keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]6x-7y=-4\implies 6x=7y-4\implies 6x+4=7y \\\\\\ \cfrac{6x+4}{7}=y\implies \qquad \stackrel{\stackrel{m}{\downarrow }}{\cfrac{6}{7}} x+\cfrac{4}{7}=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
now, since we know that slope, let's check for a perpendicular line to it
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{6}{7}} ~\hfill \stackrel{reciprocal}{\cfrac{7}{6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{7}{6}}}[/tex]
so we're really looking for the equation of aline whose slope is -7/6 and that it passes through (-6 , 5)
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{7}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{7}{6}}(x-\stackrel{x_1}{(-6)}) \implies y -5= -\cfrac{7}{6} (x +6) \\\\\\ y-5=-\cfrac{7}{6}x-7\implies {\LARGE \begin{array}{llll} y=-\cfrac{7}{6}x-2 \end{array}}[/tex]
Answer:
Please read and try to understand it :>
Step-by-step explanation:
[tex]6x-7y=-4[/tex] is not the standard format for a straight line so you have to rearrange it:
[tex]y=\frac{6}{7} x +\frac{4}{7}[/tex]
To find the equation of a perpendicular line to the given equation, you have to first find the negative reciprocal of the gradient:
[tex]-\frac{7}{6}[/tex]
Since you want to find the equation of a perpendicular line that passes a certain point, you have to substitute the coordinates to the equation to find the y-intercept:
[tex]5=-\frac{7}{6} (-6)+c[/tex]
Solving:
[tex]5=-\frac{7}{6} (-6) +c\\ \\ 5=\frac{42}{6} +c\\ \\-\frac{42}{6} +5=c\\ \\-7+5=c\\\\ -2=c[/tex]
Final equation: [tex]y=-\frac{7}{6} x -2[/tex]
b. If xⁿ=b ,then x=ⁿ√b
NEED HELP WITH GEOMENTRY ASAP
Answer:
86????
Step-by-step explanation:
I am not certain, but wouldn't it be 86?
1. In some lion prides, the ratio of female to
male lions is 3: 1. What percent of the lions
are male? (Example 1)
Plssss help
Answer:
25%
Step-by-step explanation:
Based on the given conditions, formulate
Calculate the sum or difference:
Multiply a number to both the numerator and the denominator
: Write as a single fraction:
Calculate the product or quotient:
Rewrite a fraction with denominator equals 100 to a percentage:
5 of 105 of 10 Items 34:04 Skip to resources Question The Community Center has exercise classes on Monday and Friday. The Monday class is 1 3 hours and the Friday class is 1 1 hours. 4 2Patrick attended both exercise classes last week and this week. How many hours did Patrick spend in exercise classes last week and this week? Responses A 6 1 hours 26 1 hours 2 B 3 1 hours 43 1 hours 4 C 6 1 hours 46 1 hours 4 D 8 1 hours 2
Answer:
Monday class is 1 3 hours and the Friday class is 1 1 hours. 4 2Patrick attended both exe
Step-by-step explanation:
Set up an equation and use it to solve for x.
50
(4x + 2)
Answer:
x = 12
Step-by-step explanation:
Vertical angles are congruent
50 = 4x + 2 Subtract 2 from both sides
48 = 4x Divide both sides by 4
12 = x
Trevor is baking cookies for a fundraiser. Each batch 1 of cookies requires 2 g cups of flour. If Trevor has 12.75 cups of flour, how many batches of cookies can he make?
If Ax + By = Cz
If A, B, C, x, y, and z are all positive integers then A, B, and C should all have a common prime factor.
A common prime factor means that each of the numbers needs to be divisible by the same prime number. So 15, 10, and 5 all have a common prime factor of 5 (they're all divisible by the prime number 5).
So far, so simple, and it looks like something you would have solved in high school algebra.
But here's the problem. Mathematicians haven't ever been able to solve the Beale conjecture, with x, y, and z all being greater than 2.
For example, let's use our numbers with the common prime factor of 5 from before….
51 + 101 = 151
but
52 + 102 ≠ 152
Answer: the common number is 8 for 151 and 152
Step-by-step explanation: hope this helps
what is the slope of the line
the slope would be -8/3. you go 8 down and 3 to the right.
how do you find the radius of a circle when given the central angle and arc length
arc length = 82 central angle = 135 degrees
The radius of a circle is determined as 27.95 units.
What is relation between arc and radius of circle?The arc length formula for a circle is times the radius of a circle. The arc length formula in radians is as follows: arc length = θ × r, where is in radian.Now the formula for the arc length when the central angle is given in the degrees;
arc length = (θ/360°)×(2πr)
Where, r is the radius of the circle and π = 3.14.
Write the formula for r;
r = (arc length/2π)×(360°/θ)
For the given values in question;
arc length = 82 central angle = 135 degrees.
r = (82/2×3.14)×(360°/135°)
r = (13.05)×(2.67)
r = 27.95
Therefore, the radius of the circle is found as 27.95 units.
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5. A shark is swimming 60 feet below the surface of
the ocean. There is a fish that is 25 feet deeper
in the water. Use the expression (-60) + (-25) to
describe the fish's location relative to the surface
of the ocean.
Answer:
-60x+(-85y)
Step-by-step explanation:
I need to find out if this is a horizontal or vertical compression/stretch and by what factor and also if it is a vertical, up or down, or horizontal, left to right, translation -4f(x)
The transformation rule f(x) → - 4 · f(x) is the consequence of combining a reflection about the x-axis and a vertical stretch.
What kind of rigid transformation is behind a transformation rule?
According to the statement, we must conclude what kind of rigid transformations are behind the transformation rule f(x) → - 4 · f(x). Rigid transformations are transformations applied on a function such that its form is not altered. The most common transformations are listed below:
Horizontal translation: f(x) → f(x - k), right when k > 0.Vertical translation: f(x) → f(x) + k, up when k > 0.Horizontal compression: f(x) → f(k · x), 0 < k < 1Horizontal stretch: f(x) → f(k · x), k > 1Vertical compression: f(x) → k · f(x), 0 < k < 1Vertical stretch: f(x) → k · f(x), k > 1Reflection about the x-axis: f(x) → - f(x)Reflection about the y-axis: f(x) → f(- x)Then, we find that the transformation rule f(x) → - 4 · f(x) is the consequence of combining a reflection about the x-axis and a vertical stretch.
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Multiply or divide. State any restrictions on the variables.
x²+3 x-10 / x²+4 x-12 . 3x+18 / x+3
The required simplification of rational expression is 3(x + 5) / (x + 3).
What is a rational number?
Any real number that can be represented in the form of p/q, where q is not equal to 0 is called a rational number. The decimal expansion of rational numbers is terminating and repeating.
Simplifying the rational expression: x² + 3x - 10 / x² + 4x - 12 . 3x + 18 / x + 3
Given a rational expression,
x² + 3x - 10 / x² + 4x - 12 . 3x + 18 / x + 3
On simplifying, we get,
(x² + 3x - 10).(3x + 18) / (x² + 4x - 12).(x + 3)
For numerator, (x² + 3x - 10).(3x + 18), we have,
= 3(x + 5)(x - 2)(x + 6)
For denominator, (x² + 4x - 12).(x + 3)
= (x + 6)(x - 2)(x + 3)
Now, (x² + 3x - 10).(3x + 18) / (x² + 4x - 12).(x + 3) = 3(x + 5)(x - 2)(x + 6) / (x + 6)(x - 2)(x + 3)
= 3(x + 5) / (x + 3)
The restrictionto the given rational expression is that the denominator, x + 3 should not be 0.
Hence, the required simplification of rational expression is 3(x + 5) / (x + 3).
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Find the largest prime divisor of $15^6 - 7^6$
The largest prime divisor of the expression [tex]15^{6} - 7^{6}[/tex] is 379.
Here, we are given an expression: 15^6 - 746
This can be written as-
[tex][15^{3}] ^{2} - [7^{3}] ^{2}[/tex]
now, using the property [tex]a^{2} -b^{2}[/tex] = (a + b)(a - b), we get-
[tex][15^{3}] ^{2} - [7^{3}] ^{2}[/tex]
= [tex](15^{3} +7^{3}) (15^{3} -7^{3})[/tex]
= (3375 + 343) (3375 - 343)
= 3718 × 3032
Now, here the factors of 3718 will be
3718 = 2 x 11 x 13 x 13
Here, the largest prime factor we find is 13
Similarly, the factors of 3032 will be
3302 = 2 * 2 * 2 * 379
Here, the largest prime factor we find is 379
Thus, the largest prime divisor (factor) of the given expression is 379.
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Solve the math answer
Answer:
X = 40
Step-by-step explanation:
X/5 = 8
Multiply each side by 5 to solve for x
X/5 * 5 = 8*5
X = 40
What is the answer(Also if you can please wright how you did it):)
Step-by-step explanation:
the answer to what question ?
is the request to find (solve for) x ?
if so, we have
(-3(2x - 6) + 5x)/6 = 7 + (2(-4x + 1) - 6)/3
now, I usually remove the fractions first by multiplying both sides with both denominators :
1. multiply by 6
-3(2x - 6) + 5x = 42 + 6(2(-4x + 1) - 6)/3
2. I can skip the general multiplication by 3, because the denominator 3 goes away in interaction with the new factor 6
-3(2x - 6) + 5x = 42 + 2(2(-4x + 1) - 6)
now, we do all the multiplications and see what we get :
-6x + 18 + 5x = 42 + 2(-8x + 2 - 6) =
= 42 - 16x + 4 - 12
-x + 18 = -16x + 34
15x = 16
x = 16/15
A rectangle with length 10 inches and width 5 inches. A triangle sits on top of the rectangle. The triangle has a base of 10 inches and height of 3 inches.
What is the area of the figure shown?
in²
Solve each equation by factoring. Check your answers.
4 x²+11 x+6=0
The factors of given equation are -3/4 and -2.
Rewriting the equation -
4x² + 11x + 6 = 0
The factors for the given expression will be calculated based on two factors -
1. The sum of factors should be equal to sum of numeral value of b (11 in this case)
2. The product of factors should be equal to product of numeral values of a and c (24 in this case)
As per the above rules, the appropriate factors should be 8 and 3.
Rewriting the given equation with possible factors -
4x² + 8x + 3x + 6 = 0
Taking common values
4x(x + 2) +3(x + 2) = 0
(x + 2) (4x + 3) = 0
x = -3/4, -2
Thus, the factors of given expression are -3/4 and -2.
To check the correctness of factors, we will keep each value of x in equation.
When x = -3/4
4x² + 11x + 6 = 0
4(-3/4) + 11(-3/4) + 6 = 0
9/4 -33/4 + 6 = 0
9/4 = 2.25 and 33/4 = 8.25
2.25 - 8.25 + 6 = 0
-6 + 6 = 0
0 = 0
When x = -2
4x² + 11x + 6 = 0
4(-2)² + 11(-2) + 6 = 0
16 - 22 + 6 = 0
22 - 22 = 0
0 = 0
Since both values of x give 0 on both sides of equation, the factors of equation are correct.
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solve [(6 + 2) · 5 + 4] ÷ 2 – 3 and 6 + 2 · 5 + 4 ÷ 2 – 3
Answer:
dot = times
Step-by-step explanation:
[(6 + 2) · 5 + 4] ÷ 2 – 3 and 6 + 2 · 5 + 4 ÷ 2 – 3
[(8) × 5 + 4] ÷ 2 – 3
[(8) x 9 ] ÷ 2 – 3
([ 72 ] ÷ 2 )– 3
36 -3
33
6 + 2 x 5 + (4 ÷ 2 )– 3
6 +( 2 × 5 )+ 2 – 3
(6 + 10) + 2 – 3
(16 + 2)- 3
18 -3
15
Answer:
[(6 + 2) * 5 + 4] / 2 - 3 = 19
6 + 2 * 5 + 4 / 2 - 3 = 15
Step-by-step explanation:
1.
[8 * 5 +4] / 2 - 3
You get the number 8 by adding 6 and 2 in the parentheses then rewriting the equation.
[40 + 4] / 2 -3
You get 40 by multiplying 8 and 5 then rewriting the equation.
44 / 2 - 3
44 by adding 40 and 4; rewrite the equation.
Divide 44 by 2, which would equal 22
The equation should look like : 22 - 3
Which equals 19
2.
6 + 10 + 4 / 2 - 3
You get 10 by multiplying 2 and 5 together; and rewriting the equation.
6 + 10 + 2 - 3
You get 2 by dividing 4 and 2; rewrite the equation.
18 - 3
You get 18 by adding 6, 10, and 2
Lastly you subtract 3 to 18
Which equals 15
Hope this helps!
--Blu
Use the properties of logarithms to evaluate each expression. 2 log 5+ log 40
The result obtained for the logarithms expression 2 log 5+ log 40 is 3.
What are the logarithmic functions defined as?The logarithm of a number is the exponent by which a fixed value recognized as the base must be raised in attempt to calculate that number. Because 1000 is ten to the third power, this same log of 1000 to base ten is three.
There is no such thing as a y-intercept.x = 0 is a vertical asymptote. *Note: An asymptote is a line that a graph reaches as absolute value of x as well as y increases.A logarithmic function has no horizontal asymptote.The value of the x-intercept is one.The function is spreading throughout the domain.If the base is between 0 and 1, the function reduces out over the domain.Some rules of the logarithmic functions are-
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xnow, the given expression to be evaluated is;
= 2 log 5+ log 40
Apply the Power Rule in the first term;
= log 5²+ log 40
= log 25+ log 40
Now, using the Product Rule, the expression becomes.
= log (25×40)
= log (1000)
If the base is taken as 10, then the value of the log (1000) = 3.
Therefore, the obtained value of the value of the logarithms expression 2 log 5+ log 40 is 3.
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Seven more than the product of a number 2 and 6 equals
Hence , numerical expressions for seven more than the product of a number 2 and 6 equals to 13 .
The term numerical expression is created of 2 words, numerical which means numbers, and expression which means phrase. Thus, it's a phrase involving numbers.A numerical expression in arithmetic are often a mix of numbers, and integers combined exploitation mathematical operators like addition, subtraction, multiplication, or division.It is given that product of a number 2 and 6.
On multiplying 2 and 6 , we get
2 × 3 = 6
It is given that seven more than the product of a number 2 and 6 which means that we have to add 7 in the product of a number 2 and 6 which is given by 7 + 6 = 13
Hence , the value of the given statement is 13 .
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Annie can mow 1/6 of an acre in 50
minutes. how many acres can she mow
per hour?
If Annie can mow 1/6 of an acre in 50 minutes, then in an hour, she can mow 1/5 of an acre.
How many acres can Annie mow per hour?Given the data in the question;
Annie can mow 1/6 of an acre in 50 minuteshow many acres can she mow per hour?Let x represent the number of acres that Annie can mow in hour.
Also convert 1 hour to minutes
1 hour = (1 × 60)min = 60min
Annie can mow 1/6 of an acre in 50 minutes
Annie can mow x of an acre in 60 minutes
Hence;
1/6 × 60 = x × 50
60/6 = 50x
50x = 60/6
50x = 10
x = 10/50
x = 1/5
If Annie can mow 1/6 of an acre in 50 minutes, then in an hour, she can mow 1/5 of an acre.
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Determine whether each function is an example of exponential growth or decay. Then find the y -intercept.
y=7/8(18)x
The function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.
An exponential function is defined as y = a ˣ where x is a variable, and a is a constant called the base of the function.
We are given a function:
y = 7 / 8 ( 18 ) ˣ
We need to tell whether is is a exponential growth or decay function.
We can see that the value of a ˣ = (18) ˣ
So, the value of a = 18.
Since, it is an integer and not a fraction, its value will increase with the increase in exponent x.
So, it will be a exponential growth function.
Therefore, we get that, the function y = 7 / 8 ( 18 ) ˣ is an exponential growth function.
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I need the answer for this, thanks
Given the function, calculate the following values
Answer:
6, 2, 14
Step-by-step explanation:
[tex]x=-2 \implies x<1 \implies f(-2)=2(-2)^2-2=6 \\ \\ x=1 \implies 1 \leq x<2 \implies f(1)=2 \\ \\ x=2 \implies x \geq 1 \implies f(2)=4(2)^2-2=14[/tex]
Please help, I have a time limit on each question and its almost done
Answer:
B
Step-by-step explanation:
Solve the exponent first and thats the only remotely close answer
Which story problem could be solved using the given equation 1/5 x 2/3
Answer: 2/15
Step-by-step explanation:
I DON'T KNOW OK JUST A GUESS I JUST X THE FRACTIONS FOR YOU THE REST IS ON YOU HONEY
Kumi is 16 years old. His father is 44 years old. How many years ago was Kumi's father five times as old as KUMI
Answer:
9
Step-by-step explanation:
4-x = 5(16-x)
44-x = 80-5x
4x = 36
x = 9
Ken makes trail mix. the ratio of nuts to raisins is 3 to 4. find the amount of nuts used in trail mix that had 10 cups of raisins
The amount of nuts used in trail mix that had 10 cups of raisins will be 7.5 nuts.
How to calculate the value?From the information, Ken makes trail mix. the ratio of nuts to raisins is 3 to 4.
The amount of nuts used in trail mix that had 10 cups of raisins will be:
= 10 × 3/4
= 30/4
= 7.5
Therefore, the amount of nuts used in trail mix that had 10 cups of raisins will be 7.5 nuts.
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Write an equation in slope-intercept form of the line that bisects the angle formed by BA and BC
B
v=D
y = -x +2 an equation in slope-intercept form of the line that bisects the angle.
What exactly does slope intercept mean?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.Given:
Angled formed by ray BA and ray BC is 90 degrees.
To find:
The equation of line that bisects the angle formed by ray BA and ray BC.
If a line bisects the angle formed by ray BA and ray BC, then it must be passes through point B and makes angles of 45 degrees with ray BA and ray BC.
It is possible if the line passes though point B(-1,3) and other point (-2,4).
Equation of line is
y - y₁ = y₂ - y₁/x₂ - x₁ ( x - x₁)
y - 3 = 4 - 3 / - 2 - ( -1) ( x - ( -1)
y - 3 = 1/-1 ( x + 1 )
y - 3 = -x -1
Add 3 on both sides
y = -x -1 + 3
y = -x +2
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what is 60:48 in the simplest form
Answer:
reduce a fraction to its simplest form, we divide both numerator and denominator by their GCF. 48 / 60 ÷ 12 / 12 = 4 / 5.
hope it helps.....
Answer:
5:4
Step-by-step explanation:
If both are even, I usually like to divide both the numerator and the denominator by 2 until I can no longer do so (meaning, dividing either of them by 2 would result in a fraction). This is, of course, if you cannot think of the greatest common factor off the top of your head.
[tex]\frac{60}{48} \to \frac{30}{24} \to \frac{15}{12}[/tex]
We cannot divide by 2 anymore, however, it is a lot simpler to detect now that we can divide by 3.
[tex]\frac{15}{12} \to \frac{5}{4}[/tex]