Answer:
28
Step-by-step explanation:
Let n represent the number.
Twice the sum of the number and 2 is ...
2(n +2)
Three times the difference of the number and 8 is ...
3(n -8)
The problem statement tells us these quantities are equal, so ...
2(n +2) = 3(n -8) . . . . the given quantities are equal
2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses
2n +28 = 3n . . . . . . . add 24
28 = n . . . . . . . . . . . . subtract 2n
The number is 28.
_____
Check
The sum of the number and 2 is 30; twice that is 60.
The difference of the number and 8 is 20; three times that is 60--the same number.
Tyrell does sit-ups every day. On Monday, he did 4 sit-ups. On Tuesday, he did 8 sit-ups, and on Wednesday, he did 12 sit-ups. Based on the pattern, make a conjecture about the number of sit-ups he will do on Friday.
Answer: 20 sit ups.
Step-by-step explanation: if tyrell does situps everyday on monday he does 4 sit ups and tuesday 8 situps wendsday 12 situps thursday 16 situps friday 20 situps all u do to solve is add 4 every day.
your welcome.
Solve for the width in the formula for the area of a rectangle.
formulas
1. w = A - L
2. w = AL
3. w = L/A
4. w = A/L
Use the rewritten formula to find the width of a rectangle with an area of 42 square inches and a length of 16.8 inches.
1. 2.5 inches
2. 4.2 inches
3. 12.6 inches
4. 25.2 inches
W=A/L................
2.5 inches...........
A ship leaves port at 1:00 p.m. and travels s35°e at the rate of 26 mi/hr. another ship leaves the same port at 1:30 p.m. and travels s20°w at 20 mi/hr. approximately how far apart are the ships at 3:00 p.m.?
David gained 16 pounds over the winter. he went on a diet and lost 25 pounds. then he regained 4 pounds and weighed 177 pounds. how much did he weigh originally?
David's original weight was 182 pounds, as we determined by retracing his weight changes in reverse order.
Explanation:To find out how much David originally weighed, we need to work backwards from his ending weight, taking his weight changes into account. Currently David weighs 177 pounds. However, before gaining the last 4 pounds, he would have weighed 177 - 4 = 173 pounds.
Going back further, before losing 25 pounds, he would have weighed 173 + 25 = 198 pounds. Finally, before David gained 16 pounds over the winter, his original weight would have been 198 - 16 = 182 pounds.
So, David's original weight was 182 pounds.
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The area of a rectangle is 44 ft2 , and the length of the rectangle is 3 ft less than twice the width. find the dimensions of the rectangle.
Final answer:
To find the dimensions of a rectangle where the length is 3 ft less than twice the width and the area is 44 ft², we use the relationship between the width and length to set up a quadratic equation. After solving for the width, we use that width to find the length and confirm that the area is correct.
Explanation:
To find the dimensions of the rectangle with an area of 44 ft2, we need to set up an equation based on the given relationships. Let's denote the width of the rectangle as w and the length as l. According to the problem, the length is three feet less than twice the width, so we have l = 2w - 3. The area of the rectangle is the product of its width and length, so the equation to calculate the area is w × l = 44. Substituting the expression for l into this equation yields w × (2w - 3) = 44.
Solving this quadratic equation, we distribute the width and get 2w2 - 3w = 44. By moving all terms to one side, we have 2w2 - 3w - 44 = 0. Factoring the quadratic equation or using the quadratic formula will result in two values for w, where one will be the width and the corresponding l will be the length when plugged into l = 2w - 3.
Let's find the dimensions:
Width: wLength: 2w - 3Once the values are calculated, we can confirm that the width and length provide an area of 44 ft2.
Therefore, the width of the rectangle is w= 5.5 feet.
Now, we can find the length (l):
l=2w−3=2(5.5)−3=11−3=8
So, the length of the rectangle is l=8 feet.
solve the system
x+3y=5
x+4y=6
A) (2,1)
B) (1,5)
C) (8,-1)
D (11,-2)
Answer:
A(2,1)
Step-by-step explanation:
We are given that system of equation
[tex]x+3y=5[/tex]
[tex]x+4y=6[/tex]
We have to solve the system
Subtract equation first from equation second
Then, we get
[tex]y=1[/tex]
Substitute the value of y in equation I
Then, we get
[tex]x+3(1)=5[/tex]
[tex]x=5-3=2[/tex]
Hence, the option A is true.
Answer:A(2,1)
Use multiplying by 1 to find an expression equivalent to 18/19 with a denominator of 76b.
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2 that passes through (–6, –1).
A. y = 5x + 29
B. y = –5x – 11
C. y= 1/5 x+1/6
D. y = 5x – 29
The equation of line which is parallel to y = 5x + 2 and passing through (-6, -1) is y = 5x + 29. Then the correct option is A.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Identify an equation in slope-intercept form for the line parallel to y = 5x + 2 that passes through (–6, –1).
