Answer:
f(x) = ax^2 + bx + c
I) f(1) = a + b + c = -2
II) f(2) = 4a + 2b + c = -2
III) f(3) = 9a + 3b + c = -4
II - I
IV) 3a + b = 0
III - I
V) 8a + 2b = -2
V - 2IV
2a = -2 --> a = -1
3(-1) + b = 0 --> b = 3
(-1) + (3) + c = -2 --> c = -4
f(x) = -x^2 + 3x - 4
a sunflower is planted in a garden and the height of the sunflower increases by 11% per day. 2.53 days after being planted the sunflower is 13 inches tall.
The sunflower had a height of 13 inches on day 0 and 13.91 inches on day 1.
Because sunflowers are big feeders and require a slightly alkaline soil (pH 6.0 to 7.5), make sure we put them in nutrient-rich soil. Before planting, we should also make sure the soil is weed-free. Since a sunflower is cultivated in a garden, its height grows by 7% every day. The sunflower is 15.7 inches tall 2.79 days after being planted. To get the sunflower's 1-day growth factor, apply the following calculation:
X x (1 + 0.07) ^ 2.79 = 15.7
X x 1.07 ^ 2.79 = 15.7
1.2077X = 15.7
X = 15.7 / 1.2077
X = 13
13 x 1.07 = 13.91
The sunflower therefore measured 13 inches on day 0 and 13.91 inches on day 1.
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In Figure 1, a parallelogram is drawn in a trapezium. If the area of the parallelogram is 390 cm², find the area of the trapezium.
Step-by-step explanation:
the area of the parallelogram is
baseline × height.
we know the baseline (15 cm), because as parallelogram it must have 2 pays off equal sides. so, the bottom side must be 15 cm too.
15×height = 390
height = 390/15 = 26 cm
now, the height of the triangle on the right is the same height.
and the baseline of this triangle is 25 - 15 = 10 cm.
the area of a triangle is
baseline × height / 2
so, in our case
10 × 26 / 2 = 10×13 = 130 cm²
therefore the area of the trapezium is the area of the parallelogram plus the area of the triangle :
390 + 130 = 520 cm²
helppppp me please with this question
The total weight is 57kg
The perimeter = 2×(8+6)
= 2(14) = 28m
The diagonal = √8²+6²
= √64+36
100 = 10m
The total length of the frame =
28+10 = 38 m
Therefore the total Weight =
38× 1.5 kg = 57 kg
What is the formula for weight?
The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity.
You must multiply the sectional area, length, and density collectively to determine the weight of your metal. The product must then be divided by 1,000 in order to convert the weight to kilograms. There are several online metal weight calculators that you may use to figure out the weight of your metal product.
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Amy has 4 pound of ground pork to make meatballs she uses 3/8 pound per meatball to make 9 meatballs.how many 1/8 pound meatballs can Amy make with the remaining turkey ?
Amy can make 29 meatballs from the remaining beef.
What are mathematics operations?
An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.A zero-arity operation, also known as a nullary operation, is a constant.The mixed product is an example of an arity 3 operation, also known as a ternary operation.Amy has 4 pounds of ground beef to make meatballs and he uses 3/8 pound per meatball to make 9 meatballs
We have to subtract 3/8 from 4
= 4 - 3/8
= 29/8
There are 29/8 pounds of ground beef left
Therefore the number of 1/8 pound meatball that can be produced from 29/8 pounds of ground beef can be calculated as follows;
= 29/8 ÷ 1/8
= 29
Hence Amy can make 29 meatballs
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Translate each mathematical sentence into words
Ø⊆N
"An empty set is included in set N" is the translation of the mathematical sentence.
How to translate a mathematical sentence into wordsA set is defined as a collection of well-defined objects, numbers or things. In set theory, we use different symbols to represent statements.
To translate Ø⊆N, we need to know the meaning of the symbols we have:
Ø means empty set (A set that does not contain anything).
⊆ means subset (is included in)
N means set N
So we can translate Ø⊆N as:
An empty set is included in set N or
Therefore, the mathematical sentence Ø⊆N can be translated as "an empty set is included in set N"
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What percent would you receive if you earned 8 out of 12 on a quiz?
A- 96%
B- 82%
C- 67%
Answer:
C
Step-by-step explanation:
[tex]\frac{8}{12} \times 100 \approx 67[/tex]
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is more than 8. 42?.
A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. Then the probability that the sample is more than 8.42 is 0.0029 or 0.29%.
Using the normal distribution and the central limit theorem,
The mean is μ = 8.5
The standard deviation is σ = 0.22 .
