What is the following product? Assume x greater-than-or-equal-to 0 (4 x StartRoot 5 x squared EndRoot 2 x squared StartRoot 6 EndRoot) squared.
The simplified expression for the product [tex](4x\sqrt{5x^2} )(2x^2\sqrt{6})[/tex] is:
[tex]8\sqrt{30} x^4[/tex]
The given expression is:
[tex](4x\sqrt{5x^2} )(2x^2\sqrt{6})[/tex]
Note that :
[tex]\sqrt{5x^2} = x\sqrt{5}[/tex]
The given expression can then be re-written as:
[tex](4x^2\sqrt{5} )(2x^2\sqrt{6})[/tex]
Multiplying like terms together:
[tex]8x^4\sqrt{30}[/tex]
Finally, the resulting expression can be written as:
[tex]8\sqrt{30} x^4[/tex]
Learn more here: https://brainly.com/question/25913492
Answer:
D 104 x Superscript 4 + 16 x Superscript 4 Baseline StartRoot 30 EndRoot
Step-by-step explanation:
Edg 2022
The standard form of a quadratic equation is given as y=ax^2+bx+c and vertex form is given as y=a(x−h)^2+k. Write a formula that relates the values of a,b, and c in y=ax^2+bx+c to the values of a,h, and k in y=a(x−h)^2+k. For instance, h=ax+b would be a formula that relates h to a and b.
Answers:
[tex]h = -\frac{b}{2a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
where 'a' cannot be zero.
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Explanation:
The vertex is (h,k)
The x coordinate of the vertex is h which is found through this formula
[tex]x = -\frac{b}{2a}[/tex]
For example, if we had the quadratic [tex]y = 3x^2-6x+5[/tex], then we'll plug in a = 3 and b = -6 to get: [tex]h = -\frac{b}{2a} = -\frac{-6}{2*3} = 1[/tex]
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To find the value of k, we plug that h value into the original standard form of the quadratic and simplify.
[tex]y = ax^2+bx+c\\\\k = ah^2+bh+c\\\\k = a\left(\frac{-b}{2a}\right)^2+b\left(\frac{-b}{2a}\right)+c\\\\k = a*\frac{b^2}{4a^2}+\frac{-b^2}{2a}+c\\\\k = \frac{b^2}{4a}+\frac{-b^2}{2a}+c\\\\[/tex]
[tex]k = \frac{b^2}{4a}+\frac{-b^2}{2a}*\frac{2}{2}+c*\frac{4a}{4a}\\\\k = \frac{b^2}{4a}+\frac{-2b^2}{4a}+\frac{4ac}{4a}\\\\k = \frac{b^2-2b^2+4ac}{4a}\\\\k = \frac{-b^2+4ac}{4a}\\\\[/tex]
It's interesting how we end up with the numerator of [tex]-b^2+4ac[/tex] which is similar to [tex]b^2-4ac[/tex] found under the square root in the quadratic formula. There are other ways to express that formula above. We need [tex]a \ne 0[/tex] to avoid dividing by zero. The values of b and c are allowed to be zero.
Answer:
The minimum is at (1,-8). In the equation y = (x – 1)2 – 8, h = 1 and c = 8. So, the x-coordinate of the minimum is the same as the h-value in the equation, and the y-value of the minimum is the opposite of the c-value.
Step-by-step explanation:
plato
help please i’m doing homework and i can’t fail this lesson.
Answer: y = 3x +1
Step-by-step explanation:
how to graph transformations of quadratic functions
Answer:
Shift "h" units to the right, "k" units up, and reflect over the x or y axis when needed.
Step-by-step explanation:
1) I want to talk about reflections first.
Reflections across the x-axis --> [tex]y = ax^2[/tex], a is the coefficient. if a is negative, then the equation should be reflected across the x-axis. This is known as a vertical reflection. Reflections across the y-axis --> [tex]y=a(bx)^2[/tex], b is the coefficient. If b is negative, then reflect the equation over the y-axis. There are cases where the reflection across the y-axis does not change anything. But, let's say its [tex]y=(x-3)^2[/tex]... the reflection across the y-axis is different (that equation is: [tex]y=(-x-3)^2[/tex] )2) Rigid transformations
Horizontal transformations (to the left or right): [tex]y=a(bx-h)^2[/tex], factor out b from "bx-h" and whatever h equals is the units to the right. If h is a negative number, then you move to the left. Vertical transformations (up and down): [tex]y = a(bx-h)^2+k[/tex]... k is just the units up... if k is negative then we move it down.Example (check image for visual)
We transform [tex]y = x^2[/tex] to [tex]y = -(-x-3)^2+3[/tex] , you move right 3, then reflect across the x-axis, then reflect across y-axis, then move 3 up.
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Note: In the image, the red line is the original function, the blue one is the transformed function. See if you can follow along with the verbal instructions I gave above.
Simplify this question
[tex]\\ \sf\longmapsto √64+√-81-i^2[/tex]
[tex]\\ \sf\longmapsto 8+√81i-(-1)[/tex]
[tex]\\ \sf\longmapsto 8+9i+1[/tex]
[tex]\\ \sf\longmapsto 9i+9[/tex]
The length of a certain rectangular prism is 3 less than twice the width. The height of the same prism is 4 more than
the width. Write an expression to represent the volume of the rectangular prism in terms of width (w).
V=2w? + 5w-12
V= -2w3 + 11w2 + 12w
V=2w3 +5w? - 12w
В.
С.
D
V=4w + 1
Answer:
it is c
Step-by-step explanation:
me big brain
Find the factors of f(x) given that x = −3 is a zero.
f(x) = x^3 + 12x^2 + 47x + 60
(x + 3)(x + 4)(x − 5)
(x + 3)(x + 4)(x + 5)
(x − 3)(x + 5)(x + 6)
(x + 3)(x + 3)(x − 3)
[tex]x^3+12x^2+47x+60\\\\=x^3+3x^2 +9x^2+27x+20x+60\\\\=x^2(x+3) + 9x(x+3)+20(x+3)\\\\=(x+3)(x^2+9x+20)\\\\=(x+3)(x^2 + 4x +5x +20)\\\\=(x+3)[x(x+4)+5(x+4)]\\\\=(x+3)(x+4)(x+5)[/tex]
Please quickly answer number 17&18 I will give brainliest
Answer: 17) 150°C 18) 17 minutes
Step-by-step explanation:
x represents time in minutes and y represents temperature in Celsius
17) y=10x+30
y=10(12)+30
y=120+30
y=150 - Therefore, the water temperature will be 150°C after 12 minutes
18) 200=10x+30
10x+30=200
10x+30-30=200-30
10x=170
x=17 - Therefore, the water temperature will reach 200°C after 17 minutes
I need help with this
Answer:
512
Step-by-step explanation:
64 × 8 = 512
512
64 8
16 4 2
8 2 2 1
Please write a rule for this table BEGGING
Answer:
y = 3x = 1
Step-by-step explanation:
Answer:
y = 3x - 1
Step-by-step explanation:
Check. Plug in the given x, and see if the result is the given y:
y = 3x - 1
When: (x = 8 , y = 23)
23 = 3(8) - 1
23 = (3 * 8) - 1
23 = (24) - 1
23 = 23 (True).
When: (x = 2 , y = 5)
5 = 3(2) - 1
5 = (3 * 2) - 1
5 = 6 - 1
5 = 5 (True)
When: (x = -3 , y = -10)
-10 = 3(-3) - 1
-10 = (3 * -3) - 1
-10 = (-9) - 1
-10 = -10 (True).
When (x = 9 , y = 26)
26 = 3(9) - 1
26 = (3 * 9) - 1
26 = (27) - 1
26 = 26 (True).
When you graph, simply graph the given points (bolded) onto the graph.
What is the length of DF?
F
За
IT
E
G
a +6
D
DF =
Answer:
18
Step-by-step explanation:
Triangles FEG and DEG are congruent by SAS, so DG = FG.
a+6 = 3a
6 = 2a
3 = a
3a = 3·3 = 9 = FG = DG
DF = 9+9 = 18
Write a general rule for finding the sign in a multiplication or division problem with more than two integers
An ice cream store has 31 flavors of ice cream and 10 toppings. A regular sundae has one flavor of ice cream, one topping, and comes with or without whipped cream. How many different ice cream sundaes can be ordered?
Answer:
610
Step-by-step explanation:
31 x 10= different flavour and topping combination
x2 = for the whipped cream different option
Please don’t answer just for point! I really need help~
f (x) = 3x - 2 - g (x) = 2x + 1
Answer:
Step-by-step explanation:
The answer is easy it’s 24
Solve for all values of y in simplest form.
|4 - 5y| = 16
Answer:
[tex]y=-\frac{12}{5}[/tex]
I think this is the correct answer
Solve this system of equations using the Substitution method. Don't forget to write your final answer as a coordinate point.
3x + y = -2
y = 2x + 3
Answer:
(x, y) = (-1, 1)
Step-by-step explanation:
Answer this please!!!
Answer:
$40
Step-by-step explanation:
HELP ASPAP!! ANSWER CORRECLTY
Answer:
17
Step-by-step explanation:
Answer:
plot 17
Step-by-step explanation:
12-(-5) = 12+5 = 17
if laura has a school loan of $420,a car loan of $300 and rent of $550,what must she budget just to pay those expenses?
Answer:
1270
Step-by-step explanation:
420+300+550
$420+300=720+550=1270
PLEASE HELP ASAP GOD BLESS YOU If YOU HELP ME IT WILL RAISE MY GRADE
Answer:
Hi i think its option 3 maybe just wait until someone else helps but i say option 3 but gl anyways
Step-by-step explanation:
find the domain of f(x). f(x) = √9x+36
Answer:
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]
Step-by-step explanation:
I'm assuming the 9x and the 36 are in the root
[tex]\sqrt{9x+36}[/tex]
first we must solve for x
[tex]{9x+36}\geq 0[/tex]
substract 36 to both sides
[tex]{9x}\geq -36[/tex]
divide by 9 to both sides
[tex]\frac{9x}{9} }\geq \frac{-36}{9}[/tex]
simplify left side
[tex]x\geq \frac{-36}{9}[/tex]
simplfy right side
[tex]x\geq -4[/tex]
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]-4}
h(x) = x^2 - 5x +7
Find h(-5)
Answer:
57
Step-by-step explanation:
h(-5) = (-5)^2 - 5(-5) + 7
h(-5) = 25 + 25 +7
h(-5) = 57
Answer:
[tex]\bold{h(-5)=57}[/tex]
Step-by-step explanation:
Substitute [tex]-5[/tex] for everywhere there is [tex]x[/tex]
[tex]h(x) = x^2 - 5x +7\\=-5^2 - 5(-5) +7[/tex]
[tex]-5^2 - 5(-5) +7[/tex]
PEMDAS order of operations
Parenthesis
[tex]\bold{-5\times(-5)}\\=25[/tex]
[tex]-5^2+25 +7[/tex]
Exponents
[tex]\bold{-5^2}\\=-5\times-5\\=25[/tex]
[tex]25+25 +7[/tex]
Addition
[tex]25+25+7\\=50+7\\=57[/tex]
Therefore, [tex]\bold{h(-5)=57}[/tex].
Juan texts 20 messages in 5 minutes. At this rate how many text messages can he send in 30 minutes
The answer 120 MESSAGES
Which expressions are equivalent to -56z+28?
A.) 1/2⋅(-28z+14)
B.)(-1.4z+0.7) x 40
C.) (14-7z)⋅(-4)
D.)(8z−4)(−7)
E.)−2(−28z−14)
PLEASE HELP THANK YOU!!!
Harry had $32. He spent all the money buying three notebooks for x dollars each and four packs of index cards for y dollars each. If Harry had bought five notebooks and five packs of index cards, he would have run short by $18. The following system of equations models this scenario: 3x 4y = 32 5x 5y = 50 Use the system of equations to solve for x and y. (8, 2) (1, 5) (2, 8) (5, 1).
Answer:
x = notebooks
y = indexboks
3x+4y=32 ( here is spent all money so I add 32 here )
5x+5y=50
by elemination method
3x+4y=32×5
5x+5y=50×4 ( here I'm going to eliminate y )
15 x+20y= 160
20x+20y= 200
- - = -
____________
-5x = -40
x = - 40 / -5
x = 8
here - × - = + so iam taking positive 8
now substitute the value of x in any equation
3×8+4y = 32
24 + 4y = 32
4y = 32-24
y = 8 / 4
y = 2
CHECKING
SUBSTITUTE BOTH VALUES IN ANY EQUATION
5×8+5×2 = 50
40 + 10 = 50
50 = 50
I SUBSTITUTE IN 2ND EQUATION
Answer:
(8,2)
Step-by-step explanation:
Given that:
3x + 4y = 32 --------- eq1
5x + 5y = 50 --------- eq2
From taking 5 common from eq2:
x + y = 10
Or it can also be written as:
x = 10 - y ----------eq3
Now put this value of x in eq1
3(10 - y) + 4y = 32
By simplifying:
30 - 3y +4y= 32
30 +y = 32
Subtracting 30 from both sides:
y = 32 - 30
y = 2
Putting value of y in eq 3
x = 10 - 2
x = 8
1. Rosie orders dessert at the cafe. The total bill is $50. She tips the waiter 10%.
How much money does the waiter get?
Answer:
5
Step-by-step explanation:
this means it'll be $55
A half circle is joined to an equilateral triangle with side lengths of 12 units.
What is the perimeter of the resulting shape? Type your answer in the box below.
Answer:
P = 12 pi units + 24 units.
Step-by-step explanation:
All sides of an equilateral triangle are of the same length. Here that length is 12 units. We take a circle of diameter 12 units and cut it in half through its center. Finally, we join the triangle (remembering that all of the side lengths are 12 units) to the half circle of diameter 12 units.
The half circle portion of the resulting shape has circumference 2(pi)(12 units) divided by 2, or 12 pi units. This is half the formula C = 2(pi)(r). The two non-attached sides of the triangle have a total length of 24 units.
Thus, the perimeter of the resulting figure is P = 12 pi units + 24 units.
Which type of laboratory is not required to have coved floors (where the floor runs continuous for the wall for a few inches)
The type of laboratory that is not required to have coved floors is a BSL2.
Safety in laboratories is measured through the Biosafety Level scale. This scale evaluates how much protection do people working in the laboratory need to avoid any risks while working with pathogens or toxins.
This scale goes from 1 to 4 and the 4 level represents labs in which extremely dangerous pathogens are studied, and therefore labs with the highest safety protocols.
In this context, coved floors are not required for labs classified in Biosafety level 2 because in these labs pathogens have only a moderate risk, therefore some precautions such as the coved floors are not required.
Learn more about labs in: https://brainly.com/question/14428286
alex is running in a clockwise direction around a circular track with radius 60 yards. he runs for 20 minutes at a speed of 4 yards per second. find the shortest distance between their starting point and their ending point measured along the track
Answer:
100.9 yards
Step-by-step explanation:
One circuit of the track is a distance of ...
C = 2πr = 2π(60 yd) = 120π yd.
At Alex's running rate, the distance covered in 20 minutes is ...
(4 yd/s)(20 min)(60 s/min) = 4800 yd
The number of circuits will be ...
(4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits
The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,
That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd
The shortest distance along the track to Alex's starting point is about 100.9 yards.
_____
Additional comment
The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.