9514 1404 393
Answer:
(x, y) = (1.4, -3.6)
Step-by-step explanation:
4. We choose to substitute into the second equation because it has positive coefficients.
7(1.4) +2.5y = 0.8
9.8 +2.5y = 0.8 . . . . simplify
2.5y = -9.0 . . . . . . . subtract 9.8
y = -3.6 . . . . . . . . . . divide by 2.5
The solution to the system is (x, y) = (1.4, -3.6)
solve the equation x + 5 = 12
Answer:
x = 7
Step-by-step explanation:
x + 5 = 12
Subtract 5 from both sides
5 - 5 cancels out
12 - 5 = 7
We're left with x = 7
Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N
Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
Calculate the sum of the integers from 52 to 108
Answer:3136
Step-by-s
tep explanation:
Answer:
4506
Step-by-step explanation:
you have do like this 56+57+58+59+60+.....+108 look you will 4506 as answer
Suppose you had been in charge of designing the study. What sample size would be needed to construct a margin of error of 2% with 95% confidence
Answer:
A sample size of 2401 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What sample size would be needed to construct a margin of error of 2% with 95% confidence?
This is M for which n = 0.02.
Supposing we have no estimate for the true proportion, we use [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2[/tex]
[tex]n = 2401[/tex]
A sample size of 2401 is needed.
Find the measure of the missing angle using the triangle angle sum theorm.
Your vacation cabin on the lake has three rooms. The bathroom is 12' X 6', the bedroom is 14' X 18' and the great room is 20' X 30'. The ceiling height is 10'. What is the total volume of your cabin? Group of answer choices 9420 Cubic Feet 9240 Cubic Feet 9240 Square Feet 9420 Square Feet
Answer: [tex]9240\ ft^3[/tex]
Step-by-step explanation:
Given
Dimension of the bathroom is [tex]12'\times 16'[/tex]
Dimension of the bedroom is [tex]14'\times 18[/tex]
Dimension of the great room is [tex]20'\times 30'[/tex]
Height of the ceiling is [tex]h=10'[/tex]
Total area of the cabin
[tex]\Rightarrow A=12\times6+14\times 18+20\times 30\\\Rightarrow A=72+252+600\\\Rightarrow A=924\ ft^2[/tex]
Volume of the cabin is [tex]V=A\times h[/tex]
[tex]\Rightarrow V=924\times 10\\\Rightarrow V=9240\ ft^3[/tex]
Two
1 1 sides of trapezium are bound 60 cm & 77cm
outer sides are 25cm. & 26cm Find the
area of trapezium
Answer:
area ABEC[tex]s =\frac{25 + 26 + 17}{2} = 34[/tex]
area ∆ BEC[tex] = \sqrt{34 \times 9 \times 8 \times 17} [/tex]
[tex]17 \times 3 \times 2 \times 2 = 204cm ^{2} [/tex]
area ∆ BEC
[tex] = \frac{1}{2} \times 17 \times h = 204[/tex]
[tex]h = \: \frac{204 \times 2}{17} = 24[/tex]
[tex]area \: trap \: \: abcd \\ = \frac{1}{2}(60 + 77) \times 24 \\ = 137 \times 12 = 1644cm ^{2} [/tex]
Step-by-step explanation:
❣️Jess bragoli❣️#keep learning!!
Doug split a magic cards so that he and his friends each got 6 cards.if there were 24 cards in the pack how many friends did Doug share the cards with
Answer:
Doug share the cards with his three other friends.
Step-by-step explanation:
If there were 24 cards and each person was suppose to get 6
24 ÷ 6 = 4
The cards were shared among 4 people including Doug himself.
Have a nice day :)
What is the slope of the line represented by the equation y-6 = 5(x-2)?
O A. 6
O B. 5
O C. -5
O D. 2
Answer:
B
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 6 = 5(x - 2) ← is in point- slope form
with slope m = 5 → B
Help me out please thanks
Answer:
1.5 is the correct answer
Step-by-step explanation:
The time it four hours. In those 4 hours the temperature changer by 6 degrees. So 6 divided by 4 is 1.5.
Answer: Choice D is correct. The slope is 1.5
This means that for every hour, the temperature is increasing by 1.5 degrees Fahrenheit.
=======================================================
Work Shown:
slope = rise/run
slope = (change in y)/(change in x)
slope = (change in temperature)/(change in time)
slope = 6/4 .... see note below
slope = 3/2
slope = 1.5
note: The 6 refers to the jump from -2 to 4; the denominator 4 represents the amount of elapsed time from 8 AM to 12 PM
15
Which is bigger?
15/20 or 74%
Find the volume - leave answer in terms of π
Answer:
144[tex]\pi[/tex]
Step-by-step explanation:
Volume of a Sphere :
V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]6^{3}[/tex]
V = [tex]\frac{4}{3}[/tex](216)[tex]\pi[/tex] (216 times 4, divided by 3)
V = 288[tex]\pi[/tex]
Now divide by 2, it's only half of a sphere.
Find the volume of this cylinder. Use 3 for .
V = 7r2h
14 cm
2
V = T[?]?
28 cm
Hint: Plug in the value of the
radius for r. The radius is shown
directly in the diagram.
Step-by-step explanation:
V = πr²h
V = 3 × 14² × 28
v = 16464cm³
i've been stuck on this question for 3 days ;< halp meh ples
Calculate the average time for each vehicle.
What was the average time for the Big Car? Show your work.
What was the average time for the Small Car? Show your work.
Calculate the average speed for each vehicle. Use the average time for this calculation.
What was the average speed for the Big Car? Show your work.
What was the average speed for the Small Car? Show your work.
Answer:
1.
avg time = total time/ 3
for big car :-
= 4.46/ 3
= 1.48
for small car :-
= 5.14/ 3
= 1.71
2.
avg speed = total distance/ total time
for big car:-
= 2/ 4.46
= 0.45
for small car :-
= 2/ 5.14
= 0.4
Find a number such that if 16 is added to it, the ratio of the result to the original number is 4:3
Answer:
48
Step-by-step explanation:
let the number be x and x + 16 the result of adding 16 to it, then
the ratio of the result to the original is
[tex]\frac{x+16}{x}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )
4x = 3(x + 16) = 3x + 48 ( subtract 3x from both sides )
x = 48
Help me with this problem
Answer:
Angle A is F Angle A = 57. 52+71=123. 180-123=57
Omane is 4 years older than Bremen. If the sum of their age is 60 , find Bremen's age
Answer:
Bremen's age is 28 years
Step-by-step explanation:
Bremen's age= x
Omane's age= x+4
x+x+4=60
2x+4=60
2x=60-4
2x=56
2x = 56
2 2
x=28
The following figures are not drawn to scale but AB and CD are straight lines. Find x.
Answer:
x=60
Step-by-step explanation:
solve, 180-(90+x) = 180-(30+2x)
3x-4y=-24
Identify the x- and y-intercept of the graph of each question
Answer:
x = -8 and y = 6
Step-by-step explanation:
3x - 4y = -24
Solve for y - intercept
3x - 4y = -24
To find y intercept , substitute x = 0
3 × 0 - 4y = -24
Any expression multiplied by 0 equals 0.
0 - 4y = -24
-4y = -24
Divide both sides by -4
-4y / -4 = -24/-4
y = 6
Similarly, Solve for x-intercept
3x - 4y = -24
To find x- intercept , susbtitute y = 0
3x - 4 × 0 = -24
Any expression multiplied by 0 equals 0.
3x - 0 = -24
3x = -24
Divide both sides by 3
3x / 3 = -24 / 3
x = -8
Therefore, y = 6 and x = -8
The math club sold 15 novelty erasers and made a profit of
$7. After another week, the club had sold a total of 25
erasers and made a profit of $15. Which equation models
the total profit, y, based on the number of erasers sold, X?
A. y - 15 = 0.8(x - 7)
B. y - 15 = 1.25(x - 7)
C. y - 7 = 0.8(x - 15)
D. y - 7 = 1.25(x - 15)
A triangle is rotated 90 about the origin. Which rule describes the transformation?
Answer:
1st option
Step-by-step explanation:
Under a rotation about the origin of 90°
a point (x, y ) → (- x, - y )
Answer:
your answer will be the first option
Step-by-step explanation:
edge 2021
Find the surface area or volume of each rectangular prism. (Show work pls)
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
what is 9.7 as a fraction ?
Answer:
Step-by-step explanation:
9.7 = [tex]\frac{97}{10}[/tex]
Count the number of places in the decimal number after the decimal point.
Here , there is only one place.
So, multiply and divide by 10. 9.7 *10/1*10 = 97/10
What are the coordinates of R?
Answer: y,0
Step-by-step explanation:
I 그
If minor arc AB measures 97 inches, what is the length
of the radius of circle C? If necessary, round your
answer to the nearest inch.
O 6 inches
O 12 inches
O 18 inches
O 24 inches
Answer:
The correct option is (b).
Step-by-step explanation:
Given that,
The length of the minor arc = 9 inches
We need to find the length of the radius of circle C.
Let the angle is 0.75 radians.
So,
Radius,[tex]r=\dfrac{l}{\theta}[/tex]
Put all the values,
[tex]r=\dfrac{9}{0.75}\\\\r=12\ inches[/tex]
So, the radius is 12 inches.
Please help, I also need an explanation.
help pls!!
2xy + 3xt - 7yt = 0
In the equation above, x and y are positive and
x< y. What is t in terms of x and y?
A) t= 1/2
B) t= 2xy / 3x - 7y
C) t= 2xy / 7y - 3x
D) t= xy / 2(y-x)
Answer:
B
Step-by-step explanation:
[tex]2xy + 3xt - 7yt = 0[/tex]
[tex]3xt - 7yt = - 2xy[/tex]
Factor out t
[tex]t(3x - 7y) = - 2xy[/tex]
Divide by 3x-7y
[tex]t = - \frac{2xy}{3x - 7y} [/tex]
But since x and y are positive, the answer is positive
[tex]t = \frac{2xy}{3x - 7y} [/tex]
10 pointssss!!!!!:))
write the formula of the function y whose graph is shown.
a).
[tex]y = \frac{2}{x} [/tex]
b).
[tex]y = \frac{1}{ x } + 2[/tex]
c).
[tex]y = \frac{1}{x - 2} [/tex]
plss, I need helpp!!!!
9514 1404 393
Answer:
(a) y = 2/x
Step-by-step explanation:
The vertical and horizontal asymptotes are the axes, so there is neither a vertical nor a horizontal offset to the parent function y = 1/x. There is a vertical stretch by a factor of 2, so the describing function is ...
y = 2/x
Help me solve for X I forgot how to this
Step-by-step explanation:
hope it helps you.........
Answer:
[tex]here \: is \: your \: solution : - \\ \\ here \: is \: a \: right \: traingle \: with \\ \\ base \: = 52 \: units \\ \\ hypotenuse \: = 65 \: units \\ \\ perpendicular \: = {?} \\ \\ we \: need \: to \: find \: perpendicular \\ \\ by \: using \: pythagorus \: theorem : - \\ \\ perpendicular ^{2} \: = base ^{2} + perpendicular ^{2} \: \\ \\ perpendicular^{2} \: = 65 {}^{2} - 52 {}^{2} \\ \\ perpendicular {}^{2} = (4225 - 2704) \\ \\ perpendicular {}^{2} = 1521 \\ \\ perpendicular = \sqrt{1521} \\ \\ perpendicular = 39 \: units \: \\ \\ hope \: it \: helps \: you \: [/tex]
What is the length of the dotted line in the diagram below? Leave your answer in simplest radical form. HELP PLEASE
Answer:
11.7…?
Step-by-step explanation:
Small triangle and other triangle are similar based on sas theorem (I think) so find scale factor — 2— then do Pythagorean theorem
