Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?
Slope (12,-18),(11,12)
The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.
Explanation:The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.
To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:
Slope (m) = (12 - (-18)) / (11 - 12).
This simplifies to Slope (m) = 30 / -1 = -30.
So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.
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One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered pair?
To find the value of a in the ordered pair (a,b), we can solve the given equations. Substituting ab^4 with 12 in the second equation, we get a^5 (12)^5 = 7776. Solving for a gives a = 0.03125^(1/5) = 0.5.
Explanation:To find the value of a in the ordered pair (a,b), we can solve the given equations.
From the first equation, ab^4 = 12, we can substitute ab^4 with 12 in the second equation:
a^5 b^5 = 7776
This gives us:
a^5 (12)^5 = 7776
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832
Dividing both sides of the equation by (12^5) gives:
a^5 = 7776 / (12^5) = 7776 / 248,832 = 0.03125
Taking the fifth root of both sides gives:
a = 0.03125^(1/5) = 0.5
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The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
Am I doing this right?
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
What can you say about the function that generated the following table of values
best answer is b = it has exactly 1 x intercept
Answer:
B.
Step-by-step explanation:
We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.
As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.
Therefore, this function will have only one x-intercept.
Hence, option A, C, D are discarded and option B is correct.
Braces are used in interval or roster notation?
What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?
-x+3+5(2x-6)+9(3x+11) will you answer with work shown and answer
The sum of two consecutive integers is 111. find the largest of these integers
divide 111 in half
111/2 = 55.5
take the whole number above and below 55.5
so you get 55 and 56
55 + 56 = 111
56 is the larger one
Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
Given the point (5, 6) and the slope of 5, find y when x = 21.
Solve each proportion. Show your work
solve for b, then find the value of b when a = 3.
4a=2b-7
a. -9/2
b. 5/2
c. 19/2
d. 17
Find the product of 543.1187 and 100
What is the slope of the line on the graph below?
A. -1/2
B. 1/2
C. 1
D. 2
Answer:
d on edge
Step-by-step explanation:
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
Answer:
$234.39
Step-by-step explanation:
identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0
Answer:
The answer is ellipse; 30° ⇒ answer (d)
What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Simplify the expression 3^5*6^-6/3^3*6^-4
A. 180
B. 5/2
C. 1/4
D. 3/20
Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?
How to convert decimal to binary by hand?
the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009
Answer:
The option A.) 2007 is correct
Step-by-step explanation:
The formula which is to be used is given :
[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]
where P(t) is the function of time t and t is the time in years after January 1 , 1980
Now, we need to find the year when the price will reach $4
So, substituting P(t) = 4 and finding the value of t from the given equation.
[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]
So, t = 27.49 which is approximately equals to 27.5 years
So, 27.5 years after January 1, 1980 is the year 2007
Hence, The price will reach $4 in the year 2007
Therefore, The option A.) 2007 is correct
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A= Pe^rt, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
Answer:
Rate of interest = 6%
Step-by-step explanation:
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.
Use the formula,
[tex]A=Pe^{rt}[/tex]
[tex]P\rightarrow \$2000[/tex]
[tex]r\rightarrow ?[/tex]
[tex]A\rightarrow \$2543[/tex]
[tex]t\rightarrow 4\text{ years}[/tex]
Substitute the value into formula and solve r
[tex]2543=2000e^{4r}[/tex]
[tex]e^{4r}=1.2715[/tex]
Apply ln both sides
[tex]4r\ln(e)=\ln(1.2715)[/tex]
[tex]r=0.06[/tex]
Rate of interest = 6%
Hence, The rate of interest is 6%
Write an equation for each translation of y=lxl
7 units up
Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
Hope This Helps!
Simplify 5(6x - (6 - 7y + 7x) + 6y)
-80x + 87y - 91
-5x + 65y - 30
-82x + 73y - 54
-60x + 9y - 17
None of the above
Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.
Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}
Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.
A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.
The relations given by the following sets of ordered pairs is a function is,
d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
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