Answers
The [tex] \frac{1}{4}[/tex] from [tex] \frac{1}{4} ^{3x^{2} }[/tex] can be converted into [tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]
The [tex] \frac{x}{4}[/tex] from [tex] \frac{x}{4} ^{3x }[/tex] can be converted into [tex] x^{1} [/tex] *[tex] 4^{-1} [/tex] so it will be equal to [tex] 4^{-3x^{2} } [/tex]
[tex] 4^{3x^{2} } [/tex] and [tex] 4^{-3x^{2} } [/tex] clearly not equivalent, so option A is out
Related Questions
MEDAL AND FAN!!
A bike was originally $240.00. The price was marked up 15%. What is the new price of the bike?,
Answers
Mark Up percentage = 15%
(15/100)*240
= $36
new price = $240 + $36
= $276
hope it helps :
first you should find that how much 15% of 240 is:
[tex] \frac{15}{100} = \frac{x}{240} \\ x = \frac{240 \times 15}{100} = \frac{3600}{100} = 36 [/tex]
15% of 240 is 36. then:
[tex]240 + 36 = 276[/tex]
the new price of the bike is $276
I need help with this question
Answers
.. A = (1/2)*b*h
.. Aside = (1/2)*(6 cm)*(5 cm) = 15 cm^2
The area of the triangular base is
.. Abase = ((√3)/4)*s^2 = (√3)/4*(6 cm)^2 = 9√3 cm^2
The total surface area is the base area plus the area of the three sides.
.. Atotal = Abase + 3*Aside
.. = 9√3 cm^2 +3*15 cm^2
.. = (45 +9√3) cm^2
.. ≈ 60.6 cm^2
Actually, there's an error in the picture. The height of the side should be 4, and the length of the edge should be 5. Making that adjustment, the total area is 51.6 cm^2.
It is hard to tell what is intended. Not all answers are showing, so we can't "reverse-engineer" the problem from the answers.
(40 POINTS!)
What is the center of the circle that has a diameter whose endpoints are (-3, -5) and (-11, -7)
A. (-8, -1)
B. (-7, -6)
C. (-4, -6)
Answers
The center of any circle is the midpoint of the diameter.
Let's use the midpoint formula to find the midpoint of the diameter.
The midpoint of a line segments with endpoints [tex](x_1, y_2)[/tex] and [tex](x_2, y_2)[/tex] will have a midpoint of [tex]( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Midpoint of the diameter:
[tex]( \dfrac{-3-11}{2}, \dfrac{-5-7}{2})[/tex]
[tex]=(-7, -6)[/tex]
Your answer is B. Hope this helps!
Derek's phone number, $336$ - $7624,$ has the property that the three-digit prefix, $336,$ equals the product of the last four digits, $7 \times 6 \times 2 \times 4.$ how many seven-digit phone numbers beginning with $336$ have this property?
Answers
To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits. The number of different seven-digit phone numbers that satisfy the given property is 7.
Explanation:To find the number of seven-digit phone numbers beginning with 336 that have the given property, we need to determine the number of possible combinations for the middle three digits.
The last four digits of the phone number are the product of 7, 6, 2, and 4, which is 336.
Since the three-digit prefix is also 336, the remaining three digits in the middle should be such that their product is also 336.
336 can be factored as 2 x 2 x 2 x 2 x 3 x 7. So, we need to find the number of ways to distribute these factors over the three middle digits.
Since the digits cannot be repeated, we can list down all the possibilities:
2 x 2 x 7
2 x 4 x 3
2 x 2 x 3 x 2
4 x 2 x 3
3 x 2 x 2 x 2
2 x 3 x 2 x 2
2 x 2 x 2 x 3
Each of these combinations can be arranged in different ways, resulting in multiple seven-digit phone numbers.
Therefore, there are 7 different seven-digit phone numbers beginning with 336 that have the given property.Learn more about Phone Numbers here:
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What is the value of x?
4/5 x- 1/10= 3/10
A. 1/4
B. 8/25
C. 2/5
D.1/2
Answers
given that an intercepted arc has length 6pi inches and a central angle is pi/3, find the radius
Answers
Given the equation 2x +4 = 4x -2, select the reasoning that correctly solves for x.
A.add 2, subtract 2x, then divide by 2
B.add 2, subtract 4x, then divide by -2
C.subtract 4, subtract 2x, then divide by -2
D.subtract 4, subtracts 4x, then divide by 2.,
Answers
A is the correct answer.
2x+4=4x-22x+4+2=4x-2+22x+6=4x2x-2x+6=4x-2x6/2=2x/23=xWhich are the roots of the quadratic function f(b) = b2 – 75? Check all that apply.Which are the roots of the quadratic function f(b) = b2 – 75?
Answers
b ^ 2 - 75 = 0
From here, we clear the value of b. We have then:
b = + / - root (75)
We rewrite:
b = + / - root (3 * 25)
b = + / - 5 * root (3)
So, the roots are:
b1 = 5 * root (3)
b2 = -5 * root (3)
Answer:
The roots of the quadratic function are:
b1 = 5 * root (3)
b2 = -5 * root (3)
Simplify: 8x + 4 - 5
Answers
8x + 4 - 5
8x - 1
Calculate the sum or difference.
Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger.
- ( 5 - 4 )
Subtract the numbers.
-1
8x - 1
Please answer this and thank you
If DF=78, DE=5x-9, and EF=2x+10, find EF.
Answers
5x - 9 + 2x + 10 = 78
7x+ 1 = 78
7x = 77
x = 77/7 = 11
EF = 2x + 10
EF = 2*11 + 10
EF = 22 + 10
EF = 32
Question
If DF = 78, DE = 5x-9, and EF = 2x+10, find EF.Answer
EF = 32
If AB < AC < CB in triangle ABC then which of the following is true?
Angle A < Angle B < Angle C
Angle C < Angle A < Angle B
Angle C < Angle B < Angle A
Angle A < Angle C < Angle B,
Answers
For this problem, the sides opposite each angle is proportional to the sine of the angle. Larger side = larger angle. So we've been given AB < AC < CB.
Side AB is opposite angle C
Side AC is opposite angle B
Side CB is opposite angle A
So
C < B < A
Now looking at the options, the third options matches, which is
Angle C < Angle B < Angle A
The other 3 options don't match and therefore are wrong.
Which is the graph of f(x)= square root of x
Answers
For this case what you must do is build a table with the values that the function takes when inserting a value of x.
We have then:
x f (x)
1 1
4 2
16 4
25 5
36 6
When you get a sufficient number of points, graph each orderly and see the behavior of the graph.
Answer:
The graph looks like in the attached image.
jackie set up a lemonade stand
Answers
What is the question?
The infinite sequence 1, 6, 15, 28, 45, ... exhibits which pattern? multiply the term number by 2, subtract 1 from the result, multiply by the term number, and divide the result by 2. multiply the term number by 2, multiply the result by the term number, subtract 1, and divide the result by 2. multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2. multiply the term number by 2, multiply the result by 2 times the term number, subtract 1, and divide the result by 2.
Answers
multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2.
if term number is x,
the number in the pattern for xth term is ;
multiply term number by 2 - 2x
subtract 1 - 2x - 1
multiply by 2 times the term number - (2x-1) * 2x
divide by 2 - ((2x-1) * 2x)/2
so first term x=1
((2*1-1) * 2*1)/2
2/2 = 1
second term x = 2
((2*2-1) * 2*2)/2
(3*4)/2 = 6
third term x = 3
((2*3-1) * 2*3)/2
5*6/2 = 15
fourth term x= 4
((2*4-1) * 2*4)/2
56/2 = 28
Therefore the above response shows the correct pattern
[tex]h_n=2n^2-n [/tex]
[tex] h_n=\frac{2n(2n-1)}{2}[/tex]
Let's compute a couple of them:
[tex]h_1=2(1)^2-1=1\\ h_2=2(2)^2-2=8-2=6\\ h_3=2(3)^2-3=18-3=15\\ h_4=2(4)^2-4=32-4=28\\ h_5=2(5)^2-5=50-5=45\\ [/tex]
Indeed this is our pattern.
The answer is:
multiply the term number by 2, subtract 1 from the result, multiply by 2 times the term number, and divide the result by 2.
A square prism has a base with the length of 23 cm. What is the area, in square centimeters, of the base of the prism?
Answers
Simplify each expression. Use positive exponents.
m^3 n^-6 p^0
Answers
1/n^6 is the second one
1 is the third answer
The angles opposite the congruent sides of an isosceles triangle are congruent find the value of x in the triangle TRIANGLE BOTTOM LEFT OF TRIANGLE 70 DEGREES VERY TOP OF TRIANGLE X!!!! PLS HELP WITHOUT COPY AND PASTING. SHOW ALL UR WORK
Answers
Final Answer:
In the isosceles triangle, the base angles are congruent, and the given angle at the top is [tex]\(70^\circ\)[/tex]. Using the sum of angles in a triangle, we find that the value of (x) is [tex]\(40^\circ\)[/tex]. Therefore, the final answer is [tex]\(x = 40^\circ\)[/tex].
Step-by-step explanation:
The base angles of the isosceles triangle as (A) and (B), and the vertex angle as (x). Since we know that the angles opposite the congruent sides are congruent, we have:
[ A = B ]
Now, let's consider the sum of angles in a triangle. The sum of all angles in a triangle is always [tex]\(180^\circ\)[/tex]. Therefore:
[tex]\[ A + B + x = 180^\circ \][/tex]
But since (A = B), we can rewrite this as:
[tex]\[ 2A + x = 180^\circ \][/tex]
Now, substitute (A) with [tex]\(70^\circ\)[/tex] (as given in the problem):
[tex]\[ 2(70^\circ) + x = 180^\circ \][/tex]
Simplify the equation:
[tex]\[ 140^\circ + x = 180^\circ \][/tex]
Now, isolate (x) by subtracting [tex]\(140^\circ\)[/tex] from both sides of the equation:
[tex]\[ x = 180^\circ - 140^\circ \][/tex]
[tex]\[ x = 40^\circ \][/tex]
So, the value of (x) in the given isosceles triangle is [tex]\(40^\circ\)[/tex].
Final answer:
The value of x in the isosceles triangle is 40 degrees, which is found by using the property that the angles opposite the congruent sides are congruent and the sum of the angles in any triangle is always 180 degrees.
Explanation:
To find the value of x in an isosceles triangle where one of the angles at the base is 70 degrees, we employ the property that the angles opposite the congruent sides of an isosceles triangle are also congruent. This means that the other angle at the base is also 70 degrees. Since the sum of the angles in any triangle is always 180 degrees, we can set up an equation to solve for x:
70° (angle at the left base) + 70° (angle at the right base) + x (angle at the top) = 180°
Adding the base angles together gives us:
70° + 70° = 140°
To find x, we simply subtract the sum of the base angles from 180 degrees:
180° - 140° = 40°
Therefore, the value of x, the angle at the top of the isosceles triangle, is 40 degrees.
how would you do this problem
Answers
so you would set up the problem to find x as:
5x-19=2x+14
+19 +19
____________
5x=2x+33
-2 -2
_____________
3/3x=33/3
____________
x=11
Just pug in x to the equations to solve the rest
What is n -7_> 2. ( p.s. that’s a greater than equal to sign_>)
Answers
add 7 to both sides
n ≥ 2 + 7
n ≥ 9
ANSWER: n ≥ 9
Hope this helps! :)
PLEASE HELP QUICK
HURRRY!!!!!
Answers
You've randomly surveyed some students in your science class to find the number of hours per week they study. what is the mean, based on your sample?
a.4.75 hours
b.5.05 hours
c.5.25 hours
d.5.45 hours
Answers
Answer:
D) 5.45 hours
Step-by-step explanation:
I got it correct on USATP.
Hope this helps!
From: Aug1e
.Wind is related to the movement of warm and cold air masses. Which kind of heat transfer does this represent? ANSWERS: A. radiation
B. conduction
C. convection
D. absorption
Answers
Explanation: Convection heat transfer creates wind because hotter, less dense air rises, while colder, more dense air moves downward. This movement of heated and cooled air is wind.
Answer:
Convection
Step-by-step explanation:
Question 1.1. Suppose a normal distribution has a mean of 20 and a standard deviation of 4.
A value of 26 is how many standard deviations away from the mean?
(Points : 1)
1.5
0.5
0.5
1.5
Question 2.2. Suppose a normal distribution has a mean of 20 and a standard deviation of 4.
What is the z-score of a value that is 0.52 standard deviations less than the mean?
(Points : 1)
0.52
0.13
0.13
0.52,
Answers
Our value of 26 is 6 units about the mean of 20. If each standard deviation is 4, we just divide 6 by 4. This gives us the number of standard deviations.
Question 2.2 The correct answer is -0.52
If we are 0.52 standard deviations below the mean, then our z-score is simply -0.52. The definition of a z-score is the number of standard deviations from the mean.
Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% APR. You agree to the loan but require your friend to pay you interest of 3.6% APR on the loan and your friend agrees.
Your friend pays you $200.00 at the end of the first month. How much goes toward the principal?
Answers
Let's start by calculating the interest on the first month. 1137.45 * (0.036/12) = 1137.45 * 0.003 = 3.41235
So at the end of the 1st month, the amount owed will be 1137.45 + 3.41 = 1140.86
And after the 200 payment is done, the new balance will be:
1140.86 - 200 = 940.86
Meaning that the principle reduced is: 1137.45 - 940.86 = 196.59
We could have also gotten the amount going towards the principle by subtracting the interest from the paying like: 200 - 3.41 = 196.59
The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.
How to calculate the amount?The first interest will be:
= 1137.45 × (0.036/12)
= 3.41
The amount owed at the month end will be:
= 1137.45 + 3.41
= 1140.86
The new balance after 200 payment will be:
= 1140.86 - 200
= 940.86
Therefore, the reduction in principal will be:
= 1137.45 - 940.86
= 196.59
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how do i solve this?
Answers
.. 15*8 = 10*AX
.. AX = 15*8/10 = 12
It takes Susan 3 hours to fix 2 broken cars and it takes Joseph 4 hours to fix 3 broken cars. If they work together how long will it take them to fix 17 broken cars?
Answers
Susan = 2 car / 3 hr
= 2/3
Joe = 3 car / 4 hr
= 3/4
add the rates to get the new combined rate as 17 cars in "t" hours.
2/3 + 3/4 = 17/t
Need common denominator
2/3(4/4) + 3/4(3/3) = 17/t
8/12 + 9/12 = 17/t
17/12 = 17/t
see that "t" is 12 hours
Susan and Joseph can fix 17 broken cars together in 12 hours.
Explanation:To calculate the time it takes for Susan and Joseph to fix 17 broken cars together, we can calculate their individual rates of work.
Susan takes 3 hours to fix 2 cars, so her rate is 2/3 cars per hour.
Joseph takes 4 hours to fix 3 cars, so his rate is 3/4 cars per hour.
When they work together, their rates are additive. So their combined rate is (2/3 + 3/4) cars per hour. This is equal to (8/12 + 9/12) cars per hour, which simplifies to 17/12 cars per hour.
