Answer:
y = 13x - 41
Step-by-step explanation:
Parallel lines always have the same slope since
[tex]m_{2}=m_{1}[/tex]
Thus, the slope of the second line is m = 13.
We can find the y-intercept of the line by plugging in the points for x and y, 13 for m, and solving for b:
[tex]-2=13(3)+b\\-2=39+b\\-41=b[/tex]
Solve each equation. 2 1/3(2x-3)=2 1/3
Answer: x = 2
Step-by-step explanation:
Multiply each term between the parentheses by 2 1/3.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the expression of the multiplication.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the multiplication and division of rational numbers.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]
We convert the mixed fraction to improper.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]
We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]
We move the constant to the right side and change the direction of the sign.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]
Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
The value of 3x₁ + x₂ is 7/2
How to find the value of 3x₁ + x₂?
A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
5/x - 2/x² = 2
The LCM of x and x² is x². So we have:
(5x - 2)/x² = 2
Cross multiply:
5x - 2 = 2x²
2x² - 5x + 2 = 0
Factorize:
(2x - 1)(x - 2) = 0
2x - 1 = 0 or x - 2 = 0
2x = 1 or x = 2
x = 1/2 or x = 2
Thus, x₁ = 1/2 and x₂ = 2
Therefore, the value of 3x₁ + x₂ will be:
3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2
Learn more about quadratic equation on:
brainly.com/question/1214333
#SPJ1
- Grace is trying to read as many books
over the summer as she can. Grace
has already read 15 books. She plans
to read 2 additional books per week.
Define a variable for the number of
weeks she reads additional books. Use
the variable to write an expression
for the total number of books Grace
reads over the summer.
Step-by-step explanation:
let the number of weeks be w
the total number of books Grace reads will always be 15 + something because we start with 15 and cannot unread a book
for each week, she reads 2 books. this can be represented as 2 * w
books Grace already read + books Grace reads each week = total books
15 + 2 * w = total books
Samuel will arrive at the airport on the first plane after 10 am Airplanes arrive every 50 mins beginning at 6 am when will samuels plane arrive?
Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.
What is algebraic expression?An algebraic expression is a mathematical expression that uses coefficients, unknown variables, algebraic operations, and constants. However, it is not acceptable to use an equality symbol in an expression.
Mathematical expressions and sentences come in a wide variety. the relationships between equations, numerical expressions, and algebraic expressions.
The difference between 10 am and 6 am
is 4 hours, So the the time he arrives will be a multiple of 50 grater than 4 hours
50x > 4 × 60
50x > 240
x > 240/50
x > 4.8
x = 5 (as 5 is nearest single digit no. to 4.8)
50x = 50 × 5
= 250 minutes
250 mins = 4 hours and 10 mins
6 am + 4 hours and 10 mins
= 10 hour and 10 min or 10:10 am
Thus, Samuels plane arrive will arrive at 10:10 am, in the given algebraic problem.
Learn more about algebraic expression
https://brainly.com/question/953809
#SPJ1
Date Page A merchant bought a quintal of potatoes for Rs 4000. He sold all potatoes at Rs 390 per kg.
Find his profit or loss.
Answer: The merchant made a profit of Rs 35,000 by selling the potatoes.
Step-by-step explanation:
To find the profit or loss of the merchant, we first need to calculate the revenue he earned from selling the potatoes.
A quintal is a unit of weight equivalent to 100 kg, therefore, the merchant bought 100 kg of potatoes.
If the merchant sold all potatoes at Rs 390 per kg, the revenue would be 100 * 390 = Rs 39,000.
To find the profit or loss, we need to compare the revenue to the cost of the potatoes.
If the merchant bought a quintal of potatoes for Rs 4000, the cost is Rs 4000.
To calculate the profit or loss, we can use the following formula:
Profit or loss = Revenue - Cost
Using this formula, we can calculate the profit or loss as:
Profit or loss = 39,000 - 4,000 = Rs 35,000
So, the merchant made a profit of Rs 35,000 by selling the potatoes.
