Answer:
-3x² -5x -1 = 0-3 (quadratic)-5 (linear)-1 (constant)Step-by-step explanation:
The equation will be in standard form when terms are listed in order of decreasing degree, and the right side of the equation is 0.
Standard formWe can subtract the right-side expression from both sides to get standard form.
-3x² -8 -(5x -7) = 5x -7 -(5x -7)
-3x² -8 -5x +7 = 0 . . . . . . . simplify a bit
-3x² -5x -1 = 0 . . . . . . . . . collect terms
The standard form equation can be written ...
-3x² -5x -1 = 0
CoefficientsThe quadratic coefficient is the coefficient of the term with degree 2. The quadratic coefficient is -3.
The linear coefficient is the coefficient of the term with degree 1. The linear coefficient is -5.
The constant coefficient is the coefficient of the term with no variables. The constant is -1.
__
Additional comment
We can make the leading coefficient positive by multiplying the equation by -1. This gives ...
3x² +5x +1 = 0
with quadratic, linear, and constant coefficients 3, 5, 1.
This is a legitimate answer to this question. In the case of linear equations, the "standard form" has the constant on the right side of the equal sign, and the leading coefficient is required to be positive. A negative leading coefficient can sometimes lead to errors (when the sign is overlooked), so having a positive leading coefficient is often preferred.
What is the difference between the smallest 7-digit number and the largest 6-digit number?
Answer:
the greatest 7 digit no.is = 999,99,99 the smallest 6 digit no.is= 1,00,000
Step-by-step explanation:
Sorry if I'm wrong I tried.
Find the total surface area. A. 78 B. 98 C. 69 D. 92
The total surface area of the figure is 92 m².
How to find the surface area of a figure?The surface area of a figure is the sum of the whole sides of the figure.
Therefore,
surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 + 1 / 2 (2 + 6)3.5
Hence,
surface area = 16 + 16 + 24 + 8 + 14 + 14
Therefore,
surface area = 32 + 24 + 8 + 28
surface area = 56 + 8 + 28
surface area = 92 m²
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guys please help me
Answer:
-1 and 1
Step-by-step explanation:
Reflecting D over the y-axis maps it onto (1,2).
This is supposed to map onto F(0,3), so this is a shift 1 unit left and 1 unit up.
So, the blanks are -1 and 1, respectively.
Answer: (x + [-1], y + [1])
Step-by-step explanation:
See attached. We can draw, or picture it in our heads, what the reflection would look like. Then we can pick one (or multiple to test) points and see the translation.
We can also test with a set of points. B', (2, 4) becomes G in the transformation. G is at (1, 5)
(1 - 2, 5 - 4) -> (-1, 1)
1
2. Rotate Rectangle ABCD 90° counterclockwise.
Then, translate it along the vector (3,4).
A
D
B
C
-4 -2
4
2
АУ
O
-2.
-4
2
4
X
A'(
B'(
C'(
D'(
A"(
B"(
C"(
D"(
)
)
)
)
HELP ME PLS
Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]
[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]
Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]
[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]
Graph f(x) = 2x - 3 on a coordinate plane.
Can you explain what you are going to do in order to graph this equation?
What do you expect the graph to look like?
Answer:
Create a table.
Plug values into the equation to complete the table.
Use the table to plot points on the graph.
Draw lines through the points on your graph.
The graph should look linear because there is an x that doesn't have a power greater than or less than 1.
A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
Answer:
someone please help me check my page
someone please help me check my pageStep-by-step explanation:
K
Consider a study conducted in 2018 to estimate the percentage of people from a certain region who do not use the
Internet. Complete parts (a) through (c) below.
a. If a 99% confidence level is used, how many people should be included in the survey if the researchers wanted to
have a margin of error of 7%?
There should be people included in the survey.
(Round up to the nearest person as needed.)
rred
The number of people who must be included in the survey, that is, the sample size should be 340.
We assume the sample size to be n.
The confidence interval required is 99%.
The Z-score corresponding to the 99% confidence interval is (Z) 2.58.
The true proportion (p) of the sample is not given, so we assume it to be 50% or 0.5.
The margin of error for the sample (E) is given to be 7% or 0.07.
By the formula of margin of error, we know that:
E = Z√[{p(1 - p)}/n].
Putting in the values, we have, we get:
0.07 = 2.58√[{0.5*0.5}/n],
or, (0.07/2.58)² = 0.25/n,
or, n = 0.25/{(0.07/2.58)²} = 339.6122449 ≈ 340.
Thus, the number of people who must be included in the survey, that is, the sample size should be 340.
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what is the digit of 7 in 906point7
A population of n = 10 scores has = 50 and = 5. what is the population variance? 5
The value of the Population Variance is 100.
According to the statement
we have given that the A population of N = 10 scores has μ = 50 and σ = 5. And we have to find the population variance.
So, For this purpose,
we know that the population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population.
Population variance = mean /(standard deviation/number of samples)
Population variance = μ / (σ /N )
Substitute the values in it and then
Population variance = 50 / (5 /10 )
Population variance = 50 / (0.5 )
Population variance = 100.
So, The value of the Population Variance is 100.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
A population of N = 10 scores has μ = 50 and σ = 5. What is the population variance?
a. 10
b. the square root of 5
c. the square root of 50
d. 25
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In quadrilateral qrst, angle r s t measures (5x 15)°. angle tqr measures (4x 3)°. circle p is inscribed with quadrilateral q r s t. what is the measure of angle rst?
The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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general term for -13, -11, -9, -7
The general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.
Arithmetic progression-13, -11, -9, -7
First term, a = -13Second term = -11Common difference, d = Second term - first term
= -11 - (-13)
= -11 + 13
= 2
Therefore,
Tn = a + (n - 1)d
Where,
n = number of termsTn = a + (n - 1)d
= -13 + (n - 1)2
= -13 - 2n - 2
Tn = -15 - 2n
So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.
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The river is 602 feet wide at Big Bend Corner. A boy is in the shallow
water, 135 feet from the shore. How far is the boy from the other side of
the river?
we conclude that the distance to the other side is 467 feet.
How far is the boy from the other side of the river?
We know that the width of the river is 602ft. This means that the distance from shore to shore is 602 feet.
If the boy is at a distance of 135 from the shore, then the distance to the other side is given by the difference:
d = 602ft - 135ft = 467ft
Then, we conclude that the distance to the other side is 467 feet.
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You start at (-4, 0). You move left 1 unit and down 5 units. Where do you end?
Answer: (-5, -5)
Step-by-step explanation:
(-4, 0)
Here, -4 is our x value and 0 is our y value
The x value moves horizontal (left and right) while the y value moves vertical (up and down)
If we move 1 unit left, we change x by -1 so, -4 -1 = -5
If we move 5 units down, we change y by -5 so, 0 -5 = -5
Therefore,
our new endpoint is: (-5, -5)
please help 14 points ASAP
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median: Upper quartile:
Maximum:
Interquartile range:
The desired measures for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74.Maximum: 80.IQR: 20How to find the five number summary and interquartile range of the data-set?The five number summary is composed by the measures explained below, except the IQR.
The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centered at a=1. Write the Taylor series in summation notation
Answer:
[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Step-by-step explanation:
Taylor series expansions of f(x) at the point x = a
[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]
This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.
[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]
[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]
[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]
[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]
Substituting the values in the series expansion gives:
[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]
Factoring out e⁴:
[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]
Taylor Series summation notation:
[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]
Therefore:
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Find the length of the function over the given interval. y = 3x from x = 0 to x = 2
The length of the function y = 3x over the given interval [0, 2] is 3.2 units
For given question,
We have been given a function y = 3x
We need to find the length of the function on the interval x = 0 to x = 2.
Let f(x) = 3x where f(x) = y
We have f'(x) = 3, so [f'(x)]² = 9.
Then the arc length is given by,
[tex]\int\limits^a_b {\sqrt{1+[f'(x)]^2} } \, dx\\\\= \int\limits^2_0 {\sqrt{1+9} }\, dx\\\\=\sqrt{10}\\\\ =3.2[/tex]
This means, the arc length is 3.2 units.
Therefore, the length of the function y = 3x over the given interval [0, 2] is 3.2 units
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Use the given data set to complete parts (a) through (c) below. (Use α=0.05.)
1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables
2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.
What is the linear correlation coefficient?This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.
The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159
The results of the test is in the attachment
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Pls help I’ll brainlest
Asap
Answer:
C. slope
Greetings !
The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).
Answer: slope.
Step-by-step explanation:
Using the following table determine the probability a person tests positive who does not actually have Tuberculosis.
Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:
c. 49/148.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:
p = 98/296 = 49/148.
Which means that option c is correct.
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The probability a person tests positive who does not actually have Tuberculosis is 1/100
How to determine the probability a person tests positive who does not actually have Tuberculosis?The probability is given as:
The probability a person tests positive who does not actually have Tuberculosis.
This is a conditional probability, and it can be calculated using
P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)
Using the given table of values, we have:
P = 98/9800
Evaluate the quotient
P = 1/100
Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100
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1. Find the length of a.
Answer:
Step-by-step explanation:
[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]
==> 84.57
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the
translation?
(x + 5, y-3)
(x + 5, y + 3)
(x, y)(x-3, y + 5)
(x, y) (x + 3, y + 5)
(x, y)
O(x, y)
Mark this and return
Save and Exit
lext
Submit
Answer:
(x+5, y-3)
Step-by-step explanation:
I would say this because when a plane is translated up it would be positive and when it's translated to the left it would be negative,
Which of the following fractions has the largest value 11/20 10/21 9/19 8/17 or 6/13
Answer:
11/20
Step-by-step explanation:
You could turn them all into equivalent fractions, but the common denominator would be 1,763,580. Yuck.
Look at the relationship for the numerators to the denominators. The only numerator that is more than half of its denominator is 11/20. Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5. All of the other numerators are less than half, so that they have to less than .5.
If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.
Después de 15 meses de haber prestado un capital al 5% de rédito, tengo que pagar de interés Q468.75. ¿Qué capital se ha prestado?
The capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The principal P, amount borrowed, at a certain rate of interest R%, for a time of T years, giving an interest of I, can be calculated using the formula:
P = (I * 100)/(R * T).
In the question, we are asked to find the capital borrowed, that is, the principal, when the user pays Q468.75 after 15 months at 5% of income.
Thus, Interest (I) = Q468.75, rate of interest (R) = 5%, and time (T) = 15 months = 15/12 years = 1.25 years.
Thus, the principal P, can be calculated by substituting the values in the formula: P = (I * 100)/(R * T).
P = (468.75*100)/(5*1.25),
or, P = 46875/6.25,
or, P = 7500.
Thus, the capital borrowed, or the principal when the interest was Q468.75 is Q7500.
The provided question is in Spanish. The question in English is:
"After 15 months of having borrowed capital at 5% of income, I have to pay Q468.75 in interest. What capital has been borrowed?"
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I need help here’s a picture can somone explain what I need to do??
Answer:
176 square feet
Step-by-step explanation:
add the areas of the rectangle and triangle
rectangle area is
16 times 8 which is
128
rectangle area is
1/2 times 12 times 8 which is
48
then add them
128 plus 48 is
176 square feet
Janice walks 2 kilometers every morning. how many meters does janice walk each day? a) 0.20 meters b) 20 meters c) 200 meters d) 2,000 meters
Answer: 2000 meters
Step-by-step explanation: A kilometer means 1,000 meters a kilo means 1000. So, 2 x1000 = 2000 meters.
What is the solution for x in the equation?
10x − 4.5 + 3x = 12x − 1.1
x =
Answer: x= 3.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 3.4
Step-by-step explanation:
[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]
Do the data in the table represent a direct variation or inverse variation? Write an equation to model the data in the table?
x 2 4 8 12
y 4 2 1 2/3
Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x
VariationDirect variationy = k × x
4 = k × 2
4 = 2k
k = 4/2
k = 2
when y = 2 and x = 4
y = k × x
= 2 × 4
y = 8
Indirect variationy = k/x
4 = k / 2
8 = k
when y = 2 and x = 4
y = k/x
2 = k/4
2 × 4 = k
k = 8
So,
y = k/x
y = 8/x
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Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
According to the developed scale, a radiant day is 16 times brighter than a dim day.
We assume the brightness of a dim day to be x.
According to the developed scale, the brightness of an illuminated day will be 4 times that of a dim day.
Thus, the brightness of an illuminated day = 4*the brightness of a dim day = 4x.
According to the developed scale, the brightness of a radiant day will be 4 times that of an illuminated day.
Thus, the brightness of a radiant day = 4*the brightness of an illuminated day = 4*4x = 16x.
Now, the ratio of the brightness of a radiant day to the brightness of a dim day = 16x:x = 16x/x = 16:1.
Thus, according to the developed scale, a radiant day is 16 times brighter than a dim day.
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The question provided is incomplete. The complete question is:
"Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 4 times brighter than the next lower category. For example, a day that is dazzling is 4 times brighter than a day that is radiant. How many times brighter is a radiant day than a dim day?
Dim=2
Illuminated=3
Radiant=4
Dazzling=5"
Consider the function . find the vertical asymptote(s) of f(x). x = 0, –9 x = –9 x = 0, 9 x = 9
The vertical asymptote of f(x) is (A) x = 0, –9.
What is a function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.To find the vertical asymptote of f(x):
The vertical asymptotes of a function are the zeroes of the denominator of a rational function
The function is given as: [tex]f(x) = \frac{(x-9)}{(x^{3} -81x)}[/tex]
Set the denominator to 0:
[tex]x^{3} -81x=0[/tex]Factor out x:
[tex]x(x^{2} -81)=0[/tex]Express 81 as 9^2:
[tex]x(x^{2} -9^{2} )=0[/tex]Express the difference between the two squares:
[tex]x(x-9)(x+9)[/tex]Split, [tex]x=0[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].
Solve for x:
[tex]x=0\\[/tex] or [tex]x=-9[/tex] or [tex]x+9=0[/tex].Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.
(See attachment for the graph of f(x))
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The complete question is given below:
Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).
A) x = 0, –9
B) x = –9
C) x = 0, 9
D) x = 9
Given that log 2 = 0.3010 and log 3 = 0.4771 , how can we find log 6 ?
Step-by-step explanation:
log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771
=0.7781
Answer:
[tex]\sf \log_{10}6=0.7781[/tex]
Step-by-step explanation:
Given:
[tex]\sf \log_{10} 2 = 0.3010[/tex]
[tex]\sf \log_{10} 3 = 0.4771[/tex]
To find log₁₀ 6, first rewrite 6 as 3 · 2:
[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]
Substituting the given values for log₁₀ 3 and log₁₀ 2:
[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]
Therefore:
[tex]\sf \log_{10}6=0.7781[/tex]
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