Answer:
12
Step-by-step explanation:
Given the expression:
[tex](\dfrac{(2^{-1}\times 3^2)}{(2^{2}\times 3^{-4})})^\frac{7}{2} \times (\dfrac{(2^{-2}\times 3^3)}{(2^{3}\times 3^{-5})})^\frac{-5}{2}[/tex]
We have to simplify the above expression.
Let us have a look at a few formulas:
[tex]1.\ a^b = \dfrac{1}{a^{-b}}[/tex]
[tex]2.\ a^b\times a^c = a^{b+c}[/tex]
[tex]3.\ (a^b ) ^c = a^{bc}[/tex]
Now, let us try to solve the given above expression using the formulas:
[tex]\Rightarrow (\dfrac{(3^{4}\times 3^2)}{(2^{2}\times 2^{1})})^\frac{7}{2} \times (\dfrac{(3^{5}\times 3^3)}{(2^{3}\times 2^{2})})^\frac{-5}{2}[/tex]
[tex]\Rightarrow (\dfrac{(3^{4+2})}{(2^{2+1})})^\frac{7}{2} \times (\dfrac{(3^{5+3})}{(2^{3+2})})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{6}}{2^{3}})^\frac{7}{2} \times (\dfrac{3^{8}}{2^{5}})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{\frac{42}{2}}}{2^{\frac{3\times 7}{2}}})\times (\dfrac{2^{5}}{3^{8}})^\frac{5}{2}\\\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{5\times 5}{2}}}{3^{\frac{8\times 5}{2}}})[/tex]
[tex]\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{25}{2}}}{3^{20}})\\\Rightarrow {3^{1}}\times {2^{\frac{25-21}{2}}}\\\Rightarrow 3\times 4 \\\Rightarrow \bold{12}[/tex]
It takes Mr. Martin 12 minutes to drive his bus route without stopping to pick up any passengers. For each passenger stop, he estimates that 30 seconds is added to his travel time. On Tuesday, Mr. Martin spends 14 minutes driving his route.
Which of the following is closest to the square root of 4000 A) 20 B) 60 C) 400 D) 2000
Answer:A
Step-by-step explanation:
Sqrt(4000)= 20
i need help with the top one
Answer:
2. 14
4. -6
Step-by-step explanation:
#2
(x²-4y)/2, given x=4, y=-3
[(4)²-4(-3)]/2
=[16+12]/2
=28/2
=14
------------------------
#4
19-x², given x=-5
19-(-5)²
=19-25
=-6
What part of the expression is a factor? 12+5(-3n-8)
Answer:
5
Step-by-step explanation:
A factor is a number or an expression that is multiplying something.
5 is multiplying -3n + 8.
Answer: 5 is a factor.
How do I fill this out? Im not sure how to?
Answer:
z=-21
Step-by-step explanation: (9-3)/2=(6+z)/5
We move all terms to the left:
(9-3)/2-((6+z)/5)=0
We add all the numbers together, and all the variables
-((z+6)/5)+6/2=0
We add all the numbers together, and all the variables
-((z+6)/5)+3=0
We multiply all the terms by the denominator
-((z+6)+3*5)=0
We calculate terms in parentheses: -((z+6)+3*5), so:
(z+6)+3*5
We add all the numbers together, and all the variables
(z+6)+15
We get rid of parentheses
z+6+15
We add all the numbers together, and all the variables
z+21
Back to the equation:
-(z+21)
We get rid of parentheses
-z-21=0
We add all the numbers together, and all the variables
-1z-21=0
We move all terms containing z to the left, all other terms to the right
-z=21
z=21/-1
z=-21
please someone help me to prove this...
Step-by-step explanation:
cos 20° cos 40° cos 60° cos 80°
Simplify cos 60° to ½.
½ cos 20° cos 40° cos 80°
We can use double angle formula, sin(2θ) = 2 sin θ cos θ. Multiply and divide by 2 sin 20°.
½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)
½ (sin 40° cos 40° cos 80°) / (2 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)
½ (sin 80° cos 80°) / (4 sin 20°)
Multiply and divide by 2 and use double angle formula again.
½ (2 sin 80° cos 80°) / (8 sin 20°)
½ (sin 160°) / (8 sin 20°)
Use phase shift identity sin θ = sin(180−θ).
½ (sin 20°) / (8 sin 20°)
1/16
In this case we have the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = 1 / 16, and are asked to prove that this equation is true. Let's start by using the property 'cos(s)cos(t) = cos(s + t) + cos(s - t) / 2.' Taking the bit 'cos(20°)(cos(40°)' we know that s should = 20°, and t should = 40°.
[tex]\mathrm{Using\:the\:following\:identity}:\quad \cos \left(s\right)\cos \left(t\right)=\frac{\cos \left(s+t\right)+\cos \left(s-t\right)}{2},[/tex]
[tex]\cos \left(20^{\circ \:}\right)\cos \left(40^{\circ \:}\right)=\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\\[/tex]
[tex]\mathrm{Substituting\:the\:value\:back}:\frac{\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]
This expression is indeed not simplified, but remember that we can use the identities 'cos(- 20°) = cos(20°)' and 'cos(60°) = 1 / 2.' Let's substitute one step and a time.
[tex]\cos \left(-20^{\circ \:}\right)=\cos \left(20^{\circ \:}\right): \frac{\cos \left(60^{\circ \:}\right)\cos \left(80^{\circ \:}\right)\left(\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\cos \left(60^{\circ \:}\right)=\frac{1}{2}:\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]
[tex]\frac{\frac{1}{2}\cos \left(80^{\circ \:}\right)\left(\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\cos \left(80^{\circ \:}\right)\left(1+2\cos \left(20^{\circ \:}\right)\right)}{8}[/tex]
Now that we have this 'simplified expression,' if we take the numerator as a whole in decimal form, it will = 0.5. Respectively 0.5 / 8 = 1 / 2 / 8 = 1 / 16. Hence our equation is true.
[tex]\cos \left(80^{\circ \:\:}\right)\left(1+2\cos \left(20^{\circ \:\:}\right)\right) = 0.5,\\0.5 / 8 = (1 / 2) / 8 = 1 / 16[/tex]
∠A and \angle B∠B are complementary angles. If m\angle A=(2x+10)^{\circ}∠A=(2x+10) ∘ and m\angle B=(3x+15)^{\circ}∠B=(3x+15) ∘ , then find the measure of \angle B∠B.
Answer:
[tex]54^\circ[/tex]
Step-by-step explanation:
Given :
[tex]m\angle A=(2x+10)^{\circ}[/tex]
[tex]m\angle B=(3x+15)^{\circ}[/tex]
And angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.
To find:
The measure of [tex]\angle B[/tex].
Solution:
First of all, let us learn about complementary angles.
Complementary angles are the angles whose sum is equal to [tex]90^\circ[/tex].
And we are given that angles [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.
Therefore [tex]\angle A[/tex] + [tex]\angle B[/tex] = [tex]90^\circ[/tex]
[tex]\Rightarrow 2x+10+3x+15=90\\\Rightarrow 5x+25=90\\\Rightarrow 5x=65\\\Rightarrow x =13[/tex]
Putting the value in [tex]\angle B[/tex].
[tex]m\angle B=(3\times 13+15)^{\circ} = 54^\circ[/tex]
Therefore, the answer is [tex]\bold{\angle B = 54^\circ}[/tex]
The tables show information about the scale ratios of two different maps. 2 tables. The first table is a 2-column table with 2 rows titled Map of the United States. Column 1 is labeled Centimeters with entries 3, 12. Column 2 is labeled Miles with entries 50, 200. The second table is a 2-column table with 2 rows titled Map of Africa. Column 1 is labeled Centimeters with entries 2, 15. Column 2 is labeled miles with entries 40, 300. The ratio of centimeters to miles on the map of the United States is . The ratio of centimeters to miles on the map of Africa is . The ratio of centimeters to miles on the map of the United States is the ratio of centimeters to miles on the map of Africa.
The answers are in order 3/50,1/20, greater than.
Answer:
1.b 2.a 3.b
Step-by-step explanation:
Which pair of numbers has 7 as its least common multiple? Group of answer choices 1, 7 3, 4 7, 21 14, 28
Answer:
7, 14, 14,21, and 28
Step-by-step explanation:
Only 1, 7 is pair of numbers that has 7 as its least common multiple.
Given that,
Pairs ( 1, 7 ), ( 3, 4 ), ( 7, 21), ( 14, 28).
A pair or pairs to be determined that have 7 as its least common multiple.
In mathematics, it deals with numbers of operations according to the statements.
What is Lowest Common Multiple?In arithmetic, LCM is defined as the lowest common multiple of two integers X and Y, usually represented as by LCM X, Y, and is the smallest favorable integer that is dividable by both X and Y.
Since the Least common multiple of pair of numbers has 7, this is only possible for 1 * 7, because the LCM of 1 and7 is 7. So from given option 1, 7 is the required pair.
Thus, only 1, 7 is pair of numbers that has 7 as its least common multiple.
Learn more about arithmetic here:
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Solve for x. 2x + 2 = -8 X=???? Please help!?
x = - 5
Step-by-step explanation:2x + 2 = - 8
2x = - 8 - 2
2x = - 10
x = - 10 : 2
x = - 5
Answer:
x=-5
Step-by-step explanation:
1.) 2x+2=-8 start to isolate the variable by subtracting 2 to -8
2.) 2x=-10 divide both sides by 2
3.) x=-5
Hope this helped
solve for a 36a =9 please help asap
Answer:
a = 1/4
Step-by-step explanation:
Divide each side by 36:
36a = 9
a = 1/4
Answer:
a=1/4=0.25
Step-by-step explanation:
to get the value of a divide 36 by 9.
[tex]36a=9\\ \frac{36a}{36}=\frac{9}{36}\\ a=\frac{9}{36}\\ (simplify) \\ a=\frac{1}{4}=0.25[/tex]
How many inches is 2 1/2 miles
Answer:
2.5 mile inch 158400
Step-by-step explanation:
It's on google
158400
You can just ask google
Which function has a domain of x 25 and a range of y s3?
Answer:
Step-by-step explanation:
The function has a domain x ≥ 5.
This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.
Hence, (x - 5) ≥ 0
⇒ x ≥ 5
Now, for all x values that are greater than equal to 5 the value of will be negative.
So,
⇒
⇒ y ≤ 3
Therefore, the range of the function is y ≤ 3. (Answer)
Note: Thanks rani
please help asap
solve x^4+5x^2+4=0
Answer:
[tex]x=\pm i\text{ or }x=\pm2i[/tex]
Step-by-step explanation:
So we have the equation:
[tex]x^4+5x^2+4=0[/tex]
Let's let u be equal to x². So:
[tex]u^2+5u+4=0[/tex]
Factor:
[tex](u+1)(u+4)=0[/tex]
Zero Product Property:
[tex]u+1=0\text{ or } u+4=0[/tex]
Subtract:
[tex]u=-1\text{ or }u=-4[/tex]
Replace:
[tex]x^2=-1\text{ or }x^2=-4[/tex]
Take square root:
[tex]x=\pm\sqrt{-1}\text{ or }x=\pm\sqrt{-4[/tex]
Simplify:
[tex]x=\pm i\text{ or }x=\pm2i[/tex]
Given: 2x + 3(x - 2) = 24
Prove: x = 6
Statements and Reasons?
Answer:
x=6
Step-by-step explanation:
first we'll use distributive property: we will distribute and multiply 3 by x and - 2
2x + 3x -6 = 24
then we'll add like terms which are 2x and 3x , 24 and 6 the sign of 6 will change from negative to positive:
2x + 3x =24 + 6
5x = 30
after that we will divide both sides by 5 in order to get x
5x/5 = 30/ 5
x = 6
Complete the sequence,
13, 14, 27, 41,
Answer:
68
Step-by-step explanation:
We can see that the nth term would be the sum of the previous two terms. Continuing this would result in 68.
How to Multiply six and the reciprocal of the quotient of a number and seven?
Answer:
Let N be the unknown number
The we have 6 x reciprocal of N/7 which is 6 x 7/N which is 42/N
HOPE THIS HELPS YOU
Multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.
Where M is the number.
