bearing in mind that perpendicular lines have negative reciprocal slopes hmmmmm wait a second, what's the slope of that line above anyway?
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}} x+5\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]
therefore any perpendicular line to that
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{1}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{3}{1}}\qquad \stackrel{negative~reciprocal}{+\cfrac{3}{1}\implies 3}}[/tex]
so, we're really looking for the equation of a line whose slope is 3 and runs through (1, -10)
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-10})~\hspace{10em} slope = m\implies 3 \\\\\\ \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-(-10)=3(x-1) \\\\\\ y+10=3x-3\implies y=3x-13[/tex]
Answer:
use M=(Y-Y)/(X-X)format and see what you get
Step-by-step explanation:
so it should be
-10-3/1-1
Im not sure how to explain this without having the proper set up
(2,2) = (x,y)
(1,1) = (x,y)
so if we set this up right
-13/0....
Write a function describing the relationship of the given variables.
V
varies directly with the square of
t
and when
t
=
6
,
V
=
108
V
=
Answer:
The function describing the relationship of V and t is V = 3t²
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# V is varies directly with the square of t
- Change the statement above to a mathematical relation
∴ V ∝ t²
- Chang the relation to a function by using a constant k
∴ V = kt²
- To find the value of the constant of variation k substitute V and t
by the given values
∵ t = 6 when V = 108
∵ V = kt²
∴ 108 = k(6)² ⇒ simplify the power 2
∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k
∴ 3 = k
- The value of the constant of variation is 3
∴ The function describing the relationship of V and t is V = 3t²
What is the area of the kite
Answer:
The area of the kite is 60 square feet
Step-by-step explanation:
The area of a kite is given as half multiplied by the product of the diagonals.
The longer diagonal measures 30 feet.
The shorter diagonal measures 4 feet.
The area of the kite is; [tex]\frac{1}{2}*30*4=60[/tex]
ANSWER
The area of the kite is 60 square feet
EXPLANATION
The area of a kite is half times the product of the diagonals.
The longer diagonal is 10+20=30 feet.
The shorter diagonal is 2+2 =4 feet.
The area of this kite
[tex] = \frac{1}{2} \times 30 \times 4[/tex]
This simplifies to,
[tex] = 60 {ft}^{2} [/tex]
Therefore the area of the kite is 60 square feet
could anyone help me? I will mark you as brain liest who ever helps me!
Answer:
1)163.28 (3.14*52)
2)13ft 6in (163.28/12)
3)129 times
4) 31 times
Step-by-step explanation:
1) multiply 52 times pie(3.14)
2)divide 163.28(your total) by 12
3) 1760 divided by 52
4) 1760 divided by 56.52
this is for the other 2 ones
Find the value of X
Answer:
C. 66
Step-by-step explanation:
32 + x =98
The sum of interior angles of a triangle add up to the exterior opposite angle;
solving for x yields;
x = 98 - 32
x = 66 degrees
Answer:
x = 66°
Step-by-step explanation:
Since DAC is a straight line, the angles must add up to 180° and 98° is given so the missing angles is 180° - 98° = 82°
Angles in a triangle add up 180° and 32° and 82° are given →
x + 32° + 82° = 180°
x + 114° = 180°
x = 66°
The graph of the function f(x)=6/x-3 is shown below. What is the vertical asymptote of the function
Answer:
The vertical asymptote is [tex]x=3[/tex]
Step-by-step explanation:
we know that
The vertical asymptote is the value of x that makes the denominator equal to zero:
In this problem we have
[tex]f(x)=\frac{6}{x-3}[/tex]
[tex]x-3=0[/tex]
Solve for x:
[tex]x-3+3=0+3[/tex]
[tex]x=3[/tex]
The vertical asymptote is [tex]x=3[/tex]
see the attached figure to better understand the problem
Find the specific solution of the differential equation dy/dx= 4y/x^2 with condition y(-4)=1
A. y=-1-4/x
B. y=-e^1/x
C.y=e^(-4/x)
D. None of these
This ODE is separable:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4y}{x^2}\implies\dfrac{\mathrm dy}y=\dfrac4{x^2}\,\mathrm dx[/tex]
Integrating both sides gives
[tex]\ln|y|=-\dfrac4x+C[/tex]
Given the initial condition [tex]y(-4)=1[/tex] we find
[tex]\ln|1|=-\dfrac4{-4}+C\implies C=-1[/tex]
so that the particular solution is
[tex]\ln|y|=-\dfrac4x-1[/tex]
[tex]\implies y=e^{-(1+4/x)})[/tex]
so the answer is D.
