Answer:
y = 5 - x → standard form y = -x + 5
y = 2x + 1
A: If two sides of an equation are set equal to each other, their value is a point of intersection because they will both equal a certain value.
B:
3 → 5 - 3 = 2(3) + 1 → 2 = 6 + 1 → 2 ≠ 7
2 → 5 - 2 = 2(2) + 1 → 3 = 4 + 1 → 3 ≠ 5
1 → 5 - 1 = 2(1) + 1 → 4 = 2 + 1 → 4 ≠ 3
0 → 5 - 0 = 2(0) + 1 → 5 = 0 + 1 → 5 ≠ 1
-1 → 5 - (-1) = 2(-1) + 1 → 6 = -2 + 1 → 6 ≠ -1
-2 → 5 - (-2) = 2(-2) + 1 → 7 = -4 + 1 → 7 ≠ -3
-3 → 5 - (-3) = 2(-3) + 1 → 8 = -6 + 1 → 8 ≠ -5
algebraically ↓
-x + 5 = 2x + 1 → 4 = 3x → x = 4/3
C: graphically
graph both equations and find point of intersection
We know these points are the solutions to \(5-x=2x+1\) because by setting the two equations equal to each other, we find where they intersect, and those points are the solutions to the equation.
Part B\(\begin{array}{|c|c|c|c|}\cline{1-4}\bf x&\bf5-x&\bf2x+1&\bf5-x=2x+1\\\cline{1-4}-3&8&-5&8\neq-5\\\cline{1-4}-2&7&-3&7\neq-3\\\cline{1-4}-1&6&-1&6\neq-1\\\cline{1-4}0&5&1&0\neq1\\\cline{1-4}1&4&3&4\neq3\\\cline{1-4}2&3&5&3\neq5\\\cline{1-4}3&2&7&2\neq7\\\cline{1-4}\end{array}\)
Part B and a halfSince none of those values are correct solutions, let's solve this equation algebraically, even though the question doesn't ask for us to do so.
\(\begin{aligned}5-x&=2x+1\\-x&=2x+1-5\\-x-2x&=1-5\\-3x&=-4\\x&=\boxed{\frac{4}{3}}\end{aligned}\)
Part CWe can solve the equation graphically by graphing both \(y=5-x\) and \(y=2x+1\), then finding where they meet. This is shown in the attachment below.
Order the decimal numbers from the smallest to the largest.
A) 0.1 0.4 0.2 0.3 0.8 0.6
B) 0.79 0.54 0.23 0.01 0.09 0.85
C) 1.86 1.93 2.45 1.13 5.85 3.67
A: 0.1, 0.2, 0.3, 0.4, 0.6, 0.8
B: 0.01, 0.09, 0.23, 0.54, 0.79, 0.85
C: 1.13, 1.86, 1.93, 2.45, 3.67, 5.85
john sort his 200 buttons into 4 groups.Each group has the same numbers of buttons .He gives the buttons in one group to Markie.Which equation can be used to find n,the number of buttons that john has now.n÷4=200. or 200-50=n or 200÷4=n or n-50=200
Answer:
200-50+n
Step-by-step explanation:
Determine whether the table represents a linear or nonlinear function
Answer:
nonlinear, as it isnt consistent may be wrong
Step-by-step explanation:
Answer:
It is a function, but it is nonlinear
Step-by-step explanation:
Every input is compared with exactly one output.
Order the set of integers from least to greatest 5, -3, -12, 9
Answer:
-12, -3, 5, 9
Step-by-step explanation:
ok. So the numbers are 5, -3, -12, and 9.
In these numbers, there are 2 negatives. They are -12 and -3.
In negatives, the bigger the number is, the number is smaller.
So we first put
-12, -3 as our 2 first. Then the other ones are 5 and 9.
and you obviously know that 5 is less than 9. try it out. 9-5 =4 which is positive
So then you put 5, 9
And our full answer is
-12, -3, 5, 9
Determine whether the lines x+ 7y= −3 and y = 7x + 25 are parallel, perpendicular, or neither. Justify your answer by showing all the needed work.
Answer:
perpendicular
Step-by-step explanation:
Rewrite the equations
y = (-1/7)x - 3/7 -- L1
y = 7x + 25 -- L2
Slope of L1 x Slope of L2 = -1/7 x 7 = -1
As a result, the two lines are perpendicular
dos aviones parten de una ciudad con direcciones S32°E y E57°N¿ cuál es el angulo que forma sus direcciones?
Answer:
El ángulo formado entre las dos direcciones es aproximadamente 115º.
Step-by-step explanation:
Las direcciones dadas en el enunciado significan lo siguiente:
S32ºE - 32º al este del sur.
E57ºN - 57º al norte del este.
Vectorialmente hablando, cada dirección es la siguiente:
S32ºE
\(A(x,y) = (\sin 32^{\circ}, -\cos 32^{\circ})\)
\(A(x,y) = (0.530, -0.848)\)
E57ºN
\(B(x,y) = (\cos 57^{\circ},\sin 57^{\circ})\)
\(B(x,y) = (0.545, 0.839)\)
El ángulo formado entre los dos vectores unitarios (\(\theta\)), medido en grado sexagesimales, puede determinarse mediante la siguiente ecuación vectorial:
\(\theta = \cos^{-1} \frac{A\,\bullet \,B}{\|A\|\cdot \|B\|}\)
Donde:
\(\|A\|\) - Norma de \(A(x,y)\).
\(\|B\|\) - Norma de \(B(x,y)\).
Si sabemos que \(A(x,y) = (0.530, -0.848)\), \(B(x,y) = (0.545, 0.839)\), \(\|A\| = 1\) y \(\|B\| = 1\), entonces el ángulo formado entre los dos vectores es:
\(\theta = \cos^{-1} \frac{(0.530)\cdot (0.545)+(-0.848)\cdot (0.839)}{(1)\cdot (1)}\)
\(\theta \approx 115^{\circ}\)
El ángulo formado entre las dos direcciones es aproximadamente 115º.
Convert 60 kilometers per pound to miles per hour.
To be eligible for the swim team, the mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s). The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
What is the maximum time (in seconds) that she can take on her last lap and still make the team?
52s is the maximum time that she can take on her last lap and still make the team.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that he mean pace a student needs to achieve on 5 laps of the pool is 60 seconds (s).
The student swims a lap in 63 s, 62 s, 65 s, and 58 s on her first four laps.
We need to find the maximum time (in seconds) that she can take on her last lap and still make the team
Let x be the maximum time (in seconds) that she can take on her last lap
60=(63+62+65+58+x)/5
300=63+62+65+58+x
300=248+x
Subtract 248 on both sides
300-248=x
x=52s
Hence, 52s is the maximum time that she can take on her last lap and still make the team.
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There are 3 types of PercentProblems.
a) Number compared to the Base is unknown: x/100 = ?/b
b) Base Number is unknown: a/?= x/100
c) Percent is unknown: a/b = ?/100
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8?
Answer:A. x= .100
Step-by-step explanation:because of the distance in miles
The quotient of a number and -2/3 is -9/10. What is the number?
Answer:
It's 0.6
Step-by-step explanation:
The average (A) of two numbers, m and n, is given by the formula A = m+t/2 . Find
the average of the two numbers 36 and 72.
The solution is
Answer:
\(54\)
Step-by-step explanation:
Formula for average A of two numbers m and n is:
\(A=\frac{m+n}{2}\)
Substitute the value m=36 and n=72
\(A=\frac{36+72}{2}\)
This is equivalent to:
\(A=\frac{108}{2}\)
The average is:
\(A=54\)
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Solve one and three fourths times two fourths.
A) fourteen sixteenths
B) fifteen sixteenths
C) seventeen sixteenths
D) eighteen sixteenths
Answer:
A. fourteen sixteenths
Step-by-step explanation:
\(1\frac{3}{4} x \frac{2}{4}\)
\(\frac{7}{4} x \frac{2}{4}\)
\(\frac{14}{16}\)
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♥☼☺
Answer:
A it didnt let me answer at first and it dose now
Step-by-step explanation:
during a basketball practice, mai attemoted 40 free throws and was successful on 25% of them how many successful free throws did she make?
Answer:
10 successful throws
Step-by-step explanation:
40 free throws
25% (25)
40 x 0.25 = 10
a bag contains four types of coins. The probability of drawing a penny, nickel and dime is shown below. What is the probability of drawing a single coin that has a value of at least $.10?
Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.
Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Simply put, probability is the likelihood that something will occur.
When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.
So, we have the chart:
Penny = 2/5 = 0.4
Nickel = 1/5 = 0.2
Dime = 1/4 = 0.25
Then, the probability of getting a value of at least $0.10
P(E) = 3/3
P(E) = 1
Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.
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15 pieces of candy are given to s students from a bag of candy containing 310 pieces. There are 10 pieces left over.
(s x 15) ÷ 10 = 310
(s + 15) = 310 ÷ 10
(310 − 10) ÷ 15 = s
310 ÷ (s + 15) = 10
Answer:
C. (310 − 10) ÷ 15 = s
Step-by-step explanation:
The correct answer is C. (310 − 10) ÷ 15 = s. This is because we can use the following steps to find the equation:
First, we need to find how many pieces of candy were given out in total. Since there are 10 pieces left over in the bag, and the bag originally contained 310 pieces, we can subtract 10 from 310 to get 300 pieces given out.
Next, we need to find how many pieces of candy each student received. Since 15 pieces of candy were given to s students, we can divide 300 by 15 to get the number of students. This gives us 20 students.
Finally, we need to write an equation that relates the number of students (s) to the number of pieces of candy given out (300) and the number of pieces of candy per student (15). We can do this by using the inverse operations of subtraction and division. We can multiply both sides by 15 and then add 10 to both sides to get the equation:
(310 − 10) ÷ 15 = s
This equation can be used to find the number of students if we know the number of pieces of candy in the bag, the number of pieces left over, and the number of pieces per student.
But wait, there's more! If you act now, you can also get a bonus question for free! Here it is:
If s students each received 15 pieces of candy, and there are 10 pieces left over in the bag, how many cavities will they have after eating all the candy?
There are a few possible ways to approach this question, but here is one:
- First, we need to find how many pieces of candy each student ate. Since they received 15 pieces each, and there are no leftovers, we can assume they ate all of them. So each student ate 15 pieces.
- Next, we need to find how many cavities each piece of candy causes. This may vary depending on the type and quality of the candy, but let's assume that each piece causes 0.1 cavities on average. This means that for every 10 pieces of candy, one cavity is formed.
- Finally, we need to multiply the number of pieces each student ate by the number of cavities each piece causes, and then add up all the results for all the students. This will give us the total number of cavities for the whole group. We can use this formula:
c = (15 × 0.1) × s
where c is the number of cavities and s is the number of students.
Using this formula, we can plug in the value of s that we found
c = 1.5 × 20
c = 30
✧☆*: .。. That's all folks, have fun with math! (✧ω✧) .。.:*☆✧
What is the slope of the line on the graph?
Answer:
The slope would be 7.
Step-by-step explanation:
Count the number of spaces the line goes up from point A to point B.
Which of the following is the quotient of the rational expressions shown
below? Make sure your answer is in reduced form.
7x² /2x +6 divided by 3x -5/ x+3
Answer:
(7x² / 6x - 10)
Step-by-step explanation:
To divide rational expressions, we flip the second fraction (the divisor) and multiply it with the first fraction (the dividend). Then we simplify the resulting expression, if possible.
So,
(7x² /2x +6) ÷ (3x -5/ x+3)
= (7x² /2x +6) * (x+3/3x -5)
= 7x²(x+3) / 2(x+3)(3x -5)
= 7x² / 6x - 10
Therefore, the quotient of the given rational expressions is (7x² / 6x - 10), which cannot be further reduced.
Answer:
2
7x
3
+18x+3−
x
5
Short Solution Steps
7x
2
/2x+63x−5/x+3
Express
2
7x
2
x as a single fraction.
2
7x
2
x
+6×3x−
x
5
+3
Multiply 6 and 3 to get 18.
2
7x
2
x
+18x−
x
5
+3
To add or subtract expressions, expand them to make their denominators the same. Multiply 18x+3 times
2
2
.
2
7x
2
x
+
2
2(18x+3)
−
x
5
Since
2
7x
2
x
and
2
2(18x+3)
have the same denominator, add them by adding their numerators.
2
7x
2
x+2(18x+3)
−
x
5
Do the multiplications in 7x
2
x+2(18x+3).
2
7x
3
+36x+6
−
x
5
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply
2
7x
3
+36x+6
times
x
x
. Multiply
x
5
times
2
2
.
2x
(7x
3
+36x+6)x
−
2x
5×2
Since
2x
(7x
3
+36x+6)x
and
2x
5×2
have the same denominator, subtract them by subtracting their numerators.
2x
(7x
3
+36x+6)x−5×2
Do the multiplications in (7x
3
+36x+6)x−5×2.
2x
7x
4
+36x
2
+6x−10
Step-by-step explanation:
PLEASE GIVE ME BRAINLIEST I AM LOOKING FOR A FRIEND
Darla, Ellie, and Fran ate a whole container of ice cream. Darla ate half as much as Ellie ate, and Fran ate 5 times as much as Darla ate. If the container of ice cream cost $4.00, how much, in dollars, should each person pay?
1. Find the values of for which the gradient function of the curve = 23 + 32 −12 + 3 is zero.
Hence, find the equations of the tangents to the curve which are parallel to the −axis.
To find the values of x for which the gradient function of the curve is zero, we need to find the values of x that make the derivative of the curve equal to zero.
The given function is: \(\displaystyle\sf f(x)=23x^{3}+2x^{2}-12x+3\).
To find the derivative of the function, we differentiate each term with respect to x:
\(\displaystyle\sf f'(x)=69x^{2}+4x-12\).
Now we set the derivative equal to zero and solve for x:
\(\displaystyle\sf 69x^{2}+4x-12=0\).
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the values of x:
\(\displaystyle\sf x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\).
Plugging in the values a=69, b=4, and c=-12, we get:
\(\displaystyle\sf x=\frac{-4\pm \sqrt{(4)^{2}-4(69)(-12)}}{2(69)}\).
Simplifying further, we have:
\(\displaystyle\sf x=\frac{-4\pm \sqrt{16+3312}}{138}\).
\(\displaystyle\sf x=\frac{-4\pm \sqrt{3328}}{138}\).
\(\displaystyle\sf x=\frac{-4\pm 8\sqrt{13}}{138}\).
Therefore, the values of x for which the gradient function of the curve is zero are given by \(\displaystyle\sf x=\frac{-4+8\sqrt{13}}{138}\) and \(\displaystyle\sf x=\frac{-4-8\sqrt{13}}{138}\).
To find the equations of the tangents to the curve that are parallel to the x-axis (horizontal tangents), we substitute these x-values into the original function \(\displaystyle\sf f(x)\). The resulting y-values will give the equations of the tangents.
For \(\displaystyle\sf x=\frac{-4+8\sqrt{13}}{138}\):
\(\displaystyle\sf y=f\left(\frac{-4+8\sqrt{13}}{138}\right)=23\left(\frac{-4+8\sqrt{13}}{138}\right)^{3}+2\left(\frac{-4+8\sqrt{13}}{138}\right)^{2}-12\left(\frac{-4+8\sqrt{13}}{138}\right)+3\).
For \(\displaystyle\sf x=\frac{-4-8\sqrt{13}}{138}\):
\(\displaystyle\sf y=f\left(\frac{-4-8\sqrt{13}}{138}\right)=23\left(\frac{-4-8\sqrt{13}}{138}\right)^{3}+2\left(\frac{-4-8\sqrt{13}}{138}\right)^{2}-12\left(\frac{-4-8\sqrt{13}}{138}\right)+3\).
These two equations represent the equations of the tangents to the curve that are parallel to the x-axis.
Which function's graph has the same y Intercept as the line shown?
Оу в x +1
Oy -5x + 5
O y .5x-5
O y: 5x - 1
The graph has the same y Intercept as the line shown is y = 5x - 5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We take two points from the graph as (-5, 0) and (0, -5)
So, the slope of line
slope = (-5 - 0)/ (0- (-5))
slope= -5 / 5
slope= -1
Using slope intercept form
y= mx+ b
y= -x+ b
Now, put x= -5 and y= 0 then
0 = -(-5)+ b
b= -5
So, the equation of line is
y= -x - 5
Here, the y intercept is -5.
So, the equation with same y intercept is
y = 5x - 5
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789342 x 152387 x 69248
need help please geometry
Answer: confused on what this is asking but x=3. And the sum of angle RTS=28
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Use digits to write the value of the 4 In this number.
842,963
2,485 ÷x =49 R35
PLSSS HELPPP :((((
Answer:
x = 50
Step-by-step explanation:
2485 ÷ x = 49 R 35
We know that 2485 ÷ x = 49 R 35, or 2485 ÷ x = 49 + 35
Step 1:
Now, I want to subtract 35 from the left side of the equation:
2485 ÷ x = 49 R 352450 ÷ x = 49Step 2:
Now I want to find x. We can start by multiplying both sides by x, then dividing by the coefficient.
2450 ÷ x = 492450 = 49x2450 ÷49 = xx = 50x = 50
Check:
2485 ÷ 50 = 49 R 3549.7 = 49 R 3549 + 50(7/10) = 49 R 3549 + 35 = 49 R 35-Chetan K
Find the discriminant of the quadratic equation.
2i2+6i=4
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An office manager orders one calculator or one calendar for each of the office's 60 employees. Each calculator costs $15, and each calendar costs $10. The entire order totaled $800.
Part A: Write the system of equations that models this scenario. (5 points)
Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps. (5 points)
The system of equations is.
\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)
And the solutions are y = 50 and x = 10.
How to write and solve the system of equations?Let's define the two variables:
x = number of calculators.y = number of calendars.With the given information we can write two equations, then the system will be:
\(\begin{cases}\text{x}+\text{y}=60 \\15\text{x}+10\text{y}=800 \end{cases}\)
Now let's solve it.
We can isolate x on the first to get:
\(\text{x} = 60 - \text{y}\)
Replace that in the other equation to get:
\(15\times(60 - \text{y}) + 10\text{y} = 800\)
\(-2\bold{y} = 900 - 800\)
\(-2\bold{y} = 100\)
\(\text{y} = \dfrac{100}{-2} = \bold{50}\)
Then \(\bold{x=10}\).
Therefore, the solutions are y = 50 and x = 10.
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You have saved $14,000 for a down payment on a house. Your bank requires a minimum down payment of 17%. What is the maximum price you can offer for a home in order to have enough money for the down payment? (Round your answer to two decimal places.)
The maximum price you can offer for a home is approximately $82,352.94 for a 17% down payment.
To determine the maximum price you can offer for a home, you need to calculate 17% of the total price, which will be your down payment of $14,000.
Let's assume the maximum price you can offer for the home is P dollars.
According to the given information, the down payment requirement is 17% of the total price. So, we can set up the following equation:
\(0.17P = $14,000\)
To solve for P, divide both sides of the equation by 0.17:
P = $14,000 / 0.17
Calculating this expression, we find:
P ≈ $82,352.94
Therefore, the maximum price you can offer for a home in order to have enough money for the 17% down payment is approximately $82,352.94.
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Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.
Based on the factor with the greater absolute value being positive, the factors of -48 with a difference of 19 are 16 and -3.
How to find the factors?First, find the factors of 48. They are:
1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
From these, pick out factors that have a difference of 19 when subtracted. Keep in mind that the greater absolute factor is positive which means that the other factor has to be negative as -48 is negative.
The factors with a difference of 19 would be:
16 and -3.
The difference:
= 16 + (-3)
= 16 + 3
= 19
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Find the value of p.
-25 = -4p + 19
Answer:
9.75
Step-by-step explanation:
-25 = -4p + 19
-25 - 19 = -4p
-39 ÷ -4 = p
9.75 = p
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This scale drawing shows a reduction in a figure.
What is the value of x?
Enter your answer as a decimal in the box.
X =
The value of x for the second triangle if it is the reduction of the first drawing is 6.3 feet.
Given two triangles.
Also given that, the scale drawings given are the reduction of the figure.
Most probably, the second triangle must be formed after a reduction with a scale factor of k.
Let k be the required scale factor.
The value of k can be found by taking the ratio of the corresponding sides.
k = 5.2 / 10.4
= 0.5
So all the corresponding sides will be half of the first triangle.
x = 0.5 × 12.6
= 6.3 feet
Hence the value of x is 6.3 feet.
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