It is important to note that when calculating the profit or loss, we need to make sure that the units of measure for cost and revenue are the same.
if the line passing through the points (a,2) and (4,9) is parallel to the line passing through the points (3,11) and (a+1,3) what is the value of a?
Answer:
a = 18
Step-by-step explanation:
The slopes of parallel lines are equal as
[tex]m_{2}=m_{1}[/tex]
We know that the slope formula is
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2, x2, y1, and y2 are any two points.
Thus, since the slopes are equal, we can use the slope formula to find the slopes of both lines and set them equal to each other to find a:
[tex]\frac{9-2}{4-a}=\frac{3-11}{(a+1)-3} \\\\\frac{7}{4-a}=\frac{-8}{a-2} \\\\7(a-2)=-8(4-a)\\7a-14=-32+8a\\7a=-18+8a\\-a=-18\\a=18[/tex]
If we plug in a for any of the two lines, we see that the slope is -1/2
Line 1 w/ (a, 2) & (4, 9):
[tex]\frac{9-2}{4-18}\\ \frac{7}{-14}\\ \frac{-1}{2}[/tex]
Line 2 w/ (3, 11) & (a+1, 3):
[tex]\frac{3-11}{18+1-3}\\ \frac{-8}{19-3}\\ \frac{-8}{16}\\ \frac{-1}{2}[/tex]
write an equation of a line that passes through (1,0) and is parallel to 2x+y=-4
The equation of the line that passes through (1, 0) and is parallel to the line 2x + y = -4 is: y = -2x + 2.
How to Write the Equation of Parallel Lines?The equation of a line, in slope-intercept form is y = mx + b, if two lines are parallel to each other, then the value of the slope, m, would be the same for both of them.
Given the equation, 2x + y = -4, rewrite the equation in slope-intercept form to determine the slope (m):
2x + y = -4
y = -2x - 4
The slope (m) is -2.
This means the line that passes through (1, 0) will also have a slope of -2. Substitute m = -2 and (x, y) = (1, 0) into y = mx + b, to find the y-intercept (b) of the line:
0 = -2(1) + b
0 = -2 + b
2 = b
b = 2
To write the equation of the parallel line, substitute m = -2 and b = 2 into y = mx + b:
y = -2x + 2.
Learn more about the equation of parallel lines on:
https://brainly.com/question/11345748
#SPJ1
for each pair expalin why they are equivelent 5:6 15:18
The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.
Why are the two ratios equivalent?Here we want to explain why the two ratios:
5:6 and 15:18
Are equivalent, where equivalent means that these two ratios mean the same thing.
Now, if we take any ratio
a:b
and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.
k*a: k*b
Now, let's look to our ratios:
5:6
If we multiply these 2 numbers by 3, we will get.
3*5: 3:6
15: 18
So yes, these are equivalent.
Learn more about equivalent ratios at:
https://brainly.com/question/2328454
#SPJ1
Which of the following show an equation and it’s solution?
The ones which are equation are
[tex]\frac{3}{4}l = -9\\ 4m + 2m = 72[/tex]
What is an equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
here
-3 = d/-8
or, d = 24 (different from answer)
14 = 25 - k
or, k = 11 (different from answer)
j + 1 = j/3
or, 3j + 3 = j
or, j = -3/2 (different from answer)
3/4 l = -9
or, l = -12 ( same as answer)
-15 = n + 8
or, n = -23 (different from answer)
4m + 2m = 72
or, m = 12 (same as answer)
To learn more about equations erefer to :
https://brainly.com/question/29083151
#SPJ1
riley needs to make punch for a party. One batch of punch has the ingredients shown.
cranberry juice 4 cups, lemon lime soda 1 cup, orange juice 2 cups, pineapple juice 2 cups. Write and interpret a ration that compares the cups of orange juice to the total cups in one batch of punch. Then find the cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups
If riley needs to make punch for a party. One batch of punch has the ingredients shown. The cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups is 6 cups.