A sample of 37 is taken, hence n = 37, s = 0.22/√37 i.e. s = 0.0362
The probability that the sample average is more than 8.40 is the p-value of Z when X = 8.4, hence:
Z = X - μ/σ
Z = 8.4 - 8.5/0.0362
Z = 2.76
Z = -2.76 has a p-value 0.0029
0.0029 = 0.29% probability that the sample average is more than 8.40.
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The total cost of a jacket and a pair of shoes was $91.43. if the price of the jacket was $7.65 less than the pair of shoes, what was the price of the jacket? express your answer as a simplified fraction or a decimal rounded to two places.
The price of the jacket in decimals is $ 41.89
The decimal numeral system is widely used to express both integer and non-integer numbers.
The Hindu-Arabic number system has been expanded to include non-integer values. The term "decimal notation" is used to refer to the way that numbers are represented using the decimal system.The decimal system has been developed to represent any real number in an endless number of decimals by using any number of digits after the decimal separator (see decimal representation). Since there are only a few non-zero digits beyond the decimal separator, the decimal numerals in this context are sometimes referred to as terminating decimals. An unending decimal that, at a given point, continues to use the same set of digits repeatedly is said to be recurrent.Let the price of the jacket be x.
Price of the pair of shoes = x + 7.65
Total cost of both the pieces = x + x + 7.65 = 2x+7.65
But the total cost is $91.43
Hence forming a linear equation we get :
$91.43= 2x+7.65
solving the linear equation for x we get :
x=$ 41.89
hence the cost of the jacket is $ 41.89 .
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suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
I would tell her that out of all the people who took the verbal section, 23% scored higher than she did and 77% scored at or below her score. For the math section, 94% of those who took the exam scored at or below her score and 6% scored higher than she did.
Here's the complete question:
Suppose that your younger sister is applying for entrance to college and has taken the sat. she scored at the 77th percentile on the verbal section of the test and at the 94th percentile on the math section of the test. because you have been studying statistics, she asks you for an interpretation of these values. what would you tell her?
I would tell her that out of all the people who took the verbal section, ___% scored higher than she did and ___ % scored at or below her score. For the math section, ___ % of those who took the exam scored at or below her score and ____ % scored higher than she did.
For the Verbal section: 100 - 77 = 23
For the Maths section: 100 - 94 = 6
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help me, i need the answers quickly
Answer:
#7 m∠4 = 30°
#8. m∠5 = 150
#22. A'(-6, -3), B'(-3, 4), C'(3, 5)
*** You may just want to put the coordinate points: (-6, -3), (-3, 4), (3, 5) without the A', B', C'. ***
#23. A'(6, -3), B'(3, 4), C'(-3, 5)
Step-by-step explanation:
#7 Angles 30° and ∠4 are corresponding angles and hence equal
#8 ∠4 and ∠5 are supplementary linear angles and add up to 180° So m∠5 = 180 - m∠4 = 180 - 30 = 150°
#22 Reflection about the x-axis means the x-coordinates do not change but the new y-coordinate is the negative of the original y coordinate
In other words, a point(x, y) in the pre-image becomes (x, -y) in the image
#23 With a 180° rotation both x and y axes change signs. (x, y) becomes (-x, -y)
Mike Lasueze is a salesperson in the appliance department at Wicklow Appliance Inc. He is guaranteed a minimum salary of $220 per week or 5.5% of his total sales, whichever is greater. What is his gross pay for a week in which his total sales were $8,400?
For a sale of $8400 made his gross pay is $373.21
In this question, we have been given Mike Lasueze is guaranteed a minimum salary of $220 per week or 5.5 percent of his total sales, whichever is greater.
We need to find his gross pay for a week in which his total sales were $8,400
weekly pay = $220
commission = 5.5% of sales
= 0.055 of sales
let m be the total sale and his gross pay be represented by y
So, we get an equation for the total/gross pay:
y = 0.055x + 220
Required is the gross pay y for x = 8400
y = 0.055(8400) + 220
y = 682
Therefore, for a sale of $8400 made his gross pay is $373.21
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Number 1 pls help show your work
Answer:
60
Step-by-step explanation:
0.2x = 12
x=60
:]
Which one is it help
Answer:
c the last 1
Step-by-step explanation:
bc y where the line ends on y is more than 30 and only 1 line is 5 so 35
Answer:
I think its the last one but it could also be the first
Which two transformations can be used to obtain the graph of G(x) = -4√x , from the graph of F(x)=√x?
Given: The base function
[tex]F(x)=\sqrt{x}[/tex]To Determine: The transformation that would give the function G(x)
[tex]G(x)=-4\sqrt{x}[/tex]Solution
Let us plot the graph of the base function and the new function as shown below
It can be observed that there exist a reflection across the x-axis, also a vertical stetch by a factor of 4
Hence, the correct answer is a vertical stretch by a factor of 4, followed by a reflection across the x-axis, OPTION A
Type the correct answer in the box. Use numbers instead of words. An expression is shown. 36 ÷ (4 + 2) What is the value of the expression?
The result of the expression 36 ÷ (4+2) is 6
The expression is
36 ÷ (4+2)
To solve this expression, we have to apply the arithmetic operations in the given expression
An arithmetic operation is the operation specified by combining number or variable with one arithmetic operator. The basic arithmetic operations are addition, subtraction, division and multiplication.
First do the arithmetic operations in the bracket
Add 4 and 2 in the expression
36 ÷ (4+2) = 36 ÷ 6
Divide the number 36 by 6 in the expression
36 ÷ 6 = 6
Hence, the result of the expression 36 ÷ (4+2) is 6
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MATHHHHHHHHHHHHHHHHHHHHHH LOOK AT PHOTO
Answer:
9/25
0.36
Step-by-step explanation:
Part 1:
You divide 36 by 100 to find the fraction:
36/100
Then, simplify:
36/100 = 9/25
.................................................................................
Part 2:
To find the decimal of a percentage, divide the percent by 100. When dividing by 100, you get the answer by moving the decimal point two spaces to the left.
36% = 0.36
Write the conditional and converse of the statements below:
"parallel lines have the same slope."
Converse of the statements will be as If two lines are parallel, then they have equal slopes. Conditional statement will be; If two lines have same slopes, then the lines are parallel.
How do parallel lines work?Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.
Only the slopes of two lines are same then it can be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel.
Converse of the statements will be as If two lines are parallel, then they have equal slopes.
Conditional statement will be; If two lines have same slopes, then the lines are parallel.
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URGENT NEED!
Consider the conjecture, "Any number divisible by 2 is also divisible by 4" Is each number a counterexample of the conjecture? Select yes or no
12 yes or no
19 yes or no
22 yes or no
28 yes or no
30 yes or no
Which number is next in the following sequence?
1,2,2,4,8,32
The classification of the numbers as counterexamples of the conjecture is given as follows:
12: no.19: no.22: yes.28: no.30: yes.The next number in the sequence is of 256.
Which numbers are counter example of the conjecture?The conjecture is defined as follows:
"Any number divisible by 2 is also divisible by 4"
Hence the counterexamples are the numbers that are divisible by 2 but not by 4, then they are classified as follows:
12: no. (divisible by both 2 and 4).19: no. (not divisible by 2, hence it cannot be a counterexample of the conjecture).22: yes. (divisible by 2 but not by 4).28: no. (divisible by both 2 and 4).30: yes. (divisible by 2 but not by 4).SequenceEach number in the sequence is given by the multiplication of the two previous terms, as:
1 x 2 = 2.2 x 2 = 4.4 x 2 = 8.8 x 4 = 32.Then the next number is calculated as follows:
32 x 8 = 256.
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Line a is perpendicular to line bLine a passes through the points (1,-3) and (9,-5)Line b passes through the point (-8,32)The equation of line b is y=___
y=4x+64
Explanation:
Two lines are perpendicular if the product of their slopes is -1.
Step 1: Find the slope of the line a
Line a passes through the points (1,-3) and (9,-5)
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-5-(-3)}{9-1} \\ =\frac{-5+3}{8} \\ =-\frac{2}{8} \\ =-\frac{1}{4} \end{gathered}[/tex]The slope of line a = -1/4
Step 2: Determine the slope of line b.
Let the slope of line b = k
Since the product of the two slopes is -1:
[tex]\begin{gathered} k\times-\frac{1}{4}=-1 \\ k=-1\times-4 \\ k=4 \end{gathered}[/tex]The slope of line b = 4
Step 3: Find the equation of line b.
Line b passes through the point (x1,y1)=(-8,32) and has a slope, m = 4.
Using the slope-point form of the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]Substitute the given values
[tex]\begin{gathered} y-32=4\mleft(x-\mleft(-8\mright)\mright) \\ y-32=4\mleft(x+8\mright) \\ y-32=4x+32 \\ y=4x+32+32 \\ y=4x+64 \end{gathered}[/tex]The equation of line b is y=4x+64.
What is an equation of the line that passes through the point (-4,8)(−4,8) and is parallel to the line x+y=6x+y=6?
The equation of the line that passes through the point; (-4, 8) and is parallel to x + y = 6 is; x + y = 4.
What is the equation of the line that passes through the given point and is parallel to the given line?By expressing the given linear equation in slope-intercept form; it follows that we have;
x + y = 6
y = -x + 6
Hence, the slope of the equation by comparison with; y = mx + c is; -1.
Therefore, the slope of the required equation is same as the two lines are said to be parallel.
Therefore, the required equation from point-slope form of an equation is;
( y - 8) = -1 ( x - (-4))
y - 8 = -x - 4
x + y = -4 +8
x + y = 4.
Ultimately, the required equation is; x + y = 4.
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You and your family went out to dinner if the dinner was $52 and you left a 25% tip how much did your dinner cost altogether
Using percentages we can conclude that the total cost of the dinner was $65.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total cost of dinner:
The dinner cost was $52.The tip was 25% of the dinner, then we need to find the 25% of 52 as follows:
52/100 × 25 = 13So, the tip was $13.The total cost of the diner was $52 + $13 which is $65.
Therefore, using percentages we can conclude that the total cost of the dinner was $65.
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how do i create a graph of this table? and what expression should i put.
(-5 , 0) is the point we got after slope-intercept form of equation .
What exactly does slope intercept mean?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is called as the y-intercept, and the slope refers to how sharp the line is.A line has the equation 3x + 4y + 5 = 0. Using the slope intercept form, estimate the line's slope and y-intercept.Equation from the value given table -
1) y = 3x + 15
2) y = 5x + 25
3) y = 7x + 35
4) y = 9x + 45
5) y = 10x + 50
graph attached of all equation .
(-5 , 0) is the point .
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simplify the following expression
The value of solution of expression is,
⇒ (3⁵)
We have to given that;
The expression is,
⇒ (3³ × 3⁴) ÷ 3²
Now, We can simplify by rule of exponent as;
⇒ (3³ × 3⁴) ÷ 3²
⇒ (3³ ⁺ ⁴) ÷ 3²
⇒ (3⁷) ÷ 3²
⇒ (3⁷⁻²)
⇒ (3⁵)
Thus, The value of solution of expression is,
⇒ (3⁵)
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if q= (7 -1) and r= (-4 5) find | q+ r|
Answer: 6+1=7
Step-by-step explanation:
the unit circle has center ▼ left parenthesis 1 comma 1 right parenthesis left parenthesis negative 1 comma negative 1 right parenthesis left parenthesis 0 comma 0 right parenthesis and radius ▼ 1. negative 1. startroot 2 endroot . the equation of the unit circle is ▼ y equals mx plus b. x squared plus y squared equals 1. y equals ax squared .
x^2+ y^2-2x-2y = 0 has center (1,1) and radius sqrt 2 and the circle x^2+y^2 =1 has center (0,0) and radius 1
the unit circle has center
(1,1) , ( 0,0)
and the unit circle has radius
1 , sqrt 2
for this the equation of the circle is
x^2 + y^2 = 1
if we take center as (0,0) then radius become 1
therefore equation of circle becomes x^2 +y^2 =1
similarly if we take center ( 1,1 ) and radius sqrt 2
then (x -1 )^2 + ( y-1 )^2 =2
x^2 +y^2 -2x- 2y +2 =2
this implies x^2 +y^2 -2x -2y =0
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✨Hello! I need some help it's very urgent I will be marking brainliest✨
first blank: never, sometimes, always
second blank: less than or equal to negative 3, between -3 and 3, greater than or equal to 3, greater than or equal to -3, less than or equal to 3.
third blank: positive number, less than or equal to zero, negative number, negative number, a number greater than or equal to zero.
Answer:
Sometimes, Never, and Always.
(Sounds like a good movie title).
Step-by-step explanation:
See attached image.
A family drives 4 1/2 miles in 1/10 of an hour. How many miles will they drive in 3/4 hours?
Find the measure of 44.
H
130⁰
50°
44
130⁰
50°
44 = [?]° i’m slow someone help
Answer:
Find the measure of each angle. 1. 23. =70°. 2. 45. 5. 24. 9.48 ... Exterior. ANGLE. ¥180-50=130. 6. 213 2106°. =106°. 44-10+42=180. 44 = 148
Step-by-step explanation:
Suppose point P divides the directed line segment XY so that the ratio of XP to PY is 3 to 5. Describe the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3.
Using proportions, the coordinates of point P that divides the directed line segment YX in the given ratio are found according to the following rule:
P - X = 3/8(Y - X).
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem relating the variables.
One example of application is for the coordinates of a point dividing a segment, as the distance between one end point and the dividing point is a fraction of the total length of the segment.
In the context of this problem, we have that point P divides segment XY in a 3:5 ratio, meaning that PX is 3/8 of the total distance y/x, hence the following proportional equation is built:
P - X = 3/8(Y - X).
In which:
X represents the coordinates of point X.Y represents the coordinates of point Y.This equation is used to find both the x-coordinate and the y-coordinate of P, as follows:
For the x-coordinate, P is replaced by x, while X and Y are replaced by it's respective x-coordinates.For the y-coordinate, P is replaced by y, while X and Y are replaced by it's respective y-coordinates.More can be learned about proportions at https://brainly.com/question/24372153
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which equation is equivalent to the equation 5x + 30 = 45
Answer:
A answer is A brainly helps you