To find the time it takes to fix 17 cars, we can divide the number of cars by the combined rate: 17 cars / (17/12 cars per hour) = 12 hours.
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PLS HELP!!!!! Medal!
Joey has a beach ball with a radius of 20 cm. What volume of air will it hold when fully inflated? (Round to nearest tenth.)
A) 83.8 cm^3
B) 251.4 cm^3
C) 1676.2 cm^3
D) 33,493.3 cm^3,
Answers
PLEASE HELP ME !!!!!!
CHOOSE 1 GRAPH ONLY
AND TRY TO EXPLAIN..
THERE ARE ONLY 4 GRAPHS
Answers
Factor completely: 5ab + 3ay + 5b + 3y (1 point)
(5b + 3y)(a + 1)
(5b - 3y)(a + 1)
(5b + 3y)(a - 1)
Prime
5. Factor completely: 4x3 + 28x2 + 7x + 49 (2 points)
(x - 7)(4x2 + 7)
(x - 7)(4x2 - 7)
(x + 7)(4x2 + 7)
(x + 7)(4x2 - 7)
6. Factor completely: 21x3 + 35x2 + 9x + 15 (2 points)
(3x - 5)(7x2 - 3)
(3x - 5)(7x2 + 3)
(3x + 5)(7x2 - 3)
(3x + 5)(7x2 + 3)
7. Factor completely: 10xy + 3y + 20ax + 6a (2 points)
(10x - 3)(y - 2a)
(10x - 3)(y + 2a)
(10x + 3)(y + 2a)
(10x + 3)(y - 2a)
Answers
5. ( x + 7 ) ( 4x² +7 )
6. ( 3x + 5 ) ( 7x² +3 )
7. ( 10x + 3 ) ( y + 2a )
Answer: The correct options are :
(4). (A) [tex](5b+3y)(a+1).[/tex]
(5). (C) [tex] (x+7)(4x^2+7).[/tex]
(6). (D) [tex] (3x+5)(7x^2+3).[/tex]
(7). (C) [tex] (10x+3)(y+2a).[/tex]
Step-by-step explanation: We are given to completely factor the following expressions :
Expression 4 :
The given expression is
[tex]E_1=5ab+3ay+5b+3y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The factorization of expression (i) is as follows :
[tex]E_1\\\\=5ab+3ay+5b+3y\\\\=a(5b+3y)+1(5b+3y)\\\\=(5b+3y)(a+1).[/tex]
So, option (A) is CORRECT.
Expression 5 :
The given expression is
[tex]E_2=4x^3+28x^2+7x+49~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
The factorization of expression (ii) is as follows :
[tex]E_2\\\\=4x^3+28x^2+7x+49\\\\=4x^2(x+7)+7(x+7)\\\\=(x+7)(4x^2+7).[/tex]
So, option (C) is CORRECT.
Expression 6 :
The given expression is
[tex]E_3=21x^3+35x^2+9x+15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
The factorization of expression (iii) is as follows :
[tex]E_3\\\\=21x^3+35x^2+9x+15\\\\=7x^2(3x+5)+3(3x+5)\\\\=(3x+5)(7x^2+3).[/tex]
So, option (D) is CORRECT.
Expression 7 :
The given expression is
[tex]E_4=10xy+3y+20ax+6a~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
The factorization of expression (iv) is as follows :
[tex]E_4\\\\=10xy+3y+20ax+6a\\\\=y(10x+3)+2a(10x+3)\\\\=(10x+3)(y+2a).[/tex]
So, option (C) is CORRECT.
HURRY!!! PLEASE
Which equation represents a direct variation?
y = 2x
y = x + 4
y =1/2x
y = 3/x
Answers
Answer:
A. [tex]y=2x[/tex]
Step-by-step explanation:
We are asked to find the equation that represents a direct variation.
We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.
Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].
Therefore, option A is the correct choice.