How to find the cups of orange juice?Total cup of juice for one batch:
Total cup of juice for one batch = 4+ 1 +2 +2
Total cup of juice for one batch = 9
Since 2 cup of the 9 cups are orange juice so 2/9 of each batch will be orange and since the bowl can hold 27 cups now let find the cups of orange juice.
Cups of orange juice = 2/9 ×27
Cups of orange juice =6 cups
Therefore we can conclude that the cups of orange juice is 6 cups.
Learn more about cups of orange juice here:https://brainly.com/question/16454061
#SPJ1
Calculate the combinations of 5 things 3 at a time
Answer:
5 combination 3
5 fictorial divided by (5-3)! 3!
by using the above method 10 will be your answer
The stopping distance , D, of a car after the brakes are applied varies directly as the square of the speed , S, of the car. If a car traveling at a speed of 36 miles per hour can stop in 53 feet, what is the stopping distance of a car traveling at 70 miles per hour? Round your answer to the nearest foot.
Answer: There is no way 200 is the answer. it should be 103.055
Step-by-step explanation: See, 36 miles can stop in 53 feet. We want to know how many feet are there when 70 miles fast. We can write that as 36/53 = 70/x. 36 corresponds to 70 and 53 corresponds to x. Do it and you get 103.055
Pls help. I think it's only one answer, but I need help just to make sure two more of the answers are not part of it, since the question says to choose all possible answers. Pls help quickly, I'll mark you Brainliest if it is correct.
Answer:
-5 and -3
Step-by-step explanation:
-2x + 1 > 6
[tex]-2(-\frac{5}{2}) + 1 > 6\\6 > 6[/tex]
Not an answer
-2(-5) + 1 > 6
11 > 6
An answer
-2(-2) + 1 > 6
5 > 6
Not an answer
[tex]-2(-\frac{3}{2}) + 1 > 6\\4 > 6[/tex]
Not an answer
-2(0) + 1 > 6
1 > 6
Not an answer
-2(-3) + 1 > 6
7 > 6
An answer
A small city has a population of 34000 in 1994. The population growth after 1994 is modeled by the following function where is the number of years after 1994.
P(t)=34000e 0.04t
During what year will the population reach 68000?
[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]
that's about 74 years and 325 days more or less.
based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.
Expresa estas fracciones como un número mixto realizando para ello la división correspondiente
The representation of the fraction 10/8 as a mixed number is given as follows:
[tex]\frac{10}{8} = 1\frac{1}{5}[/tex]
How to convert a fraction to mixed number?The fraction in this problem is given as follows:
10/8.
A mixed number is composed by two parts, as follows:
Integer part.Fractional part.The integer part and the fractional part are defined as follows:
Integer: quotient of the numerator by the denominator.Fractional part: remainder of the fraction divided by the divisor.For the division of 10 by 8, we have that:
The quotient is of 1.The remainder is of 2.Then the mixed number is given as follows:
[tex]1\frac{2}{10}[/tex]
The fraction 2/10 can be simplified as 1/5, hence the simplified representation is given as follows:
[tex]1\frac{1}{5}[/tex]
Missing Information and TranslationThe problem asks to represent the fraction 10/8 as a mixed number
More can be learned about fractions and mixed numbers at https://brainly.com/question/21610929
#SPJ1
please answer the following four questions.
i have left a table of the hybrid car if that helps at all.
i need help with this asap so if anyone can get back to me sooner than later i would really appreacite it.
The analysis of the distance to the Grand Canyon, and the distance traveled on an amount of gas are as follows;
1 a. The distance from the middle school to the Grand Canyon = 80 miles
2 a. The graph showing the correlation between the distance traveled to the number of gallons used, created with MS Excel is attached
b. The table of values based on the data used to create the graph, presented in a tabular form using MS Word is attached
c. The equation is; d = 10·g
d. The advantages are;
The graphical presentation is a pictorial representation of the distance
The table enables further analysis
The equation can be used to predict the distance the Hybrid can travel on an amount of gas
What is a correlation between variables?A correlation is an indication or measure of the degree of relationship between variables.
