Steps to solve:
k + 10 = 27
~Subtract 10 to both sides
k = 17
Best of Luck!
A 224 cm rope is cut so that one part is 3/4 of the other. How long is the shorter rope? The longer rope?
Given that:
Length of a rope = 224 cm
Rope is cut so that one part is 3/4 of the other.
Solution:
Let one part of a rope be x cm.
So other part of the rope is [tex]\dfrac{3}{4}x[/tex].
Total length [tex]=x+\dfrac{3}{4}x[/tex]
Now,
[tex]x+\dfrac{3}{4}x=224[/tex]
[tex]\dfrac{4x+3x}{4}=224[/tex]
Multiply both sides by 4.
[tex]7x=896[/tex]
Divide both sides by 7.
[tex]x=\dfrac{896}{7}[/tex]
[tex]x=128[/tex]
The value of one part 128 cm.
Second part [tex]=\dfrac{3}{4}x[/tex]
[tex]=\dfrac{3}{4}\times 128[/tex]
[tex]=3\times 32[/tex]
[tex]=96[/tex]
Therefore, the length of shorter rope is 96 cm and the length of longer rope is 128 cm.
Solve. Fill in the table for three consecutive even integers.
Next Integers
First Integer
Even integer
Indicated Sum
Sum of the first and third even consecutive
integers, simplified:
х
Enter the next integers in the table below.
First Integer Next Integers
Even integer.
х
(Simplify your answers. Use ascending order. Type expressions using x as the variable.)
Complete the statement below.
0 0
Sum of the first and third even consecutive integers, simplified:
(Type an expression using x as the variable.)
Answer:
1212
Step-by-step explanation:
l= 9.25 cm; A = 55.5 cm square
Answer:
shhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
Andrew walks along a road which can be modeled by the equation y=3x, where (0,0) represents his starting point. When he reaches the point (12,36), he turns right, so that he is traveling perpendicular to the original road, until he stops at a point which is due east of his starting point (in other words, on the x-axis).
What is the point where Andrew stops?
Answer:
(120,0)
Steps:
y-36=-1/3(x-12)
(0)-36=-1/3(x-12)
(-3)(-36)=x-12
108=x-12
120=x
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The point where Andrew stops is (120,0).
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the perpendicular line will be,
m × 3 = -1
m = -1/3
Substitute the point in the line,
y = -(1/3)x + C
36 = -(1/3)12 + C
36 = -4 +C
C = 40
Now, the equation of the perpendicular line will be,
y = -(1/3)x + 40
The point will be due east, therefore, the value of y = 0,
0 = -(1/3)x + 40
-40 = -(1/3)x
x = 120
Hence, the point where Andrew stops is (120,0).
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
Multiply: (x – 4)(x + 5)
(a) x2 + 5x - 20,
(b) x2 - 4x - 20,
(c) x2 - x - 20,
(d) x2 + x - 20.
Answer:
D. x2 + x - 20.
Step-by-step explanation:
(x – 4)(x + 5).
= x(x + 5) -4(x + 5).
= x2 + 5x – 4x – 20.
= x2 + x - 20.
-140=-4 (8n - 57)
What’s the answer I keep getting a decimal
Answer: n = 11.5
Step-by-step explanation:-140=-32n +228
-368=-32n
4) An art classroom has 5 boxes with sharpie pens and clipboards. Each box has 4 sharpies.
There are 25 supplies in all. How many total clipboards are there?
5 clipboards
4 sharpies times 5 boxes = 20 sharpies
25 total - 20 sharpies = 5
5 clipboards
The first term of an arithmetic sequence is 2 and the fourth term is 11
Answer:
The sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=3\,n-1[/tex]
Step-by-step explanation:
In order to define the sequence, we recall the formula for the nth term of an arithmetic sequence as:
[tex]a_n=a_1+(n-1)\,d[/tex]
where "d" is the common difference for the sequence (our unknown in this case), and the nth term is our fourth term (n = 4) which equals 11, and the first term is 2:
[tex]a_n=a_1+(n-1)\,d\\11=2+(4-1)\,d\\9=3\,d\\d=9/3\\d=3[/tex]
Therefore our sequence has common difference 3, and its general nth term can be written as:
[tex]a_n=2+(n-1)3\\a_n=3\,n-1[/tex]
what is -2(10x-1)-10x?
Answer:
[tex]-30x+2[/tex]
Step-by-step explanation:
[tex]-2(10x-1)-10x[/tex]
Use the distributive property:
[tex]-2(10x)-2(-1)-10x\\\\-20x+2-10x[/tex]
Combine like terms:
[tex]-20x-10x+2\\\\-30x+2[/tex]
:Done
Answer:
-30x+2
Step-by-step explanation:
1. Expand by distributing terms.
2. Remove parentheses.
3. Combine like terms
The half life of a drug in 3 hours. If the drug is administered with a dose of 640mgs and the patient in not allowed to drive untold only 80mgs are present. How long before the patient can drive p
Answer: 12 hours
Step-by-step explanation: 6 h = 360 min,9 h = 540 min, 12 h = 720 min
640-360=280 , 640-540=100 , 640-720=-80
What is the range of the following function
The answer: -5 ≤ y ≤ 6
The range is all the possible output or y values of the function.
Our first point is at (1, 6) and our second point is at (-4, -5)
That means our y values are 6 and -5. Let's set up a compound inequality to represent our function.
-5 ≤ y ≤ 6. This means that x is greater than or equal to -5 and less than or equal to 6.
6 more than the sum of y and x
Answer:
x=y+6
Step-by-step explanation:
The expression will be written as x + y > 6.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 6 is more than the sum of y and x. The expression will be formed as below:-
x + y > 6
Therefore, the expression will be written as x + y > 6.
The complete question is given below:-
6 more than the sum of y and x then write the expression which represents the inequality.
To know more about an expression follow
brainly.com/question/723406
#SPJ2
4-2(3x+1) - (4x-3)
Answer: 5-10x
I really hope this helps you, I tried my best to explain it!
Budget A student group has $8,000 budgeted for a field trip. The cost of transportation for the trip is $3,400. To stay within the budget, all other costs C must be no more than what amount? Write and solve an inequality. Show your work. Write your final answer in a complete sentence.
Answer:
The answer is below
Step-by-step explanation:
Let the budget be represented by B. Since the grouo has only $8,000, hence, the inequality can be represented as:
B ≤ $8000
Also, $3400 was spent on transportation. If other cost is represented by C, therefore, other cost is given as:
Other cost ≤ Budget - cost of transportation
C ≤ $8000 - $3400
C ≤ 4600
From above, to stay within the budget, all other costs must be below $4600
AB has a midpoint at (4,6). If A has a coordinates of (0,4), find the coordinates of B
Answer:
Step-by-step explanation:
(x+0)/2 = 4
x + 0 = 8
x = 8
(y+4)/2=6
y+4 = 12
y = 8
(8,8)
Which phrase best describes f(x), graphed on the coordinate plane below? On a coordinate plane, a curve goes through two cycles. The first part of the curve approaches x = negative 6, has a maximum at (negative 4, 3), and has a minimum at (negative 2, negative 2). The second part of the curve has a maximum at (1.5, 2.5), has a minimum at (4, negative 3), and approaches x = 6. f(x) is an odd function. f(x) is an even function. f(x) is both odd and even. f(x) is neither odd nor even.
Answer:
It's an odd function.
Step-by-step explanation:
Answer:
a. f(x) is an odd function.
Step-by-step explanation:
solve for y: 3y=35 pls help
Step-by-step explanation:
Because this is a multiplication equation, and we need to find one of the factors, we divide.
So 35/3=y
35/3=11.6666667
or 11.67/11.7
Hope it helps!
Find a counterexample to show that we don't always have equality.
Answer:
Hello your question is incomplete below is the complete question
Let R be a relation from A to B and S a relation from B to C.
(a) Prove that . [tex]Dom(S \circ R) \subseteq Dom(R)[/tex]
(b) Find a counterexample to show that we don’t always have equality.
answer : (b) Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]
hence: Dom ( S o R ) ≠ Dom ( R )
Step-by-step explanation:
Note : R ⊆ A * B and S ⊆ B * C
A) To prove that [tex]Dom(S \circ R) \subseteq Dom(R)[/tex]
we take note that : S o R ⊆ A x C
ATTACHED BELOW IS THE REMAINING PART OF THE SOLUTION
B) A counterexample to show that we don't always have equality
attached below is a assumptions and solution on how we arrived at the value below
Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]
hence: Dom ( S o R ) ≠ Dom ( R )
BRAINLIEST!!!!!!
Decide if the function is an exponential function. If it is, state the initial value and the base. (2 points)
y = - 3.8 ⋅ 2x
A. Exponential Function; base = x; initial value = - 3.8
B. Exponential Function; base = 2; initial value = - 3.8
C. Not an exponential function
D. Exponential Function; base = - 7.6; initial value = 1
Answer:
B. Exponential Function; base = 2; initial value = - 3.8
Step-by-step explanation:
hey there,
< The formula for exponential functions is [tex]A_{t} = A_{o} e^{kt}[/tex]. The function given DOES follow this formula (At = y, -3.8 = Ao, e = 2, k = 1, t = x) so that means it is an exponential function. C cannot be the answer.
You already know that e is the base in called the "natural base". e is equal to a number around 2. In this function, they just put it as "2". So we know that the base is equal to 2.
Ao means initial value and At means value after the experiment is done. Here, we can see Ao = -3.8 so that is the initial value.
base = 2; initial value = - 3.8 >
Hope this helped! Feel free to ask anything else.
100 POINT QUESTION + BRANLIESt What is 2+2?
Answer:
4
Step-by-step explanation:
Yeah if you don't know this one... you're... special.
A shipment of 20 DVDs has arrived at a video rental store. Based on past experience, the manager knows that 10% of all new DVDs sent to the store have a visible defect. The manager tells you to begin inspecting the new DVDs one at a time at random until you find the first DVD that has a defect. If 10% of the DVDs have a visible defect in the new shipment, what is the probability that the first DVD that has a defect is the 3rd one that you inspect? (Round your answer to 3 decimal places.)
Answer:
The probability is 0.081
Step-by-step explanation:
Here, we want to calculate the probability that the 3rd inspection will be defective.
What this means is that the first two would
not be defective.
Probability of having a defective DVD = 10% = 10/100 = 0.1
Probability of not having a defective DVD = 1 -0.1 = 0.9
So the probability of third being defective = Probability of first not defective * Probability of second not defective * Probability of third defective
= 0.9 * 0.9 * 0.1 = 0.081
Please help me please
Answer:
the last option
Step-by-step explanation:
every other one adds up to be 10/12 but the last one is 15/10
Answer:
D) 5/12 + 4/12 + 3/12 + 2/12 + 1/12
Step-by-step explanation:
5/12 + 4/12 + 3/12 + 2/12 + 1/12 = 15/12
A student is ordering a flower arrangement. She can choose any combination of roses and carnations for flower arrangement, and she does not want to spend more than $30. If roses cost three dollars each and carnations cost two dollars each which inequality represents all possible combinations of X roses and y carnations?
3X + 2y<30
2x+3y<_ 30
2X+ 3Y > 30
3X + 2Y<_ 30
Answer:
The inequality is;
2x + 3y ≤ 30
Step-by-step explanation:
Here, we want to select which of the inequalities represent all possible combinations of x roses and y carnations.
From the question, we are told that roses cost $3 and carnations cost $2
So, by buying x roses, total amount spent = $3x
By buying y carnations, total amount spent = $2y
Now, we are told that she does not want to spend more than $30, this means she can spend less than $30 or exactly $30 but cannot spend more than $30
So, by mathematical convention, we say the sum of the roses and carnations bought is less than or equal to $30
Thus we have;
2x + 3y ≤ 30
Answer:
2x + 3y ≤ 30
Step-by-step explanation:
Uhh im doing the test rn on it so yea
which product is negative
Answer:
4th option because the two negatives will become positive and the 3rd will make it negative again
Answer:
the last one which is D (D)
Some movies are profitable and others are not . Understandably , the movie industry would like to know what makes a movie successful . Data from 728 first-run movies released in 2011 suggest that longer movies actually make less profit. Identify the sample .
Answer:
The sample is the 728 first run movies released in 2011
What set of reflections would carry trapezoid ABCD onto itself?
A
D
B
С
(6 points)
O y=x, X-axis, y=x, y-axis
O x-axis, y=x, X-axis, y=x
Oy-axis, X-axis, y-axis
O x-axis, y-axis, y-axis
Can someone please solve this equation for me 5.50x=266
Answer:
1463
Hi There!
Remember, when multiplying with decimals never forget to add the decimal!
I’m having a hard time looking at this figure and I want to make sure I’m looking at it right and understanding it. Any help is greatly appreciated, I know it’s quite a bit
Step-by-step explanation:
1a) The perpendicular bisectors pass through the midpoints of the sides of the triangle and are perpendicular to the sides. They are the red lines.
1b) The angle bisectors pass through the vertices of the triangle and divide the angle into two equal parts. They are the black lines.
1c) The inscribed circle is the circle inside of the triangle. It is the blue circle.
1d) The circumscribed circle is the circle outside of the triangle. It is the green circle.
2a) The circumcenter is the center of the circumscribed circle. It is point H.
2b) The incenter is the center of the inscribed circle. It is point I.
PLEASE PLEASE PLEASE HELP
Answer:
the answer to your question is -8.5
Answer:
-3.4 × 2.5 = -8.5
Step-by-step explanation:
Since these are short decimals, you can probably convert these into fractions if you'd like.
So -3.4 = -17/5
And 2.5 = 5/2.
So just multiply this like you would multiply two fractions, just multiply across the numerator, and denominator, and then just simplify; numerator × numerator / denominator × denominator.
So
The trick when multiplying by 5 is to divide the number in half, and multiply by 10.
-17/5 × 5/2 = -17 × 5 / 5 × 2 = -17/2 × 10 / 10 = -8.5 × 10/10 = -8.5 × 1 = -8.5
(The tens just cancel and make 1 so you are just left with this answer)
You can also try splitting the decimals up into factors:
-3.4 × 2.5 = (-3 - 0.4)(2 + 0.5) = -6 + -0.8 + -1.5 + 0.2 = -6 + -1 + -1.5 = -7 + -1.5 = -8.5.
12.
1/2(4x — 2) – 2/3(6x + 9) <4
Answer: x > -11/2
svdbhtdtgifubhonj
Answer:
x>-11/2
I'm sorry, I did this all on paper and I don't really want to type it out. Please understand.
Hope this helps a little bit, though.