Which is the solution of the quadratic equation (4y – 3)2 = 72?
Answer:
y = 9.75
Step-by-step explanation:
(4y - 3)2 = 72
Opening the brackets;
8y - 6 = 72
8y = 72 + 6 = 78
y = 78 ÷ 8 = 9.75
Answer:
[tex]y = \frac{3+6\sqrt{2}}{4}\text{ and } y = \frac{3-6\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Given quadratic equation,
[tex](4y-3)^2=72[/tex]
[tex]\implies 4y - 3 = \pm \sqrt{72}[/tex] ( Taking root on both sides )
[tex]4y=3 \pm 6\sqrt{2}[/tex] ( Additive property of equality ),
[tex]y = \frac{3 \pm 6\sqrt{2}}{4}[/tex] ( Division property of equality )
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ or }y =\frac{3-6\sqrt{2}}{4}[/tex]
Hence, the solution of the given equation is,
[tex]\implies y = \frac{3+6\sqrt{2}}{4}\text{ and }y =\frac{3-6\sqrt{2}}{4}[/tex]
what is the solution to this equation?
x/5=-20
Answer:
-100
Step-by-step explanation:
Answer:
-100
Step-by-step explanation:
You need to multiply
-20 x 5= -100
Hope this helped please mark me the brainliest answer? Have a good day :)
Andy and Jacob work as technicians in a laboratory where gemstones are tested and certified. Andy has already tested 30 gemstones and continues testing at a rate of 30 gemstones per hour. Jacob has already tested 40 gemstones and continues testing at a rate of 25 gemstones per hour. Which function can Andy and Jacob use to determine the total number of gemstones they have tested after x hours? How many gemstones will they have tested after 5 hours? A. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 10. Thus, they will have tested 285 gemstones in 5 hours. B. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 70x + 55. Thus, they will have tested 405 gemstones in 5 hours. C. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 55x + 70. Thus, they will have tested 345 gemstones in 5 hours. D. The function that describes the total number of gemstones tested by Andy and Jacob in x hours is given by f(x) = 60x + 65. Thus, they will have tested 365 gemstones in 5 hours.
Answer:
Option C is correct.
Step-by-step explanation:
Andy tested gemstones already = 30
Jacob tested gemstones already = 40
Total gemstones tested by Andy and Jacob already = 30+40 = 70
Andy continue to test gemstones per hour = 30
Jacob continue to test gemstones per hour = 25
Total gemstones tested by Andy and Jacob per hour = 30 +25 = 55
The total number of gemstones tested by Andy and Jacob after x hours will be: 55x
So, the equation will be: f(x) = 55x + 70
After 5 hours i.e. x =5
f(5) = 55(5) + 70
f(5) = 275 + 70
f(5) = 345
Andy and Jacob will have tested 345 gemstones in 5 hours.
So, Option C is correct.
find the conplex conjugate of z1 of z1=i+4
Answer:
- i + 4
Step-by-step explanation:
Given a complex number a + bi then the complex conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Hence conjugate of i + 4 = - i + 4
Write the expression as a single logarithm 4 log x-6 log (x+2)
Final answer:
To combine the expression 4 log x - 6 log (x+2) into a single logarithm, we use the exponentiation and division rules for logarithms to obtain log((x^4)/(x+2)^6).
Explanation:
To write the expression 4 log x - 6 log (x+2) as a single logarithm, we can apply log rules.
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log x.
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y.
The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log x - log y.
Using these rules, we can
rewrite the given expression:
4 log x - 6 log (x+2) can be rewritten as log(x^4) - log((x+2)^6), which simplifies to log((x^4)/(x+2)^6) according to the division rule for logarithms.
The expression [tex]4 log x - 6 log (x+2)[/tex] can be simplified as a single logarithm by using the logarithm properties of exponents and division, resulting in [tex]log(x^4 / (x+2)^6).[/tex]
Explanation:The student is asking to write the expression [tex]4 log x - 6 log (x+2)[/tex] as a single logarithm. To do this, we recall two important properties of logarithms:
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: [tex]log(a^n) = n log a.[/tex]The logarithm of the division of two numbers is the difference between the logarithms of the two numbers: [tex]log(a/b) = log a - log b.[/tex]Using these properties, we can rewrite the expression:
First, apply the exponent property: 4 log x becomes log(x^4), and 6 log (x+2) becomes log((x+2)^6).Next, apply the division property:Therefore, the expression [tex]4 log x - 6 log (x+2)[/tex] written as a single logarithm is[tex]log(x^4 / (x+2)^6).[/tex]
Anyone? i dont understand
Answer:
1725ft^2
Step-by-step explanation:
Hi!
First you have to find your two bases B1 and B2, which are 50 and 65.
Then you find the height, which is 30ft.
Finally, you plug those into the equation 1/2*h*(B1+B2) and solve.
1/2*30*(50+65)
1/2*30*(115)
15*115
1725ft^2 is your answer.
I hope this helps!
Maggie spent $46.20 to by pencil sharpeners for her gift shop. If each pencil sharpener cost 60 cents how many pencil sharpeners did she buy
Answer:
Maggie bought 77 pencil sharpeners
$46.20 divided by .60 = 77
Step-by-step explanation:
46.20÷0.60= 77
Maggie can buy 77 pencil sharpeners is she would like
Please, please, pppllleeeeaassssee
Mark Brainlyest
What is the standard deviation of the following data set rounded to the nearest tenth?
30, 26, 28, 32, 28, 30
Answer:
Standard Deviation is: 2.09762 or rounded to nearest tenth is 2.1
Step-by-step explanation:
What type of number is [tex]\sqrt{13}[/tex]
Choose all answers that apply:
(Choice A)
A
Whole number
(Choice B)
B
Integer
(Choice C)
C
Rational
(Choice D)
D
Irrational
The number √{13} is an irrational number because it cannot be expressed as a ratio of two integers and is not a whole number or integer either.
The number √{13} is not a whole number, an integer, or a rational number because it cannot be expressed as a ratio of two integers. The square root of a positive number that is not a perfect square is always irrational. Therefore, the only correct choice for the type of number that represents √{13} is (Choice D) Irrational.
The scatter plot shows the study times and test scores for a number of students. How long did the person who scored 81 study?
Answer: Option A
50 minutes
Step-by-step explanation:
Observe in the diagram that the vertical axis represents the score obtained and the horizontal axis represents the study time.
To find out how many hours the person with a score of 81 studied, locate the point that is at a vertical distance of 81.
Now draw a vertical line from this point to the horizontal axis. Note that the vertical line traced intercepts the vertical axis at x= 50
Then the person who got a score of 81 studied 50 minutes
The answer is the option A
Michael earned 50.43 in 6.15 hours. how much did he earn in an hour?
Answer: $8.2
Step-by-step explanation:
Answer:
8.2 dollars an hour is the answer
Step-by-step explanation:
50.43 divided by 6.15 is 8.2
If ABC and GEF are congruent, the value of x is and the value of y is
Answer:
The value of x is 10, and the value of y is 6
Step-by-step explanation:
ABC and GEF are congruent
so
x - 8 = 2
x = 10
x - y = 4
10 - y = 4
y = 10 - 4
y = 6
Answer
x = 10, y = 6
Answer:
x = 10 and y = 6
Step-by-step explanation:
In the given figure ΔABC and ΔGEF are congruent which means all the corresponding sides of the given triangles should be congruent.
So measure of AC = mfg
x - 8 = 2
x = 2 + 8
x = 10
Similarly mBC = mEF
x - y = 4
10 - y = 4
y = 10 - 4 = 6
Therefore, answer are x = 10 and y = 6
Can someone please help me with this?
Answer:
The answer is A; 19
Step-by-step explanation:
4 × (3/4 - 2/4) + 3 × 6
= 4 × 1/4 + 3 × 6
= 1 + 3 × 6
= 1 + 18
= 19
How do I solve this?
A football punted upward has a trajectory given by the equation y = 48x − 16x2, where y represents the football's height x seconds after it has been kicked. What is the maximum height, in feet, attained by the ball?
Giving brainliest + 30 points
The maximum happens at x = -b/2a
x = -48/2(-16) = 3/2
Now replace x in the equation and solve for y:
y = 48(3/2) - 16(3/2)^2
y = -72 - 36
y = 36
The maximum height is 36 feet.
Kate is painting a ceramic paperweight shaped like a rectangular prism, as shown here. (dimensions of .8 ft , 1.2 ft, 1.2 ft)She wants to find the surface area of the paperweight so she can determine how much paint she needs.
The area of one of the bases is _____
The area of each lateral rectangular face is _____
The surface area of the paperweight is _____
Answer:
The area of one of the bases is 0.96 ft²
The area of each lateral rectangular face is 4.8 ft²
The surface area of the paperweight is 6.72 ft²
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to
SA=2B+LA
where
B is the area of one of the bases
LA is the lateral area of the prism
Find the area of one of the bases B
B=(0.8)(1.2)=0.96 ft²
Find the lateral area LA
The lateral area is the area of each lateral rectangular face
LA=2[(0.8)(1.2)]+2[(1.2)(1.2)]=4.8 ft²
Find the surface area
SA=2(0.96)+4.8=6.72 ft²
Answer: 1.44, 0.96, and then 6.72.
Step-by-step explanation:
the person who answered first is wrong.
A picture that measures 8 cm by 6 cm is to be surrounded by a mat. The mat is to
be surrounded by a mat. The mat is to be the same widt
all sides of the picture. The combined area of the mat and the picture is double the arca
What is the width of the mat to the nearest tenth? Include a diagram. (5)
Answer:
1.4 inches
Step-by-step explanation:
The picture is a rectangle 8 cm by 6 cm. The area of a rectangle is length * width. The area of the picture is 8 cm * 6 cm = 48 cm^2
After the mat is applied, the area doubles, so the new area will be 2 * 48 cm^2 = 96 cm^2.
Let the width of the mat be x. The mat has the same width all around the rectangular picture, so it adds x on each side of the length and x on each side of the width.
old length: 8
new length: 2x + 8
old width: 6
new width: 2x + 6
Area of the new rectangle with mat = new length * new width
area = (2x + 8)(2x + 6)
The new area is 96, so that give us an equation.
(2x + 8)(2x + 6) = 96
Use FOIL on the left side:
4x^2 + 12x + 16x + 48 = 96
Combine like terms, and subtract 96 from both sides:
4x^2 + 28x - 48 = 0
Divide both sides by 4:
x^2 + 7x - 12 = 0
To factor the trinomial, we need two numbers that add to 7 and multiply to -12. There are no such numbers, so we need to use the quadratic formula.
x = [-b +/- sqrt(b^2 - 4ac)]/(2a)
x = [-7 +/- sqrt(7^2 - 4(1)(-12)]/[2(1)]
x = [-7 +/- sqrt(49 + 48)]/2
x = [-7 +/- sqrt(97)]/2
x = 1.4 or x = -8.4
Since the mat cannot have a negative width, the negative solution is discarded.
Answer: The width of the mat is 1.4 inches.
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25. She hopes to earn more than that amount of money during each class. Write an inequality that models the situation and find the minimum number of students she must teach in each class so that her earnings for that hour exceeds the minimum wage in her state.
Answer:
brainliest ps :)
Step-by-step explanation:
her wage is $4.00 + s*0.5 so 7.25-4> s*.5== 3.25 > s*.5 == 6.5 > s
The inequality for the given information can be written as 6.5 > s.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25.
The inequality can be written as:-
$4.00 + ( s x 0.5 )
7.25-4 > ( s x 0.5 )
3.25 > ( s x 0.5 )
6.5 > s
To know more about inequality follow
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The distance between the two points pictured is d = Use the distance formula to find n. d = n =
Answer:
the answer is 61units
n=61
Step-by-step explanation:
3. Different sizes of ribbon need to be cut to go around various shapes. All of the following sizes are in inches.
(a) Without using your calculator, approximate the decimal equivalent of each number to the nearest
tenth
(b) Order the ribbon sizes from least to greatest.
tromont
Answer:
a. 2,2,3,3
b. 1.7 2.2 pi= 3.14 3.4= 2,2,3,3
Step-by-step explanation:
I NEED HELP PLEASE!!!!!
Answer is 1)
3V= pi•h•r^2 divide both sides by (pi•h) ; 3V/pi•h = r^2; sqrt (3V/pi•h) =r
1. Complementary Angeles
2. Angel1-37
What is angel 4
3
Angel 1-40
What is angel 5
Answer:
1. D ∠4 and ∠5
2. C 37°
3. A 50°
Step-by-step explanation:
1. Complementary angles are those that add up to 90°.
From the diagram you can see that angles 4 and 5 together form right angle, so angles 4 and 5 are complementary.
2. Angles 1 and 4 are vertical angles. Vertical angles have the same measure, so
∠4=∠1=37°
3. From 1,
∠4+∠5=90°
From 2
∠1=∠4
Since ∠1=40°, then ∠4=40°
So,
∠5=90°-40°=50°
Question 3 answer please
Answer:
34.48
Step-by-step explanation:
Use PEMDAS
12.98-(7.6÷19)+22
12.98-0.4+22
12.48+22
34.48
Answer:
34.480000000000000000000000
Step-by-step explanation:
Two video games, Star Chasers and Song Hero, had the same average price over a 10-month period. During that time, the price of Song Hero showed greater variability. If Song Hero was priced between $35 and $49 during the 10-month period, which statement is most likely true about price of Star Chasers during that time?
The highest price and the lowest price of the game differ by more than $14.
The highest price and the lowest price of the game differ by less than $14.
The mean price was more than $42.
The mean price was less than $42.
Answer:
The answer would be B. The highest price and the lowest price of the game differ by less than $14. Hope this helps!
B. The highest price and the lowest price of the game differ by less than $14.
Step-by-step explanation:Given is that the the price of Song Hero showed greater variability. This means their prices are more varied in range.
If Song Hero was priced between $35 and $49 during the 10-month period, This means the variability of Star chasers is less than [tex]49-35=$14[/tex]
Since, $14 is Song Hero’s range, the range for Star chasers should be less.
Therefore, option B is correct.
The graphs below have the same shape. f(x) = x^2 what is the equation of the graph of g(x)?
Answer:
A. [tex]g(x)=(x-4)^2[/tex]
Step-by-step explanation:
The graph of [tex]f(x)=x^2[/tex] is transformed to obtain the graph of g(x).
We can see from the diagram that, f(x) is shifted 4 units to the right to obtain the graph of g(x).
Therefore [tex]g(x)=f(x-4)[/tex].
Hence the equation of g(x) is
[tex]g(x)=(x-4)^2[/tex]
The correct answer is A.
The equation of the graph of g(x) is g(x) = (x - 4)²
How to determine the equationFrom the graph shown, we can see that the f(x) = x² as shown is shifted 4 units to the right to obtain the graph of g(x).
Then, we have that this shift can be achieved by replacing x in the equation of f(x) with x - 4 to represent the horizontal shift.
We have the equation of the graph of g(x), to be;
g(x) = (x - 4)²
This equation represents a horizontal shift of the graph of f(x) by by 4 units to the right, as g(x) remains the same shape f(x) but is shifted horizontally to the right by 4 units.
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