The value of the highlighted angle using the alternate angle theorem is 130°.
What is are alternate angles?Alternate angles are angles obtained on the opposite sides of a transversal line that have the same size.
To calculate the value of the highlighted angle, we use the alternate angles theorem.
Note: Alternate angles are equal, From the diagram,the values of the two included angles are equal
Given:
Highlighted angle = 18x+4............ Equation 119x-3 = 18x+4 (Alternate angle)Solve for x
19x-18x = 4+3x = 7Substitute the value of x into equation 1
Highlighted angle = (18×7)+4Highlighted angle = 130°Hence, the value of the highlighted angle is 130°.
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what is the square root of 199 lie between
Hi!
I'm assuming the question means what integers, so let's figure it out.
Starting from 12, 12 squared is 144, or the square root of 144 is 12.
13 squared is 169, or the square root of 169 is 13.
14 squared is 196, or the square root of 196 is 14.
15 squared is 225, or the square root of 225 is 15.
Based on that list of numbers, we can determine that the square root of 199 lies between the square root of 196 and the square root of 225 -- aka 14 and 15.
To which rational number subset(s) does the following number belong?
16.8
I. Rational Numbers
II. Natural Numbers
III. Whole Numbers
IV. Integers
The rational number subset that the number 16.8 belongs is given as follows:
I. Rational Numbers.
What are the rational numbers subsets?The rational numbers are the set of numbers that can be expressed as a ratio of two integers, where the denominator is not zero. The rational numbers are usually denoted by the symbol Q.
The subsets are given as follows:
Themselves (rational numbers): decimal numbers.Integers (Z): This subset includes all positive and negative whole numbers, as well as zero. Every integer can also be expressed as a rational number by dividing it by 1.Whole numbers (W): This subset includes all positive whole numbers and zero. Every whole number can also be expressed as a rational number by dividing it by 1.Natural numbers (N): This subset includes all positive whole numbers, excluding zero. Every natural number can also be expressed as a rational number by dividing it by 1.16.8 is a decimal number, hence it belongs only to the rational number set, not to natural, whole and integer numbers.
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Can anyone help me with this?
Answer:
59.7%
Step-by-step explanation:
A of Circle = 50.24 sq. inches
A of Rectangle = 30 sq. inches
30 ÷ 50.24 × 100 = 59.71%
Not so sure though
The graph below is a polynomial function in the form f(x)=(x-a)(x-b). What are a and b?
A=
B=
The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.
What is meant by polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. For instance, the polynomial 2x+5 has an exponent of 1. The zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most common types of polynomials in precalculus and algebra.
Given,
f(x)=(x-a)(x-b)
From the above graph, f(x) passes through points (2, 0), (-1, 0), (0, -2)
Let us take (2, 0)
(2-a)(2-b)=0
4-2b-2a+ab=0
(-1, 0)⇒(-1-a)(-1-b)=0
1+b+a+ab=0
(0, -2)⇒-2=(-a)(-b)
ab= -2
a= -2/b
4-2b-2a-2=0
-2a-2b+2=0
a+b-1=0
b²-2b+b-2=0
b(b-2)+1(b-2)=0
b= 2 or b= -1
a+2-1=0
a= -1
a-1-1=0
a=2
The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.
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DUE 10:00 PM HELP ASAP. When Sarah left your house this morning her cell phone was 80% charged and then it started to lose 8% charge for each hour there after write an equation for B in terms of t representing the charge remaining in series battery as percentage t hours after Sara left her house
Answer:
b=80-8t
Step-by-step explanation:
"b" represents the charge remaining
"t" represents the number of hrs that have passed.
"80" is the reference we will be subtracting the hours from.
"8" is the percentage per hour we will be subtracting
therefore, the equation b=80-8t would solve for the remaining battery after "t" number of hours.
Using factoring, what are all four solutions to x⁴- 16 = 0 ? Show your work.
The four solutions to the equation x⁴ - 16 = 0 are x = -2, x = 2, x = -2i, and x = 2i.
To find the solutions to the equation x⁴ - 16 = 0 using factoring, we can use the difference of squares formula.
The difference of squares formula states that for any two numbers a and b, (a² - b²) can be factored as (a + b)(a - b).
In this case, we have x⁴ - 16, which can be rewritten as (x²)² - 4².
Using the difference of squares formula, we can factor it as (x² + 4)(x² - 4).
Now, we can further factor the expression by factoring x² - 4 using the difference of squares formula again.
(x² + 4)(x - 2)(x + 2) = 0.
So, the four solutions to the equation x⁴ - 16 = 0 are x = -2, x = 2, x = -2i, and x = 2i.
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Explain how to write an equivalent expression using the
distributive property.
2(11 + y)
K
Answer: 22 + 2y
Step-by-step explanation:
2 x 11 = 22
2 x y = 2
2(11+y) = 22+2y
Answer:
22+2y
Step-by-step explanation:
2*11 + 2* y
22 + 2y
HTH
What is the gradient of the line that passes through the points (0,0) and (5,-10)
Answer:
\(\displaystyle m=-2\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Slope Formula: \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (0, 0)
Point (5, -10)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m. Slope and gradient is the same.
Substitute in points [SF]: \(\displaystyle m=\frac{-10-0}{5-0}\)[Fraction] Subtract: \(\displaystyle m=\frac{-10}{5}\)[Fraction] Divide: \(\displaystyle m=-2\)Answer:
Let "m" be the slope of the line passing through the point.
\(m = \frac{y_ 2 - y_1}{x_ 2 - x_1 } = \frac{( - 10 - 0)}{(5 - 0)} = \frac{ - 10}{5} = \boxed{- 2 }\)
-2 is the gradient of the line that passes through the points (0,0) and (5,-10).
solve the following problems by writing a proportion. a) what is 70% of 4b) 5 is what percent of 20?
We have in a) that
\(\begin{gathered} 70\cdot\text{ }\frac{4}{100}\text{ = }\frac{\text{70 }\cdot\text{ 4}}{100} \\ =\text{ 2.8} \end{gathered}\)So the answer for a) is 2.8
Now in b) we have that
\(5\cdot\text{ }\frac{100}{20}\text{ = 25}\)So the answer for b) is 25%.
help i dont feel like doing the math
Answer:
A
Step-by-step explanation:
First, we should put this equation in slope-intercept form by isolating y.
Thus, we have:
\(2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3\)
The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.
Only answer A meets these requirements.
On Saturday, a local hamburger shop sold a combined total of 369 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the
number of hamburgers sold. How many hamburgers were sold on Saturday?
hamburgers
Answer:
123
Step-by-step explanation:
Let 'x' = number of hamburgers.....then cheeseburgers = '2x'
added together they = 369
x + 2x = 369
3x = 369
x = 123 hamburgers
Please answer this math question below
The probability that at least 1 American will say that they have been decapitated is (C) 0.15.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates that the event is impossible and 1 indicates certainty.The likelihood that something will happen can be summed up as probability.We can talk about the likelihood or likelihood of different outcomes when we don't know how an event will turn out.Events that follow a probability distribution are the subject of statistics.So, the probability that at least 1 person will say yes:
We know that 15% will say yes, then:
20/100 × 15 = 3Probability formula: P(E) = favorable events/ Total events
Now, put values and solve as follows:
P(E) = favorable events/ Total eventsP(E) = 3/20P(E) = 0.15Therefore, the probability that at least 1 American will say that they have been decapitated is (C) 0.15.
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1.10.3 Test (CST): Coordinate Geometry
Question 10 of 25
What is the area of a square with sides of length 9?
A. 54 square units
B. 81 square units
C. 36 square units
O D. 18 square units
SUBMIT
The area of a square with sides of length 9 is 81 square units.
What is an area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The space enclosed by the boundary of a plane figure is called its area.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
Given that, a square with side length of 9 units, we need to find its area, We know that, the area of a square is given by the square of it side, so Area = side²
Area of the given square = 9²
= 9 x 9
= 81 sq. units
Hence. the area of a square with sides of length 9 is 81 square units.
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Since the area of the circle is startfraction pi over 4 endfraction the area of the square, the volume of the cone equals startfraction pi over 4 endfraction the volume of the pyramid or startfraction pi over 4 endfractionstartfraction pi over 4 endfraction (startfraction (2 r) (h) over 3 endfraction) or one-sixthπrh. startfraction pi over 4 endfraction the volume of the pyramid or startfraction pi over 4 endfractionstartfraction pi over 4 endfraction (startfraction (2 r) squared (h) over 3 endfraction) or one-thirdπr2h. startfraction pi over 2 endfraction the volume of the pyramid or startfraction pi over 2 endfraction or two-thirdsπr2h. startfraction pi over 2 endfraction the volume of the pyramid or startfraction pi over 4 endfraction or one-thirdπr2h.
The volume of the cone is one-third the volume of the pyramid, the area of the circle is pi/4 the area of the square because the radius of the circle is half the side length of the square.
The volume of the cone is one-third the volume of the pyramid because the cone's base is a sector of the square, and the sector takes up one-third of the square's area.
Volume of a cone: The volume of a cone is equal to (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
Volume of a pyramid: The volume of a pyramid is equal to (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
In the problem, we are told that the area of the circle is pi/4 the area of the square. This means that the radius of the circle is half the side length of the square. We can use this information to find the volume of the cone and the pyramid.
Volume of the cone: The radius of the cone is half the side length of the square, so r = s/2. The height of the cone is h. The area of the base of the cone is (pi)(r²) = (pi)(s²/4). So, the volume of the cone is (1/3)π(s²/4)h = (1/12)πs²h.
Volume of the pyramid: The area of the base of the pyramid is the same as the area of the base of the cone, which is (pi)(s²/4). The height of the pyramid is the same as the height of the cone, which is h. So, the volume of the pyramid is (1/3)π(s²/4)h = (1/12)πs²h.
As you can see, the volume of the cone is equal to one-third the volume of the pyramid.
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Q3. Here are the first four terms of a sequence: 11, 22, 44, 88...
a) Write down one expression in terms of n for the nth term of the sequence.
Answer: a(n) = 11*2^(n-1)
a1 = 11
a2 = 22 = 11.2
a3 = 44 = 11.2²
a4 = 88 = 11.2³
......
=> this is a geometic with a1 = 11
r = 2
=> \(a(n)=11.2^{n-1}\)
Step-by-step explanation:
George collected achievement score data for each child from a middle school. He has their gender, age, teacher, and score on the achievement measure as his data fields. George needs to calculate the central tendency of his variable achievement score. Which measure should he use
To calculate the central tendency of the variable "achievement score," George can use several measures, including the mean, median, and mode. The choice of measure depends on the nature of the data and the specific requirements of the analysis. Here's a brief explanation of each measure:
1. Mean: The mean is the average of all the achievement scores. It is calculated by summing up all the scores and dividing by the total number of scores. The mean is commonly used when the data is roughly symmetric and does not have extreme outliers.
2. Median: The median represents the middle value when the data is sorted in ascending or descending order. If there is an odd number of scores, the median is the exact middle value. If there is an even number of scores, the median is the average of the two middle values. The median is often used when the data has outliers or is skewed.
3. Mode: The mode is the value or values that appear most frequently in the data. It can be useful when there are prominent peaks or clusters in the distribution, or when dealing with categorical data.
The choice of the appropriate measure depends on the specific characteristics of the achievement score data, such as its distribution, presence of outliers, and the research question at hand. For example, if the data is normally distributed without outliers, the mean may provide an accurate representation of the central tendency.
However, if the data is skewed or contains extreme values, the median might be a more robust measure. Similarly, if the data is categorical or has distinct clusters, the mode could be informative.
Therefore, George should consider the nature of his achievement score data and the specific requirements of his analysis to determine the most suitable measure of central tendency.
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SOMEONE HELP PLS THIS IS DUE AT 11:59 IT’S 10:29
I have most of it done but I don’t know what 4000 divided by 12 is every time I say the right answer it says it’s wrong lol.
Step-by-step explanation:
4000 ÷ 12
= 333.333
I rounded it to 3dp
Find the distance between the points A (13, 2) and B (7, 10).
Answer:
10
Step-by-step explanation:
d = 10
For:
(X1, Y1) = (13, 2)
(X2, Y2) = (7, 10)
Distance Equation Solution:
d=(7−13)2+(10−2)2−−−−−−−−−−−−−−−−−√
d=(−6)2+(8)2−−−−−−−−−−√
d=36+64−−−−−−√
d=1–√00
d=10
HELLLPPP PLSSSSS(don’t answer if you aren’t serious this is important)
9514 1404 393
Answer:
∠Q ≅ ∠U∠Q ≅ ∠U'∠S ≅ ∠VStep-by-step explanation:
The following angles are equivalent:
Q = U = 45°
R = T = W = 225°
S = V = 90°
X = 135°
Reflection, any rigid transformation, or any uniform dilation will not change the measures of the angles. That is, U = U', for example.
So, the true angle statements are ...
∠Q ≅ ∠U∠Q ≅ ∠U'∠S ≅ ∠V
What is the quotient of
x
x +4
divided by
2x
-?
x²²x16²
-
The quotient of the given expression is (X - 4) / 2X(X + 4).
What is quotient ?
In mathematics, the quotient refers to the result of dividing one number by another. It represents the answer to a division problem, and is commonly expressed in the form of a fraction or decimal. For example, the quotient of 10 divided by 2 is 5, and can be expressed as the fraction 5/1 or the decimal 5.0.
Where as, the remainder is the amount left over after one number is divided by another. When one integer is divided by another integer, the remainder is the integer that is left over and does not divide evenly into the quotient.
To simplify the expression, we can start by factoring the denominator of the second fraction:
2X / (X² - 16) = 2X / (X + 4)(X - 4)
Then, we can rewrite the entire expression using the division by fraction rule, which states that division by a fraction is the same as multiplication by its reciprocal:
X / (X + 4) ÷ 2X / (X + 4)(X - 4)
= X / (X + 4) x (X - 4) / 2X
Next, we can simplify by canceling out common factors:
X / (X + 4) x (X - 4) / 2X
= (X / X) x (X - 4) / (X + 4) x (2 x X)
= (X - 4) / (2X² + 8X)
= (X - 4) / 2X(X + 4)
Therefore, the quotient of the given expression is (X - 4) / 2X(X + 4).
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Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price per comic? Need help!!
Answer:
$0.25
Step-by-step explanation:
Let's represent the comics by assigning it the letter C.
20C = $5.00
C = $5.00/20
= $0.25
We can confirm this by using the example where he uses 30 comics.
30C = $7.50
C = $7.50/30
= $0.25.
Therefore each comic costs $0.25
A
∠A and
∠
B
∠B are supplementary angles. If
m
∠
A
=
(
4
x
−
16
)
∘
m∠A=(4x−16)
∘
and
m
∠
B
=
(
x
+
1
)
∘
m∠B=(x+1)
∘
, then find the measure of
∠
B
∠B.
Answer:
a
Step-by-step explanation:
what in the hell type of question is that need more easy work not alien work, But just put (B/)
MARKING BRAINLEIST + 20 POINTS PLEASE HELP IS DUE TODAY
Answer: The slope is 1.5. The equation of the line is y=1.5x+3
Step-by-step explanation:
Slope is the "Rise" over the "Run" of a line. The rise is the change in y. The run is the cange in x. Take any two points. I picked (0,3) and (4,9) since they were clearly on whokle number lines. The rise is (9-3) or 6. The run is (4-0) or 4. Rise/Run = 6/4 or 1.5. The y intercept is at 3 (the value of y when x=0). The full line equation is thus y = 1.5x+3.
Write the solution set of the given homogeneous system in parametric vector form. + = X1 3x1 + 3x2 +6X3 = 0 - 9x1 - 9x2 - 18X3 = 0 - 7x2 - 7x3 = 0 = where the solution set is x = x2 X3 X = X3
The given homogeneous system of equations can be represented as a matrix equation Ax = 0, where A is the coefficient matrix and x is the vector of variables.
To find the solution set in parametric vector form, we can perform row operations on the augmented matrix [A|0] and express the variables in terms of free parameters.
The augmented matrix for the given system is:
[3 3 6 | 0]
[-9 -9 -18 | 0]
[0 -7 -7 | 0]
Using row operations, we can transform this matrix to row-echelon form:
[3 3 6 | 0]
[0 -6 -12 | 0]
[0 0 -7 | 0]
Now, we can express the variables in terms of free parameters. Let x2 = t and x3 = s, where t and s are arbitrary parameters. Solving for x1 in the first row, we get x1 = -2t - 2s.
Therefore, the solution set in parametric vector form is:
x = [-2t - 2s, t, s], where t and s are arbitrary parameters.
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help me out plz it’s due rn
Answer:
x= square root (10); x=-square root (10) or 3.16 and -3.16
Step-by-step explanation:
Eight days ago, I put 50 sheets of paper in my binder. I used the same number of sheets each day. Now!
only have 2 sheets left.
How many sheets of paper did I use each day?
sheets
Answer:
6 papers a day
Step-by-step explanation:
michelle, a basketball player, has made 14 of her 20 free throws this season. if she never misses again, how many free throws would she need to shoot to have a shooting percentage of 90 percent?
Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.
Let's denote the number of additional free throws that Michelle needs to make as "x." Since she has made 14 out of her 20 free throws this season, her current shooting percentage is:
Current shooting percentage = (Number of made free throws / Total number of attempted free throws) * 100
= (14 / 20) * 100
= 70%
To find the number of additional free throws she needs to shoot to achieve a shooting percentage of 90%, we set up the following equation:
(14 + x) / (20 + x) = 90/100
We can now solve this equation to find the value of x:
(14 + x) / (20 + x) = 0.9
Cross-multiplying gives:
0.9 * (20 + x) = 14 + x
18 + 0.9x = 14 + x
0.9x - x = 14 - 18
-0.1x = -4
Dividing both sides by -0.1 gives:
x = 40
Therefore, Michelle would need to shoot an additional 40 free throws to have a shooting percentage of 90%.
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Is 82 inches grater than 5feet and 10 inches
Answer:
False, 82 inches is not greater than 5 feet and 10 inches
Step-by-step explanation:
1 feet = 12 inches
5x12=60+10=70
82 is greater than 70.
Calculate the product below and give your answer in scientific notation.
\large{\left(800 \right) \times \left(3\times 10^{-1} \right) =\ ?}(800)×(3×10
−1
)= ?
I WILL MARK BRANNIEST Painter takes 2 3/5 hours to paint a wall how many hours will the painter take to paint 8 walls if she works at the same rate?
A 204/5
B16 3/5
C 13/5
D 101/5
Answer:
A: 20 4/5
Step-by-step explanation: