Answer:
(-3±√61)÷2
Step-by-step explanation:
First we expand the brackets to give us :
x²+5x-14 = -1 +2x
Now we make this into the quadratic format (x²+ax+b=0) by subtract -1 and 2x from both sides :
x²+3x-13 = 0
This quadratic cannot be factorized so we must use the quadratic formula :
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] or x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
a = 1 , b = 3 , c = -13
Now we simplify as much as possible by first substituting values known :
x = [tex]\frac{-3+\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]
Now we evaluate the exponent :
x = [tex]\frac{-3+\sqrt{9 -4(1)(-13)} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]
Now we multiply the numbers :
x = [tex]\frac{-3+\sqrt{9 +52 } }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{9 +52 } }{2(1)}[/tex]
Now we add the numbers :
x = [tex]\frac{-3+\sqrt{61} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{61} }{2(1)}[/tex]
Now we multiply the denominator:
x = [tex]\frac{-3+\sqrt{61} }{2}[/tex] or x = [tex]\frac{-3-\sqrt{61} }{2}[/tex]
So our final answer is (-3±√61)÷2
Hope this helped and 5 stars, a heart and brainliest please
If sin A = 4/5 find the value of cot A + tan A.
Answer:
2.08
Step-by-step explanation:
[tex]sin^{-1} 4/5 = 53.13\\tan 53.13 = 1.33\\cot 53.13 = 0.75\\1.33 + 0.775 = 2.08[/tex]
Answer:
The answer is 2
Step-by-step explanation:
[tex]Cot(x)=\frac{1}{tan(x)} =\frac{Cos(x)}{Sin(x)}[/tex]
[tex]Tan(x) = \frac{Sin(x)}{Cos(x)}[/tex]
[tex]Cos(\frac{\pi }{2} -x)=sin(x)[/tex]
This means that
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}[/tex]
This will be a long one to solve
-> apply cos identity to right side
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}[/tex]
-> simplify according to unit circle
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
->apply cos identity again
[tex]\frac{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]
If you apply for unit circle numbers,
you will get 2
I do not recommend using a calculator for these questions, but instead, turn the form into [tex]sin\frac{\pi }{2}[/tex] other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer
The performance of a cyclist in a race is affected by whether it rains or not that day. The probability the cyclist crashes is 5/8 when it rains and 1/8 when it's dry. On a given day the probability of rain is 1/3 . What is the probability that the cyclist doesn't crash on any given day? please help me
To solve this problem, we have to consider the fact that if the probability that the cyclist may crash due to some circumstance. The probability the cyclist doesn't crash at any given day is 3/8
ProbabilityThe probability the cyclist crash when it's wet or dry will be the
[tex]P = P_w_e_t * P_d_r_y[/tex]
P(wet) = 5/8P(dry = 1/8The probability the cyclist crash on any given day is
[tex]P = \frac{5}{8}*\frac{1}{8} =\frac{5}{64}[/tex]
we can subtract 1 from the value above to find the probability the cyclist doesn't crash at any given day
[tex]P = 1 - \frac{5}{64} \\P=\frac{3}{8}[/tex]
The probability the cyclist doesn't crash at any given day is 3/8
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Which system of equations has a solution of (-2,-2,-2)?
OA
s+y=0
3-==-2
s+y=z=-4
OB. 31 - y = -8
y - 3z = -8
2 + y + z = -8
OC.
1 + 2y = -6
y + 2z = -6
I-y-z = 2
OD. 1-2y + z = 0
2y +9z = -20
I= y + z = 0
The system of equations that have a solution of (-2,-2,-2) is (b) x + 2y = -6, y + 2z = -6 and x - y - z = 2
How to determine the system of equations?The attached figure represents the proper format of the equations.
The solution is given as:
(x,y,z) = (-2,-2,-2)
To determine the system of equation, we simply substitute the values of x, y and z in the equations in the options.
So, we have:
Option 1:
x + y = 0
y - z = -2
x + y - z = -4
Evaluate
x + y = 0
-2 - 2 = 0 --- False
This means that this system of equations do not have a solution of (-2,-2,-2)
Option 2:
x + 2y = -6
y + 2z = -6
x - y - z = 2
Evaluate
x + 2y = -6
-2 + 2 * -2 = -6 --- True
y + 2z = -6
-2 + 2 * -2 = -6 ---- True
x - y - z = -2
-2 + 2 + 2 = 2
This means that this system of equations have a solution of (-2,-2,-2)
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Find the amplitude of this function.
The amplitude is 2.5
Equation:
the equation to find the amplitude is (max-min) / 2.
using this equation, it would be (4 - (-1)) / 2
5 / 2 = 2.5
The pendulum of an antique clock has been damaged and needs to be
replaced. If the original pendulum completed one swing every 1.5 seconds,
how long should the new pendulum be? Use the formula:
T= 2.
1980
OA. 351 centimeters
OB. 0.25 centimeters
O C. 55.9 centimeters
O D. 234.8 centimeters
If the original pendulum completed one swing every 1.5 seconds. How long should the new pendulum be is: C. 55.9 centimeters.
How long should the new pendulum be
Using this formula
T=2π√I/g
Where:
T=1.5 seconds
l =length of pendulum
g= acceleration of gravity=9.8m/s²
Let plug in the formula
1.5 seconds=2π√I/9.8
l/9.8=0.05699
l=0.05699×9.8
l=0.5585
l=55.9 centimeters (Approximately)
Therefore How long should the new pendulum be is: C. 55.9 centimeters.
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solve these algebraic fractions please with explanation would be great
Answer:
look above
Step-by-step explanation:
hope it helps
find the area of the partial circle. use 3.14 for pi.
Thats a semi circle
Area
πr²/2π(1)²/2π/23.14/21.57cm²If you walk 6 blocks east, 2 blocks north, 3 blocks west and 4 blocks south, then what is the total distance you travel?
Answer:
6 + 2 + 3 + 4 = 15
so 15 blocks
a block is about 0.05 miles
so 15 blocks in miles is 0.75 miles
If sin A = 3/8, find the value of cosec A - sec A.
Answer:
[tex]\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]
Step by step explanation:
[tex]\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies 1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\[/tex]
[tex]\implies \dfrac 1{\cos A} = \pm\dfrac{8}{\sqrt{55}}[/tex]
[tex]\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]
Hello !!! please help me <3 will give brainle and 25 points please help !!!!
answer: 375
Step-by-step explanation:
panda bear caps: 25
they ordered 100 in total
25/100 = 1/4, a quarter
then you find a quarter of 1500
1500/4= 375
Math!! finding volume of prisms
The volume of the rectangular prism will be 16.2 cubic ft.
How to find the volume of a right rectangular prism?Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,
then its volume is given as:
V = a x b x c unit^3
The dimensions of the given rectangular prism;
Length = 2.7ft
Width = 3 ft
Height = 2 ft
The volume of the rectangular prism
V = a x b x c unit^3
V = 2.7 x 3 x 2
V = 16.2 cubic ft
Hence, the volume of the rectangular prism will be 16.2 cubic ft.
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y inversely proportional to x
when y=,x=9
work out an equation connecting y and x
What does y equal to? I think you had a typo
Find the range of the following equation for the domain {-4, 0, 3} f (x) = -2x^2 -3
The range of the function is {-34, -2, -20}
How to determine the range?The function is given as:
f(x) = -2x^2 - 2
The domain is {-4, 0, 3}
Substitute the domain values in the function.
f(-4) = -2(-4)^2 - 2 = -34
f(0) = -2(0)^2 - 2 = -2
f(3) = -2(3)^2 - 2 = -20
This means that the range of the function is {-34, -2, -20}
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27-(2c+3) = 2(c + 7) + c
Answer:
c=2
Step-by-step explanation:
We can first take out the parenthesis: 27-2c-3=2c+14+c. We can combine: -2c+24=3c+14. Then, we can subtract 14 from both sides: -2c+10=3c. Then, we can add 2c on both sides: 10=5c. To find c, we can do 10/5=2.
If the dimensions of the following cylinder are doubled, what will be the surface area of the new cylinder? 1,406.72 in. 2 2,813.44 in. 2 1,607.68 in. 2 5,626.88 in. 2
Based on the calculations, the surface area (SA) of a cylinder is equal to: B. 2,813.44 in.²
How to calculate surface area of a cylinder?Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:
SA = 2πrh + 2πr²
Where:
h is the height.r is the radius.The dimensions of this new cylinder would be equal to:
Radius = 8 × 2 = 16 in.
Height = 6 × 2 = 12 in.
Substituting the given parameters into the formula, we have;
SA = (2 × 3.14 × 16 × 12) + 2 × 3.14 × 16²
SA = 1,205.76 + 1,607.68
SA = 2,813.44 square inches.
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Complete Question:
If the dimensions of the following cylinder are doubled, what will be the surface area of the new cylinder? Radius: 8 in and Height: 6 in.
Group of answer choices.
A. 1,406.72 in.²
B. 2,813.44 in.²
C. 1,607.68 in.²
D. 5,626.88 in.²
I WILL GIVE BRAINLIEST
My mother pays my brother twice as much allowance each week as she pays me because he cleans the bathrooms. Together we get $24 each week. How much is my brother's allowance each week?
A. $4.00
B. $8.00
C. $16.00
D. $24.00
Answer:
C is the answer
Step-by-step explanation:
16+ (16/2)=16+8=24
How many tickets did Airon sell in 2018?
Answer:
11320 is the answer .hope i help you
Question 7(Multiple Choice Worth 1 points)
(02.05 LC)
Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points 0, 4 and negative 4, 0. Line g of x passes through points negative 9, 0 and negative 4, 5.
−4
−5
4
5
The value of k based on the information given will be k = 2.
How to calculate the value?It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).
The slope of x will be:
= (4 - 0)/(0 + 4)
= 4/4
= 1
By using slope point form, y = kx + 4.
Substitute x = 2.
g(-2) = -2k + 4 = 0
2k = 4
k = 4/2 = 2
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f(4)=
V
If g(x) = 2, x =
V
By looking at the given graph, we can see that:
f(4) = -10g(x) = 2 if x = 0.How to identify the value of the function?
First, we want to find the value f(4). To get that, we need to look at the graph and see the y-value of the function f(x) when x = -4.
By looking at the graph, we can see that f(4) = -10.
Now we know that g(x) = 2, and we want to find the value of x.
Then we need to see the x-value such that g(x) = 2, by looking at the graph of g(x), we can see that it is equal to 2 in the vertex, which is at x = 0.
Then g(x) = 2 when x = 0.
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Which pair of angles are vertical angles? 6 and 5 2 and 3 1 and 3 5 and 8
Answer:
1 and 3
Step-by-step explanation:
1 and 3 are vertical angles
Libby built a fence that was 56ft for over 4 days, she built the same length each day. how many inches of fence did libby build each day?
In Question 1 and Question 2, what is the distance from the center if the circle to a point on the circle? Take this idea a step further: what is the
relationship between the center of any circle and the points that lle on the circle?
Step-by-step explanation:
I don't see question 1 and 2.
but it did be way for you : the distance from the verge of a circle to a point on the circle is always the radius.
that is the whole concept of a circle : it is the line (or curve) of all points that have the same, constant distance r from a single point.
A jazz concert brought in $153,500 on the sale of 7,500 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?
The number of $15 tickets is
Answer:
the answr is 87 jistg ebcaujse
Step-by-step explanation:
3,500 tickets were sold for $15 each and 4,600 tickets were sold for $25 each.
Let x be the number of $15 tickets and y be the number of $25 tickets.
We know that:
x + y = 7,500 (the total number of tickets sold)
15x + 25y = 153,500 (the total amount of money made from ticket sales)
We can use the first equation to express y in terms of x:
y = 7,500 - x
We can substitute this expression of y into the second equation:
15x + 25(7,500 - x) = 153,500
Solving for x:
15x + 25(7,500) - 25x = 153,500
15x + 187500 - 25x = 153,500
-10x = -34,000
x = 3400
Therefore, 3,400 tickets were sold for $15 each and 7,500 - 3,500 = 4000 tickets were sold for $25 each.
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0 belongs to what family of real numbers?
Irrational
Rational, Integer, Whole
Rational
Rational, Integer, Whole, Counting
Answer:
Rational, Integer, Whole
Step-by-step explanation:
Zero(0) can be classified as a whole number, rational number, and non-negative integer.Zero is not a counting number because every counting starts with zero and counting zero (0) means nothing.Which function has the same domain as y= 2√x?
Y = √2x
Oy=2³√x
Oy=√x-2
O y = ³√x-2
The function that has the same domain as y= 2√x is (a) y = √2x
How to determine the function?The function is given as:
y= 2√x
The above function is a square root function.
All square root functions have the same domain when they are not translated.
This means that
y = √2x has the same domain as y= 2√x because it is not translated
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Find k.
10 mi
60⁰
K
30⁰
Simplify this expression.
7
12
43
36
37
36
es
A)
B)
C)
D)
11
12
003
8
33
d
Step-by-step explanation:
Sally has 90 apples and she adds a double of what she subtracts. Now, she has 1/4 of 1000. How much does she add?
Answer:
I think it's 160...
Step-by-step explanation:
1/4 of 1000 is 250
250
- 90
____
160
10
Select the correct answer.
Which equation is equivalent to the given equation?
- 4(x - 5) + 8x = 91 - 3
OA -5x = 2
OB. 5 = 17
OC. -5x = -23
OD. 5x = -12
Recet
Next
The equation that is equivalent to the given equation is 4x = 68. No answer is correct
Equations and expressionsEquations are two expressions equated to each other. Given the equation below;
- 4(x - 5) + 8x = 91 - 3
Expand
-4x + 20. + 8x = 88
Collect the like terms
4x + 20 = 88
4x = 88 - 20
4x = 68
Hence the equation that is equivalent to the given equation is 4x = 68
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8- Determine the midpoint of a line segment with the endpoints (8, 0) and
(4,6)
A. (3,6)
B. (7,3)
C. (6,3)
D. (7.6)
Can someone help pls ?
Answer:
C. (6, 3)
Step-by-step explanation:
Use the midpoint formula!
Midpoint Formula
[tex]\text{midpoint} = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
x₁, x₂ ... x-coordinates of the endpoints
y₁, y₂ ... y-coordinates of the endpoints
Given endpoints:
(8, 0)
(4, 6)
Points are in form (x, y).
Now let's substitute the variables in the formula with our values.
[tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]
[tex](\frac{8 + 4}{2}, \frac{0+ 6}{2})[/tex]
[tex](\frac{12}{2}, \frac{6}{2})[/tex]
[tex](6, 3)[/tex]
(6, 3) is our midpoint!