The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,
known as roots.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
itsA quadratic equation has two roots as it's degree is two.
We know, The general form of a quadratic equation is x² + bx + c.
Let, y = x² + bx + c.
At, (0, - 2).
- 2 = 0 + 0 + c.
c = - 2.
At, (4, 0).
0 = 4² + 4b - 2.
0 = 14 + 4b.
b = - 7/2.
So, It is x² - (7/2)x - 2 = 0.
2x² - 7x - 4 = 0.
2x² - 8x + x - 4 = 0.
2x(x - 4) - 1(x - 4) = 0.
(x - 4)(x - 1) = 0.
So, the zeroes of the function are 4 and 1.
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The circle in the center of
a basketball court is being
painted. The circle has a
radius of a feet. What is the
circumference of the circle?
Leave your solution in terms
of pi.
what's the awnser pls tell me
The circumference of the circle in a basketball court that has to be painted which has a radius of a feet is 2π.
The circumference of a circle is the distance around its edge. It is a key measurement of a circle and is used in many applications, such as finding the length of a rope needed to go around a circular object.
The formula for the circumference of a circle is given by C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The constant π is used to represent the relationship between the diameter and the circumference of a circle.
In this case, the circle has a radius of a feet, so the circumference of the circle can be calculated as follows:
C = 2π
The units of measurement for the circumference will be the same as the units of measurement for the radius, in this case feet.
So, the circumference of the circle with a radius of a feet is 2π feet, expressed in terms of π.
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A boat is heading towards a lighthouse, whose beacon-light is 150 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12∘, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21∘. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 313.6 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
From the given information AB = AC - BC.
We know, tan = opposite/adjacent.
tan12° = 150/AC.
AC = 150/0.213.
AC = 704.23.
Again,
tan21° = 150/BC.
BC = 150/0.384.
BC = 390.63.
Therefore, AB = 704.23 - 390.63 = 313.6 feet.
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Area of Trapezoids and Other Figures quick check
The area of the triangle is 11.55 square meters.
The correct option is B.
What is a Triangle?The polygon which has three sides and three vertices is called as triangle.
The sum of all the angles of the triangle is 180°.
A triangle is given.
The height of the triangle = 5.5 meters.
The base of the triangle = 4.2 meters.
The area of the triangle = 1/2 x base x height
The area of the triangle = 1/2 x 4.2 x 5.5
The area of the triangle = 11.55 square meters.
Therefore, area is 11.55 square meters.
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Using appropriate properties, find: 7/5 * 1/3 + 3/5 * (- 2/9) + 7/5 * (- 5/6)
The value of the expression is -5/6.
What is PEMDAS?The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
Given:
An expression,
7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6).
Solving further with the help of PEMDAS,
7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6)
= 7/15 - 6/45 - 35/30
= (42- 12 - 105)/90
= -75/90
= -5/6
Therefore, the value is -5/6.
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The volume of a cube is 8in^3. What is the length of one side? Show all work
A) 2in^3
B) 2.7in^3
C) 2in
D) 2.7in
Answer:
2 in
Step-by-step explanation:
Hope it helps.
On math thing
. if all 256 students from both the online and the in person sta 381 classes decide to play the game, how many total extra credit points would you expect to be rewarded (rounded to the nearest integer)?
You would expect a total of 2560 extra credit points to be rewarded (rounded to the nearest integer).
You must multiply the total number of extra credit points awarded by the number of pupils in order to find the answer to this question.
The equation would be as follows, assuming that each student receives the same number of extra credit points:
Total Extra Credit Points = Amount of Extra Credit Points per Student * Total Amount of Students
Therefore, in this case, the total amount of extra credit points to be rewarded would be:
Total Extra Credit Points = 10 * 256 = 2560
Therefore, If all 256 students from the in-person and online STA 381 classrooms choose to participate in the game, you can anticipate receiving a total of 2560 extra credit points (rounded to the nearest integer).
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A wheel chair ramp is to built 5 feet off the ground. The ramp will create an angle of elevation of 5. 22 degrees. How long should the ramp be
The Length of wheel chair ramp should be 54.94 feet. as we calculated this by given height of ramp is 5 feet and angle of elevation is 5.22 degree.
