to graph the line we first need to get its equation. The equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]Then, we have:
[tex]\begin{gathered} y-(-6)=\frac{1}{2}(x-3) \\ y+6=\frac{1}{2}x-\frac{3}{2} \\ y=\frac{1}{2}x-\frac{3}{2}-6 \\ y=\frac{1}{2}x-\frac{15}{2} \end{gathered}[/tex]Once we have the equation we can find another point on the line. If x=1 then y=-7, hence we have the point (1,-7).
Now we graph the points (1,-7) and (3,-6) and jo
shshshdggdgdgdggddgegegegegegs
We need to solve the following equation by completing the square:
[tex]x^2-4x-9=0[/tex]we first pass the 9 to sum in the right side
[tex]x^2-4x=9[/tex]now we add 4 in both sides of the equation, because (4/2)^2=4, obtaining
[tex]x^2-4x+4=9+4[/tex]simplifying
[tex](x-2)^2=13[/tex]then
[tex](x-2)=\pm\sqrt[]{13}[/tex]adding 2 in both sides of the equation we have that the solution is:
[tex]x=2\pm\sqrt[]{13}[/tex]For a standard normal distribution, find:P(Z > c) = 0.7051Find C rounded to four decimal places.
Answer:
Explanation:
The given expression is
P(Z > c) = 0.7051
P(Z > c) = 1 - P(Z < c)
1 - P(Z < c) = 1 - 0.7051 = 0.2949
From the normal distribution table, the z score for a probability value of
Identify the function in which y varies directly with x.
Let the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
As per the question statement, We are supposed to write any function in which "y" varies directly with "x" i.e., y ∝ x
Let's say y = kx be the function where "k" is the proportionality constant and y ∝ x.
Now let x = 3 and y = 6, so 6 = k*3
or k = 3
Hence for any value of "x" value of "y" would be k times the value of x and this is called the direct proportion relationship.
Hence, the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
Function: An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable).Proportionality constant: The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant ratio is another term for the constant of proportionality.To learn more about function and proportionality constant, click on the link given below:
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Find the equation of a line perpendicular to y= 1/2x+1that passes through the point (6,-2).
hurry brainiest! if right
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Answer:
square root of 2, 3, square root of 11
Step-by-step explanation:
The formula a = m – n represents the actual cost, a, of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon.
The formula for amount of the coupon is given by n = m - a.
This question can be solved using simple Linear equation. A linear equation may be defined as an expression which can be written in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. According to question we have a formula a = m - n where a is the actual cost, m is original price and n is coupon discount. The actual cost of an item will depend on the coupon discount as well as the original cost of the item. To find the coupon amount from the formula we rearrange the equation as
a = m - n
a - m = -n
=> n = m - a which will be the required formula.
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A bacteria population is modeling by b(t) = 10e^5t million bacteria after t days. how fast is the population growing after 3 days?
The population of this bacteria is growing at the rate of 10.897 trillion per day.
What is the growth rate?The growth rate refers to the change from one period to another.
It also refers to the average growth per day, especially in the case of bacteria.
Bacteria population = b(t) = 10e^5t million
The number of days, t = 3
e = 2.71828
10e^5t million = 10 x 2.71828^5x3 million
= 10 x 2.71828^15 million
= 10 x 3268984.38894 million
= 32,689,843,889,400
Growth per day = 10.897 trillion
Thus, we can conclude that the bacteria is increasing at the growth rate of 10.897 trillion per day.
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At a fruit stand , apples sell for $ 1.20 per pound . One week , the stand sold $600 worth of apples and pears . The equation below describes the situation , where A is the number of pounds of apples and P is the number of pounds of pears . 0.8a + 1.2p = 600 Which graph represents the equation?
we can calculate two points in order to know what graph corresponds to the equation
when a=0
1.2p=600
p=600/1.2
p=500
the point is (0,500) red point
when b=0
0.8a=600
a=600/0.8
a=750
the point is (750,0) green point
the answer is B
What step is needed when constructing a circle inscribed in a triangle?
Given:
Construct a circle inscribed in a triangle.
To find:
The needed step to construct.
Explanation:
The first step should be,
Construct an angle bisector from any two angles of the triangle. Mark the intersecting point as the centre of circle C.
The second step should be,
From point C, construct a perpendicular line to meet at any one side of the triangle and mark it as Y.
The third step should be,
Measure the length of CY. Use a compass to draw a circle in the triangle by using the length of CY.
So, the correct answer is,
Construct the angle bisectors of each angle in the triangle.
Final answer:
Construct the angle bisectors of each angle in the triangle.
Lena sells earrings from a booth at the arts fair. She pays $200 to rent the booth.She makes $5 from each pair of earrings she sells. Her profit, P, can be foundusing the following equation, where n is the number of pairs of earrings sold.P = 5n – 200How many pairs of earrings must Lena sell to earn a profit of $450?1- 1402- 1303- 1004- 150
P = 5n - 200
where
P: profit
n: number of pairs of earrings sold.
To find how many pairs of earrings must Lena sell to earn a profit of $450, we have to replace P = 450 into the equation and solve for n, as follows:
450 = 5n - 200
200 is subtracting on the right, then it will add on the left
450 + 200 = 5n
650 = 5n
5 is multiplying on the right, then it will divide on the left
650/5 = n
130 = n
Lena must sell 130 pairs of earrings to earn a profit of $450.
PLEASE THIS IS DUE IN AN HOUR PLEASE HELP ME PLEASE :(
The expression is:
f(-2) = 23, f(3) = 5, f(4) = 5, f(6) = 5, f(9) = -3
The function is
f(x) = 5x² + 3 x< 3
= 5 3≤x ≤ 6
= 6-x x>6
a) f(-2) for x<3
So we have 5x² + 3
5(-2)² + 3
= 5 × 4 + 3
= 20 + 3
= 23
b) f(3)
as the range is 3≤ x ≤6
for which we have a value 5
So f(3) = 5
c) f(4)
As the range is 3≤ x ≤ 6 for which the value is 5.
So f(3) = 5
d) f(6)
As the range is 3≤ x ≤ 6
So the value is 5
f(6) = 5
e) f(9)
The range is x>6 for this we have 6-x
So 6-x
= 6 - 9
= -3
Therefore the value of the function is f(-2) = 23, f(3) = 5, f(4) = 5, f(6) = 5 and f(9) = -3.
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the 7th grade fundraiser gives away a large container of gumballs to the student who is closest to guessing the correct number of gumballs in the container noticing that the container is a cube. Sally decides to count the number of gumballs along the length of one side if Sally get 729 gumballs how many gumballs did she count along one side of the container
If the container is a cube, every side is a square, so the length and the width are the same.
To get the number of gumballs based on the number of gumballs in one side, we can use the following equation
[tex]TotalGumballs=x^3[/tex]Where x is the number of gumballs along one side. So, replacing the total by 729 and solving for x, we get:
[tex]\begin{gathered} 729=x^3 \\ \sqrt[3]{729}=x \\ 9=x \end{gathered}[/tex]Answer: She counts 9 gumballs along one side of the container
Angelina can type 150 words in 5 minutes. At this rate, how many words can she type in 1 minute?
Answer:
30 words per minute
Step-by-step explanation:
Answer:
30 words
Step-by-step explanation:
her typing speed is 150 words for 5 minutes.
Since we know that she can type 5 times as much in 5 minutes than in 1 minute, we know that 150 words is 5 times as much as she would be able to type in 1 minute. The question that should be asked is "5 times what would equal 150?" The answer would be 30 words.
Shorter answer: 150 words / 5 minutes = 30 words/minute
which graph represents the equation 2 x + y =2?
start by writing the equation in the slope-intercept form
[tex]\begin{gathered} 2x+y=2 \\ y=-2x+2 \end{gathered}[/tex]this meand that the line has a slope of -2 and cuts the y-axis over 2.
the graph should look like this
Question 14<>The table summarizes results from 981 pedestrian deaths that were caused by automobileaccidents.Pedestrian DeathsDriver Pedestrian Intoxicated?Intoxicated?NoYesYes5584No248594If one of the pedestrian deaths is randomly selected, find the probability that the driver was notintoxicated but the pedestrian was. Please enter a decimal to 4 places.Calculator
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
If one of the pedestrian deaths is randomly selected.
Find the probability that the driver was not intoxicated but the pedestrians were.
We are expected to enter 4 decimal places.
Now, from the table, we can see clearly that:
[tex]\begin{gathered} \text{Probability ( the driver was not intox}icated\text{ but the pedestrians were)} \\ =\text{ }\frac{248}{981} \\ =\text{ 0.2528 ( 4 decimal places)} \end{gathered}[/tex]CONCLUSION:
The final answer is 0. 2528 ( 4 decimal places).
In AEFG, the measure of ZG=90°, the measure of ZE=26°, and GE = 4.6 feet. Find the length of FG to the nearest tenth of a foot.
Using the tangent identity:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent_{}} \\ so\colon \\ \tan (30)=\frac{8.1}{x} \\ x=\frac{8.1}{\tan (30)} \\ x=14.0ft \end{gathered}[/tex]y varies jointly as a and b , and inversely as the square root of c. y=54 , a = 3 , b=9 , and c=25. Find y when a=5 , b=6 , c=36
When a=5 , b=6 , c=36, the value of y will be 50.
Here, we are given that y varies jointly as a and b and inversely as the square root of c.
⇒ y ∝ ab/[tex]\sqrt{c}[/tex]
Let k be a constant, then we can say that-
y = kab/[tex]\sqrt{c}[/tex]
We are given that y = 54 , a = 3 , b = 9 , and c = 25.
substituting these values in the above equation, we can calculate the value of k as follows-
54 = (k*3*9)/[tex]\sqrt{25}[/tex]
54 = 27k/5
54*5 = 27k
270 = 27k
27k = 270
k = 270/27
k = 10
Now, when a=5 , b=6 , c=36, the value of y will be-
y = (10*5*6)/[tex]\sqrt{36}[/tex]
y = 300/6
y = 50
Thus, when a=5 , b=6 , c=36, the value of y will be 50.
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Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)^x
,when x represents how many years she has saved.
Xavier is also saving college. His account is modeled by this table:
X g(x)
0 200
1 270
2 364.5
3 492.08
1. After 3 years, how much does Lisa's account have in it? (Round to the hundredths
decimal place.)
2.After 3 years, how much does Xavier’s account have in it?
3.What is the positive difference in their accounts after 3 years?
Using exponential functions, it is found that:
a) Lisa's account has $489 after 3 years.
b) Xavier's account has $493 after 3 years.
c) The difference is of $4.
An exponential function is what, exactly?According to the following principle, an exponential function is modelled where the following description of the parameters is given:
The value of the function at x = 0 is known as its initial value, or a.The function's rate of change is denoted by bLisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200
b = 270/200
= 1.35
g(x) = 200 × [tex]1.35^{x}[/tex]
In 3 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa = f(3)
= 250 (1.25)³
= 489$
Xavier = f(3)
= 200 (1.35)³
= 493$
The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
493 - 489 = 4$
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Deductive Reasoning / 5913. Copy and complete the proof of Theorem 2-6: If the exterior sides of twoadjacent acute angles are perpendicular, then the angles are complementary.Given: OAI OGProve: Z AOB and 2 BOC are comp. 4.BProof:Statements0Reasons1?1. OA 1 OC2. m ZAOC = 903. m ZAOB + m2 BOC = m 2 AOC4.25. 22. Def. of 1 lines3. 24. Substitution Prop.5. Def. of comp. 4
Reasons
1. Given
3. Angle addition postulate
Statements
4.
[tex]m\angle\text{AOB}+m\angle\text{BOC}=90º[/tex]5.
[tex]\angle\text{AOB and}\angle\text{BOC are complementary}[/tex]State whether the following statement is true or false.Matrices of different orders can sometimes be multiplied.Choose the correct answer below.FalseTrue
ANSWER
True
EXPLANATION
We want to verify if matrices of different orders can sometimes be multiplied.
The order of a matrix refers to the configuration of the rows and columns of the matrix.
For matrix multiplication to occur, the dimensions of the matrices must be compatible. In other words, the number of columns inn the first matrix must be the same as the number of rows in the second matrix.
This is not affected by the number of rows in the first matrix or the number of columns in the second matrix.
Hence, under the right condition, matrices of different orders can sometimes be multiplied.
The answer is True.
Which of the following investments will earn the smallest amount of interest?
Part a: will earn the smallest amount of interest at 321.2 when 8030 is invested for 2 years at 2%
We will use the formula for all the parts:
Simple interest is interest that is simply charged on the principal amount, which is the original amount borrowed or deposited. The interest charge will only be applied once, regardless of how frequently it is applied.
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Part a:
Simple interest = 8030*2*2/100
= 321.2
Part b:
Simple interest = 1901*8*4/100
= 608.32
Part c:
Simple interest = 5330*6*2/100
= 639.6
Part d:
Simple interest = 3970*6*4/100
= 952.8
Although a part of your question is missing, you might refer to this full question: Which of the following investments will earn the smallest amount of interest? a. $8,030, invested for 2 years at 2.0% interest b. $1,901, invested for 8 years at 4.0% interest c. $5,330, invested for 6 years at 2.0% interest d. $3,970, invested for 6 years at 4.0% interest
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Write and solve a direct variation equation to find the answer
Direct Variation
If y varies directly with x, then they are related by the equation:
y = kx
Where k is a constant called the proportionality factor.
It's given that y = -38 when x = 19. Substituting those values in the equation, we can find the value of k:
-38 = k*19
Dividing by 19:
k = -38 / 19
k = -2
Now our model is complete:
y = -2x
Now it's required to find the value of x when y = -4. Substituting:
-4 = -2x
Dividing by -2:
x = -4 / (-2)
x = 2
Two different floor plans are being offered in a new housing
We kwot that the probability of an union of eventes (that can be written with the "or" sentence) is given by:
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]where X and Y are the events.
In this case, let X be the event "The buyer preferred Plan A" and let Y be the event "The buyer is in the 40 to 49 year old age group). We know that the probability is given by:
[tex]P=\frac{\text{number of favorable outcomes}}{\text{ number of possible outcomes}}[/tex]Adding all the values in the table we have that the total number of possible outcomes is 68.
For event X, we have a total of 38 favorable outcomes; hence its probability is:
[tex]P(X)=\frac{38}{68}[/tex]For event Y, we have a total of 24 favorable outcomes, hence its probabiliy is:
[tex]P(Y)=\frac{24}{68}[/tex]From the table we notice that 16 buyers preferred plan A and are in the 40 to 49 year old age group. This means that the probability of the intersection of the events is:
[tex]P(X\cap Y)=\frac{16}{68}[/tex]Plugging our probabilities in the formula for the union we have:
[tex]\begin{gathered} P(X\cup Y)=\frac{38}{68}+\frac{24}{68}-\frac{16}{68} \\ P(X\cup Y)=\frac{46}{68} \\ P(X\cup Y)=0.676 \end{gathered}[/tex]Therefore, the probability we are looking for is 0.676
factored from of polynomial need answer fast.(im sorry henry im very confused )
We have:
[tex]5p^3-10p^2+3p-6[/tex]We factor as follows:
[tex]p(5p^2-10p+3)-6[/tex][tex]\Rightarrow p(-\frac{1}{5}(-5x+\sqrt[]{10}+5)(5x+\sqrt[]{10}-5)-6[/tex]Divide monomials ( -18p^4 q^7) (-6p^3 q^8) / -36p^12 q^10
Given:
[tex]\frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}[/tex]We will use the following rules of the exponents:
[tex]\begin{gathered} \frac{a^m}{a^n}=a^{m-n} \\ a^m\cdot a^n=a^{m+n} \end{gathered}[/tex]So, the given expression will be as follows:
[tex]\begin{gathered} \frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}=(\frac{-18\cdot-6}{-36})\cdot p^{4+3-12}\cdot q^{7+8-10} \\ \\ =(-3)\cdot p^{-5}\cdot q^5 \\ \\ =\frac{-3q^5}{p^5} \end{gathered}[/tex]so, the answer will be:
[tex]\frac{-3q^5}{p^5}[/tex]What are the x and y-intercepts of the line described by the equation?
-6x+3y=18.9
Answer:
Y=6.3 and X=-3.15
Step-by-step explanation:
Plug in 0 for x and y in separate equations
-6(0)+3y=18.9
3y=18.9
3/3y=18.9/3
y+6.3
-6x+3(0)=18.9
-6x+18.9
-6/-6x+18.9/-6
x=-3.15
i need help with this question it’s for a test. i’m doing summer school to help me prepare for college.
Ok, so
We got these triangles:
We know that two triangles are similar if there's a ratio between their sides.
So, if we compare,
We got this ratio:
As you can notice, if we relation side by side, the ratio is the same. So, we could say that the bigger triangle is 1.5 times the smaller one. So, they are similar.
5p + 3 = 15Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
Hello! We can see this equation as a function like f(x) = 5x + 3 = 15
Let's think about a problem...
For example, we have a taxi that charges $5 per kilometer + a flat fee of $3.
So, we can write it as a function:
f(x) = 5x + 3
Look that x = kilometers, so this value will grow according to the amount, right?
Knowing that, let's go back to your equation, but thinking in the taxi:
5p + 3 = 15
We can say that the final price of this race was $15, but we don't know how many kilometers were covered. So, we can solve this equation and find the value of p (kilometers). Let's do it?
5p + 3 = 15
5p = 15 - 3
5p = 12
p = 12/5
p = 2.40
Now, we know that the taxi covered 2.4 km charging a fee of r$ 5 per kilometer.
How many weeks can Shanika withdraw money from her account
Step 1
Given;
[tex]\begin{gathered} Money\text{ in her account \$500} \\ Money\text{ that will be left is \$200} \\ She\text{ withdraws \$25 weekly} \end{gathered}[/tex]Hence the equation from the question will be;
[tex]\begin{gathered} 500-25x=200 \\ where\text{ x= number of weeks} \end{gathered}[/tex][tex]\begin{gathered} 500-200=25x \\ 300=25x \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]Hence, the answer will be;
[tex]12\text{ or less weeks}[/tex]A rocket is launched straight up and it takes 83 seconds to hit the ground. How long did it take the rocket to get to the top of its path?
It would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
Given that the time that rocket took to hit the ground is 83 seconds.
We are required to find the time that it took the rocket to get to the top of its path.
Suppose the height from the ground is h.
To cover the distance of 2h it would take 83 seconds.
We know that speed=Distance/time
Speed=2h/83
So, to cover the distance of h, the time will be :
Time=Distance/Speed
=h/2h/83
=(h*83)/2h
=83/2
=41.5
Hence it would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
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