Option C: [tex]a=3, b=4[/tex] is the value of a and b
Explanation:
Given that the expression [tex]\sqrt{648}=\sqrt{2^a\times3^b}[/tex]
We need to determine the value of a and b
Let us consider the term [tex]\sqrt{648}[/tex] and take the prime factorization of the term 648
Thus, we have,
648 divides by 2,
[tex]648=2 \cdot 324[/tex]
324 divides by 2,
[tex]648=2 \cdot 2 \cdot 162[/tex]
162 divides by 2,
[tex]648=2 \cdot 2 \cdot 2 \cdot 81[/tex]
81 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27[/tex]
27 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9[/tex]
9 divides by 3,
[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3[/tex]
Thus, we have,
[tex]\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}[/tex]
Therefore, equating the powers of 2 and 3, we get,
[tex]a=3, b=4[/tex]
Hence, the value of a and b is 3 and 4
Thus, Option C is the correct answer.
The values of a and b which make the equation true are; a = 3 and b = 4 respectively.
From the question; the expression given is;
[tex] \sqrt{648} = \sqrt{ {2}^{a} \times {3}^{b} } [/tex]
In essence; we have;
648 = 2^a × 3^bBy expression of of 648 as the product of its lowest factors; we have;
648 = 2 × 2 × 2 × 3 × 3 × 3 × 3.In which case; we have;
648 = 2³ × 3⁴Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.
Read more on indices:
https://brainly.com/question/1592472
Angle x and angle y are complementary. Angle x is supplementary to a 128 degrees angel. What are the measures of angle x and y
Answer: x is 52 and y is 38.
Step-by-step explanation:
x+128=180
x=52
52+y=90
y=38
Answer: X=128 y=52
Step-by-step explanation:
If x=128 take 180-128=52 and 52=y
Which of the following expressions means "five factors of 3"?
35
0
05=3
[tex]\text{Hey there!}[/tex]
[tex]\large\text{Which of the following expressions means \underline{five factors of 3} ?}[/tex]
[tex]\large\text{Basically, it is telling you that 3 is expressed as it rises to the 5th}\\\large\text{power}[/tex]
[tex]\large\text{Based on SOME of the stuff we gathered above, we solved your}\\\large\text{equation/ question!}[/tex]
[tex]\boxed{\boxed{\mathsf{Your\ answer: \boxed{\mathsf{3^5}}}}}\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Classify a triangle with angle measures of 63 degrees and 27 degrees.
A) Acute
B) Obtuse
C) Right
D) Not Possible
Yo sup??
63+27=90
therefore the other angle is 90
Hence it's a right angled triangle
correct answer is option C
Hope this helps
Jillian buys 3.6 meters of fabric. The fabric costs $5.75 for each meter. How much does Jillian spend for the fabric?I need help asap no need to give me example just answer
[help]
Vertical and horizontal line (1,-4)—do X=blank and Y=blank
Answer:
x = 1 and y = - 4
Step-by-step explanation:
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line goes through.
Here the line passes through (1, - 4) with x- coordinate 1, thus
x = 1 ← equation of vertical line
The equation of a horizontal line is
y = c
where c is the value of the y- coordinates the line goes through.
Here the line passes through (1, - 4) with y- coordinate - 4, thus
y = - 4 ← equation of horizontal line
Rewrite the expression by favoring out the greatest common factor: 9b+12
Answer:
3(3b + 4)
the GCF is 3
Step-by-step explanation:
Please Help with these 3 questions Please
Draw and classify a quadrilateral that fits each description
4 right angles, opposite sides equal in length and parallel
Opposite sides equal in length and parallel
Answer:
It would be a square or a rectangle .
Step-by-step explanation:
The quadrilateral(s) has 4 sides, and each have have 4 right angles. The opposite lengths are both the same as the are parallel. Even though the rectangle has different lengths, the opposites match.
If f(x) = x ^ 3 + 2x ^ 2 - 3 , find f(2) . A ) -19 B ) -3 C) -1 D ) 5
Answer:
13
Step-by-step explanation:
f(x) = x ^ 3 + 2x ^ 2 - 3
Let x=2
f(2) = 2 ^ 3 + 2 *2 ^ 2 - 3
= 8 +2 *4 -3
= 8 +8 -3
=13
Which equation represents a linear function that has a slope of Four-fifths and a y-intercept of –6?
y = negative 6 x + four-fifths
y = four-fifths x minus 6
y = four-fifths x + 6
y = 6 x + four-fifths
Answer:
Option B.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex]
where, m is a slope and b is y-intercept.
