Answer:
13 and 14
Step-by-step explanation:
13+ (2*13) +6= 45 which is less than 50
14+ (2*14) +6= 48 which is also less than 50.
When you do the same with 15,16, and 17 the answers all come out to be 51, 54, and 57 which are all greater than 50
Answer:
13 and 14
Step-by-step explanation:
Given : [tex]x + 2x + 6 < 50[/tex]
To Find : From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are .
Solution:
Inequality : [tex]x + 2x + 6 < 50[/tex]
Substitute x = 13
[tex]13 + 2(13) + 6 < 50[/tex]
[tex]45 < 50[/tex]
Substitute x = 14
[tex]14 + 2(14) + 6 < 50[/tex]
[tex]48 < 50[/tex]
Substitute x = 15
[tex]15 + 2(15) + 6 < 50[/tex]
[tex]51 > 50[/tex]
Substitute x = 16
[tex]16+ 2(16) + 6 < 50[/tex]
[tex]54 > 50[/tex]
Substitute x = 17
[tex]17+ 2(17) + 6 < 50[/tex]
[tex]57 > 50[/tex]
So, the values of x for which the inequality holds true are 13 and 14.
Factor this expression x^2+9x+8
Answer:(x+1) (x+8)
Step-by-step explanation:
Answer:
(x + 8)(x + 1)
Step-by-step explanation:
Consider the factors of the constant term (+ 8) which sum to give the coefficient of the x- term (+ 9)
The factors are + 8 and + 1, since
8 × 1 = 8 and 9 + 1 = 9, hence
x² + 9x + 8 = (x + 8)(x + 1) ← in factored form
One human year is said to be about 7 dog years. Cliff's dog is 5.5 years old in
human years. Find his dog's age in dog years. Round to the nearest tenth.
Answer:
38.5
Step-by-step explanation:
7 times 5.5
She wants to create a rectangular area of 1,600 square feet for her pet and can afford to purchase 160 feet of fence. In two or more complete sentences, explain the algebraic model, calculations and reasoning necessary to determine the dimensions of the rectangular area.
Answer:
Step-by-step explanation:
"Rectangular" includes "square," and in fact treating the rectangle as a square is the fastest way to "solve" this problem. The perimeter of the rectangular area is 160 ft; dividing that by 4 yields 40 ft. "40 ft square" describes the rectangle maximum area: (40 ft)^2 = 1600 ft^2.
Alternatively, let W and L represent the width and length of the rectangle. Then:
P = perimeter = 2W + 2L = 160 ft, or W + L = 80 ft, or W = 80 ft - L.
A = area = L*W = L(80 ft - L) = 1600 ft^2. Rewriting this as a proper quadratic:
80L - L^2 - 1600 = 0, or L^2 - 80L + 1600. Note that this last result factors into (L - 40)^2 = 0, so L = 40 ft. Then W = 80 ft - 40 ft = 40 ft.
This confirms that the max area is 1600 ft^2 = (40 ft)^2.
Final answer:
To find Tina's dog's fenced area dimensions, use an algebraic model with area and perimeter equations to solve for the dimensions optimizing the given constraints.
Explanation:
To determine the dimensions of the rectangular area for Tina's dog:
Algebraic Model: Let the length of the rectangle be 'l' and the width be 'w'. The algebraic equation to represent the area and perimeter constraints is lw = 1600 and 2l + 2w = 160, respectively.Calculations: Using the constraint equations, you can solve for the dimensions. For example, you can write 'l = 80/w' from the perimeter equation, substitute it into the area equation, and solve to find the dimensions.Reasoning: By setting up and solving the system of equations, you can find the dimensions that maximize the area within the given perimeter, ensuring Tina's dog has the desired 1600 square feet while staying within the budget of 160 feet of fence.The data in the table represent the height of an object over
time.
Which model best represents the data?
Height of an Object
Time (seconds) Height (feet)
05
1
50
2
70
3
48
quadratic, because the height of the object increases or
decreases with a multiplicative rate of change
quadratic, because the height increases and then
decreases
exponential, because the height of the object increases
or decreases with a multiplicative rate of change
exponential, because the height increases and then
decreases
Answer:
The correct answer option is quadratic, because the height increases and then decreases.
Step-by-step explanation:
We are given the following data in the table which represents the height of an object over time:
Time (s) Height (ft)
0 5
1 50
2 70
3 48
We know that in situation where the values increase and then decreases, a quadratic model is used.
From the values given in the table, we can see that the values of height first increased and then decreased with the increase in time.
Therefore, the model used is quadratic, because the height increases and then decreases.
Answer:
BStep-by-step explanation:
Andrew Has six sweets Mary has X sweets and Jim has twice as many as Andrew. Together they have four times as many as Mary has. Form an equation and find how many sweets Marie has.
Answer:
(6 + 2(6))/4 = M
Step-by-step explanation:
because Andrew has 6 sweets and Jim has twice the treats so that means you have to multiply 3 by 6 and then u get 18 divide it by 4 since their total equals 4 times their total.
At what value of x do the graphs of the equations below intersect?
2x – y = 6
5x + 10y = –10
Answer:
Step-by-step explanation:
The intersection is the point where two equations meet. It is calculated by substituting terms into the equations involved. For the given systems of equation, calculations are as follows:
2x - y = 6
y = 2x - 6
We substitute the equation above to the second equation.
5x + 10y = –10
5x + 10( 2x - 6 )= –10
Simplifying,
5x + 20x - 60 = -10
25x = 50
x = 2
Therefore, the intersection has the value of x equal to 2.
Answer with Step-by-step explanation:
The point of intersection of the graphs of system of equation is the solution to the system of equations.
So, we need to find the solution of the system of equations:
2x – y = 6
5x + 10y = –10
Multiplying first equation by 10 and add it to second equation.
5x+10y+10(2x-y)= -10+60
5x+10y+20x-10y=50
25x=50
⇒ x=2
Hence, value of x where the graphs of the equations
2x – y = 6
5x + 10y = –10 intersect is:
x=2
each equation and the solution is 1 point for each. Round the solution to two decimal places. a. 4x – 5 = 16 b. 35 + 3x – 11 = 23
Answer:
a: 5.25 b: -0.33
Step-by-step explanation:
a:
4x - 5 = 16
isolate the variable. this is done by putting only the variable on the left side and the numbers on the right side. when moving the 5 to the right side, it is counted as a -5 because of the minus in front. when moving it, be sure to change from - to + and vice versa.
4x = 16 + 5
4x = 21
x = 21/4
x = 5.25
b:
same process
35 + 3x - 11 = 23
move the 35 to the right, changing it to a -35
3x - 11 = 23 - 35
move the -11
3x = 23 - 35 + 11
3x = -12 + 11
3x = -1
x = -1/3
x = -0.33
Hope I could help! If you have any trouble, tell me in the comments.
Answer:
a. [tex]x=5.25[/tex]
b. [tex]x=-0.33[/tex]
Step-by-step explanation:
You need to solve for the variable "x" in each equation. Then:
a. You need to add 5 to both sides of the equation:
[tex]4x - 5 +(5)= 16+(5)\\\\4x= 21[/tex]
Now you need to divide both sides of the equation by 4, getting:
[tex]\frac{4x}{4}=\frac{21}{4}\\\\x=5.25[/tex]
b. You need to subtract 35 from both sides of the equation:
[tex]35 + 3x - 11-(35)= 23-(35)\\\\3x-11=-12[/tex]
Add 11 to both sides:
[tex]3x-11+(11)=-12+(11)\\\\3x=-1[/tex]
Now you need to divide both sides of the equation by 3, getting:
[tex]\frac{3x}{3}=\frac{-1}{3}\\\\x=-0.33[/tex]
Which description can be written as the expression
N/4-13
Answer:
(A) Joel wants to find the quotient of a number and four, minus thirteen.
Step-by-step explanation:
The correct description that can be written as the expression [tex]\frac{n}{4}[/tex] - 13 is 'Joel wants to find the quotient of a number and four, minus thirteen'.
Mathematically, an expression is a combination of numbers, variables, operations, and functions that are combined according to specific rules to represent a mathematical computation or relationship. It can be thought of as a mathematical phrase or formula.
By combining numbers, variables, operators, and functions, mathematical expressions can represent a wide range of computations and relationships.
Expressions are fundamental in mathematics as they allow us to represent and manipulate mathematical concepts, solve equations, evaluate formulas, and analyze mathematical relationships. They are used in various areas of mathematics, including algebra, calculus, geometry, and more.
Hence, the expression [tex]\frac{n}{4}[/tex] - 13 can be written as 'Joel wants to find the quotient of a number and four, minus thirteen'.
Learn more about expression here:
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you buy a house for $130000. it appreciates 6% per year. how much is it worth in 10 years
growth or decay?
write a function that represents the situation:
initial amount=
growth/decay rate:
Final answer:
The future value of the house will be approximately $232,810.10 in 10 years, calculated by compounding the initial value of $130,000 at an annual growth rate of 6%.
Explanation:
To calculate the future value of a house appreciating at a certain rate, we can use the compound interest formula: [tex]Future\ Value = Present\ Value \* (1 + growth/decay rate)^{number of periods[/tex]
In this scenario, the house is appreciating, which means it's increasing in value over time.
We're given that the initial amount (Present Value) is $130,000 and the growth rate is 6% per year.
The function that represents the situation is:
Future Value = $130,000 × (1 + 0.06)¹⁰
To find the value of the house in 10 years, we simply plug in the values:
Future Value = $130,000 × (1 + 0.06)¹⁰
Future Value = $130,000 × (1.06)¹⁰
Future Value = $130,000 × 1.790847
Future Value = $232,810.10 approximately
Therefore, the house will be worth approximately $232,810.10 in 10 years, and this represents growth, not decay.
The factorial 4! is equal to _______.
This is about permutations btw.
Answer:
24
Step-by-step explanation:
factorial(4) = 4*3*2*1
factorial(4) = 24
Answer:
the answer is b
Step-by-step explanation:
solve the system of equation below by graphing them
y= 2x-3
y=-2x+5
Answer:
Step-by-step explanation:
The pulse rate (in bpm) of a random sample of 30 Peruvian Indians was collected. The mean pulse rate of the sample was 70.2 and the standard deviation was 10.51. Compute the 95% confidence interval for the population mean.
Answer:
= 70.2 ± 3.761 bpm
Step-by-step explanation:
The question is on calculating the confidence interval for a population mean
The general expression is
CI = x ± z * δ/√n where;
CI = confidence interval,
x = mean of sample,
δ = standard deviation,
n= is sample size
z = z* value from standard normal distribution according to confidence level given.
Given that;
n= 30 x =70.2 δ=10.51 z* for 95% CI = 1.96
Then applying the expression
CI = x ± z * δ/√n
[tex]=\sqrt{n} = \sqrt{30} =5.477\\\\=\frac{10.51}{5.477} =1.919*1.96=3.761\\\\[/tex]
Cl = 70.2±3.761
= 70.2 ± 3.761 bpm
Find the greatest common factor of 13c and 9c3.
Answer:
c
Step-by-step explanation:
The Greatest Common Factor [GCF] means the LEAST DEGREE TERM possible, plus finding a common factor, in this case, between 9 and 13, which is 1, but writing it is unnecessary.
I am joyous to assist you anytime.
The greatest common factor of 13c and 9c³ is "c".
To find the greatest common factor (GCF) of 13c and 9c³, we need to determine the largest term that divides evenly into both expressions.
First, let's break down each expression into its prime factors:
13c = 13 x c
9c³ = 3² x c³
Now, let's identify the common factors between the two expressions:
Common factors of 13c and 9c³: c
To find the GCF, we take the product of the common factors, considering the lowest exponent for each common factor:
GCF = c
Therefore, the greatest common factor of 13c and 9c³ is "c".
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what is the range of g need help fast
Range is all the y values included in the graph. Look at the image below for the y values:
As you can see the highest y value this graph reaches is 6 and the lowest is -5 therefore the range is...
-5 ≤ g(t) ≤ 6
Hope this helped!
~Just a girl in love with Shawn Mendes
2 Points
Which statement best describes the function below?
f(x) = 2x2 – 3x+1
O
A. It is a one-to-one function.
3. It fails the vertical line test.
O
c. It is a many-to-one function.
O
D. It is not a function.
Answer:
A
Step-by-step explanation:
f(x) = 2x^2 – 3x + 1 is a function (its graph is a parabola that opens up), and it is one-to-one (Answer A). For each input, x, this function will return one output.
There are 5 numbers on the spinner and you spin it twice. Find the probability that you spin a 3 and then a 4? Write your answer as a simplified fraction
Answer:
1/5 for both of them is your answer.
Step-by-step explanation:
Lets see so 5 numbers on a spinner and you want a 3 and a 4, so their is only one 3 and one 4 on a spinner so your fraction would be for both of them 1/5.
Hope my answer has helped you!
How is slope formula and point-slope formula related
Step-by-step explanation:
[tex]\text{The point-slope formula of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Determine the standard form of the equation of the line that passes through (-2,0) and (8,-5)
Answer:
x + 2y = - 2
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (8, - 5)
m = [tex]\frac{-5-0}{8+2}[/tex] = [tex]\frac{-5}{10}[/tex] = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] + c ← partial equation of line
To find c substitute either of the 2 points into the partial equation
Using (- 2, 0), then
0 = 1 + c ⇒ c = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← in slope- intercept form
Multiply through by 2
2y = - x - 2 ( add x to both sides )
x + 2y = - 2 ← in standard form
A pan for baking French bread is shaped like half a cylinder. It is 12 inches long and 3.5 inches in diameter. What is the volume of uncooked dough that would fill this pan?
Step-by-step explanation:
Answer:
Since we have the diameter, we need to divide it in half to get the radius of 1.75. You then square it to get 3.0625. Next, multiply this by the height (or length in this case) to get 36.75. you can either leave it in terms of pi or multiply 36.75 to get your final answer
Step-by-step explanation:
How many liters of 10% alcohol solution and 5% alcohol solution must be mixed to obtain 40 liters of 8%
alcohol solution?
Answer:
x+y=40liters
10%x+5%y=8%×40
(2x+y)/20=8%×40
(2x+y)=64
x=24
y=16
The geometric mean of 8 and 2 is
Answer:
4
Step-by-step explanation:
The geometric mean finds the typical value of a set of numbers through multiplication. To find the geometric mean of two numbers, you take the square root of the product of the two numbers.
So in this instance, multiply the two numbers together:
[tex]2*8=16[/tex]
And take the positive square root of the product:
[tex]\sqrt{16}=4[/tex]
The geometric mean is different than the commonly-used arithmetic mean, which finds the central value of a set of numbers by dividing the set's sum total by how many numbers are in the set.
Final answer:
The geometric mean of 8 and 2 is calculated as the square root of their product, which is 4.
Explanation:
To find the geometric mean of 8 and 2, we use the formula for geometric mean which is the square root of the product of the numbers. Therefore, the geometric mean of 8 and 2 is the square root of 8 multiplied by 2, which is √(8×2).
Let's calculate it step by step:
Multiply 8 by 2 to get 16.Find the square root of 16.The square root of 16 is 4.Hence, the geometric mean of 8 and 2 is 4.
Work out the total surface area of this hemisphere which has a radius of 8cm.
Give your answer to one decimal place
To calculate the total surface area of a hemisphere with a radius of 8 cm, we use the formula A = 3πr², resulting in a total surface area of approximately 602.9 cm² to one decimal place.
Explanation:The question asks us to work out the total surface area of a hemisphere with a radius of 8cm and provide the answer to one decimal place. The total surface area of a hemisphere is given by the formula A = 2πr² + πr², where π is approximately 3.14 and r is the radius of the hemisphere. The first part 2πr² represents the curved surface area, and the second part πr² represents the area of the circular base.
Substituting 8 cm for r:
A = 2π(8²) + π(8²) = 2π(64) + π(64) = 128π + 64π = 192π cm²
Converting π to 3.14:
A = 192(3.14) = 602.88 cm². Therefore, the total surface area of the hemisphere is approximately 602.9 cm² to one decimal place.
The total surface area of this hemisphere is approximately 603.2 cm².
Calculating the Total Surface Area of a Hemisphere
To find the total surface area of a hemisphere with a radius of 8 cm, we need to consider both the curved surface area and the base area.
Curved Surface Area: The formula for the curved surface area of a hemisphere is given by 2πr², where r is the radius. Substituting the given radius (8 cm), we get:
Curved Surface Area = 2π(8 cm)² = 2π(64 cm²) ≈ 2 × 3.1415927 × 64 = 402.1 cm² (rounded to one decimal place)
Base Area: The base of the hemisphere is a circle with the area given by the formula πr². Using the radius (8 cm), we get:
Base Area = π(8 cm)² = π(64 cm²) ≈ 3.1415927 × 64 = 201.1 cm² (rounded to one decimal place)
Total Surface Area: To find the total surface area, we sum the curved surface area and the base area:
Total Surface Area = 402.1 cm² + 201.1 cm² = 603.2 cm²
Therefore, the total surface area of the hemisphere is approximately 603.2 cm².
Which statement about these triangles is true?
The Dilation is an enlargement
Answer:
b
Step-by-step explanation:
What are the coordinates of W?
