The extrema of the quadratic equation is at the vertex, and it is a minimum at:
y = -1.75
How to find the extremum of the parabola?Here we have the following quadratic equation:
y = 3x^2 - x - 2
We can see that the leading coefficient (the coefficient in the term with the largest exponent) is positive, this means that the parabola opens upwards.
This means that the vertex of the quadratic equation will be a minimum.
Remember that for a quadratic equation:
y = a*x^2 + b*x + c
The vertex is at:
x = -b/2a
So for our quadratic, the vertex is at:
x = -1/(2*3) = -1/6
Evaluating the quadratic equation there we get:
y = 3*(-1/6)^2 - (-1/6) - 2
y = -1.75
That is the minimum of the quadratic.
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PLEASE PLEASE HELP ME WITH THIS QUESTION Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
I need help it’s due by 11:59pm
I need
Range=
Domain=
Answer:
Range: [tex]\text{y} \ge 0[/tex]
Domain: [tex]\text{x} \ge 0[/tex]
Both involve "greater than or equal to 0".
==============================================
Explanation:
The domain is the set of allowed inputs (x). The smallest input allowed in this case is x = 0, as it corresponds to the left-most point (0,0) on the blue graph. There is no largest x value since it stretches forever to the right.
Either x = 0 or x > 0 which condenses to [tex]\text{x} \ge 0[/tex] and this is the domain as an inequality.
--------
The range will have us look at the possible y values or possible outputs. We have y = 0 as the smallest output possible, which corresponds to the lowest point (0,0).
There is no largest y value since the blue graph goes forever upward.
Either y = 0 or y > 0 to give us the range of [tex]\text{y} \ge 0[/tex]
125 = 7m - 1 please answer
Answer:
m=18
Step-by-step explanation:
Find the values of x and y.
yo
40°
Answer:
20°,70°
Step-by-step explanation:
X+y+90=180
X+y=90
20+y=90
y=70°
2x+180-40=180
2x=40
X=20°
The measures of angles of the triangle is x = 20° and y = 70°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , let the side be represented as BD , which cuts AC at point D
And , the measure of BD = measure of DC ( given )
And , the measure of ∠ABC = 90°
The measure of ∠BDA = 40°
So , the measure of angle ∠BDC = 140° ( angles on a straight line )
Now , the measure of angle ∠DBC = measure of ∠BCD ( given )
So , the measure of x = ( 180 - 140 ) / 2
x = 20°
And , the measure of y = 180° - 40° - 70°
y = 70°
Hence , the angles of triangle are x = 20° and y = 70°
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I need help I’m thinking its D but I’m not sure
a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the tip of her shadow moving when she is 15 ft from the base of the pole?
The speed of the tip of her shadow would be 5.714 ft/sec. ft/sec.
let H, be the height of the pole = 20 ft.
h, be the height of the woman = 6 ft.
x, be the length of the woman's shadow,
and s, be the distance from the pole to the woman = 15
by using the equation of similar triangles,
[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)
differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]
[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]
[tex]14\frac{dx}{dt} = 24[/tex],
[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.
the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.
thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.
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for a questionnaire survey of employees of a particular organisation to investigate a range of aspects of their job satisfaction, a researcher invites all 1000 employees to participate and aims for a sample of 200 men and 200 women. what method of sampling is this?
This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.
Given that,
A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.
A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata
Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.
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If polygon A is the original shape, what is the scale factor to get polygon B?
Answer:
scale factor = 2
Step-by-step explanation:
the scale factor is the ratio of corresponding sides , polygon B to polygon A
in figure A the vertical side RS = 2 units
the corresponding vertical height in figure B = 4 units , then
scale factor = [tex]\frac{4}{2}[/tex] = 2
Help QUick Help I'm begging Help pls!!!!!!!!!!!!!!
Brainliest
Our school flag is a rectangle. We are changing to a new rectangular flag design. The length of the new flag is 20% greater than the length of the old flag, and the width of the new flag is 10% less than the width of the old flag, The old school flag is 25 square feet. What is the area of the new flag?
Answer: Hence the answer is 27 square feet.
Please look at the images for more details.
Answer:
27 square feet
Step-by-step explanation:
Define the variables:
Let w be the width of the old flag.Let l be the length of the old flag.To increase a number by a certain percent, divide the percent by 100, add it to 1, then multiply the original number by this number.
If the length of the new flag is 20% greater than the length of the old flag:
[tex]\implies \textsf{Length}=\left(1+\dfrac{20}{100}\right) \timesl \times l=1.2l[/tex]
To decrease a number by a certain percent, divide the percent by 100, subtract it from 1, then multiply the original number by this number.
