Can someone help me with this pls.
Here are pairs of equivalent expressions in standard form and factored form. Find the missing symbols and numbers that make the equations true. Answers should be numbered and rewritten with the boxes replaced with the proper symbols or numbers. Show work or justification to support your choices and prove that the equations are still true.
Answers
Answer:
[tex](1)\ [12]x^2 [-][37]x - 30 = (3x + 2)(4x - 15)[/tex]
[tex](2)\ x^2\ [\ -]\ 169 = (x \[+ ]\ 13){x\ [- ]\ [13 ])[/tex]
[tex](3)\ x^2 [-]\ [9]x + 20 = (x\ [-] 5)(x- [4])[/tex]
[tex](4)\ x^2 + [11]x + 28 = (x + 7)(x + [4])[/tex]
[tex](5)\ x^2 + [5]x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Complete the boxes
Solving (1):
[tex][ \ ]x^2 [ \ ] [\ ]x - 30 = (3x + 2)(4x - 15)[/tex]
Swap the equation
[tex](3x + 2)(4x - 15) = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]
Open bracket
[tex]12x^2 -45x + 8x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]
Simplify the like terms
[tex]12x^2 -37x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]
So, we have:
[tex][12]x^2 [-][37]x - 30 = [ \ ]x^2 [ \ ] [\ ]x - 30[/tex]
i.e.
[tex][12]x^2 [-][37]x - 30 = (3x + 2)(4x - 15)[/tex]
Solving (2):
[tex]x^2\ [\ ]\ 169 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]
The above expression illustrates the difference of two squares.
So, complete the first equation with minus
[tex]x^2\ [\ -]\ 169 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]
Express 169 as 13^2
[tex]x^2\ [\ -]\ 13^2 = (x \ [\ ]\ 13)(x\ [\ ]\ [\ ])[/tex]
Apply difference of two squares
[tex](x + 13)(x - 13) = (x \[\ ]\ 13){x\ [\ ]\ [\ ])[/tex]
So, the complete expression is:
[tex]x^2\ [\ -]\ 169 = (x \[+ ]\ 13){x\ [- ]\ [13 ])[/tex]
Solving (3):
[tex]x^2 [\ ]\ [\ ]x + 20 = (x \ [\ ]5)(x - [\ ])[/tex]
20 can be expressed as: -5 * -4
So, the expression becomes
[tex]x^2 [\ ]\ [\ ]x + 20 = (x \ [- ]5)(x - [4 ])[/tex]
Expand
[tex]x^2 [\ ]\ [\ ]x + 20 = x^2 - 5x - 4x + 20[/tex]
[tex]x^2 [\ ]\ [\ ]x + 20 = x^2 -9x + 20[/tex]
So, the complete expression is:
[tex]x^2 [-]\ [9]x + 20 = (x\ [-] 5)(x- [4])[/tex]
Solving (4):
[tex]x^2 + []x + 28 = (x + 7)(x + [])[/tex]
28 can be expressed as 7 * 4
So, the expression becomes
[tex]x^2 + []x + 28 = (x + 7)(x + [4])[/tex]
Expand
[tex]x^2 + []x + 28 = x^2 + 7x + 4x + 28[/tex]
[tex]x^2 + []x + 28 = x^2 + 11x + 28[/tex]
So, the complete expression is:
[tex]x^2 + [11]x + 28 = (x + 7)(x + [4])[/tex]
Solving (5):
[tex]x^2 + []x - 24 = (x\ []\ [])(x\ []\ [])[/tex]
-24 can be expressed as -3 * 8
So, the expression becomes
[tex]x^2 + []x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]
Expand
[tex]x^2 + []x - 24 = x^2 +8x - 3x - 24[/tex]
[tex]x^2 + []x - 24 = x^2 +5x - 24[/tex]
So, the complete expression is:
[tex]x^2 + [5]x - 24 = (x\ [-]\ [3])(x\ [+]\ [8])[/tex]
An equation is formed of two equal expressions. The complete equations are:
[tex]12x^2-37x-30 = (3x+2)(4x-15)[/tex][tex](x^2-169) = (x+13)(x-13)[/tex][tex]x^2-9x+20=(x-5)(x-4)[/tex][tex]x^2 + 11x + 28 = (x+7)(x+4)[/tex][tex]x^2 + 5x - 24=(x+8)(x-3)[/tex]What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
1. The first equation that is given to us is:
[tex](?x^2)\ ?\ (?x)-30 = (3x+2)(4x-15)[/tex]
Now, if we simply expand the right-hand side of the equation we will get the equation that is mentioned on the left side of the given equation, therefore,
[tex](3x+2)(4x-15)\\\\= 12x^2-45x+8x-30\\\\=12x^2-37x-30[/tex]
Thus, the complete equation will be
[tex]12x^2-37x-30 = (3x+2)(4x-15)[/tex].
2. The second equation that is given to us is,
[tex]x^2\ ?\ 169 = (x\ ?\ 13)(x\ ?\ ?)[/tex]
Now, if look closely at the equation, and substitute the '-' in the place of '?' the equation we will be in the form of an algebraic equation, therefore, the solution of the equation can be made using the algebraic expression,
[tex]a^2-b^2 = (a+b)(a-b)\\\\(x^2-13^2) = (x+13)(x-13)\\\\\(x^2-169) = (x+13)(x-13)[/tex]
Thus, the complete equation will be
[tex](x^2-169) = (x+13)(x-13)[/tex].
3. The third equation that is given to us is,
[tex]x^2\ ?\ (?x)+20 = (x\ ?\ 5)(x-?)[/tex]
As we can see in the equation, on the left side of the equation the last digit is +20, therefore, the digits on the right side of the equation should be such that their product should be +20, as 5 is already given therefore, the other term should be 4 also, the second term is positive but we need the product to be positive, therefore, the sign of the digit 5 will also be negative.
[tex]x^2\ ?\ (?x)+20 = (x\ ?\ 5)(x-?)\\\\x^2\ ?\ (?x)+20 = (x- 5)(x-4)[/tex]
Now, if we solve the right side of the equation we will get the left side of the equation,
[tex](x- 5)(x-4)\\\\= x^2 - 4x-5x +20\\\\=x^2-9x+20[/tex]
Thus, the complete equation is
[tex]x^2-9x+20=(x-5)(x-4)[/tex].
4. The fourth equation that is given to us is
[tex]x^2 + ?x + 28 = (x+7)(x+?)[/tex]
As we can see in the equation, on the left side of the equation the last digit is +28, therefore, the digits on the right side of the equation should be such that their product should be +28, as 7 is already given therefore, the other term should be 4. Also, 28 is a positive integer, and 7 is also a positive integer, therefore, the number in the last will be positive as well.
[tex]x^2 + ?x + 28 = (x+7)(x+4)[/tex]
Now, if we solve the right side of the equation we will get the left side of the equation,
[tex](x+7)(x+4)\\\\= x^2 + 4x+ 7x + 28\\\\= x^2 + 11x+28[/tex]
Thus, the complete equation is
[tex]x^2 + 11x + 28 = (x+7)(x+4)[/tex]
5. The fifth equation that is given to us is
[tex]x^2 + ?x -24=(x\ ?\ ?)(x\ ?\ ?)[/tex]
As we can see in the equation, on the left side of the equation the last digit is -24, therefore, the digits on the right side of the equation should be such that their product should be -24, Since the product is negative, therefore, either one of the digits on the right should be negative as well, but the middle term on the right is positive, therefore, the bigger number will be positive while the smaller ones will be negative.
[tex]x^2 + ?x -24=(x+8)(x-3)[/tex]
Now, solving the right side of the equation to get the complete left side of the equation we will get,
[tex](x+8)(x-3)\\\\=x^2 -3x + 8x -24\\\\=x^2 + 5x - 24[/tex]
Thus, the complete equation is
[tex]x^2 + 5x - 24=(x+8)(x-3)[/tex]
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Related Questions
3(m - n + 2) + 6 - m
Answers
Step-by-step explanation:
may someone help me please and thank you, how do u find an equivalent fraction?? :)
Answers
Here are the ways that you can find an equivalent fraction:
Multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.
Answer:
You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount. You only multiply or divide, never add or subtract, to get an equivalent fraction.
Step-by-step explanation:
help me brainlist !!!!!
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Answer:
Every number will have a 0 or 5 in its ones place
Step-by-step explanation:
Answer:
D. Every number in the pattern will have a 0 or 5 in the ones place
Step-by-step explanation:
the next to numbers are 50,25 so all numbers have 0 in the ones place except for 25 which has a 5.
MAth problem
Need help asap please
Answers
Answer:
m 2 = 33 degrees
m 4 = 24.555
Step-by-step explanation:
3/33 = (2) 5 - 1
35.44329 - 5 (4) = 3.8
Herman joins three of his friends at the movies. They decide to share a jumbo box of popcorn to save money. A jumbo box is twelve inches on all sides. What is the volume of a jumbo box of popcorn?
Answers
Answer:
$4.25
Step-by-step explanation:
Let price of drink be x
price of tub y
You have 4x+2y=32.5 (1) and
x = y -3.5 (2)
Plug for x from (2) into (1):
4(y-3.5) + 2y = 32.5
4y -14 +2y = 32.5
6y = 14+32.5
y = (46.5)/6 = $7.75 the price of tub
x= y-3.5 = 7.75 - 3.5 = $4.25
The Slow Ball Challenge or The Fast Ball Challenge.
The Slow Ball Challenge: There will be 7 pitches, each at 60 mph. Diego estimates
that he will hit each individual pitch 80% of the time. If Diego can hit all 7 pitches, he
will win a total of $60; otherwise he will lose $10.
The Fast Ball Challenge: There will be 3 pitches, each at 90 mph. Diego estimates
that he will hit each individual pitch 70% of the time. If Diego can hit all 3 pitches, he
will win a total of $60; otherwise he will lose $10.
Which challenge should he choose?
Fast: 4.68
Slow: 4.68
Fast: 14.01
Slow: 14.01
G
Answers
Answer:
Fast ball challenge
Step-by-step explanation:
Given
Slow Ball Challenge
[tex]Pitches = 7[/tex]
[tex]P(Hit) = 80\%[/tex]
[tex]Win = \$60[/tex]
[tex]Lost = \$10[/tex]
Fast Ball Challenge
[tex]Pitches = 3[/tex]
[tex]P(Hit) = 70\%[/tex]
[tex]Win = \$60[/tex]
[tex]Lost = \$10[/tex]
Required
Which should he choose?
To do this, we simply calculate the expected earnings of both.
Considering the slow ball challenge
First, we calculate the binomial probability that he hits all 7 pitches
[tex]P(x) =^nC_x * p^x * (1 - p)^{n - x}[/tex]
Where
[tex]n = 7[/tex] --- pitches
[tex]x = 7[/tex] --- all hits
[tex]p = 80\% = 0.80[/tex] --- probability of hit
So, we have:
[tex]P(x) =^nC_x * p^x * (1 - p)^{n - x}[/tex]
[tex]P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}[/tex]
[tex]P(7) =1 * 0.80^7 * (1 - 0.80)^0[/tex]
[tex]P(7) =1 * 0.80^7 * 0.20^0[/tex]
Using a calculator:
[tex]P(7) =0.2097152[/tex] --- This is the probability that he wins
i.e.
[tex]P(Win) =0.2097152[/tex]
The probability that he lose is:
[tex]P(Lose) = 1 - P(Win)[/tex] ---- Complement rule
[tex]P(Lose) = 1 -0.2097152[/tex]
[tex]P(Lose) = 0.7902848[/tex]
The expected value is then calculated as:
[tex]Expected = P(Win) * Win + P(Lose) * Lose[/tex]
[tex]Expected = 0.2097152 * \$60 + 0.7902848 * \$10[/tex]
Using a calculator, we have:
[tex]Expected = \$20.48576[/tex]
Considering the fast ball challenge
First, we calculate the binomial probability that he hits all 3 pitches
[tex]P(x) =^nC_x * p^x * (1 - p)^{n - x}[/tex]
Where
[tex]n = 3[/tex] --- pitches
[tex]x = 3[/tex] --- all hits
[tex]p = 70\% = 0.70[/tex] --- probability of hit
So, we have:
[tex]P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}[/tex]
[tex]P(3) =1 * 0.70^3 * (1 - 0.70)^0[/tex]
[tex]P(3) =1 * 0.70^3 * 0.30^0[/tex]
Using a calculator:
[tex]P(3) =0.343[/tex] --- This is the probability that he wins
i.e.