1 a. The data for the Camper and the SUV that both use only gas, and the Hybrid car are as follows;
[tex]{}[/tex] Camper SUV Hybrid Car
Average Miles per Gallon [tex]{}[/tex] 4 8 10
Gallons of gas consumed [tex]{}[/tex] 20 10 8
Distance traveled = Number of gallons used × Miles traveled per gallon
The distance between the middle school and the Grand Canyon, using the data for the Camper, is therefore;
d = 20 gallons × 4 miles/gallon = 80 miles
The distance is 80 miles from the middle school to the Grand Canyon2. Amount of gas in gallons = g
Distance car drives in miles = d
The model used = The Hybrid car
Miles traveled per gallon = 10 miles/gallon
Therefore, d/g for the Hybrid car = 10 miles/gallon
d = 10·g
a. Please find attached the graph of the driven distance to the amount of gas used, created with MS Excel
b. The table based on the distance covered using different amount of gas can be created using the data used for creating the graph as follows;
Amount of gas; 0 1 [tex]{}[/tex] 2 3 4 5 6 7 8 9 10 11
Distance; 0 10 20 30 40 50 60 70 80 90 100 110
c. The equation that represents the distance traveled in miles, d, with the Hybrid when a specified amount of gasoline is used, g, is presented as follows;
d = 10·gd. The advantage of each representation are as follows;
The advantage of the graphical presentation is that the fuel consumption can be visualised to help better plan the tripThe advantage of presenting the data as a table allows the exact value of the distance traveled using an indicated amount of fuel, such that the cost of the journey can be more easily calculatedThe presentation of the relationship as an equation, allows for the relationship to be treated as a continuous function and to predict the amount of gas to be used or the distance the Hybrid car can drive
Learn more about writing equations here: https://brainly.com/question/1918577
#SPJ1
Consider parallelogram QRST below.
Use the information given in the figure to find mLR, mLRQS, and x.
R
Q
4x
8
36°
83°
S
T
The value of [tex]m \angle R Q S[/tex] is 40.
What is parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles. A quadrilateral with two sets of parallel sides is referred to as a parallelogram. The sides of these figurines are parallel to one another and the same hue. a form having four equally long sides.The opposite angles of a parallelogram are equal, therefore:
[tex]m \angle R=m \angle T \\[/tex]
so
[tex]m \angle R=75[/tex]
Opposite sides of a parallelogram are parallel and equal so:
[tex]Q T & =R S \\[/tex]
[tex]4 x & =12 \\[/tex]
[tex]x & =\frac{12}{4} \\[/tex]
[tex]x & =3[/tex]
[tex]$$$\angle \mathrm{TSQ}$[/tex] and [tex]$\angle \mathrm{RQS}$[/tex] are alternate interior angles, therefore:
[tex]m \angle R Q S=m \angle T S Q \\[/tex]
[tex]80: \\[/tex]
[tex]m \angle R Q S=40[/tex]
The complete question is,
Consider parallelogram QRST below. Use the information given in the figure to find m ZR, x, and m ZROS.
To learn more about parallelogram refer to:
https://brainly.com/question/970600
#SPJ1
What is the terminal point of the vector a=⟨4,3⟩ based at P=(5,2)?
Answer:
Step-by-step explanation:
The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:
Terminal point = (x,y) = (Px + ax, Py + ay)
= (5 + 4, 2 + 3)
= (9,5)
Answer:
Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3) whose base is at the point P=(5,2).
✔️ Add to point P and that
✔️Point that the vector is pointing at to find the terminal point....
➖So we can say That
✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-
(5,2)+(4,3)=(9,6)
your welcome !
