Question: Which expression is undefined in the set of real numbers? A √-4 B 0/-4 с 0-4 D - 4x0
The expression that is undefined in the set of real numbers would be = 0/-4. That is option B.
What are real numbers?Real numbers are those numbers that can either be positive or negative and that are rational or irrational numbers which are different from complex numbers.
An expression can be said to be an undefined set of real numbers when it's numerator = 0 as seen in 0/-4.
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The aquarium has 10 more red fish than blue fish. 60 percent of the fish are red. How many blue fish are in the aquarium? Show your work. (10 points)
Answer:
There are 20 blue fish in the aquarium.
Step-by-step explanation:
If 60% of the fish are red than 40% are blue. That means that 20% fish is 10 fish. 20% = 10 fish. 40% = 20 fish.
In the figure below, S is the center of the circle. Suppose that JK = 19, LK = 3x+ 1, SN = 12, and SP= 12. Find the
for
In the figure, applying perpendicular bisector theorem for chords in a circle, the value of JN = 9 1/2
How to find JN in the figureThe perpendicular bisector theorem for chords in a circle states that if a radius of a circle is perpendicular to a chord, then it bisects the chord.
In other words, the radius divides the chord into two equal segments.
This theorem is a direct consequence of the properties of perpendicular lines and congruent triangles.
applying this to the figure
JN = JK/2
JN = 19/2
JN = 9 1/2
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the expression 2x+4 is equal to what for x = 3
Answer:10
Step-by-step explanation: You plug in 3 for x so you get the equation 2(3)+4
Which becomes 6+4
Which equals 10
Please answer: h^-1(x) for this question
All the solutions are,
g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }
h⁻¹ (x) = 5x - 13
⇒ (h⁻¹ о h ) (- 3) = 3
We have to given that,
Functions g and f are defined as,
g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)
And, h (x) = (x + 13) / 5
Now, We can simplify for inverse function as,
For inverse function of g,
g = {(- 7, 7), (- 6, - 7), (- 1, 6), (3, 9)
g⁻¹ = { (7, - 7), (- 7, - 6), (6, - 1), (9, 3) }
And, Inverse function of h is,
h (x) = (x + 13) / 5
y = (x + 13) / 5
Solve for x,
5y = x + 13
x = 5y - 13
h⁻¹ (x) = 5x - 13
So, We get;
⇒ (h⁻¹ о h ) (- 3)
⇒ (h⁻¹ (h (- 3))
⇒ (h⁻¹ (- 3 + 13)/5)
⇒ (h⁻¹ (2))
⇒ 5 (2) - 13
⇒ 10 - 13
⇒ - 3
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What value of x would make 5 Superscript x Baseline equals 625 true? Enter the answer in the box
The value of x that makes [tex]5^x = 625[/tex] true is x = 4.
To determine the value of x in the equation [tex]5^x = 625[/tex], we need to find the exponent that results in 625 when applied to the base 5.
Since 625 can be expressed as 5 raised to the power of 4 ([tex]5^4 = 625[/tex]), the value of x that satisfies the equation is 4.
When we substitute x = 4 into the equation, we get [tex]5^4 = 625[/tex], which is true.
Therefore, x = 4 is the solution to the equation, indicating that 5 raised to the power of 4 equals 625.
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True or False: If the discriminant is less than zero, then the graph will never cross the x-axis.
False
True
Answer:
True
Step-by-step explanation:
If the discriminant [tex]D=b^2-4ac < 0[/tex], then there are two complex roots
If the discriminant [tex]D=b^2-4ac > 0[/tex], then there are two real roots
If the discriminant [tex]D=b^2-4ac=0[/tex], then there is only one real root
Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer. Why is ΔABC ~ ΔDEC? Use the drop-down menus to explain your answer.
The triangles are similar because they are both right triangles, so they both have an angle that is equals to 90º. They both share a common vertex, <C. So they are similar by the Angle-Angle criterion.
What are similar triangles?Two triangles are defined as similar triangles when they share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.For this problem, they have two equal angle measures, the right angle and < C, hence the third angle also must be equal, and they are similar by the Angle-Angle criterion.
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PLEASE HELP There are 30 people waiting outside in line to enter the auditorium. There are 8 times as many people already inside the auditorium. How many people are inside the auditorium?
Answer: There are 240 people inside the auditorium.
Step-by-step explanation:
30 x 8 = 240
A girl is on a bridge 38.9 m high. She throws a rock straight down at -12.5 m/s. How long does it the rock to hit the ground
Answer:
3.14 seconds
Step-by-step explanation:
Fraction 1: the quantity x plus 1 over the quantity x squared minus 25; Fraction 2: the quantity x plus 5 over the quantity x squared plus 8 times x plus 7; Find Fraction 1 times by Fraction 2.
The product of the fractions is 1/[(x - 5)(x + 7)]
How to evaluate the product of the fractionsFrom the question, we have the following parameters that can be used in our computation:
Fraction 1 = (x + 1)/(x² - 25)
Also, we have
Fraction 2 = (x + 5)/(x² + 8x + 7)
So, we have
Product = (x + 1)/(x² - 25) * (x + 5)/(x² + 8x + 7)
When factored, we have
Product = (x + 1)/(x - 5)(x + 5) * (x + 5)/(x + 1)(x + 7)
Evaluate the products
Product = 1/(x - 5) * 1/(x + 7)
This gives
Product = 1/[(x - 5)(x + 7)]
Hence, the product of the fractions is 1/[(x - 5)(x + 7)]
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Geometry
Show work and number
Using the trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:
(2). x = √116
(3). x = 90
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
(1). sinA = 5/13 {opposite/hypotenuse}
cosA = 12/13 {adjacent/hypotenuse}
tanA = 5/13 {opposite/adjacent}
By Pythagoras rule
(2). x = √(4² + 10²)
x = √(16 + 100)
x = √116
(3). 106² = x² + 56²
x² = 106² - 56²
x = √(11236 - 3136)
x = √8100
x = 90
Therefore, using trigonometric ratios:
(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;
(2). x = √116
(3). x = 90
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In quantitative literacy
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
In quantitative literacy, finding the smallest square number that is divisible by 8, 12, 15, and 20.
To solve the problem, we need to determine the least common multiple (LCM) of these four numbers.
Let's list the multiples of each number until we find a common multiple:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
From the lists above, we can see that 120 is the smallest common multiple of all the numbers. To find the smallest square number, we need to square 120:
120^2 = 14,400
The smallest square number that is divisible by 8, 12, 15, and 20 is 14,400.
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
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Nicole and her 3 friends bought 8 pounds of candy and shared them equally. How many pounds
of candy
?
3
Answer:
Each person will get 2 pounds of candy
Step-by-step explanation:
Nicole + 3 friends = 4 total
8 pounds of candy = total
total candy / total people
8/4 = 2
Use the formula ω = (θ/t) to find the value of the missing variable. Give an exact answer unless otherwise indicated. ω = (π/8) radian per min, t = 11 min
Answer:
The missing variable θ is equal to (11π)/8.
Step-by-step explanation:
Given:
ω = π/8 radian per min
t = 11 min
Step 1: Identify the formula and the missing variable.
The formula is ω = (θ/t), and we are trying to find the value of θ.
Step 2: Rearrange the formula to solve for the missing variable.
To isolate θ, we can multiply both sides of the equation by t:
ω * t = θ
Step 3: Substitute the given values.
Substituting the given values into the rearranged formula, we have:
θ = (π/8) * 11
Step 4: Simplify the expression.
To multiply fractions, we multiply the numerators and multiply the denominators:
θ = (π * 11) / (8 * 1)
θ = (11π) / 8
Step 5: Finalize the answer.
The value of the missing variable θ is (11π)/8. This is the exact answer unless otherwise indicated.
Therefore, the step-by-step process shows that the missing variable θ is equal to (11π)/8.
Applying the General Multiplication Rule A box contains four red balls and eight black balls. Two balls are randomly chosen from the box, and are not replaced. Let event B be choosing a black ball first and event R be choosing a red ball second. What are the following probabilities? P(B) = P(R | B) = P(B ∩ R) = The probability that the first ball chosen is black and the second ball chosen is red is about percent.
The probability that the first ball chosen is black and the second ball chosen is red is 24.24%
How do i determine the probability?First, we shall obtain the total balls present in the box. Details below:
Red ball (R) = 4Black ball (B) = 8Total ball =?Total ball = 4 + 8
Total ball = 12 balls
Next, we shall obtain the probability of chosen a black ball first. Details below:
Black ball (B) = 8Total ball = 12 ballsProbability of chosen a black ball first, P(B) =?P(B) = n(B) / n(T)
P(B) = 8 / 12
Next, we shall obtain the probability of chosen red as the 2nd ball. Details below:
Red ball (R) = 4Total pen = 11Probability of chosen red as the 2nd ball, P(R | B) =?P(R | B)= n(R) / n(T)
P(R | B) = 4 / 11
Finally, we shall obtain the probability that the first ball chosen is black and the second ball chosen is red. Details below:
Probability of chosen a black ball first, P(B) = 8 / 12Probability of chosen red as the 2nd ball, P(R | B) = 3 / 11Probability that the 1st ball is black and the 2nd is red, P(B ∩ R) =?P(B ∩ R) = [P(B) × P(R | B)] × 100
P(B ∩ R) = [(8 / 12) × (3 / 11)] × 100
P(B ∩ R) = 0.2424 × 100
P(B ∩ R) = 24.24%
Thus, the probability that the first ball chosen is black and the second ball chosen is red is 24.24%
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Two car services charge different rates. A charges .60 per mile plus 3.00initial charge B charges .75 per mile mile traveled . the situation is modeled bu this system where x is the number of miles traveled and y is the charge for that distance ,in cents. How many miles must each car travel for the charges to be equal and ehat is the charge for that distance
The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.
To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.
Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:
For car service A: y_A = 0.60x + 300 (in cents)
For car service B: y_B = 0.75x (in cents)
To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:
0.60x + 300 = 0.75x
Subtracting 0.60x from both sides:
300 = 0.15x
Dividing both sides by 0.15:
x = 300 / 0.15
x = 2000
Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:
y_A = 0.60(2000) + 300
y_A = 1200 + 300
y_A = 1500 cents or $15.00
So, when each car travels 2000 miles, the charges will be equal at $15.00.
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______
36 | 8,325
is it
203 R17 or 231 R9 or 231 R11 or 234 R1
The quotient is 231, and the remainder is 9 or 231 R9.
To perform long division to find the quotient and remainder of 8,325 divided by 36, you would proceed as follows:
______
36 | 8,325
- 7,200 (36 x 200)1,125
1,080 (36 x 30)45
and, 36 (36 x 1)
9
The quotient is 231, and the remainder is 9.
Therefore, the correct answer is 231 R9.
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Which three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cmWhich three lengths CAN be the lengths of the sides of a triangle? A. 12cm, 5cm, 17cm, B. 10cm, 15cm, 24cm C. 9cm, 22cm, 11cm D. 21cm, 7cm, 6cm
Based on the Triangle Inequality Theorem the possible lengths of the sides of a triangle are:
B. 10cm, 15cm, 24cmD. 21cm, 7cm, 6cmWhat are the possible lengths of the sides of a triangle?The Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, is used to determine if three lengths can be the lengths of the sides of a triangle.
Considering each option:
A. 12cm, 5cm, 17cm:
12 + 5 > 17 (not satisfied)
5 + 17 > 12 (satisfied)
12 + 17 > 5 (satisfied)
B. 10cm, 15cm, 24cm:
10 + 15 > 24 (satisfied)
15 + 24 > 10 (satisfied)
10 + 24 > 15 (satisfied)
C. 9cm, 22cm, 11cm:
9 + 22 > 11 (satisfied)
22 + 11 > 9 (satisfied)
9 + 11 > 22 (not satisfied)
D. 21cm, 7cm, 6cm:
21 + 7 > 6 (satisfied)
7 + 6 > 21 (not satisfied)
21 + 6 > 7 (satisfied)
Hence, option B and D are correct.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = [tex]\frac{1}{2}[/tex] × 100° = 50°
Anthony bought a house and the bank offered him a loan that so that he will pay for
it monthly for the next 20 years, with a 13.75% interest compounded monthly. How
much will Mark pay monthly if the house's original price is 15,000,000 pesos?
The amount that Mark will pay monthly if the house's original price is 15,000,000 pesos for 20 years at 13.75% monthly compounded interest is 183,810.81 pesos.
How the monthly payment is determined:The monthly payment can be computed using an online finance calculator that incorporates the compound interest system.
The compound interest system charges interest on both the principal and the accumulated interest for each period.
N (# of periods) = 240 months
I/Y (Interest per year) = 13.75%
PV (Present Value) = 15,000,000 pesos
FV (Future Value) = 0
Results:
Monthly Payment (PMT) = 183,810.81 pesos
The sum of all periodic payments = 44,114,593.72 pesos
Total Interest = 29,114,593.72 pesos
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100 Points! Geometry question. Find each measure. Photo attached. Please show as much work as possible. Thank you!
Answer:
a. 73°
b. 98°
Step-by-step explanation:
In quadrilateral EFGH
∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
11x+8+8x+1=180°
19x+9=180°
19x=180=9
19x=171
x=171/19
x=9°
similarly,
∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°
substituting value
6y-4+5y-3=180°
11y-7=180°
11y=180°+7
11y=187°
y=187/11
y=17°
Now
a. m∡G=8x+1=8*9+1=73°
b. m∡H=6y-4=6*17-4=98°
Which of the following is the appropriate notation when calculating conditional probabilities
The notation which is the most appropriate notation when calculating conditional probabilities is option B.
