The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:
y = a(x - r(1))(x - r(2))
A quadratic expression that is the product of two factors, each of which is a linear expression, is referred to as having a "factored form."
When an equation is in factored form, it can be expanded to recreate it in standard form by multiplying out the components. The act of factoring involves summarizing the parts of a given integer or algebraic expression.
The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:
y = a(x - r(1))(x - r(2))
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Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella.
The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has.
The number of markers that Stella has would be = 27 markers
How to calculate the number of markers?The number of markers owned by Jerry = U
The number markers owned by Stella = t +16
If U = 43
t = X
That is, 43= t + 16
Make t the subject of formula;
t = 43-16
t = 27
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Complete question;
Jerry and Stella are working on an art project together. Jerry has 16 more markers than Stella. The equation given below shows this relationship, where u represents the number of markers Jerry has, and t represents the number of markers Stella has. U = t + 16 If Jerry has 43 markers, how many markers does Stella have? Show your work
Which is better substitution or elimination?
Substitution is generally better than elimination equations because it is typically faster and easier to solve.
Substitution is generally a better method than elimination when solving equations. This is because substitution is typically faster and easier to solve. With substitution, you simply substitute one of the variables in the equation with a known value in order to solve for the other variable. This is generally easier than elimination, which involves eliminating one of the variables by adding and subtracting equations. Elimination can be more tedious, especially when dealing with large equations. Additionally, it may be difficult to eliminate one variable when the equations are not balanced or when there are multiple variables. For these reasons, substitution is generally better than elimination.
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Bird Bath Your neighbor is moving a new bird bath to his triangular back yard.
He wants the bird bath to be the same distance from each edge of the yard. Where should your neighbor place the bird bath? Explain.
Answer:
The best place for your neighbour to put the bird bath would be at the centroid of the triangular yard. The centroid is the point where the three medians of a triangle meet, and it is also the point that is equidistant from all three sides of the triangle. This way the bird bath will be the same distance from each edge of the yard, which is what your neighbour wants. To find the centroid, your neighbour can first draw the medians of the triangle and then find their intersection point.
The average of four real numbers is greater than or equal to at least one of the numbers.
This statement is always true. The average of four real numbers is calculated by adding the four numbers together and dividing by four. Therefore, the average will always be greater than or equal to the smallest of the four numbers.
True Average Of Four NumbersThe statement "The average of four real numbers is greater than or equal to at least one of the numbers" means that when you add four numbers together and divide by four, the resulting average will always be greater than or equal to one of the original numbers.
This is because the average is a measure of central tendency that is affected by all the numbers and the number that will affect the average the most will be the largest one and since the average is the sum of all the numbers divided by 4 it will be always greater than or equal to the smallest number.
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Javier opens a savings account with a deposit of $75 and begins making weekly contributions. After 1 week he has $90 saved, and after 2 weeks he has $105 saved.
Answer: what is the question?
Step-by-step explanation:
7 Sound intensity model: L = 10 log L = loudness, in decibels (dB); I = sound intensity, in watts/m2; 10 = 10-12 watts/m2 The loudness of a jack hammer is 96 dB. Its sound intensity is about.
The loudness of a compactor is 94 dB. Its sound intensity is about.
with solution please thank you
The sound intensity of the pile driver is 39.6 times that of jack hammer as per given data.
As given in the question,
L represents the loudness in decibels(dB)
I = sound intensity in watts/m²
Loudness of pile driver = 112dB
In terms of sound intensity it is equal to = (112 / 10)
= 11.2
Sound intensity in power of 10
10^(11.2) = I / 10^(-12)
⇒ I = 10^(11.2)× 10^(-12)
⇒ I = 10^( 11.2 - 12)
⇒ I = 10^(- 0.8)
⇒ I = 0.15848
⇒ I = 0.1585
Relation between the sound intensity of pile driver and th jack hammer is given by
Sound intensity of jack hammer = 0.004
Sound intensity of pile driver = 0.1585
Intensity = 0.1585 / 0.004
= 39.6 ( nearest tenth digit )
Therefore, the sound intensity of pile driver is 39.6 times that of jack hammer.
The above question is incomplete, the complete question is :
L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2
The loudness of a jack hammer is 96 dB. Its sound intensity is about 0.004.
The loudness of a compactor is 94 dB. Its sound intensity is about 0.0025.
The sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor.
The loudness of a pile driver is 112 dB. About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.
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Aisha wants to buy apples and raspberries to make a fruit tart. Apples cost $3 per pound and raspberries cost $2.75 per pound. How many pounds of fruit does she buy if she buys 3 pounds of apples and 2.5 pounds of raspberries? How many pounds of fruit does she buy if she buys x pounds of apples and y pounds of raspberries?
