[tex]~~~~~~6=2x^2 -11x\\\\\implies 2x^2 -11x -6 = 0\\\\\implies 2x^2 -12x +x-6=0\\\\\implies 2x(x-6) +(x-6) = 0\\\\\implies (2x+1)(x-6) = 0\\\\\implies x = -\dfrac 12,~~ x= 6\\\\\text{Since }~p > q,}~~ p =6~ \text{and}~ q = -\dfrac 12\\ \\\text{So,}~ p-q = 6 -\left(- \dfrac 12 \right)\\\\~~~~~~~~~~~~~=6+\dfrac 12 \\\\~~~~~~~~~~~~~=\dfrac{13}2\\\\~~~~~~~~~~~~~=6.5[/tex]
The value of p -q is 6.5.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
ax^2 + bx + c = 0
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The equation 6 = 2x^2 - 11x has two solutions, p and q, with p being greater than q.
[tex]6 = 2x^2 - 11x \\\\ 2x^2 - 11x - 6 = 0\\\\ 2x^2 - 12x + x- 6 = 0\\[/tex]
(2x + 1) (x-6) = 0
Thus, x = -1/2 , 6
Since p>q
p = 6 , q = -1/2
So, p -q = 6 - (-1/2)
= 6 + 1/2
= 13/2
= 6.5
Learn more about finding the solutions of a quadratic equation here:
https://brainly.com/question/3358603
#SPJ2
A rectangular prism is 6.9 centimeters long and 1 centimeter wide. It’s volume is 21.39 cubic centimeters. What is the height of the rectangular prism? (will mark brainliest)
The height of the rectangular prism is 3.1
[tex]6.9x=21.39[/tex]
[tex]21.39[/tex] ÷ [tex]6.9=3.1[/tex]
Sure hope this helps
Can someone help me with this please
Drag the tiles to the correct boxes to complete the pairs.
Match each equation with its solution. Log(x-1)+log5x=2
Answer:
see attached
Step-by-step explanation:
We prefer to solve these by rewriting the equations to the form f(x) = 0, then having a graphing calculator show us the x-intercepts of f(x). This is illustrated in the second attachment.
__
The applicable rules of logarithms are ...
log(a) +log(b) = log(ab) . . . for logs of any baselog(a) = b ⇔ 10^b = aln(e^a) = alog(a) = log(b) ⇔ a = b . . . . for a > 0 and b > 0We can apply these rules to the given expressions to solve for x algebraically.
__
log(x-1) ...Taking antilogs, we have ...
(x -1)(5x) = 10^2 = 100
x(x -1) = 20 . . . . . . . . . . . divide by 5
x² -x -20 = 0 . . . . subtract 20, put in standard form
(x -5)(x +4) = 0 . . . . factor
x = 5 or x = -4 . . . . . . the latter is an extraneous solution
x = 5 only
__
ln(x +5) ...Taking antilogs, we have ...
x +5 = (x +1)(x -1)
x² -x -6 = 0 . . . . . . . subtract (x+5), write in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or x = -2 . . . . . . the latter is an extraneous solution
x = 3 only
__
e^x² ...Taking natural logarithms, we have ...
x² = 4x +5
x² -4x -5 = 0 . . . . . write in standard form
(x -5)(x +1) = 0 . . . . factor
x = 5 or x = -1 . . . . values that make the factors zero
__
log₄(5x² ...Taking antilogs, we have ...
5x² +2 = x +8
5x² -x -6 = 0 . . . . . write in standard form
(5x -6)(x +1) = 0 . . . . factor
x = 6/5 or x = -1 . . . . values that make the factors zero
_____
Additional comment
A solution is extraneous when it does not satisfy the original equation. Here, solutions are extraneous because they make the argument of the log function be negative in the original equation. The log function is not defined for negative arguments. (Actually, it gives complex values for negative arguments.)
We could have gone to the trouble to determine the applicable domain of each of the log equations. It is easier to (a) use a graphing calculator, or (b) test the solutions found.
A monument has a base and a statue The base is a rectangular prism that measures 4 feet by 6 feet by 2 feet The statue is a cube with edges that are 2 feet long What is the volume of the monument
Answer:
The formula for volume is V=l*w*h
(6×4×2)×2=96 cubic feet
Answer:
The winter evening settles down
With smell of steaks in passageways.
Six o'clock.
The burnt-out ends of smoky days.
And now a gusty shower wraps
The grimy scraps
Of withered leaves about your feet
And newspapers from vacant lots;
The showers beat
On broken blinds and chimney-pots,
And at the corner of the street
A lonely cab-horse steams and stamps.
And then the lighting of the lamps.
