For this case we have the following equation:
[tex]4 ^ {(x-2)} = 8 ^ 6[/tex]
We must create equivalent expressions in the equation, so that they have equal bases:
[tex]2 ^ {2 * (x-2)} = 2 ^ {3 * 6}[/tex]
If the bases are the same, then the two expressions are only equal if the exponents are equal:
[tex]2 (x-2) = 3 * 6\\2 (x-2) = 18\\2x-4 = 18\\2x = 18 + 4\\2x = 22\\x = \frac {22} {2}\\x = 11[/tex]
Answer:
[tex]x = 11[/tex]
Option D
Answer: OPTION D
Step-by-step explanation:
You need to remember the following:
[tex]a^x=a^y\\x=y[/tex]
Then, you must descompose 4 and 8 into their prime factors:
[tex]4=2*2=2^2\\8=2*2*2=2^3[/tex]
Rewriting the expression:
[tex]2^{2(x-2)}=2^{3(6)}[/tex]
Now you get:
[tex]2(x-2)=3(6)[/tex]
Finally, you must solve for the variable "x".
Therefore, you get the following result:
[tex]2x-4=18\\2x=22\\x=11[/tex]
Can someone help ASAP I really need help 15 points
Answer:A=85 E=73 S=37 L=66.5 (or 65) T=82 P=53 D=10 O=89 C=17
Step-by-step explanation:
I am very good at Pythagorean theorem I did it this year.
To do this it is actually like the easiest thing to do in math. The formula is A²+B²=C². To do this it is easier with a scientific calculator. If you don't have one you can use this online calculator: desmos.com/scientific
Step 1. get the two number and square (²) them ( multiply that number by it) For Example 30 multiplied by 30. Or on the calculator I gave you just do 30²+40²
Step 2. After that you will get 2500. Then on the calculator get this symbol √ and but the number 2500 in front of it. it should look like this. √2500.
Step 3. After that you will get 50 which is your answer. And that is how you do Pythagorean theorem.
I hope that helped you. If you don't have a scientific calculator you can use the link I provided above. If you can't use it I reccomend buying one.
The scatter plot shows the height and weight of football
players on a team.
How many football players weigh less than 70 kilograms?
Enter your answer in the box.
the answer is two football players weigh less than 70 kilograms
Answer:
Less than 2 players.
Step-by-step explanation:
Given that the scatter plot shows the height and weight of football
players on a team.
WE have to find the number of players who weigh less than 70 kgs.
In the graph of scatter plot we find tha when y<70, there are 2 points in the graph.
Hence only two players in football weight less than 70 kgs.
The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?
A -3
b 3
c 9
d 11
Answer:
x=9
Step-by-step explanation:
The Slope is given by the following equation
m= (y2-y1) / (x2-x1)
Where x2=4, x1=x, y2=1, y1=-6, m=1 by requirements of this problem
Developing the equation we have this:
[tex]1=\frac{1-(-6)}{4-x}[/tex]
Which leaves to the following equation
[tex]5=4-x[/tex]
Resulting that x=9
The 2 ft side length of the scale drawing corresponds to a side length of 120 feet for the actual skate park. What is the scale factor?
Answer:
The scale factor is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
we know that
The scale factor is equal to the ratio between the side length of the scale drawing to the corresponding side length in the actual
so
[tex]\frac{2}{120}=\frac{1}{60}[/tex]
Answer:
1/60
Divide
Step-by-step explanation:
Find the fifth roots of 32(cos 280° + i sin 280°)
Answer:
The fifth root is 2[cos(56°) + i sin(56°)]
Step-by-step explanation:
* To solve this problem we must revise De Moiver's rule
- In the complex number with polar form
∵ z = r(cosФ + i sinФ)
∴ z^n = r^n(cos(nФ) + i sin(nФ))
* In the problem
- The fifth root means z^(1/5)
- We can put 32 as a form a^n
∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5
∴ z = 2^5[cos(280°) + i sin(280°)]
* Lets find z^(1/5)
[tex]*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)[/tex]
[tex]*(2^{5})^{\frac{1}{5}}=2^{5.\frac{1}{5}}=2[/tex]
∴ z^(1/5) = 2[cos(56) + i sin(56)]
* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]
Calculate electric force a 0.020kg balloon is charged by rubbing and then stuck to the ceiling
Answer:
Step-by-step explanation:
therefore, force F = m*g
= 0.02 kg * 9.8 m/s^2
= 0.196 Newton Force in the MKS system of units is measured in NEWTONS and results from a product of mass in Kg and acceler. the formula is s o the force=mass x acceleration. and the answer is .02x9.8^2= 1.6928ation in meters/sec^2
The electric force of a charged balloon sticking to the ceiling is due to the interaction between the balloon and the induced positive charge in the ceiling. This force is related to the principle of electrostatics and can theoretically be calculated using Coulomb's Law, but would require more details. However, for the balloon to remain stuck to the ceiling, this electrostatic force must be greater than the weight of the balloon.
Explanation:To calculate the electric force of a charged balloon sticking to the ceiling, you first need to consider the scenario as an interaction between the charged balloon and the induced charge in the ceiling. This scenario is related to the principle of electrostatics, where like charges repel and different charges attract. It is the electrostatic force that is making the balloon stick to the ceiling.
The balloon gets charged by picking up extra electrons (negative charge) when rubbed. When brought near the ceiling, these extra electrons in the balloon repel the electrons in the ceiling, causing the area of the ceiling near the balloon to be positively charged. This induced positive charge in the ceiling then attracts the negatively charged balloon. The force between the balloon and the ceiling can be caluclated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges, and inversely proportional to the square of the distance between them. However, to accurately calculate this force using Coulomb's law, we need more information such as the amount of charge on the balloon and the distance from the balloon to the ceiling.
Finally, for a balloon to stick to the ceiling, the electrostatic force must be greater than the weight of the balloon. The weight of the balloon can be calculated using the formula Weight = mass x gravity. In this case, the mass of the balloon is 0.020kg and the gravitational force is approximately 9.8 m/s². Therefore, the weight is 0.020kg x 9.8 m/s² = 0.196N. So for the balloon to stick to the ceiling, the electrostatic force must be greater than 0.196 N.
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Make q the subject of the formula 2(q+p) = 1+5q. Give your answer in the form ap-b/c where a,b and c are all positive integers
Answer:
[tex]\frac{2p-1}{3}[/tex]
Step-by-step explanation:
Since you want to get q only and q appears in both side of the equation. Try to isolate q to one side.
1) Expand 2(q+p)
2q + 2p = 1 + 5q
2) Move all q terms to one side
5q - 2q = 2p - 1
3q = 2p - 1
3) Divide 3 on both side (to isolate q)
q = [tex]\frac{2p-1}{3}[/tex]
After making q the subject of the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:
[tex]q = \frac{2p - 1}{3}[/tex]
The given equation is:
2(q + p) = 1 +5q
To make q the subject of the formula, follow the steps below
Expand the expression using the distributive rule
2q + 2p = 1 + 5q
Collect like terms by subtracting 2q from both sides of the equation
2q - 2q + 2p = 1 + 5q - 2q
2p = 1 + 3q
Subtract 1 from both sides of the equation
2p - 1 = 1 + 3q - 1
2p - 1 = 3q
Divide through by 3
[tex] \frac{2p - 1}{3} = q[/tex]
Therefore after making q the subject if the formula in the equation 2(q + p) = 1 + 5q, the resulting solution is:
[tex] q = \frac{2p - 1}{3}[/tex]
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All the dimensions of a triangle were multiple by the same factor. If the base of the triangle went from 1 centimeter to 3 centimeters, the area of the triangle was multiple by what?
6
3
9
12
Answer:
the area is multiplied by 9.
Step by Step Explanation:
Let x be the base
Let y be the height
Since all dimensions were multiplied by the same number, 3,
Original area,
1/2 × x × y = (1/2)xy
New area,
1/2 × 3x × 3y = (1/2)(9)xy
Hence, area is multiplied 9 times.
What is the value of log13
log 10=1,
log 2= 0.3010, and
log 3= 0.4771.
From these values, we can find many other log values.
log 5 = log 10 - log 2 = 0.699
log 0.5 = 0–log 2 = -0.301
log 1.5 = log 3 - log 2 = 0.1761
log 2.5 = log 5 - log 2 = 0.398
To find log of any number y:
Express y as (10^m)*(2^n)*(3^p)*(1+x).
Approximate log(1+x) as
(0.4343)*(x-x^2/2+x^3/3)
Or 0.4353*(x-x^2/2)
log y =
m + 0.3010*n + 0.4771*p + (0.4353)*(x-x^2/2+x^3/3)
To find log 13
13=2^2*3*(1+1/12)
log 13
= 2*0.3010 + 0.4771 + (0.4353)*(1/12 - 1/288+1/5184)
= 0.6020 + 0.4771 + 0.034847
= 1.1139
If the half-life of K-40 is 1.3 billion years and if a sample rock found on an island is estimated to be 1 billion years old, what percentage of the original parent K-40 would be present in the rock? Round your numerical values to the hundredths decimal place.
Answer Choices
(A) 76.92%
(B) 1.3%
(C) 58.67%
(D) 99.99%
For this case, we must make a rule of three, to find the percentage of the k-40 found in the sample found.
1.3 ----------> 100%
1 -------------> x
Where "x" represents the percentage of k-40 present in the sample found.
[tex]x = \frac {1 * 100} {1.3}\\x = 76.9230[/tex]
Rounding off we have:
76.92%
ANswer:
Option A
The percentage of parent K-40 remaining in the rock is calculated as 76.92% of the original K-40.
Percentage of parent K-40 remaining in the rock:
Calculate the number of half-lives: 1 billion years / 1.3 billion years = 0.7692 or about 0.77 half-lives.
Use the formula[tex](1/2)^n[/tex] where n is the number of half-lives to find the percentage remaining: [tex](1/2)^0.77[/tex] ≈ 0.76.
Convert to a percentage for the original K-40 remaining in the rock: 0.76 * 100% ≈ 76.92%.
The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
The area of the smaller trapezoid is 771 m2.
a.
4,096 m2
b.
4,028 m2
c.
784 m2
d.
21 m2
Answer: Option b.
Step-by-step explanation:
First, you need to calculate the ratio of the area. This is:
[tex]ratio=(\frac{64}{28})^2\\\\ratio=\frac{256}{49}[/tex]
You know that the area of the smaller trapezoid is 771 m², then you can set up the following proportion, where "x" is the area of the larger trapezoid. Then you have:
[tex]\frac{256}{49}=\frac{x}{771}[/tex]
Now you must solve for "x". Therefore, you get that the area of the larger trapezoid is:
[tex]x=(771)(\frac{256}{49})\\\\x=4,028m^2[/tex]
To the nearest whole number, the area of the other similar figure is: b. 4,028 m².
What is the Area of Similar Figures?The ratio of the areas of two similar figures equals the ratio of the square of their corresponding sides.
Thus:
Let x represent the area of the other figure.
Therefore:
771/x = (28²)/(64²)
771/x = 784/4,096
x = (771 × 4,096)/784
x = 4,028
Therefore, to the nearest whole number, the area of the other similar figure is: b. 4,028 m².
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Help with number four plz!!!!!!
Answer:
Yes
Step-by-step explanation:
First we'll find the number of total bars of soap.
8 + 8 + 11 = 27
Is 27 divisible by 27?
Yes because 27 / 3 = 9
So you could rearrange the soaps to have 9 bars in each basket.
What is the value of h when the function h(x)=x^2−8x+14 is converted to vertex form?
Answer:
h=4
Step-by-step explanation:
The given function is
[tex]h(x)=x^2-8x+14[/tex]
We add and subtract the square of half the coefficient of x.
[tex]h(x)=x^2-8x+(\frac{-8}{2})^2-(\frac{-8}{2})^2+14[/tex]
[tex]h(x)=x^2-8x+(-4)^2-(-4)^2+14[/tex]
The first three terms forms a perfect square trinomial
[tex]h(x)=(x-4)^2-16+14[/tex]
[tex]h(x)=(x-4)^2-2[/tex]
We now compare to the vertex form;
[tex]h(x)=a(x-h)^2+k[/tex]
We have h=4
Suppose f(x) = x^2 and g(x) = (3x)^2 which statement best compares with he graph of g(x) with the graph of f(x)
Answer:
Step-by-step explanation:
f(x) = x^2 and g(x) = (3x)^2. g(x) can be rewritten as 9x^2.
The graph of g(x) is similar to that of f(x), except that the graph of g(x) is the result of vertical stretching of the graph of f(x) by a factor of 9.
Answer: The graph of g(x) is horizontally compressed by a factor of 3.
Step-by-step explanation:
Got this answer right on apex
Help me find the which statements are true!!!!
Answer:
C.Step-by-step explanation:
[tex]\text{A. The absolute value of the slope of the line is equal to}\ \dfrac{HJ}{FG}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{HJ}{KJ}\\------------------------------\\\text{B. The absolute value of the slope of the line is equal to}\ \dfrac{FG}{JK}\\\bold{FALSE}\\\text{because the slope of the line is equal to}\ \dfrac{FG}{FK}\\------------------------------[/tex]
[tex]\text{C. Because triangles FGH and HJK are similar, the slope is the same}\\\text{between any two distinct points on the line.}\\\bold{TRUE}\\------------------------------\\\text{D. Because triangles FGH and HJK are not similar, the slope is found}\\\text{by using two distinct points on one of the triangles}\\\bold{FALSE}\\\text{because triangles FGH and HJK are similar (AAA)}[/tex]
Identify the equation that represents the line of best fit on this scatter plot.
30 POINTS
[tex]y=\frac{5}{7} x+2[/tex]
How?
The way you find it is easy. +2 means go up 2y. 5 is y too, so you do 2+5=7. Now go 7 positive x. The answer is this.
Hope this helped:)
Answer:
C. [tex]y=\frac{5}{7}x+2[/tex].
Step-by-step explanation:
We have been given a scatter plot. We are asked to find the equation of line of best fit.
First of all, we will find slope of line of best fit using points [tex](0,2)[/tex] and [tex](7,7)[/tex].
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-2}{7-0}[/tex]
[tex]m=\frac{5}{7}[/tex]
We can see that y-intercept of line of best fit is 2.
We will write our equation in slope intercept form [tex]y=mx+b[/tex], where,
m = Slope,
b = The y-intercept.
Upon substituting [tex]m=\frac{5}{7}[/tex] and [tex]b=2[/tex] in slope-intercept form, we will get:
[tex]y=\frac{5}{7}x+2[/tex]
Therefore, the equation of line of best fit for given scatter plot is [tex]y=\frac{5}{7}x+2[/tex] and option C is the correct choice.
Bob's bill for dinner at surefire steak house was $45. In addition he piad 5°\° of the bill in tax and he left a tip for 15°\° of the bill how much did Bob spend for tax and tip combined how much did Bob spend in all?
Answer:
$54
Step-by-step explanation:
First
45 times .05= 2.25
Second
45 plus 2.25
Third
45 times .15= 6.75
Fourth
45+2.25+6.75
Answer:
$54
Step-by-step explanation:
Okay. if the bill in tax was 5% and the tip is 15% just add them up to make it easier. Now, you have 20%, and you have to now find 20% of 45, make 20% into .20, do .20x45 which equals 9 which represents $9. Finally, add $9 (from tip and tax) to $45 (how much the food cost) = $54
No problem!
How to draw 30/4 in to an mix number
7 1/2
Divide 30 by 4 to get 7 with a remainder of 2. This means the answer is 7 2/4.Simplify the fraction. 2/4 is the same as 1/2, so the answer is 7 1/2.divide 30 by 4. you’ll get 7 remainder:2 take the whole number you got:7 take the remainder:2 (that will be ur numerator) then take the divisor:4
you’ll get 7 2/4
(simplest form is 7 1/2)
HELP IM ♀️ CONFUSED WILL GIVE BRAINLIEST AND 10 points CAN SOMEONE HELP WITH MY HOMEWORK QUESTIONS
Answer:
1 3/4
Step-by-step explanation:
8.25-6.5
Answer:
I believe it is B
Lowest- 6 1/2 inches
Tallest- 8 1/4 inches
6 1/2-8 1/4= 1 3/4
I am sorry if this is wrong.
A small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery. Find the constant of proportionality for the number of pies baked and loaded on a truck for delivery. A.48 B. 60 C. 96 D. 144
Answer:
Constant of proportionality should be 48.
Step-by-step explanation:
Given that a small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery.
Now we need to find about what is the constant of proportionality for the number of pies baked and loaded on a truck for delivery.
Number of baked pies = 180
Number of pies loaded on truck for delivery = 80% of baked pies
= 0.80(180)= 144 in 3 hours.
So number of pies loaded per hour = 144/3= 48
Hence constant of proportionality should be 48.
PLZZZZZZZZZZZZZ HELP I NEED TO PASS THIS TEST I WILL GIVE BRAINLIST ANSWER TO WHO ANSWERS IT RIGHT
A statue has the shape of a square pyramid. The side length of the square base is 20 feet. The slant height of the monument is 16 feet. What is the height of the monument? Enter your answer, rounded to the nearest tenth of a foot, in the box.
____
|___| ft
Answer:
[tex]b=12.5[/tex] ft
Step-by-step explanation:
From this description we can draw this diagram
Now we can use the Pythagorean theorem to find the height.
[tex]10^2+b^2=16^2\\\\b^2=256-100\\\\b=\sqrt{156}[/tex]
This square root is equal to
[tex]b=12.489[/tex]
Which rounds to
[tex]b=12.5[/tex] ft
What is the slope if the line x+3y = 10
Answer:
the slope is -1/3
the Y intercept is 10/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
We want to get the equation in slope intercept form (y=mx+b) where m is the slope and b is the y intercept
x+3y = 10
Subtract x from each side
x-x+3y = -x+10
3y = -x+10
Divide each side by 3
3y/3 = -1/3x +10/3
y = -1/3x +10/3
The slope is -1/3 and the y intercept is 10/3
can someone help me with this?
V=ABh
S=a +b+c
————-
2
=83.5
find the solution to the system
y=x^2+8x+2
y=7x+4
A(-2,-10) and (1,11)
B(2,10) and (-1,-11)
C(-2,-34) and (1,11)
D no solution
Answer:
A
Step-by-step explanation:
Given the 2 equations
y = x² + 8x + 2 → (1)
y = 7x + 4 → (2)
Substitute y = x² + 8x + 2 into (2)
x² + 8x + 2 = 7x + 4 ( subtract 7x + 4 from both sides )
x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
Substitute these values into (2) for the corresponding values of y
x = - 2 : y = - 14 + 4 = - 10 ⇒ (- 2, - 10)
x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)
The solutions are (- 2, - 10) and (1, 11) → A
a number is chosen at random from 1 to 50 find the probability of selecting factors of 36
Answer:
9/50 or 18%
Step-by-step explanation:
The factors of 36 are-
123469121836That's 9 factors. 1-50 means that it is a 9 out of 50 chance, or 80%.
When a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50.
What is probability?Probability is the ratio that shows us how likely an event will occur from a given set of events.
We can find the required probability below:The factors of 36 are:
36 = 2*2*3*3
Therefore the factors of 36 are 2 and 3.
Total number of factors = 2
Total number of numbers from 1 to 50 = 50
The probability of selecting factors of 36 = P(selecting factors of 36)
= 2/50
The probability of getting a factor of 36 when a number is chosen at random is 2/50.
Therefore, we have found that when a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50.
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A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?
The correct answer is: D) 30 inches
Explanation:
We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:
f(3) = -2(3)(3-8)
f(3) = -2(3)(-5)
f(3) = -6(-5)
f(3) = 30
Therefore, the correct answer is 30 inches! Thank you for your inquiry, your welcome for the answer and explanation!
The correct answer is: D) The height of the arch, measured 3 inches from the left side of the arch 30 inches
What is the height?
In math, height can be defined the vertical distance from the top to the base of the object. It is measured in cm, inches, meters, etc.
We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:
f(3) = -2(3)(3-8)
f(3) = -2(3)(-5)
f(3) = -6(-5)
f(3) = 30
Therefore, the correct answer is 30 inches
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What is the measure of Angle F, to the nearest degree?
Can some body help me with number 12 it’s due tomorrow.
Answer:
Mean = 51.375
Mode = 55,44
Step-by-step explanation:
add all the numbers up and divide by 8
find the most repeating numbers.
Answer:
Mean: 51.375
Median: 51.5
Mode: 44, 55
Hope This Helps! Have A Nice Day!!
7x+(2x+7)=9x+7 show work
it is true 9x=9x
7x+(2x+7)=9x+7
7x+2x+7=9x+7
-7. -7
7x+2x=9x
9x=9x
the class kept track of rainy and sunny days. During the 54 days, classified rainy or sunny, the ratio of rainy days is 7 to 14. How many sunny days were there?
There are 36 sunny days
1:2
1 + 2 = 3
54/3 = 18
1 • 18 = 18
2 • 18 = 36
There are 36 sunny days.
Hope this helps!
If it does then I would appreciate it if you could make me brainliest.