DEFINITIONS AND FORMULAS
The equation of a linear graph is given to be:
\(y=mx+b\)where m is the slope of the graph and b is the y-intercept.
To calculate the slope given a table, we can use the formula:
\(m=\frac{y_2-y_1}{x_2-x_1}\)SOLUTION
Function 1: The equation of the graph is given to be
\(p=-\frac{3}{2}r-5\)Therefore, the y-intercept of the graph is given to be:
\(b=-5\)Function 2: Recall that the y-intercept of a graph is the y-value when x = 0.
On checking the graph, we can see that when r = 0, p = -5.
Therefore, the y-intercept is:
\(b=-5\)ANSWER
The functions have the same y-intercept.
OPTION C is correct.
1. (-3+ -5)(9+ 16)=
_____________
-10
2. (14 + -32) + (-20 + 14) =
___________________
-4
Answer:1. -210 2. -24
Step-by-step explanation:
Summerfield is 6 miles due north of the airport, and Castroville is 8 miles due east of the airport. How far apart are Summerfield and Castroville?
Answer:
10 miles
Step-by-step explanation:
Right triangle
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
Sqrt 100 = c
C = 10
Will someone help me with this basic geometry?
The value of x in the right angle placed is equal to 16
Right AnglesA right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life. It can be seen in the corners of a room, the edges of boxes, the screen of a mobile phone, and so on. The sides of a square and a rectangle always form a right angle with each other. In radians, it is represented as π/2. Let us discuss more about a right angle in this article.
A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.
In the given question, we can set an equation and find the value of x
90 = 26 + 4x
Lets solve for x
4x = 90 -26
4x = 64
x = 16
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A square has a a side lenght of 5 feet what is its area?
Answer:
25 sq feet
Step-by-step explanation:
Length = 5 feet
Area = (Length)²
= 5²
= 25 sq feet
whatt is the equation of the line that passes through the points (-3,-3) and (3,1)
Answer:
\( m=\frac{y_2 -y_1}{x_2 -x_1}\)
And replacing we got:
\( m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}\)
And we can use one of the points in order to find the intercept like this:
\( -3= \frac{2}{3} (-3) +b\)
\( b =-3 +2=-1\)
And the equation would be given by:
\( y= \frac{2}{3}x -1\)
Step-by-step explanation:
We want an equation given by:
\( y=mx+b\)
where m i the slope and b the intercept
We have the following two points given:
\( (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)\)
We can find the slope with this formula:
\( m=\frac{y_2 -y_1}{x_2 -x_1}\)
And replacing we got:
\( m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}\)
And we can use one of the points in order to find the intercept like this:
\( -3= \frac{2}{3} (-3) +b\)
\( b =-3 +2=-1\)
And the equation would be given by:
\( y= \frac{2}{3}x -1\)
Which similarity statement is true for rectangles JKLM and PQRS, given that JK=6, JM=5, QR=15, and PQ=12.5? A. rectangle JKLM ~ rectangle PQRS B. rectangle JKLM ~ rectangle QRSP C. rectangle JKLM ~ rectangle RQPS D.rectangle JKLM~ rectangle SRQP
Answer:
B: rectangle JKLM ~ rectangle QRSP
Step-by-step explanation:
5/6=0.83
12.5=0.83
JK corresponds to QR
JM corresponds to PQ
rectangle JKLM ~ rectangle QRSP
Help question 3 thanks
Answer:
C. 115.2
Step-by-step explanation:
First, divide what you know, 4,000 seeds by 8 lbs. This gives us 500. From here, divide the 57,600 by 500 to get 115.2 :) hope this helps lmk if you need clarification
Based on the equation 6x + 2y = 30, what is the missing value in the table?
Х
у
?
0
3
5
15
30
Answer:
6(5) + 2(0) = 30
the equal sign is missing
Step-by-step explanation:
6 times 5 is 30 + 2 times 0 is 0 = 30
Answer: 5
Step-by-step explanation: On Edgenuity!!!!!!!!!!!!!!
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
3(7/5x + 4) - 2(3/2 - 5/4x)
Problem
3(7/5x + 4) - 2(3/2 - 5/4x)
Solution
For this case we can start distributing the terms and we got:
3*(7/5x) + 3*4 - 2*(3/2) + 2*(5/4 x)
And if we simplify we got:
21/5x +12 -3 + 10/4x
Now we can aggrupate the terms and we got:
(21/5 +10/4) x + (12-3)
67/10 x + 9
Each of the following functions f,g,h, and h represents the amount of money in a bank account in dollars as a function of time x, in years they are each written in form m(x)= a•b
Answer:
f(x) : exponential growth
g(x); exponential growth
h(x): exponential growth
j(x): exponential decay
Step-by-step explanation:
In an exponential function such as
\(m(x) = a \cdot b^x\)
the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative
If b > 1, it is a growth function
If b < 1 then it is a decay function
If b = 1 neither growth or decay function values are constant
In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function
Answer:
O f(x) : exponential growth
O g(x); exponential growth
O h(x): exponential growth
O j(x): exponential decay
Step-by-step explanation: I used to do this before :)
Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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The diameter of a quarter is about 1 in.
You trace around the edge of the quarter on a sheet of paper.
What is the area of the circle on the paper?
Use 3.14 as an approximation for π. Round your answer to the nearest tenth.
Answer: The area is going to be 0.8
Step-by-step explanation: The diameter is 1
You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.
After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14
3.14(0.5)^2= 0.785
you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.
So, the Area is 0.785 but after rounding it is 0.8.
Hope that helped :)
A bag is filled with an equal number of red, yellow, green, blue, and purple socks. The theoretical probability of a child drawing 2 yellow socks from the bag with replacement is one fifth. If the experiment is repeated 175 times, what is a reasonable prediction of the number of times he will select 2 yellow socks?
one fifth
10
25
35
35 is a reasonable prediction of the number of times he will select 2 yellow socks?
what is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
What is event?In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.
In the given question,
The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:
P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25
So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.
To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:
E(X) = n * p
where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.
In this case, n = 175 and p = 1/25. So,
E(X) = 175 * (1/25) = 7
Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.
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Decide whether the rates are equivalent. Maria saves $50 in 4 months.
Ralph saves $60 in 5 months
Answer:
The rates are not equivalent since Maria saves $0.50 more per month than Ralph.
Step-by-step explanation:
We can determine if two rates are equivalent by comparing the rates at which they save per month.
Maria's savings per month:
Both 50 and 4 can be divided by 2, which gives us 25/2. As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.
Ralph's savings per month:
Both 60 and 5 can be divided by 5, which gives us 12. Thus, Ralph saves $12 per month.
Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.
Determine whether 548 is greater than or less than 373. Then write the expression showing this using < or >.
Answer:
548 > 373
Step-by-step explanation:
548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.
The ">" symbol is used to represent "greater than" in mathematical comparisons.
Hope this helps!
A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $184. Determine the total number of CDs and videos sold.
Answer:
28 CD and 12 Video
Step-by-step explanation:
6 (x) + 4 (y) = 184
6 (28) + 4 (12) =184
168 + 48 = 184
What is the slope of a line that contains the points (-6 , 1) and (4 , -4)?
Answer:
-1/2
Step-by-step explanation:
For this question we use the slope formula: \(m = (y_{1} - y_{2})/(x_{1}-x_{2})\)
chug and plug: m = (1 - (-4))/(-6-4)
m = -0.5 or \(-\frac{1}{2}\)
The slope of a straight line passing through the points (-6 , 1) and (4 , -4) is -1/2.
What is Slope of a straight line?The slope of a straight line measures the rate of change of variable 'y' with respect to independent variable 'x'. Mathematically -
m = (y₂ - y₁)/(x₂ - x₁)
Given is a line that passes through the points (-6 , 1) and (4 , -4).
The slope of a straight line passing through two points is given by -
m = (y₂ - y₁)/(x₂ - x₁)
The coordinates given are (-6 , 1) and (4 , -4).
Substituting them in the formula, we get -
m = (- 4 - 1)/(4 + 6)
m = (- 5)/(10)
m = -1/2
m = -1/2
Therefore, the slope of a straight line passing through the Points (-6 , 1) and (4 , -4) is -1/2.
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The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
Help plz:)))I’ll mark u Brainliest
Answer:
18 foot ladder will reach at 14.4 feet up the wall.
Step-by-step explanation:
Triangles formed by the ladder against wall and the ground are similar,
ΔABC ~ ΔDEC
Therefore, their corresponding sides will be proportional.