Given,
Multiply six and the reciprocal of the quotient of a number and seven.
We need to find this expression.
What does quotient mean?
It means to divide.
The quotient of a and b:
= a ÷ b.
= a / b
Find the expression.
Let the number be M.
Now,
The quotient of a number and 7 can be written as:
= M ÷ 7
= M / 7
Reciprocal of the quotient of a number and seven.
= 1 / (M/7)
= 7 / M
Now,
Multiply six and the reciprocal of the quotient of a number and seven.
It can be written as:
= 6 x 7 / M
= 42 / M
Thus multiply six and the reciprocal of the quotient of a number and seven can be written as 42/M.
Learn more about the quotient of a number and its reciprocal here:
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find the mean of first five prime
numbers
Answer:
5.6
Step-by-step explanation:
(2+3+5+7+11)/5
=5.6
ray BD bisects ∠ABC m∠ABD if m∠ABC = 5/2 y and m∠DBC = (y+5)degrees
Step-by-step explanation:
BD bisects ∠ABC. Therefore:
m∠DBC = ½ m∠ABC
y + 5 = ½ (5/2 y)
y + 5 = 5/4 y
4y + 20 = 5y
y = 20
Therefore, m∠ABC = 50°, and m∠ABD = 25°.
An online music club sells compact discs for $13.95 each plus a single $1.95 shipping charge. If Maria's total bill was $85.65, how many compact discs did Maria purchase? Hint: write an equation for the situation, then solve it. Please put only the number of CD's purchased in the space provided.
Answer:
6 CD's
Step-by-step explanation:
$85.65 - $1.9 = 5 $84.15
$84.15 ÷ $13.95 = 6
help pls. Find the value of x.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 15 °}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{x + 30 ° + 100 ° + 3x - 10 ° = 180 °}[/tex]
( Sum of angle in straight line )
Collect like terms
⇒[tex] \sf{4x + 30 ° + 100 ° - 10 ° = 180 °}[/tex]
Calculate the sum or difference
⇒[tex] \sf{4x + 120 ° = 180 °} [/tex]
Move 120 to right hand side hand change it's sign
⇒[tex] \sf{4x = 180 ° - 120 °}[/tex]
Subtract 120 from 180
⇒[tex] \sf{4x = 60 ° }[/tex]
Divide both sides of the equation by 4
⇒[tex] \sf{ \frac{4x}{4} = \frac{60}{4} }[/tex]
Calculate
⇒[tex] \sf{x = 15 °}[/tex]
Hope I helped!
Best regards!!
Pls help!! I need the answer immediately
Answer:
i). x³ + 9x² + yz - 15
ii). -21m³np - 8p⁵q + mnp + 4mn + 100
Step-by-step explanation:
Question (38)
i). Two expressions are -5x² - 4yz + 15 and x³+ 4x²- 3yz
By subtracting expression (1) from expression (2) we can the expression by addition which we can get expression (1).
(x³+ 4x²- 3yz) - (-5x² - 4yz + 15) = x³ + 4x² - 3yz + 5x² + 4yz - 15
= x³ + 9x² + yz - 15
ii). -15m³np + 2p⁵q - 6m³pn + mnp + 4mn - 10qp⁵+ 100
= (-15m³np - 6m³np) + (2p⁵q - 10qp⁵) + mnp + 4mn + 100
= -21m³np - 8p⁵q + mnp + 4mn + 100
Exercises 5-8 refer to a bag filled with 3 yellow balls, 4 green balls, 2 blue balls, and 1 orange ball.
S.What is the probability of picking a red ball out of the bag?
6. What is the probability of picking a blue or yellow ball?
7. What is the probability of picking an orange ball?
8.What is the probability of picking a green ball?
9. What is the probability of picking a green or orange ball?
Answer:
s. 0/10
6. 5/0
7. 1/10
8. 4/10
9. 5/10
Find the next three terms in the pattern 4, 2,0,-2,-4, ... and complete the description of the pattern.
(select)
to get to the next term. The next three terms are
Answer:
[See Below]
Step-by-step explanation:
✦ First you have to determine the rule:
✧ The rule is -2
○ 4 - 2 = 2
○ 2 - 2 = 0
○ 0 - 2 = -2
○ -2 - 2 = -4
○ And the rule would go on and on...
✦ And now that you know the rule, you have to determine the next terms:
✧ -6
✧ -8
✧ -10
~Hope this helps Mate. If you need anything feel free to message me.
please help i need this answered as soon as possible!!! -Use ΔDEF, shown below, to answer the question that follows:
Answer:
X= 139
Step-by-step explanation:
the square on the E means its a right side so that would be 90 degrees. All triangles add up to 180. F would be 41 degrees. that mean X is 139 i think.
Answer:
36.083
Step-by-step explanation:
SOHCAHTOA
Cosine is adjacent over hypotenuse, so the
cos(49) = the adjacent side (x) || over the hypotenuse (55)
cos(49) = x/55
55cos(49) = x
x = 36.083
Find the distance between two numbers on the number line -3 1/4, -6 1/2
Answer:
[tex]3\frac{1}{4}[/tex]
Step-by-step explanation:
Given the two -3 1/4 and -6 1/2 numbers on the line, the distance between he numbers can be gotten by simply taking the differences between both values as shown;
[tex]= -3\frac{1}{4} -(-6\frac{1}{2} )\\ \\= -\frac{13}{4} + \frac{13}{2}\\ \\= \frac{-13+26}{4}\\ \\= \frac{13}{4} \\\\= 3\frac{1}{4}[/tex]
Hence the distance between two numbers on the number line is [tex]3\frac{1}{4}[/tex]
Can somebody help me with this ?? :)
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1220
1420
1620
1820
2020
2220
2420
According to the table, what is the monthly pay for a worker with 0 hours of
training?
Answer:
$1,020
Step-by-step explanation:
There is a $200 difference in the every monthly pay.
Because of this we know that the first month was an amount minus $200.
If we subtract 1220 and 200, you get the pay of 1020 for 0 hours.
You are making a banner in the shape of an isosceles triangle. The banner will have ribbon on the edge. You have 15 yards of ribbon. You want the legs of the banner to each be 5 feet shorter than twice the base. Remember that isosceles triangles have two legs of equal length. What is the length of the base and each leg?
Answer:
The length and base are 10/3 and 25/3 respectively
Step-by-step explanation:
Given:
Represent the sides with S and the base with B
Shape: Isosceles Triangle
[tex]S= B- 5[/tex]
[tex]Perimeter , P= 15[/tex]
Required
Determine the base and legs of the triangle;
The perimeter (P) of a triangle is calculated as thus;
[tex]P = S+ S + B[/tex]
[tex]P = 2S + B[/tex]
Substitute B- 5 for S
[tex]P = 2(B - 5) + B[/tex]
[tex]P = 2B - 10 +B[/tex]
Substitute 15 for P
[tex]15 = 2B - 10 + B[/tex]
Collect Like terms
[tex]2B + B = 15 + 10[/tex]
[tex]3B = 25[/tex]
Divide through by 3
[tex]B = \frac{25}{3}[/tex]
Recall that [tex]S= B- 5[/tex]
[tex]S = \frac{25}{3} - 5[/tex]
Take LCM
[tex]S = \frac{25 - 15}{3}[/tex]
[tex]S= \frac{10}{3}[/tex]
Hence, the length and base are 10/3 and 25/3 respectively
Which is the function represented by the table?
Answer:
f(x)= -2x + 1
Step-by-step explanation:
The function we will find is to be written in slope-intercept form, which is y=mx+b.
One way to find the answer would be by graphing the function, wich you can do on an online calculator or a sheet of paper.
Another way to get to our answer without even having to graph is by finding the y-intercept, or the b, of the function given in the table.
We can do this by looking at the 0 value of the table. The table tells us that the y-intercept is 1.
So, we have to look at our options and see which one has +1 for the y-intercept.
The option f(x)=-2x+1 is the answer
How to check your work: input the given x values into the chosen function, in this case f(x)= -2x + 1
So for example, you could check that this answer is the function by doing
f(-1) = -2(-1) + 1f(-1) = 2 + 1 f(-1) = 3Make sure to do this to all values.
Hope this helps!