Answer:
(-b,c)
Step-by-step explanation:
The coordinates are going to be the same as (b,c), except it is on the other side of the y axis, making it negative on the x axis. B is the replacement for x in this case, so the first option is correct. Hope this helps :)
Answer:
The correct answer is first option
(-b, c)
Step-by-step explanation:
From the figure we can see that, a trapezium.
To find the coordinates of W
The coordinates (-a, 0) and (a, 0) are same distance from the O.
Similarly the coordinate W and (b, c) are same distance from the point Therefore the coordinates of W is (-b, c)
The correct answer is first option
Which equation can be used to represent “six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?
6 + 2(x + 4) = (3 – x)
6 + 2(x + 4) = (x – 3)
(6 + 2)(x + 4) = (3 – x)
(6 + 2)(x + 4) = (x – 3)
Answer:
a. 6 + 2(x + 4) = (3 – x)
Step-by-step explanation: just took the test
Which system of equations can be used to find the roots of the equation4x^5-12x^4+6x=5x^3-2x?
Answer:
y = 4x^5 - 12x^4 + 6x and
y = 5x^3 - 2x
Step-by-step explanation:
The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;
y = 4x^5 - 12x^4 + 6x and
y = 5x^3 - 2x
We simply formulate two equations by splitting the left and the right hand sides of the given equation.
The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.
The roots of the given equation will be given by the points where these two equations will intersect.
The graph of these two equations is as shown in the attachment below;
The roots are thus;
x = 0 and x = 0.813
Katie wants to buy some popcorn for her family at the theater. Each small tub of popcorn costs $3 and each large tub of popcorn costs $4. She needs to buy at least 7 tubs of popcorn, but she only has $24 in her wallet.
If the solution region represents the number of small and large tubs of popcorn that Katie can buy, determine which graph represents the solution set to the system of inequalities representing this situation.
Final answer:
The importance of graphs in representing solutions to systems of inequalities for purchasing decisions.
Explanation:
Katie's Situation:
Each small tub costs $3, and each large tub costs $4.
Katie needs to buy at least 7 tubs and has $24 in her wallet.
Graph Representation: The graph with the shaded region where the solution to the system of inequalities lies would show the combinations of small and large tubs Katie can buy within her budget.
Please help! What is x, 8 points!
Answer:
Step-by-step explanation:
Replace tan^2(x) with sin^2 (x ) / cos^2(x)
2 sec(x) sin^3(x) = cos(x) * sin^2(x) / cos^2(x) Cancel cos(x) with cos^2(x)
2 sec(x) sin^3(x) = sin^2(x) / cos(x) Multiply by cos(x) both sides
2 sec(x)*cos(x)*sin^3(x) = sin^2(x) Divide sin^2(x) both sides
Note sec(x) and cos(x) will cancel when multiplied. giving you one
2 sin^3(x) / sin^2(x) = sin^2(x) / sin^2(x) Do the division
2 sin(x) = 1 Divide by 2
sin(x) = 1/2
x = sin-1(1/2)
x = 30 degrees or 150 degrees.
So the answers are pi/6 and 5/6 pi
PLZ HELP QUICKLY! ON A TIMER! What is the answer in the attached image?
Answer
Given
the relative frequency tables in the figure below (Note: the tables are not in the same order as in the problem statement)
Find
which table is best suited to answer the question
A) the percentage of home viewers who prefer to watch horror movies
B) the percentage of people surveyed who prefer to watch comedy movies at home
C) the percentage of viewers with a preference for drama who watch at the theater
Solution
The figure shows the best choices for answering A, B, and C.
table 2 is best for A (it is normalized by viewing location)
table 3 is best for B (it is normalized over the whole sample)
table 1 is best for C (it is normalized by genre)
Which of the following describes how to translate the graph y = lxl to obtain the graph of y = lx - 6l?
shift 6 units up
shift 6 units down
shift 6 units left
shift 6 units right
Answer:
To answer your question the graph will go 6 units to the right because the absolute value bar means the "-6" will become +6 so therefore 6 units right.
the pictures show the y=|x| & the y=|x-6|
Answer:
shift 6 units up
Step-by-step explanation:
When you are moving the graph from the center, you only have to put a 0 to the X and in that way you can know where is it going to be located
So it will end up like this:
y = lx - 6l= l0 - 6l= 6
So since its the absolute value, and in this case you have to move the graph upwards to the (0,6)