Answer:
Starting with the equation:
-2x + 6 = -x^2
First, we can rearrange it to put it in standard quadratic form:
x^2 - 2x - 6 = 0
To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:
x^2 - 2x + 1 - 1 - 6 = 0
The first three terms can be written as a perfect square:
(x - 1)^2 - 7 = 0
Add 7 to both sides:
(x - 1)^2 = 7
Now we can take the square root of both sides:
x - 1 = ±√7
Add 1 to both sides:
x = 1 ± √7
So the solutions to the equation are:
x = 1 + √7 or x = 1 - √7
mark me brilliant
given h(t)=4t and k(t)=t+5t−1 , determine the expressions that are equal to these combinations of h(t) and k(t) . h(t)+k(t) h(t)−k(t) h(t)+k(t)h(t)−k(t) t2+t+4t2+9t−4 −t2+9t−4t2+t+4 t2+4t+4t2−1 −t2+t+4t2−t −t2+4t−6t2−1 t2+9t−4t2−t
The expressions are written as;
h(t)+k(t) = 10t - 1
h(t)−k(t) = -2t + 1
How to determine the expressionsNote that algebraic expressions are described as expressions that are made up of coefficients, variables, terms, constants and factors.
These expressions are made up of arithmetic operations, which includes;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
h(t)=4t
k(t)=t+5t−1
To determine the value of h(t) + k(t), we have;
4t + t + 5t - 1
add the like terms, we get;
10t - 1
To determine h(t) = k(t)
4t- t - 5t + 1
add like terms
-2t + 1
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Suppose that the function h is defined as follows.
For the given function h(x) the points can be plotted on,
(-1,-1)(0,0)(1,1)(2,2)The given function h(x) is having four conditions and each condition can be clearly discussed below:
Given that for the first condition, the x-axis is ranging from -1 [tex]\leq[/tex] x < 0, the y-axis point is present exactly at -1. Similarly, for the second condition, the x-axis is ranging from 0 [tex]\leq[/tex] x < 1, and the y-axis point is present at 0. For the third condition, the x-axis is ranging from 1 [tex]\leq[/tex] x < 2, and the y-axis point is at 1.Finally, for the fourth condition, the x-axis is ranging from 2 [tex]\leq[/tex] x < 3, and the y-axis point is at 2.From, the above analysis we plotted the graph and attaching below.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Step-by-step explanation:
x = -2 or x = 2
x + 2 = 0 or x - 2 = 0
(x + 2) (x - 2) = 0
x² - 4 = 0
#CMIIW(-2-3)-(4-5)+ (−1+6)−(−9+8)=
Answer:
Step-by-step explanation:
(-2-3)-(4-5)+ (−1+6)−(−9+8)
-5-4+5-1+6+9-8
-9+4+15-8
-5+7
2
Mrs Marcus combines her books and magazines then divides them among 10 different tables. If a represents the number of books and d represents the number of magazines Mrs. marcus has, write an expression to show how many books would be on each table.
An expression to show how many books would be on each table is a/10
To find out how many books would be on each table, we need to divide the total number of books by the number of tables.
First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.
Next, we need to divide a by 10, the number of tables. This gives us the expression:
a/10
So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.
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Complete question is:
Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.
A) y = −2.78x + 33.6
B) y = −2.78x + 48.5
C) y = 2.78x + 33.6
D)y = 2.78x + 48.5
The equaltion for the line of best fit would be,
y = 0.67x + 4.05
The points on the scatter plot are: (1, 3.8), (2, 5.8), (3, 6.2) , (4, 7.5) , (5, 7.2), (6, 8.3), (7, 9.3), and (8, 8.5 )
First we find the mean of the x-values and mean of the y-values.
The mean of the x-values would be,
[tex]\bar{X}[/tex] = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8
[tex]\bar{X}[/tex] = 4.5
and the mean of the y-values would be,
[tex]\bar{Y}[/tex] = (3.8 + 5.8 + 6.2 + 7.5 + 7.2 + 8.3 + 9.3 + 8.5) / 8
[tex]\bar{Y}[/tex] = 7.075
The sum of squares (SSX) = 42
And the sum of products (SP) = 28.2
Regression Equation would be,
y = mx + c
m = SP/SSX
= 28.2/42
= 0.67143
And the y-intercept would be,
c = 4.05357
So, the equation for the line of best fit would be,
y = 0.67143x + 4.05357
Number of Households = 0.67143 (time) + 4.05357
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Find the complete question below.
The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Number of Households with points at 1 comma 3 and 8 tenths, 2 comma 5 and 8 tenths, 3 comma 6 and 2 tenths, 4 comma 7 and 5 tenths, 5 comma 7 and 2 tenths, 6 comma 8 and 3 tenths, 7 comma 9 and 3 tenths, and 8 comma 8 and 5 tenths.
please help for this question
The dilation of the object is given by the coordinates:
(-6,-8)
(-2, 0)
(-2, -8)
A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer.
For the first dilation
Original points are
(2,1)
(4,5)
(4,1)
Multiply by scale factor
(2,1) x 2 = (4,2)
(4,5) x 2 = (8, 10)
(4,1) x 2 = (8, 2)
This given us the coordinates of triangle B).
For the second dilation
(2,1)
(4,5)
(4,1)
Adjust for the center of dilation which is (5,5)
(2,1) less (5,5) = (-3, -4)
(4,5) less (5,5) = (-1, 0)
(4,1) less (5,5) =(-1, -4)
Multiply the New original point by scale factor
(-3, -4) x 2 = (-6,-8)
(-1, 0) x 2 = (-2, 0)
(-1, -4) x 2 = (-2, -8)
Thus, the new coordinates of the dilated triangle C are:
(-6,-8)
(-2, 0)
(-2, -8).
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Mrs Smith uses 5 lemons to make 2/3 gallon lemonade. How many gallons of lemonade can Mrs Smith make with 15 lemons?
What does |23| mean?
3d *5d*2=?
Please what is 3d times 5d times 2
Answer:
[tex]30d^2[/tex]
Step-by-step explanation:
Amanda’s new job has a 50% employer match on the first 4% of her salary contributed to her 401(k). How much was deposited in Amanda’s account if she makes $61,000 a year and she took advantage of the entire contribution match?
Answer:
$2,440 + $1,220 = $3,660
Step-by-step explanation:
If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:
$61,000 x 0.04 = $2,440
Since her employer has a 50% match on the first 4% of her salary, they would contribute:
$2,440 x 0.5 = $1,220
The numbers of polio cases in the world are shown in the table for various years.
Year Number of polio cases (thousands)
1988 350
1992 138
1996 33
2000 4
2005 3.2
2007 1.3
PREDICT THE NUMBER OF POLIO CASES IN 2014
hint: The function F gives the number of thousands of polio cases
The value of t is given as 2.3 years.
How to solvewe get the table for function as
t f(t)
8 350
12 138
16 36
20 4
25 3.2
27 1.3
So it is better to model the data by using an exponential model
using a graphing calculator we get our model as
f(t)=a(b)^t
[tex]f(t)=\boldsymbol{3648.6915(0.7380)^t}[/tex]
we have an exponential decay, so we get a rate of decrease as
b=1-r
r=1-b=1-0.738=0.262=26.2\\%
So the number of polio cases is decreasing by 26.2% per year
The number of polio cases in 2014 is
t=2014-1980=34
f(34)=3648.6915(0.7380)^{34}=0.1991389
this is in thousands so we get the number of cases in 2014 approximately as
[tex]0.1191389*1000 \approx \boldsymbol{119} \textup{ cases}[/tex]
for 1 case of polio :
f(t)=0.001
3648.6915(0.738)^t=0.001
we get
[tex]t=\frac{\ln (\frac{0.001}{3648.6915})}{\ln(0.738)}\approx 50[/tex]
so we get year as
1980+50={2030},
to find half life
[tex]\frac{a}{2}=a(b)^t[/tex]
[tex]b^t=\frac{1}{2}[/tex]
[tex]0.738^t=\frac{1}{2}[/tex]
[tex]t=\frac{\ln (1/2)}{\ln (0.738)}\approx\boldsymbol{2.3} \textup{ years}[/tex]
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Someone help i really need help with this
Step-by-step explanation:
step A is incorrect.
-40/5 does not equal to -40/-5.
-40/-5 is equal to 40/5 as we can simplify the negative 1 out.
Answer:
The correct answer is step A
Anna saved $20 in a jar each month for 2 3/4 years. she spent 75% of her savings on a computer. how much money did anna have left in the jar
Anna has $165 left in the jar. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?All real numbers are supposed to be explained by the four fundamental operations, often known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that Anna saved $20 in a jar each month for 2 complete years and for 9 months of next year.
So, total months = 9 + 12 + 12 = 33
Now, using the multiplication operation, we get
⇒ Total money saved = 33 * 20
⇒ Total money saved = $660
It is given that she spent 75% of her savings on computer.
So, using the subtraction operation, we get
⇒ Amount left = 660 - 75%
⇒ Amount left = $165
Hence, Anna has $165 left in the jar.
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A survey asked students whether they have any siblings and pets. The survey
data are shown in the relative frequency table.
Pets
No pets
Total
Siblings
0.3
0.45
0.75
OA. 30%
OB. About 67%
O C. 75%
D. 40%
Given that a student has a sibling, what is the likelihood that he or she also
has a pet?
The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.
Let A denote the event that a student does not have a sibling.
Let B denote the event that a student has a pet.
Then A∩B will denote the event that the student does not have a sibling but he has a pet.
Let P denote the probability of an event in this question.
Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.
P(B|A)
We know that:
[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]
Also from the table, we have:
P(A)=0.25
and P(A∩B)=0.15
Hence,
[tex]P(B|A) = \frac{0.15}{0.25}[/tex]
[tex]P(B|A) = \frac{3}{5}[/tex]
[tex]P(B|A) = 0.6[/tex]
which in percentage is:
0.6 * 100 = 60 %
Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.
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The volume of a cube depends on the length of its sides. This can be written
in function notation as v(s). What is the best interpretation of v(4) = 64?
A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. 4 of these cubes will have a total volume of 64 cubic feet.
OD. A cube with a volume of 4 cubic feet has side lengths of 64 feet.
Answer:
C is the correct answer.
The area of a rectangular shaped rug is 81 square feet. If the rug is 9 ft long, what is ire perimeter?
The perimeter of the rug is 36ft
What is perimeter?Perimeter is the total length around the outside of a shape. The perimeter can be found by adding all the sides of the shape.
Perimeter of a rectangle is expressed as ;
P = 2(l+w)
The area of the rug is 81ft²
area = l× w
length = 9ft
width of the rug = 81/9 = 9ft
Therefore the perimeter of the rug will be
P = 2(l+w)
P= 2( 9+ 9)
P = 2 × 18
P = 36 ft
therefore the perimeter of the rectangular rug is 36ft
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Someone help i really need help with this
The equation which can be used to find the amount the admission tickets cost would be 4x + 25 = 175. The cost of the admission tickets would therefore be $ 37.50.
How to find the equation ?The total spent by Ms. Boi was $ 175.00 so this is what the entire equation would be equal to. The cost of admission tickets will be denoted as x because they are the unknown figure.
There are 4 tickets purchased so the equation would be:
4 x Cost of tickets - Parking cost = Total spent
4 x - 25 = 175
The cost of each admission ticket is:
4 x - 25 = 175
x = 150 / 4
x = $ 37.50
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pls help quickly!!
Factor completely
3zy²x + y²x - 12zx - 4x
Select one:
a. x (3z + 1) (y + 2)(y-2)
b. None of these.
c.xy (3z + 1)(y-2)
d. x (3z + 1) (4z-3)
e. x (3z-1) (y + 2)²
The frequency table below shows a student’s quiz scores. One data value in the table is missing. If the mean of the data set is 2.2, what is the score for the missing data item? A. 0 B. 1 C. 2 D. 3
Answer:
B. 1
Step-by-step explanation:
Let's use the formula for finding the mean of a set of data:
mean = (sum of all data values) / (number of data values)
We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:
2.2 = (sum of all 10 data values, including x) / 10
Multiplying both sides by 10, we get:
22 = sum of all 10 data values, including x
We can then subtract the sum of the known data values from both sides to find the missing value:
22 - (01 + 12 + 23 + 31 + 42 + 51) = x
22 - (0 + 2 + 6 + 3 + 8 + 5) = x
x = 22 - 24 = -2
However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:
If the missing score is 0:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10
2.2 = 18 / 10
2.2 = 1.8
This is not true, so the missing score cannot be 0.
If the missing score is 1:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10
2.2 = (18 + ?) / 10
22 = 18 + ?
? = 4
So the missing score is 1, and the answer is B.
Answer:
Answer is B
Total scores/total frequency =mean
54/24=2,25
If you added a score of 1
55/25=2,2
Step-by-step explanation:
hope that helps you
Work out the largest integer value that x could take if
x+7<13
Answer:
The answer is going to 5
Step-by-step explanation:
I hope this helps you
Thereare6redmarblesand11orangemarblesinabag.Yourandomly choose one of the marbles. What is the probability of choosing a red marble
The probability of choosing a red marble is 6/17.
What is the probability of choosing a red marbleThe probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.
To calculate this probability, we can use the formula:
P(red marble) = number of red marbles / total number of marbles
In this case, we substitute the numbers we know:
P(red marble) = 6 / 17
So the probability of choosing a red marble is 6/17 or approximately 0.35.
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what is five term in 12,16,21,27
Answer:
34
Step-by-step explanation:
This is sequnce has an easy pattern with adding 1 to the difference every time and goes +4, +5, +6 , so the next should be +7
Answer: think it’s a5=34
Step-by-step explanation:
which fraction is the smallest? 3to4, 2/3, 10:12, 2to1
The smallest fraction is 8/12, which is equivalent to 2/3.
How to determine the smallest fractionTo compare fractions, it's best to convert them all to a common denominator.
3/4 is equivalent to 9/12
2/3 is equivalent to 8/12
10/12 is equivalent to 5/6
2/1 is equivalent to 24/12
So, the smallest fraction is 8/12, which is equivalent to 2/3.
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A meter in a taxi calculates the fare using the function f(x) = 2.56x + 2.40. If x represents the length of the trip, in miles, how many miles can a passenger travel for $20?
A passenger can travel 6.875 miles for $20 using the given taxi fare function.
To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.
The equation we need to solve is:
2.56x + 2.40 = 20
To solve for x, we can start by subtracting 2.40 from both sides of the equation:
2.56x = 17.60
Next, we can divide both sides by 2.56:
x = 6.875
This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.
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The combinations for the lockers at school consist of 3 numbers. Each number in the combination can be a number from 0-29. How many locker combinations are possible?
Answer:
87 I think.
Step-by-step explanation:
29 x 3 = 87
2.1/0.7=3 but how do you work it out (I cheated and used a calculator)
Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:
0.7 | 2.1
1.4 (3 times 0.7 is 2.1)
-----
0.7
0.0 (there is no remainder)
Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.
Answer:
see below
Step-by-step explanation:
2.1
-----
.7
Multiply the top and bottom by 10 to get rid of the decimals.
2.1 *10 = 21
.7 * 10 = 7
21/7 = 3
Can someone help me with this pls
Answer:
Subtract the powers, 8-4.
When you simplify that equation itself, the answer is 10,000.
So when you do 10⁴, it's 10,000.
Determine whether y=9(-5)^x represents an exponential function
Answer: Yes, y = 9(-5)^x represents an exponential function.
An exponential function is a function in the form y = ab^x, where a and b are constants and b is a positive real number not equal to 1. The base, b, is raised to the power of x, and the resulting value is multiplied by the constant a.
In the given function, we have a = 9 and b = -5. Although b is negative, it is still a real number not equal to 1, so the function is still considered exponential. Furthermore, the exponent x is a variable, which is raised to a constant base -5, meeting the definition of an exponential function.
Therefore, y = 9(-5)^x is an exponential function.
Step-by-step explanation:
McKenzie painted a yellow rectangle that measured 8 1/2 in. wide and 11 in. long for part of a mural she was working on. She also painted a
purple rectangle that was 1/4 the size of the yellow rectangle. What is the area of the purple rectangle that McKenzie painted?
Answer:
23.375 in^2
Step-by-step explanation:
To find the area of a rectangle or square, you need to multiple the length by the width.
The length: 8.5
Width: 11
8.5*11 = 93.5
Now we divide by 4
93.5/4
23.375