Alfred Tennyson - Summer Night
Alfred Tennyson was another poet who made great use of visual imagery. See if you can get a clear picture of the summer night he describes in this poem "Summer Night:"
Now sleeps the crimson petal, now the white;
Nor waves the cypress in the palace walk;
Nor winks the gold fin in the porphyry font:
The firefly wakens: waken thou with me.
Now droops the milk-white peacock like a ghost,
And like a ghost she glimmers on to me.
Now lies the Earth all Danaë to the stars,
And all thy heart lies open unto me.
Now slides the silent meteor on, and leaves
A shining furrow, as thy thoughts in me.
Now folds the lily all her sweetness up,
And slips into the bosom of the lake.
So fold thyself, my dearest, thou, and slip
Into my bosom and be lost in me.
William Wordsworth - I Wandered Lonely as a Cloud
Next is an excerpt from "I Wandered Lonely as a Cloud" by William Wordsworth. The first and last stanzas show a progression of the poet's emotions using visual imagery.
I wandered lonely as a cloud
That floats on high o'er vales and hills,
When all at once I saw a crowd,
A host, of golden daffodils;
Beside the lake, beneath the trees,
Fluttering and dancing in the breeze.
For oft, when on my couch I lie
In vacant or in pensive mood,
They flash upon that inward eye
Which is the bliss of solitude;
And then my heart with pleasure fills,
And dances with the daffodils.
Advertisement
Theodore Rothke - My Papa’s Waltz
This famous poem by Theodore Rothke is an excellent example of olfactory and tactile imagery with plenty of visual imagery thrown in for good measure. The effect is powerful.
The whiskey on your breath
Could make a small boy dizzy;
But I hung on like death:
Such waltzing was not easy.
We romped until the pans
Slid from the kitchen shelf;
My mother’s countenance
Could not unfrown itself.
The hand that held my wrist
Was battered on one knuckle;
At every step you missed
My right ear scraped a buckle.
You beat time on my head
With a palm caked hard by dirt,
Then waltzed me off to bed
Still clinging to your shirt.
William Carlos Williams - This Is Just to Say
"This Is Just to Say" is an amazing example of gustatory imagery or imagery involving taste. There’s more going on beneath the surface of this poem, but the vivid description of taste draws the reader in.
I have eaten
the plums
that were in
the icebox
and which
you were probably
saving
for breakfast
Forgive me
they were delicious
so sweet
and so cold
Step-by-step explanation:
A, B and C lie on a straight line.
Given that angle
y
= 135° and angle
z
= 103°, work out
x
.
Answer:
x = 42
Step-by-step explanation:
a striaght line = 180°
z + y + x = 180
103 + 135 + x = 180
138 + x = 180
subtract 138 from both sides
138 - 138 + x = 180 - 138
x = 42
Answer:
what shape it is
Step-by-step explanation:
wat is the shape
Can someone help
kaitlin buys candy that costs $8 per pound. she will spend less than $40 on candy. what are the possible numbers of pounds she will buy?
use p for the number ofpounds kaitlin will buy.
write your answer as an inequality solved for p.
Answer:
x≤5p
Step-by-step explanation:
40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds
a girl exercises every day for half an hour how many minutes in total for over 5 days
Answer:
150 minutes
Step-by-step explanation:
30 × 5 = 150 minutes
A bag contains 8 red marbles, 4 blue marbles, and 1 green marble. if a marble is selected at
random, what is the probability that it is not blue?
Answer:
the odds that it not blue is 9 /13 or .692
Step-by-step explanation:
whats 9499 to the nearest thousand??? I NEED THE ANSWER A.S.A.P
Answer:
9000
Step-by-step explanation:
1,2,3,4 round down
5,6,7,8,9 round up
Look at the 100's column for rounding to the nearest 1000
What is the solution for x in the equation?
-2x+14+10x=34
A. x=5/2
B. x=2/5
C. x=1/8
D. x=6
The graph of the function above is shown below. Which of the following statements about f(x) is true? A. The function f(x) does not have an inverse because it never crosses the x-axis. B. The function f(x) has an inverse because it passes the horizontal line test. C. The function f(x) does not have an inverse because it does not pass the horizontal line test. D. The function f(x) has an inverse because it passes the vertical line test.
Answer:
The correct answer is b)
Step-by-step explanation:
please help me I need assistance
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-15})\qquad (\stackrel{x_2}{14}~,~\stackrel{y_2}{r}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{(-15)}}}{\underset{run} {\underset{x_2}{14}-\underset{x_1}{2}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{4}}\implies \cfrac{r+15}{12}~~ = ~~\cfrac{3}{4}\implies r+15 = \cfrac{12\cdot 3}{4} \\\\\\ r+15=9\implies \boxed{r=-6}[/tex]
Simplify 85.84
O A. 820
O B. 169
O C. 89
O D. 649
Step-by-step explanation:
it seams like this question is wrong
6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is (1 point)
not drawn to scale.
11 m
12 m
6√3
01,540 m²
0770 m²
0396 m²
0749 m²
Area of hexagon
6(1/2BH)3BH3(6√3)(12)216√3m²Now
area of upper 6 triangles
3BH3(11)(12)396m²Total area
396+216√3770.112m²770m²Answer:
770 m²
Step-by-step explanation:
The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).
Apothem: The line segment from the center of the regular polygon to the midpoint of one of its sides.
Area of the base
The base of the prism is a regular polygon with 6 sides (hexagon).
[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]
where:
n = number of sidess = side lengtha = apothemGiven:
n = 6s = 12 ma = 6√3Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]
Area of one side
The sides of the regular pyramid are congruent triangles.
[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]
Given:
base = 12 mheight = 11 mSubstitute the given values into the formula:
[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]
Total Surface Area
[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]
You need a loan and your friend, Joey, will lend you the $1250 you need. He has you sign a promissory note for four years with an annual simple interest rate of 5.5%. What is the total amount that you will pay Joey at the end of the four years?
$1525
$4225
$2750
$275
Answer:
$1525
Step-by-step explanation:
5.5% out of $1250= 68,7568,75 x 4 (years) = 2751250 + 275 = 1525Guys, Please Help me Fast
I will help u so fast, first
you help me
can u answer this
some fanicial and environmental damages that have been made by cars.
please help me
this is exam
teacher giving us 10 minutes to discuss about and I am in washroom of school writing this
PLS HELP ILL MARK U BRAINLIST
Answer:
∠ FLW = 112°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ FLW is an exterior angle of the triangle , then
∠ FLW = x + 32 , that is
2x - 48 = x + 32 ( subtract x from both sides )
x - 48 = 32 ( add 32 to both sides )
x = 80
Then
∠ FLW = 2x - 48 = 2(80) - 48 = 160 - 48 = 112°
How would you write this expression as a sum or difference?
The provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
What is a logarithm?It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
[tex]= \rm log_3(\sqrt[5]{x} . y)[/tex]
As we know:
log(mn) = logm + logn
logmⁿ = nlogm
[tex]= \rm log_3({x^{\dfrac{1}{5}}} . y)\\\\= \rm log_3({x^{\dfrac{1}{5}}} )+log_3 (y)\\\\= \rm \dfrac{1}{5}log_3({x^{}} )+log_3 (y)\\\\[/tex]
Thus, the provided log can be written as sum of (1/5)log₃(x) + log₃(y) after using the log property.
Learn more about the Logarithm here:
brainly.com/question/163125
#SPJ1
There are six people on a bus. This is in total. At the first stop, eight more people get on. At the second, four get on and two hop off. At the third stop, the bus becomes practically full as 15 passengers get on. Four get off. At the last stop, 8 people get off. How many people are on the bus?
Just a fun problem for you :D
P.S. Answer it correctly ;)
Answer:
This was a nice way to spend my time :) how'd I do?
Step-by-step explanation:
Total: 6
1. +8
After stop 1, total is 14 people
2. +4, -2
After stop 2, total is 16 people
3. +15, -4
After stop 3, the total is 27 people
4. -8
Total # of people on the bus: 19
(A little voice in the back of my mind is telling me that I overthought this entire problem, and that the answer is just 6)
solve for x.
thanks!!
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
Use the Intersecting Chords Theorem to solve for x:
[tex]\overline{\rm TP}\cdot\overline{\rm PR}=\overline{\rm QP}\cdot\overline{\rm PS}\\\\(x+3)(x)=(6-x)(2x)\\\\x^2+3x=12x-2x^2\\\\3x^2+3x=12x\\\\3x^2-9x=0\\\\3x(x-3)=0\\\\x=0,\: x=3[/tex]
The solution [tex]x=0[/tex] however, does not make sense because the chords have lengths, so [tex]x=3[/tex] is the only sensible answer.
Intersecting Chords Theorem States:
|QP| * |PS| = |TP| * |PR||6-x| * |2x| = |x+3| * |x|12x -2x² = x² + 3x-2x² -x² = 3x -12x-3x² + 9x = 0-3x(x -3) = 0x - 3 = 0, -3x = 0x = 3, 0As Length cannot be zero or negative here. x = 3
If the total profit per month is 200000 and the revenue per month can be obtained as twice the cost per month minus 50000. what is the revenue and cost?
Answer:
300,000
Step-by-step explanation:
[tex]2000000 - 50000 = 150000[/tex]
[tex]150000 \times 2 = 300000[/tex]
What transformations would result in the image shown?
Δ ABC is reflected over the x-axis and translated right 1 unit.
Δ ABC is reflected over the y-axis and translated up 1 unit.
Δ ABC is reflected over both axes.
Δ ABC is translated right 4 units and up 1 unit.
4.
Triangle DEF is shown below.
E
19-6 m
I
10-4 m
13-2 m
D
It has sides of length 10.4metres, 13.2metres and 19.6metres.
Calculate the size of angle EDF.
Answer:
111.75 degrees
Step-by-step explanation:
EDF = cos^-1((b²+c²-a²)/2bc)
EDF = cos^-1((10.4²+19.6²-13.2²)/2(10.4)(19.6))
EDF = 111.75 degrees
Which box and whisker plot accurately shows the data set below
3rd
Step-by-step explanation:
i am not sure though so confirm it
Answer:
Its the THIRD choice.
Step-by-step explanation:
The values in ascending order are:
6 6 7 9 11 14 15 15 17 19 21 23 23 23 28 31
So the median = (15+17)/2 = 16.
The lowest and highest values are 6 and 31.
The lower quartile is 10.
The upper quartile is 23.
Six workers are hired to harvest blueberries from a field. each is given a plot with an area of 84 ft2. which equation will tell you the total area of the blueberry field
The equation that represents the total area of the blueberry field will be y = 84x.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Six workers are hired to harvest blueberries from a field.
Each is given a plot with an area of 84 square ft.
Then the equation that represents the total area of the blueberry field will be
Let x be the number of workers and y be the total area field. Then we have
y = 84x
Then the area of the total field will be
y = 84 (6)
y = 504 square ft
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ1
im rlly frickin lost
pls help
Answer:
so far he has saved 27 dollars however he needs 33 more dollars
Step-by-step explanation:
okay so if it says "____ of x" you normally have to multiply (of is a hint)
so first lets see how much he saved
0.45(60) = 27
he saved 27 dollars so far. to find how much more he has to save, you have to do the amount he needs minus the amount he already has
sooo
60 - 27 = 33
uhhh im not sure what the graph table thing on the right is, but i hope this helps a little
edit: ohhhhh so in the table all you have to do is fill in the information. im sure u can do it, but if you still dont know how to just reply here and ill help!
a tub shaped like a cylinder with a diameter of 18 inches, And a height of 20 inches Is filled to the top with water. Six spherical balls each with a diameter of 8 inches Are placed in the tub and they sink. some water overflows the tub, this amount equals a combined volume of the spheres. Find the exact and the approximate of water that remains in the tub.
The approximate amount of water that remains in the tub after the 6 spherical balls are placed in the tub are 3479.12 in³.
What is the approximate amount of water that remains in the tub?The first step is to determine the volume of the cylinder.
Volume of the tub = πr²h
Where:
r = radius = diameter / 2 = 18/2 = 9 inches h = height π = 3.143.14 x 9² x 20 = 5086.8 in³
The second step is to determine the volume of the 6 balls.
Volume of a sphere= 4/3πr³
r = diameter / 2 = 8/2 = 4 inches
6 x (3.14 x 4/3 x 4³) = 1607.68 in³
Volume that remains in the tub = 5086.8 in³ - 1607.68 in³ = 3479.12 in³
To learn more about the volume of a sphere, please check: https://brainly.com/question/13705125
#SPJ1
Consider the following data set with 20 scores { 23 15 16 15 25 14 14 18 26 23 25 24 14 25 29 15 24 29 21 19}. How many scores are below or equal to the 60th percentile?
Answer:
60th percentile = 23.5
Step-by-step explanation:
Put numbers in order from lowest to highest:
14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29
Formula:
60th percentile = 60% x Total number of elements
We have 20 scores,
60th percentile = 60% x 20
= 0.60 x 20
= 12
the 60th percentile is the 12th number on the list
14, 14, 14, 15, 15, 15, 16, 18, 19, 21, 23, 23, 24, 24, 25, 25, 25, 26, 29, 29
The 60th percentile is between 23 and 24
23 + 24 / 2 = 23.5
(2y + 5) (5y + 7)
Simplify your answer.
Answer:
10y^2 + 39y + 35
Step-by-step explanation:
Simplify using FOIL
Can someone explain how to convert a quadratic function in standard form to vertex form using the "complete the square" method? Oh, please give steps so I can write them down
The required steps are explained below to convert the quadratic function into a perfect square.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the quadratic function be y = ax² + bx + c.
The first step is to take common the coefficient of x². We have
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c[/tex]
Add and subtract the half of the square the coefficient of x,
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c[/tex]
Then we have
[tex]\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c[/tex]
These are the required step to get the perfect square of the quadratic function.
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ1
