A 16-foot piece of string is cut into two pieces so that the longer piece is 1 foot longer than twice the shorter piece.
Find the lengths of both pieces.
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Part 1
What is the length of the shorter piece?
What is the length of the longer piece?
Answer:
Shorter piece: 5 Longer piece: 11
Step-by-step explanation:
(2x+1)+(x)=16
3x+1=16
3x=15
x=5
Anne’s family drives to her uncle’s house for vacation, and they take two separate cars. anne’s car travels 383.5 miles between 10:15 am and 4:45 pm. the equation y = 58x represents the relationship between the distance, y, in miles and the time, x, in hours that anne’s sister’s car traveled. if both cars are traveling at constant rates, which car â€" anne’s or her sister’s â€" would you expect to arrive at their uncle’s house first? explain how you know.
Anne's family wouldn't have gotten there until about 5:55 pm.
How Distance is that?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.The arrival time is the travel time added to the start time. The travel time is given by ...
time = distance/speed
At 50 miles per hour, the travel time would be ...
time = 383.5/50 = 7.67 . . . . hours
The fraction of an hour is ...
(0.67 hours)×(60 min/hour) = 40.2 min
Adding the travel time to the start time, we get an arrival time of ...
10:15 am + 7:40 = 17:55 = 5:55 pm
Anne's family wouldn't have gotten there until about 5:55 pm.
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4. Solve x - 2 = 1.
Which statement shows the correct justification for the step used to solve the
equation?
O Add 1 to each side.
O Add 2 to each side.
O Subtract 1 from each side.
O Subtract 2 from each side
Answer:
x=3
Step-by-step explanation:
or,x-2=1
or,x=2+1
or,x=3
A 2-lb sample of an unknown liquid occupies a volume of 47.6 in.3 for the liquid determine (a) the specific volume, in ft3/lb, and (b) the density, in lb/ft3.
The specific volume is 0.0135 ft^3
The density is 74.07 lb/ft^3
Here,
A 2-lb sample of an unknown liquid occupies a volume of 47.6 in^3.
We have to find the specific volume and density.
What is Specific volume?
Volume is a measure of the amount of space occupied by an object.
Now,
Mass = 2 lb
Volume = 47.6 in^3
= 0.027 ft^3
Hence, Specific volume = volume/ mass = 0.027/2 = 0.0135 ft^3
And, Density = mass/ volume = 2/ 0.027 = 74.07 lb/ft^3
So, The specific volume is 0.0135 ft^3
The density is 74.07 lb/ft^3
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What is the degree of x^2+3x+y?
Answer: 2
Step-by-step explanation:
as x is to a power of 2 so degree is 2
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Which shows the expression below simplified?
A. 8 × 10-3
B. -1.4 x 10-3
C. 8x10-1
D. 8×104
0.00056+ (7 x 10-²)
Answer:
A.77
B.-17
C.79
D.832
E.0.07056
Step-by-step explanation:
A.=8×10-3
=80-3
=77
B.=-1.4×10-3
=-14-3
=-17
C.=8×10-1
=80-1
=79
D.=8×104
=832
E.=0.00056+(7×10^-2)
=0.00056+0.07
=0.07056
79 tens X 27 tens with rounding
12÷3×5-4 to the 2nd power
I have two answers depending on the format. I'm not sure if the entire function is to the 2ndpower or not. Either way, it's either 256 or 4.
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Enrollment at a golf academy has grown exponentially since the academy opened. A graph depicting this growth is shown. Determine the percentage rate of growth.
1.5%
5%
50%
0.5%
GRAPH IS BELOW
Answer:
We can see that after 2 years, enrollment becomes 35 instead of 15.
35/15=2.333...)
Since it's exponential, take sqrt(2.333...)=about 1.5
So the growth is 50%
13 X 3
vrcubdavbytayvtcecgvfgdcvfcevfd6bdcb7dvfb7svfb7gbx7bgbr
Answer:
39
Step-by-step explanation:
1x3=3 9x3=9 so together 39
11) Mike is thinking of two numbers. Their difference is 12. If one of the numbers is 19, what is the other
number? Is there only one answer? If not, what is the other possibility for the second numbe? Explain
your reasoning.
Answer: 7, and 31
Step-by-step explanation:
7 + 12 = 19 or 19 - 12 = 7
19 + 12 = 31
The other number will be - 7.
Yes, There is only one answer.
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 difference of two numbers is 12.
And, one of the numbers is 19.
Now,
Let two numbers are x and y.
So, We get;
x + y = 12
Here, one of the numbers is 19.
So, x = 19
We get;
x + y = 12
19 + y = 12
y = 12 - 19
y = - 7
Thus, The other number will be - 7.
Yes, There is only one answer.
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A triangle has angles measuring 45°, 55°, and 80°. It is dilated by a scale factor of 2. What are the angle measures, in order from least to greatest, of the dilated image?
The angle measures, in order from least to greatest, of the dilated image 45°,55° and 80°.
A dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.
Euclidean space, In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula.
Dilations preserve angle measures, regardless of the scale factor. Therefore, the angle measures of the image will be the same of that of the pre-image, so our answer is still 45 °, 55 °, and 80 °.
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Answer:45,55,80
Step-by-step explanation: dilations preserve angles measures regardless of the scale factor. Therefore the angle measures of the image will be the same of that of the pre-image ,so our answer is still 4545,5555,8080 .
Combine like terms
x - 5 + 3x (to the second power) + 2 IM BEGGING PLEASE I NEED HELP
This is my last question then I’m all set
Answer:
. .......... ok............
a traffic study has shown that the probability that 55 cars will pass over a small bridge in a 4-4-minute period is 0.16.0.16. what are the odds against exactly 55 cars passing over the bridge in that time?
4:21 are the odds against exactly 55 cars passing over the bridge in that time.
What is Probability?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.Probability of 0.16, thus, for 100 trials, 16 successes and 84 failures, and the odd is:
16:84, which, simplifying by 4, is 4:21.
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5) If the sun is out, then it is daytime.
Converse:
Inverse:
Contrapositive:
the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
How to find the converse, inverse, and contrapositive statements?
If we have two propositions P and Q, then we have a conditional statement:
If P then Q.
The converse statement is: if Q then P
The inverse statement is: if Not P, then Not Q.
The contrapositive statement is: if Not Q, then Not P.
The conditional statement is:
"If the sun is out, then it is daytime"
So we have:
P = the sun is out.
Q = it is daytime.
Then the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
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sam is 6 years older than mia. mia is 3 years younger than alice. if sam is 19 years old, how old is alice?
a) 17
b) 16
c) 10
d)18
e) 15
Given m∠ADC= 118°, find m∠ADB.
118=11x-7+5x-3
118=16x-10
128=16x
8=x
11x-7=adb
88-7=adb
81 degrees
John runs the same number of kilometres each day.write an expression to represent the number of kilometre john ran in june last year
An algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
Given that, John runs the same number of kilometres each day.
We need to find an algebraic expression to represent the number of kilometres John ran in June month last year
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Let us assume that john is running 'a' kilometres per day.
We know that June month composed of total 30 days
So the algebraic expression for the number of kilometres John ran in June last year = Number of kilometres running per day × Number of days in the month of June
=a × 30=30a
Therefore, an algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
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One. Hundred deer were released into a wildlife preserve. The population of deer over a certain number of years is shown.
(Picture for table included)
The polynomial equation that models these data is P(x)=2x^4+46x^2+100
After how many years does the deer population decline to zero?
A. 4
B. 3
C. 6
D. 5
Answer:
5 years. Correct answer is D.
Step-by-step explanation:
The area of a rectangular carpet is given by the quadratic function A(x) = x(x + 30), where A(x) is the area and x is the width of the carpet in feet. What are the restrictions on the domain of the function and its inverse?
The inverse of the function is; f⁻¹(x) = - 15 ± √(x + 225)
What is the Inverse of the Function?We have been given a quadratic function f(x) = x(x + 30) and we need to restrict the domain such that it becomes a one to one function.
Now, the given function can also be written in vertex form as;
f(x) = (x + 15)² - 225
We know that vertex of this quadratic function occurs at (-15, -225).
Further, we know that range of this function is (-225, ∞).
If we restrict the domain of this function to either (-∞, -225) or (-225, ∞) , it will become one to one function.
Let us know find its inverse;
y = (x + 15)² - 225
Upon interchanging x and y, we get:
x = (y + 15)² - 225
Solving for y gives;
y = - 15 ± √(x + 225)
Thus, the inverse of the function is;
f⁻¹(x) = - 15 ± √(x + 225)
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Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one third times the quantity x plus 3 end quantity squared minus 3 question mark?
The graph of g(x) is narrower than f(x) and is shifted to the right 3 units and down 3 units.
The graph of g(x) is narrower than f(x) and is shifted to the left 3 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the right 3 units and down 3 units.
Answer: The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units.
Step-by-step explanation: I took the quiz and got it right
The function f(x) = x² is transformed and became g(x) = 3(x+2)² -1 has the graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 unit.
What are graph transformations ?By applying suitable graph transformation we can shift, stretch, shrink, a given graph along x and y axis.
According to the given question given a graph f(x) = x² and g(x) is 3(x+3)² - 3.
Let us break transformations of g(x) one by one.
g(x) = 3f(x) which implies it's amplitude or vertical stretch is increased by a factor of 3.
Now, g(x) = 3(x+3)² implies the graph is shifted towards left by 3 units as x + 3 = 0 is x = -3.
Now, g(x) = 3(x+3)² - 3 implies that the whole graph has been shifted 3 units down along the y axis.
Hence the graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units.
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-3x+29=17 would it be 3 , 4 5 6 7 8 9
Answer:
x=4
Step-by-step explanation:
[tex]-3x+29-29=17-29 < - Subtract[/tex]
[tex]-3x=-12[/tex]
[tex]\frac{-3x}{-3}=\frac{-12}{-3} < - Divide[/tex]
[tex]x=4[/tex]
Dan and David are marking exam papers. Each set takes Dan 35 minutes and David 1 hour. Express the times Dan and David take as a ratio.
Give your answer in its simplest form
Answer:
35:1
Step-by-step explanation:
Answer:
7 : 12
Step-by-step explanation:
the times must be of the same measure.
1 hour = 60 minutes , then
Dan : David = 35 : 60 = 7 : 12 ← in simplest form
The product of 5 and a number minus 7 is 23
Answer:
6
Step-by-step explanation:
5*6 is 30 - 7 is 23
work backwards
im stuck on 5 ÷ 3/4 =
Silvio wants to find the perimeter of quadrilateral abcd. he begins by computing the length of side ab using the distance formula. finish silvio’s work to find the length of side ab. what is the perimeter of quadrilateral abcd? 15 units 17 units 18 units 20 units
Silvio wants to find the perimeter of quadrilateral abcd. he begins by computing the length of side ab using the distance formula. finish silvio’s work to find the length of side ab. The perimeter of quadrilateral abcd is 20 units.
What is a perimeter?The total length of a shape's boundary is referred to in geometry as the perimeter of the shape. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
A regular polygon's perimeter is equal to the product of all of its sides, which is equal to the number of sides times the length of a side.
We use the general method to get the perimeter of an irregular shape since the sides of an irregular polygon might not all be the same length.
Therefore, the irregular polygon's perimeter equals the total of its sides.
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Ms. Jordan bought a box of 32 granola bars. Every day each of her three children ate one granola bar for lunch. Now there are only 11 bars left. Which equation can be used to find the number of days, n, that the children ate the bars for lunch? 32 = -11 32 = 3n - 11 32 = +11 O 32 3n+ 11
The calculation for calculating the number of days the youngsters ate the bars for lunch is 11 = 32 - 3x.
What exactly does it mean to "solve an equation"?An equation is a mathematical expression that represents the equivalence of two or more mathematical expressions.
When someone asks you to solve an equation, they typically want to determine the unknown values for which the equation is true (the equality between expressions should hold true for those values).
An equation's solutions are the values of the variables involved in the equation for which the equation holds true.
Given that Ms Jordan purchases a box of 32 granola bars every day, each of her three children consumes one granola bar for lunch, there are only 11 bars remaining.
The algorithm for calculating the number of days the youngsters ate the bars for lunch;
11 = 32 - 3x
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Your answer should be a polynomial in standard form.
(x-2)(x-1)
Answer: (x-2)(x-1)=x²-3x+2
Step-by-step explanation:
[tex](x-2)(x-1)=\\(x-2)x-1(x-2)=\\x^2-2x-x+2=\\x^2-3x+2=0[/tex]
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