What is the notation for conditional probabilities?The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."
In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.
Thus option B is correct.
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The Maths GCSE test scores of 240 students are shown in the histogram below.
The required median is 110- 120 and the upper quartile of the scores is 110-120.
Given that, the data from the histogram is
CI | f
80-90 | 5
90-100, | 3
100-110, | 4
110-120, | 4
120-130, | 3
130-140, | 3
140-150, | 2
150-160 | 2
To find the median and upper quartile of the given scores, make the cumulative frequency table.
The cumulative frequency table is given below.
CI | f | cf
80-90 | 5 | 5
90-100, | 3 | 8
100-110, | 4 | 12
110-120, | 4 | 16
120-130, | 3 | 19
130-140, | 3 | 22
140-150, | 2 | 24
150-160 | 2 | 26
N = 26.
The median is the N/2 th score when N is even.
Median = 13th score = 110-120 scores
To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.
Upper quartile = (3/4 x 26)th score.
Upper quartile = 19.5th score.
The upper quartile score range is 110 - 120.
Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The surface area of each solid is listed below:
Case A: A = 584.988 ft²
Case B: A = 320π in²
How to determine the surface area of a solidIn this problem we must determine the surface area of each of two solids, that is, the sum of the areas of all faces, whose area formulas are introduced below:
Square
A = l²
Where l is the side length.
Triangle
A = 0.5 · w · h
Where:
w - Widthh - HeightCircle
A = π · r²
Where r is the radius.
Lateral side of a cylinder
A = 2π · r · h
Where h is the height of the cylinder.
Now we proceed to determine the surface area of each solid:
Case A:
A = (14 ft)² + 4 · 0.5 · (14 ft) · √[(7 ft)² + (12 ft)²]
A = 584.988 ft²
Case B:
A = 2π · (8 in)² + 2π · (8 in) · (12 in)
A = 320π in²
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Robert has some nickels and some dimes. He has a maximum of 29 coins worth no less than $2.20 combined. If Robert has 10 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Robert's dimes are anywhere between 17 and 19.
Explanation:Nickels
are worth 5 cents, and
dimes
are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.
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Which two points could be removed to make this relation a function?
A. Points R and S
B. Points Q and T
C. Points P and Q
D. Points Q and R
Option (D) D. Points Q and R is used to removed to make this relation a function.
To determine which two points could be removed to make the relation a function, we need to check if there are any repeated x-values (inputs) in the given set of points. In a function, each input should have a unique output.
Let's analyze the given options:
A. Points R and S: (R, 3), (S, 5)
B. Points Q and T: (Q, 2), (T, 5)
C. Points P and Q: (P, 1), (Q, 2)
D. Points Q and R: (Q, 2), (R, 3)
In this case, if we remove points Q and R, we eliminate the repeated x-value of 2, which ensures that each input has a unique output. Therefore, the answer is:
D. Points Q and R.
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Find the missing side length.
1) 10 / ?
2) 24 / 15
( look at photo )
Cylindrical solid has a circumference of 132cm,height is 30cm.what is the area of the solid
Step-by-step explanation:
Cylinder LATERAL S.A. = circ X Height = 132 cm X 30 cm = 3960 cm^2
PLUS the two ends = two X pi r^2
the circumference = pi * d = 132 cm
then diameter = 132 / pi then radius = 1/2 132 / pi = 66/ pi
so end areas : two * pi (66/ pi)^2 = 2773.1
TOTAL = 3960 + 2773.1 = 6733.1 cm^2
Martin's school is due west of his house and due south of his friend Hayley's house. The
distance between the school and Hayley's house is 12 kilometers and the straight-line
distance between Martin's house and Hayley's house is 13 kilometers. How far is Martin's
house from school?
The distance between Martin's house and the school is 5 kilometers.
How to solve for distanceTo find the distance between Martin's house and the school, we can use the Pythagorean theorem.
Let's represent the distance between Martin's house and the school as x kilometers.
According to the given information:
Distance between Martin's house and Hayley's house (hypotenuse) = 13 kilometers
Distance between the school and Hayley's house (one side of the right triangle) = 12 kilometers
Using the Pythagorean theorem, we have:
x[tex]x^2 + 12^2 = 13^2[/tex]
Simplifying the equation:
[tex]x^2 + 144 = 169x^2 = 169 - 144x^2 = 25[/tex]
Taking the square root of both sides:
x = √25
x = 5
Therefore, the distance between Martin's house and the school is 5 kilometers.
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