Answer:
24 ft.
Step-by-step explanation:
Radius = 4 ft
Central angle = 6°
Arc length = radius × central angle
= 4 × 6°
= 24 ft.
what are the pair of intergers whose product is -12
Answer:
The answer is -4×3 or -3×4 or -6×2 or -2×6 or -1×12 or -12×1
Step-by-step explanation:
Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?
Answer:[tex]x=-\frac{1}{3}, 4[/tex]
Step-by-step explanation:
Graphs intersect the x-axis where y=0, so we can set f(x)=0.
[tex]3x^2 - 11x-4=0 \\ \\ (3x+1)(x-4)=0 \\ \\ x=-\frac{1}{3}, 4[/tex]
Answer:
negative x intercept is at -1/3
positive x intercept 4
Step-by-step explanation:
Brian ordered 3 large cheese pizzas and a salad. The salad cost $4.95. if he spent a totai of $47.60 including the $5 tip, how much did each pizza cost? (Assume there is no tax).
Each pizza cost $ 12.65
What is an Equation ?An Equation is used in determination of unknown variables in an expression .
It is given that
Brian ordered 3 large cheese pizzas and a salad.
The salad cost $4.95
Total amount spend = $47.60
Tip = $5
The amount spend in food is $ 47.60-5
= $42.60
Let the price of Pizza is x then the equation that can be formed to determine the price of pizza is
3x + salad = 42.60
3x + 4.95 = 42.60
3x = 37.65
x = $12.65
Therefore each pizza cost $ 12.65
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Answer:
12.55
Step-by-step explanation:
Please help me!! matrices question! ASAP
The circumcenter is the center of the. circle
The circumcenter is the center of the circle which goes through the triangle's vertices, so the circumcenter of the triangle and the center of that circumscribed circle MUST be the same point.
The same goes for the incenter and the center of the inscribed circle, though these will not, in general, be the same point as the circumcenter.
Answer: Another name of circumcenter is, " Circumscribed circle ". The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of the polygon's vertices & the center of that circle is called the circumcenter. All polygons that have circumcircles are known as cyclic polygons. However, all polygons does not have a circumcircle. Only regular polygons, triangles, rectangles, and right-kites can have the circumcircle and thus the circumcenter as well.
You may find that the circumcenter of a triangle as the most common thing asked in exams and it is generally what schools begin with. So, some brief information about the circumcenter of a triangle is given below. You may safely ignore them if you haven't learned them yet.
The circumcenter of triangle can be found out as the intersection of the perpendicular bisectors (the lines that are at right angles to the midpoint of each side) of all sides of the triangle. This means that the perpendicular bisectors of the triangle are concurrent (meeting at one point). All triangles are cyclic and hence, can circumscribe a circle, therefore, every triangle has a circumcenter.
Property 1: All the vertices of the triangle are equidistant from the circumcenter.
Property 2: All the new triangles formed by joining O to the vertices are Isosceles triangles.
Property 3: Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle
Property 4: In an acute-angled triangle, circumcenter lies inside the triangle
Property 5: In an obtuse-angled triangle, it lies outside of the triangle
Note- Location for the circumcenter is different for different types of triangles.
The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:
Step 1: Draw the perpendicular bisector of any two sides of the given triangle.Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be noted that, even the bisector of the third side will also intersect at P.P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
does someone mind helping me with this problem? Thank you!
There are boys and girls in a class in the ratio 1: 12 there are 77 more girls than boys. how many boys are there?
Let's set up some variables:
b: # of boysg: # of girlsLet's set up some equations based on the informative given:
boys to girls ratio ⇒ 1: 12(Mathematical form) g = 12b
77 more girls than boys(Mathematical form) g = b + 77
Let's put the equation together:
g = 12b -- equation 1
g = b + 77 -- equation 2
(equation 2)'s value of g into (equation 1)
12b = b + 77
11b = 77
b = 7
There are 7 boys.
Answer: 7 boys
Hope that helps!
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Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?
Pretest: Manipulating and Interpreting Expressions
Drag each expression to the correct location on the table.
Place each algebraic expressions next to its corresponding verbal description.
5³-²-1 (5-4)³
the difference of 5 times the cube of x cubed and
the quotient of 4 times x and 3
5 times the cube of x divided by 4 times x
the quotient of the difference of 5 times x cubed and 4 and x
the cube of the difference of 5 times x and 4
Submit
Answer:
9
Step-by-step explanation:
0
whats 27 x 300 / 34 x 6
Answer:
Use Calculator:
Approximately. 1429.411
Step-by-step explanation:
Hope it Helps!!!
If g:
x = 2x-3 4 find 9^-1 (-3)
The inverse function of g(x) will be g⁻¹(x) = (4x + 3) / 2. Then the value of the inverse function, at x = -3, will be 4.5.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
g(x) = (2x – 3) / 4
Then the inverse function of g(x) will be
g⁻¹(x) = (4x + 3) / 2
Then the value of the inverse function, at x = -3, will be
g⁻¹(-3) = [4(-3) + 3] / 2
g⁻¹(-3) = -4.5
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Which of the following is equivalent to √?
O
2
√2
O 2√2
2+√√√2
Answer:
2 sqrt(2)
Step-by-step explanation:
To simplify a square root
sqrt(8)
sqrt(4*2)
sqrt(4) sqrt(2)
2 sqrt(2)
Answer:
2√2
Step-by-step explanation:
√8 =[tex]\sqrt{4 \times 2}[/tex]
= 2√2 (√4 = 2)
Hence, 2√2 is the required answer.
Drag the tiles to the correct boxes. Not all tiles will be used.
Which equation could represent each graphed polynomial function?
y = 14 - 5x² + 4
y = x³ + 27
y = x(x + 3)(x - 2)
y = (x + 1)(x − 3)(x² + 1)
y = x⁴- 5x² + 4 represents the first graph.
y = x(x + 3)(x - 2) represents the second graph.
How to Interpret the graph of a Polynomial?
1) The first polynomial is;
y = x⁴- 5x² + 4
Simplifying this gives us;
y = x⁴- 4x² - x² + 4
y = x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Thus, the zeros of this polynomial are; x = -2, -1, 1, 2
From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So graph (1) represents the polynomial y = x⁴- 5x² + 4
2). The second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
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It costs $15 to get into the county fair and $2 per pack of ride tickets, t. If you buy 10 packs of ride tickets, how much total would you spend?
Answer:
35$
Step-by-step explanation:
You multiply $2 x 10 = 20$ then add 15$ + 20$ = 35$
light a flashes every 5 seconds Light b flashes every 6 seconds light c flashes every 7 seconds work out how long it will take for all of them to flash
Answer:
210 seconds
Step-by-step explanation:
LCM of 5,6 and 7
Which equation describes the same line as y- 5 = -2(x+4)?
OA. y=-2x-8
B. y=-2x - 2
OC. y=-2x - 3
OD. y=-2x+9
SUBI
Answer:
C
Step-by-step explanation:
We have
y - 5 = -2(x + 4)
Expanding the RHS by multiplying by 2 gives us
y - 5 = -2x -8
Moving -5 from LHS to RHS (reverses sign)
y = -2x -8 + 5 or
y = -2x -3
C. y=-2x - 3 , equation describes the same line as y- 5 = -2(x+4).
Here, we have,
We have been given an equation in point-slope form and we are asked to find the equation of same line.
y- 5 = -2(x+4)
Upon using distributive property , we will get,
=> y- 5 = -2x - 8
We have
y - 5 = -2(x + 4)
Expanding the RHS by multiplying by 2 gives us
y - 5 = -2x -8
Moving -5 from LHS to RHS (reverses sign)
y = -2x -8 + 5 or
y = -2x -3
Therefore, the equation y = -2x -3 represents the same line as our given equation.
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What is the measure of m? 6 3 n 18 m = [?] Give your answer in simplest form. Enter
By solving a system of equations, we will see that m measures 12 units.
How to get the measure of m?
Notice that we have 3 right triangles.
Then we can write the equations:
cos(a) = 6/m
For the small triangle on the left, where m is the hypotenuse.
cos(a) = m/(6 + 18)
For the larger triangle (the one composed of the two triangles).
Where in both equations, angle "a" is the one in the top left.
Then we have the system of equations:
cos(a) = 6/m
cos(a) = m/(6 + 18)
Then we can write:
6/m = m/(6 + 18)
If we simplify the expression, we get:
6*(6 + 18) = m^2
6*(24) = m^2
144 = m^2
√144 = m = 12
Then we conclude that m measures 12 units.
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3/4=6/x x =
!!!!PLEASE HELP I WILL MARK BRAINLIEST!!!!
Answer:
x=8
Step-by-step explanation:
You cross multiply, 6 times 4 is 24, so what times 3 is 24. 8 times 3 is 24.
Answer:
x = 8
Step-by-step explanation:
There are several ways you can solve a proportion like this. Most of the algebraic solutions involve what amounts to multiplying both sides by (4x/3). There are also graphical solutions and solutions that rely on relations that make fractions be equal.
__
cross multiplicationThe method of solution usually recommended is to "clear fractions" and then solve the resulting one-step linear equation. To "clear fractions," multiply both sides of the equation by the least common denominator: 4x.
[tex](4x)\dfrac{3}{4}=(4x)\dfrac{6}{x}\\\\3\cdot x=4\cdot6\qquad\text{looks like "cross multiplication"}[/tex]
We describe this as "cross-multiplication" because it looks like each numerator has been multiplied by the opposite denominator.
This "one-step" linear equation is solved by dividing by the coefficient of x, which is 3:
[tex]\dfrac{3x}{3}=\dfrac{4\cdot6}{3}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]
Note that we could have done these operations in one step. The two steps, multiply by 4x and divide by 3, are identical to the one step, multiply by (4x/3).
[tex]\left(\dfrac{4x}{3}\right)\cdot\dfrac{3}{4}=\left(\dfrac{4x}{3}\right)\cdot\dfrac{6}{x}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]
__
compare fractionsWe can see the solution almost immediately if we rewrite the fractions so they have the same numerator.
[tex]\dfrac{3}{4}=\dfrac{6}{x}\\\\\dfrac{3\cdot2}{4\cdot2}=\dfrac{6}{x}\\\\\dfrac{6}{8}=\dfrac{6}{x}\ \Longrightarrow\ \boxed{x=8}[/tex]
The same thing happens if we multiply the equation by the inverse of either side.
[tex]\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{4}{3}\right)\dfrac{3}{4}=\left(\dfrac{4}{3}\right)\dfrac{6}{x}\ \Longrightarrow\ 1=\dfrac{8}{x}\ \Longrightarrow\ \boxed{x=8}\\\\\textsf{ or ...}\\\\\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{x}{6}\right)\dfrac{3}{4}=\left(\dfrac{x}{6}\right)\dfrac{6}{x}\ \Longrightarrow\ \dfrac{x}{8}=1\ \Longrightarrow\ \boxed{x=8}[/tex]
__
graphical solutionIf the equation is rewritten to a form that has a value of 0 at the solution, then the x-intercept of the graph will be the solution to the equation.
3/4 = 6/x . . . . . . . . original equation
6/x -3/4 = 0 ⇒ f(x) = 0
f(x) = 6/x -3/4
The graph shows the solution to f(x) = 0 is x=8.
what does ([tex](x^{2}+4x)(x)[/tex] equal
the first definition of an element was made by
The length of an arc of a circle is 26/9 pi
centimeters and the measure of the corresponding central angle is 65 degrees. What is the length of the circle's radius?
The radius will be equal to 7.55 centimeters.
What is the length of arc of the circle?The arc length is the curved length on the circumference of a circle suspended by a small angle.
The radius will be calculated as follows:-
r = [tex]\dfrac{Arc}{Angle}[/tex]
r = [tex]\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}[/tex]
r = [tex]\dfrac{9.07}{1.20}[/tex]
r = 7.55 centimeters
Therefore the radius will be equal to 7.55 centimeters.
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HELP!!
Which compound inequality is represented by the graph?
-5-4-3-2-1 0 1 2 3 4 5
O-2
0-2 ≤x≤4
O x < -2 or x ≥ 4
O x≤-2 or x > 4
Answer: Choice C
[tex]x < -2 \text{ or } x \ge 4[/tex]
==========================================
Reason:
The portion on the left represents [tex]x < -2[/tex] because of the open circle at -2 and shading pointing to the left. This represents all numbers smaller than -2.
The portion on the right represents all values that are 4 or larger; hence [tex]x \ge 4[/tex]. Note the use of a closed circle at 4 to include this value.
We connect those two inequalities with the keyword "or" because x can only pick one of those options, but not both at the same time.
Question 33 of 45 You may use your calculator for this question. A particle moves along a line so that at time t where 0 ≤t≤n, its position is given by s(t)=-4 sint- t/2+10. What is the acceleration of the particle the 2 first time its velocity equals zero?
The particle's velocity at time [tex]t[/tex] is equal to the first derivative of its position at that time, and acceleration is the second derivative.
We have
[tex]s(t) = -4\sin(t) - \dfrac t2 + 10 \implies s'(t) = -4\cos(t) - \dfrac12 \implies s''(t) = 4\sin(t)[/tex]
Find when the velocity is zero:
[tex]s'(t) = -4\cos(t) - \dfrac12 = 0 \implies \cos(t) = -\dfrac18 \implies t = \cos^{-1}\left(-\dfrac18\right) \approx 1.696[/tex]
At this time, the acceleration of the particle is approximately
[tex]s''(1.696) \approx \boxed{3.969}[/tex]
(B)
Pls help and explain tyyy
Answer:
11) 195312
13) 5461
Step-by-step explanation:
11)
15÷(-3) = -5
(-75)÷15 = -5
375÷(-75) = -5
It’s clear that the common ratio of this geometric sequence is -5
Then using the sum formula for geometric sequences :
[tex]S_{11}=\left( -3\right) \times \frac{1-\left(-5 \right)^{8} }{1-(-5)} =-\frac{1}{2}\times(1-(-5)^8)=195312[/tex]
……………………………………………………
13)
[tex]S_{13}=1\times \frac{1-4^{7}}{1-4} =-\frac{1}{3} \times(1-4^{7})=5461[/tex]
Which of the following situations could be represented with the following system of equations?
Option B is correct for the given system of equations.
The given system of equations 13(v-w)=52 and 12(v+w)=72.
What are systems of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Now, 13(v-w)=52⇒v-w=4-----(1) and 12(v+w)=72⇒v+w=6------(2).
By adding (1) and (2), we get
v-w+v+w=4+6⇒2w=10⇒w=5
By substituting w=5 in equation (1), we get v-5=4⇒v=9.
Thus, the statement "Andy flew his model aeroplane at full speed straight into the wind for 13 seconds before turning it around and flying directly with the wind for 12 seconds. The aeroplane flew 72 yards on the way out and 52 yards on the way back" is correct for the given system of equations.
Therefore, option B is correct for the given system of equations.
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Helppppp!!!!!! Find m<1
Answer:
87 = <1
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
124 = 37 + <1
Subtract 37 from each side
124 -37 = <1
87 = <1
To hire a bicycle it costs $6 for each day plus a fixed charge of $15
a) Maria pays $39 to hire a bicycle. How many days does she hire it for.
Answer:
4 days
Step-by-step explanation:
1) Derive a formula.
Let b = bicycle
Let x = the number of days
A set up equation: b = 6x + 15
2) If she pays 39 to hire a bicycle, substitute 39 into b, then solve for x.
39 = 6x + 15
39 - 15 = 6x
24 = 6x
24/6 = x
4 = x
x = 4
Since x is the number of days, she hired the bicycle for 4 days.
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Let x1 = 21, y1 = −15, and y2 = 9, and let y vary inversely as x. Find x2.
Answer:
The value of [tex]x_{2}[/tex] from inverse variation is (-35).
Step-by-step explanation:
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.
An inverse variation can be represented by the equation
xy=k .
That is y varies inversely as x if there is some nonzero constant k.
Here, the product is given by :
x1y1=x2y2
21 x (-15)=x2 x 9
(-315) / 9 = x2
x2=(-35)
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Which statement describes how the graph of the given polynomial would change if the term -3x^6 is added?
y=2x^6+9x^5-7x^3-1
The correct answer will be option B which is the ends of the graph will extend in the opposite direction.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given equation is as follows:-
y = 2x⁶ + 9x⁵ -7x³ -1
When the term -3x⁶ is added the equation will be reduced in the following form.
y = -3x⁶+2x⁶ + 9x⁵ -7x³ -1
y =-x⁶+9x⁵ -7x³ -1
When we plot the graph of the above equation we will see that the graph will be reduced to the form in which both the ends of the graph lie opposite to each other.
The graph of the equation is attached with the answer below.
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Answer:
B is the correct answer
Step-by-step explanation:
write the equation of the line in fully simplified slope-intercept form
Answer:
y=-x+4
Step-by-step explanation:
First use slope formula using 2 points.
(0,3) and (1,2)
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{2-3}{1-0}=\frac{-1}{1} =-1[/tex]
Slope is -1.
Now, use point-slope formula.
y-y1=m(x-x1)
Plug in the information that we have.
y-3=-1(x-0)
Use distributive property.
y-3=-x+1
Add 3 to both sides.
y=-x+4
It is now in slope-intercept form.
Hope this helps!
If not, I am sorry.
PLEASE HELP ASAP!!!!!!!!!
The terminal ray of angle θ drawn in standard position passes through (1,−3).
What is the value of cscθ?
Enter your answer in the box. Enter your answer in simplest form.
csc0=
The radius of the circle is
[tex] \sqrt{ {1}^{2} + {( - 3)}^{2} } = \sqrt{10} [/tex]
meaning that
[tex] \sin( \theta ) = \frac{ - 3}{ \sqrt{10} } [/tex]
Thus,
[tex] \csc \theta = - \frac{ \sqrt{10} }{3} [/tex]
The value of csc θ is √10/ (-3).
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.
As,
(1,−3) is in quadrant 4 and csc is negative.
Using Pythagoras,
H=√ 1² + (-3)²
H= √10
So, cosec θ= H/P
= √10/ (-3)
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