I will give brainliest, if you get this correct
Depend on the following data
30 25 23 41 39
27 41 24 32
Find
A. The arithmetic mean, median, mode and range.
B. The upper and lower quartile, 7 and 50 .
C. Variance and coefficient of variation.
D. Pearson coefficient of skewness and kurtosis
Answer:
A.
Arithmetic mean: The sum of the data divided by the number of data points. (For the first set of data: (30+25+23+41+39)/5 = 31.4)
Median: The middle value when the data is arranged in order. (For the first set of data: 30, 23, 25, 39, 41 => 25)
Mode: The value that appears most frequently in the data. (For the first set of data: No value appears more than once, so there is no mode.)
Range: The difference between the highest and lowest values in the data. (For the first set of data: 41-23 = 18)
B.
To find the upper and lower quartile, you need to first arrange the data in order and then divide it into four equal parts.
Lower quartile (Q1) is the median of the lower half of the data.
Upper quartile (Q3) is the median of the upper half of the data.
For the first set of data: Q1 = (23+25)/2 = 24, Q3 = (39+41)/2 = 40
7th and 50th Percentile:
To find 7th percentile, pick 7th item from ordered data set and if not possible then take the average of 6th and 8th items.
To find 50th percentile, pick the median of the data set.
For the first set of data: 7th percentile = 25, 50th percentile = 25
C.
Variance: A measure of the spread of the data. It is calculated by taking the average of the squared differences from the mean.
Coefficient of variation (CV) : A normalized measure of the spread of the data. It is the ratio of the standard deviation to the mean.
D.
Pearson coefficient of skewness: A measure of the asymmetry of the data about the mean. A positive skewness indicates that the tail on the right side of the probability density function is longer or fatter than the left side. Conversely, a negative skewness indicates that the tail on the left side is longer or fatter than the right side.
Kurtosis: A measure of the "peakedness" of the data. A high kurtosis means that the data has heavy tails (outliers) or a distinct peak near the mean, whereas a low kurtosis means that the data has light tails (no outliers) or a flat peak near the mean.
If P(E)= 0.9 and P(F) = 0.8, show that P(EF) >0.7. In general, show that
P(EF) > P(E) + P(F) - 1
Answer:
P(EF) > 0.72 and in general, P(EF) > P(E) + P(F) - 1
Step-by-step explanation:
We know that P(EF) = P(E and F) = P(E|F) * P(F) = P(F|E) * P(E) (by the definition of conditional probability).
For the specific case given, P(E)= 0.9 and P(F) = 0.8,
P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > P(E) * P(F) = 0.72
In general,
P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > min(P(E|F) * P(F), P(F|E) * P(E) ) = P(E) * P(F)
P(EF) > P(E) * P(F) = P(E) + P(F) - 1
This is because P(E|F) and P(F|E) are always less or equal to 1.
4. The thickness of a textbook is b mm. Write the expression for each of the following:
The thickness of 5 stacked textbooks?
The thickness of each page, if the pages are numbered to 225?
When the thickness of a textbook is b mm the expressions for:
thickness of 5 stacked textbooks = 5b mm
thickness of each page, if the pages are numbered to 225 = b / 225
How to write the expressions for each conditionThe thickness for each of the condition is written as follows
For the thickness of 5 stacked textbooks
= b + b + b + b + b
= 5b
For thickness of each page, if the pages are numbered to 225
In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book
= b / 225
Learn more about division at:
https://brainly.com/question/941863
#SPJ1
Find general solution. Show steps of derivation. Check your answer by substitution.
y´=sec^2(y)
So on solving the provided question we cans ay that trigonometry y =sec^2(y); y = 1/[tex]\sqrt{2}[/tex]
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
y´=sec^2(y)
here, y = 90
y = sec^2(90)
y = 1/[tex]\sqrt{2}[/tex]
To know more about trigonometry visit:
https://brainly.com/question/29002217
#SPJ1
2+2=4 right…………………………….