[tex]P(Win) =0.343[/tex]
The probability that he lose is:
[tex]P(Lose) = 1 - P(Win)[/tex] ---- Complement rule
[tex]P(Lose) = 1 - 0.343[/tex]
[tex]P(Lose) = 0.657[/tex]
The expected value is then calculated as:
[tex]Expected = P(Win) * Win + P(Lose) * Lose[/tex]
[tex]Expected = 0.343 * \$60 + 0.657 * \$10[/tex]
Using a calculator, we have:
[tex]Expected = \$27.15[/tex]
So, we have:
[tex]Expected = \$20.48576[/tex] -- Slow ball
[tex]Expected = \$27.15[/tex] --- Fast ball
The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.
#3 Find the r and the surface area
Answers
Answer:
r will be half of your diameter so 11 divided by 2 = 5.5 is your new radius.
To find surface area we use the basic formula:
4πr^2
4 x 3.14 x 30.25(radius squared, 5.5 x 5.5 = 30.25) = 379.94 ft^2 is your surface area
Point F is on the line CD. Find the measure of angle CFE
Answers
Answer:
∠ CFE and ∠ DFE are adjacent angles and are supplementary, sum to 180°
∠ CFE + 152° = 180° ( subtract 152° from both sides )
∠ CFE = 28°
Step-by-step explanation:
Adjacent angles share the common side as well as a common vertex (corner point), and they do not overlap. If we decompose the term "adjacent angles".
Adjacent angles:Its common side and vertex will be shared by the adjacent angles.If the total of two angles equals 180°, they are said to be supplementary angles.A linear pair is created when two additional angles are next to one another. 180° is equal to the sum of two adjacent supplementary angles.We have,
∠ EFD = 152°
∠ CFE and ∠ DFE are adjacent angles and are supplementary, summing to 180°
⇒ ∠CFE + ∠EFD = 180° (Linear pair)
⇒ ∠CFE +152° = 180°
⇒ ∠CFE= 180°-152°
⇒ ∠CFE= 28°
Find out more about the adjacent angles here:
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6x^3 +8x^2 -4x = factor this problem
Answers
please help me please
Answers
Answer:
x= 21/16
Step-by-step explanation:
-3x+7--19x=28
-3x+19x=28-7
16×=21
×=21/16
Which of the following is not a Pythagorean triple?
O A. (5, 12, 13)
O B. (6, 8, 10)
O C. (9, 12, 15)
O D. (4,6,7)
Answers
Option D is correct, the pair (4,6,7) is not a Pythagorean triple
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
A Pythagorean triple is a set of three positive integers a, b, and c that satisfy this theorem (a² + b² = c²).
Checking each of the given options, we have:
A. (5, 12, 13):
5² + 12² = 25 + 144 = 169 = 13². This is a Pythagorean triple.
B. (6, 8, 10):
6² + 8² = 36 + 64 = 100 = 10². This is also a Pythagorean triple.
C. (9, 12, 15):
9² + 12² = 81 + 144 = 225 = 15². This is a Pythagorean triple.
D. (4, 6, 7):
4² + 6² = 16 + 36 = 52 ≠ 7². This is not a Pythagorean triple.
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Drag each amount to the correct location on the expression
Last month, the daily balance in Joana's credit card account was $1,000 for 9 days, $750 for 10 days, $850 for 4 days, and $900 for 7 days.
Complete the expression to find Joana's average daily balance.
750
1,000
900
30
850
90
) + 10(
) + 71
)
) + 4
( )
Answers
Answer:
Average daily balance ≈ $873
Step-by-step explanation:
We are told the balance were;
$1,000 for 9 days
$750 for 10 days
$850 for 4 days
$900 for 7 days
Thus;
Average = ΣFx/Σx
Where ΣFx = (1000 × 9) + (750 × 10) + (850 × 4) + (900 × 7)
ΣFx = $26,200
Σx = 9 + 10 + 4 + 7
Σx = 30
Thus;
Average daily balance = 26200/30
Average daily balance ≈ $873
Answer:
9(1,000) + 10(750) +4(850) + 7(900)
(30)
Step-by-step explanation:
The cost to rent a surfboard at the beach is $10.25 an hour plus an insurance fee of $25. Keith spent $55.75 when renting a surfboard on a recent trip to the beach. For how many hours did Keith rent the surfboard?
Answers
Answer: Keith spent 3 hours renting the surfboard.
Step-by-step explanation:
h=hour
10.25h+25=55.75
55.75-25= 30.75
30.75/10.25= 3
and if you want to check you can do
10.25(3)+25=
which would equal to 55.75
Roediger and Karpicke (2006) investigated whether the test-enhanced learning effect (the demonstration that repeated testing improves memory for material) was due merely to repeated exposure to material. They randomly assigned participants to one of two study conditions (study-study or study-test) and to one of three retention interval conditions (final test at a delay of 5 minutes, 2 days, or 1 week). The dependent variable was the proportion of idea units recalled from an encyclopedia passage. How many cells does this study have
Answers
Answer:
6 cells
Step-by-step explanation:
2 by 3 between groups ANOVA will be performed where independent variables are 2 and dependent variables are 3.There are total 6 cells
Independent Var 1 Independent Var 2
Dependent Var 1 1*1 1*2
D. VAr 2 2*1 2*2
D. Var 3 3*1 3*2
There are total six cells.
Study-Study Study-Test
5 minutes, 1*1 1*2
2 days, 2*1 2*2
1 week 3*1 3*2
Help pls guy I love you that was along time it since I just want to review
Answers
b. 29.4cm = 294mm
c. 7400ml = 7.4 litres
d. 7.6ha = 76000m^2
e. 85cm^2 = 8500mm^2
f. 3.2cm^3 = 3200mm^3
WILL MARK BRAINLIEST
Let Events A and B be described as follows:
P(A) = doing yard work
P(B) = it raining
The probability that it will rain this weekend is 68% The probability of doing yard work this weekend and it raining is15%. If the probability of doing yard work is 53%, are doing yard work and it raining independent?
Answers
does anybody know the answer??
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Explanation: hwvhwkahwhskwo
help me figure out this question please
Answers
Answer:
A
Step-by-step explanation:
Radius = 3.25
Base = πr² = π(3.25)²
Height = 12
Volume = Bh = π(3.25)²(12)
Someone plz help me
Answers
Answer:
If you are finding the volume the answer is (3x4)x4
Step-by-step explanation:
Formula for the volume of a rectangular prism is length times width times height
solve for the value of y
Answers
Answer:
y=8
Step-by-step explanation:
the sum of the three angles is 180
57 + 90 + 5y-7 = 180
5y + 140 = 180
5y = 40
y = 8
3. Sohail needs to take a 4-day loan of $750 000 for his small business. How much interest will he need to pay if
interest is charged at 2.2% per year, simple interest?
a. $90.41
b. $542.47
d. $180.82
c. $361.64
Answers
Answer:
180.82
Step-by-step explanation:
750,000 x .022=16,500 per year
16,500/365 days =45.2055/day
45.2055 x 4 days = 180.82
1. If it takes 56 square inches of paper to wrap a label around a can of soup that is 7 inches tall, how far
is it around the can?
A.6 inches
inches
B. 10 inches
C. 8 inches
D. 9 inches
Answers
Answer:
c 8 inches
Step-by-step explanation:
-4/9x-5/72x+1/8x= -56 please help me guys
Answers
Answer:
[tex]x=144[/tex]
Step-by-step explanation:
Therefore, [tex]x=144[/tex] should be your final answer.
how can you use the structure of a two way frequency table to complete it
Answers
Pease help this is due sopn
Answers
Answer:
value of a=90-24=66
value of b=90+66=156
value of c,
c-18=24
c=24+18=42
Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (0,3), (4,0), (4,3)
Answers
Answer: rectangle not sure tho
Step-by-step explanation:
Answer:
Step-by-step explanation:
i chose B:square, i out in the points and that what shape came up. srry if im wrong
hi! please help i’ll give brainliest
Answers
Answer:
A because the river is fastest at that shore
Step-by-step explanation:
a circle is drawn in a coordinate plane centered at (8,15) and a radius of 3 units.
Answers
Answer:
(x - 8)² + (y - 15)² = 9
Step-by-step explanation:
Assuming you want the equation.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (8, 15 ) and r = 3 , then
(x - 8)² + (y - 15)² = 9
A(n) _______ is a mapping that does not change the size of the original figure.
A. Isometry
B. Mapping
C. Image
D. Preimage
Answers
Answer:
A(n) isometry is a mapping that does not change the size of the original figure.
Answer:
Isometry
Step-by-step explanation:
Isometry is a mapping that does not change the size of the original figure.
solve this the link is down below