If 7.02 is subtracted 43.8 the correct answer will be
To solve 49^3x = 343^2x+1, write each side of the equation in terms of base ____
Each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].
Solving Equations by Expressing Equations in Terms of their BasesTo solve an equation, the bases can be made equivalent and cancelled out by creating exponents.
Given:
[tex]49^{3x} = 343^{2x + 1}[/tex]
First, express each side by simplifying their bases and make them equivalent. Let the base be 7.
Thus:
[tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex]
To solve, cancel the bases to have, 2(3x) = 3(2x + 1) and solve for x.
Therefore, each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].
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Answer: 7 then B on edge
Step-by-step explanation:
Answer: it’s
Step-by-step explanation:
A rectangular board is 18 feet by 24 feet. How far from the center of the board should the foci be located in order to cut the largest elliptical tabletop from the board?
a. 7.94 ft
b. 4.06 ft
c. 15 ft
d. 15.9 ft
x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b
Center (0, 0):
h = 0
k = 0
a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:
General : (x - h)² / a² + (y - k)² / b² = 1
(x - 0)² / (12)² + (y - 0)² / (9)² = 1
x² / 144 + y² / 81 = 1
Focus = c:
_____
c = √a² - b²
_______
c = √(12)² - (9)²
______
c = √144 - 81 = sqrt63 = 7.9372
Focus : ( -7.9372, 0) and ( 7.9372, 0)
The correct answer is: a. 7.94 ft
Step 1
To find the distance from the center of the board to the foci of the ellipse that will result in the largest possible elliptical tabletop, we can use the formula:
[tex]\[ c = \sqrt{a^2 - b^2} \][/tex]
where:
- a is half the length of the major axis (which is half of the longer side of the rectangle)
- b is half the length of the minor axis (which is half of the shorter side of the rectangle)
Step 2
Given that the rectangle is 18 feet by 24 feet, [tex]\( a = \frac{24}{2} = 12 \)[/tex] feet and [tex]\( b = \frac{18}{2} = 9 \)[/tex] feet.
Step 2
Now, we can substitute these values into the formula:
[tex]\[ c = \sqrt{12^2 - 9^2} \]\[ c = \sqrt{144 - 81} \]\[ c = \sqrt{63} \][/tex]
Taking the square root of 63 gives us approximately 7.94 feet.
You randomly select one card from a standard deck. event a is selecting a fivea five. determine the number of outcomes in event
a. then decide whether the event is a simple event or not.
In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:
Probability = 4 / 52 = 1 / 13
Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.
Joseph needs to find the quotient of 3216 divided by 8. In which place is the first digit of the quotient?
A car company said that its top five models had the following fuel efficiency ratings: 26.3 mpg, 28.95 mpg, 33.6 mpg, 35 mpg, 38.24 mpg. What is the average mpg rating of these five models, recorded to the appropriate degree of precision? A. 32 mpg B. 32.0 mpg C. 32.4 mpg D. 32.42 mpg
The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.
To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:
Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.
The sum is 162.09 mpg.
Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.
The average is 32.418 mpg.
To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.
A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
The value of "a" is 2.
To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.
First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).
Substituting the coordinates, we have:
m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2
Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):
1 = 2a + b
To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."
Using (-1, -5):
-5 = 2(-1) + b
-5 = -2 + b
b = -3
Now we can substitute the values of "b" and "a" into the equation:
1 = 2a - 3
To isolate "a," we add 3 to both sides:
1 + 3 = 2a
4 = 2a
Dividing both sides by 2, we find:
2 = a
Therefore, the value of "a" is 2.
78 million converted in scientific notation
The correct answer is:
7.8 × 10⁷
Explanation:
To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us
7.8 × 10⁷
Write 96 39/40 as a decimal
write 60 as the product of two factors
working together Katherine and Julianna can plant new trees on there recently divorced land in 4 days working alone it would take Giuliana to days longer than it would take Catherine to plant the trees how long would it take Katherine working alone to plant the trees
You just won a contest! you will receive $100,000 a year for 20 years, starting today. if you can earn 12 percent on your investments, what are your winnings worth today?
Use the formula to evaluate the series -3+6-12+24-...-a7
Formula:Sn=a1(1-r^n)/1-r
In the formula for a finite series, a1 is the first term, r is the common ratio and n is the number of terms.
On a blueprint, a wall that is 45 feet long is 6 inches long. How long should a girder appear on the blueprint if the girder is actually 30 feet long?
Answer:
4 inches
Step-by-step explanation:
1 foot = 12 inches
45 feet --- 6 inches
From this we can conclude that the scale of the Blueprint is:
1 foot in actual = 1/90 foot on blueprint
If the girder is actually 30 feet long, then
30 feet --- (1/90*30*12) inches
30 feet --- 4 inches
***ANSWER ASAP****
Use synthetic division to solve (x^3-x^2-17x-15)/(x-5)
Answer: [tex]1x^2+4x+3[/tex]
Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).
We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .
In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:
And we divide them by 5 using synthetic division method.
______________
5 | 1 -1 -17 -15 Getting first number down.
| 5 20 -15 Multiplying each down number by
- - - - - - - - - - - - - - - - divisor 5.
1 4 3 0 5×1=5 , 5×2=20, 5×2=15
Subtracting those products from coefficients.
Now, writing the final polynomial degree 1 less than 3, that is 2.
So, [tex]1x^2+4x+3[/tex] would be our quotient.
What is the value of m?
13m+3−56m=−15
The value of m in the equation [tex]13m +3 -56m = -15[/tex] is [tex]\frac{18}{43}[/tex]
Given: [tex]13m +3 -56m = -15[/tex]
To find: value of m
To find the value of m we need to move all the terms containing variables on LHS and the constants on RHS. This can be done as follows:
[tex]13m +3 -56m = -15\\13m -56m =-15-3\\[/tex]
Now we can solve for m as follows:
[tex]13m-56m =-15-3\\-43m = -18\\[/tex]
The negative sign on both LHS and RHS will cancel out and it will give us:
[tex]m = \frac{18}{43}[/tex]
Since 18 and 43 do not have any common multiples so the fraction cant be simplified further. So, [tex]m = \frac{18}{43}[/tex]
Use the distributive property to create an equivalent expression to 54+18x
Answer:
An equivalent expression to 54+18x, using the distributive property is 18(3+x)
Step-by-step explanation:
In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.
We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that
[tex]1=\frac{18}{18}[/tex]
then we can distribute the denominator, so we calculate:
[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]
And the equivalent expression to (54+18x) is 18(3+x).
A contractor is building a circular swimming pool. The radius of the circle 12 feet. He needs to know the circumference in order to buy tile to put around the edge of the pool. What is the circumference if he uses =22/7 ?
"is it possible for four consecutive even numbers to have a sum that is ten more than the sum of the smallest two numbers"
Kathryn, a college student, works part time at a coffee house. She worked 5 StartFraction 7 Over 20 EndFraction hours on Monday, 4 and one half on Tuesday, 6 and three fourths on Wednesday, 3 and one fourth on Thursday, and 7 on Friday. How many hours did she work altogether? She worked nothing hours altogether.
Answer: I’m just adding this to verify that the other answer was correct
Find the circumference of a circle with a diameter of 6 cm. Leave your answer in terms ofmc149-1.jpg.
9mc149-3.jpg cm
12mc149-4.jpg cm
24mc149-5.jpg cm
6mc149-2.jpg cm
Answer:
D. [tex]6\pi\text{ cm}[/tex].
Step-by-step explanation:
We are asked to find the circumference of a a circle with a diameter of 6 cm.
We will use circumference of circle to solve our given problem.
[tex]C=\pi\cdot D[/tex], where,
C = Circumference of circle,
D = Diameter of circle,
Upon substituting [tex]D=6\text{ cm}[/tex] in above formula we will get,
[tex]C=\pi\cdot 6\text{ cm}[/tex]
[tex]C=6\pi\text{ cm}[/tex]
Therefore, circumference of our given circle would be [tex]6\pi\text{ cm}[/tex] and option D is the correct choice.
x2= 121 can anyone solve it
Speed skiing takes place on a course that is 2/3 mile long. How many feet long is the course? Show work too
1 mile = 5280 feet
5280 * 2/3 =
5280 *2 = 10560
10560/3 = 3520
it is 3520 feet long
all the types of shapes that can be created by taking cross-sections of a cube
Answer:
✅ triangle
✅ pentagon
✅ hexagon
✅ trapezoid
❌ octagon
Step-by-step explanation:
7-4.9t=15+7.6t solve for t
Show the tens fact you used. Show the difference.
14-6=
10-?=?
Question 1:
14 - 6 = ?
Further ExplanationTo determine the difference between 14 and 6 is the same is 14 – 6. In other words, the different is the result we get if we subtract both values.
Therefore, the difference between 14 and 6 is 8.
14 – 6
= 8.
There is always three parts in any subtraction equation and these include:
The number that is being subtracted from also called minuendThe number that is being subtracted from the minuend, also called subtrahendThe differences, which is the result you get from subtracting the subtrahend from minuendQuestion 2:
10 - ? = ?
Further ExplanationThe given question means you should for a number that when being subtracted from 10 will give the same number.
Therefore, to solve the question, let the missing be X
10 – X = X
If you simplify the equation, then you should have:
10 = X + X
10 = 2X (divide both side by 2)
[tex]\frac{10}{2}[/tex] = [tex]\frac{2x}{2}[/tex]
5 = X
X = 5
Therefore, the answer for question 1 and 2 are 8 and 5 respectively
LEARN MORE:
Show the tens fact you used write the difference 14 https://brainly.com/question/13620963Show the tens fact you used. Write the difference. https://brainly.com/question/1904682KEYWORDS:
differencetens factsubtractionequationminuendy=0.6x–3;(–2,2) parallel lines
The graph shows a line and two similar triangles.
The equation of the line will be y = 4/3x + 3. The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
From the given graph the slope will be calculated as:-
Rise = 4
Run = 3
Slope = Rise / Run = 4 / 3
The y-intercept is 3.
The equation can be written as:-
y = mx + c
y = 4/3x + 3
Therefore, the equation of the line is y = 4/3x +3.
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a quarterback made 345 pass completions during one football season. if this was 60% of his attempts,how many passes did he attempt?
divide completions by percentage
345 / 0.60 = 575 pass attempts
What is the area of a circle with a radius of 7 cm? (Use 3.14 for pi and round to the nearest tenth.)
Answer:
[tex]153.9\ cm^{2}[/tex]
Step-by-step explanation:
Hello, thanks for asking this question here at Brainly, I think I can help you with this
the area of circle is given by:
[tex]Area=\pi * radius^{2} \\[/tex]
Step one
Let
[tex]\pi =3.14\\and\\r= 7 cm[/tex]
Step two
put the values into the equation
[tex]Area=\pi * radius^{2} \\Area=3.14* (7 cm)^{2}\\ Area=3.14* 49\ cm^{2} \\Area=153.9\ cm^{2} \\[/tex]
Hence, the area of a circle with radius 7 cm is 153.9 cm2
I hope it helps,do not hesitage in asking me anything about this, have a great day