The slope of the parallel lines is the same.
Then the equation will be
y = 5x + c
And the line is passing through (-6, -1), then the value of c will be
-1 = 5(-6) + c
c = 30 - 1
c = 29
Then the equation of line which is parallel to y = 5x + 2 and passing through (-6, -1) is y = 5x + 29.
Then the correct option is A.
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The length of a rectangle is 2 in. more than twice its width. if the perimeter of the rectangle is 28 in., find the dimensions of the rectangle.
What is the simplified form of the expression? -(4)^-2
Answer:
The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
Step-by-step explanation:
Given : Expression [tex]-\left(4\right)^{-2}[/tex]
We have to write the simplified form of the given expression [tex]-\left(4\right)^{-2}[/tex]
Consider the given expression [tex]-\left(4\right)^{-2}[/tex]
Apply exponent rule , [tex]\:a^{-b}=\frac{1}{a^b}[/tex]
[tex]4^{-2}=\quad \frac{1}{4^2}[/tex]
[tex]\frac{1}{4^2} =\frac{1}{16}[/tex]
Thus, The given expression [tex]-\left(4\right)^{-2}[/tex] becomes [tex]-\frac{1}{16}[/tex]
If y=x+2 were changed to y=x-1 how would the graph of the new function compare with the first one
Answer: C shifted down :)
Answer:
it would be shifted down
is 2xy = -8 a function
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
When the transverse and conjugate axes of a hyperbola are both the same length, the diagnosis and appropriate are said to be rectangular.
The equation is given below.
2xy = -8
Separate the variable 'y', then we have
2xy = -8
xy = -4
y = -4/x
The equation 2xy = -8 is a rectangular hyperbola which is an example of the function.
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Sunitha is 24 years older than her daughter kavitha. 6 years ago Sunitha was thrice as old as Kavitha. Find their present ages
In the above figure, ∠AOB = 80°. What does ∠ACB equal?
A. 80°
B. 10°
C. 160°
D. 40°
ACB would be half of AOB
80/2 = 40
answer is D 40 degrees
Hour hand of a watch rotates 30 degrees every hour, how many rotations makes in 6 days
if a job pays $45,000 per year, you live in a state where your total tax burden is 22%, and you receive a weekly paycheck, what is your take-home pay from each paycheck?
Answer:
$190.38 per week
Step-by-step explanation:
45,000 x .22 (the tax) is 9,900
9,900 / 52 (weeks in a year) is 190.384
Rounded, your answer is $190.38 per week
Which equation has the steepest graph
Answer:
b
Step-by-step explanation:
If you run a 10 kilometer race in 43 minutes 30 seconds, what is your average time per mile? what is your average speed in miles per hour?
A coach needs both small and large cones to set up an obstacle course. The coach knows that there are fewer than 30 cones in the storage room. The coach needs at least a dozen large cones.
Let x represent the number of small cones and y represent the number of large cones.
Which inequalities model the situation? Select each correct answer.
x+y≤30
x>0
x+y<30
y≥12
y>12
Answer: The correct options are,
x+y < 30
y ≥ 12
Step-by-step explanation:
Here, x represent the number of small cones and y represent the number of large cones.
∵ Large cones are at least 12,
⇒ y ≥ 12,
Now, total cones = x + y
∵ There are fewer than 30 cones,
I.e. x + y < 30,
Now, number of cones can not be negative,
⇒ x, y ≥ 0
In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 17 prospective jurors?
Final answer:
To find the different ways of choosing a panel of 12 jurors and 2 alternates from 17 prospective jurors, calculate the combinations separately (C(17, 12) for jurors and C(5, 2) for alternates) and multiply them, yielding a total of 61,880 different ways.
Explanation:
The question asks in how many different ways a panel of 12 jurors and 2 alternates can be chosen from a group of 17 prospective jurors. To solve this, we use the concept of combinations in mathematics. Since the order in which we select the jurors and alternates does not matter, we are dealing with combinations, not permutations.
First, we choose the 12 jurors from the 17, which is the combination of 17 taken 12 at a time. This can be calculated using the formula for combinations:
C(n, k) = n! / (k! * (n - k)!),
where 'n' is the total number of items, 'k' is the number of items to choose from, and '!' denotes factorial.
For the 12 jurors, we compute C(17, 12) which equals 17! / (12! * (17 - 12)!) = 17! / (12! * 5!) = 6188.
Next, we need to choose 2 alternates from the remaining 5 jurors. The calculation is C(5, 2) which equals 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = 10.
Since choosing jurors and alternates are independent events, we multiply the two combinations to get the total number of different ways to choose the panel:
6188 (ways to choose jurors) * 10 (ways to choose alternates) = 61,880 different ways.
Formulate the recursive formula for the following geometric sequence.
{-16, 4, -1, ...}
Answer: divide by -4
Step-by-step explanation:
What is the coefficient of x7 in the expansion of (1 + x)11?
Final answer:
Using the binomial theorem, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is found by calculating '11 choose 7', which is 330.
Explanation:
The coefficient of x⁷ in the expansion of (1 + x)¹¹ can be found using the binomial theorem. To find the coefficient of x⁷, we look for the term that comes from choosing x seven times in the expansion. This corresponds to the 8th term, because the terms are indexed from 0, where the binomial coefficient is found by calculating "11 choose 7" or C(11, 7).
To calculate "11 choose 7", use the formula:
C(n, k) = n! / [k!(n-k)!], which gives us:
C(11, 7) = 11! / [7!(11-7)!] = 11! / (7!4!) = (11×10×9×8) / (4×3×2×1) = 330
Therefore, the coefficient of x⁷ in the expansion of (1 + x)¹¹ is 330.
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
Answer:
Step-by-step explanation:
Y = total weight of books
X = number of books
6 = weight (in ounces) of 1 book
total weight of books = weight of books x number of books
Y = 6X
Answer:
Only 0,0 You don't order negative numbers of books which eliminates the first two pairs. And you don't order 1/2 a book which eliminates the last pair.
Step-by-step explanation:
If you order 0 shirts they will weight 0 ounces is the only viable solution.
Which situation CANNOT be represented by this equation? -13x+15=9
A-The water level in a tank measures 1515 inches and is decreasing every 1313 of a minute. At what rate, xx, does the water level need to decrease per minute to reach a depth of 99 feet?
B-The water level in a tank measures 99 inches and is rising 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 1515 inches deep?
C-The water level in a tank measures 1515 inches and is decreasing 1313 of an inch every minute. How many minutes, xx, will it take for the water level to measure 99 inches deep?
THE ANSWER IS: PLEASE MARK AS BRAINLIST
The water level in a tank measures 9 inches and is rising 13 of an inch every minute.
How many minutes, x, will it take for the water level to measure 15 inches deep?
Given the parent functions f(x) = 3x + 2 and g(x) = 5x − 10, what is g(x) − f(x)?
g(x) − f(x) = 5x − 8 − 3x
g(x) − f(x) = 5x − 12 − 3x<--------------------
g(x) − f(x) = 3x − 8 − 5x
g(x) − f(x) = 3x + 12 − 5x
Points earned on this question: 2
Answer:
Option B. g(x) - f(x) = 5x - 3x - 12
Step-by-step explanation:
In this question the given functions are
f(x) = 3x + 2
g(x) = 5x - 10
Now we have to calculate the value of g(x) - f(x)
g(x) - f(x) = (5x - 10) - (3x +2)
= 5x - 10 - 3x - 2
= (5x - 3x) - (10 + 2)
= 5x - 3x - 12
Option B. (5x - 3x - 12) is the answer.
Chris's uncle has a model car. the model is 6 inches long and 3 inches wide. the actual car is 75 inches long. what is the car's actual width, if we assume the model's proportions are accurate? if necessary, round to the nearest tenth of an inch.
I believe the right answer would be 37.5
A fisherman separated 1/10 of his catch into 2 equal bins.What fraction is the entire catch was in each bin?A. 20/1 B. 5/1 C. 1/20 D. 1/5 Plz help me plz i need help with this right now.
Patricia donated 1 pint of blood to the blood bank.The lab assistant divided patricia's blood equally into 3 bags.How much blood was in each bag?
Each bag contained [tex]\(\frac{1}{3}\)[/tex] pint of blood.
To solve the problem, we need to divide the total amount of blood donated by Patricia equally into 3 bags. Patricia donated 1 pint of blood.
Since there are 3 bags, we divide 1 pint by 3 to find out how much blood is in each bag. The division is straightforward:
[tex]\[ \frac{1 \text{ pint}}{3 \text{ bags}} = \frac{1}{3} \text{ pint per bag} \][/tex]
Therefore, each bag contains [tex]\(\frac{1}{3}\)[/tex] pint of blood. This is the simplest form of the fraction, and there is no need to convert it to a different unit or simplify it further. The answer is [tex]\(\frac{1}{3}\)[/tex] pint per bag.
Each face of a pyramid is an isosceles triangle with a 82° vertex angle. What are the measures of the base angles? PLZ help
WILL GIVE BRAINLIEST
The value of the base angle will be 49 degrees.
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
A vertex is an angle that is connected to a vertex of an n-dimensional polytope in geometry. It refers to the angle created by two lines colliding in two dimensions.
Given that each face of a pyramid is an isosceles triangle with an 82° vertex angle.
The base angle will be calculated by using the formula below:-
Base angles = (180°-vertex)/2=(180-82)/2
Base angles = 98/2=49°
Base angles = 49°
Therefore, the value of the base angle will be 49 degrees.
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Select all that justify the following statement.10 + x • 12 = 12x + 10
10 + x*12 = 12x+10
since the left side can be re-written as 12x+10 this does equal the right side
so any real number ( any value of x ) will work