Y > 0) \approx 0.4129[/tex]
Thus, the probability that the post box will outweigh the Kellogs box is 0.4129 approximately.
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The probability that a randomly selected Post box outweighs a Kellogg's box is approximately 50%.
To find the probability that the Post box will outweigh the Kellogg's box, we need to calculate the difference in weights between the two brands and then determine the probability that this difference is positive.
Let X be the weight of a box of Post Corn Flakes and Y be the weight of a box of Kellogg's Corn Flakes.
We are given that:
- For Post Corn Flakes, X ~ N(μ = 64.1, σ = 0.5)
- For Kellogg's Corn Flakes, Y ~ N(μ = 63.9, σ = 0.4)
We want to find P(X > Y), which is the probability that a randomly selected box of Post Corn Flakes weighs more than a randomly selected box of Kellogg's Corn Flakes.
Now, let Z = X - Y. We are interested in finding P(Z > 0).
The mean and standard deviation of Z can be calculated as follows:
- Mean of Z: μ_Z = μ_X - μ_Y = 64.1 - 63.9 = 0.2 oz
- Standard deviation of Z: σ_Z =[tex]sqrt(σ_X^2 + σ_Y^2) = sqrt(0.5^2 + 0.4^2)= sqrt(0.25 + 0.16)= sqrt(0.41) = 0.64 oz[/tex]
Now, we standardize Z:
Z = (X - Y - μ_Z) / σ_Z
Therefore,
P(Z > 0) = P((X - Y - μ_Z) / σ_Z > 0)
= P((X - Y) > μ_Z)
= P((X - Y) > 0.2)
Now we look up the z-score corresponding to Z = 0.2:
z = (0.2 - μ_Z) / σ_Z
= (0.2 - 0.2) / 0.64
= 0
The probability that Z is greater than 0 is equal to the probability that the standardized Z-score is greater than 0, which is 0.5.
Therefore, the probability that the Post box will outweigh the Kellogg's box is 0.5 or 50%.
Ava started a savings account with $500 after 6 months her savings account balance was $731 find the rate of change
Answer:
$38.50/mo
Step-by-step explanation:
Rate of change = change in balance/time.
Change in balance = $731 - $500 = $231
Rate of change = $231/6 mo = $38.50/mo
Answer:
31.60%
Step-by-step explanation:
(731−500)÷731=0.3160
0.3160×100=31.60%
Hope it helps!
Example 5 suppose that f(0) = −8 and f '(x) ≤ 9 for all values of x. how large can f(3) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 3] . there exists a number c such that f(3) − f(0) = f '(c) − 0 so f(3) = f(0) + f '(c) = −8 + f '(c). we are given that f '(x) ≤ 9 for all x, so in particular we know that f '(c) ≤ . multiplying both sides of this inequality by 3, we have 3f '(c) ≤ , so f(3) = −8 + f '(c) ≤ −8 + = . the largest possible value for f(3) is .
[tex]f'(x)[/tex] exists and is bounded for all [tex]x[/tex]. We're told that [tex]f(0)=-8[/tex]. Consider the interval [0, 3]. The mean value theorem says that there is some [tex]c\in(0,3)[/tex] such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
Since [tex]f'(x)\le9[/tex], we have
[tex]\dfrac{f(3)+8}3\le9\implies f(3)\le19[/tex]
so 19 is the largest possible value.
Given a differentiable function with f(0) = -8 and f'(x) ≤ 9 for all x, we use the Mean Value Theorem to find that f(3), at its largest, can be 1.
Explanation:In this mathematics problem, we are given that f is a differentiable function with f(0) = -8 and its derivative f'(x) ≤ 9 for all x. We aim to calculate the possible maximum value of f(3). To do this, we apply the Mean Value Theorem for the interval [0, 3]. By this theorem, there exists a number 'c' in this interval such that the derivative at that point is equal to the slope of the secant line through the points (0, f(0)) and (3, f(3)). Thus, we get the equation: f(3) - f(0) = f'(c). Rearranging this, we get f(3) = f(0) + f'(c). Substituting the given values, f(3) = -8 + f'(c).
Since we know f'(x) ≤ 9 for all x, this means f'(c) ≤ 9 as well. Replacing this in the equation we get f(3) ≤ -8 + 9 = 1. Hence, the largest possible value for f(3) is 1.
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Plz help me..
WILL GIVE BRAINLIEST
Answer:
B, 3x - 5
Step-by-step explanation:
Factor by grouping to get (3x - 5)(2x + 3).
Factor 6x2−x−15
6x2−x−15
=(3x−5)(2x+3)
Answer:
(3x−5)(2x+3)
The trail is 2982 miles long.It begins in city A and ends in city B.Manfred has hiked 2/7 of the trail before.How many miles has he hikes?
Answer:
852
Step-by-step explanation:
One angle of a triangle measures 60°. The other two angles are in a ratio of 7:17. What are the measures of those two angles?
Answer:
35° and 85°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Since one angle = 60° then the sum of the other 2 angles = 120°
Sum the parts of the ratio 7 + 17 = 24 parts, hence
[tex]\frac{120}{24}[/tex] = 5° ← value of 1 pat of the ratio, hence
7 parts = 7 × 5° = 35°
17 parts = 17 × 5° = 85°
note that 60° + 35° + 85° = 180°
Evaluate each log without a calculator
[tex]log_{243^{27} }[/tex]
[tex]log_{25} \frac{1}{5}[/tex]
QUESTION 1
The given logarithm is
[tex]\log_{243}(27)[/tex]
Let [tex]\log_{243}(27)=x[/tex].
We rewrite in exponential form to get;
[tex]27=243^x[/tex]
We rewrite both sides of the equation as an index number to base 3.
[tex]3^3=3^{5x}[/tex]
Since the bases are the same, we equate the exponents.
[tex]3=5x[/tex]
Divide both sides by 5.
[tex]x=\frac{3}{5}[/tex]
[tex]\therefore \log_{243}(27)=\frac{3}{5}[/tex]
QUESTION 2
The given logarithm is
[tex]\log_{25}(\frac{1}{5} )[/tex]
We rewrite both the base and the number as power to base 5.
[tex]\log_{5^2}(5^{-1})[/tex]
Recall that: [tex]\log_{a^q}(a^p)=\frac{p}{q} \log_a(a)=\frac{p}{q}[/tex]
We apply this property to obtain;
[tex]\log_{5^2}(5^{-1})=\frac{-1}{2}\log_5(5)=-\frac{1}{2}[/tex]
9 minutes left to finish this!! I need help!
Joey is 17 years older than his sister Pat. In 6 years, Joey will be 7 more than twice Pat’s age then. How old are Joey and Pat today?
Answer:
p = 4
j = 21
Step-by-step explanation:
Joey = j
Pat = p
j = p + 17
(j+6) = 2*(p + 6) + 7 Simplify this. Remove the brackets.
j + 6 = 2p + 12 + 7 combine like terms
j + 6 = 2p + 19 Subtract 6 from both sides
j +6-6 = 2p +19-6
j = 2p + 13
================
Equation j = 2p + 13 and j = p + 17
2p + 13 = p + 17 Subtract p from both sides
2p-p+13 =p-p + 17
p + 13 = 17 Subtract 13 from both sides
p = 17-13
p = 4
============
j = p + 17
j = 4 + 17
j = 21
Answer:
Joey is 21; Pat is 4
Step-by-step explanation:
The problem statement supports two equations in Joey's age (j) and Pat's age (p):
j - p = 17
(j +6) -2(p +6) = 7
Subtracting the second equation from the first, we have ...
(j -p) -((j +6) -2(p +6)) = (17) -(7)
p +6 = 10 . . . . . simplify
p = 4 . . . . . . . . . subtract 6
J = 17 +4 = 21
Joey is 21; Pat is 4.
Which line contains the point (2, 1)?
a)4x-y=7
b)2x+5y=4
c)7x-y=15
d)x+5y=21
what is the best approximation of the area of a circle with a diameter of 17 meters? Use 3.14 to approximate pi.
a. 53.4 m2
b. 106.8 m2
c. 226.9 m2
d. 907.5 m2
[tex]\bold{Hey\ there!}[/tex]
[tex]\bold{What\ is\ the\ best\ approximation\ of\ the\ area\ of\ a\ circle\ with\ a\ diameter\ of\ 17\ meters.}[/tex] [tex]\bf{Use\ 3.14\ to \ approximate\ pi\}[/tex][tex]\bold{Firstly,\ highlight\ your\ key\ terms:} \\ \bold{\bullet \ \underline{Approximation\ of\ the\ area\ of\ a \ circle\ with\ a\ diameter\ of\ 17.}}}\\ \\ \bold{\bullet\ \underline{Use\ 3.14\ to\ approximate\ pi}}[/tex][tex]\bold{17\times3.14=53.38}[/tex][tex]\bold{If\ we're\ rounding\ upward\ then\ your\ answer\ would\ be\ A.53.4m^2}[/tex][tex]\boxed{\boxed{\bold{Answer:A).53.4m^2}}}}\checkmark[/tex][tex]\bold{Good\ luck\ on\ your\ assignment\ \& enjoy\ your\ day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Answer:
The answer is c 226.9 m2
Step-by-step explanation:
Hope this helps
The ratio of petunias to geraniums in the greenhouse was 15 to 2. Combined there was 1020. How many geraniums were in the greenhouse.
in short, we simply split the total amount by the given ratio, so we'll split or divide 1020 by (15 + 2) and then distribute accordingly.
[tex]\bf \cfrac{petunias}{geraniums}\qquad 15:2\qquad \cfrac{15}{2}~\hspace{7em}\cfrac{15\cdot \frac{1020}{15+2}}{2\cdot \frac{1020}{15+2}}\implies \cfrac{15\cdot \frac{1020}{17}}{2\cdot \frac{1020}{17}} \\\\\\ \cfrac{15\cdot 60}{2\cdot 60}\implies \cfrac{900}{120}\implies \stackrel{petunias}{900}~~:~~\stackrel{geraniums}{120}[/tex]
The total number of geraniums in the greenhouse is 120. This was determined by calculating the value of each 'part' in the provided petunia to geranium ratio and then multiplying the number of geranium 'parts' by this value.
Explanation:The question provides a ratio of petunias to geraniums in the greenhouse, which is 15:2. This is the same as saying for every 15 petunias, there are 2 geraniums. If you combine the parts of the ratio, you get a total of 17 parts (15 petunias + 2 geraniums). We know that the total number of flowers in the greenhouse is 1020.
Now, we'll figure out what each 'part' is equal to in the real world. To do that, we divide the total number of flowers by the total number of parts, so 1020 ÷ 17 = 60. This tells us each 'part' in our ratio is equal to 60 flowers.
From there, since we need to find the number of geraniums, we multiply the number of geranium 'parts' by the value of each 'part'. So, the number of geraniums in the greenhouse is 2 (The geranium 'parts') x 60 = 120 geraniums.
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If 5 bags of apples weigh 12 1/7 pounds, how many pounds would you expect 1 bag of apples to weigh?
Answer:
2 and 3/7 pounds
Step-by-step explanation:
Convert the mixed number to an improper fraction
12 1/7 becomes 85/7
This represents 5 bags, so divide it by 5 to see what one bag should weigh...
(85/7)/5 becomes (85/7)/(5/1)
which becomes
(85/7)*(1/5) (division is the same as multiplying by the reciprocal)
85/35
17/7 (reduce the fraction by factoring out a 5 from top and bottom)
2 and 3/7 pounds
Help pleaseee!!! (Photo attached)
Answer:
length of base is 10
Step-by-step explanation:
The area of the entire firgure is 1600 cm^2. There are 4 equal sized pennants, so each pennant is 1600/4 = 400
the bottom pennant has area 400 and is triangular shaped. the area of a triangle is 1/2 b h.
A = 1/2 b h given height is 80 and area is 400. plug these values in
400 = 1/2 b (80)
400 = 40 b divide both sides by 40
b = 10
Please help! I'll mark brainiest!
Match the x-coordinates with their corresponding pairs of y-coordinates on the unit circle.
Answer:
Step-by-step explanation:
2 on top goes to last on the bottom or b goes to d
1st one one top goes to the 2nd one on bottom or a goes to b
last one on top goes to the third one on bottom or d goes to c
The last two witch are 3rd on top and first one together
Hope this helped it took me a long time :)
The x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex][tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex][tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex][tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]What is the equation of the circle with radius r units, centered at (x,y) ?If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
A unit circle refers to a circle with unit radius (r = 1 unit) and positioned at center ( coordinates of origin = (h,k) = (0,0))
Thus, the equation of unit circle would be:
[tex]x^2 + y^2 =1[/tex]
Getting expression for y in terms of x,
[tex]x^2 + y^2 =1\\\\y = \pm \sqrt{1 - x^2}[/tex]
Using this equation to evaluate x for all given y:
Case 1: y = ±√5/3[tex]\pm \dfrac{\sqrt{5}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{5}{9} = 1 - x^2\\\\x^2 = \dfrac{4}{9}\\\\x = \pm \dfrac{2}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get:
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex]
Case 2: y = ±√7/3[tex]\pm \dfrac{\sqrt{7}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{7}{9} = 1 - x^2\\\\x^2 = \dfrac{2}{9}\\\\x = \pm \dfrac{\sqrt{2}}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex]
Case 3: y = ±3/5[tex]\pm \dfrac{3}{5} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{9}{25} = 1 - x^2\\\\x^2 = \dfrac{16}{25}\\\\x = \pm \dfrac{4}{5}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex]
Case 4: y = ±2√2/3[tex]\pm \dfrac{2\sqrt{2}}{3} = \pm \sqrt{1-x^2}\\\\\text{Squaring both the sides}\\\\\dfrac{8}{9} = 1 - x^2\\\\x^2 = \dfrac{1}{9}\\\\x = \pm \dfrac{1}{3}[/tex]
From the options available, the fourth block seems valid.
Thus, we get: [tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]
Thus, the x and y coordinates on the circle will be such that they satisfy the equation of the unit circle.
[tex]y = \pm \dfrac{\sqrt{5}}{{3}} \rightarrow \left(\dfrac{2}{3}, y\right)[/tex][tex]y = \pm \dfrac{\sqrt{7}}{{3}} \rightarrow \left(\dfrac{\sqrt{2}}{3}, y\right)[/tex][tex]y = \pm \dfrac{3}{5} \rightarrow \left(\dfrac{4}{5}, y\right)[/tex][tex]y = \pm \dfrac{2\sqrt{2}}{{3}} \rightarrow \left(\dfrac{1}{3}, y\right)[/tex]Learn more about equation of a circle here:
https://brainly.com/question/10165274
Factor
x + x²y + x³y²
and
10ℎ³????³ – 2h????² + 14hn
You randomly choose one of the tiles. Without replacing the first tile. What is the event of the compound event? Write your answer as a fraction or percent rounded to the nearest tenth. 20 is the number of
Answer:
87777777777777777777777777
Step-by-step explanation:
help
Which expression is equivalent to 8(a-6)
a. 8a-48
b. 2a
c. 8a-6
d. 48a
The correct answer would be A.
A.
You can distribute the 8
Distribute 8 to a and multiply them = 8a
Distribute 8 to -6 and multiply them = -48
= 8a-48
A right triangle has side lengths that are consecutive integers and has a perimeter of 12 ft. What are the angles of the triangle
Answer:
The 3 angles are 36.87, 53.13 and 90 degrees.
Step-by-step explanation:
This right triangle ABC has sides 3, 4 and 5 units.
To find the angles:
sin A - 3/5 gives m < A = 36.87 degrees
sin B = 4/5 gives m < B = 53.13 degrees.
HELPPPPP ... Question 18
Answer:
Part a) The volume of the prism Q is two times the volume of the prism P
Part b) The volume of the prism Q is two times the volume of the prism P
Step-by-step explanation:
Part 18) we know that
The volume of a rectangular prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=B(2h)=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
so
The volume of the prism Q is two times the volume of the prism P
b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=(2B)h=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
The volume of the prism Q is two times the volume of the prism P
Dana walks 3/4 miles in 1/4 hours. What is dana's walking rate in miles per hour?
Dana’s waking rate in miles per hour is 3 mph.
I did 3/4 x 4 = 3 because she walked 1/4 a mile and I needed to figure out the miles per one whole hour.
I hope this made sense and helped you.
2x+3x+4x=180
9x=180
x=20
how did they get 20, am i missing something
➷ We'll work from here:
9x = 180
To isolate x, you would need to divide both sides by 9
x = 180/9
Solve:
x = 20
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer: ❤️Hello!❤️ x = 20
Step-by-step explanation: Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x+3*x+4*x-(180)=0
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
9x - 180 = 9 • (x - 20)
Step 2 :
Equations which are never true :
2.1 Solve : 9 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : x-20 = 0
Add 20 to both sides of the equation :
x = 20