The rule of the slope of a line has 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)
We will take the altitude from A to the opposite side of BC
Then we will find the slope of BC first
x1 = 3 and y1 = 4. point B
x2 = -2 and y2 = 6. point C
We will substitute them in the rule above
[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]The slope of BC = -2/5
Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2
[tex]m_{\perp}=\frac{5}{2}[/tex]The form of the equation in point-slope is
y - y1 = m(x - x1)
m = 5/2
Since point A is lying on the altitude from A to BC, then
x1 = 1 and y1 = -2 point A
Substitute m and coordinates of point A in the form of the equation above
y - (-2) = 5/2 (x - 1)
[tex]y+2=\frac{5}{2}(x-1)[/tex]The equation of the altitude from A to BC is
y + 2 = 5/2 (x - 1)
please write the value of x and the equation used.
Zachary pays $68 per month and $5 per months for gigabytes
X be the number of gifabytes
SO, price of x gigabytes = 5x
total budget = 5x + Amount paid :
So, y = 5x + 68
Answer: y = 5x + 68
Determine the end (long run) behavior for: f(x)=−2(x−1)3(x+2)2
The end behavior of the function f(x) = −2(x−1) * 3(x+2) * 2 is
as x tends to ∞, f(x) tends to -∞as x tends to -∞, f(x) tends to -∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behaviorThe given function is:
f(x) = −2(x−1) * 3(x+2) * 2
The given function is first expanded
= −2(x−1) * 3(x+2) * 2
= (-2x + 2) * (3x + 6) * 2
= (-4x + 4) * (3x + 6)
= -12x² - 36x + 24
The end behavior is determined by the leading term = -12x²and it is described as
x ⇒ ∞ f(x) ⇒ -∞
x ⇒ -∞ f(x) ⇒ -∞
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Pls help me answer these 2 questions
Answer:
Step-by-step explanation:
A = 1 plus negatives out be minusing positive
B= -8 minus negatives would be nega tive plus negatives
rules
If you love to love your a lover
if you hate to hate your a lover
if you love to have ur a hater
if you hate to love ur a hater
this all relates to positive and negative addition and subtraction
Answer:
4+(-3) = 1
-6-2= -8
Step-by-step explanation:
Same sign add
Different sign subtract
Keep the sign of the bigger number
A kitten weighs 5 pounds what is the kilograms
Nelson, this is the solution:
Let's recall that 1 pound = 0.4536 kg, therefore:
• 5 pounds = 0.4536 * 5
,• 5 pounds = 2.268 kilograms
How to go from radians to degrees
Answer:
Recall that:
[tex]360^{\circ}=2\pi\text{ radians.}[/tex]Therefore:
[tex]1^{\circ}=\frac{2\pi}{360}radians,[/tex]or
[tex]1\text{ radian=}\frac{360^{\circ}}{2\pi}degrees.[/tex]Wich is an example of multiplicative identityA. a×1=aB. a+0=aC. a+(-a)=0orD. a×1/a=1
Multiplicative Identity:
The multiplicative identity property states that if a number is multiplied by 1, the result is that number.
Examples:
[tex]\begin{gathered} a\times1=a \\ 5\times1=5 \\ 20\times1=20 \\ y\times1=y \end{gathered}[/tex]Therefore, the example of multiplicative identity is option A
[tex]a\times1=a[/tex]Simplify using exponent B-³
Answer:
B^-3
1/B³
Step-by-step explanation:
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A pair of linear equations is shown:
y = −3x + 5
y = x + 2
Which of the following statements best explains the steps to solve the pair of equations graphically?
On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2.
On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1.
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
The graph that shows the solution to the pair of linear equations is shown below. The best explanation for the step to take is: A. the first line is the red line while the second line is the blue line.
How to Solve a Pair of Linear Equations Graphically?To find the solution to a pair of linear equations using a graph, plot the given equations on a graph using their slopes and their y-intercepts.
The point where the two lines intersect is the solution to the pair of linear equations.
Given the linear equations:
y = −3x + 5
y = x + 2
The graph of y = -3x + 5 has a slope of -3 and a y-intercept of 5, while the graph of y = x + 2 has a slope of 1 and a y-intercept of 2.
The diagram that shows the graph where the two lines intersect at point (0.75, 2.75) is shown below.
The solution is: (0.75, 2.75)
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4 Which expressions represent the area of the triangle in square feet? Select all that apply. A. 48.9 B 16 +8719 D 16119 318319 E 16)(9) 1889)
Answer
Options B, C and D are correct.
Area = ½ × 14 × 9 = (14)(9) ÷ 2
Area = ½ (6 + 8) (9)
= ½ (6)(9) + ½ (8)(9)
= 63 ft²
Explanation
We are asked to pick out the options that give the area of the triangle.
To do that, we need to first note that the area of a triangle is given as
Area = ½ × Base × Height
For the triangle in the question
Base = 6 + 8 = 14 ft
Height = 9 ft.
So, the area of the triangle is
Area = ½ × Base × Height
Area = ½ × 14 × 9
We can then break this down for the two triangles in the one big triangle as
Area = ½ × 14 × 9 = (14)(9) ÷ 2
Area = ½ (6 + 8) (9)
= ½ (6)(9) + ½ (8)(9)
= 63 ft²
Hope this Helps!!!
Solve: x−6−−−−−√=x−6 . Enter the exact answers. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter.
ANSWER:
x = 6; 7
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{x-6}=x-6[/tex]We solve for x:
[tex]\begin{gathered} \left(\sqrt{x-6}\right)^2=\left(x-6\right)^2 \\ \\ x-6=x^2-12x+36 \\ \\ x^2-12x-x+36+6=0 \\ \\ x^2-13x+42=0 \\ \\ -13x=-6x-7x \\ \\ x^2-6x-7x+42=0 \\ \\ \left(x^2-6x\right)+\left(-7x+42\right)=0 \\ \\ x\left(x-6\right)-7\left(x-6\right) \\ \\ \left(x-6\right)\left(x-7\right)=0 \\ \\ x-6=0\rightarrow x=6 \\ \\ x-7=0\operatorname{\rightarrow}x=7 \\ \\ \text{ We check each solution, as follows:} \\ \\ \sqrt{6-6}=6-6\rightarrow0=0\rightarrow\text{ True} \\ \\ \sqrt{7-6}=7-6\rightarrow1=1\rightarrow\text{ True} \\ \\ \text{ Both solutions are correct therefore:} \\ \\ x=6;7 \end{gathered}[/tex]Please help with this word problem,Laurie, Moesha, and Carrie went to the mall. Laurie spent $20, Moesha spent $25, and Carrie spent $30. How many did they spend in all?
To determine how much they all spent we need to add the expenses of each person: Laurie, Moesha, and Carie. This is shown below:
[tex]\begin{gathered} \text{ total=Laurie+Moesha+Carrie} \\ \text{total}=20+25+30=75 \end{gathered}[/tex]They spent a total of $75.
I need help & I need to know what the equation is at the bottom too
Given the following question:
Filling a table of values is very simple when we are already given the values of x, so what we need to do to fill in the rest of the table for f(x) and g(x) is substitute x for each of the table values given for x.
To start off we are given 1 so we substitute 1 in for x in both f(x) and g(x) and solve.
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=1 \\ f(x)=6(1)+3 \\ 6\times1=6 \\ 6+3=9 \\ f(x)=9\text{ \lparen first table of values for f\lparen x\rparen\rparen} \\ g(x)=5x^2-x \\ 5(1)^2-x \\ 1^2=1 \\ 5\times1=5 \\ 5-1=4 \\ g(x)=4 \end{gathered}[/tex]Second table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=2 \\ f(x)=6(2)+3 \\ 6\times2=12 \\ 12+3=15 \\ f(x)=15 \\ g(x)=5(2)^2-2 \\ (2)^2=4 \\ 5\times4=20 \\ 20-2=18 \\ g(x)=18 \end{gathered}[/tex]Third table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=3 \\ f(x)=6(3)+3 \\ 6\times3=18+3=21 \\ f(x)=21 \\ g(x)=5(3)^2-3 \\ 3^2=9 \\ 5\times9=45 \\ 45-3=42 \\ g(x)=42 \end{gathered}[/tex]Final table of values:
[tex]\begin{gathered} f(x)=6x+3 \\ g(x)=5x^2-x \\ x=4 \\ f(x)=6(4)+3 \\ 6\times4=24 \\ 24+3=27 \\ f(x)=27 \\ g(x)=5(4)^2-4 \\ 4^2=16 \\ 5\times16=80 \\ 80-4=76 \\ g(x)=76 \end{gathered}[/tex]g(x)=5x^2-x eventually exceeds f(x) given the table of values.
True or false. 3|48,025
Find the area of the surface of a sphere of radius r, which is generated when rotating a semicircle centered at the origin, is rotated about its diameter.
The surface area of a sphere of radius r is
PEOPLE WHO ARE GOOD AT MATH CAN YOU PLEASE HELP ME!!!
The cost of using 19 HCF of water is $32.49
Given in the question:
The monthly cost (in dollars) of the water use (in dollars) is a linear function of the amount of water used (in hundreds of cubic feet, HCF)
The cost for using 17 HCF of water is using $32.13
and, the cost of using 35 HCF is $61.83.
To find the cost of using 19 HCF of water.
Now, According to the question:
The cost for using 17 HCF of water is $32.13
and, the cost of using 35 HCF is $61.83.
To find the slope:
(17, 32.13) and (35, 61.83)
Slope = (61.83 - 32.13)/ (35 - 17) = 1.65
We know that:
Formula of slope :
y = mx + b
32.13 = 1.65 x 17 + b
b = 1.14
The equation will be :
C(x) = 1.65x + 1.14
Now, To find the cost of using 19 HCF of water.
C(19) = 1.65 × 19 + 1.14
C(19) = $32.49
Hence, the cost of using 19 HCF of water is $32.49.
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Dillon went out for dinner with four friends. All had the same meal and dessert, except for Dillon who did not order the $5 dessert. The total bill came to $45. Write an equation to determine how much each of his friends paid for their meal.
The equation to determine each of his friends paid for their meal would be; 4x + x - 5 = 45.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that the Dillon and 4 friends went for dinner.
They all had the same meal except Dillion who did not order the 5 dollars dessert.
The Total bill paid = $45
Let the amount paid by each friend = x
Then Amount paid by dillion = x - 5
4x + x - 5 = 45
5x - 5 = 45
5x = 45 + 5
5x = 50
x = 10
Thus, the Amount paid by each of the 4 friends = $10
Hence, Amoubt paid by Dillion is $10 - $5 = $5
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If angleA and angleB are supplementary, and angleA = (3x - 9)°, and angleB = (2x + 14)degree, find x.
The values of x in the supplementary angles is 35.
What are supplementary angles?Supplementary angles refer to the pair of angles that always sum up to 180°.
Two angles are Supplementary when they add up to 180 degrees.
Therefore, for angle A and angle B to be supplementary they must add up to 180 degrees.
Hence,
∠A + ∠B = 180°
∠A = 3x - 9
∠B = 2x + 14
Therefore,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 175 / 5
x = 35
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The required value of x would be 35 degrees which are supplementary angles
We have been given that angle A and angle B are supplementary angles
∠A = 3x - 9 and ∠B = 2x + 14
Whenever two angles are supplementary, their sum is 180 degrees.
As per the property of supplementary angles,
The given angles add up to 180 degrees.
Thus, ∠A + ∠B = 180°
Substitute the values of ∠A and ∠B in the above equation,
3x - 9 + 2x + 14 = 180
5x - 9 + 14 = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 35
Hence, the supplementary angles have a value of 35 for x.
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The second step in the process for factoring the trinomial x-5x - 36 is to:
There are several ways that you can follow to from two binomials from this trinomial, for example, you can do it by following these steps:
1.write two sets of parenthesis, both with the term x
2. write a list of all the factors of 36
3. find the sum of the factors of 36
4. choose the factors whose sum equals 7 and write them into the two parenthesis
Then, the second step in the process of factoring this trinomial is: option D, to write a list of all the factors of 36
Solve the system by the substitution method.
15x - y = 55
y = x² + 1
Answer:
Point Form: (8,65) , (7,50)
Equation Form:
x = 8, y = 65
x = 7, y = 50
Step-by-step explanation:
Unbounded Limits and Asymptotes Part B
Answer: -0
Step-by-step explanation: cause one is negative 0 and then the other is 0
PLEASE HELP I WILL GIVE BRAINLYEST!! ALGEBRA 1 MATH HW
Answer: a. the weight of a burger with 0 patties is not 0 ounces because
the burger has to have weight, it cannot just be 0 ounces because you will not feel anything in your hand.
b. For patty 0 the weight is 0 oz, For patty 1 the weight is 6.6 oz, For patty 2 the weight is 22.2 oz, For patty 3 the weight is 46.8 oz.
Im sorry but I do not know what to do for C, I hope this helps. Sorry that I couldn't help you with c, but good luck!!
:)
Step-by-step explanation:
Suppose that the relation T is defined as follows.T = {(0,6), (2, -8), (-8, 2), (-3, -3)}What is the domain and range?
Given the follwing relation T:
[tex]T=\mleft\lbrace(0,6\mright),(2,-8),(-8,2),(-3,-3)\}[/tex]to write the domain, we have to gather all the first components of each ordered pair. In this case, the domain is:
[tex]DomT=\mleft\lbrace0,2,-8,-3\mright\rbrace[/tex]the range will be the second component of each ordered pair:
[tex]Range(T)=\mleft\lbrace6,-8,2,-3\mright\rbrace[/tex]Х m . In the segment shown point M is the mi M the midpoint of AB. Given AM = 3x+ 12 and MB = MB = 5x -4, find the length of AM. DP A M B M
From the information provided, M is the midpoint of line segment AB. This implies that the segments AM and MB are two equal halves of the entire length,
Therefore, we would have the following;
[tex]\begin{gathered} AM+MB=AB \\ \text{Also,} \\ AM=MB \\ \text{Where;} \\ AM=3x+12,MB=5x-4 \\ We\text{ now have;} \\ 3x+12=5x-4 \\ \text{Collect all like terms;} \\ 12+4=5x-3x \\ 16=2x \\ \text{Divide both sides by 2;} \\ \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}[/tex]Where AM = 3x+12, we now have;
[tex]\begin{gathered} AM=3x+12 \\ AM=3(8)+12 \\ AM=24+12 \\ AM=36 \end{gathered}[/tex]ANSWER:
Segment AM = 36
A(n)= 3+(n -1)(5)A(2) = 8A(4) = ?I understand how to do the steps however it's still hard for me to do.The example, I looked at was A(n)= A(1) + (n -1)dA(n)=15+(n-1)(4)A(4)=15+(4-1)(4)A(4)=15+(3)(4)A(4)=15+12A(4)=27Still a bit tough.
Step 1:
Write the equation
A(n) = 3 + (n - 1)5
Step 2:
To find A(2)
Compare A(2) with A(n)
You can see that n = 2 for A(2)
Next, substitute n = 2 in A(n) = 3 + (n-1)5 to find A(2)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ A(2)\text{ = 3 + (2 - 1) }\times\text{ 5} \\ A(2)\text{ = 3 + 1}\times5 \\ A(2)\text{ = 3 + 5} \\ A(2)\text{ = 8} \end{gathered}[/tex]Step 3
Let find A(4)
[tex]\begin{gathered} A(n)\text{ = 3 + (n - 1)5} \\ \text{From A(4), n = 4} \\ A(4)\text{ = 3 + ( 4 - 1 ) }\times\text{ 5} \\ A(4)\text{ = 3 + 3}\times5 \\ A(4)\text{ = 3 + 15} \\ A(4)\text{ = 18} \end{gathered}[/tex]Final answer
A(4) = 18
Which of the following sets is considered a null set
The null set is the set containing weeks with eight days.
We are given four statements that describe a set of elements. We need to find the null set. The null set is one that does not have even a single element present in it.
The first set consists of mugs with handles. It is not a null set because most mugs have handles.
The second set is of dogs with four legs. It is not a null set because most dogs have four legs.
The third set consists of weeks with eight days. It is a null set because each week has only seven days.
The fourth set is of books with pages. It is not a null set because most books have pages.
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help meeeeee pleaseee !!!!!!!!!
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
If a given set has nine elements, how many of its subsets have more than two elements ?
Total subsets of a set containing 9 elements having more than 2 elements = 466
What is a set?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things. A set with a single element is a singleton, while a set with no elements is an empty set. A set can either be infinite or have a finite number of items. If all of the items in two sets are identical, then the sets are equal. Modern mathematics is rife with sets. In fact, since the first part of the 20th century, Zermelo-Fraenkel set theory has been the de facto method for constructing solid foundations for all areas of mathematics.
C₉³+C₉⁴+C₉⁵+C₉⁶+C₉⁷+C₉⁸+C₉⁹
C₉³ = 84 subsets consisting of 3 elements
C₉⁴ = 126 subsets consisting of 4 elements
C₉⁵ = 126 subsets consisting of 5 elements
C₉⁶ = 84 subsets consisting of 6 elements
C₉⁷ = 36 subsets consisting of 7 elements
C₉⁸ = 9 subsets consisting of 8 elements
C₉⁹ = 1 subsets consisting of 9 elements
Total subsets of the set having 9 elements containing more than 2 elements = 84+126+126+84+36+9+1
= 466
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Did I correctly or incorrectly solve the equations below?From the information given, find the quadrant in which the terminal point determined by t lies. Input I, II, III, or IV.(a) sin(t)<0 and cos(t)<0 , quadrant_____III_____ ;(b) sin(t)>0 and cos(t)<0 , quadrant____II______ ;(c) sin(t)>0 and cos(t)>0, quadrant______I_____;(d) sin(t)<0 and cos(t)>0, quadrant____IV_______ ;
We know that the sine function is positive in the first and second quadrant; we also know that the cosine function is positive in the first and fourth quadrant.
WILL MARK BRAINLIEST IF CORRECT! the verticals of a triangle are A (2, 5), B (1, 2) and C (3, 1). Find the coordinates of the image after a reflection in the y-axis
the coordinates of the image after a reflection in the y- axis are =A (5,2), B (2,1) and C(1,3)
what is coordinates?A pair of number that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x ,y)the x-value and y- value
Firstly, we want to reflect across the x-axis When we reflect a point (x,y) over x-axis, we get (x,-y)
So;
A ( 2,5) becomes (2,-5)
B (1,2) becomes (1,-2)
C ( 3,1) becomes (3,-1)
Then we proceed to rotate 90 degrees counterclockwise about the origin
Here we have;
(x, y) becomes (-y ,x)
(2,-5) becomes (5,2)
(1,-2) becomes (2,1)
(3,-1) becomes (1,3)
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a figure with a perimeter of 84 units is dilated by a factor of 3/4. the perimeter of the dilated figure is ___ units.
If the perimeter is 84 and it is dilated by a factor of 3/4 , then the perimeter of the dilated figure can be calculated by multiplying 84 by 3/4
That is;
Perimeter of dilated figure = 3/4 x 84
=63 units