When you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is: 2. irrational number.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegersWhat is an irrational number?An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.
In conclusion, when you take the square root of 11, the result is neither a terminating nor a repeating decimal. Therefore, it is an irrational number.
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x=20
(Type a whole number.)
(x+21)° =
(Type a whole number.)
The whole number for the value (x + 21) is 41.
what is a whole number ?All integers starting from 0 are called whole numbers. The opposite of their corresponding positive numbers, the negative numbers are additive. The blackboard bold math Z or boldface Z is a common way to represent the set of integers in mathematical terminology.
given,
x = 20
then by putting the value of x = 20 in
(x + 21)° we get,
= (20 + 21)°
= 41°
Hence, the whole number of (x + 21) is 41
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Selena is making cookies. to make one dozen cookies, she needs 1/3 cup of brown sugar. how many cups of brown sugar does selena need to make 2 1/2 dozen cookies?
Answer:
5/6 cup
Step-by-step explanation:
[tex] \frac{1}{3} \times 2 \frac{1}{2} = \frac{1}{3} \times \frac{5}{2} = \frac{5}{6} [/tex]
Multiply if possible. Then simplify. ∛9 .∛3
The answer is = 3
The phrase simplifies the way to make something less challenging to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as easy as possible. We do this by dividing the numerator and the denominator by using the most important number which could divide into both numbers precisely.
Cross-cancellation is a simplification that may be executed earlier than. that is wonderful because simplifying earlier than the method while you do multiply, you'll have smaller numbers, and smaller numbers are easier to paint with.
Simplifying a rectangular root just means factoring out any best squares from the radicand, shifting them to the left of the unconventional image, and leaving the opposite factor within the radical image. If the variety is an ideal square, then the novel signal will disappear when you write down its root.
[tex]\sqrt[n]{a}[/tex][tex]\sqrt[n]{b}[/tex]=[tex]\sqrt[n]{ab}[/tex] , a[tex]\geq[/tex]0, b[tex]\geq[/tex]0
[tex]\sqrt[3]{9}[/tex][tex]\sqrt[3]{3}[/tex] = [tex]\sqrt[3]{9.3}[/tex]
[tex]\sqrt[3]{9.3}[/tex]
multiply the number 9.3 = 27
[tex]\sqrt[3]{27}[/tex]
[tex]\sqrt[3]{27}[/tex] =3
=3
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Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
2 x+y=16
4 x-y=1
The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: 2x + y = 16 and 4x - y = 1
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take the expression, 2x + y = 16
Applying log on both sides, we get,
log (2x + y) = log (16)
log (2x + y) = log (2⁴)
log (2x + y) = 4 log (2)
To Check Results,
Taking exponential on both sides,
e^[log (2x + y)] = e^(4 log 2)
2x + y = e^(log 2⁴)
2x + y = 2⁴
2x + y = 16
Thus, the answer is verified.
Take expression, 4x - y = 1
Applying log on both sides, we get,
log (4x - y) = log 1
log (4x - y) = 0
To Check Results,
Taking exponential on both sides,
e^[log (4x - y)] = e^0
4x - y = 1
Thus, the answer is verified.
Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
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∠A and \angle B∠B are supplementary angles. If m\angle A=(3x-10)^{\circ}∠A=(3x−10)
∘
and m\angle B=(8x-19)^{\circ}∠B=(8x−19)
∘
, then find the measure of \angle A∠A.
Applying the definition of supplementary angles, the measure of angle A is: 47°
What is the Definition of Supplementary Angles?The definition of supplementary angles states that two angles are referred to as supplementary angles if they give a sum of 180 degrees when added together.
Given that angle A and angle B are supplementary angles, therefore, based on the definition of supplementary angles, measure of angle A + measure of angle B = 180 degrees.
Measure of angle A = 3x - 10
Measure of angle B = 8x - 19
Substitute
3x - 10 + 8x - 19 = 180
Combine like terms
11x - 29 = 180
11x = 180 + 29
11x = 209
11x/11 = 209/11
x = 19
Measure of angle A = 3x - 10
Plug in the value of x
Measure of angle A = 3(19) - 10
Measure of angle A = 57 - 10
Measure of angle A = 47°
Thus, applying the definition of supplementary angles, the measure of angle A is: 47°
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Answer:Measure of angle A = 3x - 10
Measure of angle B = 8x - 19
Substitute
3x - 10 + 8x - 19 = 180
Combine like terms
11x - 29 = 180
11x = 180 + 29
11x = 209
11x/11 = 209/11
x = 19
Measure of angle A = 3x - 10
Plug in the value of x
Measure of angle A = 3(19) - 10
Measure of angle A = 57 - 10
Measure of angle A = 47°
Thus, applying the definition of supplementary angles, the measure of angle A is: 47°
Step-by-step explanation:
Need the answer for the function as stated in the photo
The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
Over the interval [tex]3\le x\le5[/tex], we have
[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]
In the diagram to the left, ABC and DCB are right angles. Which of the following is closest to the length of segment DE?
A.) 4.5
B.) 5.6
C.) 38.3
D.) 42.9
I think it is C, but am I correct?
The perimeter of a rectangle is 108 meters. Find the length and width if the length is an integer and the width is 4 times the next consecutive integer.
The length of the rectangle is 45 yard and the width of the rectangle is 9 yard.
What is the perimeter of a rectangle?WE have Given that the length of a rectangle is 5 times its width, and the perimeter is 108 yd.
Let the width of rectangle be 'x' yard and the length of the rectangle is '5x' yd . also the length is five times the width.
we know that,
The Perimeter of the rectangle = 2(length + width)
The perimeter of rectangle is 108 yd.
Therefore the perimeter = 2( 5x + x )
108 = 2( 6x )
108 = 12x
108/12 = x
x = 9
Therefore, the width of given rectangle is 9 yard, and
The length of the rectangle is 5x = 5 * 9 = 45 yd.
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Find the average rate of change of g(2) = -4 + 4 between the points (-3,16) and (4,-12)
The average rate of change of the function between the points is -4/7
What are average rates of change?The constant average rates of change of a function is also regarded as the slope or the gradient of the function
How to determine the average rates of change?Here, we have the points to be
(-3, 16) and (4, 12)
The average rates of change between these points is calculated as
Average rate of change = [f(b) - f(a)]/[b - a]
So, we have
Average rate of change = [12 - 16]/[4 + 3]
Evaluate the sum and the difference
So, we have
Average rate of change = -4/7
Hence, the average rate of change between the points is -4/7
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Aisha buys 2 packets of bread rolls costing £1.20 for each packet 1 bottle of ketchup costing £2.10 3 packets of biscuits Aisha pays with a £10 note. She gets 70p change. Work out the cost of one packet of biscuits. You must show how you get your answer. Optional working Answer: £|
The cost of one packet of biscuit is £1.60.
What is the cost of one packet of biscuit?The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.
Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup
Total cost of bread rolls = cost per packet x number of packets bought
2 x £1.20 = £2.40
Total cost of ketchup = cost of one bottle x number of bottles bought
1 x £2.10 = £2.10
Total cost of biscuits = cost of one packet x number of packets bought
3 x b = 3b
Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b
Total amount paid by Aisha = note given - change received
£10 - 70p
£10 - £0.70 = £9.30
Total amount paid by Aisha = total cost
£9.30 = £4.50 + 3b
£9.30 - £4.50 = 3b
£4.80 = 3b
b = £4.80 / 3
b = £1.60
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Four stores are having a sale on cans of Sprite. The sale prices are listed below:
Shop A: 6 cans for $5.10
Shop B: 6 cans for $5.70
Shop D: 12 cans for $10.80
Shop C: 12 cans for $9.60
Which store has the best buy?
Answer:
Shop C
Step-by-step explanation:
Without any calculations, you can eliminate stores B and D.
Shop A: $5.10/6 = $0.85/can
Shop C: $9.60/12 = $0.80/can
Answer:
It would be B
Step-by-step explanation:
Because A is 1.17 per can
B is 1.05 per can
D is 1.11 per can
and C is 1.25 per can
Show that the following equation is true for all values of a and b .
[(a-b)+1]⁵=a⁵ - 5a⁴ (b-1) + 10a³ (b-1)² - 10a² (b-1)³ + 5a(b-1)⁵- (b-1)⁵
8272936388272o274o4i49484i484748474
Step-by-step explanation:
2-2=Fish
Which expression represents the model?
9*1/6
Step-by-step explanation:
1= 6/6 and there are 9 boxes so multiply 9*1/6
pls pls help whoever gets it right gets a crown
Answer:
x = -5
Step-by-step explanation:
[tex]2x + 32 + x = 17[/tex]
[tex]3x + 32 = 17[/tex]
[tex]3x = - 15[/tex]
[tex]x = - 5[/tex]
please help ASAP ggggggggggggggggggggggggggggggggggggggggg
Answer:
237500000000
Step-by-step explanation:
1.14 × [tex]10^{6}[/tex] = 1140000
4.8 × [tex]10^{-6}[/tex] = 0.000005
1140000 ÷ 0.000005 = 237500000000
Find the inverse function for:
f(x) = 2x^3 - 3
Answer:
f−1(x)=3√4(x+3)/2 :)
Are ∠2 and ∠5 vertical angles? Explain your reasoning.
Answer:
no
Step-by-step explanation
an example of vertical angles would be 6 and 8
pls give brainliest :)
factor the following
the equation is f(x) = x^3+27
The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.
How to factor a cubic equation
In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:
f(x) = x³ + 27
f(x) = (x + 3) · (x² - 3 · x + 9)
f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)
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plss help me am paying 100 points !!!!!!!!! At an amusement park there are 2 rides. the lightning bolt starts at a elevation of 15ft. from the platform and speeds the passengers to an elevation of 327 ft. The highest loop on the twirl mater is 295 ft and the lowest tunnel goes 21 ft underground. which ride ha the greatest elevation and how much is the change in elevation?
a) Lightning bolt : 312 ft
b) Lightning bolt : 327
C) Twirl Master : 274
d) Twirl Master : 316
Answer:
The correct answer is B - 327 ft.
