Answer:
\(1(x - 2)(x + 3)\)
Step-by-step explanation:
from the two x-intercept we can write the function as
\(a(x - 2)(x - ( - 3) ) = a(x - 2)(x + 3)\)
we still have one coefficent to determine from the y intercept
\(a(0 - 2)(0 + 3) = - 6 \\ a( - 2)(3) = - 6 \\ a = 1\)
The art club had an election to select a president. 80 out of the 100 members of the art club voted in the election. What percentage of the members voted?
Answer:
80%
Step-by-step explanation:
A percentage can also be represented as a fraction with the denominator of 100. If 80 out of 100 (Fraction Form: \(\frac{80}{100}\)), then 80% of the art club members voted.
monica is standing in a building looking out a window at a tree the tree is 121 feet away from monica monica line of sight to the top of the tree creates a 42 degree angle of depression. what is the height of the tree rounded to the nearest tenth
Answer:
89.9 feets
Step-by-step explanation:
The diagrammatic representation of the problem is attached below.
The height, h of the tree can be calculated using the trigonometric relation :
Cosθ = adjacent / hypotenus
Cos 42 = h / 121
0.7431448 = h / 121
Height, h of tree = 121 * 0.7431448
Height = 89.9 feets
Will Give Brainleist! Plz help me on this problem
Which equation represents a line with slope 3/5 of and y-intercept of -1 ?
Answer:
y = 3/5x - 1
i think that's what's supposed to be there...
f(x) =x(x-1) on R to R
find A and B such that g: A to B defined by g(x)=f(x) is bijective
this is an algebra question, help.
details are needed
Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.
To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.
So, let's assume that g(x1) = g(x2). Then, we have:
f(x1) = f(x2)
x1(x1-1) = x2(x2-1)
x1^2 - x1 = x2^2 - x2
x1^2 - x2^2 - x1 + x2 = 0
(x1 - x2)(x1 + x2 - 1) = 0
Since x1 and x2 are distinct, we must have x1 + x2 = 1.
But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.
To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.
So, let's solve the equation f(x) = y for x:
x(x-1) = y
x^2 - x - y = 0
Using the quadratic formula, we get:
x = (1 ± √(1 + 4y))/2
Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.
Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.
Find the value of X.
Given the following proportion, find x
3/7 = 6/x
Answer:
x = 14
Step-by-step explanation:
3/7 = 6/x
3(x) = 6(7)
3x = 42
x = 14
Answer:
3/7 = 6/x
3x = 6*7
3x = 42
x = 42/3
x = 14
I hope you can know this answer...
A bakery sells vanilla cupcakes and chocolate cupcakes. It sold 276 vanilla cupcakes in a day. 8% of the cupcakes sold that day were chocolate. How many total cupcakes did the bakery sell that day?
ASSAP
Answer:
hello!!!
300 cupcakes
please read the explanation.. it always helps... trust me...
Step-by-step explanation:
alrighty here it goes...
okay.. so we start by reading the problem (duh) but also underlining the important numbers that we need. yes, it really is that simple, trust me....
okay so the percentage of chocoalte cupcakes was 8% and the amount of vanilla cupcakes was 276.
we start by taking 100% - 8% = 92% so the amount of vanilla cupcakes sold was 276 which is also 92% of the total amount of cupcakes.
so now we need to find out 92% of what number gets us 276.
the percentage formula (in this problem) should be as follows:
92/100 x (total amount of cupcakes) = 276
to solve for total amount of cupcakes you do 276 x 100 then you divide by 92 to get your answer (which is 300)
i hope this helps!!!
Answer:
300
Step-by-step explanation:
How many solutions will the equation have?
|x- 13| - 5= -5
Answer: x=13
Step-by-step explanation: Hope this help :D
Answer:
One Solution
__________
x = 13
__________
Explanation:
| x – 13 | – 5 = -5
[Add 5 to both sides to isolate | x – 13 | and cancel out –5]
| x – 13 | – 5 + 5 = -5 + 5
[Reduce]
| x – 13 | = 0
[An absolute value can include both a positive and negative value so |x| = n → x = ±n ]
x – 13 = ± 0
[Add 13 to both sides to get the value of x]
x – 13 + 13 = 13 ± 0
x = 13 ± 0
[Adding or subtracting zero will leave you with the same number]
x = 13
The bicycle shop advertised all mountain bike price of a 1/3 Discount what is the amount of discount if a bicycle originally cost $327 what is the discount price of the bicycle
Answer:
109
Step-by-step explanation:
do you take 1/3 / 327=109
Evaluate the limits
\(x > \ln(x)\) for all \(x\), so
\(\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}\)
Similarly, \(\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}\)
We can of course see the limits are identical by replacing \(x\mapsto e^x\), so that
\(\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)\)
You can also rewrite the limands to accommodate the application of l'Hôpital's rule. For instance,
\(\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)\)
Using the rule, the limit here is
\(\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0\)
so the overall limit is
\(\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty\)
Drag each number to a box to complete the table. Each number may be used once or not at all
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Your friend printed a picture of a regular 18-gon. She wants to cut the 18-gon into right triangles. If she divides the figure into 36 right triangles, what are the measures of the non-right angles of each triangle?
The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.
The sum of the interior angles of a regular 18-gon can be found using the formula:
S = (n - 2) × 180 degrees
n is the number of sides of the polygon.
Substituting n = 18 we get:
S = (18 - 2) × 180 degrees
= 2880 degrees
The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.
Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.
The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.
Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.
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If a seed is planted, it has a 80% chance of growing into a healthy plant. If 7 seeds are planted, what is the probability that exactly 4 don't grow
Answer:
The probability that exactly 4 don't grow is P=0.0287.
Step-by-step explanation:
This random variable can be modeled with a binomial distribution.
The sample size is n=7, the total amount of seeds planted.
The probability of success is p=0.8.
The probability that k seeds grow in the sample is:
\(P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{7}{k} 0.8^{k} 0.2^{7-k}\\\\\\\)
If exactly 4 don't grow, this means that exactly 7-4=3 seeds grow.
Then, we have to calculate P(x=3):
\(P(x=3) = \dbinom{7}{3} 0.8^{3}\cdot 0.2^{4}=35*0.512*0.0016=0.0287\\\\\\\)
given that we assume that all numbers are distinct, explain why it is without loss of generality to assume that a > d
Since it has no impact on the result or solution of the problem, assuming that a > d does not reduce the generality of the statement. If a > d, the issue can be solved by simply swapping the values of a and d.
It makes no difference to the problem whether an is more or less than d because we are presuming that each integer is distinct. Furthermore, by supposing that a > d, the problem's variables can be arranged consistently, making it simpler to comprehend and resolve. As a result, making the assumption that a > d does not reduce the generality of the solution because the problem remains the same and the assumption may be readily changed if necessary.
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a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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how many pattern blocks rhombuses would 4 triangles create
Four triangles can create a set of pattern blocks that includes a total of four rhombuses.
To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.
To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.
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What is the solution to this system of equations? 10 y = x - 2; y = - 0.5x + 7 10 (3, 2); (6, 4); (4, 6); (2, 3)
Answer:x=bx2 is the answer
Step-by-step explanation:
35÷ 2 using an area model and using long division and the distributive property to record the work
Answer:
17.5
Step-by-step explanation:
i just used a calculator my man
Lesson 18.1 choosing a bank
There are many banks but nowadays SBI is the one of popular bank of World.So I choose SBI bank for explanation.
Details about SBI bank:
State Bank of India (SBI) is one of the largest and oldest banks in India. It was founded in 1806 as the Bank of Calcutta and later became the Imperial Bank of India in 1921. In 1955, the bank was nationalized and became the State Bank of India.
SBI is headquartered in Mumbai and has a widespread network of branches across India as well as in other countries. The bank offers a wide range of financial products and services such as savings and current accounts, loans, credit cards, investment options, insurance, and many more.
SBI is known for its advanced technology and customer-centric approach. The bank has implemented various digital initiatives to make banking easy and convenient for its customers. SBI's mobile app and internet banking portal are among the most popular digital channels used by customers.
Apart from traditional banking services, SBI has also been actively involved in various social initiatives such as promoting financial literacy, supporting education, healthcare, and environment conservation. The bank has also launched many welfare schemes for the benefit of its customers and society at large.
SBI is recognized as a global banking leader and has received many prestigious awards and accolades over the years. The bank has also been ranked among the top banks in the world by leading international publications.
Overall, SBI is a reliable and trustworthy bank that has played a significant role in shaping the Indian banking industry.
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Correct question is " Choose a name of a perticular bank and write about the bank."
HELP 100 POINTS ANSWER IT PLEASE
Answer:
\(\boxed{\text{\large $ y=96.1\sqrt{x} $}}\)
Step-by-step explanation:
Using a graphing calculator, plot (x,y) points
x = no. of jobsy = no. of workers neededand plot the functions from the options to know which function fits the data
Answer:
Step-by-step explanation:
Using a graphing calculator, plot (x,y) points
x = no. of jobs
y = no. of workers needed
and plot the functions from the options to know which function fits the data
Which of the following is an equation of the line that has a slope of - 3 and passes through the point (-6, 2)?
Answer:
y = -3x - 16
Step-by-step explanation:
m = -3 ; (-6 , 2)
Slope point form : y - y1 = m(x -x1)
y - 2 = -3(x - [-6])
y - 2 = -3(x + 6)
y -2 = -3x + 6*(-3)
y - 2 = -3x - 18
y = -3x - 18 + 2
y = -3x - 16
maya needs 54 cubic feet of soil for her garden. she already has 4.5 cubic feet of soil. Each bag contains 1.5 cubic feet of soil. How many bags of soil should maya purchase?
Answer:
33 bags
Step-by-step explanation:
she has 4.5 ft³
she needs 54 ft³
she must get an additional
54 ft³ - 4.5 ft³ = 49.5 ft³
each bag has 1.5 ft³
(49.5 ft³)/(1.5 ft³) = 33
Answer: 33 bags
A set of three vectors \(\( \left\{\mathbf{v}_{1}, \mathbf{v}_{2}, \mathbf{v}_{3}\right\} \)\) in a vector space is an orthogonal set if each is vector is a non-zero vector, and if every vector is orthogo
The vectors are linearly independent and the given statement is true.
what are vectors?a quantity with both direction and magnitude, especially when used to map out where one point in space is in relation to another.
Given, A set of three vectors {v₁, v₂, v₃} in a vector space is an orthogonal set.
Since,
Two vectors a and b are orthogonal if a is perpendicular to b.
Also, it is known that the dot product of perpendicular vectors is 0, that is a⋅b=0.
A set of vectors where each pair of vectors is orthogonal is said to be an orthogonal set.
For every other vector in the set. In other words, if we take any two vectors from the set, their dot product (also known as the inner product) will be zero.
Formally, let v1, v2, and v3 be three non-zero vectors in a vector space V. We say that they form an orthogonal set if:
v1⋅v2 = 0
v1⋅v3 = 0
v2⋅v3 = 0
where ⋅ represents the dot product (or inner product) of two vectors.
It is important to note that the concept of an orthogonal set is closely related to the idea of orthogonality in geometry, where two lines or planes are said to be orthogonal if they meet at right angles.
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state , giving reasons, which of the following if meaningless:
a. (-12, 0 ]
b. ( 1, -13 ]
Both of the intervals given are meaningful intervals in mathematics, but they are different types of intervals.Therefore, the interval (1, -13] is meaningless because it does not contain any real numbers.
What is intervals?An interval is a number or range of values between two endpoints.
The endpoints can be included or excluded from the interval, and the interval can be open, closed, or half-open depending on whether the endpoints are included or excluded.
The interval (-12, 0] is a closed interval, which includes the endpoint 0, and all real numbers between -12 and 0.
The square bracket indicates that the endpoint 0 is included in the interval.
The interval (1, -13] is an empty interval, which includes no real numbers, since there is no number that is greater than 1 and less than or equal to -13. This interval is meaningless because it does not contain any numbers.
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50 Points! Multiple choice algebra question. Suppose you deposit $1000 in an account paying 4% annual interest, compounded continuously. Find the balance after 10 years. Photo attached. Thank you!
The balance after 10 years is equal to: A. $1491.82.
How to determine the balance after 10 years?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
\(A(t) = P_{0}e^{rt}\)
Where:
A(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.When time, t = 10 years, the future value can be calculated as follows:
\(A(t) = 1000e^{0.04 \times 10}\\\\A(t) = 1000e^{0.4}\)
A(t) = 1000(1.49182469764)
A(t) = 1491.82469764 ≈ $1491.82.
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I need ya help please
Factor the expression 26p + 8q - 10
Answer:
factor 2 out of 26p+8q-10 2
Step-by-step explanation:
2 (13+4p-5)
Write the Plural! Spanish, help!!
what is b x b equialent to?
Answer:
b^2
Step-by-step explanation:
You're going to add the exponents from b x b, both carry a 1 in their powers (or exponents)
so b^1 + b^1 = b^2
Answer:
b^2
Step-by-step explanation:
b*b = b^2
Estimate the difference. 9 1/2 - 1 6/7
Answer:
9 1/2= 19/2 & 1 6/7= 13/7
Now equalising denominator we will get,
133/14 & 26/14
Now finding difference:
(133-26)/14
= 107/14 is the difference
Answer:
107/14
Step-by-step explanation:
Hope this helps