Here it is given that the height of ramp from ground is 5 feet and angle of elevation is 5.22 degree .Now we can see that this is a height and distance question. For that we have to use trigonometric ratio. And all trigonometric ratio are the angle of right angle triangle so here we have to find tangent of angle
so tanФ = perpendicular /base
and in this question the perpendicular is 5 feet and and the base we have to find and angle 5.22 degree.
let the length of ramp is = y and then put the value on formula we have
tan 5.22 = 5/y
y = 5/(tan5.22) = 5/0.091 =54.94
The length of wheel chair ramp is 54.94 feet .
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five cards are dealt without replacement from this deck. what is the probability that at least two of the four cards dealt have the same numeric value (1 through 20)?
The probability that at least two of the four cards dealt have the same numeric value (1 through 20) is approximately 0.907.
To calculate the exact probability, we need to consider the different ways that two or more cards could have the same numeric value. If two cards have the same numeric value, there are 19 ways to choose that value and 2 ways to choose the two cards with that value. The probability of this happening is 19 * (2 / 20 * 19 / 19) * (18 / 18 * 17 / 18) * (16 / 17 * 16 / 17) * (15 / 16 * 15 / 16) = 19 * (1/190) = 0.1.
Similarly, we can calculate the probability of three or four cards having the same numeric value. Adding these probabilities, we get an estimate of 0.907 for the probability that at least two of the four cards dealt have the same numeric value.
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In kite PQRS, measure of angle QPO=50° and measure of angle QRO=70°. Find measure of angle PSR
The measure of angle PSR in a kite PQRS, is equals to the 60°.
We have a kite PQRS, present in above figure. The measure of angle QPO = 50°
The measure of angle QRO = 70°
We have to determine the measure of angle PSR. As we see in figure, there is four right angled triangles as ∆POQ, ∆OQR , ∆POS and ∆OSR.
measure of angle POS = measure of angle SOR = 90°
measure of angle SPO = measure of angle QRO = 70° ( Since alternative angles)
Similarly, measure of angle SRO
= measure of angle QPO = 50° ( Alternative angles )
So, measure of angle PSR = measure of angle PSO + measure of angle RSO --(1)
Measure of angle RSO = 180° - measure of angle ROS - measure of angle SRO
= 180° - 90° - 50° = 40°
Also, Measure of angle PSO = 180° - measure of angle POS - measure of angle SPO = 180° - 90° - 70° = 20°
So, from equation (1),
measure of angle PSR = measure of angle PSO + measure of angle RSO
= 40° + 20°
= 60°
Hence, required measure of angle is 60°.
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Complete question:
The above figure completes the question. In kite PQRS, measure of angle QPO=50° and measure of angle QRO=70°. Find measure of angle PSR.
Simplify each expression.
(a^2b^-3/a^-2b^2), a and b don’t equal 0
Answer:
[tex]a^4b^{-5}\text{ or }\frac{a^4}{b^5}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{a^2b^{-3}}{a^{-2}b^2}=a^{2-(-2)}b^{-3-2}=a^4b^{-5}=\frac{a^4}{b^5}[/tex]
For each pair of numbers, determine by what percent the second number is greater than the first. Also determine by what percent the first number is less that the second.
We can conclude for the pair of number (a, b), where {b > a} -
we can write {b} is (100b/a)% of {a}. {a} will be {100 - 100b/a}% less than {b}.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a pair of numbers.
Since the numbers are not given, assume the pair to be (a, b).
Let -
{b} = x% of {a}
{b} = {x/100} x {a}
x = (100b/a)
Now, we can write {b} is (100b/a)% of {a}.
Then, we can write that {a} will be {100 - 100b/a}% less than {b}.
Therefore, we can conclude for the pair of number (a, b), where {b > a} -
we can write {b} is (100b/a)% of {a}. {a} will be {100 - 100b/a}% less than {b}.To solve more questions on functions, visit the link below-
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Differentiate the function
y=(5x² +7√x)/(4x)
y’=
Refer to the attached image.
WILL GIVE BRAINLIESTT!!!
Use the regression line yhat = 101 12x to find the residual for the point (7,17).
Answer:
Since the residual is very close to 0 and residual= actual y value so it is 8.
Please give me Brainlest:)
Step-by-step explanation:
help please! i haven't got an ounce of energy in my body to do this
Answer:
Step-by-step explanation:
Mr. lama has a piece of land of 10 kattha. he constructed a square pond of length 55 m for fish farming within it. how much space of his land is left? find it in sq.m?(1 kattha= 338.63 m^)
Answer:
361.3 m²left
Step-by-step explanation:
10 kattha =3386.3sqm
sq pond of 55m side, area = 55*55 =3025
so 3386.3 - 3025 = 361.3 m²left
a bottomless dolphin is 96 inches long .there are 12 inches in a foot use the equation 12d=96 to find d, the length of the bottomless dolphin in feet
Factor the expression using the greatest common factor.
-12z+16z4 - 3z²
The expression's factored version, which employs the greatest common factor, is -z(12z-16z3 + 3z).
Factoring using the greatest common factorThe largest number that can be split into exactly two or more other numbers. It is the "best" thing for making fractions simpler!
Given the expression below
-12z+16z^4 - 3z²
We are to factor the expression using the greatest common factor
Find the factors of each terms
-12z = -12 * z
16z^4 = 16 * z * z^3
-3z^2 = -3 * z * z
Since -z is common to the factors, hence the factored form of the expression using the greatest common factor is -z(12z-16z^3 + 3z)
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I'm having a problem with this can anyone help?
Which equation below represents a proportional relationship?
There may be more than 1 correct answer.
y = 7x
y = 1/7 x
y = x
y = 7x + 2
The equations that represent direct proportion are
y = 7x -- proportionaly = 1/7 x-- proportionaly = x-- proportionaly = 7x + 2-- not proportionalHow to determine the proportional relationship equationsFrom the question, we have the following parameters that can be used in our computation:
The list of options
A proportional linear equation is represented as
y = kx
Where
The constant of proportionality is k
Using the above as a guide, we have the following:
y = 7x -- proportionaly = 1/7 x-- proportionaly = x-- proportionaly = 7x + 2-- not proportionalRead more about direct variation at
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In the diagram KG, JF, AE and AH intersect at point A. Use this diagram for problems 1-3.
1. Describe the relevant angle relationships in the diagram.
2. Write and solve an equation to find the value of x
3. What are the measures if
As a result, the measurements of angles KAG and JAF are both 90, and the measure of arc KG is 2 * 90 = 180. Angle HAE and angle HAF are both 90 degrees.
What is angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.
Here,
In the diagram, since KG, JF, AE, and AH intersect at point A, we know that angle KAG = angle JAF (both are inscribed angles and intercept the same arc), and angle HAE = angle HAF (both are alternate interior angles and are equal in measure).
To find the value of x, we need to use the angle relationships. Since angle KAG = angle JAF, and they are both inscribed angles, they are equal to half the measure of the intercepted arc KG. We also know that angle HAE = angle HAF, so we can use them to find the measure of KG.
Let's call the measure of KG = 2x. Then, angle KAG = angle JAF = x, and angle HAE = angle HAF = x.
Adding the measures of angle KAG and angle HAE, we get x + x = 2x = 180. Solving for x, we get x = 90.
So, the measures of angle KAG and angle JAF are 90, and the measure of arc KG is 2 * 90 = 180. The measures of angle HAE and angle HAF are also 90.
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Under the translation (x+3, y-1) the point (3, 4) will become (0,5)
Answer:
The y and m2 and the m (0, 2) when x=3
Step-by-step explanation:
Kweku drives about 18,000 miles a year. How much would he save in a year buying electricity for the Desla electric compared to buying gas for the deswagon? and about how long would it take to makeup for the higher sale price of the desla electric?
Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon.
To make up for the higher sale price,
it will take him more than 66 years.
What is subtraction?Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.
Given:
Deselectric costs $11900 more than the Deswagon.
Unit cost:
Deselectric: $0.11 per mile.
Deswagon: $0.12 per mile.
Kweku drives about 18,000 miles a year.
That means
the cost for each car;
Deselectric: 18000 x 0.11 = $1980
Deswagon: 18000 x 0.12 = $2160
The more cost is,
= $2160 - $1980
= $180 of savings in a year.
Now, the make-up for the higher sale price,
= 11900/180
= 66.11 in years.
Therefore, it will take him more than 66 years.
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A bag contains red and blue counters in the ratio 3:5. There are 90 red counters in the bag. What is the total number of counters in the bag?
Answer:
The total number of counters in the bag is 150.
Step-by-step explanation:
There are 90 red counters and the ratio of red to blue is 3:5, which means that for every 3 red counters there are 5 blue counters. Thus, 90 red counters would mean that there are 5/3 times as many blue counters, or 150/3 = 50 blue counters. Therefore, 90 red counters + 50 blue counters = 150 counters in total.
In the years from 2010 to 2015, the population of the District of Columbia is expected to decrease about 0.9% annually. In 2010, the population was about 530,000. What is the population of the District of Columbia expected to be in 2015?
Answer: 506,150
First we must divided 0.9 into 530,000 to find out how much of the population will decrease each year.
0.9% of 530,000 is 4770. Which means that each year, 4,770 people will move the District of Columbia. From 2010 to 2015, that is 5 years, which means that we have to multiply 4,770 by 5.
4770 x 5 is 23850.
Next we have to subtract the amount of people who moved.
530,000- 23,850 is 506,150
This means by 2015, the expected population will be 506,150 in the District of Columbia.
I hope this helped & Good Luck <3 !!!
fill in the table using the equation
Answer: 11, 16, 26, 41
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If p − 1 is a factor of p4 + p2 + p − k, the value of k is __.
The value of k is given as follows:
k = 2.
How to obtain the value of k?The polynomial for this problem is defined as follows:
P(p) = p^4 + p² + p - k.
We have that p - 1 is a factor of the polynomial, meaning that according to the Factor Theorem, P(1) = 0.
Hence, considering that when p = 1, P = 0, the value of k is obtained as follows:
1^4 + 1² + 1 - k = 1
3 - k = 1
k = 3 - 1
k = 2.
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What is (f+g)(x)?
f(x)=4x+6
g(x)= -5x
Write your answer as a polynomial or a rational function in simplest form.
Answer:
(f + g)(x)= -x + 6.
Step-by-step explanation:
The sum of two functions, f(x) and g(x), is given by (f + g)(x) = f(x) + g(x).
So, for f(x) = 4x + 6 and g(x) = -5x,
(f + g)(x) = f(x) + g(x) = (4x + 6) + (-5x) = -x + 6.
The result is a linear function and is already in the simplest form, so it cannot be further simplified.
a regular hexagon is a six-sided figure with all sides equal and all six angles equal. find the length of the sides if the perimeter of the regular hexagon is 372in.how do you find the mean height
The mean height of the hexagon is 21.33 in.
The Mean of HexagonTo find the length of the sides of a regular hexagon with a perimeter of 372 inches, you must divide the perimeter by 6. This gives you a result of 62 inches for the length of each side. The other steps are:
To find the mean height of the hexagon, you must first calculate the area. To do this, you can use the formula for the area of a regular hexagon, which is A = (3√3)/2 × a², where a is the length of one side. Substituting the side length of 62 inches, the area of the hexagon is A = (3√3)/2 × 62² = 7943.3 sq. in. From this, the mean height of the hexagon can be calculated by dividing the area by the perimeter, which gives a mean height of h = 7943.3/372 = 21.33 in.Learn more about The Hexagon here:
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A 95% confidence interval is found to be (28, 32). The sample standard deviation is 7 and the sample size is 49. If you wanted a smaller interval, what could you do?
C. Increase sample size to 64
Answer:
See below
Step-by-step explanation:
If we increase the sample size, we will decrease the margin of error, creating a smaller interval. This is why option C is the most appropriate answer!
Find the corresponding range viewing the window [-5,5]
From the graph, the range in the viewing window is [-3,3]
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
f(x)= -100|x| + 75
Take few values for x and find corresponding f(x) values
The graph will be symmetrical in nature
It is absolute value function
Example:
when x=0.75
f(x) = -100(0.75)+75
= -75+75
= 0
Range is the y values
From the graph, the range in the viewing window is [-3,3]
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5. A cliff-jumper of mass 68.0 kg stands on the edge of a cliff and possesses 16,800 J of potential energy. How high up is this lunatic from the base of the cliff?
The potential energy of an object is given by the equation:
PE = mgh
where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height.
Rearranging this equation, we get:
h = PE / (mg)
Substituting the given values, we get:
h = 16800 J / (68.0 kg x 9.81 m/s^2)
h = 24.8 meters
Therefore, the cliff-jumper is standing 24.8 meters above the base of the cliff.
Answer:
h
Step-by-step explanation: