5n² can be expressed as, 5n² = 3² x 5⁵ x x⁶
Given that n can be written as the product of the primes as
n = 3 x 5² x x³
This expression for n is called the prime factorization of n.
We need to express 5n² as such a product of primes.
For that taking square of n, add the power 2 with the existing powers of 3,5 and x,
So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶
So 5n² = 5(3² x 5⁴ x x⁶)
Multiplying 5 with the existing power of 5, 5⁴,
⇒ 5n² = 3² x 5⁵ x x⁶
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5. Which is the vertex of the quadratic function f(x) = 2x² - 4x - 6?
(-1,8)
O (1,8)
O (1,-8)
O(-1,-8)
The given quadratic polynomial function f(x) = 2x² - 4x - 6 has the vertex at (1, -8). Thus, the correct option is option C.
A quadratic polynomial function is a function which may be written in the form of ax² + bx + c = 0 where a, b and c are coefficients and x is the variable of the function. The quadratic polynomial function forms a parabola when plotted on the graph.
To find the vertex to the quadratic polynomial function we determine the value of x coordinate by the formula (-b/2a) and substitute the value of x in the polynomial function to get the value of y coordinate.
f(x) = 2x² - 4x - 6.
x coordinate = (-b/2a)
x = (4/2×2)
x = 4/4
x = 1
Now, the value of y coordinate = 2(1)² - 4(1) - 6
y = -8.
Thus, the given quadratic polynomial function f(x) = 2x² - 4x - 6 has the vertex at (1, -8).
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What is the greatest common factor of 16 , 24 , 48
Answer:
8
Step-by-step explanation:
The biggest common factor number is the GCF number. So the Greatest Common Factor 16, 24, 48 is 8.
please make my answer as brainelist
Which equation has the solution x = 2
A.) 2x - 3 = 19 B.) 3x + 2 = 18 C.) 4x - 4 = -4 D.) 5x + 1 = 10
[tex]a)2x - 3 = 19 \\ = > 2x = 19 + 3 \\ = > x = \frac{22}{2 } \\ = > x = 11 \\ b)3x + 2 = 18 \\ = > 3x = 18 + 2 \\ = > 3x = 20 \\ = > x = \frac{20}{3} \\ = > x = 6.66666667 \\ c)4x - 4 = - 4 \\ = > 4x = - 4 + 4 \\ = > x = \frac{0}{4} \\ x = 0 \\ d)5x + 1 = 10 \\ = > 5x = 10 - 1 \\ = > 5x = 9 \\ = > x = \frac{9}{5} \\ x = 1.8[/tex]
therefore 1.8 =2 or x is not equal to 2
Samantha works on the weekends doing hair for her classmates.For every head she does ,she charges 26$ complete the table
Answer:
Charge 26, 78, 130, 182, 234
Step-by-step explanation:
If Heads is (1,3,5,7,9) CHARGE and charge is (26,0,0,0,0) if 1 head=26 then you can just multiply or use repetitive addition if you were to multiply do 3x26=78, 5x26=130, 7x26=182, and 9x26=324. If you were to use repetitive addition do 26+26+26=78, 26+26+26+26+26=130, 26+26+26+26+26+26+26=182, and 26+26+26+26+26+26+26+26+26=234.
I hope it helps!
~XxBells is a cute girlxX~
Swine flu is attacking porkopolis. the function s ( t ) = 10 t + 8 determines how many people have the swine flu at a given time where t is in days and s ( t ) is the number of people in hundreds. evaluate s ( 16 )
f(x)=6x+5 , g(x)=−f(x) , and h(x)=f(−x) .
The domain of the function f (x) = x2 + 6x + 5 over the function g(x) = x3 + x2 − 4x − 4 is {x ∈ ℝ| x ≠ −1, −2, 2}.
The main limiting issue with the domain this function is potentially picking an x-value that makes that denominator equal 0, because dividing by 0 is bad.
So, the domain will be all real numbers, except for those that make g(x)=0.
g(-1) = 0, g(-2)=0, and g(2) = 0, so -1, -2, and 2 must be excluded from the domain.
Your answer is {x ∈ ℝ| x ≠ −1, −2, 2}.
Therefore, we get that, the domain of the function f (x) = x2 + 6x + 5 over the function g(x) = x3 + x2 − 4x − 4 is {x ∈ ℝ| x ≠ −1, −2, 2}.
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Your question was incomplete. Please refer the content below:
Given f (x) = x2 + 6x + 5 and g(x) = x3 + x2 − 4x − 4, find the domain of f over g of x period
{x ∈ ℝ}
{x ∈ ℝ| x ≠ −5}
{x ∈ ℝ| x ≠ −1, −2, 2}
{x ∈ ℝ| x ≠ −2, 2}
NEED HELP URGENT WILL GIVE EXTRA POINTS AND BARINLIEST
X=[?]
Answer: x=30 degrees
Step-by-step explanation:
The lines form two triangles which form a larger triangle.
The larger triangle has two known degree measures which are two 60 degree angles. The missing angle is the sum of the two X's. Triangles add up to 180 degrees.
180=60+60+x+x
180=120+2x
2x+120-120=180-120
2x=60
2x/2=60/2
x=30 degrees
Answer:
30
Step-by-step explanation:
180- (60+60)=60/2
considering all the various sources of caffeine, it is estimated that 80 percent of americans regularly use caffeine in some form, and that the average intake is blank per day.
With regard to all the different sources of caffeine, it really is estimated that 80 percent of Americans frequently consume caffeine in some way, with an average daily intake of 200–250 mg.
Caffeine:A methylxanthine class stimulant, caffeine stimulates the central nervous system. It is employed as a cognitive enhancer to improve alertness and attentional function. In order to increase the release of the neurotransmitters acetylcholine, caffeine works by preventing adenosine from binding to the adenosine A1 receptor.
What alters caffeine's effects on the body?Because caffeine is a stimulant, it makes your nervous system and brain work harder. Additionally, it causes a greater flow of hormones like cortisol and adrenaline throughout the body. Caffeine can help you feel energized and alert in small doses.
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I understand that the question you are looking for is:
Considering all the various sources of caffeine, it is estimated that 80 percent of Americans regularly use caffeine in some form, and that the average intake is ______ per day.
(14+24i)-(26-3i)+10i(11+11i) in standard form
Answer:
Step-by-step explanation:
14+24i-26+3i+110+100i
A-98+137i
43.3(blank) subtract 12.82 I’m giving off 20 points for this
On subtracting 12.82 from 43.3 we get 30.48 as answer.
How to subtract decimal numbers?
Write down decimal numbers such that the number from which you have to subtract is written first and number which you have to subtract from the fist number is written just below it such that the decimal is just lined below another decimal
For example if we have to subtract 4.2 from 12.8
we write it like 1 2 . 8
- 0 4 . 2
______
0 8 . 6 and the starting from right start subtracting
Given 43.3-12.82
4 3 . 3 0
- 1 2 . 8 2
_______________
3 0 . 4 8
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Which of the following is a factor of the following expression? Select all that apply.
1/3x - 2
Answer:
2 is the factor i think
Step-by-step explanation:
can i get a brainlist?
1. Caroline practices piano as much as 2 hours a day Monday through Thursday, and she practices up to 3 hours on Sunday. Write an inequality to show the number of hours that she practices in one week.
Step-by-step explanation:
2 hours a day for M-Th would be 8 hours. Sunday >up to< 3 hours. In 1 week, you'd have the 4 days ×2hrs ea day plus the 3hrs from Sunday... In one week she (assuming she did the full 3hrs) would have done 11hrs of piano practice. Not sure completely what to do but that's my first part that I do to figure it out if that helps any...
international travel is usually more expensive than domestic travel. a recent survey found that the average per-person cost of a 12-day international vacation is $1,755. this includes transportation, food, lodging, and entertainment.
Answer:
a. 7.78%
b.
c. lower
Step-by-step explanation:
I need help asap!! (Measurement)
Thank you to the people who’ve helped me :)
Anais bought 2 1/2 yards of ribbon. She had 2 feet 8 inches of ribbon left after trimming some curtains. Anais uses 58 inches of ribbon to trim the curtains.
Given that:
Anais bought of ribbon
And she had 2 feet 8 inches left after trimming some curtains.
The first thing to do is to convert all units to inches;
From standard conversion rate.
1 yard = 36 inches
As such of ribbon in inches will be:
= 5 × 18 inches
= 90 inches of ribbon bought.
Similarly, since 1 foot = 12 inches.
