Answer:
Step-by-step explanation:
x = 9/5
The solution of the equation [tex]x^2 + 3x - 9 = 0[/tex] by completing the square would be [tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex].
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that the equation is,
[tex]x^2 + 3x - 9 = 0[/tex]
Now completing the square as
[tex]x^2 + 3x - 9 = 0[/tex]
Add and subtract by 9/4,
[tex]x^2 + 3x + \dfrac{9}{4} - \dfrac{9}{4} - 9 = 0[/tex]
[tex]x^2 + 3x + ( \dfrac{3}{2})^2 - \dfrac{9}{4} - 9 = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{9}{4}+ 9) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 - ( \dfrac{45}{4}) = 0[/tex]
[tex](x + \dfrac{3}{2} )^2 = ( \dfrac{45}{4})[/tex]
Taking square root on both sides,
[tex](x + \dfrac{3}{2} ) = \pm ( \dfrac{\sqrt{45}}{2})[/tex]
Therefore, the solution of an equation is,
[tex]x = \pm ( \dfrac{\sqrt{45}}{2} - \dfrac{3}{2} )[/tex]
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Ben makes $39,600 a year. What the maximum amount he can afford for a mortgage each month ?
Answer:825
Step-by-step explanation:
Brainliest and 10 points for answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
How do you find the x- and y-intercepts of an equation?
A) To find the x-intercept, substitute 0 for x. To find the y-intercept, substitute 0 for x.
B) To find the x-intercept, substitute 0 for x. To find the y-intercept, substitute 0 for y.
C) To find the x-intercept, substitute 0 for y. To find the y-intercept, substitute 0 for x.
D) To find the x-intercept, substitute 0 for y. To find the y-intercept, substitute 0 for y.
Answer:
To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.
Answer:
C
Step-by-step explanation:
A, B, and D don't make sense
PLEASE HELP!!
The figure is made up of a rectangle and 2 right triangles.
What is the area of the figure?
O 1259 units2
O 1292 units2
O 1413 units2
O 1566 units2
The rectangle is 28×34 and the two triangles are (1/2) 11 (28) and (1/2) (9)(34)
A = 28(34) + (1/2) 11 (28) + (1/2) (9)(34)
A = 1259
Answer: 1259 sq units
Olivia flips a two-sided counter and then spins a spinner with six equal-size sections labeled 1 through 6. One side of the counter is red. The other side is yellow. She performs this experiment 80 times. The relative frequency of tossing red and spinning a number greater than three was 25 . What is the difference between the number of expected outcomes and the number of actual outcomes?
Answer:
The difference between the number of expected outcomes and the number of actual outcomes = 5
Step-by-step explanation:
She tosses a two sided counter and spins a spinner with six equal sized sections numbered 1 to 6.
Probability of the counter landing on either of the two sides is exactly = (1/2)
Probability of the counter landing on the red side = (1/2)
Probability of the spinner landing in a region greater than 3 = Probability of the spinner landing in a region of 4, 5 or 6. = (3/6) = (1/2)
In one toss and spin, the probability of a toss landing on red and the spinner landing on a number greater than 3 = p = (1/2)×(1/2)
p = (1/4)
Expected number of times that a toss will land on a red and a spinner will land on a number greater than 3 in 80 trials
= np = 80 × (1/4) = 20
Number of actual times that the toss lands on a red and a spinner lands on a number greater than 3 in 80 trials = 25
The difference between the number of expected outcomes and the number of actual outcomes = 25 - 20 = 5
Hope this Helps!!!
Please, someone, help me quickly!!
Answer:
(B)
Step-by-step explanation:
The value of 9 is more than the value than 4.
Therefore,
9 > 4.
4 is not greater than 9, and nine is not less than four.
Brainilest Appreciated!
can someone help with this please,, also explain if you can..
Answer:
story 1
Step-by-step explanation:
because it says 2 higher than -2 so -2+2 is 0
Can someone help and explain A and B please...
Find an explicit formula for the geometric sequence 3, 15, 75, 375...
Answer:
3 * 5 ^ (n-1)
Step-by-step explanation:
3 is the first term and it multiplies by 5
The explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
The standard explicit formula for a geometric sequence is expressed as:
[tex]T_n = ar^{n-1}\\[/tex]
a is the first term
r is the common ratio
n is the number of terms
Given the sequence of numbers 3, 15, 75, 375...
r = 15/3 = 75/15 = 5
a = 3
Substitute the given parameters into the formula to have:
[tex]T_n = ar^{n-1}\\T_n=3(5)^{n-1}[/tex]
Hence the explicit formula for the geometric sequence is [tex]T_n = 3(5)^{n-1}[/tex]
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i need your help please asap
Step-by-step explanation:
First we will calculate the total amount spent on each website so
Website A = 49.95 + 4.39 = 54.34
Website B = 47.68 + 6.95 = 54. 63
So website A is cheaper by €0.29
In a right triangle, sin (40 – x)° = cos (3x).What is the value of x?
Answer:
Value of x = 25
Step-by-Step Explanation:
~ Knowing that, in a right triangle ~
sin(40-x)=cos(3x) ⇒
sin(40-x)=sin(90-3x) ⇒
40 - x = 90 - 3x ⇒
40 - x +3x=90 - 3x +3x =>
40+2x=90 =>
2x=50 =>
x = 25
Now it is proven to be that,
x = 25
PLEASE HELP AGAIN, SORRY I SUCK AT MATH.
Answer:
C. 24 degrees
Step-by-step explanation:
All triangle must be 180 degrees in total. So you have to add all the known degrees together to find the missing degree.
120+36=156
Then subtract the sum of the known angles from 180 to find the degree of the unknown angle
180-156=24
Answer: C
Step-by-step explanation:
I'll explain why.
The sum of the angles in a triangle must be equal to 180º. We already know 2 of the 3 angles, therefore, we can make an equation to find x.
The sum of the angles (x+36+120) must be equal to 180 (=180)
x+36+120=180
Combine like terms
x+156=180
Subtract 156 to isolate x
x=180-156
x=24
Select the table that represents a linear function.
Answer:
D
Step-by-step explanation:
A linear function has a constant slope. Meaning that for any equal change in x, there will be an equal change in y.
What is the sum of 1-2 and V-18?
Answer:
v-19
Step-by-step explanation:
Answer:
It depends on what you mean.
Step-by-step explanation:
If its to separate questions,
1-2= 1
V-18= -13
If its one whole question then
1-2 - V-18= 14
1-2 / V-18= -0.07692307692
1-2 * V-18= -13
1-2 + V-18= -12
Hope this helps! :D
HELP!!!!!!!!!
Plz Show working:)
Step-by-step explanation:
Hope this help you !! ;))answer of (ii) : perimeter = 66m
area = 272m^2
What is the mean absolute deviation of this data set? 26, 31, 32, and 39
Answer:
3.5
Step-by-step explanation:
26, 31, 32, and 39
First we need to find the mean
(26+ 31+ 32+ 39) /4
128/4 = 32
The mean absolute deviation is sum of the positive difference between the number and the mean divided by the number of terms
((32-26)+ (32-31)+ (32-32)+ (39-32)) /4
14/4
3.5
Need help please owo with all of them
Answer:
d, c and a
Step-by-step explanation:
O///O
bz is tangent to circle o. ac is a diameter. mbc=90. mcd=30. mde=20.
state the theorem(s) that you used to find the measures of angles 1-10.
Answer:
1. Arc angle
2. Angle at circumference
3. Base angle of an isosceles triangle
4. Sum interior of angles in a triangle
5. Sum interior of angles in a triangle
6. The sum of angles on a straight line
7. Sum interior of angles in a triangle
8. Sum interior of angles in a triangle
9. Angle from a tangent to the radius of a circle
10. Alternate angles of line crossing two parallel lines
Step-by-step explanation:
Here, we note that, the angles where derived as follows;
1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°
2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference
∴ The angle at the circumference, angle 2 = 180°/2 = 90°
3. Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°
4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)
∴ 25° + 90° + ∡C = 180°
Hence ∡C = 180° - (90° + 25°) = 65°
5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius
Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives
∡8 + 90° + 30° = 180°, hence;
∡8 = 180° - (90° + 30°) = 60°
∡8 = opposite ∡8 = 60°
Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)
Therefore ∡5 = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°
6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)
Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°
7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)
∡E + ∡2 = 180° (The sum of angles on a straight line)
∴ ∡E = 180° - ∡2 = 180° - 90° = 90°
Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°
∴ ∡7 = 35°
8. ∡8 = 60° as found above
9. ∡9 = 90° (Angle from a tangent to the radius of a circle)
10. ∡10 = ∡8 = 60° (Alternate angles).
The price of a gallon of milk, in dollars, is measured in the
Answer:ones
Step-by-step explanation:
Jake received a student loan for $12,000. He plans on paying off the loan in five years. At the end of five years, J. Cole have paid $3600 in interest. What is a simple interest rate on the student loan?
Answer:
The simple interest rate on the student loan is 6%.
Step-by-step explanation:
To solve for the simple interest rate, use the formula for total simple interest:
[tex]I = Prt[/tex]
[tex]I[/tex] = total interest paid
P = principal, or starting value
r = interest rate in decimal form
t = time in years
State known values
P = 12,000
t = 5
[tex]I[/tex] = 3,600
Substitute known values and isolate "r"
[tex]I = Prt[/tex]
3,600 = (12,000) (r) (5)
3,600 = (60,000) r
r = 0.06
Since "r" is given as a decimal, convert this to a percentage by multiplying by 100.
0.06 = 6%
∴ The simple interest rate on the student loan is 6%.
Answer=6%
Step-by-step explanation:
Principal(P)=12000
Time(T)=5 yrs
Interest(I)=3600
We have,
I=PTR/100
3600=(12000*5*R)/100
3600*100=60000*R
R=360000/60000
R=6%
Hey, I need some help with this:
Give an example of what an inverse operation is and how they are used in solving equations
Inverse operations are an operation that undoes each other. For example, addition and subtraction, multiplication and division, squares and square roots.
For example, we have the equation:
2 + 2 = 4
The inverse of this equation is:
4 - 2 = 2
Best of Luck!
233 is equal to r more than 48?
Answer:
R = 152
Step-by-step explanation:
what i did was if it is talking about more than 48 something plus 48 is 200 so
200 - 48 = 152
r = 152
so 200 is 152 more than 48
Hope this helpsBrainliest plzAsk any more math questions if you wantCan someone help with step by step
Answer:
See explanation
Step-by-step explanation:
[tex] In\: \triangle ABC \:\&\: \triangle EDC\\
\angle ABC \cong \angle EDC... (Right \: \angle s) \\
\angle ACB \cong \angle ECD... (Vertical \: \angle s) \\\therefore \triangle ABC \sim \triangle EDC... (By\: AA\: Postulate) \\[/tex]
Which of the following is equivalent to the complex number i8?
Choose 1 answer:
mi
1
-1
pl
Stuck? Watch a video or use a hint.
Report a problem
Answer:
1
Step-by-step explanation:
note that i² = - 1
Thus
[tex]i^{8}[/tex]
= i² × i² × i² × i²
= - 1 × - 1 × - 1 × - 1
= 1 × 1
= 1
The value of complex number is 1. Therefore, the option B is the correct answer.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
The given complex number is i⁸.
We know that, i²=-1
Now, i⁸ can be written as i²×i²×i²×i²
= -1×(-1)×(-1)×(-1)
= 1
Therefore, the option B is the correct answer.
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Please Help!!! As quickly as possible!!!
Answer: Bristol's heart rate reaches a maximum of 120
bpm
Step-by-step explanation:
Answer:
Bristol's heart rate reaches a maximum of 120 bpm
At the end of yoga class, Bristol's heart rate returned to her resting heart rate
The graph that models Bristol's heart rate is a parabola
Step-by-step explanation:
Find the volume of the cone
Answer:
12π
Step-by-step explanation:
Volume of the cone is πr^2 * h / 3
r = 3
h = 4
9π * 4 / 3 = 12π
Answer: 37.6991118
Step-by-step explanation:
A running track is 1/4 of a kilometre. What is the
total distance a runner travels if he goes three
times round the track?
How many times would you have to go round the
track to run 2 kilometres?
Willow has read 1/7 of the books in the library.
Answer:
If a runner went around the track 3 times, he would have ran 3/4 of a kilometre. He would have to run around the track 8 times to run 2 kilometres.
Step-by-step explanation:
Answer:He would have to go around the track 8 times to get 2 kilometers
Step-by -step explanation:
-1 3/7 • (-3 2/5)
Find the product simplify if possible
Answer:
6 4/5
Step-by-step explanation:
-1 3/7 • (-3 2/5)
Let's turn them both into fractions with no whole numbers to make this easier:
-10/7 • -17/5
Now we can multiply straight across much easier!
170/35 (the negatives canceled each other out)
34/5 (simplified)
6 4/5 (answer)
Hope this helps! Please mark Brainliest :)
I need help nothing is working for the answer p÷3> 2
Answer:
p > 6
Step-by-step explanation:
Given
[tex]\frac{p}{3}[/tex] > 2 ( in fractional form )
Multiply both sides by 3 to clear the fraction
p > 6
Answer:
honestly idk
Step-by-step explanation:
it may be p (1/3)
hope this is right:000
Find the interquartile range (IQR) of the data plot below
Answer:
3.5
Step-by-step explanation:
0 1 1 3 3 3 4 5 7
median= 3
Q1= 1
Q3= 4.5
4.5-1= 3.5
Answer:3.5
0,1,1,3,3,3,4,5,7
PLEASE HELP FAST
Which transformation preserves size and shape. Choose ALL correct answers
A) Dilations
B) Rotations
C) Translations
D) Reflections
Question 2
Which transformations preserve orientation?
A) Translations
B) Rotations
C) Reflections
D) Dilations
Answer:
A) Dilation C)Reflections or B) Rotations
Step-by-step explanation:
