As A and B are vertical angles, the measures of angle A and B is 98° each.
What in geometry are Vertical Angles?When two lines collide, vertical angles are created. The angles that are directly opposite one another, out of the four that are generated, are vertical angles. Additionally, they are known as "vertically opposed angles." All of these angles are equal.
Vertical angles are created when two straight lines cross. Angles vertically are consistently congruent and equal. As the two sets of non-adjacent angles created by crossing two lines superimpose on one another, vertical angles are congruent.
As A and B are vertical angles,
6x - 16 = 4x + 22
⇒ 2x = 38
⇒ x = 19
Measure of Angle A is 98°
Measure of Angle B is 98°
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Is 4/8 equivalent to 7/8
Answer:
is 7 more than 4 or 4 more than 7?
Step-by-step explanation:
JUST USE YOUR BRAIN!
Answer:
no
Step-by-step explanation:
of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no
Find the degree measure of the indicated angle.
Answer:
75 degree
Step-by-step explanation:
35+70+75=180 degree
A cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F. The table shows temperature readings for the cake.
a. Given a room temperature of 70⁰F , what is an exponential model for this data set?
The exponential model for the given data set is [tex]y(x) = 70 + (110)e^{-0.135x}[/tex].
Given that cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F and the table shows temperature readings for the cake and the room temperature is 70°F.
Temperature at time = 0 min, y₀= 180° F
Ambient (room) tempertaure = y₁ = 70° F
Using Newton's cooling method,
y(x) = y₁ + (y₀ - y₁)e⁻ⁿˣ
y(x) = 70 + (180-70)e⁻ⁿˣ
y(x) = 70 + (110)e⁻ⁿˣ
Given, at x=5 min, y(5) = 126,
y(5) = 70 + (110)e⁻⁵ⁿ = 126
Solving, e⁻⁵ⁿ = (126-70)/110 = 0.5091
Taking and log and solving for n,
- 5n = log(0.5091)
-5n= -0.67511
n = 0.135
Thus, the exponential model is [tex]y(x)=70+(110)e^{-0.135x}[/tex]
Hence, an exponential model for given data set when a room temperature of 70°F is [tex]y(x)=70+(110)^{-0.135x}[/tex].
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What is the value of x that makes the given equation true?
4x 3-12x13
—
A. 0x = -3
B. O x = 0
C. O x = 1
D. O x = 16
The value of the x is 1 in the linear equation. Thus, option C is correct.
According to the statement
We have to find that the value of the x.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is:
4x−3=−12x+13
Then
we have to solve it
4x−3=−12x+13
4x+12x = 3+13
16x = 16
x = 16/16
x =1.
When we put x =1 in the given equation and then i satisfy the equation and give same values after calculation.
So, The value of the x is 1 in the linear equation. Thus, option C is correct.
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In a survey, respondents were asked which type of activity they enjoyed most while on vacation. The bar graph shows the responses of males and females.
How many more males than females said that bike riding was their favorite activity?
Answer: 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Identify rise over run (please!)
Which sum or difference is equivalent to the following expression?
2x+3/4
A. x/2 + 3/4
B. x/2 - 3/4
C. 3x/4 + 3/4
D. 8x +24
The expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
How to Find Expressions that are Equivalent?Express the given expressions in their simplest form to determine the expression that is equivalent to (2x + 3)/4.
A. x/2 + 3/4
Find the common denominator. The common denominator is 4. Therefore:
= 2(x) + 1(3)/4
= (2x + 3)/4
x/2 + 3/4 ≠ (2x + 3)/4
Thus, the expression, x/2 + 3/4 is equivalent to (2x + 3)/4.
B. x/2 - 3/4 = (2x - 3)/4
Therefore, x/2 - 3/4 ≠ (2x + 3)/4
C. 3x/4 + 3/4 = (3x + 3)/4
Therefore, 3x/4 + 3/4 ≠ (2x + 3)/4
D. 8x + 24 ≠ (2x + 3)/4
Therefore, 8x + 24 ≠ (2x + 3)/4
In summary, we can conclude that, the expressions, x/2 - 3/4, 3x/4 + 3/4, and 8x +24x/2 + 3/4 is not equivalent to (2x + 3)/4. Thus, the expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.
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0.3596 is considered a rational number. What makes this number rational
Answer:
see explanation
Step-by-step explanation:
a rational number has the form
[tex]\frac{a}{b}[/tex] , where a and b are integers
given
0.3596 ← with 6 in the [tex]\frac{1}{10000}[/tex] place
= [tex]\frac{3596}{10000}[/tex] = [tex]\frac{899}{2500}[/tex] ← a rational number
Write 987.6 in scientific notation.
Decimal value Scientific Notation
987,650,000 9.8765 × 108
2/3p - 11 = 1/3p -15
p=_
Answer:
p = - 12
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] p - 11 = [tex]\frac{1}{3}[/tex] p - 15
multiply through by 3 to clear the fractions
2p - 33 = p - 45 ( subtract p from both sides )
p - 33 = - 45 ( add 33 to both sides )
p = - 12
Answer:
-12
Step-by-step explanation:
(sorry its a bit messy - hope it helps though!)
Evaluate each logarithm.
log₃9
The value of the expression log₃9 is 2.
The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.
Log a to the base b can be written as- log a/ log b.
Moreover, log [tex]a^{k}[/tex]= k log a, for all non negative values of a
Here, we are given a logarithmic expression- log₃9
We can expand this as-
log₃9 = log 9/ log 3
= log [tex]3^{2}[/tex]/ log 3
= 2 log 3/ log 3
= 2
Thus, the value of log₃9 is 2.
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4 metode la 381-(x+y)=15
Answer:
codec log 8x + y =15
Step-by-step explanation:
have a good day!
The leg of a right triangle is 3 units and the hypotenuse is 11 units. What is the length, in units, of the other leg of the triangle? HURRY PLEASE!!!
a
112 units
b
square root 112 units
c
130 units
d
square root 130 units
The correct option is (b) square root 112 units
Step-by-step explanation:By using Pythagoras theorem,
a² + b² = c²where a & b = legs of triangle and c = hypotenuse
Hence:
3² + b² = 11²9 + b² = 121b² = 121 - 9b² = 112b = √1122. Plot two numbers that are 5 units from zero on the number line.
Answer:
5 and -5
This is because these 2 spots are exactly 5 spaces from 0.
mile
long. You walk 3 laps around the lake in the morning
and 2 laps in the evening. Your friend walks the same
1
total distance as you on a 1--mile track. How many
2
laps does your friend walk?
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 3/2 mile track.
The total laps of our friend runs is 3laps.Given that
The sidewalk around a lake is 9/10 mile long.You walk 3 laps around the lake in the morning and 2 laps in the evening.Your friend walks the same total distance as you on a 3/2 mile track.To find
How many laps does your friend walks?So, according to the question
we have,
The length of sidewalk around the lake = 9/10 miles.Total distance walk by you = 9/10 (3+2)= (9 ×5)/10
= 4.5 miles.
Now, from question
Your friend walk same distance travel by you on 3/2 mile track.So, Total laps walk by your friend
= ( Total distance walk by you)/(Total length of your friends track)
= [tex]\frac{4.5}{(\frac{3}{2}) }[/tex]
= [tex]\frac{4.5\times 2}{3}[/tex]
= 9/3 = 3
Answer:
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6) On a map scale 1cm to 250m the area of
a car park is 3cm². What is the actual
area of the care park in hectares? (1 hectare=10,000m^2)
The actual area of the care park in hectares is 18.75
As per the known fact, ratio of measurement on scale is equal to the ratio of measurement in real. So, writing the equation first -
Area of car park = 3 cm²
Keep the value of 1 cm in the above mentioned equation.
Area of car park = 3 × (250)²
Taking square
Area of car park = 3 × 62,500
Performing multiplication
Area of car park = 1,87,500 m²
Converting the area in hectares
10,000 m² = 1 hectare
1,87,500 m² = (1 ÷ 10,000) × 1,87,500
1,87,500 m² = 18.75 hectares.
Therefore, the actual area of the care park is 18.75 hectares.
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Solve each equation.
2x=8
Solution of this polynomial equation is x = 4
What are polynomial equations ?In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
2x = 8
=> 2x / 2 = 8 /2
=> x = 4
Thus solution for given equation is x = 4.
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Carson wants to divide 128 by 3.2. What is the place value of the first digit in his answer?
tenths
ones
tens
hundreds
Answer:Tenths
Step-by-step explanation:Hope it helps
Write each expression as a single natural logarithm. ln a-2 ln b+1/3 ln c
We have expression ln a-2 ln b+1/3 ln c as a single natural logarithm
㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We have been asked to express ln a-2 ln b+1/3 ln c as a single natural logarithm.
⇒ ln a-2 ln b+1/3
⇒ ㏑ (a) - ㏑ (b²) + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ln a-2 ln b
⇒ ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
Use the quotient property of logarithms for ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]
⇒ ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
Finally, we have expressed ln a-2 ln b+1/3 ln c as a single natural logarithm ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]
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Question 6(Multiple Choice Worth 2 points)
(Linear Relationships MC)
At a restaurant, hot chocolate can be purchased in three different cup sizes. A 12-ounce cup costs $1.97, a 16-ounce cup costs $2.62, and a 20-ounce cup costs $3.27.
Which statement is true based on the given description?
O The description shows a linear relationship, but not a proportional relationship.
O The description shows a linear relationship and a proportional relationship.
O The description does not show a linear relationship or a proportional relationship.
O The description shows a proportional relationship, but not a linear relationship
We need to know about linear and proportional relationship to solve this problem. Statement 2 is true, the description shows a linear relationship and a proportional relationship.
Linear relationship is a relationship between two variables where if one increases the other increases or if one decreases the other decreases. The varibales in a linear relationship form a straight line on graph. Proportional relationship is the relationship between two variables where the ratio between pairs of different data always remains constant. In the given question, a 12 ounce cup costs $1.97, a 16 ounce cup costs $2.62 and a 20 ounce cup costs $3.27. The price of each cup increases with increase in capacity of the cup, so we can say that the cup capacity and price have a linear relationship. The ratio between each pair can be given by
12/1.97=6.10
16/2.62=6.10
20/3.27=6.10
The ratios between every pair is same, so it is a proportional relationship.
Thus we found that the description shows a linear relationship and a proportional relationship between the cup capacity and it's price, statement 2 is the right option.
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Data points are considered to be unusual if they are more than two standard deviations
away from the mean. Which data points in each distribution are considered to be unusual?
Show all work.
Answer:
Step-by-step explanation:
30 and 20
The product of two factors is 1. One of the factors is 1. Can you tell what the other factor is? A. Yes; the other factor is 0 since 0 × 1 = 1. B. Yes; the other factor is 1 since 1 × 1 = 1. C. No; any number times 0 is 0, so there is no way to know what the other factor is. D. No; any number times 1 is 1, so there is no way to know what the other factor is.
Please help I have to turn in my homework by tonight at 11:00 PM!
The product of two factors is 1. One of the factors is 1. B. Yes; the other factor is 1 since 1 × 1 = 1.
How to calculate the value?From the information given, the product of two factors is 1 and one of the factors is 1.
Let the other number = y
The other number will be:
1 × y = 1
y = 1
Therefore, the other number is 1
In conclusion, the correct option is B.
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given f(x)=x-2, write the new function if the y-intercept is decreased by six units.
Answer:
f(x) = x - 8
Step-by-step explanation:
“Solve the equations”3x*3-9x^2-54x=0
Answer:x=6 x=-3
Step-by-step explanation:
3x(x^2-3x-18)=0
(X-6)(x+3)=0
X-6=0. X+3=0
+6=+6. -3=-3
X=6. X= -3
simply fully: square route 8 x square route 18
Answer:
12
Step-by-step explanation:
[tex]\sqrt{8} * \sqrt{18} =12[/tex]
Write
24/25
as a percentage.
Answer: 96%
How to Solve
Formula:
y ÷ x *100
Substitute
=> 24 ÷ 25 * 100
Lets Multiply 24 * 100 (or you can divde 24 and 25 then multiply with 100. do as you're convenience, answer will remain)
Answer 2400
Now As our formula says divide 2400 by 25
Answer 96
Hence 96%
So, 24/25
as a percentage is 96%
All done!
Answer:
96%
Step-by-step explanation:
First, divide 100 but 25 (the denominator) and you get 4. This means that to get a number over 100, which is a percentage you need to multiply the initial fraction by 4. You get 96/100, and you can remove the 100 to get 96%
Classify each number as rational or irrational
how do you divide 1/2 by -4
Answer:
Step-by-step explanation:
1/2÷4 = 1/8 = 0.125.
[tex]\cfrac{1}{2}\div -4\implies \cfrac{1}{2}\div \cfrac{-4}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{-4}\implies {\LARGE \begin{array}{llll} -\cfrac{1}{8} \end{array}}[/tex]
Solve each equation. If necessary, round to the nearest ten-thousandth.1/2log x+log 4=2
For logarithmic equation 1/2 log x + log 4 = 2, the value of x is 34,040.25
How can a logarithmic equation be solved?Step 1: Using exponentiation principles, isolate a logarithmic expression (with the same base) on both sides of the equation.
Step 2: balance the arguments.
Step 3: Solve the resultant equation.
Step 4: Double-check your answers.
Given,
1/2 log x + log 4 = 2
log x^(1/2) + log 4 = 2
using logₐ(m.n) = logₐ(m) + logₐ(n)
log e (4 (x^1/2)) = 2
e² = 4x^(1/2)
7.38 = 4√x
Squaring on both sides -
54.4644 = 16x
x = 54.4644 / 16
x = 34,040.25
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PLEASE HELP and explain in the answer
The missing numbers are 17,66,13, 9 3 and 15 respectively .
The rules given to us are-
first row consist of a number which is the sum of two numbers of middle row
Third row consist of a number which is the product of two numbers of middle row
The first part
The sum of 6 and 11 is 17 and the product of 6 and 11 is 66
17
6 11
66
The second part
To find the second number of middle row we need to divide 36 by 4 and we get 9 and the sum of 4 and 9 is 13
13
4 9
36
The third part
To find the numbers of middle row we need to find the factors of 45 that sum up to 18
The factors of 45 are 3*3*5
The factor 15 and 3 satisfy both the requirements
18
3 15
45
Hence, The missing numbers are 17,66,13, 9 3 and 15 respectively
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