The missing base for the expression x² = 100 is given by:
± x = 10.
How to find the missing base?The expression in this problem is given as follows:
x² = 100.
The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.
To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:
x = plus/minus square root of 100.
The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:
x = ± 10.
Plus/minus 10 because both of these statements are true:
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we have 5 multiple choice questions with four choices with two correct answers each. if we just randomly guess on each of the 5 questions, how many questions do you expect to choose correct answers? (no need to be integer for the number of questions)
The expectation of getting correct option out of total choice of 5 question.
What is probability?
Probability is the ratio of number of favorable outcomes to the total number of outcomes.It can not be more than 1.
According to given data:we have five question each of them has four choice, two out of them are correct.
Number of correct choice in one question = 2
Total number of choice in a question = 4
probability to get correct option of one question = 2/4 = 0.5.
Then the probability of 5 question = 5(0.5) = 2.5
Thus, the expectation of correct choice is 2.5.
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9500000000000000 in standard form
IF T² = 4π² (h² + k²)
hg
Express k² in terms of T, g and h
The value of the expression in the form of k² will be (T²/4π²)-h²).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is T² = 4π² (h² + k²). The expression for the value of k² will be calculated as,
T² = 4π² (h² + k²)
(h² + k²) = T² / 4π²
k² = (T² / 4π²) - h²
Therefore, the value of the expression in the form of k² will be (T²/4π²)-h²).
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cheyenne needs to cut a piece of paper so that she has exactly 1/3 of it. if the length of the paper is 11 inches, how long will be the piece that she cuts?
The lengths of the piece she should cut is = 3 2/3
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
1/3 of 11=1/3*11=11/3=3 2/3hence,The lengths of the piece she should cut is = 3 2/3
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Is it a, b, or c, and if A what goes in the box
Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.
Given equation,
[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]
For values (-∞,-7)
equation stands true
For values (-7,5)
equation stands false
For values (5,12)
equation stands true
For values (12,∞)
equation stands false
Hence, x ∈ (-∞,-7)∪(5,12).
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I will give 100 pts for anwser asap Determine which integer(s) from the set S:{−24, 2, 20, 35} will make the inequality five sixths m minus five is less than one half m plus 3 false.
S:{−24, 2}
S:{35}
S:{−24, 2, 20}
S:{20}
None of the values in the given set makes the inequality false.
Given that,
To check for the expression 5m/6 - 5 < m/2 + 3, whether the set of values S:{−24, 2, 20, 35} holds or not.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
given expression,
5m/6 - 5 < m/2 + 3
5m/6 - m/2 < 3 + 5
(5m - 6m)/6 < 8
-m < 48
m > -48
Thus, none of the values in the given set make the inequality false.
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The expressions 25x−(6x+12) and (25x−6x)+12 are
The expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.
In this question we have been given two expressions 25x−(6x+12) and (25x−6x)+12
We know that the associative property of addition.
For any real numbers a, b, c
a + (b + c) = (a + b) + c
Consider an expression,
25x − (6x + 12)
= (25x - 6x) + 12 ..........(Associative property)
Therefore, the expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.
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Find the least common denominator. Then express each fraction using the least common denominator. 3/4 and 5/6
I need a answer
Answer:
The least coomon denominator is 12, so
9/12 and 10/12
34°
56°
124°
146°
Some help would be nice
Answer:
146 degrees
Step-by-step explanation:
Sum of all triangle angles equal 180 degrees
We know 2
56 and 90 so we add them
90+56=146
Now we subtract to 180 to find the third angle of the triangle
180-146=34
To find x we gotta subtract 34 from 180 since it’s on a flat plane
180-34=146
angle x=146 degrees
hopes this helps please mark brainliest
What is wrong I need help
I don’t understand it
Answer:
Step 2 is incorrect
Step-by-step explanation:
Step 2 is where you are distributing out -5. Step 2 should be distribution rather than division property of equality.
The variable y has a proportional relationship with x as suggested by the graph. Use the graph to find the constant of proportionality.
Answer: THE ANSWER IS 26
I'll give 45 points and brainiest The coordinates of the vertices of trapezoid EFGH are E(−8, 8), F(−4, 12), G(−4, 0), and H(−8, 4). The coordinates of the vertices of trapezoid E′F′G′H′ are E′(−8, 6), F′(−5, 9), G′(−5, 0), and H′(−8, 3).
Which statement correctly describes the relationship between trapezoid EFGH and trapezoid E′F′G′H′?
Responses
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by translating it down 2 units and then reflecting it over the y-axis, which is a sequence of rigid motions.
trapezoid E F G H, is congruent to , trapezoid E prime F prime G prime H prime, because you can map , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime, by translating it down 2 units and then reflecting it over the , y, -axis, which is a sequence of rigid motions.
Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime, .
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by reflecting it across the x-axis and then translating it up 14 units, which is a sequence of rigid motions.
trapezoid E F G H is congruent to trapezoid E prime F prime G prime H prime because you can map trapezoid E F G H to trapezoid E prime F prime G prime H prime by reflecting it across the x -axis and then translating it up 14 units, which is a sequence of rigid motions.,
Trapezoid EFGH is congruent to trapezoid E′F′G′H′ because you can map trapezoid EFGH to trapezoid E′F′G′H′ by dilating it by a factor of 34 and then translating it 2 units left, which is a sequence of rigid motions.
For the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :
"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"
As given in the question,
Trapezoid EFGH with coordinates of vertices:
E(−8, 8), F(−4, 12), G(−4, 0), and H(−8, 4).
Trapezoid E'F'G'H' with coordinates of vertices:
E′(−8, 6), F′(−5, 9), G′(−5, 0), and H′(−8, 3).
First option is not correct as there is no translation.
Third, Fourth, and Fifth options are not correct as both the trapezoids are not congruent.
Only option second describe it correctly which is:
Both the trapezoid are not congruent as there is no sequence of rigid motion that maps EFGH to E'F'G'H'.
Therefore, for the given coordinates of the vertices of trapezoid EFGH and E'F'G'H' the following statement is true and explain the relationship correctly :
"Trapezoid EFGH is not congruent to trapezoid E′F′G′H′ because there is no sequence of rigid motions that maps trapezoid EFGH to trapezoid E′F′G′H′.
trapezoid E F G H, is not congruent to , trapezoid E prime F prime G prime H prime, because there is no sequence of rigid motions that maps , trapezoid E F G H, to , trapezoid E prime F prime G prime H prime,"
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The record for the most hot dogs eaten is 73 hot dogs in 10 minutes. one hot dog and bun has a mass of 85 g. how many kg of hot dogs did the record-holder eat?
The record-holder ate 6.205 kilograms of hot dogs.
How do you prove that?We are given that 73/10 hotdogs per minute is the record for the most hot dogs eaten and one hot dog and bun has a mass of 85 grams. Also, one kilogram is equal to 1,000 grams. Solving this problem would involve converting units.
In order to find out how many kilograms of hot dogs the record holder ate, we first need to convert 85 grams to kilograms. Since a kilogram is equal to 1,000 grams, 85 grams = 85 / 1,000 = 0.085 kilograms.
Then, we multiply 0.085 by 73 to get 6.205. We can conclude that the record-holder ate 6.205 kilograms of hot dogs.
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Ray buys a computer game for $38. He uses a coupon to receive 15% off the price of the game. After the coupon is deducted, he must pay 6% sales tax. What is the tota cost of the game, to the nearest cent? A $28.00 C. $34.58 D. $36.56
Which of the following is a line that is parallel to the line defined by the equation 4x+7y=49−2x+4y?
a
3y+40=3x+10
b
y=20x+15
c
4y=10x+15
d
y=4x−2
e
2y+x=40−3x
A line parallel to the line 4x + 7y = 49 - 2x + 4y must have a slope of - 2.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given a line that is 4x + 7y = 49 - 2x + 4y.
7y - 4y = - 2x - 4x + 49.
3y = - 6x + 49.
y = - 2x + 49/3.
Now, lines parallel to each other have the same slope.
Now if we simply the given options none of the lines have a slope of - 2 so none of the given lines are parallel to the line 4x + 7y = 49 - 2x + 4y.
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the sum of two nonzero real numbers is 44 times their product. what is the sum of the reciprocals of the two numbers?
The sum of the reciprocal of the two numbers is 44.
Let a and b be the two number
It is given that the sum of the number is equal to 44 times their product.
So from this, we get an equation:
a + b = 44 ab -------(1)
Now we have to find the sum of the reciprocal of the two numbers.
1/a + 1/b = b + a/ ab
= a + b / ab -------(2)
As from equation (1) we have
a + b/ ab = 44
Now put this value in equation (2) we get
1/a + 1/ b = 44
Therefore the sum of the reciprocal of the two numbers is 44.
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In the triangle below, with right angle G, suppose that m/F= (3x-14)° and mZH=(5x-16)°.
Find the degree measure of each angle in the triangle.
The degree measure of each angle in the triangle is
∠H = 59°
∠F = 39°
Angle sum property of triangle says that sum of all the triangle is always equal to 180°
∠G is given to us as 90°
So by applying the property we an say that
90 + (3x - 14) + (5x - 16) = 180
8x = 180 - 90 + 14 + 16
8x = 120
x = 15
∠H = 5x - 16
∠H = 5*15 - 16
∠H = 75 - 16
∠H = 59°
∠F = 3x - 14
∠F = 3*15 - 14
∠F = 45 - 14
∠F = 39°
Therefore ∠H = 59° and ∠F = 39°
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.
How to derive a quadratic equation by factorizationIn this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:
y = (x - r₁) · (x - r₂)
y = (x + 2) · (x - 2)
Second, expand the expression derived in the previous step by algebra properties:
y = (x + 2) · x - (x + 2) · 2
y = x² + 2 · x - 2 · x - 4
y = x² - 4
Third, write the resulting expression:
y = x² - 4
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The area, Acm², of a patch of mould is measured daily. The area, n days after the measurements started, is given by the formula A = Asub0b^n". When n = 2, A = 1.8 and when n = 3, A = 2.4. Find the value of b.
Answer:
b = (4/3), with rounding
Step-by-step explanation:
Area = A, in cm^2
n = days
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
------------------
Data:
n = 2, A = 1.8
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
n = 3, A = 2.4
2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]
Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex]. Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
b(1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex])
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] . We can eliminate this term in the above relationship by substituting 2.4:
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
1.8b = 2.4
b = 1.3333
or (4/3)
Check:
Does the value of (4/3) for b work for both data points? To check this, we do need to assume an initial starting area. Lets assume the starting area, [tex]A_{0}[/tex] = 1.
n = 2, A = 1.8, b = (4/3)
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = 1*[tex](4/3)^{n}[/tex]
1.8 = 1.78 Close enough?
n = 3, A = 2.4, b = (4/3)
2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]
2.4 = 1*[tex](4/3)^{3}[/tex]
2.4 = 2.37 Close enough?
XY
Y
a. (1, 1) and (7,5)
The slope of the line that passes through (1, 1) and (7, 5) is 2/3
How to calculate the slope of the line?From the question, the points are given as
a. (1, 1) and (7,5)
Rewrite the above points properly
So, we have the following ordered pairs
(1, 1) and (7,5)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (1, 1) and (7,5)
Substitute the known values in the above equation
So, we have the following equation
Slope = (5 - 1)/(7 - 1)
Evaluate
Slope = 2/3
Hence, the slope of the line is 2/3
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Possible question
Find the slope of the line that passes through a. (1, 1) and (7,5)
i count in equal steps my first number is -2 my fifth number is 26 whats my third number
The required third number will be 12 when numbers are in the A.P.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given data as
first number = - 2
fifth number = 26
Assume that the given numbers are in the A.P.
The formula to find the general term of an arithmetic sequence is,
Tₙ = a₁ + (n-1)d ...(i)
Substitute the value of n = 5 and a₁ = -2 in the above formula
T₅ = a₁ + (5-1)d
26 = -2 + 4d
4d = 28
d = 7
For finding the third term (number):
T₃ = -2 + (3-1)7
T₃ = -2 + (2)7
T₃ = -2 + 14
T₃ = 12
Therefore, the required third number will be 12 when numbers are in the A.P.
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what is the slope that passes through (-10,17) (-9,17)
Answer: m=0
Step-by-step explanation: (-10,17) & (-9, 17) are 2 points away from each other on the x-axis, there is no difference in y. Therefore the answer is zero.
mary invests £12000 in a savings account.
the account pays 1.5% compound intrest per year.
y is inversely proportional to x.
when y=7, x=9
a) work out an equation connecting y and x.
b) work out the value of y when x=21.
pls show step by step working out.
Using a proportional relationship, it is found that:
a) The equation is: y = 63/x.
b) When x = 21, the numeric value is of y = 3.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.
When the two variables are inversely proportional, we have a inverse proportional relationship, in which the output variable y is obtained by the division of k by the input variable x, as follows:
y = k/x.
For this function, when y = 7, x = 9, hence the constant is obtained as follows:
7 = k/9
k = 9 x 7
k = 63.
Hence the equation is:
y = 63/x.
The numeric value of the function when x = 21 is given as follows:
y = 63/21 = 3.
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What is an equation of the line that passes through the point (2,-2)and is perpendicular to the line 5x-2y=4
Answer:
y=-0.4x - 1.2
given the measurements; 6 cm, 10 cm, 17m. Check if three measurements can form a angle
stackoverflow the sum of three numbers is $96$. the first number is $6$ times the third number, and the third number is $40$ less than the second number. what is the absolute value of the difference between the first and second numbers?
The absolute value of the difference between the first and second numbers is 5.
Here we have to find the difference between the first and the second numbers.
There are three statements.
Let a, b, and c be the first, second, and third numbers respectively.
The first statement is that the sum of the three number is 96.
The second statement is that the first number is 6 times the third number.
a = 6c
The third statement is that the third number is 40 less than the second number.
c = b - 40
b = c + 40
The sum of the three numbers is 96.
a + b + c = 96
6c + c + 40 + c = 96
8c = 96 - 40
8c = 56
c = 7
As a = 6c and b = c + 40
Now put the value of c as 7 we have:
a = 6 × 7
= 42
b = 7 + 40
= 47
Difference between the first and second numbers= 47 - 42
= 5
Therefore the difference is 5.
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There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
b. Find the number of marbles that are not blue
Step-by-step explanation:
There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.
a. Find the percentage of marbles that are not blue.
100% - 40% = 60%
b. Find the number of marbles that are not blue.
60% = 0.6
0.6 * 185 = 111 marbles
Help please I will give brainliest this is due in an hour!!!
Answer:
yes for helena: not sure for edwin
Step-by-step explanation:
for helena, it would be a 270 cc rotation and then scale
for edwin, again im not sure, but it could be a refection and then scale
an iq test is designed to have scores that have a standard deviation of . a simple random sample of students at a large university will be given the test in order to construct a confidence interval for the mean iq of all students at the university. how many students must be tested so that the margin of error will be equal to points?
The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.
When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.
From standard normal tables,
P( -2.326 < Z < 2.326) = 0.98 here
The sample size required here is computed as:
n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12
Therefore, the required sample size, in this case, is 71.
To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.
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COMPLETE QUESTION:
An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)
the local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $60, balcony tickets are $42, and mezzanine tickets are $40. one particular night, sales totaled $107,588. there were 152 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 432 more than 3 times the number of mezzanine tickets sold. how many of each type of ticket were sold?
z = 134 (number of mezzanine units sold)
b = 834 (number of balconies sold)
m = 1120 (number of main floor sales)
Equations:
60m + 42b + 40z = 107,588
m = b + z + 152
b = 3z + 432
Substitute for "b" to get m = 4z + 584
------
Substitute for m and b and solve for "z"::
60(4z+584) + 42(3z+432) + 40z = 107588
240z + 35040 + 126z + 18144 + 40z = 107588
406z + 53184 = 107588
406z = 54404
z = 134 (# of mezzanine sold)
Solve for "b" and for "m" using z = 134
b = 3(134) + 432
b = 834 (# of balcony sold)
m = 834 + 134 + 152
m = 1120 (# of main floor sold)
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