\(\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}\)
\(\frac{AB}{DE}= \frac{BC}{EC}\)
\(\frac{18}{10}=\frac{BC}{8}\)
BC = \(\frac{18\times 8}{10}\)
= 14.4
Therefore, 18 foot ladder will reach at 14.4 feet up the wall.
Can you please help me
Answer:
first graph
Step-by-step explanation:
x > n
the graph will have an open circle at the value n , indicating that x cannot equal n ( note solid circle if x ≥ n )
the arrow from n will point in the right direction, indicating values of x greater than n.
the graph representing x > n is the first graph
It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end. How long will it take you to read 6.25 pages and also take the test?
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.
The number of minutes to read 6.25 pages will be given as,
⇒ 6.25 x 0.8
⇒ 5 minutes
The number of minutes to take the test will be given as,
⇒ 5.5 - 5
⇒ 0.50 minute
⇒ 0.50 x 60
⇒ 30 seconds
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
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multiply [4, 0, -1, 2, -3, -1]x[0, 1, -3, 1]
Please Help...
Multiplication of the given matrix is not possible by definition of matrix multiplication.
Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Expression for multiply,
⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]
Since, We can see that;
First matrix have order 1 x 6
And, Second matrix have order 1 x 4
We know that;
Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.
Hence, By given matrices we get;
Number of column in first matrix (6) ≠ number of rows in second matrix (1)
So, Multiplication of the given matrix is not possible by definition of matrix multiplication.
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An election ballot asks voters to select four city commissioners from a group of
twelve candidates. In how many ways can this be done?
Answer:
Step-by-step explanation:
C(16, 4) = 1820 ways
16
C
4 = (16x15x14x13) / (4x3x2x1)
This Venn diagram shows the pizza topping preferences for 9 students. LIKES LIKES PEPPERONI OLIVES Joe Kalie Petal Noah Owen Let event A = Student likes pepperoni. Let event B = Student likes olives. What elements are in A and B? OA. (Maria, Zack, Bo} B. (Petal, Owen, Julia) C. (Joe, Kalie, Noah, Maria, Zack, Bo, Julia} OD. (Petal, Owen) Maria... Zack Bo Julia
The elements that are in A and B in the Venn diagram that represents the pizza topping preferences are (Maria, Zack, Bo).
What elements are in A and B?
A venn diagram represents information in a set using circles. The intersection of both circles represents those that like both pepperoni and olives. This is element A and B.
The names at the intersection of both circles are (Maria, Zack, Bo).
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Antoinette buys 6 pounds of
tangerines. She pays with a $10 bill.
How much did she spend?
Answer:
10 = 6 pounds
1.67 = 1 pound
Step-by-step explanation:
Answer:
$1.67
Step-by-step explanation:
Hope its correct have a great day!
will mark brainliest if the answer is correct
Answer:
Kennedy will earn 21.7 dollars per hour.
A geometric sequence has only positive terms. The third term is 100 and the eighth term is 3.125.
Find the common ratio.
The common ratio of a geometric sequence will be;
⇒ r = 5 / 10
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
In a geometric sequence,
The third term is 100 and the eighth term is 3.125.
Now,
We know that;
The nth term of geometric sequence is,
⇒ \(T_{n} = a r^{n - 1}\)
Hence, The third term is;
⇒ \(T_{3} = a r^{3 - 1} = 100\)
⇒ \(a r^{2} = 100\) ..(i)
And, The eighth term is,
⇒ \(T_{8} = a r^{8 - 1} = 3.125\)
⇒ \(a r^{7} = 3.125\) ..(ii)
Divide equation (ii) by (i), we get;
⇒ ar⁷ / ar² = 3.125/100
⇒ r⁷ / r² = 3125 / 100000
⇒ r⁷⁻² = 3125 / 100000
⇒ r⁵ = 3125 / 100000
⇒ r = 5/10
Thus, The common ratio of a geometric sequence will be;
⇒ r = 5 / 10
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Bryson's cat had six kittens this summer. Each kitten weighs 5 1/3 ounces. How much did all the kittens weigh together?
Each kitten weighs 5 1/3 ounces. Converting this weight to improper fraction, it becomes
16/3 ounces
Since the total number of kittens is 6, the weight of all the kittens is
16/3 * 6 = 32 ounces
The total weight is 32 ounces
Someone please please help ASAP.