Convert 32 yards to inches
Answer:
1152
Step-by-step explanation:
32 * 36 lol
every yard is 36 inches
For this performance assessment we are going to return to the fact that the sum of the three interior
angles of a triangle is 180 *. Your task will be to demonstrate that we can know this is true by
making an argument based on previously proved statements and logical ways of reasoning. In fact,
you are going to have an opportunity to prove this statement in two different ways.
The proof is shown below:
What is Angle Sum Property?Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Given:
CB || HE
Now using the property of parallel lines.
So,
<HAC = <ACB (alternate interior angles)
<EAB= <ABC (alternate interior angles)
Now, HAE is a straight line then
<HAC + <CAB + <EAB = 180 ( linear pair)
<ACB + <CAB + <ABC = 180
Hence, the sum of the three interior angles of a triangle is 180.
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1.79 − 0.67 pls give me a answer
Answer: 1.12
Step-by-step explanation:
Answer:
1
1.12 is the exact value. 1 is an estimate.
Step-by-step explanation:
[tex]1.79 = 2\\0.67 = 1\\2 - 1 = 1\\\mathrm{(Estimate)~1 < 1.12~but > 0~and~1}\\\mathrm{Therefore,}\\= 1.12[/tex]
Solve the following expression when
t = 6 and d = 8
t+d divided by 8-6
Step-by-step explanation:
t+d = is equal to 8+6=14
14divided by 8-6 equal to 14 divided by 2
Answer is 7
What’s the slope of the line that passes through the points (10,6) and (6,6)
Answer:
Slope is 0.
Step-by-step explanation:
If you graph these points, it is a horizontal line. Horizontal lines have ZERO slope.
Using slope formula:
subtract y's and put that on top of a fraction. Subtract x's and put that on the bottom of the fraction.
6-6 goes in top and 10-6 goes on the bottom.
slope = m = 0/4 = 0
Slope is zero.
Need help do not understand this problem at all
The function is f (x) = 3/4 x - 1.
What is Linear equation?
A linear equation is an algebraic equation with slope m is defined as,
y = mx + b
Where, b is the y - intercept.
Given that;
Slope of function (m) = 3/4
f (-12) = -10
Now,
A linear equation with slope m is defined as,
f (x) = mx + b
Substitute m = 3/4,
f (x) = 3/4 x + b
Apply the condition f (-12) = -10 we get,
f (-12) = 3/4 * (-12) + b
- 10 = 3 * (-3) + b
- 10 = - 9 + b
b = - 10 + 9
b = - 1
Substitute value of m and b in linear equation we get;
The function is,
⇒ f (x) = 3/4 x - 1.
Hence, The function is f (x) = 3/4 x - 1.
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E is the midpoint of DF¯¯¯¯¯, DE=6x+1 and EF=7x−4. Find DE, EF, and DF.
31, 31, 56
37, 37, 74
31, 31, 62
22, 22, 44
Given that E is the midpoint of DF, the numerical values of DE, EF, and DF are 31, 31, and 62 respectively.
What are the numerical values of DE, EF, and DF?A midpoint is simply a point that divides a segment into two equal halves.Given the data in the question;E is the midpoint of D
Segment DE = 6x + 1Segment EF = 7x − 4Since E is the midpoint of DF, DE is equal to EF.
Segment DE = Segment EF
6x + 1 = 7x - 4
Solve for x:
6x - 7x = - 4 - 1
-x = -5x = 5
Now, the numerical values of DE, EF, and DF will be;
Segment DE = 6x + 1 = 6(5) + 1 = 30 + 1 = 31Segment EF = 7x − 4 = 7(5) - 4 = 35 - 4 = 31Segment DF = Segment DE + Segment EF = 31 + 31 = 62Learn more about midpoint here: https://brainly.com/question/28689713
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Megan is thinking of a number that is divisible by both 9and 7. What is the smallest possible number that Megan is thinking?
Answer:
Step-by-step explanation:
63
because 9x7=63
and 7x9=63
Do you think that the measures of central tendency (mean, median, mode) tell you the entire picture of a data set? Why or why not?
Answer:
Step-by-step explanation:
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most
Model with mathematics. Graph the fraction -3/8 on the number line
The number line (d) represents the location of the fraction -3/8 on the number line
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
How to model the fraction on a number line?The fraction is given as
-3/8
The above number is a negative number and it is greater than -1
This means that the location of the number line is between 0 and -1
To plot the number line, we make use of 8 intervals between 0 and -1 ( as represented by the number lines in the options)
The third point to the left of 0 represents -3/8
This means that the number line (d) represents the location of the fraction -3/8 on the number line
Hence, the number line (d) represents the location of the fraction -3/8 on the number line
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The area of a rectangle is 132.99 in2 and the length is 14.3 in. Find the width.
4.6 in.
12.9 in.
9.3 in.
18.7 in.
Answer:9.3
Step-by-step explanation:
Area= length times width
132.99= 14.3xw
Divide by 14.3
W= 9.3