write an equation of a line passing through the point (-6,-3) and perpendicular to JK with J (-2, -7) and K (6,5)
Answers
EXPLANATION
Given the point: (-6,-3) and the vector JK with J=(-2,-7) K=(6,5)
First we need to the slope of the vector applying the slope formula:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing the ordered pairs J=(-2,-7) and K=(6,5) give us the slope:
[tex]\text{Slope}=\frac{(5-(-7))}{(6-(-2))}=\frac{12}{8}=\frac{3}{2}[/tex]Now, we have the slope and we can use this to find the line that contains the point (-6, -3) applying the generic form:
y= -2x/3 + b where -2/3 is the negative and reciprocal slope perpendicular to the vector JK.
Finally, replacing the point (-6,-3) give us the y-intercept, b,
-3 = -2(-6)/3 + b
Multiplying terms:
-3 = 12/3 + b ---> -3 = 4 + b
Subtracting 4 to both sides:
-3 - 4 = b
Switching sides:
b= -7
The linear equation is y = (-2/3)x - 7 OPTION B
Related Questions
You want to enlarge a picture by a factor of 4.5 from its current size of 4 inches by 6 inches. What is the size of the enlarged picture?a. 18 in. by 27 in.b.8.5 in. by 10.5 in.c. 18 in. by 10.5 in.d. 8.5 in. by 27 in.
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If we want to enlarge the picture by a factor of 4.5, the perimeter will also increase by the factor of 4.
[tex]\begin{gathered} \text{New dimension =}4.5\text{ (old dimension)} \\ \text{New dimension=4.5 (4 by 6)} \\ \text{New dimension=18 inches by 27 inches} \end{gathered}[/tex]Hence, the correct option is Option A
x to the 9th power times x to the 5 power
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Dr. Wells saw 960 patients last year. This year, the number of patients he saw was 25%higher. How many patients did Dr. Wells see this year?
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.Since the old number of patients is 960
Since it is increasing by 25%, then
We will find the amount of 25% of 960, then add it to 960
[tex]\begin{gathered} I=\frac{25}{100}\times960 \\ I=240 \end{gathered}[/tex]Add it to 960 to find the new number of patients
[tex]\begin{gathered} N=960+240 \\ N=1200 \end{gathered}[/tex]Dr Wells saw 1200 patients
Sketch one cycle of the graph of each function 16. y= -2 sin 8x
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Answer:
• Amplitude = 2
,• Period = π/4
Explanation:
Given the function:
[tex]y=-2\sin(8x)[/tex]In order to sketch the graph of y, we need to find its amplitude and period.
Comparing the function with the general sine function:
[tex]y=a\sin(bx+c)+d[/tex]We have that:
[tex]\begin{gathered} Amplitude=|a|=|-2|=2 \\ Period=\frac{2\pi}{|b|}=\frac{2\pi}{8}=\frac{1}{4}\pi \end{gathered}[/tex]Next, using these values, we sketch one cycle of the graph below:
Val measures the diameter of a ball as 14 inches. How many cubic inches of air does this ball hold, to thenearest tenth? Use 3.14 forn.The ball holds aboutcubic inches of air.
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we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]In this problem we have
r=14/2=7 in ----> the radius is half the diameter
pi=3.14
substitute the given values
[tex]\begin{gathered} V=\frac{4}{3}_{}\cdot(3.14)\cdot(7^3) \\ V=1,436.0\text{ in\textasciicircum{}3} \end{gathered}[/tex]answer is 1,436.0 cubic inches5.Find the measures of themissing side of the righttriangle usingPythagorean Theoremequation.106K
Answers
Pythagoras Theorem:
In a right angle triangle, the sum of square of base and perpendicular is equal to the square of Hypotenuse .
Hypotenuse² = Perpendicular² + base²
In the given figure, we have:
Base = k
Hypotenuse = 10
Perpendicular = 6
Substitute the valus and solve for k,
[tex]\begin{gathered} \text{Hypotenuse}^2=Perpendicular^2+Base^2 \\ 10^2=6^2+k^2 \\ 100=36+k^2 \\ k^2=100-36 \\ k^2=64 \\ k=\sqrt[]{64} \\ k=8 \\ \text{Base, k = 8} \end{gathered}[/tex]The missing side is 8
Answer: 8
Find from first principles the derivative of f:x maps to (x+2)all squared
Answers
Given:
[tex]f(x)=(x+2)^2[/tex]Required:
To find the first principles
Explanation:
First principle,
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}[/tex][tex]=\lim_{h\to0}\frac{(x+h+2)^2-(x+2)^2}{h}[/tex][tex]=\lim_{h\to0}\frac{x^2+(h+2)^2+2x(h+2)-x^2-4-4x}{h}[/tex][tex]=\lim_{h\to0}\frac{h^2+4+4h+2xh+4x-4-4x}{h}[/tex][tex]\begin{gathered} =\lim_{h\to0}\frac{h^2+4h+2xh}{h} \\ \\ =\lim_{h\to0}\frac{h(h+4+2x)}{h} \\ \\ =\lim_{h\to0}(h+4+2x) \\ =2x+4 \end{gathered}[/tex]Final Answer:
[tex]2x+4[/tex]Calculating number of periods?How long will an initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest?
Answers
For an initial amount P with an annually compounded interest rate r, after t years the total amount A is is given by:
[tex]A=P(1+r)^t[/tex]Then we have:
[tex]\begin{gathered} \frac{A}{P}=(1+r)^t \\ \ln\frac{A}{P}=t\ln(1+r) \\ t=\frac{\ln\frac{A}{P}}{ln(1+r)} \end{gathered}[/tex]For P = $10,000, A = $23,750 and r = 0.05, we have:
[tex]t=\frac{\ln\frac{23750}{10000}}{\ln(1+0.05)}\approx17.73\text{ years}[/tex]Triangle MNO was reflected over the x-axis Given M(-5,-1)Find the coordinate M
Answers
When we perform the reflection of a figure over the x-axis, we just have to change the sign of the y-coordinate of each point, like this: P(x,y) -> P'(x,-y).
Then after a reflection of the triangle, the point M goes from (-5,-1) to (-5, 1)
Then the correct answer is the last option (-5, 1)
I need help with this question please. This is non graded.
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To determine the factor of the given polynomial, first, we rewrite it as follows:
[tex](16x^2+4x)+(-20x-5).[/tex]Now, notice that:
[tex]\begin{gathered} 16x^2+4x=4x(4x^+1), \\ -20x-5=-5(4x+1). \end{gathered}[/tex]Factoring out the 4x+1, we get:
[tex](16x^2+4x)+(-20x-5)=(4x-5)(4x+1).[/tex]Answer: [tex](4x+1).[/tex]The length of your step is 34 inches (in.). If you walk 10,000 steps in a day, how many feet (ft.) will you walk? ?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
step length = 34 inches
walking = 10000 steps
Step 02:
feet to inches
1 feet = 12 inches
1 step --------------- 34 inches
10000 steps ------- x
1 * x = 10000 * 34
x = 340000
340000 inches * ( 1 feet / 12 inches)
28333.33 feet
The answer is:
You will walk 28333.33 feet .
Round $43,569.14 the nearest dollar
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To find:
Round $43,569.14 the nearest dollar
Solution:
The number after the decimal is less than 50. So, the amount $43,569.14 rounded to the nearest dollar is $43,569.
Thus, the answer is $43569.
Write an equation to find the necessary score on the final exam for a student to earn an A (90%) in the class.
Answers
For the given table:
We will find the necessary score on the final exam for a student to earn an A (90%) in the class.
so,
The equation will be:
[tex]92\cdot(0.2)+95\cdot(0.3)+88\cdot(0.2)+x\cdot(0.3)=90[/tex]now, solve the equation to find x:
[tex]\begin{gathered} 64.5+0.3x=90 \\ 0.3x=90-64.5 \\ 0.3x=25.5 \\ x=\frac{25.5}{0.3} \\ \\ x=85 \end{gathered}[/tex]So, the answer will be:
The student needs a score of 85% on the final exam to earn a 90%
When 27 is subtracted from the square of anumber, the result is 6 times the number. Findthe negative solution.
Answers
Given: A statement, "When 27 is subtracted from the square of a
number, the result is 6 times the number."
Required: To determine the number.
Explanation: Let the number be x. Then according to the question-
[tex]x^2-27=6x[/tex]Rearranging the equation as -
[tex]x^2-6x-27=0[/tex]The quadratic equation can be simplified as follows-
[tex]\begin{gathered} x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x+3)(x-9)=0 \\ x=-3\text{ or }x=9 \end{gathered}[/tex]Final Answer: The negative solution is-
[tex]x=-3[/tex]Please see the picture below. Indeed help with parts of the question
Answers
Given
[tex]\frac{(x-4)^2}{4}-\frac{y^2}{9}=1[/tex]Find
Values of a and b for this conic section
Explanation
As we know the standard equation for conic section is given by
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]where (h , k) be the vertex
vertices (h+a , k) and (h-a , k)
given equation can be rewrite as
[tex]\frac{(x-4)^2}{2^2}-\frac{y^2}{3^2}=1[/tex]on comparing , we get
a = 2 and b = 3
Final Answer
Therefore , the value of a = 2 and b = 3
this temperature to Fahrenheil. 1.3 If 1 cm'- 1 ml and 1 000 cm -1 4. Determine the following: 1.3.1 How many cm' are in 875 ? 1.3.2 How many t are there in 35,853 cm'?
Answers
We will solve it as follows:
1.3.1: We transform liters to cubic centimeters:
[tex]x=\frac{875\cdot1000}{1}\Rightarrow x=875000[/tex]So, there are 875 000 cubic centimeters.
1.3.2: We transfrom cubic centimenters into liters:
[tex]x=\frac{1\cdot35853}{1000}\Rightarrow x=35.853[/tex]So, there are 35.853 liters.
The size of a population of bacteria is modeledby the function P, where P(t) gives thenumber of bacteria and t gives the number ofhours after midnight for 0 < t < 10. Thegraph of the function P and the line tangent toP at t= 8 are shown above. Which of thefollowing gives the best estimate for theinstantaneous rate of change of P at t = 8?
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Answer: The graph of the P(t) has been provided, we have to find the instantaneous slope of P(t) at t = 8:
[tex]Slope=m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore we need two y values and two x values, which can be obtained as follows:
[tex]\begin{gathered} t=8 \\ \\ \therefore\Rightarrow \\ \\ x_1=t_1=8-0.1=7.9 \\ \\ y_1=P(t_1)=P(7.9) \\ \\ x_2=t_2=8+0.1=8.1 \\ \\ y_2=P(t_2)=P(8.1) \\ \\ \therefore\rightarrow \\ \\ Slope=\frac{P(8.1)-P(7.9)}{t_2-t_1}\rightarrow(1) \\ \end{gathered}[/tex]Equation (1) corresponds to the third, option, therefore that is the answer.
What is the equation of the line that passes through the given points (2,3) and (2,5)
Answers
Solution:
The equation of a line that passes through two points is expressed as
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ where \\ (x_1,y_1)\text{ and} \\ (x_2,y_2)\text{ are the coordinates of the points } \\ through\text{ which the line passes} \end{gathered}[/tex]Given that the line passes through the points (2,3) and (2, 5), this implies that
[tex]\begin{gathered} x_1=2 \\ y_1=3 \\ x_2=2 \\ y_2=5 \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} y-3=\frac{5-3}{2-2}(x-2) \\ \Rightarrow y-3=\frac{2}{0}(x-2) \\ multiply\text{ through by zero} \\ 0(y-3)=2(x-2) \\ \Rightarrow0=2x-4 \\ add\text{ 4 to both sides} \\ 0+4=2x-4+4 \\ \Rightarrow4=2x \\ divide\text{ both sides by the coefficient of x, which is 2} \\ \frac{4}{2}=\frac{2x}{2} \\ \Rightarrow x=2 \\ \end{gathered}[/tex]Hence, the equation of the line that passes through the given points (2,3) and (2,5) is
[tex]x=2[/tex]Solve the system of equations 2x - 3y = 4 and 9x - 8y = - 26 by combining the
equations.
Answers
[tex]\sf \Large \boxed{\sf +}\\ \sf \Large \boxed{\sf +}\\\\ \sf \Large \boxed{\sf 11x+-11y=-22}\\\\ 2x+9x-3y-8y=4-26\\Combine\\11x-11y=-22\\Simplify\\x-y=-2\\x=y-2\\Plug\ the\ value\ in\ the\ equation\\2(y-2)-3y=4\\2y-4-3y=4\\-y-4=4\\-y=8\\y=-8\\Solve\ for\ x\\9x-8(-8)=-26\\9x+64=-26\\9x=-90\\x=-10[/tex]
A researcher wants to study the amount of protein in pet food. Which one of the following is most likely to give theresearcher more accurate results?-take a sample of cat foods alone-take a sample of dog foods alone-take a sample of all pet foods mixed together-divide the pet foods into two different groups, cat and dog, and take a sample from each group
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He will need to take sample of at least two different sample of pet food in order to analyze it more accurate. So, the researcher should:
divide the pet foods into two different groups, cat and dog, and take a sample from each group.
need answer with steps[tex]( - 3 - 5i) + (4 - 2i)[/tex][tex](7 + 9i) + ( - 5i)[/tex]
Answers
We are given the following complex numbers
[tex](-3-5i)+(4-2i)[/tex]To perform the addition of the complex numbers, simply add the like terms together.
[tex](-3-5i)+(4-2i)=(-3+4)+(-5i-2i)=(1-7i)[/tex]Similarly,
[tex](7+9i)+(-5i)=\mleft(7\mright)+\mleft(9i-5i\mright)=(7+4i)_{}[/tex]Therefore, the result of the complex addition is
[tex]\begin{gathered} 19.\: (1-7i) \\ 20.\: (7+4i) \end{gathered}[/tex]A fence is purchased and constructed as shown. There are 250 feet of fence used for the chorale. Determine the values for x and y that will maximize the area. Round your answers to the nearest tenth if needed. Type the value for the x dimension in the first blank (you do not need to type x = , but label your answer). Type the value for y in the second blank (you do not need to type y =, but label your answer).
Answers
2x + 3y = 250
y = (250 - 2x)/3 (1)
S = x * y
= (-2/3x + 250/3)*x
= -2/3(x - 125/2)^2 + 125^2/6
x = 125/2
Replacing the value of x in (1)
y = 125/3
In a direct variation, y = 18 when x = 6. Write a direct variation equation that shows therelationship between x and yWrite your answer as an equation with y first, followed by an equals signSubmit
Answers
40 model A cars were sold that week. what else can you say about this bar model?
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From the diagram
Ratio of model A car to model B car = 4:6
Ratio of model A to model B = 4:6
Ratio of model B to model A = 6:4
Ratio of model A to total = 4:10
Ratio of model B to total = 6:10
If 40 model A cars sold
I know that 60 model B cars was sold.
What's the sum of ten terms of a finite arithmetic series if the first term is 13 and the last term is 89?
Answers
The sum of the n first terms in an arithmetic series is given by the following formula
[tex]S_n=n\cdot(\frac{a_1+a_n}{2})[/tex]Where a_1 represents the first term, a_n represents the n-th term, and n the amount of terms we want to sum.
The first term of our sequence is 13, the tenth term is 89 and the amount of terms is 10. Plugging those values in our formula, we have
[tex]S_{10}=10\cdot(\frac{13+89}{2})=10\cdot51=510[/tex]This sum is equal to 510.
I need to solve this problem and name the concepts used in the problem
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In a pie chart, the sum of the angles for each variable or item is 360 degrees. also, the total percentage is 100
Looking at each flavor,
27% chose Glazier freeze, = 27/100 * 360 = 97.2 degrees
25% chose Fierce grape = 25/100 * 360 = 90 degrees
15.5% chose Extreme Citrico = 15.5/100 * 360 = 55.8 degrees
13.5% chose Cool Blue = 13.5/100 * 360 = 48.6 degrees
11.5% chose Lemon ice = 11.5/100 * 360 = 41.4
We want to determine the degrees for others
Therefore,
97.2 + 90 + 55.8 + 48.6 + 41.4 + others = 360
333 + others = 360
others = 360 - 333
others = 27 degrees
The correct option is C
The concept used is converting the given percentages to degrees and equation them to 360 degrees
100% is equivalent to 360 degrees
A principal of S2400 is invested at 8.75% interest compounded annually How much will the investment be worth after 7 years?
Answers
Explanation
The question wants us to determine the amount $2400 will yield after 7 years if compounded annually at a rate of 8.75%
To do so, we will use the formula:
[tex]\begin{gathered} A=P(1+r)^t \\ where \\ P=\text{ \$2400} \\ r=8.75\text{ \%=}\frac{8.75}{100}=0.0875 \\ t=7 \end{gathered}[/tex]Thus, if we substitute the values above we will have
[tex]\begin{gathered} A=\text{ \$}2400(1+0.0875)^7 \\ A=\text{ }\$2400\lparen1.0875\rparen^7 \\ A=\text{ \$2400}\times1.79889 \\ A=\text{ \$4317.34} \end{gathered}[/tex]Therefore, after 7 years, the investment will be worth $4317.34
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 11z
Answers
Answer:
smaller x value: -1,-8larger x value: 5,16The parenthesis part is already taken care of by the teacher.
=================================================
Explanation:
y is equal to x^2-9 and also 4x-4. We can equate those two right hand sides and get everything to one side like this
x^2-9 = 4x-4
x^2-9-4x+4 = 0
x^2-4x-5 = 0
Then we can use the quadratic formula to solve that equation for x.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-5)}}{2(1)}\\\\x = \frac{4\pm\sqrt{36}}{2}\\\\x = \frac{4\pm6}{2}\\\\x = \frac{4+6}{2} \ \text{ or } \ x = \frac{4-6}{2}\\\\x = \frac{10}{2} \ \text{ or } \ x = \frac{-2}{2}\\\\x = 5 \ \text{ or } \ x = -1\\\\[/tex]
Or alternatively
x^2-4x-5 = 0
(x-5)(x+1) = 0
x-5 = 0 or x+1 = 0
x = 5 or x = -1
------------------------------
After determining the x values, plug them into either original equation to find the paired y value.
Let's plug x = 5 into the first equation:
y = x^2-9
y = 5^2-9
y = 25-9
y = 16
Or you could pick the second equation:
y = 4x-4
y = 4(5)-4
y = 20-4
y = 16
We have x = 5 lead to y = 16
One solution is (x,y) = (5,16)
This is one point where the two curves y = x^2-9 and y = 4x-4 intersect.
If you repeat the same steps with x = -1, then you should find that y = -8 for either equation.
The other solution is (x,y) = (-1,-8)
Answer:
[tex](x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x^2-9\\y=4x-4\end{cases}[/tex]
To solve by the method of substitution, substitute the first equation into the second equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x+1=0 \implies x=-1[/tex]
[tex]\implies x-5=0 \implies x=5[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}[/tex]
[tex]\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
If the ones digit in a two-digit number is even, the number is a composite number. Which odd ones digit also tells you the number must be a compositenumber? Explain.
Answers
Okay, here we have this:
Considering that a composite number is a number that is not prime, the only number one of the units that tells us that a two-digit number is composed is 5, since every number ending in 5 is a multiple of 5.
show that the triangles are similar by measuring the lengths of their sides and comparing the ratios of their corresponding sides
Answers
ANSWER
EXPLANATION
The ratio between corresponding sides of similar triangles is constant - in other words, the ratio between each pair of corresponding sides gives the same value.
As shown in the questions, the ratios between corresponding sides are,
[tex]\begin{gathered} \frac{DE}{AB}=\frac{3}{2}=1.5 \\ \frac{DF}{AC}=\frac{1.5}{1}=1.5 \\ \frac{EF}{BC}=\frac{2.4}{1.6}=1.5 \end{gathered}[/tex]Since the three ratios between corresponding sides are the same, 1.5, the triangles are similar.