[tex]6x^2-x=2\implies 6x^2-1x-2=0 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{-1}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]
[tex]x = \cfrac{ -(-1) \pm \sqrt { (-1)^2 -4(6)(-2)}}{2(6)}\implies x = \cfrac{1\pm\sqrt{1+48}}{12} \\\\\\ x = \cfrac{1\pm\sqrt{49}}{12}\implies x = \cfrac{1\pm 7}{12}\implies x = \begin{cases} \frac{8}{12}\to &\frac{2}{3}\\[1em] -\frac{6}{12}\to &-\frac{1}{2} \end{cases}[/tex]
Maya is helping a gardener plant 300 bulbs. They plant 20% of the bulbs on Monday and 30% of the bulbs on Tuesday. Maya says this means they have planted 50 bulbs so far. Label and shade the model. Then use your model to explain why Maya's statement is not reasonable.
Answer:
because the total is 300 not 100 so 50 is not reasonable because that is the percentage they planted and since it is more than 100 then it should be a percent of 300 not 100. Maya is wrong about placing 50 bulbs instead they placed 150.
Step-by-step explanation:
I am having trouble with this problem. I can’t figure it out. I have tried everything but can’t figure it out. After I figure out the problem I have to check it by writing out the problem and replacing the y with the number it equals. At the end it should equal 6
The picture is a different problem but this is what the check looks like
6=-y+42+-2y
Answer:
16 = y
Step-by-step explanation:
So you have the equation 6=-y+42+-2y
Find the y first
6=-y+42+-2y
add all y's together
6=-3y+42
subtract 42 on both sides
-48 = -13y
16 = y
------------------------------------------------
Now do the check:
Plug in 16 where ever it says y in the original equation
6= -(16) + 42 + -2(16)
open the brackets
6= -16+42-32
solve
6=26-32
6 = 6
Hope this helps
Han rides his bike for 50 miles over 4 hours.How long will it take him to ride 75 miles?
Answer:
6 hours.
Step-by-step explanation:
This is directly proportional, meaning if you multiply one side by a number, you multiply the other side by the same number. For the ratio 50:4, you would have to multiply 1.5 to 50 to get 75 miles, so you would also have to multiply 4 by 1.5. This would get you 6 hours.
2yx= 4 is it a linear function?
Answer:
No, it is not a linear function, rather a rational function
Step-by-step explanation:
Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:
2yx=4
yx=2
y=2/x
The triangles shown below must be congruent. True or False?
Answer:
they are technically congruent due to same angles n same or equal sides
Answer:
A. TrueStep-by-step explanation:
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
so your amswer is A. True
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $160 and first class tickets for $950. She used her total budget for airfare for the trip, which was $3650. How many first class tickets did she buy? How many coach tickets did she buy?
Answer:
Money for coach tickets is $1280 and money for first class is $7600
Step-by-step explanation:
8 x 160 = 1280
8x 950 = 7600
What do you measure the amount of water in a vase
Approximately 19% of physics majors in the US are women. To test whether your college differs significantly from the national average, you take a random sample of 50 physics majors at your college and find that 11 are female. Calculate the appropriate test statistic to determine whether your college differs significantly from the national rate
Testing the hypothesis, it is found that the appropriate test statistic is z = 0.54.
At the null hypothesis, it is tested if the proportion of women physics majors in your college is the same as the national average of 19%, that is:
[tex]H_0: p = 0.19[/tex]
At the alternative hypothesis, it is tested if the proportion is different, that is:
[tex]H_1: p \neq 0.19[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.19, n = 50, \overline{p} = \frac{11}{50} = 0.22[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.22 - 0.19}{\sqrt{\frac{0.19(0.81)}{50}}}[/tex]
[tex]z = 0.54[/tex]
A similar problem is given at https://brainly.com/question/24166849
How many solutions does the system of equations below have? (PLEASE HELP)
y=−9x−2
y=−9x−2
Answer:
y= -54-2
y= -56 &
x= -54/ -9
x= 6
Step-by-step explanation:
y= -9x-2
-9x= y+2 divide bothe side by -9
x=y+2/-9
y= -9(y+2/ -9) -2 = (y+2)-2
y= -2(y+2)
y= -2y-4
y+2y= -4
3y= -4 divide bothe side by 3
y= -4/3
x=y+2/ -9
x= -4/3+2/-9
x= -2/3× -9
x=18/3
x=6
Problem example: For the given sequence: -2,2,6,10,14,18
Write a recursive formula to find the nth term: a = an-1+4
Write a explicit formula to find the nth term: a = -2 + 4(n-1)
What is the 64th term in the sequence?
Answer:
250
Step-by-step explanation:
You can take the explicit formula and simply substitute the n value with 64:
-2 + 4 * (64 - 1)
-2 + 4 * (63)
-2 + 252
250
Which could be the first 4 terms of an arithmetic sequence ?
Part A
Triangle ABC is reflected across the
X-axis to form triangle A'B'C'. What are
the coordinates of C after the
reflection? (Draw the image across the
Taxis)
Do
76
A. (-6,4)
B. (3,-2)
C. (4, -6)
D. (6,-4)
Answer:
D) (6, -4)
Step-by-step explanation:
pt C has coordinates of (6,4)
if you reflect that point across the x-axis the x-value remains the same and the y-value continues to be 4 units from the x-axis, but below it instead of above it
Determine whether the distribution is a discrete probability distribution
X. 1 2 3 4 50
P(x) 0.28 0.45 0.11 0.08 0.08
Is the distribution a discrete probability distribution?
O A. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive.
OB. No, because each probability is not between 0 and 1, inclusive.
O c. Yes, because the sum of the probabilities is equal to 1.
OD. No, because the sum of the probabilities is not equal to 1.
Answer:
A child psychologist is interested in the number of times a newborn baby’s crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let X = the number of times per week a newborn baby’s crying wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.
P(x) = probability that X takes on a value x.
x P(x)0 P(x = 0) = 250
1 P(x = 1) = 1150
2 P(x = 2) = 2350
3 P(x = 3) = 950
4 P(x = 4) = 450
5 P(x = 5) = 150
Step-by-step explanation:
pa follow po pls.
What does x= in the equation, 7(x-5=x+13
Answer:
X equals 8.
Step-by-step explanation:
Firstly, you remove the parentheses
Secondly, you move the terms
Then you collect like terms and add the numbers
Lastly, you divide both sides which gives you 6 x = 48,
so your answer is 8.
Hope this helped.
Answer:
x = 8
Step-by-step explanation:
Calculating purely on the assumption the question is equal to 7(x - 5) = x + 13
7(x - 5) = x + 13
7x - 35 = x + 13 ⇒ expand brackets
7x - 35 + 35 = x + 13 + 35 ⇒ add 35 to both sides
7x = x + 48
7x - x = x + 48 - x ⇒ subtract x from both sides
6x = 48
[tex]\frac{6x}{6} = \frac{48}{6}[/tex] ⇒ divide both sides by 6
x = 8
Hope this helps!
Find the distance between points A(−1, 5) and B(0, 4) to the nearest tenth.
Answer:
1.4
Step-by-step explanation:
Use the distance formula
d= √(x2-x1)² +(y2-y1)² , where x1, x2, y1, y2 are the coordinates of the points
A(x1 = −1, y1 = 5) and B(x2 = 0, y2 = 4)
d= √(0 - -1 )² +(4 - 5)²
d= √(1)² +(-1)²
d= √2
d= 1.414213562, round to the nearest tenth
d≈ 1.4
Eric is helping his younger sister learn division. He is having a hard time explaining what a remainder is. Help Eric out by describing what a remainder is in your own words. What is the remainder when 76 is divided by 3?
Answer:
1
Step-by-step explanation:
The remainder is what’s left when you divide. The part you cannot divide.
You can divide 75 by 3 = 25, so the remainder is 1.
$250, 3.4%, 3 years what would my interest be?
What is the equation in slope-intercept form of the line that passes through the points (-4, 6) and (-2,5) ?
y=20 - 8
y=-30+4
y=-22 +4
y = -x + 8
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}}\implies \cfrac{-1}{-2+4}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-\cfrac{1}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-6=-\cfrac{1}{2}(x+4)\implies y-6=-\cfrac{1}{2}x-2\implies \underset{\textit{slope-intercept form}}{y=-\cfrac{1}{2}x+4}[/tex]
In how many ways can a student answer the questions on the test if the student can leave answers blank
Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.
The given function for the height of the Ferris wheel is a sinusoidal equation.
a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotationReasons:
The function that gives the height of the Ferris wheel is presented as follows;
[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]
Where;
x = The number of minutes since the ride began
y = The height in feet of Emily
a) Required:
The radius of the Ferris wheel
Solution:
Comparing the given equation with the general equation of a Ferris wheel, we have;
[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]
The amplitude of the Ferris wheel = A = 30.48
The amplitude, A = The largest distance from the center = The radius, r
A = r
Therefore;
The radius of the Ferris wheel, r = A = 30.48 feet
b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;
[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]
By comparison, we have;
[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]
Therefore;
[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]
The time it takes Emily to make one rotation, T = 4.25 minutes
Learn more here:
https://brainly.com/question/21165143
Ali has q quarters. Tom has four more quarters than Ali.
Drag and drop the expressions into the boxes to write an expression that represents the number of quarters Ali and Tom have together.
Response area + Response area
Answer: x(.25)+(4+x(.25))=y
Step-by-step explanation:
1. set up the equation-
Ali has an unknown amount of quarters so make that x.
We know quarters are 25 cents so .25 if he has one quarter you put that one quarter into x, 2 into x and so on
Tom has 4 more, since he has 4 more it is 4+x and one again times .25
2. that is it
find an equation for the line below
Answer:
y = 1/3 x + 14/3
Step-by-step explanation:
We can identify the two points shown easily.
They are (-2, 4) and (4, 6).
First, we find the line of the slope of the line that contains those two points.
slope = m = (y2 - y1)/(x2 - x1) = (6 - 4)/[4 - (-2)] = 2/6 = 1/3
Now we use one point and the slope to find the y-intercept.
y = mx + b
Let's use point (4, 6) and the slope, 1/3.
6 = (1/3)(4) + b
18/3 = 4/3 + b
b = 18/3 - 4/3
b = 14/3
The equation is
y = mx + b
y = 1/3 x + 14/3
Simplify: 7√(1/3) + 2 1/3√(1/3) + 3√(147)
Step-by-step explanation:
7 √(1/3) - 2 1/3 √(1/3) +3√147
→7(1/√3) - (7/3)(1/√3) +3√(3×7×7)
→ (7/√3) - (7/3√3) +3×7√3
→ (7/√3) - (7/3√3) + 21√3
On Rationalising the denominators then
→ [ 7√3/(√3×√3)]-[7√3/(3×√3×√3) +21√3
The Rationalising factor of√3 =√3
→ (7√3/3)-[7√3/(3×3)]+21√3
→ (7√3/3)-(7√3/9)+21√3
LCM of 3 and 9 = 9
→ [(3×7√3)-(7√3)+(9×21√3)]/9
→ (21√3-7√3+189√3)/9
→[(21-7+189)√3]/9
→ [(210-7)√3]/9
→ 203√3/9 Ans.
Hope this helps.
Circle the multiplication problem that does not belong with the other three. explain 12×8=,22×4=,42×2=,33×3=
Answer: 12 x 8
Step-by-step explanation: The other three are not the basic multiplication facts from 0 - 12.
its urgent .have an exam tomorrow .pls help
The angle of elevation of the top of a pole as seen from a point 13 ft away from the base is double its angle of elevation as seen from a point 47 ft farther from the pole. Find the height of the pole above the level of the observer's eyes. 10) A) 34 ft B) 86 ft C) 60 ft D) 45 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
Let the angle of elevation of the top of the pole from a point 47 ft away be α.
Let the angle of elevation of the top of the pole from the point 13 ft away be β.
Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.
If the height of the pole above the level of the observer's eye is h, we have that
tanβ = tan2α = h/13 and tanα = h/47
From trigonometric identities tan2α = 2tanα/(1 - tan²α)
Substituting the values of the variables into the equation, we have
tan2α = 2tanα/(1 - tan²α)
h/13 = 2h/47 ÷ [1 - (h/47)²]
Dividing through by h, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
Cross-multiplying, we have
1/13 = 2/47 ÷ [1 - (h/47)²]
1 - (h/47)² = 2/47 × 13
1 - (h/47)² = 26/47
(h/47)² = 1 - 26/47
(h/47)² = (47 - 26)/47
(h/47)² = 21/47
Taking square-root of both sides, we have
h/47 = √(21/47)
Cross-multiplyng, we have
h = √(21/47) × 47
h = √(21 × 47)
h = √987
h = 31.42 ft
The height of the pole above the level of the observer's eyes is 31.42 ft
Learn more about height of a pole here:
https://brainly.com/question/10375496
with a diameter of 9 cm
Use their work to answer
questions 1-2
A-3.14
A-254.34
1 Describe Ben's mistake in solving for the
area of the circle.
Ben forgot that finding the area is not using the diameter, but using the radius. The radius is 1/2 of the diameter, so r=4.5. Then you would use the formula [tex]\pi*r^{2}[/tex], which would be 3.14x4.5x4.5, which is 63.585 cm squared.
The function c(h)= (20h)/(h^2+2) models the concentration of a medication in the bloodstream h hours after it’s injection into the muscle tissue.
-Does the graph have a vertical asymptote? If so, give the equation of the vertical asymptote and explain why this would be a concern or not. If the function does not have a vertical asymptote, explain why.
-Find the horizontal asymptote, what does it mean in the context of this problem?
-Does the function cross the horizontal asymptote? Does it make sense in the relation to this problem?
I have the answers, I just don’t understand how to explain them in the context of the problem.
Answer:
Step-by-step explanation:
What’s it’s answer I am wonder
what is the value of x?
(3x-1)º
(3x-1)))))]))))))))])))))))))))))])))))))))))))))))))))))
In the coordinate plane, the points A(-8, -6), B(-9, 11), and C(3. - 7) are reflected over the y-axis to the points A, B, and C', respectively. What are the coordinates of A' B', and C'?
Answer:
A' = (8,-6)
B' = (9,11)
C' = (-3,-7)
Step-by-step explanation:
When reflecting a point over the y axis, multiply the point's x coordinate by -1. Do this for each point and you have your answer.
