Answer:
y = [tex]\frac{1}{4}[/tex] x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{4}[/tex] x - 1 ← is in this form
with slope m = [tex]\frac{1}{4}[/tex]
• Parallel lines have equal slopes, thus
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (8, 5) into the partial equation
5 = 2 + c ⇒ c = 5 - 2 = 3
y = [tex]\frac{1}{4}[/tex] x + 3 ← equation of parallel line
Simplify this expression HELP ASAP
Answer:
B
Step-by-step explanation:
Noting the following rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
Given
([tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex])( [tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex] )
Each term in the second factor is multiplied by each term in the first factor
= [tex]\sqrt{2}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) + [tex]\sqrt{3}[/tex]([tex]\sqrt{5}[/tex] - [tex]\sqrt{7}[/tex]) ← distribute parenthesis
= [tex]\sqrt{10}[/tex] - [tex]\sqrt{14}[/tex] + [tex]\sqrt{15}[/tex] - [tex]\sqrt{21}[/tex]
Identify an equation in point-slope form for the line perpendicular to
y=-4x - 1 that passes through (-2,7).
O A. y-7 - -4(x +2)
O B. y+2- (x-7)
O C. y+7 -- (x-2)
O D. y-7 - 3(x+2)
SUBMIT
Answer:
A. y - 7 = -4(x + 2)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. In addition, I recall that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes], so -4 really should be replaced with ¼, but if your assignment says otherwise, then this is the answer.
To find the equation of a line perpendicular to y=-4x -1 that passes through (-2, 7), we take the negative reciprocal of -4 to find the slope of the perpendicular line. Plugging in the values (-2, 7) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).
Explanation:To find the equation of a line perpendicular to a given line, we need to determine the slope of the perpendicular line. The given equation is in the form y = mx + b, where m represents the slope. The slope of the given line is -4. To find the slope of the perpendicular line, we take the negative reciprocal of -4, which is 1/4. Now that we have the slope, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Plugging in the values (-2, 7) for (x1, y1) and 1/4 for the slope, we get the equation y - 7 = 1/4(x + 2). Therefore, the correct answer is A. y - 7 = -4(x + 2).
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log; (3x+2) = log,(4x-6)
Answer:
x = 8
Step-by-step explanation:
Using the rule of logarithms
log x = log y ⇔ x = y
Given
log(3x + 2) = log(4x - 6), then
4x - 6 = 3x + 2 ( subtract 3x from both sides )
x - 6 = 2 ( add 6 to both sides )
x = 8
8. Let f(x) = x 2 + 3x − 12 what is the average rate of change from x = 3 and x = 5?
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]
The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of t
product when it is sold at a unit price of x dollars.
-0.5x2 + 221 – 224
What is represented by the zero(s) of the expression?
A.
the unit price(s) when the profit is equal to 0
B.
the unit price(s) when profit is greatest
c.
the profit when the unit price is equal to 0
OD.
the profit when the unit price is greatest
Reset
Next
Answer:
A. The answer is our unit prices when our profit is 0
Step-by-step explanation:
The zeros are the x-intercepts, when the curve passes through the x-axis.
I'm going to call our function P
P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)
The answer is our unit prices when our profit is 0
The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.
Explanation:The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.
The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.
-0.5x^2 + 221x - 224 = 0We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.The zero(s) of the expression will give us the unit price(s) at which the profit is equal to 0.Learn more about Quadratic equations here:https://brainly.com/question/30098550
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Simplify the expression. 8P3
Answer:
336
Step-by-step explanation:
Using the definition of n[tex]P_{r}[/tex] = n ! / (n- r) !
where n ! = n(n - 1)(n - 2).... × 3 × 2 × 1
8[tex]P_{3}[/tex]
= 8 ! / (8 - 3) !
= 8 ! / 5 !
= [tex]\frac{8(7)(6)(5)(4)(3)(2)(1)}{5(4)(3)(2)(1)}[/tex]
[ cancel 5(4)(3)(2)(1) on numerator/denominator
= 8 × 7 × 6 = 336
ANSWER
[tex]^8P_3 = 336[/tex]
EXPLANATION
Recall that;
[tex]^nP_r = \frac{n!}{(n - r)!} [/tex]
The given expression is:
[tex]^8P_3[/tex]
We substitute n=8 and r=3
[tex]^8P_3 =\frac{8!}{(8- 3)!} [/tex]
[tex]^8P_3 =\frac{8!}{(5)!} [/tex]
This simplifies to :
[tex]^8P_3 =\frac{8 \times 7 \times 6 \times 5!}{5!} [/tex]
We cancel out the common factors to get:
[tex]^8P_3 = 8 \times 7 \times 6[/tex]
[tex]^8P_3 = 336[/tex]
20points! What is the percent of change from 134 to 106? Round to the nearest percent!
Answer:
Step-by-step explanation:
it's -2
The percentage change of 134 to 106 will be -20.89% .
Given ,
Number changed from 134 to 106 .
Now,
Here initially the number was = 134
After reduction the number was = 106
Percentage change = final - initial / initial * 100
Final number = 106
Initial number = 134
so,
Percentage change = 106 -134/134 * 100
Percentage change = -28/134 *100
Percentage change = -20.89%
Thus the percentage change is -20 .89% and the negative sign shows the declining nature of number .
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A student skipped a step when she tried to convert 26 hours into seconds,
and she got the following incorrect result:
26 hours
60 seconds
1 minute
- 1560 seconds
What conversion ratio did she skip in this multiple-step conversion?
60 minutes
O
A.
1 hour
60 seconds
1 minute
1 hour
60 minutes
1 minute
60 seconds
Help ASAP
Final answer:
The student missed the conversion from minutes to hours. The correct conversion is 26 hours × 60 minutes/hour × 60 seconds/minute, which equals 93,600 seconds.
Explanation:
Identifying the Missed Conversion Step
The student was attempting to convert 26 hours into seconds but arrived at an incorrect result of 1560 seconds. The error occurred because the student skipped the correct conversion ratio between minutes and hours. For such conversions, it is essential to use the correct conversion factors: 60 minutes per hour and 60 seconds per minute.
Correct Conversion Process
To convert 26 hours to seconds:
First, convert hours to minutes: 26 hours × 60 minutes/hour = 1560 minutes.
Then, convert minutes to seconds: 1560 minutes × 60 seconds/minute = 93,600 seconds.
Therefore, the correct number of seconds in 26 hours is 93,600 seconds.
Factor completely 3x4 − 30x3 + 75x2. 3(x − 5)2 3x2(x − 5)2 3x2(x2 − 10x + 25) 3x2(x + 5)(x − 5)
Answer:
The complete factorization is 3x² (x - 5)² ⇒ 2nd answer
Step-by-step explanation:
* Lets revise how to factorize a trinomial
- Find the greatest common factor of the coefficients of the three terms
∵ The trinomial is 3x^4 - 30x³ + 75x²
- The greatest common factor of 3 , 30 , 75 is 3
∵ 3 ÷ 3 = 1
∵ 30 ÷ 3 = 10
∵ 75 ÷ 3 = 25
∴ 3x^4 - 30x³ + 75x² = 3(x^4 - 10x³ + 25x²)
- Now lets find the greatest common factor of the variable x
∵ x² is the greatest common factor of the three terms
∵ x^4 ÷ x² = x²
∵ 10x³ ÷ x² = 10x
∵ 25x² ÷ x² = 25
∴ 3(x^4 - 10x³ + 25x²) = 3x² (x² - 10x + 25)
- Lets factorize (x² - 10x + 25)
∵ √x² = x
∵ √25 = 5
∵ 2 × 5 × x = 10x
∴ x² - 10x + 25 is a completing square
∴ (x² - 10x + 25) = (x - 5)²
∴ 3x² (x² - 10x + 25) = 3x² (x - 5)²
* The complete factorization is 3x² (x - 5)²
Answer:
3x^2 (x-5)^2
Step-by-step explanation:
3x^4 − 30x^3 + 75x^2
We can factor out a 3x^2 from each term
3x^2 (x^2 -10x +25)
The term inside the parentheses can be factored
What 2 numbers multiply to 25 and add to -10
-5*-5 = 25
-5+-5 = -10
3x^2 (x-5) (x-5)
3x^2 (x-5)^2
HELLLLLLPPPPPP!!!!!!!!!
Answer:
A
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1
= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms
= - 2x² - 8x + 12 → A
The property tax on a $160,000 home is $3,840. At this rate, what is the property tax on a home appraised at $260,000? $
Answer:
$6240
Step-by-step explanation:
Find the rate by dividing property tax by the appraisal value.
[tex]\frac{3840}{160000}=0.024[/tex]
Now multiply the appraised value by this rate to find the property tax.
[tex]260000*0.024=6240[/tex]
The property tax on a home appraised at $260,000 is $6,240.
Explanation:To find the property tax on a home appraised at $260,000, we can set up a proportion using the given information. The property tax on a $160,000 home is $3,840, so we have:
$160,000 : $3,840 = $260,000 : x
Using cross-multiplication, we can solve for x:
x = ($260,000 * $3,840) / $160,000
Calculating this, we find that the property tax on a home appraised at $260,000 is $6,240.
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What is the total surface area of the cone? 147π cm2 224π cm2 175π cm2 273π cm2
Answer:
Step-by-step explanation: I believe you would just take 147 + 224 + 175 + 273 = 819pi cm2
So your answer would be 819pi cm2
The answer is 224 pi
.....................................
Witch table shows a proportional relationship between a and b
Answer:
Option B is correct.
Step-by-step explanation:
A proportional relationship is a relationship between two variables where the ratio between the two variables is always the same.
Divide b/a for each option, the option having same ratio for the complete tables have proportional relationship
a)
9/3 = 3
12/4 = 3
20/5 = 4
b)
25/20 = 5/4
30/24 = 5/4
40/32 = 5/4
c)
12/4 = 3
15/5 = 3
24/6 = 4
d)
4/3 = 4/3
9/6 = 3/2
12/16 = 3/4
So, Option B is correct.
Answer: Second Option
Step-by-step explanation:
It is said that two variables a and b are propocionales if when b increases then a increases in a constant rate.
That is, a and b are proportional if the quotient between b and a is always equal to a constant k.
[tex]\frac{b}{a}=k[/tex]
To know which of the tables shows a proportional relationship identify in which of the tables the division of b between a always is constant
You can verify that the table where the quotient of b enters a is always constant is in the second table
[tex]\frac{b}{a}=\frac{5}{4}[/tex]
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
A. 0
B. 2.5
C. 4.5
D. 11.5
Answer:
B
Step-by-step explanation:
f(0) - f(-3) = area under f'(x) from x=0 to x=3.
We can find the area under f'(x) in this interval by finding the area of the triangle formed by the line.
A = 1/2 b h
A = 1/2 (3) (3)
A = 4.5
f(0) - f(-3) = 4.5
Since f(0) = 7:
7 - f(-3) = 4.5
f(-3) = 7 - 4.5
f(-3) = 2.5
3(b+4)+8=-3 as a linear equation.
For this case we have the following equation:
[tex]3 (b + 4) + 8 = -3[/tex]
If we apply distributive property to the terms within the parenthesis we have:
[tex]3b + 12 + 8 = -3[/tex]
We add similar terms to the left side of the equation:
[tex]3b + 20 = -3[/tex]
Subtracting 20 from both sides of the equation:
[tex]3b = -3-20\\3b = -23[/tex]
Dividing between 3 on both sides of the equation:
[tex]b = - \frac {23} {3}[/tex]
In mixed number we have:
[tex]b = -7 \frac {2} {3}[/tex]
Answer:
[tex]b = -7 \frac {2} {3}[/tex]
Angle f and angle G are complementary. The measure angle f is four times the measure of angle G. What is the measure of each angle?
Complementary means they add to 90°
f=90-g
f=4g
4g =90-g
5g=90
g=18
f=4g=4(18)=72
Answer: f=72°, g=18°
The system shown is _____.
consistent
equivalent
inconsistent
Answer:
consistent
Solution at (3,2)
Step-by-step explanation:
A consistent and independent solution to a system of linear equations is one point
A consistent and dependent solution to a system of linear equations is where they are the same line ( they could also be called equivalent)
An inconsistent solution is where there is no solution, the lines do not cross
Since the lines cross at exactly one point, this is a consistent and dependent solution
The solution is at x = 3 ( 3 units to the right of the origin)
and y = 2 ( 2 units up from the origin)
(3,2)
Answer:
Consistent :)
Step-by-step explanation:
Area of circle with radius of 2
Answer:
[tex]4\pi[/tex] or 12.56
Step-by-step explanation:
[tex]\pi r^{2}[/tex] is the formula to find the area of a circle.
if we plug '2' in... [tex]\pi2^{2}[/tex]
which equals to [tex]4\pi[/tex]
if we multiply 4 with pi, it equals to 12.56
Answer:
Area of circle = 12.56 sq. units
Step-by-step explanation:
radius = 2
Area of circle = π r² sq. units
= 3.14 * 2 * 2 = 12.56 sq. units
Simplify.
3√7/25−√28/25+√63/25
Answer:
4√7/5
Step-by-step explanation:
to take a root of a fraction, take the root of the numerator and denominator separately3×√7/5-√28/5+√63/5
calculate the product3√7/5-2√7/5+3√7/5
calculate the sum or difference4√7/5
The simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].
What is system of equations?System of equations is a finite set of equations for which common solutions are sought.
We have,
[tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex]
Now,
Take LCM, of the given fraction,
We get,
[tex]\frac{3\sqrt{7} -\sqrt{28}+\sqrt{63}}{25}[/tex]
Now,
Simplify by rewriting every number in numerator in form of [tex]\sqrt{7}[/tex],
i.e.
[tex]\frac{3\sqrt{7} -\sqrt{4*7}+\sqrt{9*7}}{25}[/tex]
Now,
[tex]\frac{3\sqrt{7} -2\sqrt{7}+3\sqrt{7}}{25}[/tex]
Now,
Every digit is in the form of [tex]\sqrt{7}[/tex],
So,
Simplify,
We get,
[tex]=\frac{4\sqrt{7}}{25}[/tex]
So,
This is the simplified form of the given equation.
Hence, we can say that the simplified value of [tex]\frac{3\sqrt{7} }{25} -\frac{\sqrt{28} }{25} +\frac{\sqrt{63} }{25}[/tex] will be [tex]\frac{4\sqrt{7}}{25}[/tex].
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what is −7−4p−(−5) ??
Answer:
Step-by-step explanation:
−7−4p+5
−4p+(−7+5)
Ans
−4p−2
your answer is: -4p - 2
Explanation:
first, ignore the -4p for now. do the small equation without the variable. SO, we would do 7 - 5 = 2.
there aren't any addition symbols being used in the equation and there aren't any other numbers with the p variable. this means that the -4p will stay the same. so we would end up with -4p - 2
(this isn't the normal way of solving this, but I did my own way and got the same answer)
please answer and thank you!!!
Answer:
In the photos
Step-by-step explanation:
First, create your trees (following instructions on the photo you attached). Then, circle the prime numbers in each tree you made. If the prime number shows up once put that number once on your prime factorization. If the prime number appears multiple times, put the number down and have an exponent (the exponent is determined by how many times that number appears).
Hope this helps a bit,
Flips
1. Two lines, A and B, are represented by the following equations: Line A: 2x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? (4 points) It is (2, 2). There are infinitely many solutions. It is (4, 0). There is no solution.
Answer:
It is (2, 2).
Step-by-step explanation:
what is the distance between the points (2 -3) and (-6 4) on the coordinate plane
Answer:
√113
or
10.6301458127
Step-by-step explanation:
Plug the coordinated into this equation and make sure you match up the corrdinates in the correct order
d = √(x2 - x1)^2 + (y2 - y1)^2
The number next to the number does NOT mean multiply it mean like this
(x2, y2) and (x1, y1) so you would plug them in like this:
d = √(-6 - 2)^2 + (4 - (-3))^2
d = √(-8)^2 + (7)^2
d = √(64 + 49
d = √113
or 10.6301458127
Answer with Step-by-step explanation:
The distance(d) between the points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here, we have to find distance between (2,-3) and (-6,4)
(a,b)=(2,-3) and (c,d)=(-6,4)
[tex]d=\sqrt{(-6-2)^2+(4-(-3))^2}[/tex]
[tex]d=\sqrt{8^2+7^2}[/tex]
[tex]d=\sqrt{64+49}[/tex]
[tex]d=\sqrt{113}[/tex]
Hence, the distance between the points (2 -3) and (-6 4) on the coordinate plane is:
[tex]\sqrt{113}[/tex]
What is the product -9x(5x-2x)
Answer:
−27x2
Step-by-step explanation:
It's -27x to the second power so the small 2 at the end
Kasey has a job that pays $865 per week. How much is withheld from each paycheck for Social Security?
Kasey has $53.63 withheld from her weekly paycheck of $865 for Social Security, which is calculated by multiplying her weekly pay by the Social Security tax rate of 6.2%.
Explanation:The question asks us to calculate how much is withheld from Kasey's paycheck for Social Security.
With a weekly pay of $865, we need to find 6.2% of that amount since that is the percentage deducted for Social Security taxes.
To find this amount, we multiply $865 by 0.062.
Calculation: $865 × 0.062 = $53.63
Therefore, $53.63 is withheld from Kasey's paycheck each week for Social Security.
select the two values of x that are roots of this equation 2x^2 + 7x + 6=0
A. X=-3
B. X=-3/2
C. X=-4
D. X=-2
Answer:
x = -2 or x = -3/2 thus B. & D. are the answer
Step-by-step explanation:
Solve for x:
2 x^2 + 7 x + 6 = 0
Hint: | Factor the left hand side.
The left hand side factors into a product with two terms:
(x + 2) (2 x + 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x + 2 = 0 or 2 x + 3 = 0
Hint: | Look at the first equation: Solve for x.
Subtract 2 from both sides:
x = -2 or 2 x + 3 = 0
Hint: | Look at the second equation: Isolate terms with x to the left hand side.
Subtract 3 from both sides:
x = -2 or 2 x = -3
Hint: | Solve for x.
Divide both sides by 2:
Answer: x = -2 or x = -3/2
Answer:
B and D
Step-by-step explanation:
Given
2x² + 7x + 6 = 0
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 6 = 12 and sum = + 7
The factors are + 4 and + 3
Use these factors to split the x- term
2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 3) = 0
Equate each factor to zero and solve for x
x + 2 = 0 → x = - 2 → D
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B
What is the midpoint of (3.2,2.5) and (1,6,-4.5)
Answer:
(2.4 , -1)
Step-by-step explanation:
Too many commas in second ordered pair but this is how I will interpret the question:
Find the midpoint of (3.2,2.5) and (1.6,-4.5)
So just average x's : (3.2+1.6)/2 =4.8/2=2.4
And
just average y's : (2.5+-4.5)/2=-2/2=-1
The midpoint is (average x's , average y's)
Your midpoint is (2.4 , -1 )
answer (2.4 , -1)
A 52-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
Answer:
The length of the shorter piece is 13 inches
Step-by-step explanation:
Let's represent the longer piece of pipe with the variable L and the shorter piece of pipe with variable S.
Since the pipe is going to be the length of L and S together, we can make this equation:
L+S=52
Also we know that the longer piece is three times the shorter piece or
L=3S
Substitute the second equation into the first equation.
L+S=52
3S+S=52
4S=52
Divide both sides by 4
4S/4=52/4
S=13 inches
The length of the shorter piece is 13 inches....
To find the length of longer piece, put the value S=13 in L=3S
L=3S
L=3(13)
L=39 inches
The length of the longer piece is 39 inches....
3x^2-x-2=0
Show all work please
Answer:
[tex]\large\boxed{x=-\dfrac{2}{3}\ or\ x=1}[/tex]
Step-by-step explanation:
[tex]3x^2-x-2=0\\\\3x^2+2x-3x-2=0\\\\x(3x+2)-1(3x+2)=0\\\\(3x+2)(x-1)=0\iff3x+2=0\ \vee\ x-1=0\\\\3x+2=0\qquad\text{subtract 2 from both sides}\\3x=-2\qquad\text{divide both sides by 3}\\x=-\dfrac{2}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]
Based on the table below, evaluate f(1).
Answer:
f(1) = 24
Step-by-step explanation:
f(1) is the value of f(x) when x = 1, that is from the table
f(1) = 24