If the width of the new flag is 10% less than the width of the old flag:
[tex]\implies \textsf{Width}=\left(1-\dfrac{10}{100}\right) \times w =0.9w[/tex]
[tex]\boxed{\textsf{Area of a rectangle}=\sf width \times length}[/tex]
Therefore, given the area of the old flag is 25 ft²:
[tex]\implies wl=25[/tex]
To find the area of the new flag, substitute the expressions for width, length and wl into the formula for area of a rectangle:
[tex]\begin{aligned}\textsf{Area of new flag}&=\sf width \times length\\&=0.9w \times 1.2l\\&=0.9 \times 1.2 \times wl\\&=1.08 \times 25\\&=27\sf \;\; ft^2\end{aligned}[/tex]
Therefore, the area of the new flag is 27 square feet.
Patricia’s brother Kevin likes his lemonade. Best way to use a ratio of 3 tablespoons of lemon juice to 24 ounces of water. Does Kevin favorite lemonade juice taste the same as Patricia
Kevin favorite lemonade juice can't taste the same as Patricia's.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
1 table spoon = 0.5 ounce
Therefore, 24 ounces will be:
= 24 × 0.5
= 12 tablespoon
In this case, they have different tablespoon and therefore won't have same taste.
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you want to order posters to advertise your band. a company charges $109.95 for the first 100 posters and $65 for each additional 100 posters. a. write the equation where $y$ represents the total cost (in dollars) as a function of $x$ , the number (in hundreds) of posters ordered.
The required question based on number of posters is y = 109.95 + 65x.
The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.
Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.
y = 109.95 + 65x
Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.
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Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm? PLEASE
Answer:
Step-by-step explanation:
-22.7
in how many ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards? a) 120 b) 42,504 c) 5,100,480 d) 25 e) 4 f) none of the above.
In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
Define combination.Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given,
Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:
Through combination:
²⁴C₅
24!/51(24-5)!
Simplifying:
24!/5!(19!)
24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1
42504
In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.
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What is an equation of the line that passes through the points (4, -2) and (2, 3)
The slope-Intercept form of the given line is y=1.5x.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,
Slope of the line, m = (-2 - 3)/(4 - 2)
= 3 / 2
= 1.5
Now, the equation of the line passing through (2, 3) can be written as,
y = mx + c
(3) = 1.5(2) + C
3 = 3 + C
3 - 3 = C
C = 0
Substitute all the value in the equation of the line,
y = m(x) + c
y = 1.5(x) + 0
y = 1.5x
Hence, the equation of the given line is y=1.5x .
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The measure of an angle is 60.5°. What is the measure of its supplementary angle?
Answer:
119.5
Step-by-step explanation:
Since supplementary is 180 degrees, 180-60.5=119.5
I need help like asap !!!
only numbers and decimal points
Answer:
c = 11.46 yd
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ c² = (8.1)² + (8.1)²
→ c² = 65.61 + 65.61
→ c² = 131.22
→ c = √131.22
→ [ c = 11.46 yd ]
Hence, value of c is 11.46 yd.
a study by tourism ontario revealed that 50% of the vacationers going to toronto visit the cn tower, 40% visit skydome and 35% visit both. what is the probability that a vacationer will visit at least one of these magnificent attractions?
0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
Calculation50% of the vacationers going to toronto visit the CN tower= 0.5
40% visit skydome= 0.4
35% visit both=0.35
P( At lease one) = P(Toronto) + P(Skydome) - P(Both)
P( At lease one) = 0.4 + 0.5 - 0.35
P( At lease one) = 0.55
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Determine whether the relation is a function. Then list the domain and range.
{(1, -2), (-1,2), (-2,4), (1,3)}
The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and the independent variable.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The domain of the function is defined as the set of all the possible values of the function.
The domain of the relation is 1,-1,-2, and 1. The range of the function is -2,2,4, and 3.
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When the p-value is used for hypothesis testing, the null hypothesis is rejected if?.
The null hypothesis is rejected if the p-value is lower than or equal to the chosen significance threshold; otherwise, it is not. To put it another way, if p, reject [tex]H_{0}[/tex]; if p>, do not reject [tex]H_{0}[/tex].
This criterion, known as (alpha) in null hypothesis testing, is often set to 05. The rejection of the null hypothesis is if there is less than a 5% probability that a result as dramatic as the sample result would occur if the null hypothesis is accepted. The outcome is referred to as statistically significant when this occurs.
If a statistical test is run with a threshold of significance = 0.1, 0.05, and 0.01 the null hypothesis was rejected.
The alternative hypothesis is taken into consideration instead of the null hypothesis if the P value is less than alpha, the predetermined level of statistical significance.
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In quadrilateral BADC, AB=AD and BC=DC. Which of the following contains only true statements?
Answer:
abad
Step-by-step explanation:
5) Can you give some real world examples (at least two for each) of positive and negative slope?
The positive slope is tilted towards the right on a coordinate plane and the negative slope is tilted towards the left on the coordinate plane.
What is the positive and negative slope?When two variables have a positive slope, it means that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.
A line that slopes downward from left to right is said to have a negative slope. In other words, the rise-to-run ratio of the line is negative.
The graph of the two real-life situations is attached with the answer below. In which the equation y = 4x means that the value of y is increasing by 4. Similarly, the equation for negative slope is y = -4x means that the value of y is increasing in opposite direction by factor 4.
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Use function notation to write the rule for each function
f{(0,1) (1,3) (2,5) (3,7) (4,9)}
Answer: y=2x+1
Hope this helps
3y minus 27 i have no idea
3(y-9)
Step by step explanation:3y-27
Factorizing
3(y-9)
Hi if someone could help me I would be very grateful.
I submitted a photo of the questions
Answer:
5/12
6/15
10/18
Step-by-step explanation:
1) In a group of 80 children, 35% of the
children are girls. 9 of the girls chose
volleyball as their favourite sport.
What percentage of the girls chose
volleyball?
11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.
Given that,
35 percent of the 80 kids in the group are girls. 9 of the female students selected volleyball as their preferred sport.
We have to find what percentage of the female students chose volleyball.
The total children's are 80.
The 35% are girls.
9 have selected the volleyball
So,
9/80
0.1125
The percent is
11.25%
Therefore, 11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.
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8 Here are the descriptions of two numbers.
The smallest multiple of 5 greater than 1000
The largest multiple of 9 with three digits
Work out the difference between these two numbers.
Micah is making salsa at a factory using tomatoes
and onions in the ratio of 5:2. If the total volume
of salsa Micah makes is 147 cups, find the volume
of the tomatoes Micah uses.
Answer: 21 Tomatoes
Step-by-step explanation:
5 + 2 = 7
147 / 7 = 21
21 Tomatoes
re-write the statement 19 + 7 divided by 2 - 5
by including one pair of brackets to make the total value equal to 8
Re-write the statement 19 + 7 divided by 2 x 6 + 1 by including two pairs of brackets to make the total value equal to 2
Answer:
[19+7] / [2 x 6 + 1]
Step-by-step explanation:
[19+7] / [2 x 6 + 1]
[26] / [13]
[2]
If p is portional to q and p =4.5 when q= 12 .
Find the relationship between p and q
P when q =16
Q when p= 2.4
The relationship between variables p and q is given by p = kq. Also, the value of the variable p when q = 16 is 6 and when p = 2.4, the variable q is 6.4.
How to determine the proportional relationship?Mathematically, a proportional relationship can be represented with the following mathematical expression:
p = kq
Where:
p and q are the variables.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = p/q
Constant of proportionality (k) = 4.5/12
Constant of proportionality (k) = 0.375.
When q = 16, the variable p is given by:
p = kq
p = 0.375 × 16
p = 6.
When p = 2.4, the variable q is given by:
q = p/k
q = 2.4/0.375
q = 6.4
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the probability that jacie will eat cheese on any given day is 0.6 while the probability that robyn will eat cheese on any given day is 0.25. if these events are independent, what is the probability that jacie or robyn will eat cheese on a randomly selected day?
The probability for Jacie or Robyn would consume cheese on a random day is 0.15.
What is defined as the independent events?Two occurrences are considered independent if indeed the occurrence of one does not alter the likelihood of the occurrence of the other. The mathematical expression of event independence A and B is the chance of both A and B occurring being equal to the sum of both the probabilities of both B and A (i.e., P) (A and B).The likelihood of Jacie eating cheese on any particular day is 0.6.
The likelihood of Robyn eating cheese on any particular day is 0.25.
Both events are independent.
As a result, the probability for Jacie or Robyn would consume cheese on a random day is;
P(Jacie or Robyn) = P(Jacie). P(Robyn)
P(Jacie or Robyn) = 0.6 x 0.25
P(Jacie or Robyn) = 0.15
Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.
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