Aisha bought 5.5 pounds of fruit if she buys 3 pounds of apples and 2.5 pounds of raspberries and she buys x + y fruits if she buys x pounds of apples and y pounds of raspberries.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that,
We have to calculate the total pound if Aisha bought 3 pounds of apples and 2.5 pounds of raspberries.
Total pounds = 3 pounds + 2.5 pounds = 5.5 pounds
If x pounds of apples and y pounds of raspberries are bought,
Total pounds = x + y
Hence the total pounds is calculated by adding the amount of pounds of apples and raspberries to get 5.5 pounds and x + y pounds.
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how many right triangles with distinct sizes have all three vertices taken from the array of dots below? two triangles are to be considered distinct if their side lengths are not the same 3 lengths.
An infinite number of triangles can be drawn with any 3 dots. I choose these 3 dots.
how many right triangles with distinct sizes have all three vertices taken from the array of dots below?
Since there are three sides in triangle, there must be three points where these sides can meet, so all triangles have three vertices. Since a right triangle is a triangle, and all triangles have three vertices so a right triangle has three vertices.3 dots =84 combinations of 3 dots. However, not all combinations of 3 dots form triangles. If all 3 vertices fall on the same horizontal or vertical line, we get a straight line rather than a triangle.In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read therefore.To learn more about triangle refers to:
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Find the slope of the line graphed below.
Answer:
-4/4 = -1
Step-by-step explanation:
Answer: -4/4
Step-by-step explanation:
m = slope
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
-3,-1 1,-5 are the corrdinates
(-5) - (-1) = -4
1 - (-3) = 4
Gi sells televisions. He earns a fixed amount for each television and an additional $15 if the buyer gets an extended warranty. If Gi sells 19 televisions with extended warranties, earns 1,425. How much is the fixed amount Gi earns for each television?
PLEASE HELP ME WITH THIS QUESTION
Answer:
$60
Step-by-step explanation:
19 times 15 = 285
1425-285=1140
1140 divided by 19 = 60
To check: Divide 1425 by 75 to get 19.
Calculating Volume Practice
In a shape or space, volume refers to the quantity that can be accommodated.
Exactly how is volume determined?It's a formula: V = lwh. six-faced solid object in three dimensions. an indication of an object's length. an indicator of an object's width.
In a shape or space, volume refers to the quantity that can be accommodated. Remember that volume is equal to the number of cubes that can completely occupy a space. Area is the number of squares that can cover a space (in square units) (cubic units). For calculating volume, each 3D shape has a formula.
In a shape or space, volume refers to the quantity that can be accommodated.
The complete question is,
In 7th grade mathematics, what is volume?
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Question Find the value of y for the given value of x. y=3x+2;x=0.5
Answer:
y=3.5
Step-by-step explanation:
y=3(0.5)+2
y=1.5+2
y=3.5
Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the f(x) plant exceed that of the g(x) plant? month (x) f(x) = 3x g(x) = 5x + 12 1 3 17 2 9 22.
In the 4th month, the height of the f(x) plant exceeds that of the g(x) plant. This can be solved using the concept of polynomials.
What is polynomials?When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
Exponents that may be added, subtracted, or multiplied are a part of algebraic expressions called polynomials.Different forms of polynomials exist. linear equations with monomial coefficientsa polynomial with a single term called a monomial.Binomial quadratic equation (A binomial is a polynomial with two, unlike terms).Month (x)
f(x) = 3x / g(x) = 5x + 12
⇒f(x) × g(x) = 3X
⇒g(x) = 3X/ 5x + 12
At 4th month let x = 4
f(x) =g(x)
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The complete question is as follows:
Two different plants that grow each month at different rates are represented by the functions f(x) and g(x). In what month does the height of the f(x) plant exceed that of the g(x) plant?
Month (x) / f(x) = 3x / g(x) = 5x + 12
1 / 3 / 17
2 / 9 / 22
A) Month 3
B) Month 4
C) Month 5
D) Month 6
A frequency table of grades has five classes (A, B, C, D, F) with frequencies of 4, 14, 15, 5, and 1 respectively.
Using percentages, what are the relative frequencies of the five classes?
So the relative frequencies of the five classes are:
A: 10.25%
B: 35.89%
C: 38.46%
D: 12.82%
F: 2.56%
What is the Frequency?
Frequency refers to the number of times a specific event or value occurs within a set of data. It is a measure of how often something happens or occurs.
