The domain of the given situation is 0≤t≤10.
Explain domainThe elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain. If a function f: A B exists that maps each element of A to an element of B, then A is the domain, and B is the co-domain. When (a, b) ∈ R, the image of element 'a' under the relation R is supplied by 'b'.
Given, the average hiking rate is 3 miles per hour.
The number of hours you plan hiking for is 10 hours.
Now, as we know that time can't be negative so we know that the domain must have t≥0.
And it is given that you plan to hike for 10 hours so the domain must also have t≤10.
Therefore, the domain of the given situation is 0≤t≤10.
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What is the distance between A and B? Round your answer to the nearest tenth. (4 points) A coordinate plane is shown. Point A is located at negative 1, 5, and point B is located at 4, 1. A line segment connects the two points. ?
The distance between the 2 points A(-1, 5) and B(4, 1) is √41.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.So, the diatence between A(-1, 5) and B(4, 1):
Formula: d=√((x2 – x1)² + (y2 – y1)²Now, calculate as follows:
d=√((x2 – x1)² + (y2 – y1)²d=√((4 – (-1))² + (1 – 5)²d=√(5)² + (-4)²d=√25 + 16d=√41Therefore, the distance between the 2 points A(-1, 5) and B(4, 1) is √41.
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in your own words state the segment addition postulate.
see the attached figure
the points A, B and C are collinear (the three points lies on the same line)
so
AC=AB+BC ------> by addition segment postulate
the total length is equal to the sum of its parts
X'Y'Z' is the image of XYZ under a dilation through point C. XZ=30 and X'Z'=10
What scale factor was used in the dilation?
The scale factor that was used in the dilation is 3
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, say, 2.
The image of XYZ after dilation through point C is X'Y'Z. X'Z' = 10 and XZ = 30
For Calculating the scale factor, er divide XZ and X'Z'
So, we have :
[tex]\frac{XY}{X'Y'} =\frac{30}{10} =3[/tex]
Hence, the scale factor that was used in the dilation is 3.
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Suppose chang places $7000 and an account that pays 2% interest compounded each year. Assume that no withdraws are made from the account.Follow the instructions below. Do not do any rounding
In general, the compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ n\rightarrow\text{ number of times the interest is applied per period of time \lparen t\rparen} \\ t\rightarrow\text{ years} \end{gathered}[/tex]In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,
[tex]A=7000(1+\frac{0.02}{1})^{1*t}=7000(1.02)^t[/tex]a) Set t=1
[tex]\begin{gathered} t=1 \\ \Rightarrow A(1)=7000(1.02)^t=7140 \\ \end{gathered}[/tex]The answer to part a) is 7140b) Set t=2,
[tex]A(2)=7000(1.02)^2=7282.8[/tex]The answer to part b) is 7282.8Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.
Geo wants to buy a new home. The sales price is 185000. He has prequalified for a loan at 5.4% interest over 30 years with a 5% down payment and closing cost of 3% of the sales price. How much are the closing costs?
Answer:
$5,550.
Explanation:
The sales price = $185,000
The closing cost = 3% of the sales price.
Thus:
[tex]\begin{gathered} \text{Closing Price=3\% of }$\$185,000$ \\ =\frac{3}{100}\times185,000 \\ =0.03\times185,000 \\ =\$5,550 \end{gathered}[/tex]The closing cost is $5,550.
4 g = 16 g= please solve
To solve for g in the expression 4g=16, we need to follow these steps:
[tex]\begin{gathered} 4g=16 \\ \frac{4}{4}\times g=\frac{16}{4} \\ g=\frac{16}{4}=4 \end{gathered}[/tex]Given the function () = log2( + 4) − 2 :a. On a sheet of graph paper, use transformations to graph the function. Show theasymptote on your graph using a dashed or dotted line and write its equation.b. State the domain and range of this function.c. Algebraically calculate the x-intercept of the graph of this function.
Answer:
a)
b)
[tex]Domain:(-4,\infty)[/tex][tex]Range:(-\infty,\infty)[/tex]
c) x-intercept is 0
Explanation:
Given:
[tex]f(x)=\log_2(x+4)-2[/tex]a) See below the graph of different transformations of the given function;
The equation of the vertical asymptote as shown on the graph is x = -4
b) The domain of a function is the set of possible input values for which the function is defined. The domain of a graph is the set of possible values from left to right.
Looking at the given graph, we can see that the domain of the function is;
[tex]Domain:(-4,\infty)[/tex]The range of a graph is the set of values from the bottom to the top of the graph. Looking at the graph, we can see that the range is;
[tex]Range:(-\infty,\infty)[/tex]c) We'll follow the below steps to determine the x-intercept of the function;
Step 1: Substitute f(x) with 0;
[tex]0=\log_2(x+4)-2[/tex]Step 2: Add 2 to both sides;
[tex]\begin{gathered} 0+2=\log_2(x+4)-2+2 \\ 2=\log_2(x+4) \end{gathered}[/tex]Step 3: Apply the below rule;
[tex]\begin{gathered} \log_ab=c \\ b=a^c \end{gathered}[/tex][tex]\begin{gathered} 2^2=x+4 \\ 4=x+4 \\ 4-4=x \\ 0=x \\ \therefore x=0 \end{gathered}[/tex]So the x-intercept is 0
Graph the equation on the coordinate plane. y=12x−3
In order to draw a straight line on a graph at least two points are needed.
The graph for the given straight line is shown in the diagram.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The given equation is as below,
y = 12x − 3
Substitute x = 0 in the above equation to get,
y = 12 × 0 - 3
=> y = -3.
Substitute y = 0 in the above equation to get,
0 = 12x - 3
=> x = 3 / 12
=> x = 1 / 4
Now, draw a line through these two points on the coordinate plane to get the graph of y = 12x − 3.
The graph of y = 12x − 3 is given in the following diagram.
Hence, the graph of the given equation is drawn by finding the intercepts.
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Figure 1 and Figure 2 below are congruent. Which angle corresponds to angle L?
Answer:
angle E
Step-by-step explanation:
Have 109% in geometry
PLEASE HELP NEED THIS NOW DUE IN AN HOUR!!
Write and simplify an expression to represent the perimeter of the triangle shown. What is the perimeter of the triangle if y equals 3 feet?
(Please show work)
The perimeter of the triangle is 31 feet when the value if y is 3 feet.
Perimeter of the triangle:
Perimeter of the triangle is obtained by the total distance around the edges of a triangle.
The standard form for the perimeter of the triangle is
P = a + b + c.
where
a, b and c refers the edges of the triangle.
Given,
Here we have the triangle with the side values are (y + 5) feet, (3y + 5) feet, and (4y - 3) feet.
Then we have to find the perimeter of the triangle when the value of y is 3 feet.
We know formula of the perimeter of triangle, so first we have to calculate the side values of it, by apply the value of y as 3,
Apply the value of y as 3 feet then we get the value of the edges are
=> y + 5 => 3 + 5 = 8 feet
=> 3y + 5 => 3(3) + 5 = 14 feet
=> 4y - 3 => 4(3) - 3 = 9 feet.
Therefore, the edges of the triangle are 9ft, 14 ft and 9 ft.
Now, we have to apply the values on the formula of the perimeter of the triangle is, then we get
=> P = 8 + 14 + 9
Then the value of P = 31
Therefore, the value of the perimeter of the triangle is 31 feet.
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carmen wants to estimate the percentage of people who lease a car. she surveys 250 individuals and finds that 105 lease a car. find the margin of error for the confidence interval for the population proportion with a 95% confidence level. z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576. Use the table of common z-scores above, around the final answer of threee decimal place
Answer: 0.049
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.061
Pls, answer in a minute. PLS
Answer: No, It is not a right-angled triangle.
Step-by-step explanation:
Find the length of the last side first. To do this, add AB and BC together, then deduct that sum from the 22 cm circumference of Triangle ABC.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
22cm - 13cm = 9cm
Since the hypotenuse of a triangle is always its longest side, we can be certain that the side we identified is the hypotenuse. The Pythagorean Theorem can now be used to determine whether the triangle is a right triangle.
Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse. The triangle is a right triangle if a2 + b2 do equal c2.
8² + 5² = 9²
64 + 25 = 81
89 > 81
The triangle is not a right triangle, but since a and b are longer than c, we can conclude that it is obtuse.
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what type of function is this? (quadratic or exponential)
Answer:
exponential
Step-by-step explanation:
a builder wishes to fence in 60,000 m2 of land in a rectangular shape. because of security reasons, the fence along the front part of the land will cost $2 per meter, while the fence along the other three sides will cost $1 per meter. how much of each type of fence will the builder have to buy in order to minimize the cost of the fence? what is the minimum cost?
To minimize the cost, the builder should but 200 meters of fence costs at $2 per meter and 800 meters of fence costs at $1 per meter. The minimum cost is $1,200.
Recall that if we have a function f(x), then at the extremum point, its derivative is equal to zero.
f ' (x) = 0
In the given problem, let:
p = length of the rectangle
q = width of the rectangle
Then,
p x q = 60,000 or q = 60,000/p
Assume that the front side is p, then the function that describe the cost is:
f(p,q) = 2xp + 1 x (p + q + q)
f(p,q) = 3p + 2q
f(p) = 3p + 2 x 60,000/p
f(p) = 3p + 120,000/p
Take the derivative:
f '(p) = 3 - 120,000/p² = 0
p² = 40,000
p = 200 meters
Substitute p = 200 to get q,
q = 60,000/200 = 300
Hence, the type of fences the builder have to buy to minimize the cost is:
200 meters fence with cost $2 per meter and 200+300+300= 800 meters fence with cost $1 per meter.
The minimum cost is:
f(p) = 3p + 120,000/p
f(min) = f(200) = 3x200 + 120,000/200 = $1,200
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Stella is a salesperson who sells computers at an electronics store. She makes a base pay amount each day and then is paid a commission as a percentage of the total dollar amount the company makes from her sales that day. Let P represent Stella's total pay on a day on which she sells x dollars worth of computers. A graph of P is shown below. Write an equation for P then state the y-intercept of the graph and determine its interpretation in the context of the problem.
step 1
Find the slope of the line
the slope is giving by the formula
m=(y2-y1)/(x2-x1)
we need two points
From the graph we take the points
(0,80) and (4000, 140)
substitute
m=(140-80)/(4000-0)
m=60/4000
m=6/400
m=3/200
m=0.015
step 2
Find the equation of the line in slope intercept form
P=mx+b
we have
m=0.015
b=80
therefore
P=0.015x+80
Remember that the y-intercept is the value of y when the value of x is zero
In this problem
the y-intercept represent a base pay amount each day
so
$80
2. Which equation is y=-3x²-12x - 2 rewritten in vertex form?
Oy=-3(x + 2)² +10 .
Oy=-3(x - 2)² +10
Oy=-3(x + 2)² - 14
Oy=-3(x - 2)²-2
Answer:
the first : y = -3(x + 2)² + 10
Step-by-step explanation:
let's do the operations :
-3(x + 2)² + 10 = -3(x² + 4x + 4) + 10 = -3x² - 12x - 12 + 10 =
= -3x² - 12x - 2
and that's exactly the original expression.
Ryan is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $7.40 per hour. How many hours did he work at each job the week that he made $150.80.
We could write the following equations according to the problem:
Hours equation:
[tex]a+b=22[/tex]And, the payment equation: (cents)
[tex]620a+740b=1508[/tex]We could solve this system of equations using the elimination method:
[tex]\begin{cases}a+b=22 \\ 620a+740b=1508\end{cases}[/tex]We're going to multiply the first equation by -620:
[tex]\begin{cases}-620a-620b=-13640 \\ 620a+740b=15080\end{cases}[/tex]Now, we're going to sum both equations eliminating variable a, so we get a linear equation in terms of b:
[tex]\begin{gathered} 120b=1440 \\ b=12 \end{gathered}[/tex]Now we know that he did 12 hours at job b.
As he worked 22 hours in total, then he worked 10 hours at job a.
Answer:
Step-by-step explanation:
a+b = 22 -- equation 1
6.20a + 7.40b = 150.80 replacing decimals
620a + 740b = 15080 --- equation 2
From eq. 1 a = (22 - b)
putting a's value in equation 2
620(22 - b) + 740b = 15080
13640 - 620b + 740b = 15080
120b = 15080 - 13640
b = 1440/120 = 12
From equation 1 a + 12 = 22
a = 10
Verify your answer by equation 2 putting the value of a and b
620*10 + 740*12 = 15080
If G¹(x) is the inverse of G(x), what is the value of G¹(G(x))?
Ο A. x
OB. x¹
O C. 1
OD. O
SUBMIT
The value of G⁻¹(G(x)) is x , So the correct answer among the following options is A) x
What is function?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.
What is inverse function?An inverse function, sometimes known as an antI function, is a function that can change into another function. In other words, if any function "f" takes x → y, then the inverse of that function will take y to x. The inverse of a function denoted by "f" or "F" is denoted by "f-1" or "F-1." Not to be mistaken with an exponent or a reciprocal in this case is (-1).
Given, function G(x)
inverse of the given function G⁻¹(x)
Let G(x) = x
Then G⁻¹(x) = x
So value of G⁻¹(G(x)) is,
Put G(x) = x,
Hence, G⁻¹(G(x)) = x
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Hello,Can you help me with the following: Evaluate the give binomial coefficientQuestion # 63
(63)
From the question, we are to evaluate the given binomial coefficient.
(90)
( 2 )
Using the formula:
(n) = n! = n! = 1
(0) 0!(n - 0)! 1 * n!
inputting into the formula
90C2 = 90!
2!(90-2)!
90C2 = 90!
2!(88)!
90C2 = 14857159644817614973095227336
2 * 18548264225739843911479684564
90C2 = 14857159644817614973095227336
3709652845179687822959369129
90C2 = 4005
4. Is 4(2x - 3) < 8(x + 1) always, sometimes, or never true?
The given inequality is always true for all real numbers.
Given, the inequality is :
4(2x - 3) < 8(x + 1)
Reduce the greatest common factor for both of the sides of the inequality:
2x - 3 < 2(x+1)
Apply Multiplicative distribution law:
2x - 3 < 2x + 3
Rearrange unknown terms to the left of the side of the equation:
2x - 2 < 2 + 3
Combine the like terms:
0 < 2+3
Calculate the sum or the difference.
0 < 5
The solution of the inequality is always true.
Hence we get the solution as the inequality being true to all real numbers.
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mr. x teaches freshman english, and mrs. x teaches freshman history. they hosted a party at their home for members of their classes and their dates. twenty-three of the students were in mr. x's class, 31 were in mrs. x's class, 9 were in both mr. and mrs. x's classes, and 18 other students were in neither class. how many students were at the party?
twenty-three of the students were in mr. x's class, 31 were in mrs. x's class, 9 were in both mr. and mrs. x's classes, and 18 other students were in neither class. then there are 63 students in the party
twenty-three of the students were in mr. x's class,
31 were in mrs. x's class,
9 were in both mr. and mrs. x's classes,
and 18 other students were in neither class.
therefore 23+31 - 9 =45
and 18 were other students
hence it becomes 45+18= 63 students were in the party
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Susie makes bracelets to sell at a local craft fair. At each craft fair, she sells 16 more bracelets than the last time. At her first craft fair, she sold 82 bracelets. At her second craft fair, she sold 98 bracelets. At her third craft fair, she sold 114 bracelets. If this pattern continues, how many bracelets will she sell at her sixth craft fair? 120 bracelets 130 bracelets 146 bracelets 162 bracelets
Answer:
162 bracelets
Step-by-step explanation:
1st - 82 bracelets
2nd - 98
3rd - 114
4th - 130
5th - 146
6th - 162
“One subtracted
from the
product of 4 and
a number is 1 1”
how would i write it??
if I had matrix [1 2 0 -1 -3 2 ; 0 0 1 3 -3 1; 0 0 0 1 -1/6 1/2; 0 0 0 0 1 3/11; 0 0 0 0 0 0]. i need to find the general solution of the systemI was given a system of linear equations and told to put it in reduced row echelon form and then find the general solution of the system. I'm not sure how to write each x1 = , x2=
With the given matrix, the system of equations you have is:
[tex]\begin{gathered} x_1+2x_2-x_4-3x_5=2 \\ x_3+3x_4-3x_5=1 \\ x_4-\frac{1}{6}x_5=\frac{1}{2} \\ x_5=\frac{3}{11} \end{gathered}[/tex]Then, you already know x5=3/11.
Now replace these value in the equation above and solve for x4:
[tex]\begin{gathered} x_4-\frac{1}{6}\cdot\frac{3}{11}=\frac{1}{2}^{} \\ x_4-\frac{3}{66}=\frac{1}{2} \\ x_4-\frac{1}{22}=\frac{1}{2} \\ x_4=\frac{1}{2}+\frac{1}{22} \\ x_4=\frac{22+2}{44}=\frac{24}{44} \\ x_4=\frac{6}{11} \end{gathered}[/tex]Now, replace x4 and x5 into the next above equation:
[tex]\begin{gathered} x_3+3\cdot\frac{6}{11}-3\cdot\frac{3}{11}=1 \\ x_3+\frac{18}{11}-\frac{9}{11}=1 \\ x_3+\frac{9}{11}=1 \\ x_3=1-\frac{9}{11}=\frac{11-9}{11} \\ x_3=\frac{2}{11} \end{gathered}[/tex]find slope and y-intercept of 2x+3y=12
Answer:
Slope = -2/3
y-intercept= (0,4)
Step-by-step explanation:
Hope this helps!!!
Answer:
slope= - 2/3
y-intercept = 4
Step-by-step explanation:
convert to y=mx+b where m = slope and b= y-intercept
2x+3y=12
3y= -2x+12
y = -2/3x+4
slope= - 2/3
y-intercept = 4
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PLEASE HELP QUICK 25 POINTS
Solve the following system of equations algebraically:
y = x² - 14x + 23
y=-3x + 5
Answer:
x=9, x=2
Step-by-step explanation:
Since both expressions (x^2 - 14x + 23 and -3x+5) are equal to y, set those expressions equal to each other and solve for x.
x^2 - 14x + 23 = -3x + 5
subtract 5 from both sides
x^2 - 14x + 23 - 5 = -3x + 5 - 5
x^2 - 14x + 18 = -3x
add 3x to both sides
x^2 - 14x + 3x + 18 = -3x + 3x
x^2 - 11x + 18 = 0x
factor.
(x-9)(x-2) = 0
Because the product of these two things equals 0, we know that one of these terms must equal to zero.
x-9 = 0 or x-2 = 0
it can be either, so solve for both.
x-9 + 9 = 0 + 9 or x-2 + 2 = 0 + 2
x = 9 or x=2
PLEASE HELP ME OUT 12x^2+4x-1
Answer:
(6x-1)(2x+1)
Step-by-step explanation:
12x²+4x-1 (find two numbers that when you add or subtract them the ANS will be the coefficient of x and those same numbers when you multiply them the ANS will be the product of 12 and -1) then replace the middle term with those numbers.
12x²+6x-2x-1
(12x²+6x)(-2x-1)
6x(2x+1)-1(2x+1)
(6x-1)(2x+1)
what is the median of 6 5 9 9 6 7 and 6
Answer:
6
Explanation:
To know the median, we first need to organize the data from least to greatest, so:
5 6 6 6 7 9 9
Then, the median will be the value that is in the middle, so:
5 6 6 6 7 9 9
Therefore, the median is 6 because there are 3 values to the left of 6 and 3 values to the right of 6.
help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
The ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds.
What is quadratic equation?A second-order polynomial equation in one variable with the notation x = ax2 + bx + c = 0 and a 0 is known as a quadratic equation. It is a second-order polynomial problem, which guarantees that it has at least one solution according to the fundamental theorem of algebra.
Calculations = 213 solve for t
213 = -16t² + 128t
in standard form
16t² - 128t + 213 = 0
using shridharacharya formula
t = 2.4 , 5.6
so the ball will be 213ft above the ground after 2.4 secs and after 5.6 seconds
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Be Precise Of the number of sixth grade students at a middle school, 120 prefer online magazines over print magazines. Of the number of seventh grade students, 140 prefer online magazines. A student said that this means a greater percent of seventh grade students prefer online magazines than sixth grade students. Is the student correct? Choose the correct statement that uses precise mathematical language to explain. Multiple choice question. cross out A) no; A percent compares the part to the whole. In this case, the only known value is the part. To compare percents, the whole, the total number of sixth grade students and the total number of seventh grade students, must be known. cross out B) yes; A percent compares the part to the part. In this case, both parts are known. The number of sixth grade students who prefer online magazines, 120, can be compared to the number of seventh grade students who prefer online magazines, 140. So, a greater percent of seventh grade students prefer online magazines than sixth grade students. cross out C) no; A percent must always be less than 100. There are 120 sixth grade students who prefer online magazines and 140 seventh grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percents. cross out D) yes; A percent compares the part to the whole. In this case, the known values are 120, which is the part, and 140, which is the whole. Because 140 is greater than 120, a greater percent of seventh grade students prefer online magazines than sixth grade students. Need help with this question? Tools are not currently accessible ©2022 McGraw Hill. All Rights Reserved. Privacy CenterOpens in a new window Terms of UseOpens in a new window Minimum Requirements
No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
What is a percentage?It is a branch of Mathematics. It is a number or ratio expressed in the form of a fraction. A percentage can be denoted by the symbol %. It is a dimensionless number and it does not have any unit of measurement. The percentage is mainly used in shopping malls for giving discounts on clothes to customers. And the percent is used in salary increments in the company. The percentage is a very easy concept to learn by students or any other person. Percentage plays a key role in our daily life.
The number of students cannot be compared as percentages as the total number of students for both grades are not given.
So, the correct option is (c) No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
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