Answer:
a = 3, b = 12
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b
Lets expand the right side:
(x-a)^2-b = (x-a)(x-a)-b
(x-a)(x-a)-b = x^2 -2ax + a^2 - b
The left side is equal to the right, as per the original equation:
x^2-6x-3 = x^2 -2ax + (a^2 - b)
Compare each term:
1) x^2 = x^2 OK
2) -6x = -2ax; a = 3 so that -6x = -2(3)x
3) -3 = (a^2-b); a^2 = (b-3)
a = [tex]\sqrt{b-3}[/tex]
a is 3, from above
3 = [tex]\sqrt{b-3}[/tex]
9 = b-3
b = 12
Charis invested 140. She earned a simple interest of 3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
The amount received by Charis on Simple interest in 2 years will be $8.4
What is Simple Interest?
The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).
It's formula is given by S.I. = PRT/100 where P = principle amount
R= rate and T = time.
Main Body:
P= $140
R= 3%
T= 2 years
so S.I. = 140*2*3/100
S.I. = $ 8.4
Hence total amount received by Charis at the end of 2 years will be $8.4
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The red figure is congruent to the blue figure. Which choice describes a sequence of transformations in which the blue figure is the image of the red figure?
1. Rotate the triangle 90º counterclockwise about the origin and then translate it 7 units left and 1 unit up.
2. Rotate the triangle 90º clockwise about the origin and then translate it 7 units left and 1 unit up.
3. Rotate the triangle 90º counterclockwise about the origin and then translate it 1 unit left and 7 units down.
4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.
What is a rotation?In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).
From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:
(x, y) → (y, -x)
Ordered pair A = (-5, 2) Ordered pair A' = (2, 5)
Ordered pair B = (-5, 6) Ordered pair B' = (6, 5)
Ordered pair C = (-1, 2) Ordered pair C' = (2, 1)
After a translation of 1 unit left and 7 units down, we have:
Ordered pair A' = (2, 5) → Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)
Ordered pair B' = (6, 5) → Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)
Ordered pair C' = (2, 1) → Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)
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What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
It take an ant farm 2 day to conume 1/2 of an apple. At that rate, in how many day will the ant farm conume 2 apple?
the ant will take 8 days to consume 2 apples.
Given, an ant takes 2 days to consume 1/2 of an apple.
We have to find the number of days ant will take to consume 2 apples.
So, ant takes 2 days = consumption of 1/2 apple
ant takes 4 days = consumption of 1 apple
Consumption of 1 apple = ant takes 4 days
Consumption of 2 apples = ant takes 4×2 days
Consumption of 2 apples = ant takes 8 days
Hence, the ant will take 8 days to consume 2 apples.
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For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.
Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.
50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.
It will be demonstrated by:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This suggests the number of victories.
Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.
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The question is -
For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
Examine the equation below used for determining the balance on a bank account. Look through this chapter and your notes to help you write a problem that could be modeled by the equation.
The balance on the bank account at the end of the third quarter of the year is 2,630.80
How to find the compound interest?
Compound interest is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest is found using the formula
A=P(1+r/n)ⁿˣ where:
A= Amountr= interest raten= number of interest applied per period and x= number of time periodTherefore, the amount (A)=2630.80
The P=2500
interest rate is 0.17%
Number of interest applied per period is 365 periods and
number of time period is 3.
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1. Why is identifying
the domain and range important when
defining a function?
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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helppp PLSSSSSSSSSSSSS I NEEED HELPPPPPPPPPPPPPPPPP
Answer:
15c + 19d
Step-by-step explanation:
Here to simplify we have to add like-terms
3c + 14d + c + 11c + 5d = ( 3c + c + 11c) + ( 14d + 5d) = 15c + 19d
Glad to Help
3b(2x-z^3)=2h-7gx change the subject to x
Answer:
Step-by-step explanation:
3b(2x - z^3) = 2h - 7gx Distribute 3b
6bx - 3bz^3 = 2h - 7gx Add 3bz^3 to both sides
6bx = 3bz^3 + 2h - 7gx Add 7gx to both sides
6bx + 7gx = 3bz^3 + 2h Factor left side, factor out a gcf of x
x(6b + 7g) = 3bz^3 + 2h Divide both sides by (6b + 7g) to isolate x
x = (3bz^3 + 2h)/ (6b + 7g)
The number of computer security breaches is expected to increase at a yearly rate of
86%.
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
a physics professor wants to know what percent of physics majors will spend the next several years doing post-graduate research. he has the following probability distribution. x p (x) 1 0.35 2 0.2 3 0.15 4 ? 5 0.10 6 0.05 (a) on average, how many years would you expect a physics major to spend doing post-graduate research?
It can take 3 years that a physics major to spend doing post-graduate research
Given that,
A physics professor is curious about the proportion of physics majors who will pursue post-graduate study during the coming years. He has the probability distribution shown below. x P(x) x*P (x) 1 0.35 2 0.20 3 0.15 4 5 0.10 6 0.05
To find P(X<=3)
P(X<=3)=P(X=0,1,2,3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
= 0.35+0.20+0.15
= 0.7
P(X<=3)=0.7
Hence, A physics major may need to spend three years conducting post-graduate research. and the probability that a physics major will spend no more than three years conducting post-graduate research is 70% or 0.7
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Explain how the equations 2/3m=-4 and -4m=24 are equivalent?
Both 2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent
What are algebraic expressions?Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.
They are also known to be made up of some arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracket ParenthesesWe have the equations;
2/3m=4 and -4m=24
Let's solve for m in the first equation
12m = 2
Divide both side by coefficient of m
m = 2/ 12 = 1/ 6
For the second equation
-4m = 24
Divide both sides by - 4
m = 24/-4
m = 6/ -1
Take inverse
m = 1/6
Hence, the equations are equivalent
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Pls help/ A function (x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
The function rule in slope-intercept form is y = -4x - 2
How to calculate the slope-intercept form of this function?Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following data points:
Point (x, y) = (-1, 2)
Point (x, y) = (0, -2)
In Mathematics, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 2)/(1 - 0)
Slope, m = -4/-1
Slope, m = -4
Note: The y-intercept occurs at the point where the x-value is equal to zero (0).
Now, we can write the function rule for this line in slope-intercept form as follows:
y = mx + c
y = -4x - 2
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Decrease 330 km by 54%.
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
A class of 25 children shares 600 beads.
On a day when 1 child is absent, what is the ratio of the number of children present to the number of beads?
Answer:
Step-by-step explanation:
The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.
The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
The equation for the function of the ordered pair is y =10x+2.
What is equation for the function?
An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.
Here in given order pair , let us take any two points,
[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]
Now using slope formula,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m =10/1 = 10
Now using equation formula,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-2 =10(x-0)
=> y-2 = 10x
=> y=10x+2.
Therefore equation of the following order pair is y = 10x+2.
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consider performing a partial f test to test for the inclusion of pctrush in the model. either in words or formula, what are the null and alternative hypotheses for this test?
The null and alternative hypothesis of the pctrush are explained below.
Given that;
By performing a partial F-test;
In hypothesis testing, the F test is a statistical test that is used to determine whether or not the variances of two populations or two samples are equal. The data in a f test follows a f distribution. In this test, two variances are divided and compared using the f statistic. Depending on the problem's characteristics, a f test can be either one- or two-tailed.
The one-way ANOVA (analysis of variance) test is run using the f value discovered after running the f test. More information on a f test, the f statistic, its critical value, formula, and how to perform a f test for hypothesis testing will be provided in this article.
The f test statistic is used in a test called the f test to determine if the variances of two samples (or populations) are equal. An f test needs a f distribution in the population and independent events for the samples in order to be valid. The null hypothesis can be rejected after conducting the hypothesis test if the f test results are statistically significant; otherwise, it cannot be rejected.
Null hypothesis:
The idea that there is no influence on the population is known as the null hypothesis.
We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). If not, we are unable to rule out the null hypothesis.
Although it may sound odd, statisticians only accept the phrase "fail to reject." Avoid using words like "prove" or "accept" when referring to the null hypothesis.
Alternative hypothesis:
The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected.
Your research hypothesis and your alternate hypothesis are frequently identical. It is, in other words, the assertion that you anticipate, or hope will be accurate.
The complement of the null hypothesis is the alternative hypothesis. The exhaustive nature of null and alternative hypotheses ensures that they account for all potential outcomes. Additionally, they are mutually exclusive, so only one of them can be true at once.
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answer please will give 20 points
Answer:plot the point (2,5)
Step-by-step explanation:
Graph the equation by using the slope intercept method
For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
As given in the question,
Given equation is equal to :
4x + 3y = 21
To get the slope intercept form of the given equation we have,
Subtract 4x from both the sides of the given equation we have,
4x + 3y - 4x = 21 - 4x
⇒ 3y = 21 - 4x
Now divide by 3 on both the sides of the equation we get,
3y / 3 = (-4/3)x + (21/3)
⇒ y = (-4/3) x + 7
Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.
When x = 0 ⇒ y = 7
y= 0 ⇒ x = 21 /4
Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
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Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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In ΔSTU, TU = 11, US = 17, and ST = 18. Which statement about the angles of ΔSTU must be true?
For the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
As given in the question,
In the given triangle STU,
TU = 11
US = 17
ST = 18
we can see that
TU < US < ST
⇒ 11 < 17 < 18
⇒ 11 + 17 = 28
⇒ 28 > 18
All the sides of the triangle are not equal to each other.
This implies that all the angles opposite to the unequal sides are also not equal to other.
Therefore, for the given triangle STU all the angles of ΔSTU are not equal to each other is the true statement .
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Write an expression for the following situation: 4 less than 20 times some number.
A. 20-x-4
B. 20 + x - 4
C. 20x - 4
D. 20 - x + 4
Answer: D
Step-by-step explanation: Took the test
Eva says
3
4
is equivalent to
15
20
. Check her work by completing the table of equivalent ratios.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
What is a Ratio?A ratio indicates the number of times one number contains another.
To find the equivalent ratio of 3/4 write the table of 3 in one column of the table and write the table of 4 in another column of the table.
The equivalent ratio table is:
3 4
6 8
9 12
12 16
15 20
The above table indicates that 3/4 = 6/8 = 9/12 = 12/16 = 15/20.
Therefore, from the table, 3/4 is equivalent to 15/20.
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The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
You must use the drawing tool to show how the line of best fit has been used to get your answer.
A weatherman says that temperatures are lower on days when there is less sunshine.
d) Does the scatter graph support this? (1)
A yes B no C can't say
Total marks: 5
Answer:
See attached worksheet.
Step-by-step explanation:
The worksheet summarizes the steps for analyzing the data on the graph. Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town. There are techniques for ensuring a line such as this fits the actual data as closely as possible. These techniques draw a line that has the least overall deviation from the actual data. For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner: There is a proportional change in y for every set change in x. That change is known as the slope. The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.
Hey, I haven't been able to get any of these right, I wasn't a there the day we learned this and i'm needing help getting the rest of it done before 3:00. Could any of you please help me out on this, it'd mean a lot!
The correct graph for each of the equations are respectively;
5) Graph C
6) Graph A
7) Graph B
How to Interpret Linear Equation Graphs?The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
5) We are given the linear equation as;
-9x + 3y = 0
3y = 9x + 0
y = 3x + 0
The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C
6) We are given the linear equation as;
4x - 6y = 12
Rearranging we have;
6y = 4x - 12
y = ⁴/₆x - 2
y = ²/₃x - 2
Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A
7) The correct graph of the function 25x - 10y = -50 is the graph B.
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
Find x if AC= 17, BD = 2x - 6, AD= x + 16, and BC = 6
Answer:
Hey, hope it helps my friend
Step-by-step explanation:
In the image
Marsha deposited $5500 into a savings account 4 years ago. The simple interest rate is 5% How much money did Marsha earn earn in interest?
Marsha deposited $5500 into savings with 5% interest rate
1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]
2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]
3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]
4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]
Find g(x), where g(x) is the translation 2
units left of f(x)= -5x + 5.
Answer:
g(x)=(-5x+2)+5
Step-by-step explanation:
