By solving a system of equations we can see that the quadratic equation is:
y = x^2 + 3x + 10
How to write a quadratic equation that passes through the given points?
A general quadratic equation is given by:
y = a*x^2 + b*x + c
We want this quadratic equation to pase through the points (-2, 8), (1, 14), and (0, 10).
using the last point, we know that when x = 0, we must have y = 10, then:
10 = a*0^2 + b*0 + c
10 = c
So our quadratic equation is:
y = a*x^2 + b*x + 10
Now we use the other two points to write a system of equations:
8 = a*(-2)^2 + b*(-2) + 10
14 = a*(1)^2 + b*1 + 10
If we simplify these, we get:
-2 = 4*a - 2b
4 = a + b
Isolating a in the second equation we get:
a = 4 - b
Now we replace that in the other equation:
-2 = 4*(4 - b) - 2b
-2 = 16 - 4b -2b
-2 - 16 = -6b
-18/-6 = b = 3
Now that we know the value of b, we replace it in the equation for a:
a = 4 - b = 4 - 3 = 1
Then the quadratic equation is:
y = x^2 + 3x + 10
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I forgot how to do these, and i don’t remember whether they have two answers or not.
Solve for d.
-7| d - 1 | = -11
Answer:
=18/7
=−4/7
Step-by-step explanation:
Divide both sides by -7
−7|−1|=−11
The negatives are canceled.
Simplify
|−1|=11/7
Split the problem into two cases: one positive and one negative
=18/7
=−4/7
A 138 inch pipe is cut into two pieces one piece is two times the length of the other. What is the lenfth of the shorter pipe?
Answer: 46 inches
Step-by-step explanation: the larger piece is 92 inches 92+46=138
Identify each sequence as arithmetic, geometric, or neither. Then find the next two terms. 45,90,180,360, .............
45,90,180,360, .... is a geometric sequence. The next two terms are 720, 1440.
In an arithmetic sequence, the difference between two subsequent terms is constant. This difference between two subsequent terms is usually called common difference (d), and its value is:
d = a(n) - a(n-1)
Where a(n) is the nth term and a(n-1) is the (n-1)-th term.
In a geometric sequence, the ratio (r) between two subsequent terms is constant.
r = a(n)/a(n-1)
The given sequence is: 45,90,180,360, .....
We can check that:
(90 - 45) is not equal to (180 - 90) and to (360 - 180)
So, there is no common difference in the given sequence.
Let us now check the ratio:
90/45 = 180/90 = 360/180 = 2
The ratio between two subsequent terms is constant, that is 2. Therefore, we can conclude that the given sequence is a geometric sequence with a(1) = 45 and r = 2.
In a geometric sequence, the next term is obtained by multiplying the current term by its ratio.
Hence, the next two terms are calculated as:
360 x 2 = 720
720 x 2 = 1440
or 720, 1440.
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A random survey was conducted to determine where families vacationed. The results indicated that P(B)=0.6, P(B ^M)=0.2 , and the probability that a family did not vacation at either destination is 0.1 .
b. What is the probability that a family visiting the beach will also visit the mountains?
The probability that a family to visit the beach also will travel the mountains is 0.33.
What exactly is a Venn diagram?A Venn diagram is a graph that uses circles to represent relationships between objects or finite groups of objects. Circles that intersecting share properties, but circles that do not overlap do not.
Please see the Venn diagram.
P(B) [the entire blue circle] = 0.6 is the probability of such a family vacationing there at beach.
P(B∩M) [the red/blue intersecting intersection of two circles] = 0.2 is the possibility of a family taking a vacation in both locations.
Using the property of independent event: Two events are considered independent if the incidence of one does not affect the likelihood of occurrence of the other.
As, occurrence of family visiting the beach will also visit the mountains is an independent event. Thus,
The formula for the independent event is;
P(B | M) = P(B∩M)/P(B)
P(B | M) = 0.2/0.6
P(B | M) = 0.33
Therefore, the probability of the occurrence that family visiting the beach will also visit the mountains is 0.33.
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Which of the following is NOT an example of a situation in which an employee can apply the Family and Medical Leave Act of 1993?
O During birth and care of a newborn child
After placement of an adopted or foster care child
O When caring for a great-aunt or great-uncle with a serious medical condition
O When unable to work because of a serious medical condition.
what is two and four nineths plus two thirds
Answer:
3 1/9
Change 2/3 to 6/9. Add 6/9 + 4/9 to get 10/9. Make a mixed number, 1 1/9. Add 2, 3 1/9.
1) 28/z - z/4 + 1 1/8, when z = 4
A) 7 1/8
B) 4 7/8
C) 9 1/8
D) -5 7/8
2) n+23.1/ 3n - 8n, when n = 2.1
A) -12.8
B) -8.4
C) 20.8
D) -20.8
Answer:
Step-by-step explanation:
9 + 11 = 10 so 120=69 69-5 = 13 answer is 13
f(x)=6^x and g(x)=14^x labeled on graph
f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
What do we mean by the graph?While many people use the terms "graph" and "chart" interchangeably, they are not the same thing. Charts are tables, diagrams, or pictures that clearly and concisely organize large amounts of data. Charts are used to interpret current data and make predictions. Graphs, on the other hand, concentrate on raw data and show trends over time. A graph is defined as a diagram that depicts the relationships between two or more things. A pie chart is an example of a graph. Bar graphs, circle graphs, and line graphs are the three most common types of graphs. Each type of graph is appropriate for displaying a different type of data.So, f(x)=6ˣ and g(x)=14ˣ on graph as:
Refer to the graph given below.Therefore, f(x)=6ˣ and g(x)=14ˣ on the graph are shown (refer to the graph given below).
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Need help please asap
Step-by-step explanation:
the circle standard form is
(x - h)² + (y - k)² = r²
(h, k) are the coordinates of the center of the circle.
r is the radius of the circle.
I cannot draw here, but I can describe the details.
9.
the center is therefore at (-1, 2). and the radius is 5.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (-1, 2 + 5) = (-1, 7)
down : (-1, 2 - 5) = (-1, -3)
left : (-1 - 5, 2) = (-6, 2)
right : (-1 + 5, 2) = (4, 2)
10.
the center is therefore at (3, 0). and the radius is 4.
to graph the circle mark the 4 points with radius distance up, down, left and right of the center.
up : (3, 0 + 4) = (3, 4)
down : (3, 0 - 4) = (3, -4)
left : (3 - 4, 0) = (-1, 0)
right : (3 + 4, 0) = (7, 0)
11.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
remember, this is via Pythagoras in a right-angled triangle
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
for the distance between 2 points the direct distance is the Hypotenuse, and the x and y coordinate differences are the legs.
distance² = r² = (7 - 2)² + (-1 - -1)² = 5² + 0² = 5² = 25
so, the equation is
(x - 2)² + (y + 1)² = 25
12.
we have the h, k coordinates of the center.
for the radius we need to find the distance between the center and the given point.
distance² = r² = (4 - 1)² + (6 - 2)² = 3² + 4² = 9 + 16 = 25
so, the equation is
(x - 1)² + (y - 2)² = 25
Evaluate each expression for x=-2,0,1 , and 4.
(3/5)x-2
The value for x=-2,0,1 and 4 are -16/5, -2, -2/5, 2/5 respectively.
What does solving for x means?Find the value of x that would make the equation you see true is what it means to "solve for x." Consider the following formula: x + 1 Equals 3. If you were to attempt to solve it, you would need to identify a value for x such that it yields three when one is added.
Given expression is -
(3/5)x-2
For x = -2
The value of expression will be = (3/5)(-2) - 2
= -16/5
For x = 0
The value of expression will be = (3/5)(0) - 2
= -2
For x = 1
The value of expression will be = (3/5)(1) - 2
= -2/5
For x = 4
The value of expression will be = (3/5)(4) - 2
= 2/5
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A trapezoid has a height of 12 inches, a base length of 9 inches, and an area of 150 square inches. What is the length of the other base?
The length of other base is 16 inch.
The area of trapezoid is given by the formula -
Area = 1/2×(a+b)×height, where a and b represents the two different bases. Let a be the length of 9 inches and b be the length of other base.
150 = 1/2×(9 + b)×12
Shifting 2 to Left Hand Side and performing multiplication on both sides.
150×2 = (9 + b)×12
300 = 108 + 12b
12b = 300 - 108
12b = 192
Shifting 12 to Right Hand Side of equation to find the other base
b = 192 ÷ 12
Performing division
b = 16 inch
Hence, the length of other base is 16 inch.
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Identify a pattern and find the next three numbers in the pattern. 8,16,24,32, . . .
The next three numbers are - 40, 48, 56,..
The pattern belongs to multiples of 8.
Complete pattern is - 8,16,24,32,40, 48, 56,..
What is pattern completing?Examine the pattern's initial three to four numbers. What connection exists between these numbers, you could ask. For instance, the first three to four numbers in this mathematical pattern are 1, 3, 6, and 10. As the numbers rise, it appears that you must add to obtain the subsequent number. You begin by adding 2, then 2, 3, and then 4. Therefore, if you put this on paper, you probably notice a pattern emerging.
To test whether your solution works, try the remaining pieces of the pattern that was provided.
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Out of 30 candidates applying for a post, 17 have degrees, 15 diplomas and 4 neither degree nor diploma. How many of them have both.
Answer:
the answer is 6.
Step-by-step explanation:
solution is given in the photo
hi
let's rule ot first candidate with nothing :
as they are 4 , remains : 30 -4 = 26
Now let call X number of candidate with both degrees and diplomas
we have : 17+15 -X = 26
-X = 26 - 32
-X = -6
x = 6
We have to withdraw from categorie degree and diplomas 6 people who have both and then counted twice.
So figues goes as follow :
nothing : 4
degrees only : 11
diplomas only : 9
both degree and diplomas : 6
total : 4 +11 +9 +6 = 30
HELP: Write whether the ratio demonstrates a proportional relationship
Sandra swam 8 laps in 16 minutes. George swam 18 laps in 38 minutes.
Answer:
16/8 = 2
38/18 = 2.1
But 2.1 is approximately equal to 2, hence a proportional relationship.
I need help with the problem 5/6 ÷ 3/4
Answer:
10/9 or 1 1/9
Explanation:
Multiply by the reciprocal
cancel out the greatest common factor
multiply the fractions
and you get 10/9 or 1 1/9
c. Choose two numbers other than 1 and 1 . Generate a Fibonaccilike sequence from them. Write the first ten terms of your sequence, find the sum, and divide the sum by 11. What do you notice?
The two numbers other than 1 and 1 are 2 and 3 finally get the 34 means 7 th term in the sequence.
What is Fibonacci sequence and what are the first ten terms?The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.
from the question
Let take the first term as 2.
and second term as 3.
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
The Fibonacci sequence includes the numbers 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on.
Sum=2+3+ 5 + 8 +13 + 21+
34+55+89+144 = 374 is what we get when we add up the numbers in the series.
The first ten Fibonacci numbers sum is 374.
now divided the sum by 11.
374/11 = 34.
so,to get the 34 means 7 th term in the sequence.
Hence, the two numbers other than 1 and 1 are 2 and 3. finally get the 34 means 7 th term in the sequence.
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-6x+6=4x-24
with work, if that's alr
Answer:
x = 3
Step-by-step explanation:
-6x+6-6=4x-24-6
-6x=4x-30
-6x-4x=4x-30-4x
-10x=-30
-10x/-10=-30/-10
Given two terms of each arithmetic sequence, find a₁ and d . a₄=-34.5 and a₅=-12.5
The two terms of each arithmetic sequence [tex]a_{4}[/tex] = 34.5, [tex]a_{5}[/tex] =12.5 are d = 47 and a = -106.5.
What is sequence?[tex]a_{4}[/tex] = 34.5
34.5 = a +3d.............1
[tex]a_{5}[/tex] =12.5
-12.5 = a + 4d...........2
equating equation 1 and 2
34.5 = a +3d
-12.5 = a + 4d
d = 47
d = 47 ..............3
from equation 3
a = -106.5
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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You stand on a street corner and record the gender of the first twelve people who pass by. if the city is half male and half female, what is the probability that you will record all females?
The probability is 6.
Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and one refers to an event with the highest possibility. The type of probability we will use to solve this problem is the geometric distribution.
The geometric distribution is defined as a discrete probability distribution representing the probability of consecutive failures before success in a Bernoulli trial. There could be only two possible outcomes; either True (1) or False (0).
Bernoulli's trial is an experiment in which we have only two possible outcomes, success or failure. In other words, the geometric distribution repeats Bernoulli trials until it succeeds, then stops. So, achieving success is the ultimate goal and is the point that stops Bernoulli's trials from happening further.
Geometric distribution, the class of probability distributions, is based on three key assumptions, and these assumptions are defined as:
The studies conducted are independent. Each event is independent of the other.Each attempt has only two outcomes: success or failure. If an event has any other possible outcome other than 0 and 1, it can not be classified as a Bernoulli trial.The probability of success, indicated by p, is the same for each trial.Now for our given problem, we stand on a street corner and record the gender of the first twelve people who pass by. The condition here is the city is half male and half female. Now to find the probability, we will consider the possibility of each of the twelve events. Since half of the population is Female, the probability of one single event is;
p = 1/2 (50 %)
The overall probability is the sum of all the individual probabilities:
P ( ALL FEMALE)
= 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2
= 6
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(4x^2y)(8x^5y^3 find product of monomials
The product of the monomials is 32x^7y4
What is a monomial?A monomial is said to be a product of powers of variables with a non-negative integer exponents, or a product of variables.
Monomials include numbers, variables or multiple numbers or variables multiplied together.
Given the monomials;
(4x²y)(8x^5y³)
Finding the product is simply done by multiplying the two expressions, we have
The product of the numbers = 4 × 8 = 32
The product of the 'x' variables = x^2 + 5 = x^7
The product of the 'y' variables = y^1 + 3 = y^4
32x^7y4
Thus, the product of the monomials is 32x^7y4
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Jackson asked a representative sample of 30 of his classmates about their favorite arctic animal for an upcoming science project.
Fill in the table to show reasonable predictions for the whole class.
His class has a total of 240 students.
Favorite Arctic Animal
Polar Bear 12
Reindeer 9
Seal 3
Walrus 6
Answer:
These are the estimates:
Polar Bear: 96
Reindeer: 72
Seal: 24
Walrus: 48
Step-by-step explanation:
240/30=8
Multiply the amount of people that like each animal by 8 to estimate how many out of 240 like that animal.
12*8=96
9*8=72
3*8=24
6*8=48
Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth.
C=18 in.
A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that circumference of the circle is 18 inches. Therefore, the radius and the diameter of the circle can be written as,
Circumference of circle = 2 × π × (Radius of the circle)
18 inches = 2 × π × (Radius of the circle)
(Radius of the circle) = 18 in/ (2 × π)
The radius of the circle = 2.8648 inches
Diameter of circle = 2 × (Radius of the circle)
= 2 × 2.8648 inches
= 5.7296 inches
Hence, the radius and the diameter of the circle are 2.8648 inches and 5.7296 inches, respectively.
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Find the greatest common factor of the following terms. a^8b^6,-a^6b^3
Reason:
The 'a' terms are a^8 and a^6. We go for the smallest exponent when forming the GCF. Go for the largest exponent when finding the LCM.
The b terms are b^6 and b^3. The smaller exponent is b^3, which is also part of the GCF
We have a^6 and b^3 combine to form a^6b^3
A rectangle has a perimeter of 15 inches. If the length is two times the sum of 3 and the width find the dimensions of the rectangle.
Answer:
See below
Step-by-step explanation:
Perimeter = 2( L + W ) L = 2 (3+W) <==== given
15 = 2 ( 2(3+W) + W)
15 = 2 ( 6 +3W)
15 = 12 + 6W
3 = 6W
W = 1/2 inch L = 2(3+W) = 7 inches
A Dutch company built a submarine that can hold 10 passengers and 1 pilot. The submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet. To show this feature to a buyer the submarine dove to a depth of −872[tex]\frac{5}{12}[/tex]feet. The automatic feature then raised the submarine 50[tex]\frac{3}{5}[/tex]feet per minute. How much time, in minutes, does it take for the submarine to reach the certified depth? Round your answer to the nearest tenth of a minute.
The time, in minutes that it take for the submarine to reach the certified depth is 12.85 minutes.
How to illustrate the information?From the information, the submarine has a safety feature that will automatically raise the submarine if it goes below the certified depth of −650feet.
It should be noted that the automatic feature then raised the submarine 50 3/5 feet per minute.
Therefore, the time needed to reach the depth will be:
= 650 / 50 3/5
= 650 / 50.6
= 12.85 minutes
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Explain the difference between a constant and a coefficient.
The constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
Here,
The constant is the number that includes in the expression. It is a fixed value that does not change over time
Example : 2x+5
Where 5 is the constant
The coefficient is the number that write along with the variable in the expression
Example : 2x+5
Where 2 is the coefficient.
Hence, the constant is the number that includes in the expression and the coefficient is the number that write along with the variable in the expression.
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How can you tell that the student made an error when factoring? Explain the error.
Factor:
6x²-x-12
6x²9x + 8x - 12
3x(2x-3)-4(-2x +3)
Step-by-step explanation:
For a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
6
⋅
−
12
=
−
72
and whose sum is
b
=
−
1
.
−
1
out of
−
x
.
6
x
2
−
(
x
)
−
12
Rewrite
−
1
as
8
plus
−
9
6
x
2
+
(
8
−
9
)
x
−
12
Apply the distributive property.
6
x
2
+
8
x
−
9
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
2
x
(
3
x
+
4
)
−
3
(
3
x
+
4
)
Factor the polynomial by factoring out the greatest common factor,
3
x
+
4
.
(
3
x
+
4
)
(
2
x
−
3
)
Slope
1/5
y-intercept = -2
I need this in slope intercept form. Can someone help?
Answer:
y= 1/5x + (-2)
Step-by-step explanation:
What is an equation of the line that passes through the point (4,1)(4,1) and is perpendicular to the line 2x-y=42x−y=4?
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
What is the equation of a perpendicular line?The equation of the line is given below.
2x - y = 4
Then the slope of the perpendicular line will be
y = 2x - 4
m = 2
Then the equation of the line will be
y = -(1/2)x + d
Then the line is passing through (4, 1), then we have
1 = -(1/2)4 + d
3 = d
The equation of the line which is perpendicular to 2x - y = 4 and passing through (4, 1) will be y = (-1/2)x + 3.
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100 POINTS + BRAINLEIST ANSWER ASAP
Answer:
BC = 21
Step-by-step explanation:
AB + BC = AC
[tex]7x + 8 + 3x + 6 = 64[/tex]
[tex]10x + 14 = 64[/tex]
[tex]10x = 50[/tex]
[tex]x = 5[/tex]
BC = 3(5) + 6 = 21
