[tex]\left\{\begin{array}{ccc}2x+7y=1\\2x-4y=12&\text{change the signs}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+7y=1\\-2x+4y=-12\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad11y=-11\qquad\text{divide both sides by 11}\\.\qquad\qquad \boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\2x+7(-1)=1\\2x-7=1\qquad\text{add 7 to both sides}\\2x=8\qquad\text{divide both sides by 2}\\\boxed{x=4}\\\\Answer:\ \boxed{x=4\ and\ y=-1\to(4,\ -1)}[/tex]
Katelyn did this work to solve an equation. Did she make an error?
4(x-2)-3=7x
4x-2-3=7x
Answer: The right answer is this:
Katelyn did make an error. She also needs to multiply 4 by −2.
4−8−3=7
Step-by-step explanation:
Answer:
Katelyn did make an error. She also needs to multiply 4 by −2.
4x−8−3=7x
Step-by-step explanation:
Which of the following sets represents the range of the function shown?
Answer:
{0, -1, 11, 13 }
Step-by-step explanation:
the range of the function are the corresponding values of y from the set of points, in ascending order, that is
{0, -1, 11, 13 }
Answer:
Step-by-step explanation:
The range is the set of y values of the function.
{0, -1, 11, 13]
How would I put equations like these in Standard Form?
4x-y-7=0
3x+9= (7/2)y
y=-4x+12
y=(-3/4)x+(5/4)
The standard form:
[tex]Ax+By=C[/tex]
[tex]4x-y-7=0\qquad\text{add 7 to both sides}\\\\\boxed{4x-y=7}[/tex]
[tex]3x+9=\dfrac{7}{2}y\qquad\text{multiply both sides by 2}\\\\6x+18=7y\qquad\text{subtract 18 and 7y from both sides}\\\\\boxed{6x-7y=-18}[/tex]
[tex]y=-4x+12\qquad\text{add 4x to both sides}\\\\\boxed{4x+y=12}[/tex]
[tex]y=-\dfrac{3}{4}x+\dfrac{5}{4}\qquad\text{multiply both sides by 4}\\\\4y=-3x+5\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=5}[/tex]
solve the inequality algebraically. express your answer using interval or set notation. graph the solution set. -5 less than or equal to 4 - 3x less than or equal to 2
Step-by-step explanation:
This ≤ inequality sign means:
Less than/Equal toNo more thanAt mostMaximum of-5 ≤ 4
And then:
-3x ≤ 2
OR:
-5 ≤ 4 -3x ≤ 2
Hi!!! Sorry, I didn't know if they were suppose to be together or separate, so I just did it both ways!!! :) Really sorry if I am wrong...
S is a geometric sequence. (Square root x-1),1 and (square root x+1) are the first three terms of s. Find the value of x.
Answer:
x = ± [tex]\sqrt{2}[/tex]
Step-by-step explanation:
given the 3 terms of a geometric sequence
[tex]\sqrt{x-1}[/tex], 1, [tex]\sqrt{x+1}[/tex], then the common ratio r
r = [tex]\frac{\sqrt{(x+1)} }{1}[/tex] = [tex]\frac{1}{\sqrt{(x-1)} }[/tex] ( cross- multiply )
[tex]\sqrt{(x+1)(x-1)}[/tex] = 1 ( square both sides )
(x + 1 )(x - 1 ) = 1 ← expand factors on left side )
x² - 1 = 1 ( add 1 to both sides )
x² = 2 ( take the square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
The value of x is ±[tex]\sqrt{2}[/tex].
What is a Geometric Sequence?It is a sequence, where the ratio of two consecutive terms in a sequence are constant.It is a finite or infinite sequence.Geometric Sequence G is given by: G = a, ar², ar³,..... (a = first term; r = constant ratio)Given:
Geometric Sequence with first three terms.
[tex]\sqrt{x-1},1, \sqrt{x+1[/tex]
We have to find the value of x.
Now, if the given sequence is geometric then we can find the common ratio of the sequence.
The common ratio is given by:
r = [tex]\frac{1}{\sqrt{x-1} }[/tex] and r = [tex]\frac{\sqrt{x+1} }{1}[/tex]
Now, we can equate the both the values of r to solve for the value of x.
[tex]\frac{\sqrt{x+1} }{1} = \frac{1}{\sqrt{x-1} }[/tex]
Now, multiplying the numerator on both sides by [tex]\sqrt{x-1}[/tex], we get:
[tex]\sqrt{x+1} \sqrt{x-1} =1[/tex]
[tex]\sqrt{(x-1)(x+1)}=1[/tex]
[tex]\sqrt{x^2-1} =1[/tex]
Now, squaring on both sides of the equation, we get:
⇒ x² - 1 = 1
⇒ x² = 2
Now, taking square root on both the sides, we get:
⇒ x = ±[tex]\sqrt{2}[/tex]
Therefore, for a given geometric sequence the value of x will be ±[tex]\sqrt{2}[/tex].
Learn more about the Geometric Sequence here: https://brainly.com/question/14565307
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Heidi's mom made flower arrangements for a party.She made 4 times as many rose arrangements as tulips arrangements.Heidi's mom made a total of 40 arrangements. How may arrangements of each type did Heidi's mom make?
Answer: 32 Rose Arrangements & 8 Tulip Arrangements
Step-by-step explanation: The number of arrangements for each flower is unknown (n) but the total is known, 40 arrangements. There are 4 times as many rose arrangements than tulip meaning 4n rose + n tulip = 40, 4n + n = 40, 5n = 40, 40 ÷ 5 = n, n = 8. Roses = 4n = 4x8= 32. Tulips = n = 8.
Which function is the best inverse of f(x)=x2-9
Answer:
The inverse is sqrt(x+9)
Step-by-step explanation:
f(x)=x^2-9
To find the inverse of the function, we interchange x and y and solve for y
y = x^2 -9
x = y^2 -9
Add 9 to each side
x+9 = y^2 -9+9
x+9 = y^2
Take the square root of each side
sqrt(x+9) = sqrt(y^2)
sqrt(x+9) = y
f^-1 (x) = sqrt(x+9)
Literal Equations
c-b/a=1
Equation for a
a= b/c - 1
Equation for b
b= ca - a
Equation for c
c= b/a + 1
20.8 is 32% of what number
[tex]\begin{array}{ccc}20.8&-&32\%\\x&-&100\%\end{array}\qquad\text{cross multiply}\\\\32x=(20.8)(100)\\\\32x=2080\qquad\text{divide both sides by 32}\\\\\boxed{x=65}[/tex]
Answer: 20.8 id 32% of 65.The number that 20.8 is 32% of is 65, achieved by setting up an equation representing 32% of a number equal to 20.8 and solving for that number.
Explanation:The question is asking you to find a number such that 32% of it equals 20.8. You represent this situation mathematically as '32/100 * X = 20.8', where 'X' is the number we need to find. Solving for 'X' gives us 'X = 20.8 ÷ (32/100)'. Performing this operation gives us 'X = 65'.
So, 20.8 is 32% of 65, which is the solution to the problem. The primary focus here is understanding percentages and how to solve these types of questions.
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You are 5 feet tall. What is your height in meters (m)?
Answer:
1.524
Step-by-step explanation:
Answer:
1.52 meters
Step-by-step explanation:
Today lan wants to run less than 7/12 mile.Write a fraction with a denominator of 4 to represent a distance that is less than 7/12 mile.
Answer:
the answer is 1/4 because 7/12 is larger than 1/2 but 1/4 is 2x smaller
Step-by-step explanation:
Each year, thousands of people visit Yellowstone national park. Audiotapes for visitors include interviews with early settlers and information about geology, wildlife, and activities of the park. The revenue r(x) from the sale of x tapes is r(x)=9.5x. Suppose that the function for the cost of manufacturing x tapes is c(x)=0.8x+1940.
What function could be used to find the profit on x tapes?
a. Write the profit function.
b.find the profit on 500, 1000, and 5000 tapes.
c. Check by finding the revenue and the cost for each number of tapes and subtracting to find profit
Answer: p(x) = 8.7x - 1940
p(500) = $2410
p(1000) = $6760
p(5000) = $41,560
Step-by-step explanation:
p(x) = r(x) - c(x)
= 9.5x - (0.8x + 1940)
= 9.5x - 0.8x - 1940
= 8.7x - 1940
**********************************************************************
p(500) = 8.7(500) - 1940
= 4350 - 1940
= 2410
p(1000) = 8.7(1000) - 1940
= 8700 - 1940
= 6760
p(5000) = 8.7(5000) - 1940
= 43,500 - 1940
= 41,560
***************************************************************************
p(500) = r(500) - c(500)
= 9.5(500) - [0.8(500) + 1940]
= 4750 - (400 + 1940)
= 4750 - 2340
= 2410
p(1000) = r(1000) - c(1000)
= 9.5(1000) - [0.8(1000) + 1940]
= 9500 - (800 + 1940)
= 9500 - 2740
= 6760
p(5000) = r(5000) - c(5000)
= 9.5(5000) - [0.8(5000) + 1940]
= 47500 - (4000 + 1940)
= 47500 - 5940
= 41,560
FAST!! the hcf of 2 numbers is 98 and there LCM is 2352..the sum of their numbers may be
Answer:
Step-by-step explanation:
I hope it will help you
Attachment
What is the surface area of a cone with a 6 in. diameter and a length (slant height) of 8 in.?
The formula of a surface area of a cone:
[tex]SA=pi rl+\pi r^2[/tex]
r - radius
l - slant height
We have the diameter d = 6 in and a slant height l = 8 in.
[tex]d=2r\to r=6in:2=3in[/tex]
Substitute:
[tex]SA=\pi(3)(8)+\pi(3^2)=24\pi+9\pi=\boxed{33\pi\ in^2}[/tex]
Using a calculator and the formula, calculate the APR. Choose the correct answer.Bob Businessman offers credit at 20% interest per year.
Answer:21.9
Step-by-step explanation:i just finished this question on a test and got it right hope this helps
solving multi step equations x+x+2=3(x+1)+12
Can someone please help me with this question? Thanks if you do!
A secant is a line that intersects a circle at two points.
Therefore your answer is
[tex]\boxed{D.\ \overline{AD}}[/tex]
OB - radius
DE - tangent
FC - chord
AB - some segment
sheral got theses socres on her spelling test
95,89,99,85,82
what is the mean of absolute devitationof her test scores
how to solve the algebraic expression 25=5/3(d+5/8)
Answer:
Alright well solve for d by cross multiplying
Exact form: d = 115/8
Decimal form: d = 14.375 Hope this helps have a nice day : )
Step-by-step explanation:
−4/1a−4= 4/7a−3 solve for a
Answer:
a = (-7)/32 or a= 0.21875
Step-by-step explanation:
Solve for a:
-4 a - 4 = (4 a)/7 - 3
Put each term in (4 a)/7 - 3 over the common denominator 7: (4 a)/7 - 3 = (4 a)/7 - 21/7:
-4 a - 4 = (4 a)/7 - 21/7
(4 a)/7 - 21/7 = (4 a - 21)/7:
-4 a - 4 = (4 a - 21)/7
Multiply both sides by 7:
7 (-4 a - 4) = (7 (4 a - 21))/7
(7 (4 a - 21))/7 = 7/7×(4 a - 21) = 4 a - 21:
7 (-4 a - 4) = 4 a - 21
Expand out terms of the left hand side:
-28 a - 28 = 4 a - 21
Subtract 4 a from both sides:
(-28 a - 4 a) - 28 = (4 a - 4 a) - 21
-28 a - 4 a = -32 a:
-32 a - 28 = (4 a - 4 a) - 21
4 a - 4 a = 0:
-32 a - 28 = -21
Add 28 to both sides:
(28 - 28) - 32 a = 28 - 21
28 - 28 = 0:
-32 a = 28 - 21
28 - 21 = 7:
-32 a = 7
Divide both sides of -32 a = 7 by -32:
(-32 a)/(-32) = 7/(-32)
(-32)/(-32) = 1:
a = 7/(-32)
Multiply numerator and denominator of 7/(-32) by -1:
Answer: a = (-7)/32
The solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].
To solve the equation [tex]\(\frac{-4}{1}a - 4 = \frac{4}{7}a - 3\) for \(a\)[/tex], follow these steps:
1. Simplify the equation by multiplying both sides by their respective denominators to eliminate the fractions:
[tex]\[ 7(-4a - 4) = 1(4a - 3) \][/tex]
2. Distribute the numbers outside the parentheses:
[tex]\[ -28a - 28 = 4a - 3 \][/tex]
3. Move all terms containing a to one side of the equation and constants to the other side:
[tex]\[ -28a - 4a = -3 + 28 \][/tex]
4. Combine like terms:
[tex]\[ -32a = 25 \][/tex]
5. Solve for a by dividing both sides by -32:
[tex]\[ a = \frac{25}{-32} \][/tex]
Therefore, the solution to the equation is [tex]\(a = -\frac{25}{32}\)[/tex].
Complete the statement about the tables below. Then, choose a rule for each. x y 0 5 1 7.5 2 11.25 This table represents a(n) relationship. Rule: x y 0 -6 1 12 2 30 This table represents a(n) relationship. Rule:
The first table represents an exponential relationship.
Rule: [tex]\(y = 5 \times 1.5^x\)[/tex]
The second table represents a linear relationship.
Rule: [tex]\(y = 6x - 6\)[/tex]
The first table represents an exponential relationship.
Rule: The rule for the first table can be expressed as [tex]\(y = 5 \times 1.5^x\)[/tex]. Each (y) value is obtained by multiplying the previous (y) value by 1.5.
The second table represents a linear relationship.
Rule: The rule for the second table can be expressed as [tex]\(y = 6x - 6\)[/tex]. Each (y) value is obtained by multiplying the corresponding (x) value by 6 and then subtracting 6.
Apex please help
a.)graph d
b.) graph b
c.) graph a
d.) graph c
Answer:
GRAPH D
Step-by-step explanation:
BECASUE IT IS THE WRIGHT ANSWER
express 4.08 as mixed number
Answer:
its 4 2/25 :P
Step-by-step explanation:
hi!!!
what is the image of the point (-6,2) after a 90 degree counterclockwise rotation
What is the value of y ?enter your answer in the box
Answer:
I believe the answer is 20.
Step-by-step explanation:
what is the standard deviation of the numbers 77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Answer:
The standard deviation of the numbers is 16.154.
Step-by-step explanation:
The given observations are
77,45,72,56,98,60,70,89,50,80,95,70,34,77,65,70,70,82,86,86
Average or mean of the data is
[tex]\bar{X}=\frac{\text{Sum of observations}}{\text{Total number of observations}}[/tex]
[tex]\bar{X}=\frac{1432}{20}=71.6[/tex]
The Standard deviation of the data is
[tex]\sigma=\sqrt{\frac{\sum (X-\bar{X})^2}{n}}[/tex]
[tex]\sigma=\sqrt{\frac{5218.8}{20}}[/tex]
[tex]\sigma=\sqrt{260.94}[/tex]
[tex]\sigma=\sqrt{16.154}[/tex]
Therefore standard deviation of the numbers is 16.154.
How do you solve this?
Answer:
Multiply 60 by .40
60 * .40 = 24
Answer is B
Step-by-step explanation:
So I don't if I'm right help would be much appreciated
Answer:
A is the correct equation
Step-by-step explanation:
Will mark brainliest! :D
Answer: 137 + 4(n-1)
Step-by-step explanation:
137 + 4(n-1)
Okay, let's test this starting with week 1:
137 + 4(1-1)
137 + 4*0
137, which is correct because she starts with 137.
Week 2:
137 + 4 (2-1)
137 + 4 * 1
137 + 4
141
Alright, let's see if it is correct if we do week 5:
137 + 4 (5-1)
137 + 4(4)
137 + 16
153
To know that 153 is right we could do 137 + 4 + 4 + 4 + 4, which equals 153.
jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is 1/15. The theoretical probability of rolling a 2 is 1/6 What could Jamie do to make his experimental results more closely match the theoretical probability?
Answer:
Answer is to increase trials
Step-by-step explanation:
Theoretical Probability is what it is expected to happen whereas Experimental Probability is what actually happens.
What Jamie should take into serious consideration is that Experimental probability gets gradually closer to theoretical probability as the number of trials increases.
In other words, Jamie needs to increase the number of trials in order to match experimental and theoretical probabilities every time more and more.
Answer: letter A
to increase the number of trials
Step-by-step explanation: