Answer:
Firstly, we'll apply the below identity.
[tex]{\boxed{\sf{(a+b)^{2} = a^{2} + b^{2} +2ab}}}[/tex]
Applying the above identity.
⇒ (√5 + √2)²
⇒ (√5)² + (√2)² + 2×(√5)×(√2)
⇒ 5 + 2 + 2√10
⇒ 7 + 2√10
Comparing the LHS and RHS
⇒ 7 + 2√10 = a + b√10
∴ a = 7 and b = 2.
Which of the following is an expression with no
restrictions? (This involves factoring & rationals)
3x-4
____
x + 2
13x + 4
_____
24
x-3
___
x-3
Answer:
Step-by-step explanation:
13x+4/24
Rationals means that a variable would be in the denominator. In this case, only 24 is just a number
Solve the quadratic equation 9x ^ 2 - 6x = 11 using the quadratic formula.
Answer:
x = 1.48803, x= -0.821367
Step-by-step explanation:
9x²-6x=11
9x²-6x-11=0
use quadratic formula: x = [- b ± √b²- 4ac)]÷ 2a
Answer:
x =1+2{3 over 3
Step-by-step explanation:
I would appreciate if someone could explain this to me , thanks
Answer: 0.001389
Step-by-step explanation:
Since you have 6 probabilities that it could be red, you get 1/6. Now, you took 1 probability out of 6, so now you only have 5. So you multiply 1/6 by 1/5. Now you have only 4 cards. Multiply 1/ 6 * 1/5 * 1/4 and keep going (e.g 1/6 * 1/5 * 1/4 * 1/3 * 1/2 * 1). This comes out to 0.00138888888, or rounded to six decimal places, 0.001389.
If my answer was helpful, please mark it as brainliest. The other dude's answer was WRONG.
Find last year's salary if, after a 4% pay raise, this year's salary is 31,720
Answer:
30500[tex].[/tex]
Step-by-step explanation:
104%=31,720
100%= x
[tex]\frac{(31720)(100)}{104}=30500[/tex]
A triangle has one side length of 2x
2 + 5x + 3. The other two sides of the triangle have lengths x
2 + 2x and
3x − 2. Determine the simplified expression that represents the total perimeter of the triangle.
The simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
How to determine the perimeter?The side lengths are given as:
2x^2 + 5x + 3, 2 + 2x and 3x - 2
Add these lengths to determine the perimeter (P)
P = 2x^2 + 5x + 3 + 2 + 2x + 3x - 2
Collect like terms
P = 2x^2 + 5x + 2x + 3x + 3 + 2 - 2
Evaluate the like terms
P = 2x^2 + 10x + 3
Hence, the simplified expression that represents the total perimeter of the triangle is 2x^2 + 10x + 3
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In a fourth-grade class, students are making cookies to learn about fractions. They are using a set of measuring cups and spoons for their measurements. This learning is best described as:
In a fourth-grade class, students are making cookies to learn about fractions. They are measuring using measuring cups and spoons. This learning is best described as formal standard measurement.
A standard unit of measurement is a quantifiable language that helps everyone understand the association of the object with the measurement. It is expressed in inches, feet, and pounds, in the United States, and centimeters, meters, and kilograms in the metric system.
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i need help with this one
Answer:
horizontal asymptote of y = -7
Step-by-step explanation:
The parent function is shown on the coordinate plane. The graph of the parent function has a horizontal asymptote (an imaginary line that the graph approaches, but never touches or intersects) of y = 0.
Since the function of g(x) = e^x - 7 is the graph of the parent function translated 7 units down, the function would have a horizontal asymptote of y = -7.
In the diagram, ABCDE is a regular pentagon. The sides AB and DC are produced to meet at F. Find the angles x, y and z.
Answer:
x = 108°
y = 72°
z = 36°
Step-by-step explanation:
Finding unknown angles:If all sides are equal in a pentagon, then it is a regular pentagon.
n = the number of sides = 5
Sum of all angles in a pentagon = (n -2) * 180
= (5 - 2)* 180
= 3 *180
= 540°
Sum of each angle of regular pentagon = 540 ÷ 5
= 108°
[tex]\sf \boxed{\bf x= 108^\circ}[/tex]
Linear pair: If the non common arm of adjacent angles form a straight line, then the adjacent angles are called linear pair and they add up to 180°
∠DCB + y = 180 ° {Linear pair}
108 + y = 180
y = 180 - 108
[tex]\sf \boxed{\bf y = 72^\circ}[/tex]
Exterior angle property of triangle: The exterior angle equals the sum of opposite interior angles.
In Δ BCF ,
x = y + z
Now, substitute the values of x and y , and we can find the value of z.
108° = 72 + z
108 - 72 = z
[tex]\sf \boxed{\bf z = 36^\circ}[/tex]
Quick algebra 1 question for 50 points! :)
Answer:
a. $6
b. the point (1,6)
c. slope of line is y=6x, plug in 1 as x
Step-by-step explanation:
Answer:
Adam deposit $6 each week
I determined the answer, based on the point (1,6)
For question c, slope of line is y = 6x because 1 will not count in here
Step-by-step explanation:
When I was in Algebra 1, I did get this similar question.
The Boden brothers had a 25-meter swimming race at a pool. Michael gave Hasson a 3-meter head start. Use the given data below to determine who won the race and by how many seconds.
Hasson’s Swim
A graph with points (6, 9.6), (8, 11.8), (10, 14), and (12, 16.2).
Michael’s Swim
A 2-column table with 4 rows. Column 1 is labeled Time (seconds) with entries 6, 8, 10, 12. Column 2 is labeled Distance (meters) with entries 8.4, 11.2, 14, 16.8.
won the race by about
seconds.
For Hasson’s Swim the data is a graph with points (6, 9.6), (8, 11.8), (10, 14), and (12, 16.2), and Michael’s Swim A 2-column table with 4 rows. Column 1 is labeled Time. Micheal won by 2 sec. This is further explained below.
Who won the race by about seconds?Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.
In conclusion, Micheal won by 2 sec.
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Answer:
1. Michael
2. 2 seconds
Step-by-step explanation:
flash is the best show on netflix
HELP ASAP
Given: ABCD is a parallelogram and ABC is a right angle.
Prove: BD is congruent to AC.
ABC is a right angle
ABCD is a parallelogram
Opposite sides of a parallelogram are equal
So
BC=ADAB=DCOpposite angles are equal
<B=<D
Hence
∆ABC and ∆CDB are congruent by SAS
BD=ACWhat is the area of a rectangle with vertices at (−3, −1), (1, 3), (3, 1), and (−1, −3)?
Do not round any side lengths
Using the distance formula, the area of the rectangle is: 16 units².
What is the Area of a Rectangle?Area of a rectangle = (length)(width).
Given the vertices:
A(−3, −1)B(1, 3)C(3, 1)D(−1, −3)Area = (AB)(BC)
Apply the distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB and BC:
AB = √[(1−(−3))² + (3−(−1))²]
AB = √[(4)² + (4)²]
AB = √32
BC = √[(1−3)² + (3−1)²]
BC = √[(−2)² + (2)²]
BC = √8
Area = (√32)(√8) = √256
Area = 16 units²
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Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?
because both triangles appear to be equilateral
because∠MNL and ∠ONP are congruent angles
because one pair of congruent corresponding angles is sufficient to determine similar triangles
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
Answer: because ∠MNL and ∠ONP are congruent angles
Step-by-step explanation:
Options 1 and 4 are wrong because we cannot base our answer on assumptions from the diagram.
Option 3 is wrong because you need two pairs of corresponding congruent angles to prove similar triangles, not just 1.
Which of the following is the equation for the graph shown?
The equation of an ellipse for the graph shown is [tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
How to determine the equation?Since the given coordinates of the vertices and foci have the form (-5, 0) and (5, 0) and (-2, 0) and (2, 0) respectively, this ultimately implies that the major axis of this ellipse is the x-axis.
Thus, the standard form of the equation of this ellipse is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
Next, we would solve for b² by using this equation:
b² = a² - c²
b² = 5² - 2²
b² = 25 - 4
b² = 21.
Substituting the parameters into the standard equation of an ellipse, we have;
[tex]\frac{x^2}{5^2} + \frac{y^2}{21^2} = 1[/tex]
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In a sequence, each number is 2 less than double the previous number. morgan finds the number directly before 48 in the sequence. his answer has two digits. he adds these two digits to get a new number. what is the new number
The new number in the sequence is found to be 7.
What is the term of the sequence?In mathematics, a sequence is a list of components, usually numbers, where the components' order is important. Here, everything fits into a predetermined pattern.
A sequence can be arranged in either ascending or descending order.
There are certain unique sequences, including the triangular number series, square number sequence, cube number sequence, geometric sequence, Fibonacci sequence, and harmonic sequence.
According to the question, the sequence follows the pattern:
Next number=2(Previous number)-2
On substituting the values,
48=2(Previous number)-2
50=2(Previous number)
Previous number=[tex]\frac{50}{2}[/tex]=25
New number=sum of digits of the previous number in the sequence
=2+5
=7
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What is the range of the function f(x) = 3/4|x| - 3
All real numbers
All real numbers less than or equal to 3
All real numbers less than or equal to -3
All real numbers greater than or equal to -3
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
all real numbers greater than or equal to –3
Step-by-step explanation:
|x| has a range of all real numbers greater than or equal to zero, so f(x) = |x|-3 will have a range of ...
all real numbers greater than or equal to -3
Determine an equivalent expression by rationalizing the denominator: (5√3)/(4-√6)
Step-by-step explanation:
so when you want to rationalize the denominator when it's in the form [tex](a-\sqrt{b})[/tex] you multiply by the conjugate which is [tex](a+\sqrt{b})[/tex] which is where the sign is the opposite. This is because it's using the difference of squares to get rid of the square root. Because [tex](a-b)(a+b) = a^2-b^2[/tex] this will remove the square root since it's going to become square and the ab - ab will cancel so there will be no square root
Multiply by conjugate
[tex]\frac{5\sqrt3}{4-\sqrt6} * \frac{4+\sqrt6}{4+\sqrt6}\\[/tex]
Simplify:
[tex]\frac{20\sqrt{3} + 5\sqrt{6 * 3}}{16-6}[/tex]
Simplify radical
[tex]\frac{20\sqrt{3} + 15\sqrt{2}}{10}\\[/tex]
You could go further and do
[tex]2\sqrt{3} + 1.5\sqrt{2}[/tex]
The data below represent the number of days absent per year in a population of three employees of a small company:
1 4 7
Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compare the mean of all the samples means and also compute the population mean. Are they equal? What is the property called?
Repeat (a) for all the sampling distribution of the mean in (a) for n= 3. Which sampling distribution has less variability? Why?
Assuming that you sample with replacement, repeat (a) through (c) and compare the results. Which sampling distribution have the least variability – those in (a) or (b) ? Why?
The sampling distribution is illustrated below.
How to illustrate the sampling?Based on the information given, the population is illustrated as 1, 4, 7. The sample without replacement will be:
Sample Mean
1 and 4. 2.5
1 and 7. 4
4 and 7. 5.5
The population mean will be:
= (1 + 4 + 7)/3
= 4
The sample mean is an unbiased estimator of the population mean.
The sampling with replacement illustrates that the mean will be:
= 36/9 = 4
Also, when n = 3, the number of samples will be:
= 3³ = 27
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An 84-foot building casts a 98-foot shadow. What is the angle that the sun hits the building? HINT: Draw a picture.
Answer:
40.6°
Step-by-step explanation:
The building and the shadow are perpendicular to each other (or intersect at a 90° angle).
Meaning that this is a triangle problem.
We are making a triangle from the building to the shadow and a diagonal line connecting the ends of both.
We need to find the angle at the top of the building. The opposite side of the angle is 84. The adjacent side is 98.
Opposite / Adjacent = Tan X
So if we go to the calculator:
[tex]tan^{-1} (\frac{84}{98}) = 40.6[/tex]
The answer is 40.6 degrees.
When p2 – 4p is subtracted from p2 + p – 6, the result is
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
When [tex]\bf{p^2-4p}[/tex] is subtracted from[tex]\bf{p^2+p-6}[/tex], the result is...?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
[tex]\bf{Subtract:}[/tex]
[tex]\bf{p^2+p-6-p^2-4p}[/tex]. | combine like terms
[tex]\bf{p^2-p^2+p-4p-6}[/tex] | simplify
[tex]\bf{0p^2-3p-6}[/tex] | simplify
[tex]\bf{-3p-6}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{-3p-6}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Answer:
5p - 6
Step-by-step explanation:
p² + p - 6 - (p² - 4p) ← distribute parenthesis by - 1
= p² + p - 6 - p² + 4p ← collect like terms
= 5p - 6
Which ordered pair would form a proportional retationship with the points in the graph?
4,4
6,9
9,6
8,5
Answer:
(9, 6)
Step-by-step explanation:
the given points are
(3, 2)
(6, 4)
so, can you see, how the sequence continues ?
I see immediately that for every 3 additional units of x we add 2 units of y.
so, yes, the next point in the sequence is
(6 + 3, 4 + 2) = (9, 6).
so, this point (or ordered pair) follows the same ratio or proportional relationship between x and y as the points already in the graph.
in other words, they are on the same line following the same slope ("y coordinate change / x coordinate change" when going from one point on the line to another).
Glven: AABC with DE || AC
AD CE
EB
Prove: DB
B
1. DE
2.
Statement
E
Reason
C
given
If two parallel lines are
cut by a transversal, the
corresponding angles are
congruent.
What is the missing step in this proof?
OAZCAB
OB. ZADE
OC.
OD. ZCABLEDB, ZACB DEB
LACB, LEDB ZDEB
ZDBE, ZCED= LEBD
ZCAD ZACE, ZADEZCED
The missing statement in the proof is; AB/BD = CB/EB
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
The given proof is the triangle proportionality theorem which states that the segments formed by side DE are proportional.
The two column proof is presented as follows;
Statement Reason
1. DE || AC 1. Given
2. ∠CAB ≅ ∠EDB 2. Corresponding angles formed between ║ lines
3. ΔABC ~ ΔDBE 3. AA criterion for similarity
4. AB/BD = CB/EB 4. Corr. sides of similar Δs are prop.
5. AB = AD + DB 5. Segment addition CB = CE + EB
6. (AD + DB)/(DB) = (CE + EB)/(EB) 6. Substitution Property of Equality
7. (AD)/(DB) + 1 = (CE)/(EB) + 1 7. Division
8. (AD)/(DB) = (CE)/(EB) 8. Subtraction Property of Equality
Hence, the missing statement in the proof is; AB/BD = CB/EB
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What is the value of g( − 3) when g(x) = 2x-2
Hello,
[tex]g(x) = 2x - 2[/tex]
[tex]g(-3) = 2 \times (- 3) - 2 = -6 - 2 = -8[/tex]
Answer: g(-3) = -8
Given that:
g(x) = 2x - 2To find g(-3), insert (x = -3):
⇒ g(-3) = 2(-3) - 2
⇒ g(-3) = -6 - 2
⇒ g(-3) = -8
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For random samples of size 100 from a population, the mean of the sample means from all possible samples is _________ ____ the population mean.
For random samples of size 100 from a population, the mean of the sample means from all possible samples is less than the population means.
The suggestion of the pattern means will equal the population suggest. the standard deviation of the distribution of the sample means, called the same old blunders of the suggested, is the same as the population trendy deviation divided by means of the rectangular root of the sample length (n).
The general sample suggests components for calculating the pattern mean.
The populace suggest is the mean or average of all values within the given population and is calculated by using the sum of all values within the population denoted with the aid of the summation of X divided by way of the number of values in the population that's denoted with the aid of N.
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Quadrilateral A B C D is rotated 145 degrees about point T to form quadrilateral A prime B prime C prime D prime.
Quadrilateral ABCD is rotated 145° about point T. The result is quadrilateral A'B'C'D'. Which congruency statement is correct?
ABCD ≅ A'B'C'D'
ABCD ≅ A'D'C'B'
CDAB ≅ A'D'C'B'
CDAB ≅ C'B'A'D'
The correct answer is option A which is ABCD ≅ A'B'C'D'.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
Quadrilateral ABCD is rotated at 145° about point T. The result is quadrilateral A'B'C'D'.
ABCD ≅ A'B'C'D'is correct Since the quadrilateral remains the same even after rotation of 145 degrees. Its corresponding sides and angles will remain the same.
Thus ABCD is congruent to A'B'C'D'.
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Answer: The answer is A
Step-by-step explanation:
A triangle has integer length sides. If two sides of the triangle are 16 and 21, how many possible lengths are there for the third side
There are 31 possible lengths for the third side.
Unknown Side + 16 > 21
Unknown Side > 5
16 + 21 > Unknown Side
37 > Unknown Side
Unknown Side < 37
So, the possible integer lengths range from
6 - 36
= 36 - 6 + 1
= 31 possible lengths
The length of the third side of a triangle has to continually be among (but not equal to) the sum and the distinction among the alternative facets. As an instance, take the example of two, 6, and seven. and consequently, the 0.33 facet length has to be extra than four and less than eight.
The regulation of Cosines to calculate the unknown aspect, then use the Law of Sines to find the smaller of the opposite angles and then use the 3 angles add to 180° to find the final attitude.
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What is root -9 + root -12 written as a complex number in the form a + bi ?
Answer:
Step-by-step explanation:
I assume you are talking about square roots when you say root...
Sqrt(-9) = 3i
Sqrt(-12) = 2Sqrt(3)i
Complex number is 3 + 2Sqrt(3) i
eric borrowed 5,000 to buy a used car. he agreed to make monthly payments of 175.00 for 36 months how much will how actually pay the bank
If Eric agreed to make monthly payments of 175.00 for 36 months, the total amount of money he will pay the bank is 6,300.
How much will Eric pay the bank?
Given that;
Amount of money borrowed = 5000Monthly payment = 175.00Number of month = 36Total amount of money paid to the bank = ?To determine the total amount of money that Eric will pay the back, we simply multiply his monthly payment and the number of months.
175.00 × 36
= 6,300
Hence, if Eric agreed to make monthly payments of 175.00 for 36 months, the total amount of money he will pay the bank is 6,300.
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PLS HELP I NEED THIS QUICK THANK YOU IN ADVANCE
Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 5x-17
y = x + 3
OA. (5,8)
OB. (4,7)
O C. (1,-12)
OD. (5,-17)
Answer:
A(5 ; 8)
Step-by-step explanation:
y = 5x - 17
y = x + 3
5x - 17 = x + 3
⇔ 5x - x = 3 + 17
⇔ 4x = 20
⇔ x = 20/4
⇔ x = 5
y = 5 + 3 = 8
So (5 ; 8)
Answer:
We can use the substitution method to solve the system of equations.
Since y = x + 3, we can substitute this expression for y in the first equation:
y = 5x - 17
x + 3 = 5x - 17
Subtracting x from both sides, we get:
3 = 4x - 17
Adding 17 to both sides, we get:
20 = 4x
Dividing both sides by 4, we get:
x = 5
Substituting this value of x into either equation, we get:
y = x + 3 = 5 + 3 = 8
Therefore, the correct ordered pair is (5, 8), which corresponds to the point where the two lines intersect.
The correct answer is (A) (5,8).
May someone help me please?