It is given that slope of line is 4/5 and y-intercept is -6.
Substitute m=4/5 and b=-6 in the above formula.
[tex]y=\dfrac{4}{5}x+(-6)[/tex]
[tex]y=\dfrac{4}{5}x-6[/tex]
Hence, the correct option is B.
Sort the phrases according to whether or not they require a hyphen.
in eighty two days
Needs Hyphen
Does Not Need Hyphen
twenty six letters
the fourth person in line
three thousand years
two thirds of the class
Answer:
Needs hyphen: -in eighty two days -twenty six letter - two thirds do the class
Doesn’t need hyphen: -the fourth person in line -three thousand years
Step-by-step explanation:
Answer:
Needs hyphen:
in eighty two days
twenty six letters
two thirds of the class
Does not need Hyphen:
the fourth person in line
three thousand years
Step-by-step explanation:
Hyphen needed for numbers between 21-99
A sketch of Jessie’s neighborhood is shown below. Which equation can Jessie use to determine x, the distance from home to school?
Answer:
Hello the Answer is A!
Step-by-step explanation:
Here's how to do it
When you have the triangle of her school you add your first to angles together and subtract from 180. Then you are going to set is up as law of sine. So the order would be 6/sin110* = x/sin50*
Hope this helps <3
The distance from home to school will be 5 meters.
Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
From the given image the distance between the home and school is followed by the square 3 meters from the home and the school is 4 meters making a right-angle triangle.
The minimum distance between the school and the home will be calculated as;-
D = √ ( 3² + 4² )
D = √ ( 25 )
D = 5 meters'
Therefore, the distance will be 5 meters.
To know more about the Pythagorean theorem follow
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40 pts! please answer asap!
∠A and ∠B are supplementary angles. The measure of ∠A is three time the measure of ∠B.
Part A: Write an equation to represent the supplementary angle relationship between ∠A and ∠B.
Part B: Use the equation to find the measures of ∠A and ∠B.
[tex]\huge{\underline{\mathfrak{\red{Answer}}}}[/tex]
let A=3x then B=x
also given,
A+B=90°
3x+x=90
4x=90
x= 22.5°
then 3x= 3×22.5= 67.5
A= 67.5
B=22.5
Answer:
20 points
Step-by-step explanation:
15 POINTS. Pls match and state clearly. :)
Solve for x.
8 - 4x - 28 = 4
x=_________
Answer:
x=6
Step-by-step explanat
Solve each equation.
a. 10 = 4y
b.5y = 17.5
c. 1.036 = 10y
d. 0.6y = 1.8
e. 15 = 0.1y
Answer:
a. y = 2.5
b. y = 3.5
c. y = 0.1036
d. y = 3
e. y = 150
Step-by-step explanation:
a. 10 ÷ 4 = 2.5
b. 17.5 ÷ 5 = 3.5
c. 1.036 ÷ 10 = 0.1036
d. 1.8 ÷ 0.6 = 3
e. 15 ÷ 0.1 = 150
Gavin is training for a marathon and varies his workouts from day to day. Gavin ran 10 MPH during Monday's workout and 50% slower during Tuesday's workout. How fast did he run on Tuesday?
MPH
Solution:
Given that,
Gavin ran 10 MPH during Monday's workout
50% slower during Tuesday's workout
Therefore,
Speed in tuesday = 50 % slower than monday
Which means,
Speed in tuesday = 10 - 50 % of 10
Solve the above
[tex]\text{ Speed in tuesday } = 10 - \frac{50}{100} \times 10\\\\\text{ Speed in tuesday } = 10 - 0.5 \times 10\\\\\text{ Speed in tuesday } = 10 - 5\\\\\text{ Speed in tuesday } = 5\\\\[/tex]
Thus, he ran 5 mph in tuesday
If your sisters brother is 12 on his 16th birthday, how many dishes can he fold?
A.) Orange
B.) Closet
C.) Nike
D.) 7
Answer:
none of them, its actully an ant eater
Step-by-step explanation:
Grace starts with 100 milligrams of a radioactive substance. The amount of the
substance decreases by each week for a number of weeks, w. She writes the
expression 100(-)w to find the amount of radioactive substance remaining after w
weeks.
Ryan starts with 1 milligram of a radioactive substance. The amount of the substance
decreases by 40% each week for a number of weeks, w. He writes the expression (1 -
0.4)" to find the amount of radioactive substance remaining after w weeks.
Use the drop-down menus to explain what each part of Grace's and Ryan's
expressions mean.
Answer:
100 is grace's initial amount. w is how much of the substance is being decrased each week. in ryan's equation, 1 is 100% of the substance, so the initial amount, and 0.4 is the amount that is being decreased.
Step-by-step explanation:
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation:
(9x2 + 10x + 4) − (9x2 + 5x − 1)
For this case we must simplify the following expression:
[tex](9x ^ 2 + 10x + 4) - (9x ^ 2 + 5x-1)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\9x ^ 2 + 10x + 4-9x ^ 2-5x + 1 =[/tex]
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
[tex]9x ^ 2-9x ^ 2 + 10x-5x + 4 + 1 =\\5x + 5[/tex]
Answer:
[tex]5x + 5[/tex]
The farthest distance a satellite signal can directly reach
is the length of the segment tangent to the curve of Earth's
surface. If the measure of the angle formed by the tangent
satellite signals is 135, what is the measure of the intercepted
satellite
arc on Earth? (The figure is not drawn to scale.)
Answer:
45°
Step-by-step explanation:
The sum of interior angles of the quadrilateral that has vertices at the center of the Earth, the two points of tangency, and the satellite is 360°. The angles at the points of tangency are 90°, so the angle at the satellite and the central angle are supplementary.
The arc has a measure of 180° -135° = 45°.
joe and Eric have to ship 75 packages. Joe can do the job alone in 5 hours. if Eric helps, they get it done in 4 hours. How long would it take Eric to do the job alone?
Eric took 20 hours to do the job alone.
Step-by-step explanation:
Given :
Total work = 75 packagesJoe took 5 hours to complete the total work.The amount of work Joe alone can do per hour = 75/5 = 15 packages.
The amount of work Joe and Eric together do per hour = 75/4 = 18.75
The amount of work Eric alone can do per hour = 18.75 - 15 = 3.75
The time Eric took to complete the entire work = 75 / 3.75 = 20 hours.
Is the relation a function? Yes or No? (4,5),(4,-7), (4,2), (4,0), (4,9)
Answer:
No, because 4 is repeated in the domain.
Step-by-step explanation:
Answer:
No it's not a function
Step-by-step explanation:
When the domain repeats either once or more, it's never a function
Which recursive definition represents the sequence {4,6,8,10...)?
A). a1 = 4; an-1-2
B). a1 = 4; an-1 + 2
C). a1 = 2; an-1 + 2
D). a1 = 4; 2an-1 - 2
Answer:It’s b
Step-by-step explanation:USA test prep answer
Which inequality is equivalent to -m> 15
This inequality can be simplified.
~Divide -1 to both sides (flip the symbol since we're dividing a negative number)
-m/-1 < 15/-1
m < -15
Best of Luck!
Answer:
m < -15
Step-by-step explanation:
Step 1: Multiply both sides by -1
-m > 15
-m * -1 > 15 * -1
Since you multiply by a negative, you must flip the sign
-m * -1 > 15 * -1
m < -15
Answer: m < -15
A recipe calls for 2 cups of flour of flour to make 3 dozen cookies. Is 3 cups of flour enough to make 60 cookies?
Answer:
no it is not
Step-by-step explanation:
it would be 54
Answer:
No
Step-by-step explanation:
2 cups of flour --> 36 cookies
3 cups of flour ----> x
2/3 = 36/x
x = 54 cookies
3 Cups of flour yields 54 cookies, but its not enough flour for 60 cookies.
11. Simon arrived at work at 8:15 A.M. and left work at 10:30 P.M. If Simon gets paid by the hour at a
rate of $10 and time and / for any hours worked over 8 in a day. How much did Simon get paid?
A. $120.25
B. $160.75
C. $173.75
D. $180
E. $182.50
Answer:
D
Step-by-step explanation:
Here is a balanced hanger:
If a square weighs 5 grams, and a triangle weighs 2 grams, how much does a circle weigh?
I don't know exactly i think its either 3 grams or 7 grams or 2 1/2 grams
sorry if its wrong
the area of a rectangular window is 7098cm^2 . if the length of. the window is 91 cm, what is it’s width?
Answer:
78
Step-by-step explanation:
7098 / 91 = 78
hope i helped
10. Write the number 2,049 in
expanded form.
Step-by-step explanation:
[tex]2049 = 2 \times 1000 + 0 \times 100 + 4 \times 10 + 9 \times 1 \\ = 2000 + 0 + 40 + 9 \\ = 2000 + 40 + 9[/tex]
Answer:
2,000 + 0 + 40 + 9
Explanation:
Expanded form or expanded notation is a way of writing numbers to see the math value of individual digits.
Hope this helps
- Amelia The Unknown