The amount of curtains left after trimming is:
= ( ( 2 × 12 ) + 8 )inches
= (24 + 8) inches
= 32 inches
If Anais bought 90 inches of ribbon and she had 32 inches of ribbon left after trimming some curtains.
It implies that the number of inches of ribbon that Anais used is:
= 90 inches - 32 inches
= 58 inches
ill give you crown if you answer this right btw its a fraction
Answer:
3/1
Step-by-step explanation:
Beginning from 10, you count upward until you come across a point that's directly underneath a number to the x-axis.
In this case, you'd go upward 3 times, locating the y-axis at 30.
Then you would go either left or right and count how many times you do that.
In this case, you'd go right 1 time, locating the x-axis at 10.
Hence, the slope would be rise over run, or y over x.
In this case, the slope would be 30/10.
To simplify that, it would be 3 over 1.
To simplify it even more, it would just be 3.
Hope this helps.
Please answer both questions!
-
1. The measure of an angle is 177°. The measure of its supplementary angle is ___
degrees.
2. The measure of an angle is 47.1°. The measure of its complementary angle is ___
degrees.
Answer:
1. 3
2. 42.9
Step-by-step explanation:
1. 180 - 177 = 3
2. 90 - 47.1 = 42.9
Classifi the following sequence as either arithmetic or geometric. then state the common difference or ratio and find the missing terms 64,-32,16,-8
The sequence is in geometric series. Common ration= - 1/2, missing number i.e., the 5th term = 4
An arithmetic series is one where each term is equal to the one before it plus some number. Whereas a geometric series is one where each term equals the one before it multiplied by a certain value.
Here the sequence is Geometric series as from the sequence we are getting the common ratio.
Common ratio = [tex]\frac{-32}{64}[/tex] = [tex]\frac{16}{-32}[/tex] = -[tex]\frac{1}{2}[/tex]
Now we have to find the 5th term of the sequence.
We know the formula to find the nth term of the geometric series which is:
[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]
[tex]a_{5}[/tex] = 64 [tex](\frac{-1}{2} )^{4}[/tex]
[tex]a_{5}[/tex] = 64/16
= 4
Therefore the missing number is 4.
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Los extranjeros ilegales ingresan a los Estados Unidos a una tasa de 200 cada día. Alrededor de 25000 son
aprendidos cada año.
¿Cuántos:
a) son aprendidos cada semana?
b) extranjeros ilegales permanecen en el país cada día, de acuerdo a estas
estimaciones?
Usando proporciones, los números se dan de la siguiente manera:
a) 1400 personas.
b) 132 personas al dia.
¿Qué es una proporción?Una proporción es una fracción de una cantidad total, y las medidas se relacionan usando una regla de tres. Debido a esto, se pueden construir relaciones entre variables, ya sea directas (cuando ambas aumentan o ambas disminuyen) o inversamente proporcionales (cuando una aumenta y la otra disminuye, o viceversa), para encontrar las medidas deseadas en el problema, o ecuaciones para encontrar estas medidas.
En este problema, hay que:
200 personas son aprendidas a cada día.En una semana hay 7 dias.Así, la candidad de personas aprendidas cada semana es:
7 x 200 = 1400 personas.
Por año, el número de personas que llega sin ser aprendida es dada por:
365 x 200 - 25000 = 48,000.
Por día, esta cantidad es dada por:
48000/365 = 132 personas al dia.
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Which ordered pair is not included in a graph y = 2x + 5? Group of answer choices (0, 0) (1, 7) (0.5, 6) (2, 9)
Answer:
All of the given ordered pairs are correct\included.
Step-by-step explanation:
The total height of 6 layers of wedding cake is 80 cm 4 mm. What is the height of each layer?
Answer: 13 cm 34 mm
Step-by-step explanation:
(80 cm 4 mm) * 1 layer/6 layers=
(80 cm 4 mm) * 1/6=
(80 cm 4 mm)/6=
(80 cm+4 mm) * 1/6=
80 cm/6 + 4 mm/6=
80/6 cm + 4/6 mm=
(78+2)/6 cm + 2/3 mm=
78/6 cm + 2/6 cm + 2/3 mm=
13 cm + 2/6 * 1000 mm + 2/3 mm=
13 cm + 1/3 * 1000 mm + 2/3 mm=
13 cm + 1000/3 mm + 2/3 mm=
13 cm+1002/3 mm=13 cm 34 mm
Divide. (6×1011)÷(3×1015) 2×10−12 times 10 inverse 2×10−72 times 10 to the negative 7 power 2×10−42 times 10 to the negative 4 power 2×100
The value of the division (6×1011)÷(3×1015) is the negative 4 power 2×10.
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.
Division can be interpreted as an equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.
Thus, [tex]a \div b[/tex] = a divided in b equal parts.
WE have been given that (6×10^11)÷(3×10^15) .
Simplify;
(6×10^11)÷(3×10^15)
To solve the exponent first;
10^11 - 15 = 10^-4
Now we get;
(6 )÷(3×10^-4)
2 ×10^4 = 2 ×10 ×10×10×10
= 20,000
Hence, the value of the division (6×1011)÷(3×1015) is the negative 4 power 2×10.
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find the volume of the parallelepiped with adjacent edges pq, pr, and ps. p(−2, 1, 0), q(3, 4, 3), r(1, 4, −1), s(3, 6, 4)
The volume of the Parallelepiped with adjacent edges pq, pr,and ps = 136
Geometrically, the Scalar triple product:
[tex]{\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )} \mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})[/tex]
is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.
Given three vectors, there is a product, called scalar triple product, that gives , the volume of the parallelepiped that has the three vectors as dimensions.
So,
Given : p(-2,1,0) , q(3,4,3), r(1,4,-1), s(3,6,4).
pq = ( -2-3 ,1-4 ,0-3) = (-5,-3,-3)
pr= (-2-1, 1-4, 0+1) = (-3,-3,1)
ps= ( -2-3, 1-6, 0-4) = (-5,-5,-4)
pq = (-5 , -3 , -3)
pr = (-3, -3, 1)
ps= (-5, -5, -4)
The scalar triple product is given by the determinant of the matrix (3×3)
that has in the rows the three components of the three vectors:
[tex]\left[\begin{array}{ccc}-5&-3&-3\\-3&-3&1\\-5&-5&-4\end{array}\right] \\\\-5(12+5)-3(12+5)-3(15-15)\\-5(17)-3(17)-3(0)\\-85-51\\-136\\[/tex]
So, The volume never be negative then by applying vector
v = |-136|
v= 136
the volume of the parallelepiped with adjacent edges pq, pr,and ps = 136
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I need help (If you know you get brainliest)
800 x 10
Answer:
8000
Step-by-step explanation:
800 × 10 = 8000
--------------
Answer:
8000
Step-by-step explanation:
= 800 × 10 ( adding 800 ten times )
= 8000 ( and got 8000)
A gardener spread 3 4/5 bags of mulch evenly over his 2 equal-sized vegetable beds. How
much mulch did he put on each vegetable?
Therefore 1 9/10 bag of mulch is put on each vegetable bed.
Given a gardener spread 3 4/5 bags of mulch evenly over his 2 equal-sized vegetable beds.
We need to find how much he put on each vegetable bed as
Let the number of bags of mulch put on each vegetable bed be x
∴ 2 * x = 3 4/5
2 x = 19 / 5
x = 19 / 10
x = 1 9/10 bag
Therefore 1 9/10 bag of mulch is put on each vegetable bed.
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Ms. Rivera has 134 crayons. About how many
crayons does she have? Round to the nearest 100.
Answer:
she has 130 crayons 100 crayons divided by 2 = 50 crayons each divide 30 by 2 =15
then she has the four crayons left divide those by 2
Giovanni's tech fingerboard is about 25 mm wide and 100mm longe .giovanni wants to make a larger scale drawing of the tech deck on an 8 1/2 inch by 11-inch piece of paper.select a scale that is most appropriate for the scale drawing .
A scale factor of 2 would be the perfect scale for the scale drawing.
How to interpret Scale Drawing?We are given original dimensions of tech fingerboard as;
Length = 100 mm
Width = 25 mm
Now, from conversions we know that;
1 inch = 25.4 mm
Since Giovanni wants to make a larger scale drawing on an 8 1/2 inch by 11-inch piece of paper, then we can say that;
11-inch = 25.4 * 11 = 279.4 mm
8 1/2 inch = 8 1/2 * 25.4 = 215.9 mm
Thus;
New Length/old length = 279.4/100 = 2.794
Since that is the maximum scale for the drawing paper, then we can say that something lesser like a scale factor of 2 would be the perfect scale for the scale drawing.
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Select a number to make the following statement true.
0.07 is 10 times as great as
A. 0.1
B. 0.7
C. 0.001
D. 0.007
Answer:
D
Step-by-step explanation:
a×10=0.07
a=0.07/10
=0.007
Answer:
D
Step-by-step explanation:
0.007 if you multiply this by 10 you move the decimal one place to the right, t hat would be 0.07
Several students attempted to solve the system of equations and . Which one is correct? An image of a coordinate plane shows two lines. A line labeled negative 2x plus y equals 4 crosses the x-axis at (negative 2, 0) and the y-axis at (0, 4). A line labeled x plus y equals 1 crosses the y-axis at (0, 1) and the x-axis at (1, 0). The lines intersect at a point that is one unit left of the origin and two units up from the origin. The solution is . An image of a coordinate plane shows two lines. A line labeled negative 2x plus y equals 4 crosses the y-axis at (0, 4) and the x-axis at (2, 0). A line labeled x plus y equals 1 crosses the x-axis at (negative 1, 0) and the x-axis at (1, 1). The lines intersect at a point that is 1 unit right of the origin and 2 units up from the origin. The solution is . An image of a coordinate plane shows two lines. A line labeled negative 2x plus y equals 4 crosses the y-axis at (0, 4) and the x-axis at (2, 0). A line labeled x plus y equals 1 crosses the x-axis at (negative 1, 0) and the y-axis at (0, 1). The lines intersect at a point that is 1 unit right of the origin and 2 units up from the origin. The solution is . An image of a coordinate plane shows two lines. A line labeled negative 2x plus y equals 4 crosses the x-axis at (negative 2, 0) and the y-axis at (0, 4). A line labeled x plus y equals 1 crosses the y-axis at (0, 1) and the x-axis at (1, 0). The lines intersect at a point that is one unit left of the origin and two units up from the origin. The solution is .
the graph of the parabola y=1/4(x+2)^2-6 is shown on the coordinate plane below according to the graph for which values of x is y always positive ?
Answer: x∈(-∞,-2√6-2)U(2√6-2,+∞)
Step-by-step explanation:
[tex]\displaystyle\\y=\frac{1}{4} (x+2)^2-6\\y > 0\\Hence,\\\frac{1}{4}(x+2)^2-6 > 0 \\\\\frac{1}{4}(x+2)^2-6+6 > 0+6\\\\\frac{1}{4}(x+2)^2 > 6\\[/tex]
Multiply both parts of the equation by 4:
[tex](x+2)^2 > 24[/tex]
Extract the square root of both parts of the inequality:
[tex]|x+2| > \sqrt{24} \\|x+2| > \sqrt{4*6} \\|x+2| > 2\sqrt{6}[/tex]
Expand the modulus - we get a set of inequalities:
[tex]\displaystyle\\\left [{{x+2 > 2\sqrt{6}\ \ \ \ (1) } \atop {-(x+2) > 2\sqrt{6} \ \ \ (2)}} \right.\\[/tex]
Multiply both parts of inequality (2) by -1 and reverse the sign of the inequality:
[tex]\displaystyle\\\left [ {{x+2-2 > 2\sqrt{6}-2 } \atop {x+2 < -2\sqrt{6} }} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x+2-2 < -2\sqrt{6} -2}} \right. \ \ \ \ \ \left [ {{x > 2\sqrt{6}-2 } \atop {x < -2\sqrt{6}-2 }} \right.[/tex]
Thus,
[tex]x\in(-\infty,-2\sqrt{6}-2)U(2\sqrt{6} -2,+\infty)[/tex]
how do i find s??? I'm legit crying help.
Applying the exterior angle theorem, the value of s in the triangle is: 74.
How to Apply the Exterior Angle Theorem?In the image shown above, the angles, s - 44° and s° are interior opposite angles to the exterior angle of the triangle that is given as s + 30°.
Based on the exterior angle theorem, the sum of s - 44° and s° is equal to s + 30°.
Therefore:
s - 44 + s = s + 30 [exterior angle theorem]
Combine like terms
2s - 44 = s + 30
2s - 44 - s = s + 30 - s [subtraction property of equality]
s - 44 = 30
s - 44 + 44 = 30 + 44 [addition property of equality]
s = 74
Therefore, applying the exterior angle theorem, the value of s in the triangle is: 74.
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