A relative frequency is a measure of how often a certain event or value occurs within a set of data, expressed as a proportion or percentage of the total number of events or values.
To find the relative frequencies of the five classes in percentage, you need to divide the frequency of each class by the total number of observations, and then multiply by 100 to express the result as a percentage.
The total number of observations can be found by adding up the frequencies of all five classes: 4 + 14 + 15 + 5 + 1 = 39
To find the relative frequency of class A, divide the frequency of class A (4) by the total number of observations (39) and then multiply by 100: 4/39 * 100 = 10.25%
Similarly, you can find the relative frequencies for the other classes:
Class B: 14/39 * 100 = 35.89%
Class C: 15/39 * 100 = 38.46%
Class D: 5/39 * 100 = 12.82%
Class F: 1/39 * 100 = 2.56%
So the relative frequencies of the five classes are:
A: 10.25%
B: 35.89%
C: 38.46%
D: 12.82%
F: 2.56%
It's worth noting that the sum of all relative frequencies should be equal to 100%.
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A cube-shaped box has a surface area of 384 cm2. Jason stacks 12 of these boxes to make a display for his store. What is the total volume in cubic centimeters of the boxes in the display?
The total volume in cubic centimeters of the boxes in the display is 4608√6.
Therefore the answer is 4608√6.
The formula for finding surface area of a cube of side a is
A = 4a²
The formula for finding volume of a cube of side a is
V = a³
Given that surface area of a cube is 384 cm², that is
4a² = 384 cm²
a² = (384/ 4) cm²
Therefore, a = 4√6 cm
Now volume of a single cube can be found by
V = a³
V = (4√6 cm)³
V = 384√6 cm³
Therefore volume of 12 such cubes is
= 12V
= 12×384√6 cm³
= 4608√6 cm³
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Which type of triangle is this triangle with length of sides 7 cm 8 cm and 9 cm? (a) Triangle with lengths of sides 7 cm, 8 cm and 9cm. (b) ABC with AB = 8.7 cm, AC = 7 cm and BC = 6cm. (c) PQR such that PQ = QR = PR = 5cm. (d) DEF with D = 90 degrees (e) XYZ with Y = 90 and XY = YZ (f) LMN with L = 30, M = 70 and N = 80.
So, option (a) is the correct answer.
(a) Triangle with lengths of sides 7 cm, 8 cm and 9cm is a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 9^2 = 7^2 + 8^2, which is true, hence the triangle has a right angle.
(b) ABC with AB = 8.7 cm, AC = 7 cm and BC = 6cm can't be determined as it depends on the angles, as the sides are given but the angles are not.
(c) PQR such that PQ = QR = PR = 5cm is an equilateral triangle. This is because in an equilateral triangle all three sides are of equal length.
(d) DEF with D = 90 degrees can't be determined as only the angle is given, we need the length of the sides as well
(e) XYZ with Y = 90 and XY = YZ can't be determined as the angle and the sides are not enough information
(f) LMN with L = 30, M = 70 and N = 80 is not a triangle as the sum of two sides is less than the other side, hence the triangle inequality theorem is violated.
Therefore, Option (a) is the correct answer.
It's worth noting that a triangle can be defined by its three sides as well as by its three angles, but in any case, we need enough information to determine the type of triangle.
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A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.
Distance to Stations
Time in Minutes
(x) Distance in Miles
(y)
24 18
44 33
76 57
96 72
What is the constant of proportionality for this relationship?
the constant of proportionality for this relationship is 3/4
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, A poster at the train station shows the number of miles to different stations and the time it takes for the train to travel there.
Time in Minutes(x) Distance in Miles(y)
24 18
44 33
76 57
96 72
From the general formula of constant of proportionality
constant of proportionality = y/x
constant of proportionality (k) = 18/24
constant of proportionality (k) = 3/4
Therefore, 3/4 is the constant of proportionality for this relationship.
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What can I change in this equation to make it true
x-6y=4
Answer: y=1/6x−2/3
Step-by-step explanation:
-6y= x-4
/-6 . /-6
y= 1/6x-2/3
*somethin like this*
Scenario #2
There are 3 identical snow jackets available for purchase at 3 different
stores. The original prices of the jackets are as follows
Store #1 SHO
Store #2 $98
Store #3: $105
The jacket at store #Ils on sale for 18% off. The jacket at store #2 has
an advertised price in this weeks catalog that is a 15% decrease from the
original price. Both jackets at store #I and store #2 have an 8% tax
attached, after the discounts are applied Store #3 is online and does not
have sales tax The original price of the jacket is a 10% increase from the
now advertised sales price There is a $3. 99 shipping and handling fee.
Which store has the best deal
The total cost at Store #2 is the lowest due to the combination of the 15% discount, 8% tax, and no shipping and handling fee.
Store #1 SHO
Original price: $98
Discount: 18%
Discounted price: $80.04
Tax: 8%
Total price: $86.44
Store #2
Original price: $98
Discount: 15%
Discounted price: $83.10
Tax: 8%
Total price: $89.78
Store #3
Original price: $105
Discount: 10%
Discounted price: $94.50
Tax: 0%
Shipping & Handling: $3.99
Total price: $98.49
Therefore, Store #2 has the best deal on the snow jacket, with a total price of $78.37 after discounts and taxes are applied.
The best deal for the snow jacket is at Store #2. After applying the discounts and taxes, the total price of the jacket is $78.37. The original price at Store #2 is $98 and the discount is 15%, bringing the discounted price to $83.10. The tax is 8%, bringing the total price to $89.78. Store #1 has an 18% discount and an 8% tax, resulting in a total price of $86.44. Store #3 has a 10% discount, no tax and a $3.99 shipping and handling fee, resulting in a total price of $98.49. Therefore, Store #2 is the best deal.
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find the midpoint of the line segment.
Answer:
(-3,0)
Step-by-step explanation:
Step-by-step explanation:
Bottom line point
( -5, -3 )
( -1, 3 )
Midpoint:
( -3, 0 )
What is the inverse operation of log?
The inverse operation of log is antilog.
Mathematicians use the logarithm to express the inverse function of exponentiation. That is, the logarithm of a given number p is the exponent to which another fixed number, the base b, must be raised in order to obtain that number p. In the simplest case, the logarithm counts how many times the same factor appears in repeated multiplication.
The sum of the logarithms of two numbers says a and b, is the logarithm of the product of the two numbers. Both numbers must have the same base. In other words, this theorem is known as the “product rule for logarithms”.
The difference of the logarithms of two numbers, such as a and b, is equal to the logarithm of their division. Even in this case both numbers should have the same base. There is another name for this theorem, which is the “quotient rule for logarithms”.
Let f(x) = logₐx
y = logₐx
Now, to find the inverse of the function, swap the variables x and y.
x = logₐy
y = aˣ
Thus, the inverse operation of log is antilog.
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A bicyclist starts from rest and accelerates along a straight path to a speed of 12.15 m/s in a time of 4.5 seconds. What is the bicyclist’s acceleration in m/s2?
A. .37
B. 54.7
C. 2.7
D. 6.8
The bicyclist’s acceleration is 2.7 m/s²
the correct answer is an option (C)
We know that the acceleration is nothing but the change in velocity over the change in time.
A = Δv / Δt
where, Δv = change in velocity
Δt = change in time
A = acceleration
Here, we have been given a bicyclist starts from rest and accelerates along a straight path to a speed of 12.15 m/s in a time of 4.5 seconds.
So, Δv = 12.15 m/s and Δt = 4.5 seconds
Using above formula of the acceleration would be,
A = Δv / Δt
A = 12.15 / 4.5
A = 2.7 m/s²
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Unit 7: right triangles and trigonometry 7-5H
Applying the trigonometric ratios, the values of x are:
1. x = 7.3
2. x = 33.3
3. x = 21.3
4. x = 31.9
5. x = 25.6
6. x = 11.0
7. x = 41.8°
8. x = 64.2°
What are the Trigonometric Ratios?These ratios include:
sin ∅ = opp./hyp.tan ∅ = opp./adj.cos ∅ = adj./hyp.1. ∅ = 63
adj. = x
hyp. = 16
Therefore,
cos 63 = x/16
x = cos 63 * 16
x = 7.3
2. ∅ = 39
opp. = 27
adj. = x
Therefore,
tan 39 = 27/x
x = 27/tan 39
x = 33.3
3. ∅ = 49
adj. = 14
hyp. = x
Therefore,
cos 49 = 14/x
x = 14/cos 49
x = 21.3
4. ∅ = 15
adj. = x
hyp. = 33
Therefore,
cos 15 = x/33
x = cos 15 * 33
x = 31.9
5. ∅ = 52
opp. = x
adj. = 20
Therefore,
tan 52 = x/20
x = tan 52 * 20
x = 25.6
6. ∅ = 27
hyp. = x
opp. = 5
Therefore,
sin 27 = 5/x
x = 5/sin 27
x = 11.0
7. ∅ = x
opp. = 4
hyp. = 6
Therefore,
sin x = 4/6
x = sin^(-1)(4/6)
x = 41.8°
8. ∅ = x
adj. = 14
opp. = 29
Therefore,
tan x = 29/14
x = tan^(-1)(29/14)
x = 64.2°
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shari has twelve cards, numbered from one to twelve. she randomly draws three cards with replacement. what is the probability that shari draws an even card and then two odd cards?
Shari has twelve cards, numbered from one to twelve. She randomly draws three cards with replacement. What is the probability that Shari draws an even card and then two odds.
a. 3/8
b. 1/16
c. 1/4
d. 1/8
I think the answer is 3/8.
Simplify the radical √√189².
O 3√2d
O 20³√3
Od√180
3d+√2a
Answer:
The first step is to simplify the double radical.
√√189² = √(189²) = √(189*189) = √(35281)
Now, we simplify the radical by finding the prime factorization of 35281:
35281 = 189² = (189)(189) = (363)(363) = (3²*63²)
So, we can simplify the radical as:
√35281 = √(3²63²) = 3√(63²) = 3√(6363) = 3√3969 = 3√(31323) = 3√(3²1323) = 3*63 = 189
Therefore, √√189² = √(189*189) = √35281 = 189
Step-by-step explanation:
For what value of k will roots of the equation be real and equal if 9x 2 3kx 4 0?
A quadratic equation 9x² + 3kx + 4 = 0 has equal roots. Thus, the values of k are -4, and +4.
What is quadratic equation?The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here.
The given problem can be solved using the concepts of quadratic equations.
1. The given quadratic equation is 9x² + 3kx + 4 = 0.
2. For an equation to have equal roots the value of the discriminant is 0,
=> The discriminant of a quadratic equation ax² + b x + c = 0 is given by the formula,
=> Discriminant ( D ) = [tex]\sqrt{b^2 - 4ac}[/tex]
=> For equal roots D = 0.
3. Substitute the values in the above formula:
⇒ [tex]\sqrt{(3k)^2 - 4*9*4}[/tex] = 0
⇒ [tex]{9k^2 - 144}[/tex] = 0
⇒9k² = 144
⇒ k² = 16
⇒ k = ± 4
Therefore, the values of k are -4, and +4.
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determine whether the underlined number is a statistic or a parameter.
in a study of all 2462 seniors at a college, it is found that 55% own a vehicle.
choose the correct statement below.
a. statistic because the value is a numerical measurement describing a characteristic of a population
b. parameter because the value is a numerical measurement describing a charateristic of a sample
c. parameter because the value is a numerical measurement describing a characteristic of a population
d. statistic because the value is a numerical measurement describing a characteristic of a sample
Since the value is a numerical measurement representing a property of a sample, it is statistical.
Given that a sample of workers is chosen, and it is discovered that 55% of them possess a car.
Let's first clarify the distinction between a parameter and a statistic before moving on to the questions.
Parameters are numerical summaries of population statistics. However, statistics are numerical summaries of sample data.
Sample is a subset of the population; as such, it is just a small percentage of the whole population.
The percentage of the sample of employees in this case is 55%. Statistic refers to a numerical representation of data about a sample.
The value is statistical since it is a numerical measurement that describes a property of a sample.
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y + z = 4
y - z = 8
Step-by-step explanation:
the answer is in the photo
What is K in the equation y?
The amount of the constant k is known as the "constant of proportionality".
What is K in an equation?Given any position, we can calculate k by dividing the y-coordinate by the x-coordinate because k is constant (the same for every point). Where k is the constant of variation, y = kx.
We refer to a relationship between two variables as having a direct relationship when the equation for the relationship is of the form y = kx, where k is a constant. The "constant of proportionality" is the value of the constant k.
For some constant k, often known as the proportionality or variational constant, y=kx. (Some textbooks will refer to direct variation as "y varies as x," "y varies proportionally as x," or "y is directly proportional to x.
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una sala de cine redujo el tamaño de sus bolsas se palomitas de maiz enun 20%. Si las bolsas viejas contenian 15 tazas de palomitas de miaz. cuanto contienen las bolsas nuevas?
Luego de reducir la cantidad de palomitas en 20% en las bolsas, la nueva cantidad es 12 tazas.
¿Cuanto contienen las bolsas nuevas?Recordar que para si tenemos un valor V y a este lo decresemos en un porcentaje X, el nuevo valor será:
V' = V*(1 - X/100%)
En este caso, sabemos que originalmente teniamos 15 tazas de palomitas de maiz, y el valor de X será 20%.
Entonces tendremos:
V' = (15 tazas)*(1 - 20%/100%)
V' = (15 tazas)*0.8 = 12 tazas
Eso es lo qe contienen las nuevas bolsas.
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