Answer:
1.5 is the number.
Explanation:
Let the number be 'n', this is 100% - original number.
When increased by 40%, 100% + 40% = 140%.
140% × n = 2.1
1.4n = 2.1
n = 2.1/1.4
n = 1.5
Hence, the original number is 1.5.
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:
can someone help me with this problem pleaseee
Answer:
x-intercept: (-5, 0)
y-intercept: (0, -4)
Step-by-step explanation:
The x-intercept is as the name implies when the line intersects the x-axis (the horizontal axis) or when y is equal to 0. If you look at the graph it intersects the x-axis at (-5, 0). The y-intercept follows the same concept except it's when it intersects the y-intercept (vertical axis) or when x is equal to 0. If you look at the graph it, it intersects the y-axis at (-4, 0).
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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if sin theta=-3/5 in quadrant III what is cos theta
Answer:
Just simply input in your calculator arcsin of -5/6. Arcsin is the sign that looks like sin to the power of -1, even though it doesn't mean sin to the power of -1. This comes out to 303.6 degrees. So, it actually isn't in quadrant 3, it's in quadrant 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:
Calculate the following limit:
[tex]\displaystyle \lim_{x \to \infty}{\dfrac{\log(x^8 - 5)}{x^2}}[/tex]
If we evaluate at infinity, we have:
[tex]\bf{\displaystyle L = \lim_{x \to \infty}{\frac{\log(x^8 - 5)}{x^2}} = \frac{\infty}{\infty} }[/tex]
However, the infinity of the denominator has a higher order. Therefore, we can conclude that [tex]\boldsymbol{L = 0.}[/tex]
However, proving that the limit is 0 without using L'Hopital or the "order" criterion is complicated. To do so, let us denote:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} }[/tex]
To find the limit, we must look for two functions h(x) and g(x) such that h(x)≤ f(x)≤ g(x) and
[tex]\boldsymbol{\displaystyle \lim_{x \to \infty}{h(x)} = 0, \qquad \lim_{x \to \infty}{g(x)} = 0}[/tex]
If we find these functions, then we can conclude that [tex]\bf{\lim_{x \to \infty}{f(x)} = 0.}[/tex]
First, let's note that when x⁸ - 5 > 1, then log(x⁸ - 5) > 0 (and this is true when x is large). Likewise, we have that x² > 0 for x > 0. Therefore, we have:
[tex]\boldsymbol{\displaystyle f(x) = \frac{\log(x^8 - 5)}{x^2} \geq 0}[/tex]
when x "is big enough". Thus, we have h(x) = 0 where it is clear that [tex]\bf{\lim_{x \to \infty}{h(x)} = 0.}[/tex]
To find the second function, let's first note that \log is an increasing function, so since x⁸ ≥ x⁸ - 5, then log(x⁸) ≥ log(x⁸ - 5). So we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} }[/tex]
now, if we take y = e^y, then we can write
[tex]\boldsymbol{\displaystyle \frac{\log(x^8)}{x^2} = \frac{\log(e^{8y})}{e^{2y}} = \frac{8y}{e^{2y}}}[/tex]
A very important property about the exponential function is
[tex]\boldsymbol{\displaystyle e^x > \frac{x^n}{n!}}[/tex]
For any n [tex]\bf{n \in \mathbb{N}}[/tex] and x > 0. If we take n = 2, then we have
[tex]\boldsymbol{\displaystyle e^{2y} > \frac{(2y)^2}{2!} = \frac{4y^2}{2} = 2y^2}[/tex]
From this it follows that
[tex]\boldsymbol{\displaystyle \frac{1}{e^{2y}} < \frac{1}{2y^2} }[/tex]
Therefore, we have to
[tex]\boldsymbol{\displaystyle \frac{\log(x^8 - 5)}{x^2} \leq \frac{\log(x^8)}{x^2} < \frac{8y}{2y^2} = \frac{4}{y} = \frac{4}{\log x} }[/tex]
yes, [tex]\bf{g(x) = 4/\log x}[/tex] where [tex]\bf{\lim_{x \to \infty}{g(x)} = 0}[/tex]. Also, [tex]\bf{h(x) \leq f(x) < g(x)}[/tex]. Therefore, [tex]\bf{\lim_{x \to \infty}{f(x)} = 0}[/tex].
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\sf{\purple{Pisces04}}}}}}}[/tex]
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
Answer:
I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.
Step-by-step explanation:
See attached graph.
The value of f(–10) = 82 False
f(-10) = (-10)^2 - 5*(-10) + 12
f(-10) = (100) +50 + 12
f(-10) = 162
The graph of the function is a parabola. True
The graph of the function opens down. False
The graph contains the point (20, –8). False
The graph contains the point (0, 0). False
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
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Find the volume of a cube with side lengths of 12 cm
Answer:
1728 cm³
Step-by-step explanation:
Finding the volume of a cube is a simple process that is easy to remember. The formula for finding the volume of a cube is commonly taught as L × W × H (Length × Width × Height). This formula also works with finding the volume of rectangular prisms.
Since the shape you're finding the volume of is cube, the length is equal to its width as well as its height.
The first step of this problem is to plug in known values to the formula. Since length L = 12 cm, width W and height H are also equal to 12 cm.
12 × 12 × 12 is the new expression. The next step is to simplify this expression by multiplying.
Based on times tables, 12 × 12 = 144. So, the expression can be partially simplified to 144 × 12 for easier multiplication.
144 × 12 can be split into an addition problem based on the Distributive Property of Multiplication:
144 × (10 + 2) Expand the expression to remove parentheses.
144 × 10 + 144 × 2 Multiply 144 × 10 and 144 × 2.
1440 + 288 Add the two addends.
1728 Remember to add back the units!
1728 cm³
The volume of a cube with side lengths of 12cm is 1728 cm³.
Note:
This step-by-step explanation is for better understanding how to do this mentally or without a calculator. In a calculator, finding the volume of a cube can be found by inputting either of these:
(Side Length) × (Side Length) × (Side Length) =
(Side Length) [(x³) or (³), depending on the model of calculator] =
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.
A dog sits at a corner of a square with side length 44 meters. the dog runs 10 meters along a diagonal toward the opposite corner. it stops, makes a 90 degrees right turn and runs 5 more meters. a scientist measures the shortest distance between the dog and each side of the square. what is the average of these four distances in meters?
Refer to the figure given below while reading the solution.
Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.
And then position B when traveled 5 m towards the right turning 90°.
We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).
Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).
Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.
The shortest distance of B from PQ = AC-ADThe shortest distance of B from SR = 44-(AC-AD)The shortest distance of B from SP = AC+ADThe shortest distance of B from RQ = 44-(AC+AD)So, the average of the shortest distances of B from each side is [tex]\frac{(AC-AD)+44-(AC-AD)+(AC+AD)+44-(AC+AD)}{4}=\frac{44+44}{4}=22[/tex]
Hence, the average of the shortest distance of B from each side is 22 m
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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)
Jared bought eighteen doughnuts to share with his coworkers. If each doughnut cost c cents, which expression represents his total cost?
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.
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
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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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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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.
The inverse of the function f(x) = 1/2x + 10is shown.
h(x) = 2x-0
What is the missing value?
Answer:
20
Step-by-step explanation:
the inverse of
y=1/2x + 10
is
x=1/2y+10
from here you just solve for y
x-10 = 1/2y
2(x-10) = y
2x-20 = y
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.
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
What is the distance from -5 to 0?
0, because 151=0
O 5, because 1-51=5
O5, because 1-51=-5
O-5, because 1-51 = -5
7 of 23 QUESTIONS
SUBMIT
Answer:
distance between -5 to 0 = 5 units
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
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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$
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]
does someone mind helping me with this problem? Thank you!
Solve for x in the equation
X
O x=-11±25
O x=-11+25
0 x--11+5√/5
Ox--11,5/5
2
x²+11x+121-125
4
=
Answer:
The answer for this question is c
The value of x from the quadratic term equation is x = ( -11/2 ) ± ( 5√5 ) / 2
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 11x + 121/4 = 125/4
Subtracting ( 125/4 ) on both sides , we get
x² + 11x + ( 121 - 125 ) / 4 = 0
x² + 11x - 1 = 0 be equation (1)
On simplifying , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
So , x = [ -11 ± √ ( 11 )² - 4 ( 1 ) ( -1 ) ] / 2
On further simplification , we get
x = -11 ± √ ( 121 + 4 ) / 2
x = [ -11 ± √125 ] / 2
x = ( -11/2 ) ± ( 5√5 ) / 2
Therefore , the roots of the equation are x = ( -11/2 ) ± ( 5√5 ) / 2
Hence , the quadratic equations are solved
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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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Please help me!! matrices question! ASAP
n + 7
------- = 2
13
Answer:
19
Step-by-step explanation:
(n+7)/13 = 2 [given]n+7=26 [multiply both sides by 13]n=19 [subtract 7 from both sides]