Answer:
Step-by-step explanation:
x^2 + 2x + 1 = 17
x^2 + 2x = 17 - 1
x^2 + 2x = 16
x^2 + 2x + 1 = 16 + 1
(x + 1)(x + 1) = 17
(x + 1)^2 = 17
x + 1 = sqrt 17
x = -1 (+ - ) sqrt 17
x = -1 + sqrt 17 or x = -1 - sqrt 17 <===
Answer:
x = -1 + square root 17
Step-by-step explanation:
I took the test
what do you think about when you get sick? Check any that apply
Answer:
What are the answer choices? I'd be happy to help!
Solve the inequality 2n -3 ≥ 5 and graph the solutions
Answer: n ≥ 4
Step-by-step explanation: To solve for x in this inequality, your goal is the same as it would be if you were solving an equation which is to get x by itself on one side of the inequality.
Since 3 is being subtracted from 2n, add 3 to both sides of the inequality to get 2n ≥ 8. Now since n is being multiplied by 2, we need to divide by 2 on both sides of the inequality to get n ≥ 4.
Our next task is to graph n ≥ 4 on a number line and to do that, we start with a closed dot at 4. The reason we use a closed dot at 4 is because not only is n greater than 4 but it's also equal to 4. Next we draw an arrow going to the right on our number line to represent all numbers greater than 4.
When graphed, it should look something like the image attached.
What is the mean?
Round to the nearest tenth if needed.
Value
Frequency
1 2 3 4 5
713 2 2
O 2.4
O
3
•
2
O
7.2
the answer is 2.4
Mean=\frac{\sum fx}{\sum f}
Where:
f is the frequency
x is the value
\frac{3+7+5+6+2+x}{6} =5
23+x=30
x=30-23
x=7
\therefore Mean=\frac{1 \times 7 + 2 \times 1+ 3 \times 3 + 4 \times 2 + 5\times 2}{15}
=\frac{7+2+9+8+10}{15} =\frac{36}{15} =2.4
Therefore, the mean = 2.4
sorry if its a bit confusing
Answer:
Its 2.4
Step-by-step explanation:
What is the inverse of the fuction f(x)= x+3
Answer:
Inverse of function f(x) is y =x-3
Step-by-step explanation:
Given:
f(x) = (x+3)
To Find:
Inverse of f(x)
Solution:
Inverse of the function:
Let f: X -> Y be a function with domain X and target set Y. Then g is the inverse of f if g is a function with domain Y and target set X such that
g(f(x)) = x for all x in X
f(g(y)) = y for all y in Y.
f has an inverse function if and only if f is both one-to-one and onto. If f is one-to-one and onto, then its inverse function g is defined implicitly by the relation g(f(x)) = x.
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
Let y = f(x) = x+3
So, swapping the variables: y=x+3 becomes x=y+3
Now, solve the equation x=y+3 for y.
y=x−3
y=x−3
This is a copy of the worksheet my son was given from school, can anybody look at this and tell if this is being done correctly, because it doesn’t look right to me....
It looks good to me!
Can someone help me with this plz?
Answer:
option (4)
Step-by-step explanation:
As a function x can only have one unique value that it maps to.
(1)
(10, 12 ) ← No since (10, 11 ) is already part of the function
(2)
(15, 13 ) ← No since (15, 18) is already part of the function
(3)
(17, 10 ) ← No since (17, 12 ) is already part of the function
(4)
(11, 13 ) ← Yes as no other value with x = 11
Anna is trying to figure out how much her 10-mile taxi ride is going to cost. It costs $5 to be picked up by the taxi, and
each mile costs an extra $2. Which equation should Anna use to calculate her cost?
Answer:
5+2(10)
Step-by-step explanation:
5+2(10)
5+ 20
$25 for 10 miles
find the constant m and b in the linear function f(x)=mx+b so that f(6)=9 and the straight line represents by f has slope -4
Answer:
The constant m=-4, and b=33
Step-by-step explanation:
F(x)= MX+b
If f(6)=9 then x=6, m= -4
9= -4(6) + b
9= -24 + b
b= 9 + 24
b= 33
Therefore the constant m, which is the slope is -4 and b which is the intercept is 33
Given the linear function f(x) = mx + b, we see the slope m as -4. Using the point (6,9), we find the y-intercept b to be 33.
Explanation:In the linear function 'f(x) = mx + b', 'm' represents the slope of the line and 'b' is the y-intercept. As it's given that the slope is -4, we replace 'm' in the equation with -4 to get 'f(x) = -4x + b'. Now, we use the point (6,9) which lies on the line, allowing us to find the value of 'b'. Substituting x = 6 and f(x) = 9 into the equation, we get 9 = -4*6 + b. After solving this equation, we find that b = 33. Therefore, the constants are m = -4 and b = 33.
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A company sells furniture for home assembly. Their largest bookcase has shelves that should be 105 cm, with a tolerance of 0.8 cm (105cm 0.8cm). A set of six shelves had lengths of 105.3 cm, 105.2 cm, 104.1 cm, 105.1 cm, and 105.9 cm. Find the minimum and maximum allowable shelf length. Which , if any, of the shelves are not within the specified tolerance?
Answer:
Minimum allowable shelf length = 105 cm - 0.8 cm = 104.2 cm
Maximum allowable shelf length = 105 cm + 0.8 cm = 105.8 cm
The third shelf measuring 104.1 cm is not within the specified tolerance.
The fifth shelf measuring 105.9 cm is also not within the specified tolerance.
Step-by-step explanation:
i)A company sells furniture for home assembly. Their largest bookcase has shelves that should be 105 cm, with a tolerance of 0.8 cm (105cm 0.8cm). A set of six shelves had lengths of 105.3 cm, 105.2 cm, 104.1 cm, 105.1 cm, and 105.9 cm. Find the minimum and maximum allowable shelf length. Which , if any, of the shelves are not within the specified tolerance?
ii) Minimum allowable shelf length = 105 cm - 0.8 cm = 104.2 cm
iii) Maximum allowable shelf length = 105 cm + 0.8 cm = 105.8 cm
iv) The third shelf measuring 104.1 cm is not within the specified tolerance.
The fifth shelf measuring 105.9 cm is also not within the specified tolerance.
Each side of the regular hexagon below measures 8 cm. What is the area of the hexagon? A hexagon is shown. A triangle with a 60 degree angle is drawn using one of the sides of the hexagon. 96 StartRoot 3 EndRoot square centimeters 192 StartRoot 3 EndRoot square centimeters 384 StartRoot 3 EndRoot square centimeters 768 StartRoot 3 EndRoot square centimeters
Answer:
The area of the hexagon is A. 96√3 cm²
Step-by-step explanation:
Let's recall the formula of the area of an hexagon, this way:
Area = (3√3/2) * s²
Area = (3√3/2) * 8²
Area = (3√3/2) * 64
Area = 192√3/2
Area = 96√3 cm²
The area of the hexagon is A. 96√3 cm²
Answer:
A. is correct
Step-by-step explanation:
Hope that this helps. Peace and Love
Randy has two 28-pound blocks of ice for his snow cone stand. 1). How many pounds of ice does randy have at his snow cone stand? 2). How many tons of ice is there? Write your answer from number 2 as a fraction and a decimal.
Randy has 56 pound blocks of ice for his snow cone stand
Tons of ice is 0.028 tons or [tex]\frac{7}{250} \text{ tons }[/tex]
Solution:
Randy has two 28-pound blocks of ice for his snow cone stand
1). How many pounds of ice does randy have at his snow cone stand?
Calculate the total pounds that Randy has
Total pounds = 2 x 28 = 56
Thus Randy has 56 pound blocks of ice for his snow cone stand
2) How many tons of ice is there?
Total pounds of ice = 56 pounds
So we have to convert 56 pounds to tons
Use the conversion factor
1 pound = 0.0005 ton
Therefore, 56 pounds is equal to,
56 pound = 0.0005 x 56 tons = 0.028 tons
Thus in decimal we got, 0.028 tons
Convert to fraction form,
[tex]0.028 = \frac{0.028}{1000} \times 1000 = \frac{28}{1000} = \frac{7}{250}[/tex]
Thus tons of ice is 0.028 tons or [tex]\frac{7}{250} \text{ tons }[/tex]
The perimeter of a rectangle is 34 units. Its width is 6.5 point, 5 units.
The perimeter of a rectangle is 34 units. Its width W is 6.5 units.
Write an equation to represent the perimeter in terms of the length L, and find the value of L
Answer:The length of rectangle is 10.5 units
Solution:Given that,
Perimeter of rectangle = 34 units
Width of rectangle = 6.5 units
Let "L" be the length of rectangle
The perimeter of rectangle is given by formula:
Perimeter = 2(length + width)
Substituting the values we get,
[tex]34 = 2(L + 6.5)[/tex]
Thus the equation is found
Solve for "L"
[tex]L + 6.5 = \frac{34}{2}\\\\L + 6.5 = 17\\\\L = 17 - 6.5\\\\L =10.5[/tex]
Thus length of rectangle is 10.5 units
14 - r < 9 ; r = 6 is the given value a solution of the inequality?
Answer:
YESStep-by-step explanation:
14 - r < 9
Put r = 6 and check inequality:
14 - 6 < 9
8 < 9 TRUE
By substituting r = 6 into the inequality 14 - r < 9, we find that the inequality holds true, indicating that r = 6 is a solution to the inequality.
Explanation:To determine if r = 6 is a solution to the inequality 14 - r < 9, we simply substitute the value of r into the inequality and check the result.
Substituting r = 6 into the inequality gives us:
14 - 6 < 9
Which simplifies to:
8 < 9
Since 8 is less than 9, the inequality holds true,
which means that r = 6 is indeed a solution to the inequality 14 - r < 9.
Julia planet a rectangle garden that is 20 feet long she plays 56 feet of fencing around her Garten what is the width of her Garten what is the area
The width of rectangular garden(b) = 8 feet and
The area of rectangular garden = 160 square feet
Step-by-step explanation:
Given,
The length of rectangular garden(l) = 20 feet and
The perimeter of rectangular garden(fencing) = 56 feet
To find, the width of rectangular garden(b) = ? and
The area of rectangular garden = ?
We know that,
The area of rectangular garden = 2(l + b)
⇒ 2(20 + b) = 56
⇒ 20 + b = 28
⇒ b = 28 - 20 = 8 feet
The width of rectangular garden(b) = 8 feet
∴ The area of rectangular garden = l × b
= 20 feet × 8 feet
= 160 square feet
Hence, the width of rectangular garden(b) = 8 feet and
the area of rectangular garden = 160 square feet
The width of Julia's garden is 8 feet, and the area of her garden is 160 square feet. The calculations were made using the perimeter and area formulas for rectangles.
To find the width of Julia's rectangular garden and its area, we can use the given information:
The garden is 20 feet long, and the total perimeter of the garden is 56 feet.
Step-by-Step Solution:
The formula for the perimeter P of a rectangle is given by:
P = 2L + 2W
where L is the length and W is the width.
We know the following values:
L = 20 feet
P = 56 feet
Substitute these values into the perimeter formula:
56 = 2(20) + 2W
Simplify and solve for W:
56 = 40 + 2W
56 - 40 = 2W
16 = 2W
W = 8 feet
Now we can find the area A of the garden using the formula for the area of a rectangle:
A = L × W
Substitute the values we have:
A = 20 × 8
A = 160 square feet
The width of Julia's garden is 8 feet, and the area of her garden is 160 square feet.
A parcel is 90 cm x 50 cm x 60 cm. What length of string is required to tie it up, if the string goes round each way twice (in all six rounds) and 50 cm are needed for the knots?
Answer:
88 because I just solved it on a white board
Mr. Torres spent $30.00 to buy 9/1/2 pounds of ground beef and chicken for a family cookout. If the price of ground beef was $4.50 per pound and chicken was $3.00 per pound, how many pounds of each did he buy?
Answer:
Therefore Mr. Torres buys 1 pound of ground beef and 8.5 pounds of chicken.
Step-by-step explanation:
i) Let x be the number of pounds of ground beef
ii) Let y be the number of pounds of chicken.
iii) therefore x + y = 9.5 pounds
iv) also we have 4.5 x + 3 y = 30 dollars
v) multiplying the equation in iii) by 3 we get 3x + 3y = 28.5
vi) Subtracting the equation in v) from the equation in iv) we get 1.5 x = 1.5
vii) Therefore x = 1 pound
viii) substituting the value of x in vii) in the equation in iii) we get
1 + y = 9.5 . Therefore y = 8.5 pounds.
ix) Therefore Mr. Torres buys 1 pound of ground beef and 8.5 pounds of chicken.
Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?
On a coorindate plane, an exponential function starts in quadrant 3 and increases and approaches y = 0 in quadrant 4. It crosses the y-axis at (0, 6) and goes through (1, negative 3).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and crosses the y-axis at (0, 6).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6).
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first qudrant. It goes through the y-axis at (0, 6) and goes through (1, 3).
The correct graph representing a reflection of the function f(x) = 6(0.5)^x across the x-axis is one that shows the function decreasing into quadrant 4, crosses the y-axis at (0, -6), and approaches y=0 in quadrant 3, precisely matching the expected transformations due to reflection.
Explanation:To find the graph that represents a reflection of f(x) = 6(0.5)^x across the x-axis, it's important to understand what reflection across the x-axis entails. Reflecting a function across the x-axis means taking every point (x, y) on the graph of the function and transforming it into a point (x, -y). Thus, for the function f(x) = 6(0.5)^x, this transformation results in a new function g(x) = -6(0.5)^x. This produces a graph where all y-values are the negatives of the original function's y-values.
Among the provided options, the correct representation of this reflection would be: "On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6)." This description matches the characteristics of the reflected function by correctly indicating the new y-intercept at (0, -6) and demonstrating the behavior of the function decreasing into quadrant 4 while approaching y=0 in quadrant 3.
Write an equation of the line parallel to y=3x+2 that passes through (-1, -2)
Answer:
[tex]y=3x+1[/tex]
Step-by-step explanation:
From the question, we are given;
The equation y = 3x + 2A point (-1, -2)We are required to determine the equation of a line parallel to the given line and passing through the point (-1, -2)
We are going to determine the gradient of the line first; when an equation is written in the form of y = mx + c, where m is the gradient.y = 3x + 2, m₁ = 3
But, m₁ = m₂ for parallel lines Therefore, the gradient of the line in question, m₂ is 3With the gradient, m₂=3 , and a point (-1, -2) we can get its equation;Taking another point (x, y)...
Then;
[tex]\frac{y+2}{x+1}=3[/tex]
[tex]y+2=3(x+1)\\y+2=3x+3\\y=3x+1[/tex]
Therefore; the equation of the line is [tex]y=3x+1[/tex]
7/12% of a quantity is equal to what fraction of the quantity?
Answer:
12 = 22 × 3
Step-by-step explanation:
The fraction equivalent of 7/12% of a quantity is 7/12000.
Explanation:The question is asking to derive the fraction equivalent of 7/12% of a quantity. In mathematics, a percent is a way of expressing a fractional amount using a ratio whose denominator is 100. Therefore, to convert a percent to a fraction, we write the value of the percent as a fraction with a denominator of 100.
In this case, 7/12% can be expressed as (7/12)/100. Simplifying this fraction, we get 7/12000, which is the fraction of the quantity that 7/12% represents.
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1. How many different sets of 8 songs are possible for Janine's play list? Assume that the
order of the songs doesn't matter.
Answer:
40320
Step-by-step explanation:
the first song on the list could be 8 possible songs;
and the second song on the list could be 7 possible songs after the first one was set;
the third song on the list could be 6 possible songs after the first and second songs were set;;
the fourth song on the list could be 5 possible songs after the first ,second and third songs were set;;
the fifth song on the list could be 4 possible songs after four songs were set;
the sixth song on the list could be 3 possible songs after five songs were set;
the seventh song on the list could be 2 possible songs after six songs were set;
the eighth song on the list could be 1 possible songs after seven songs were set.
so THERE ARE 8X7X6X5X4X3X2X1 DIFFERENT SETS
To calculate the number of combinations, we use the combination formula in combinatorics. However, the total number of songs available is required to provide a specific answer.
Explanation:To determine the number of different sets of 8 songs possible for Janine's play list, we have to use the combination formula of combinatorics. Combinatorics is a branch of mathematics concerning the study of countable or finite discrete structures. The combination is a selection of items where order does not matter. The formula for combination is: C(n, r) = n! / [r!(n-r)!]
where:
'n' is the total number of items (in this case, we don't know the total number of songs available),'r' is the number of items to choose (in this case, 8 songs),'!' denotes a factorial, meaning the product of an integer and all the integers below it, e.g. 4! = 4*3*2*1.Therefore, to answer the question, we would need to know the total number of songs available to Janine. Once we know that, we can substitute that number for 'n', and use the formula to calculate.
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place the numbers 0 to 8, in the magic square so that sum of the numbers in each row, column,and diagonal is the same number, 12
Answer:
[tex]\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}[/tex]
Step-by-step explanation:
A magic square can be made by putting the average number in the middle spot. Here, there are 3 numbers in each row, column, or diagonal that total 12, so their average is 12/3 = 4.
There are only 2 pairs of numbers that total 12: (8+4) and (7+5). These must be in the same row and column as the digit 0. If 0 were on a diagonal, we would need three pairs of numbers that total 12, so 0 cannot be on a diagonal.
Our square has 4 in the middle and 0 in a side spot, so it could look like ...
[tex]\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}[/tex]
Final answer:
To solve the 3x3 magic square with numbers 0 through 8 adding up to 12, place the numbers strategically so that each row, column, and diagonal sum to the magic constant. One solution involves putting the number 4 in the center and arranging opposite pairs that add to 8 around it.
Explanation:
To place the numbers 0 to 8 in the magic square so that the sum of the numbers in each row, column, and diagonal is the same number, 12, you have to carefully choose where to place each number. A 3x3 magic square using the numbers 0 through 8 is indeed possible with each line adding up to 12. Here's one solution:
2 7 3
6 4 2
4 1 7
Following this pattern ensures that the sum of each row, column, and diagonal line equals 12. Here's the step-by-step process:
Start by placing the number 4 in the middle of the grid, because in a 3x3 magic square, the center is always one-third of the magic constant (12 in this case).
Next, remember that opposite numbers around the center number must be pairs that add up to 8 (since 4 + 8 = 12 which is the magic constant).
Arrange the pairs strategically across the square so that they add up to 12 in each line.
For instance, placing 2 opposite to 6 and 7 opposite to 1 makes sure that rows, columns, and diagonals all sum to 12.
Four thousand four hundred ninety two
Answer:
4,492
Step-by-step explanation:
I really don't know the meaning of this question but that's the number.
examples of reflex action
Answer: putting arms in front when falling to catch self.
Stretching arm out to protect passenger when breaking suddenly
Step-by-step explanation:
I NEED THE ANSWER ASAP PLEASE
Answer:
7
Step-by-step explanation:
the answer would be 7 because if there is 2 in per hour just go 2,4,6,8,10,12
and then count all the numbers i did and that will be your answer (7)
which property is (4.5+5.4)+3.2=4.5+(5.4+3.2)
Answer:
associative property of addition
Step-by-step explanation:
A change of grouping is the associative property of addition.
How can u get hundred as a denominator as 209 over 25
Hundred as a denominator as 209 over 25 is obtained by mulyiplying numerator and denominator by 4
[tex]\frac{209}{25} = \frac{836}{100}[/tex]
Solution:
Given that we have to get hundred as a denominator as 209 over 25
Thus the given fraction is:
[tex]\rightarrow \frac{209}{25}[/tex]
Now we have to get 100 as denominator
If you multiply both the numerator and denominator of a fraction by the same non-zero number, the fraction remains unchanged in value.
Therefore, equivalent fractions can be created by multiplying or dividing the numerator and denominator by the same number
Muliply and divide by 4, so that 25 muliplied by 4 gives 100
[tex]\rightarrow \frac{209}{25} = \frac{209 \times 4}{25 \times 4} = \frac{836}{100}[/tex]
Thus the denominator is 100
what is the answer to y=3/2x+4 graphing
Please give brainlest and thanks
Answer:The final answer is 4 4
Step-by-step explanation: Graph the line using the slope and y-intercept, or two points.Slope: 3/2
i dont understand this help pls
Answer:3/5
Step-by-step explanation:
What is being done to the variable in the equation 3 + g = -9?
A. The number 3 is being added to it.
B. The number 3 is being subtracted from it.
C. The number -9 is being added to it.
D. The number -9 is being subtracted from it.
Answer:
its A
Step-by-step explanation:
not gonna explain it cause I dont have to ._. plus it wasnt that hard
Mr.Changs class has 28 students 4/7 of whom are girls. Which equation shows how to determine the number of girls in Mr. Chang’s class
I think 7 of them are girls and the rest are boys and how i got this answer is I took the 28 and divided it by 4 and got 7.
There are 16 girls in Mr. Chang's class.
the correct equation to determine the number of girls in Mr. Chang's class is [tex]\( 28 \times \frac{4}{7} = 16 \)[/tex]
The correct option is (b).
let's break down the problem step by step.
Given:
Total number of students = 28
Proportion of girls = 4/7
To find the number of girls in Mr. Chang's class, we need to multiply the total number of students by the fraction representing the proportion of girls.
So, we calculate:
[tex]\[ \text{Number of girls} = 28 \times \frac{4}{7} \][/tex]
Now, let's multiply:
[tex]\[ 28 \times \frac{4}{7} = \frac{28 \times 4}{7} \][/tex]
[tex]\[ = \frac{112}{7} \][/tex]
Now, we can simplify this fraction:
[tex]\[ \frac{112}{7} = 16 \][/tex]
So, there are 16 girls in Mr. Chang's class.
Therefore, the correct equation to determine the number of girls in Mr. Chang's class is:b.[tex]\( 28 \times \frac{4}{7} = 16 \)[/tex]
complete question given below:
Mr. Chang's class has 28 students, 4/7 of whom are girls. Which equation shows how to determine the number of girls i Mr. Chang's class?
a.28+ 4/7 =49
b.28* 4/7 =16
c.4/7 / 28= 1/49
d.7/4 -28= 1/16