Answer:
72
Step-by-step explanation:
3x12=36
36x2=72
Given the equation px^2 + 8x + 8 = 0 has equal roots find the value
of p.
[tex]\\ \sf\longmapsto px^2+8x+8=0[/tex]
Equal roots means Discriminate=0
[tex]\\ \sf\longmapsto D=0[/tex]
[tex]\\ \sf\longmapsto b^2-4ac=0[/tex]
[tex]\\ \sf\longmapsto 8^2-4(8)(p)=0[/tex]
[tex]\\ \sf\longmapsto 64-32p=0[/tex]
[tex]\\ \sf\longmapsto 32p=64[/tex]
[tex]\\ \sf\longmapsto p=2[/tex]
Answer:
p = 2Step-by-step explanation:
Since the roots are equal, the given equation should be a perfect square:
px² + 8x + 8 = 0Let p = 2q, since with odd value of p we can't get a perfect square:
2qx² + 8x + 8 = 0, divide all terms by 2qx² + 4x + 4 = 0The value of q should be 1 to make it a perfect square:
x² + 4x + 4 = 0(x + 2)² = 0Since q = 1, the value of p is:
p = 2q = 2*1 = 210.
Write an equation for the translation of y = |x|.
15.5 units down
A. y = |x| + 15.5
B. y = |–15.5x|
C. y – 15.5 = |x|
D. y = |x| – 15.5
Answer:
D
Step-by-step explanation:
a cars gas tank holds 15 gallons of gas. the car used up 9 gallons of gas. what percent of the gas in the tank is remaining?
9514 1404 393
Answer:
40%
Step-by-step explanation:
15 -9 = 6 gallons remain. The fraction remaining can be expressed as a percentage by multiplying it by 100%.
fraction remaining = (remaining gallons)/(capacity) = 6/15 = 2/5
percent remaining = 2/5 × 100% = 40%
Can somebody help me as soon as possible
Answer:
It's decreasing quickest between 3:23 and 3:24 (where the steepest drop on the graph is)
Answer:
3:23-3:24
…………………..
[tex]70 \times 20[/tex]
I need help please
[tex] \sf \: 70 \times 20[/tex]
[tex]\sf \longmapsto1400[/tex]
OR the question can also be written as
[tex] \sf \: 70 (20)[/tex]
[tex]\sf \longmapsto1400[/tex]
What is the place value in the 9 in the decimal 409.5
Answer:
The 9 is in the ones place.
:)
Solve for this variable shown
Y=
Answer:
how is traffic to + 54 degree + 42 degree then that 96 degree - by 180 degree you get you will get 84 degree
Help help help help help help
Answer:
where is the questions I don't know
A piece of wire 22 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
9.56 m of the wire should be used for the square, to maximize the total area of the wire
Let x be the side length of the square.
So, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
Let y represent the side length of the equilateral triangle.
So, the perimeter of the triangle is:
[tex]\mathbf{P_t=3y}[/tex]
The length of the wire is given as:
[tex]\mathbf{P=22}[/tex]
This implies that:
[tex]\mathbf{P_s + P_t=22}[/tex]
Substitute values for Ps and Pt
[tex]\mathbf{4x + 3y=22}[/tex]
Make y the subject
[tex]\mathbf{y=\frac{22 -4x}3}[/tex]
For an equilateral triangle of side length y, the height (h) of the triangle is:
[tex]\mathbf{h =\frac y2\sqrt 3}[/tex]
The area of the triangle is then calculated as:
[tex]\mathbf{A_t = \frac 12 yh}[/tex]
This gives
[tex]\mathbf{A_t = \frac 12 y\times \frac y2\sqrt 3}[/tex]
[tex]\mathbf{A_t = \frac{y^2}{4}\sqrt 3}[/tex]
The area of the square is:
[tex]\mathbf{A_s = x^2}[/tex]
So, the total area is:
[tex]\mathbf{A = A_s + A_t}[/tex]
[tex]\mathbf{A = x^2 + \frac{y^2}{4}\sqrt 3}[/tex]
Substitute [tex]\mathbf{y=\frac{22 -4x}3}[/tex]
[tex]\mathbf{A = x^2 + (\frac{22 - 4x}{3})^2 \times \frac{\sqrt 3}{4}}[/tex]
Differentiate
[tex]\mathbf{A' = 2x + \frac{\sqrt 3}{4} \times \frac 19 \times 2(22 - 4x) \times (-4)}[/tex]
[tex]\mathbf{A' = 2x - \sqrt 3 \times \frac 19 \times 2(22 - 4x) }[/tex]
[tex]\mathbf{A' = 2x - \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Set to 0
[tex]\mathbf{2x - \frac{2\sqrt 3}9 (22 - 4x) = 0}[/tex]
Rewrite as:
[tex]\mathbf{2x = \frac{2\sqrt 3}9 (22 - 4x) }[/tex]
Divide through by 2
[tex]\mathbf{x = \frac{\sqrt 3}9 (22 - 4x) }[/tex]
Multiply through by 9
[tex]\mathbf{9x = \sqrt 3 (22 - 4x) }[/tex]
Open bracket
[tex]\mathbf{9x = 22\sqrt 3 - 4x\sqrt 3 }[/tex]
Collect like terms
[tex]\mathbf{9x +4x\sqrt 3= 22\sqrt 3 }[/tex]
Factor out x
[tex]\mathbf{x(9 +4\sqrt 3)= 22\sqrt 3 }[/tex]
Solve for x
[tex]\mathbf{x= \frac{22\sqrt 3}{9 +4\sqrt 3} }[/tex]
Simplify
[tex]\mathbf{x= \frac{38.11}{9 +6.93} }[/tex]
[tex]\mathbf{x= \frac{38.11}{15.93} }[/tex]
[tex]\mathbf{x= 2.39 }[/tex]
Recall that, the perimeter of the square is:
[tex]\mathbf{P_s=4x}[/tex]
So, we have:
[tex]\mathbf{P_s=4 \times 2.39}[/tex]
[tex]\mathbf{P_s=9.56}[/tex]
Hence, 9.56 m of the wire should be used for the square
Read more about maximizing lengths at:
https://brainly.com/question/3433355
What is the value of the digit in the number based on the location of the digit
Answer:
Do u have a photo??
Step-by-step explanation:
cuzz I do not know
Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply. Multiple select question. cross out A) (0, 0) cross out B) (1, −25) cross out C) (−2, 5) cross out D) (−1, 25) cross out E) (4, 10) cross out F) (−5, 2)
9514 1404 393
Answer:
A) (0, 0)
B) (1, −25)
D) (−1, 25)
Step-by-step explanation:
For the point to lie on the line, the y-value must be -25 times the x-value. That is the case for points A, B, D.
Without writing the equation x^2 = 8y in the standard form, state whether the graph of this equation is a parabola, circle, ellipse, or hyperbola.
A- parabola
B- ellipse
C- hyperbola
D- circle
Step-by-step explanation:
Given -
x
2
=
8
y
It is a parabola opening up.
The general form of the equation of a parabola opening up is -
x
2
=
4
a
y
-8x + 14y = -30
4x - 7y = 18
Answer:
I think you may have written it down wrong because no solution for that is possible.
What are the roots of the polynomial function x^4 +7x^2-144=0
Answer:
Step-by-step explanation:
[tex]x^4+7x^2-144=0\\x^4+16x^{2} -9x^{2} -144=0\\x^{2} (x^{2} +16)-9(x^{2} +16)=0\\(x^{2} +16)(x^{2} -9)=0\\(x^{2} -(-16))(x^{2} -3^2)=0\\(x^{2} -16 \iota^2)(x+3)(x-3)=0\\(x^{2} -(4\iota)^2)(x+3)(x-3)=0\\(x+4\iota)(x-4\iota)(x+3)(x-3)=0\\x=\pm4 \iota,\pm3[/tex]
write an equation for the red line.
Answer:
Its is the second one
Step-by-step explanation:
Remember: rise over run
The b of the equation is -2 because that is how far it goes down on the y axis.
The slope is 3x.
Put the slope like this 3/1= rise/run
Sorry for the delayed response!
Pre Points Follow por more
nani .-. why tho?
why need followers?
must reason why
Answer:
JUPITER SATURN MARS
Step-by-step explanation:
12 out of 15 soccer players attended practice. What percentage of soccer players attended practice?
Answer:
1.25
Step-by-step explanation:
Answer:
12/15 > 4/5 equals 80%
Step-by-step explanation:
In which pair can figure “a” take figure “b”
Answer:
2
Step-by-step explanation:
a^6 + b^6 ≤ 12 a^2 b^2 - 64
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that
[tex]\rm \longmapsto\:a > 0 \: \: and \: \: b > 0[/tex]
and
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} \leqslant 12 {a}^{2} {b}^{2} - 64[/tex]
can be rewritten as
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} + 64 - 12 {a}^{2} {b}^{2} \leqslant 0[/tex]
[tex]\rm \longmapsto\: {( {a}^{2}) }^{3} + {( {b}^{2} )}^{3} + {(4)}^{3} - 3( {a}^{2})( {b}^{2})(4) \leqslant 0[/tex]
We know
[tex]\mathfrak{ {x}^{3}+{y}^{3}+{z}^{3}-3xyz =(x + y + z)( {x}^{2}+{y}^{2}+{z}^{2}-xy-yz - zx}[/tex]
So, using this identity, we get
[tex] \rm( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) \leqslant 0[/tex]
Let we consider,
[tex]\bf{ \longmapsto\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}}[/tex]
can be rewritten as
[tex]\bf{ \: = \dfrac{1}{2}\bigg[2{a}^{4} + 2{b}^{4} + 32 - 2{a}^{2} {b}^{2} - 8 {b}^{2} - 8{a}^{2}\bigg]}[/tex]
[tex]\bf{ = \dfrac{1}{2}\bigg[{a}^{4} + {a}^{4} + {b}^{4} + {b}^{4} + 16 + 16 - 2{a}^{2} {b}^{2} - 8 {b}^{2} - 8{a}^{2}\bigg]}[/tex]
can be re-arranged as
[tex]\bf{ \: = \dfrac{1}{2}\bigg[({a}^{4} + {b}^{4} - 2{a}^{2} {b}^{2})+({b}^{4} + 16- 8 {b}^{2}) + (16 + {a}^{4} - 8{a}^{2})\bigg]}[/tex]
[tex]\bf{ \: = \dfrac{1}{2}\bigg[( {a}^{2} - {b}^{2})^{2} + {( {b}^{2} - 4) }^{2} + {( {a}^{2} - 4)}^{2} \bigg]}[/tex]
As sum of squares can never be negative.
[tex]\bf {⇛\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2} \geqslant 0}[/tex]
[ Equality of zero holds when a = b = 2 ]
And if a and b are distinct, then
[tex]\bf{⇛\:{a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2} > 0}[/tex]
and
[tex]\bf{( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) > 0}[/tex]
So,
[tex] \bf{( {a}^{2}+{b}^{2} + 4)( {a}^{4} + {b}^{4} + 16 - {a}^{2} {b}^{2} - 4 {b}^{2} - 4 {a}^{2}) \geqslant 0}[/tex]
So, for the given statement,
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} \geqslant 12 {a}^{2} {b}^{2} - 64[/tex]
So, we concluded that
If a = b = 2, then
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} = 12 {a}^{2} {b}^{2} - 64[/tex]
And
If a and b are distinct, then
[tex]\rm \longmapsto\: {a}^{6} + {b}^{6} > 12 {a}^{2} {b}^{2} - 64[/tex]
So, given statement is partially true for a = b = 2 otherwise false.
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)
Answer: Choice C
(x, y) → (x – 3, y + 5)
=================================================
Explanation:
The "5 units up" portion means that each y value increases by 5. Therefore, we go from y to y+5. Going from x to x-3 means that we shift each point 3 units to the right.
For example, if the starting point is (1,7), then we have the following steps:
[tex](x,y) \to (x-3,y+5)\\\\(1,7) \to (1-3,7+5)\\\\(1,7) \to (-2,12)\\\\[/tex]
The point (1,7) moves 5 units up and 3 units to the left to arrive at (-2,12).
Note that the order doesn't matter. We could start moving 5 units up, then go 3 units left. Or we could start going 3 units left, then 5 units up. We'll arrive at the same destination.
Help this is due today!!!!!
Answer:
D
Step-by-step explanation:
-1/2m=-18
m=36
answer is D
Answer:
m = 36
Step-by-step explanation:
[tex]\frac{1}{3} m+3-\frac{5}{6}m=-15[/tex]
Combine like terms:
[tex](\frac{1}{3} m+(-\frac{5}{6}m)[/tex]
[tex](\frac{2}{6} m+(-\frac{5}{6}m)[/tex]
[tex]-\frac{3}{6}m = -\frac{1}{2} m[/tex]
[tex]-\frac{1}{2}m+3=-15[/tex]
Subtract 3 from each side:
[tex]-\frac{1}{2}m=-18[/tex]
Multiply each side by -2:
[tex]m = 36[/tex]
Write the ratio in simplest form as a fraction.
32 inches to 1 foot
Answer:
8/3
Step-by-step explanation:
1 foot = 12 inches, so it would be 32/12. After simplifying and dividing 4 on both sides, you would get 8/3.
Wendy is conducting a marketing survey. She mailed 35,400 surveys and got 12,744 responses. What is the percentage
Answer:
0.036%
Step-by-step explanation:
what is the simplest form of
-1/4 + 3/8
---------------
5/8
for 20 pts
Answer:
the fraction in simplest form is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Hope this helps!
Answer:
you may not find this helpful,
Step-by-step explanation:
0.125 is the answer
Please, if you can answer this, answer my other similar ones as well. I appreciate any help so much!
Answer:
C. Definition of Supplementary Angles
Step-by-step explanation:
You know this because they are opposites
I hope I could help!!!
Alguien me dice si ya está correcto el trabajo?
Answer:
el que está debajo del que está marcado con un círculo es correcto
Step-by-step explanation:
I need help with math. Brainiest will be yours. Tell me if the file is not loading.
Easy question:
Pump A can fill a tank of water in 6 hours. Pump B can fill the same tank in 10 hours. How long would it take the two pumps, working together, to fill the tank?
Answer:
3 hours and 45 minutes
Step-by-step explanation:
let's assume the tank has a volume of x liters.
let's assume the speed of filling it is x/6 liters per hour for A and x/10 liters per hour for B.
the formula to calculate the time is:
time = volume / speed
If the pumps work together, the total speed is x/6 + x/10, which is 16/60 x
So the time this takes is:
time = x / (16/60 x) = 60/16 hours = 3.75 hours = 3 hours and 45 minutes.
A TV has an original price of $549. Enter the new price after the given percent of change.
20% decrease
The new price is $
.
Answer:
439.20
Step-by-step explanation:
to find 549 deceased by 20% percent you need to find what's 20% percent of 549 is.
8.
Graph y = |x| – 5.
A. Graph a
B. Graph b
C. Graph d
D. Graph c
Answer:
D. Graph c
Step-by-step explanation:
I got this answer correct on Gradpoint
