Answers
1. 1. Vocabulary What does the exponent in the expression [tex]5^{6}[/tex] tell you?
Answer: it means that [tex]5[/tex] is multiplied by itself [tex]6[/tex] times: [tex]5^{6} =5*5*5*5*5*5=15625[/tex]
1. 2. [tex]4*4=4^{2}=16[/tex]
The power is [tex]2[/tex] or square, notice how the geometric model is made out of dots forming a flat square.
1. 3. [tex]2*2*2*2=2^{3} =8[/tex]
The power is [tex]3[/tex] or cube, notice how the geometric model is a cube.
1. 4. [tex]9*9=9^{2}=81[/tex]
The power is [tex]2[/tex] or square, notice how the geometric model is a flat square.
2. 5. [tex]7^{2} =49[/tex]
2. 6. [tex](-2)^{4} = -2*-2*-2*-2=4*4=16[/tex]
2. 7. [tex](-2)^{5} =16*-2=-32[/tex]
2. 8. [tex]-(\frac{1}{2})^{4}=-(\frac{1^{4} }{2^{4}})=-(\frac{1}{16})=-\frac{1}{6}[/tex]
3. 9. [tex]81=9^{x}, \frac{81}{9} = 9,9*9=9^{2}[/tex]
3. 10. [tex]100000=10^{x} , \frac{100000}{10} =10000, \frac{10000}{10}=1000, \frac{1000}{10}=100, \frac{100}{10}=10,[/tex]
[tex]10*10*10*10*10=10^{5}[/tex]
3. 11. [tex]-64 = -4^{x}, \frac{-64}{-4}=16, \frac{16}{-4}=-4, -4*-4*-4=-4^{3}[/tex]
3. 12. [tex]10 = 10^{x}, \frac{10}{10}=1, 10*1=10 =10^{1}[/tex]
3. 13. [tex]81 =3^{x}, \frac{81}{3}= 27,\frac{27}{3}=9, \frac{9}{3}=3, 3*3*3*3=3^{4}[/tex]
3. 14. [tex]36=-6^{x} , \frac{36}{-6}= -6, -6*-6=(-6)^{2}[/tex]
4. 15. Technology First week => [tex]3[/tex] hits, every week => the number of hits triples, means [tex]3^{3}[/tex], 5th week => hits every week * 5 = [tex]3^{3}*5=27*5=135[/tex] hits.
I apologize if there's any misspelling or wrong answer.
Related Questions
please help i need this answered as soon as possible!!! -Use ΔDEF, shown below, to answer the question that follows:
Answers
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
Four more than twice a number is –10.
Answers
Four more than twice a number is –10 is the same as 2n + 4 = 10
Steps to solve:
2n + 4 = 10
~Subtract 4 to both sides
2n = 6
~Divide 2 to both sides
n = 3
Best of Luck!
Pls help!! I need the answer immediately
Answers
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
Which function has a domain of x 25 and a range of y s3?
Answers
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
ray BD bisects ∠ABC m∠ABD if m∠ABC = 5/2 y and m∠DBC = (y+5)degrees
Answers
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°.
i need help with the top one
Answers
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)
Answers
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.
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.
Answers
How to Multiply six and the reciprocal of the quotient of a number and seven?
Answers
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:
https://brainly.com/question/673545
#SPJ2
Which of the following is closest to the square root of 4000 A) 20 B) 60 C) 400 D) 2000
Answers
Answer:A
Step-by-step explanation:
Sqrt(4000)= 20
Which is the function represented by the table?
Answers
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!
Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how much money would you owe in taxes at the end of the year?
Answers
Answer: You would owe $1,263 and 75c! Have a fantastic day!
Can somebody help me with this ?? :)
Answers
Solve for x. 2x + 2 = -8 X=???? Please help!?
Answers
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
Complete the sequence,
13, 14, 27, 41,
Answers
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.
Find the cosine ratio of angle 0
Answers
Answer: cos(0) = 1
hope this helped
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?
Answers
Answer:
s. 0/10
6. 5/0
7. 1/10
8. 4/10
9. 5/10
please someone help me to prove this...
Answers
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]
Given: 2x + 3(x - 2) = 24
Prove: x = 6
Statements and Reasons?
Answers
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
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.
Answers
The answers are in order 3/50,1/20, greater than.
Answer:
1.b 2.a 3.b
Step-by-step explanation:
What two rational expressions sum to 2x+3/x^2-5x+4
Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.
Answers
Answer:
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Step-by-step explanation:
Given the rational expression: [tex] \frac{2x + 3}{x^2 - 5x + 4} [/tex], to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
[tex] x^2 - 5x + 4 [/tex]
[tex] x^2 - 4x - x + 4 [/tex]
[tex] (x^2 - 4x) - (x + 4) [/tex]
[tex] x(x - 4) - 1(x - 4) [/tex]
[tex] (x- 1)(x - 4) [/tex]
Thus, we now have: [tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex]
Step 2: Apply the concept of Partial Fraction
Let,
[tex] \frac{2x + 3}{(x- 1)(x - 4)} [/tex] = [tex] \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
Multiply both sides by (x - 1)(x - 4)
[tex] \frac{2x + 3}{(x- 1)(x - 4)} * (x - 1)(x - 4) [/tex] = [tex] (\frac{A}{x- 1} + \frac{B}{x - 4}) * (x - 1)(x - 4) [/tex]
[tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
Step 3:
Substituting x = 4 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(4) + 3 = A(4 - 4) + B(4 - 1) [/tex]
[tex] 8 + 3 = A(0) + B(3) [/tex]
[tex] 11 = 3B [/tex]
[tex] \frac{11}{3} = B [/tex]
[tex] B = \frac{11}{3} [/tex]
Substituting x = 1 in [tex] 2x + 3 = A(x - 4) + B(x - 1) [/tex]
[tex] 2(1) + 3 = A(1 - 4) + B(1 - 1) [/tex]
[tex] 2 + 3 = A(-3) + B(0) [/tex]
[tex] 5 = -3A [/tex]
[tex] \frac{5}{-3} = \frac{-3A}{-3} [/tex]
[tex] A = -\frac{5}{3} [/tex]
Step 4: Plug in the values of A and B into the original equation in step 2
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{A}{x- 1} + \frac{B}{x - 4} [/tex]
[tex] \frac{2x + 3}{(x- 1)(x - 4)} = \frac{-5}{3(x- 1)} + \frac{11}{3(x - 4)} [/tex]
Answer:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2
Step-by-step explanation:
find the mean of first five prime
numbers
Answers
Answer:
5.6
Step-by-step explanation:
(2+3+5+7+11)/5
=5.6
help pls. Find the value of x.
Answers
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!!
Explanation:
(x + 30) + 100 + (3x - 10) = 180 (straight angle)
x + 30 + 100 + 3x - 10 = 180
4x + 120 = 180
4x = 180 - 120
4x = 60
x = 60/4
x = 15 degree
Therefore, x = 15 degree
How many inches is 2 1/2 miles
Answers
Answer:
2.5 mile inch 158400
Step-by-step explanation:
It's on google
158400
You can just ask google
please help asap
solve x^4+5x^2+4=0
Answers
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]
∠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.
Answers
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]
Which pair of numbers has 7 as its least common multiple? Group of answer choices 1, 7 3, 4 7, 21 14, 28
Answers
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:
brainly.com/question/14753192
#SPJ2
solve for a 36a =9 please help asap
Answers
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]
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?
Answers
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.
There is a £200 difference between every hour and pay
Find the distance between two numbers on the number line -3 1/4, -6 1/2
Answers
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]