Answer: yes, it is
Step-by-step explanation:
Answer:4
Step-by-step explanation:
When given a set of cards laying face down that spell P, E, R, C, E, N, T, S, determine the probability of randomly drawing a vowel.
A. two eighths
B. six eighths
C. two sevenths
D. six sevenths
Probability is a metric used to express the possibility or chance that a particular event will occur. Two eighths of a vowel will be drawn at random. Option A is correct.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The formula for calculating probability is expressed as:
Probability = expected/total outcome
If the given a set of cards laying face down that spell P, E, R, C, E, N, T, S, then the total outcome is:
n(S) =8
If a vowel is selected randomly, hence the expected outcome is;
E = {E, E}
n(E) = 2
P(vowel) = 2/8
Hence the probability of randomly drawing a vowel is two eighths
Learn more on probability here: https://brainly.com/question/10558496
#SPJ1
Answer: A: 2/8 (Two Eighths)
Step-by-step explanation:
Select the correct answer. What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)? A. y = 3 B. x = 3 C. x = 5 D. y = -5
Answer:
Choice B: x = 3
Step-by-step explanation:
The standard equation of a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]
where
(h, k) is the vertex and |p| is the focal length
The given equation is
[tex](y - 3)^2 = 8(x - 5)[/tex]
Convert this to standard form and compare with general equation
Switch the sides of the equationAnswer: Choice B: x = 3
There is a 60% chance for snow over the next three days. Find the probability that it snows all three days
Answer:
21.6%
Step-by-step explanation:
Each day is independent, so the probability of snow all three days is:
(0.60)³ = 0.216
There is a 21.6% chance that it snows all three days.
What is the slope of the line that passes through the points (3,8) and (-2,13)?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]
Answer:
[tex]\boxed{\bf Slope(m):-1}[/tex]
Step-by-step explanation:
We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).
The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.
[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]
[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]
[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]
[tex]\bf m=-\cfrac{5}{5}[/tex]
[tex]\bf m=-1[/tex]
Therefore, the slope is -1.
__________________
Hope this helps!
Have a great day!
4. Solve the triangle using either Law of Cosines or Law of Sines. In △DEF, f=25, e=8 and m∠F=131°.
AngleD= AngleE= Angle d=
Round your final answer to the nearest tenth. **
Using cosine law and sine law, the value of angle E and D are 14° and 35° and the length of side d is 19 units
What is Law of CosineThe law of cosines is a mathematical formula used to calculate the measure of a third side of a triangle when two sides and the angle between them are known. It is also used to calculate the angles of a triangle when all three sides are known. The formula is: c² = a² + b² - 2ab cos(C).
In this given problem, triangle DEF can be;
f² = e² + d² - 2(e)(d) cos(F)
But we don't know the length of side d
Using sine law
f / sin F = e / sin E
25 / sin 131 = 8 / sin E
sin E = 8 * sin 131 / 25
E = 13.97°
E = 14°
Using sum of angles in a triangle
D + E + F = 180°
D = 180 - (14 + 131)
D = 180 - 145
D = 35°
Using cosine law;
d² = e² + f² - 2(e)(f)cos(D)
Substituting the values into the formula;
d² = 8² + 25² - 2(8)(25)cos(35)
d = 19
Learn more on cosine law here;
https://brainly.com/question/4372174
#SPJ1
Danny takes a rectangular piece of fabric and cuts from one corner to the opposite corner. If
the piece of fabric is 9 centimeters long and 12 centimeters wide, how long is the diagonal
cut that Danny made?
Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.
The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)
So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm
Therefore, the diagonal cut that Danny made is 15 centimeters long.
Step-by-step explanation:
fully factor (x^2 + 4)(x -3)
Answer: x³ - 3x² + 4x - 12
Step-by-step explanation:
Using FOIL:
x³ - 3x² + 4x - 12
Answer:
x=1
Step-by-step explanation:
(x^2+4)(x-3)
"x^2=x*x=x"
(x+4)(x-3)
x+1
x/x/
x=1
