Answers
The solution is listed below:
[tex]3 x^{2} +27 \\ \\ =3( x^{2} +9) \\ \\ =3( x^{2} +3^{2}) \\ \\ =3( x^{2} -(3i)^{2}) \\ \\ =3(x-3i)(x+3i) \\ \\ =(3x-9i)(x+3i) [/tex]
Related Questions
T-Shirts R Us advertises shirts as shown below. mc002-1.jpg Which quantities in the advertisement represent a unit rate?
Answers
Answer:
C.) $10 per shirt
Step-by-step explanation:
have a nice day
The option C is more simplified answer for given condition, unit rate is $10.
What is unit rate?When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.
Given
There are 5 shirts in the image given to us composed of 3 white shirts and 2 black shirts.
A rate with 1 as its denominator is known as a unit rate.
Option A: A ratio of 3:2 or a fraction of 3/2 is indicated by 3 white shirts and 2 white black shirts.
The denominator is not 1, hence this cannot be a unit rate.
Option B: 5 white shirts to 2 black shirts. This cannot be a unit rate because the fraction 2/5 will not have 1 as the denominator.
Choice C: $10 for each shirt. Because it represents a ratio of 10:1 or a fraction of 10/1, this rate is a unit rate. Therefore, the price of 5 shirts will be $50.
D: $50 for each shirt. Because option C has provided us with a more straightforward sum of $10, which we must accept as we are dealing with unit rates, this would not be a unit rate in this question.
Hence Option C is most suitable answer.
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The complete question is in image.
Which of the following statements is true? If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are proportional. If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional. None of the choices are correct.
Answers
The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.
Explanation:The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.
To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.
Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.
hello can you please help me posted picture of question
Answers
The favorable outcomes in this case are the numbers divisible by 3. So the numerator lists the numbers that are divisible by 3, which are the favorable outcomes.
So, the answer to this question is option C
Given: ΔSTQ, ST = TQ
Line SD is perpendicular to TQ
m∠1=32°
Find: m∠S, m∠T, m∠Q
Answers
__________________________________________________________
Explanation:
__________________________________________________________
To find "m∠Q" :
Consider the triangle formed by ∠D , ∠1, and ∠Q ;
Given m∠1 = 32° ;
and m∠D = 90° (a "right triangle" ; as shown in "image attached" ;
and by definition, all triangles have 3 angles and 3 sides; and all 3 angles of a triangle add up to 180° ;
→ m∠Q = 180 − (90 + 32) = 180 − 122 = 58 ;
_______________________________________________________
Since this is an "isosceles triangle" ;
→ m∠S = m∠Q = 58° .
Since all angles of any triangle add up to " 180° " ;
→ m∠T = 180 − (58 + 58) = 180 − 116 = 64 ;
____________________________________________
Answer: m∠S = 58 ° ; m∠T = 64 ° ; m∠Q = 58 ° .
____________________________________________
Answer:
s=58 degrees, Q=58 degrees, T=64 degrees
Step-by-step explanation:
Consider the triangle formed by ∠D , ∠1, and ∠Q ;
Given m∠1 = 32° ;
and m∠D = 90° (a "right triangle" ; as shown in "image attached" ;
and by definition, all triangles have 3 angles and 3 sides; and all 3 angles of a triangle add up to 180° ;
→ m∠Q = 180 − (90 + 32) = 180 − 122 = 58
G a family has five children. if it is just as likely to have a boy as a girl, what is the probability that 3 of the children are girls and 2 are boys?
Answers
what is 0.0003840 expressed in scientific notation
Answers
0.0003840 = 0.003840/10 = 0.03840/100 = 0.3840/1000 = 3.840/10000
The one we're interested in is the last one, which has one non-zero digit to the left of the decimal point. The power of 10 in the denominator is the 4th power (the number of zeros is 4). 10^4 in the denominator is equivalent to multiplying by 10^(-4) in the numerator.
Expressed in scientific notation,
[tex]0.0003840=3.840 \cdot 10^{-4}[/tex]
0.0003840
Written in scientific notation!
Move the decimal point.
.00384 x 10^1
.0384 x 10^2
.384 x 10^3
3.84 x 10^4
38.4 x 10^5
Given a mean of 24.5 and a standard deviation of 1.7, within how many standard deviations of the mean do the values 24, 23, 28, 23, 24, and 25 fall?
Answers
Given mean = 24.5 and standard deviation = 1.7
Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].
Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].
Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].
Given values are 24, 23, 28, 23, 24, and 25.
So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.
Simplify the expression 6sqrt2/sqrt3
Answers
First you factor the 6
[tex] \frac{2 * 3 \sqrt{2} }{ \sqrt{3} } [/tex]
Simplify
[tex]2 \sqrt{2} * \sqrt{3} [/tex]
Multiply the square roots
[tex]2 \sqrt{6} [/tex]
The answer is [tex]2 \sqrt{6} [/tex]
Hope this helps!
Find the volume of the given prism round it to the nearest tenth, 6 cm, 3.9 cm, 13.2 cm
Answers
(6 cm)*(3.9 cm)*(13.2 cm) ≈ 308.9 cm³
John's monthly salary is 7,000. If John deposits 0.75 of his paycheck into a savings account. How much money does he put in his savings account every month?
Answers
John deposits $5,250 into his savings account every month, which is 75% of his monthly salary.
The student's question is about how much money John deposits into his savings account from his monthly salary. To solve this, we calculate 0.75 (or 75%) of John's monthly salary of 7,000.
Calculation: 0.75 imes 7,000 = 5,250
So, John deposits $5,250 into his savings account every month.
find the range for the given data in 115, 534, 122, 599, 417, 289 A) 534 B) 167 C)115 D)484
Answers
Find the area of the circle in terms of Pi
Answers
1) A = pi* (3^2)
2) A = 9pi
The area in terms of pi is 9pi cm^2.
I got 9pi cm^2, but it is always helpful to double check work. Hope this helps!
r - the radius
We have the diameter of the circle: d = 6cm.
d = 2r, therefore
2r = 6cm → r = 3cm
Substitute to the formula:
[tex]A=\pi\cdot3^2=9\pi\ cm^2[/tex]
Find the perimeter and the area of a rectangle measuring 8 1/4 yd long by 4 1/8 yd wide
Answers
perimeter = 2 * 8.25 + 2 * 4.125 =
16.50 + 8.25 =
24.75 yards
The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface area of the pyramid?
Answers
[surface area of the pyramid]=area of the base+4*[area of one lateral triangle]
area of the base=14*14------> 196 cm²
area of one lateral triangle=b*h/2
b is the length side of the square
b=14 cm
h is the slant height
h=15 cm
area of one lateral triangle=14*15/2-----> 105 cm²
[surface area of the pyramid]=196 cm²+4*[105 cm²]-----> 616 cm²
the answer is
616 cm²
Randy worked 18 hours each week for four weeks. for each of the next four weeks, he worked 1/3 fewer hours as the previous four weeks. what was the total number of hours he worked for the eight weeks
Answers
from 5th week to 8th week: 18 x 1/3 x 4 = 48 hours
72 + 48 = 120 hours
Sunny's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants. For every 3 tomato plants in Sunny's garden, there is 1 ____ plant.
Answers
from the list of plants there are 3 squash plants
3 squash plants x 3 tomato plants = 9 total tomato plants
the answer is Squash Plants
Answer: Squash plant is the right answer to fill the blank.
Step-by-step explanation:
Since we have given that
Number of tomato plants = 9
Number of pepper plants = 5
Number of squash plants = 3
Number of pumpkin plants = 6
Since the ratio of tomato plants to squash plants is 9 : 3 = 3 : 1.
So, for every 3 tomato plants in Sunny's garden, there is 1 squash plant.
Hence, Squash plant is the right answer to fill the blank.
The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.
Answers
the z-score is given by:
z=(x-μ)/σ
where:
σ-standard deviation
μ- mean
we are required to evaluate for x, given that P(x<X)=0.05
The value of z that corresponds to 5% will be:
z=-1.65
thus plugging our values we obtain:
-1.65=(x-62)/11
solving for x we get:
-18.15=x-62
thus
x=-18.15+62
x=43.85
x~44
Thus the lowest score is 44
The lowest marks that a student can have and still be awarded a passing grade is 44.
Step-by-step explanation:
Given :
Mean, [tex]\mu = 62[/tex]
Standard Deviation, [tex]\sigma = 11[/tex]
Calculation :
z score is given by,
[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)
Value of z corresponds to 5% is,
[tex]z =-1.65[/tex]
from equation (1) we get,
[tex]-1.65=\dfrac{x-62}{11}[/tex]
[tex]x=43.85[/tex]
[tex]\rm x = 44 \;\;(Approx)[/tex]
The lowest marks that a student can have and still be awarded a passing grade is 44.
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write the ratio 41 to 100 as a percent
Answers
Answer:
[tex]41\%[/tex]
Step-by-step explanation:
we have the ratio
[tex]\frac{41}{100}[/tex]
To write as percent, multiply the ratio by 100
so
[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]
Hey can you please help me posted picture of question
Answers
C. G(x)=x-6
The explanation is shown below:
You have that the patern function of the linear function is: F(x)=x. By definition, the patern function is the most basic function in the families of functions. If you have the linear function f(x)=x and you shifted it 6 units down, the function will be: f(x)=x-6, which inficates the it moves 6 units on the –y axis. Therefore, as you can see, the correct answer is the option mentioned above (The option C).
You are laying an asphalt driveway. How much area must you cover if the driveway is 21 feet long and 10.5 feet wide?
Answers
An asphalt driveway has the shape of a rectangle
so
area of rectangle=long*wide
area=21*10.5-----> 220.5 ft²
the answer is
220.5 ft²
Simplify 5(7y+2) can someone help me with the steps on how to simplify this problem and answer as an expression
Answers
Distribute (multiply) the 2 to the numbers in the parentheses.
35y + 10
How would you solve 1/8 divided by 6
Answers
The required 1/8 divided by 6 is equal to 1/48.
To solve 1/8 divided by 6, we can rewrite it as a fraction. The reciprocal of 6 is 1/6, so the division problem becomes (1/8) * (1/6). To multiply fractions, we multiply the numerators together and the denominators together.
Step 1 is given as:
= (1/8) * (1/6)
Step 2(simplification) is given as:
= 1 * 1 / 8 * 6
= 1/48
Therefore, the required 1/8 divided by 6 is equal to 1/48.
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How do I answer this dot plot?
Answers
Data Set A (mean, median, standard deviation) = (29.7, 29.5, √12.71)
Data Set B (mean, median, standard deviation) = (27.95, 27, √6.1475)
1. False. Data Set B is skewed to the right.
2. TRUE. 27.95 is within 3 of 29.7.
3. False. √12.71 ≠ √6.1475
4. False. The mean of Data Set A is 29.7.
5. False. Data Set A has the higher standard deviation.
6. TRUE. 29.7 is close to 29.5.
The true statements are
• the 2nd one
• the 6th one
Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 8 yellow balls and the second urn contains 9 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
Answers
This is because you have to start with the probability of each urn. The first urn has 13 total balls (5 white and 8 yellow). Since 5 of them are white, the odds of pulling a white ball are 5/13. Then find the same for the second urn (9 white and 2 yellow). Therefore there are 11 total balls and 9/11 chance of getting a white one. After finding both, multiply them together to get the answer.
[tex] \frac{5}{13} [/tex] * [tex] \frac{9}{11} [/tex] = [tex] \frac{45}{143} [/tex] = 31.5%
p(white ball) = 5/13
For the second urn:
p(white ball) = 9/11
Since the two drawings are independent events, the probability of both happening is the product of the individual probabilities.
p(drawing two white balls) = 5/13 * 9/11 = 45/143
Arnob may want to borrow his cousin’s tent, which is shown below. He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. (Picture below)
What is the center height of this tent, to the nearest tenth of a foot?
4.1 feet
8.1 feet
9.8 feet
12.0 feet
Answers
In this question, we will use Pythagoras theorem in order to find the height of the tent.
The center height of tent is 8.1 feet.
What is right triangle?Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
What is Pythagoras theorem?A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
perpendicular² + base² = hypotenuse²
Given,
Side length of each triangle = 4 feet
Hypotenuse of each triangle = 9 feet
Shared side = x
Given the triangles are right angled,
According to Pythagoras theorem,
a² + b² = c²
Here, a = 4 , b = x , c= 9
Substitute the values in Pythagoras theorem,
4² + x² = 9²
16 + x² = 81
x² = 81 - 16
x² = 65
Taking square root on both sides
x = √65
x = 8.062
x = 8.1 (Rounding nearest tenth)
Hence, the center height of tent is 8.1 feet.
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Corey drew 8 shapes. Four are squares, two are triangles, and the rest are parallelogram. Write two fractions that name the part of the shapes that are quadrilaterals
Answers
6(4 squares and 2 parallelograms) out of 8
6/8 = 3/4
The two fractions are 6/8 and 3/4.
hey can you please help me posted picture of question
Answers
The function and its inverse are reflected about the line y=x. This means that the x and y values are replaced.
So, if a function has a point (2,3) the same point on its inverse will moved be (3,2). This happens for all the points.
Therefore, the statement is false.
Factor the Following Expression using the greatest common monomial factor. (x^p+2)(y^p+2) + (x^p+2)(y^p-1) + (x^p+1)(y^p+1) + (x^p+1)(y^p-1)
Answers
[tex]x^{p+2}y^{p+2}+x^{p+2}y^{p-1}+x^{p+1}y^{p+1}+x^{p+1}y^{p-1}\\\\=(x^{p+1}y^{p-1})(xy^{3}+x+y^{2}+1)[/tex]
A) suppose you will receive $200 in 16 years. how much money in year 6 is equivalent to this amount?
Answers
simplify
200/16=12.5
12.5*6=75
Answer = 75
HELP
Given right triangle ABC.
In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.
A.5
B.√36
C.√61
D.√11
Answers
A²+B²=C²
6²+5²=C²
36+25=C²
61=C²
√61=C
So the answer is C.
Answer:
Correct answer is option C (√61)
Step-by-step explanation:
in this question we have given a right triangle in which
∠C=[tex]90^{0}[/tex]
BC = 6 and AC = 5
we have to find the length of the hypotenuse, AB=?
To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")
In ΔABC by Pythagoras theorem
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)
put values of BC and AC in equation 1
[tex]AB^{2}=5^{2}+6^{2}[/tex]
[tex]AB^{2}=25+36[/tex]
[tex]AB^{2}=61[/tex]
AB=√61