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(x - 3)(x + 9) = -27
Expand the brackets:
x^2 + 9x - 3x - 27 = -27
Simplify:
x^2 + 6x - 27 = -27
+ 27 to both sides
x^2 + 6x = 0
Factorise:
x(x + 6)
The solutions are x = 0, x = -6
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Answer: If you would like to solve (x – 3)(x + 9) = –27, you can do this using the following steps:
(x – 3)(x + 9) = –27
x^2 + 9x - 3x - 27 = -27
x^2 + 6x - 27 + 27 = 0
x^2 + 6x = 0
x * (x + 6) = 0
1. x = 0
2. x = -6
The correct result would be x = 0.
Step-by-step explanation:
In the diagram, point O is the center of the circle and m∠ADB = 43°. If m∠AOB = m∠BOC, what is m∠BDC?
Answer:
B - 43
Step-by-step explanation:
The required measure of the angle m∠BDC is 43°.
Given that,
In the diagram, point O is the center of the circle, and m∠ADB = 43°. If m∠AOB = m∠BOC, what is m∠BDC is to be determined.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
Property of circle -
"The angle subtended by an arc of the circle to the center point of the circle is double the angle subtended by the same arc on any point the circumference of the circle."
So,
From the above property,
Angle subtended by Arc AB at center or m∠AOB is 2 * 43 = 86°
From given m∠AOB = m∠BOC,
Implies
m∠BOC = 86°
Angel subtended by arc BC at D is m∠BDC = m∠BOC /2
= 86 /2
= 43°
Thus, the required measure of the angle m∠BDC is 43°.
Learn more about circle here:
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Find the height of the tree. Show steps
Answer:
Step-by-step explanation:
I don't say u have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
If you spin the following spinners, what is the probability it lands on a vowel and an even number?
Answer:
1/5
Step-by-step explanation:
vowels are a,e,i,o,u
2/5 times 3/6
even numbers are 2,4,6
6/30= 1/5
Answer:
2/5 * 1/2 = 1/5
Step-by-step explanation:
The First Spinner there are 2 vowels out of the 5 making the first fraction 2/5
The Second Spinner has 3 even numbers making it 3/6.
With 3/6 we can simplify it to 1/2.
Then Multiply to determine the probability
4. You sketch a right triangle that has a
hypotenuse of 12 centimeters, and one leg
that is 7 centimeters. How many centimeters
Is the other leg?
Answer:
√95 cm
Step-by-step explanation:
To solve, you need to use the pythagorean theorem, or a^2 + b^2 = c^2
The hypotenuse is the c and let one leg be b. You can write:
a^2 + 7^2 = 12^2
a^2 + 49 = 144
Now, you need to solve for a:
a^2 = 144 - 49
a^2 = 95
a = √95 cm, or about 9.75cm
Answer these questions.
What is the value of x, if 105% of 90 is equal to 200% of x?
The data set on the right represents
A teacher recorded all of his students' grades on
the final exam as:
DONE
62, 77, 78, 80, 82, 82, 83, 84, 85, 87, 89,95
Consider the formulas:
A: 52_ (x1 - x* +(x2 - x)2 + ... + (xin – x)2
n-1
(y - x)+(x2-x+ +(An - x}}
n-1
co2
(x2 – 40)2 + (x2 – 42+ +(x3 - ?
B.SE
(x2 - 4) + (x2 - 4 +
N
+(9-4)
Answer:
The correct option is C
(SEE THE ATTACHMENT)
Step-by-step explanation:
The question is unclear because the options given doesn't make any sense. We can consider the questions incomplete, After searching the internet, I found out what was the question and its options actually are. I hope it helps
(YOU CAN SEE THE ATTACHMENT BELOW)
Q) WHICH FORMULA SHOULD BE USED TO CALCULATE VARIANCE?
ANSWER)
We know that there are 2 types of variance, Population variance and sample variance. As in this question, we are considering all the values of the data to find variance. we'll find Population Variance. If we would considered only some values (sample) from the data (population), we would have considered to find sample variance.
Population Variance is given as sigma squared which is calculated by sum of square variables minus mean, divided by number of observation in population.
[tex]\sigma^2=\frac{\sum(x_i-\mu)^2}{N}[/tex]
which is represented by option C
Answer:
The data set on the right represents
✔ the population B
.
Which formula should be used to calculate the variance?
✔ C
What is the variance?
✔ 58.5
What is the value of the t that satisfies the equation below?
5(t + 2) - 3(2t + 1) = -2
1.
0
2.
-2
3.
9
4.
15
Solution,
5(t+2)-3(2t+1)=-2
or,5t+10-6t-3=-2
or,5t-6t+10-3=-2
or,-t+7=-2
or,-t=-2-7
or,-t=-9
t=9
Hope it helps
Good luck on your assignment
Answer:
[tex]t = 9[/tex]
Step-by-step explanation:
[tex]5(t + 2) - 3(2t + 1) = - 2 \\ 5t + 10 - 6t - 3 = - 2 \\ - t + 7 = - 2 \\ - t = - 2 - 7 \\ - t = - 9 \\ t = 9[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
2x^3y^2 (3x^2 – 5xy + y^2)
Answer:
6x⁵y² -10x⁴y³+2x³y⁴
Step-by-step explanation:
2x³y²(3x² -5xy+y²)
6x⁵y² -10x⁴y³+2x³y⁴
Which sequence are geometric? Select three options
It took John 16 minutes to cook 8 eggs. How long would it take to cook 15 such eggs?
Answer:
30 minutes
Step-by-step explanation:
First, you need to find the amount of time it takes to cook one egg. To do this, you do 16/8 to get 2 minutes per egg. Then, since you need to cook 15 eggs, you do 15 times 2 to find the total amount of time to cook. You should get 30.
The endpoints of VW are V(-4,9) and W(1,-6). Find the coordinates of the midpoint M
Answer:
(-3/2 or 1.5, 3/2 or 1.5)
x = -3/2 or -1.5
y = 3/2 or 1.5
Step-by-step explanation:
the midpoint formula is x1+x2/2 and then y1+y2/2 so -4 +1 = -3/2 for x. for y, 9 + -6 = 3/2. so the midpoint would be (-3/2 or 1.5, 3/2 or 1.5) depending on if you’re using decimals or fractions
The midpoint of VW is (-3/2,3/2).
What is midpoint of a line ?The midpoint of a line divides a line segment into two equal parts and the point is called the midpoint.
According to the given question the endpoints of VW are V(-4,9) and W(1,-6) and we have to find midpoint of VW.
We know midpoint of x is (x₁+x₂)/2 and midpoint of y is (y₁+y₂)/2.
Here V is (x₁,y₁) = (-4,9) and W is (x₂,y₂) = (1,-6).
∴ Midpoint of x is
= (-4 + 1)/2
= -3/2.
AND
Midpoint of y is
= {9 + (-6)}/2
= 3/2.
learn more about midpoint here :
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Find the volume of the pyramid.
Answer:
7
Step-by-step explanation:
Formula=area of base x height / 3
A= ( 3 x 1 ) x 7 / 3
A= 3 x 7 / 3
A= 21 / 3
A= 7
The circumference of circle A is three times the circumference of circle B. Which statement about the areas of the circles is true? *I'll mark brainliest for first answer
what’s the answer to this ?
Answer: 12.73 cm
Step-by-step explanation:
The clock will move in a circular motion
The radius if the circle is 7.6 cm
So circumference= 2πr
= 2×22/7×7.6
=47.75 cm
Degree covered in 16 minutes=
360/60×16
= 96°
Now, since distance covered in 1° =
47.75/360 = 0.133
Distance covered in 96° =
47.75/360×96 = 12.73 cm ( approx.)
Please ANswer!!!
x^2 +25 + 2 = 2x^2 + 30
Will mark brianliest!
Solve, please!!!
Answer:
x^2 +25 + 2 = 2x^2 + 30
X^2 + 27 = 2X^2 + 30
- 27 - 27
X^2 = 2X^2 + 3
-X^2 = 3
X = SQRT. - 3
Answer:
± sqrt(3) i =x
Step-by-step explanation:
x^2 +25 + 2 = 2x^2 + 30
Combine like terms
x^2 + 27 = 2x^2 +30
Subtract x^2 from each side
x^2 + 27 - x^2 = 2x^2 - x^2 +30
27 = x^2 +30
Subtract 30
27-30 = x^2
-3 = x^2
Taking the square root of each side
±sqrt(-3) = sqrt(x^2)
±sqrt(-3) =x
±sqrt(-1) sqrt(3) =x
We know the square root of -1 = i
± sqrt(3)i =x
what is the approximate area of the cirlle shown below
Answer:
43ft^2
Step-by-step explanation:
A=πr^2
A=π×3.7^2
A=π×13.69ft^2
A=43ft ^2
Plzz mark brianliest if it suit your question..
What is 30% of 550cm3
Answer:
165cm³
Step-by-step explanation:
30% of 550cm³=30/100 *550cm³=3*55cm³=165cm³
If a credit card holder has a low APR. The minimum monthly payments will be?
A. higher
B. lower
C. unchanged
D. fluctuating
Answer:
Option B, the minimum monthly payments will be LOWER
Step-by-step explanation:
We can proof this by using hypothetical scenario below:
John has $1,500 with APR of 10% payable in 48 month equal instalment
Timmy has $1,500 with APR of 8% payable in 48 month equal instalment
Let us calculate monthly payment in each case
=pmt(rate,nper,-pv,fv)
rate is the monthly rate which APR/12
nper is 48
pv is the balance on the card which is $1,500
fv is the total monthly repayment which is unknown
John monthly payment=pmt(10%/12,48,-1500,0)=$38.04
Timmy monthly payment=pmt(8%/12,48,-1500,0)=$ 36.62
Since Timmy with a lower APR has a lower monthly payment, option B is correct
Susie leases a $13,000 car for three years. The estimated resell value at the end of the lease term is $7,683. The interest rate is 5.1%. Susie will pay on her lease monthly. What is the depreciation fee?
a) $43.95
b) $147.69
c) $249.53
d) $7,683.00
Answer:
The depreciation fee is the difference between the initial value of the car and its estimated resell value at the end of the lease term. In this case, the depreciation fee is $13,000 - $7,683 = $5,317.
To calculate the monthly payment on the lease, you would need to know the length of the lease in months, the interest rate, and the depreciation fee. You can then use the following formula to calculate the monthly payment:
Monthly payment = (Interest rate / 12) x (Initial value - Resell value) / Length of lease in months
For example, if the length of the lease is 36 months, the monthly payment would be:
Monthly payment = (5.1% / 12) x ($13,000 - $7,683) / 36 months = $114.78
Keep in mind that this is just an example calculation and the actual monthly payment on Susie's lease may be different depending on the specific terms of the lease agreement.
Step-by-step explanation:
I NEED TO QUICKLY PLS HELP ME PPLLSSSSS
AB, BE, and CF are all diameters of the circle. The measure of angle AOB is 40 degrees. The measure of angle DOF is 120 degrees.
Find the measure of angle COD.Find the measure of angle BOC.
Find the measure of angle COD
Angle COD is 60 degrees
angle BOC is 80 degrees
Because angle DOE is vertically opposite to angle boa, it is also 40 degrees. we know that angle DOF is 120, so angle FOE is 120-40 = 80 degree, and angle BOC is vertically opposite do it is 80 degrees.
since angle COD lies on a straight line it adds up to 180 degrees, so 180- 120 = 60 degrees
Katie and Tyler are working at their lemonade stand. They have sold 1/2 of a pitcher of lemonade and now have 1/3 of a pitcher left to sell.
What fraction of a pitcher of lemonade did they start with?
Answer:
5/6
Step-by-step explanation:
first you simplify the fractions into 6's. why, because 6 is the common denominator for these two fractions
1/2= 3/6
1/3= 2/6
now you add 2/6 plus 3/6
If k, m, and n are all prime numbers, list all factors of k∙m∙n.
Answer:
Factors of kmn are 1, k, m, n, km, mn, kn and kmn
Step-by-step explanation:
Given: k, m, and n are prime numbers
To find: factors of k∙m∙n
Solution:
A number is said to be prime if it has exactly two factors: 1 and the number itself
x is said to be a factor of y if x can divide y exactly.
Here,
1 can divide kmn
k can divide kmn
m can divide kmn
n can divide kmn
km can divide kmn
kn can divide kmn
mn can divide kmn
kmn can divide kmn
So, factors of kmn are 1, k, m, n, km, mn, kn and kmn
What are the solutions of x²-2x+2=0?
Answer:
A
Step-by-step explanation:
[tex]x^2-2x+2=0[/tex]
Plugging this into the quadratic formula:
[tex]x=\dfrac{2\pm \sqrt{4-8}}{2}=\dfrac{2\pm 2i}{2}= 1\pm i[/tex]
Therefore, the correct answer is choice A. Hope this helps!
Charles wants to analyze his last 9 math test scores with a
box plot to see how spread apart they are.
Arrange the scores in order, from lowest (on the left) to
highest
Answer:
We need numbers to graph it.
Step-by-step explanation:
You gotta give us the functions.
Answer:
80,84,86,87,90,91,92,94,100
Start is 80. End is 100. Lower Q is 85. Higher Q is 93
Range of scores is 20
Median of scores is 90
The LQR of scores is 8
Edge. 2021
Luke is flying a kite and realizes that 400 feet of string are out. The angle of the stream with the ground is 50°. How high is Luke’s kite above the ground
Answer:
Luke's kite is 306.4 feet high above the ground
Step-by-step explanation:
To find the height of Luke's kite above the ground, we will follow the steps below:
We can solve the problem using trigonometric ratio;
that is;
SOH CAH TOA
sinФ = opposite/hypotenuse
cosФ= adjacent/hypotenuse
tanФ=opposite/adjacent
From the diagram below:
opposite = x where x represents the height of Luke's kite above the ground
hypotenuse = 400
Ф = 50
The best trig ratio to use is sin
sinФ = opposite / hypotenuse
sin 50° = [tex]\frac{X}{400}[/tex]
cross-multiply
x = 400 sin 50°
x≈306 .4 feet
Luke's kite is 306.4 feet high above the ground
Graph the equation y = 1/3x - 5
Answer:
(0,-5) (3,-4) (6,-3) draw a straight line through them all
Step-by-step explanation:
the -5 means it goes down on the y-axis by 5
the 1/3 means it goes up 1 and right 3
Answer:
(0,-5) (3,-4) (6,-3) draw straight line across them :)
PLEASE HELP FAST WILL MARK BRAINLYEST!!!.which choices are in the solution set of the equation below 10x=15 A. 2.5 B. 2 C.5 D. 3 E. 1 F. 1. 5
Answer:
F) 1.5
Step-by-step explanation:
10x = 15
Divide both sides by 10
10x/10 = 15/10
x = 1.5
Answer:
Option F
Step-by-step explanation:
=> 10x = 15
Dividing both sides by 10
=> x = 1.5
Which of the following scenarios could be modeled by a step function? A. A moving company charges $65 per hour. They round minutes up to the next hour.
B. A sports shop tracks its total monthly sales of surfboards over 5 years. They note a peak in sales every year in the months of June and July followed by a steady decline and almost no sales during the winter months.
C. A restaurant allows patrons to choose one meat and two sides from their lunch menu for a set price. Additional sides are $2.50 each.
D. A savings account at Best Bank provides an interest rate of 8% per year on accounts with balances of at least $1,000
Answer:
A. A moving company charges $65 per hour. They round minutes up to the next hour.
Step-by-step explanation:
Let's define
x: hours worked
C(x): cost charged
The step function will be:
C(x) = 65 0 ≤ x ≤ 1
C(x) = 130 1 < x ≤ 2
C(x) = 195 2 < x ≤ 3
and so on.
Convert the following sum into a product. cosx + cos3x + cos5x + cos7x
Answer:
[tex]4\cos x\cos (4x)\cos (2x)[/tex]
Step-by-step explanation:
Given: [tex]cosx + cos3x + cos5x + cos7x[/tex]
To convert: the given sum into product
Solution:
Use formula: [tex]\cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )[/tex]
[tex]cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ][/tex]
[tex]cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)[/tex]
Which of the following does not have any dimension? Question 13 options: A) Line B) Point C) Ray D) Line segment
Answer:
B) Point
Step-by-step explanation:
Lines have length because they extend forever in both directions. Rays extend forever in one direction. Line segments have length. A point does not have any dimension.
Answer:
B
Step-by-step explanation:
