Answer:
2 erasers cost $1.20
Step-by-step explanation:
Nigel bought 10 pencils and 5 erasers for $8.
We can write this algebraically:
10p + 5e = 8
We know that the price of 2 pencils is $1. That is $0.50/Pencil.
So, p = $0.50. Now we can plug that into out equation and find the price of one eraser:
10(0.50) + 5e = 8
5 + 5e = 8
5e = 3
e = $0.60
Now, we have the price of one eraser, $0.60, and we can multiply this by 2 to find the price of 2 erasers, which equates to $1.20.
The driving distance from Seattle to Portland is 175 miles. Your car gets 25 miles per gallon. If gasoline is $2.80 per gallon, how much will the round trip from Seattle to Portland and back cost in dollars?
Answer:
$980
Step-by-step explanation:
Given the cost of gasoline = $2.80/mile
Total Distance = 175miles x 2 (Back and forth)
= 350 miles
Total Cost = Cost of gasoline x Total Distance =
= $2.80 x 350
= $980
The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The driving distance from Seattle to Portland is 175 miles.
Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Now,
Since, The driving distance from Seattle to Portland is 175 miles.
Hence, The total distance from Seattle to Portland and back = 175 + 175
= 350 miles
And, Your car gets 25 miles per gallon and the cost of gasoline is $2.80 per gallon.
Hence, The cost of gallon = 350/25 x $2.50
= 100 x $2.50
= $250
Thus, The total cost of the trip from Seattle to Portland and back cost in dollars will be;
⇒ $250
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George buys a computer. He pays a deposit of £200 and six monthly instalments of £55_
How much does George pay for his computer in total?
Bella wants to know how long her dog is. She measure its body and finds that it is 54 cm long. Then she measures the tail and find it is 34 cm long. How long is Bella's dog from body to tail?
Answer:
88 cm
Step-by-step explanation:
body to tail = length of body + length of tail
body to tail = 54 cm + 34 cm
body to tail = 88 cm
Which transformations will produce similar, but not congruent, figures?
Select each correct answer.
Square ABCD is dilated by a scale factor of and then translated 1 unit right to form square A” B" C"D"
Square ABCD is translated 8 units right and 8 units up and then reflected across the y-axis to form
square A"B" C"D"
Square ABCD is reflected across the x-axis and then dilated by a scale factor of 2 to form square A" B" C"D"
Square ABCD is rotated 270" clockwise and then dilated by a scale factor of to form square A" B”C” D”
Answer:
The correct answers are A B D
Step-by-step explanation:
hope this helped!
The depth of a certain part of the Earth's seabed is 36,024 feet. How deep is it in (a) fathoms? (b) leagues (marine)?
The depth of the sea bed is 5104 fathom and 1.986 league
What is a Seabed ?The bottom of an ocean , the ocean floor is called Seabed .
It is given that
The depth of a certain part of the Earth's seabed is 36,024 feet
The depth in fathom is given by = depth in feet / 6
The depth in fathom is = 36024 / 6
= 5104 fathom
1 league = 6046.1 * 3 feet = 18138.1 feet
The depth in League (marine) = Depth in feet / 18138.1
The depth in League (marine) = 36024/18138.1
= 1.986 league
Therefore the depth of the sea bed is 5104 fathom and 1.986 league.
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The number of measles cases has increased by 5.3% since 2000.
Express your answer rounded correctly to the nearest hundredth.
Stated another way, the number of measles cases is
times what it was in 2000.
Express your answer rounded correctly to the nearest tenth of a percent.
Stated another way, the number of measles cases was
% of what it is now.
The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x
How to express the number of measles?Let the initial number of measles in 2000 be represented as:
Initial = a
The rate of increase is given as:
Rate, r = 5.3%
The number of measles in x years after 2000 is represented as:
y = a * (1 +r)^x
Substitute r = 5.3%
y = a * (1 + 5.3%)^x
So, we have:
y = a * (1 + 0.053)^x
Evaluate the sum
y = a * (1.053)^x
To express to the nearest hundredth, we approximate to 2 decimal places
y = a(1.05)^x
To express to the nearest tenth, we approximate to 1 decimal place
y = a(1.1)^x
Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x
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To find the possible roots of the polynomial 4x3 + x4 – 7x2 – 8x - 8
divide factors of ± __ by factors of ± __ .
The complete statement is divide factors of ± 8 by factors of ± 1
How to complete the statement?The polynomial is given as:
4x^3 + x^4 - 7x^2 - 8x - 8
Rewrite properly as:
x^4 + 4x^3 - 7x^2 - 8x - 8
The first term in the above equation is 1 i.e. 1x^4, while the last term is 8
To determine the possible rational roots, we divide the factors of the last term i.e. 8 by the factors of the first term i.e. 1
Hence, the complete statement is divide factors of ± 8 by factors of ± 1
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The line whose equation is y=4x+2 has a y-intercept with coordinates
Answer: 2xy
Step-by-step explanation: 2xy is the answer bra
how is -x^6+7x^5 considered a sixth degree binomial?
Answer:
Polynomial, 6. Constant. The highest value of the exponent in the expression is known as the Degree of Polynomial. The degree of a polynomial is the largest exponent. It is also known as an order of the polynomial. While finding the degree of the polynomial, the polynomial powers of the variables should be either in ascending or descending order.
Step-by-step explanation:
A term is defined as a part of an equation separated by a +/- operation. Because there is a + operation separating two terms (-x^6 and 7x^5), the expression is a binomial, meaning the expression has two terms.
The highest exponent or degree, present in the expression is to the power of 6. Therefore, the expression is in the sixth degree.
Taken together, the expression is a sixth-degree binomial.
Use the interactive to make a line that passes through the points 3'2 and -1'-1 slope
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
Equation of a lineThe standard equation of a line is expressed as y= mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points on a line (3, 2) and (-1, -1)
Slope = -1-2/-1-3
Slope = 3/4
Determine the y-intercept
2 = 3/4(3) + b
2 = 9/4 + b
b = 2 - 9/4
b = -1/4
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
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Which is the graph of 2x - 4y > 6?
-4 -2
2
-2
2
RUTA
4-2
414
2
O
W
4 -4-2
414
2
-2
O
2
RY
4
-2
2
211
Answer:
(d) see attached
Step-by-step explanation:
There are a couple of quick checks you can do to identify the correct graph.
__
shading and line styleFind a variable with a positive coefficient, and write that in the given relation to the inequality symbol:
x >
This tells you ...
shading is to the right of the line (where x-values are greater)the line is dashed (the = case is not included)location of the lineThe x-coefficient is a factor of the constant, so the x-intercept of the boundary line is easily found. Set y=0, and you have ...
2x = 6
x = 3
The boundary line you're looking for has an x-intercept at x=3.
__
The correct graph is shown in the attachment.
Which set of side lengths forms a right triangle?
O2, 3, 13
O4, 6, 10
O 9, 12, 18
O 15, 36, 39
Step-by-step explanation:
hope you can understand
Q5
The following are data from an independent measures experiment comparing
two treatment conditions:
Treatment 1
n=8
M = 8
SS=104
Treatment
n=8
M = 14
SS = 120
a. Do these data indicate a significant difference between the two
treatments?
b. Compute r2 and interpret the size of the treatment effect.
Answer:
A 2kg block is moved a long a level floor by a horizontal force of 20N if the coefficient of sliding friction is 0.4
what is the acceleration of the blove
Find the distance between the parallel lines y=x-5 and y=x+6
Answer:
11
Step-by-step explanation:
i don't know
Instructions: Complete the following proof by dragging and dropping the
correct reason in the spaces below.
Statement
Complete the Proof
8x5= 2x + 1
6x5=1
6x = 6
x = 1
Reason
1
Someone help proofs aren’t my thing
The solution to the given linear equation is x=1
Solution to linear equationLinear equations are equations that has a leading degree of 1.
Given the linear equation as shown below;
8x - 5= 2x + 1
Subtract 2x from both sides
8x - 2x - 5 = 2x + 1-2x
6x - 5 = 1
Add 5 to both sides
6x - 5 + 5 = 5 + 1
6x = 6
Divide both sides by 6
6x/6 = 6/6
x = 1
Hence the solution to the given linear equation is x=1
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What is the value of x?
The value of x in the segment is 3
How to determine the value of x?Using the secant and segment theorem, we have:
x * (x + 21) = (x + 1) * (x + 1 + 14)
Evaluate the sum
x * (x + 21) = (x + 1) * (x + 15)
Expand
x^2 + 21x = x^2 + 15x + x + 15
Subtract x^2 from both sides
21x = 15x + x + 15
Evaluate the like terms
5x = 15
Divide both sides by 5
x = 3
Hence, the value of x is 3
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A is the set of integers greater than or equal to -9 and less than or equal -2
B = {-30, -27, 20, 24, 28}
a) Find the cardinalities of A and B.
n(A)=
n(B) =
Answer:
The cardinality Of Set A= 8, Set B = 5
SET :an organized collection of objects
Cardinality : It is defined as how many elements make in a set or other grouping.
Step1: Integers greater than or equal to -9 and less than or equal to -2 are
= -9,-8,-7,-6,-5,-4,-3,-2
Step 2: Form a set using given elements, we have
Set A = {-9,-8,-7,-6,-5,-4,-3,-2}
Step 3: Count the no. of elements
we have, no. of elements is 8.
For given Set B = {-30, -27, 20, 24, 28}
we have, no. of elements is 5.
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f(x) = 3x² + 5x - 2
g(x) = 5x³-4x² + 4
Find (f + g)(x)
Answer: [tex]5x^3 - x^2 + 5x+2[/tex]
Step-by-step explanation:
[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]
Which expression is equivalent to 2x² - x + ?
O A
O
B
C
D
²(x - 2)²
2
IN
2 X-
16
Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]
Step-by-step explanation:
[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]
Consider the matrix [tex]A_{4x4}, det(A) = -2[/tex]
Show that the following is true or false:
[tex]det(adj(2A^{-1}) =-2^{9}[/tex]
We found a counterexample, so the statement is false.
Is the statement true?
Let's use the matrix:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
This is a 4x4 matrix with determinant equal to -2.
The inverse matrix is:
[tex]\left[\begin{array}{cccc}1/2&0&0&0\\0&-1&0&0\\0&0&-1&0\\ 0&0&0&-1 \end{array}\right][/tex]
If we multiply it by 2, we get:
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&-2&0&0\\0&0&-2&0\\ 0&0&0&-2 \end{array}\right][/tex]
The adjoint of that is the original matrix, actually:
[tex]\left[\begin{array}{cccc}-2&0&0&0\\0&1&0&0\\0&0&1&0\\ 0&0&0&1 \end{array}\right][/tex]
Which we already know, has a determinant of -2.
So the statement is false, as we found a counterexample.
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Helppppppoppppoppppppppppppppp
What is the solution to this system of equations 5x+2y=29
X+4y=13
Answer:
(5, 2 )
Step-by-step explanation:
5x + 2y = 29 → (1)
x + 4y = 13 → (2)
multiplying (1) by - 2 and adding to (2) will eliminate y
- 10x - 4y = - 58 → (3)
add (2) and (3) term by term to eliminate y
- 9x + 0 = - 45
- 9x = - 45 ( divide both sides by - 9 )
x = 5
substitute x = 5 into either of the 2 equations and solve for y
substituting into (2)
5 + 4y = 13 ( subtract 5 from both sides )
4y = 8 ( divide both sides by 4 )
y = 2
solution is (5, 2 )
What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)2+3?
-5
-3
O
3
O5
The value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = x²
The above function is a parent function.
The translation: vertical translation from the graph of the parent function.
F(x) → f(x) + 3
F(x) = x² + 3
The above function will shift vertical up by 3 units.
Thus, the value is 3 which represents the vertical translation from the graph of the parent function f(x)=x² option third 3 is correct.
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What is the product? Assume x≥0.
(√3x + √5)√15x+2√30)
A. 3x√√5 +3√165x+10√√6
B. 3x√5+6√10x +5√3x +10√6
C. 3x√√5+10√6
D. 6√3x+10√6
The product of (√3x + √5)(√15x+2√30) assuming x ≥ 0 is 3√5x² + 6√10x + 5√3x + 10√6
What is the product of the expression?It follows from the task content that the expression given whose product is to be evaluated is;
(√3x + √5)(√15x+2√30)
Hence, by multiplying the terms with each other accordingly; we have;
= (√45x² + 2√90x + √75x + 2√150)
= 3√5x² + 2√90x + √75x + 2√150
= 3√5x² + 2×3√10x + √75x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 2√150
= 3√5x² + 2×3√10x + 5√3x + 10√6
= 3√5x² + 6√10x + 5√3x + 10√6
Ultimately, the product of the expression is; 3√5x² + 6√10x + 5√3x + 10√6
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easy:
Clara buy: 300 apples, 74 potato, 15 eggs e 2 phone.
how many things did he buy in all?
Hard:
There are 92 boys in a school, the girl 100.How many more girl are there than boys?
Answer:
easy = 391 items
hard = there are 8 more girls than there are boys
Solve the equation -8 = -3 - 6 cube root x^2
a. 0.76, -0.76
b. 4.98
c. 3.87
d. 1.53, -1.53
Answer:
0.76
Step-by-step explanation:
-8+3=-6x^(2/3)
-5=-6 x^(2/3)
-5/-6=x^(2/3)
(2/3)√{5/6}=x
0.76=x
x=0.76
The graphs of exponential functions f and g are shown on the coordinate plane below.
Answer:
-5
Step-by-step explanation:
Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5
A 3-column table with 3 rows. Column 1 is labeled Unit Fraction with entries StartFraction 1 Over 10 EndFraction, one-fourth, c. Column 2 is labeled Fraction with 100 in the denominator with entries StartFraction 10 Over 100 EndFraction, b, StartFraction 50 Over 100 EndFraction. Column 3 is labeled Percent with entries a, 25 percent, 50 percent.
Complete the table by finding the missing equivalent form for each row.
a =
b =
c =
The missing equivalent forms are: a = 10%, b = 25/100 and c = 1/2
Complete questionUnit Fraction Fraction with 100 in denominator Percent
1/10 10/100 a
1/4 b 25%
c 50/100 50%
Complete the table by finding the missing equivalent form for each row.
How to determine the missing equivalent forms?From the above table, we have the following equations
a = 10/100
b = 25%
c = 50/100
The variable a must be in percentage.
So, we have:
a = 10/100
Express as percentage
a = 10%
The variable b must be a fraction with 100 in denominator
So, we have:
b = 25%
Express as fraction
b = 25/100
The variable b must be a unit fraction
So, we have:
c = 50/100
Divide the fraction by 50/50
c = 1/2
Hence, the missing equivalent forms are:
a = 10%, b = 25/100 and c = 1/2
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What is the solution set of -xl = -10?
No solution since absolute value can't be equal to negative numbers
PLEASE GIVE BRAINLIEST
The ratio of the number of fiction book is 9:4, the different between the number of fiction and non fiction is 245
Answer:
Step-by-step explanation:
The ratio of the number of fiction books is 9:4
the difference between the number of fiction and nonfictionn is 245
so if the number of fiction books = 9x
then the number of nonfiction books = 4x
then difference = 9x-4x = 5x
the difference is given 245
then 5x= 245
x=[tex]\frac{245}{5}[/tex]=49
number of fiction books =49×9=441
number of nonfiction books =49×4=196
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