Answers
[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
[tex]a\:=\:2[/tex], [tex]b\:=\:-1[/tex] and [tex]c\:=\:-3[/tex]
7) [tex]3 {a}^{2} - b[/tex]
Plugging in the values of [tex]a[/tex] and [tex]b[/tex], we have
[tex] = 3( {2})^{2} - ( - 1)[/tex]
[tex] = 3(2 \times 2) + 1[/tex]
[tex] = 3 \times 4 + 1[/tex]
[tex] = 12 + 1[/tex]
[tex] = 13[/tex]
Hence, [tex]\boxed{ c. \:13 }[/tex] is the correct option.
8) [tex] {a}^{3} {b}^{3} - abc[/tex]
Plugging in the values of [tex]a[/tex] and [tex]b[/tex] and [tex]c[/tex], we have
[tex] = ({2})^{3} ( { - 1})^{3} - 2( - 1)( - 3)[/tex]
[tex] = (2 \times 2 \times 2)( - 1 \times - 1 \times - 1) - 2(3)[/tex]
[tex] = (8)( - 1) - 6[/tex]
[tex] = - 8 - 6[/tex]
[tex] = - 14[/tex]
Hence, [tex]\boxed{ d.\:-14 }[/tex] is the correct option.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]
7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]
[tex] \huge\underline{\sf{\red{Given:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]
[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]
[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]
[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]
[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]
[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]
[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]
[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{7.)\:13}}}}[/tex]
8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]
[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]
[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]
[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]
[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]
[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{8.)-14}}}}[/tex]
[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
#CarryOnLearning
[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]
Related Questions
Which of the following is NOT true about mathematical induction?
A.The first possible case is always n = 1.
B.Mathematical induction depends on a recursive process.
C.It can be used to prove that 1 + 2 + 3+...+n =
n(n+2)
2
D. Since Sn is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely.
Answers
Answer:
A. the first possible case is always n = 1
Step-by-step explanation:
Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers
Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0
Therefore, the statement which is not true is that the first possible case is always n = 1
Find the equation of the line that passes through the point (-5,7) and is perpendicular to the line y=-x+12.
Answers
Answer:
y=x+12
Step-by-step explanation:
y=-x+12; is a line with slope m1=-1
to find perpendicular slope of intersecting line take the negative inverse of m1. so -1*(1/(-1))=1=m2
use equation for a line of y=m*x+b and put in the point (-5,7) and solve for b=the y axis intercept
7=1*(-5)+b
7=-5+b
12=b
so
y=x+12
Please help me
The question is write the question for the table given.
The multiple choices are
Y=1/3x
Y=1/2x
Y=3x
Y=2x
Answers
Answer:
The answer is Y=3x
when x is 0, y is 0
y=3x
Y= 3 X 0 = 0 (correct)
when x is 1, y is 3
y=3x
y=3 X 1= 3 (correct)
when x is 2 , y is 6
y=3x
y= 3 X 2= 6 (correct)
when x is 3, y is 9
y=3x
y= 3 X 3= 9 (correct)
when x is 4, y is 12
y=3x
y= 3 X 4= 12 ( Correct)
Which sign makes the statement true?
5.01 x 10-3 ? 0.00105
Answers
Answer:
47.1 > .00105
Step-by-step explanation:
Given :
5.01×10-3 ? 0.00105
Now,
5.01×10-3 ? 0.00105
50.1-3?0.00105
47.1?0.00105
From the above equation, we can say that 47.1 is greater than 0.00105
Therefore, 47.1 > .00105
Surface area is the sum of the areas of all the surfaces of a three-dimensional object.
(True or false)
Answers
Answer: True
Think of a 3D box. It has 6 faces and the surface area is the total of all six individual rectangular faces. This idea applies to any polyhedron.
Sora paid $26.46 for 8.4 gallons of gasoline. How much was each gallon of gasoline?
$0.211
$0.315
$2.11
$3.15
Answers
Answer:
last one
Step-by-step explanation:
Joe and Becky are buying fish for their new aquarium. The expression 3g + 4a represents the cost in dollars of buying fish
where 'g' is the number of guppies purchased and 'a' is the number of angel fish purchased. Find the cost of fish if they buy 12 guppies and 4 angel fish. Explain your work.
Answers
Answer:
$52
Step-by-step explanation:
Find the cost by plugging in 12 as g and 4 as a into the expression:
3g + 4a
3(12) + 4(4)
36 + 16
= 52
So, the cost will be $52
According to the Rational Root Theorem, -2/5 is a potential rational root of which function? ) = 4x4.72#*#25 O Foxo = 9x47x+10 OF) = 10x - 729 Fox) = 25x4.72
Answers
Answer:
Option (4)
Step-by-step explanation:
Option (1)
f(x) = 4x⁴- 7x²+ x + 25
Possible rational roots will be,
[tex]\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}[/tex]
For the given function,
Possible rational roots = [tex]\frac{\pm 1, 5, 25}{\pm 1,2}[/tex]
= [tex]\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (2)
f(x) = 9x⁴- 7x²+ x + 10
Possible rational roots = [tex]\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (3)
f(x) = 10x⁴- 7x²+ x + 9
Possible rational roots = [tex]\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is not the possible root.
Option (4)
f(x) = 25x⁴- 7x²+ x + 4
Possible rational roots = [tex]\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}[/tex]
= [tex]\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}[/tex]
Therefore, [tex]-\frac{2}{5}[/tex] is the possible rational root.
Option (4) will be the answer.
Solve for w. Show your work! 5w + 16 - 9 - 8w = 19
I'll give brainly
Answers
-3w+7= -7
-3w=12
W=-4
I need help on this question, URGENT so please help asap
Answers
Answer: D is correct since the two angles are vertical angles and can be proven congruent by the vertical angle theorem
Step-by-step explanation:
Select the outlier in the data set.
93
82
10
61
99
89
84
95
75
98
If the outlier were removed from the data set, would the mean increase or decrease?
Answers
Answer:
10
The mean would increase after the outlier is removed
Step-by-step explanation:
An outlier in a dataset is a number that differs significantly from the other data in the set.
In this question, 10 is the number that differs significantly from the other data in the set. Thus, it is the outlier.
Mean = sum of the numbers / total number
Mean including the outlier =
(93+ 82 + 10 + 61 + 99 + 89 + 84 + 95 + 75 + 98) / 10 = 78.6
Mean without the outlier =
(93+ 82 + 61 + 99 + 89 + 84 + 95 + 75 + 98) / 9 = 86.2
the mean increased after the outlier was removed
Answer plsssss………………
Answers
Answer:
The corresponding angles theorem works for cases where we have two parallel lines intersecting another line.
Two lines are parallel if, at any point, the distance between these two lines is always the same.
Now, if we look at the image, we can see that the distance between the two horizontal lines changes (is smaller at the right and larger at the left)
Thus, these lines are not parallel.
Then the corresponding angles theorem can not be used here, and we have that:
∠9 ≠ ∠10
one dozen mangoes cost $120.00. what is the cost of 8 mangoes??
Answers
Answer:
$80.00
Step-by-step explanation:
12m = 120
m = 10
Therefore, 8m must equal 80.
Answer:
The cost of 8 mangos would be $80.00
Step-by-step explanation:
A dozen is equal to 12 so its 10 bucks per mango since there are 12 mangos
Help please no links
Answers
Answer:
D
Step-by-step explanation:
The question states you need a square. That means whatever you do, must leave a square number like 49 or 64
If you add 6 or 7 to 56 you do not get 64 A and C are both wrong.
If you subtract 7 from 56 you get 49 which is a perfect square and all 4 sides will equal 7.
What is the completely factored form of this polynomial?
x^4- 8x^2 + 16
A. (X+2)^2(x-2)^2
B. (x^2-4)^2
C. (x^2+4)(x+2)(x-2)
D. (x+2)(x-2)
Answers
Answer:
A. (x + 2)²(x - 2)²
Step-by-step explanation:
x⁴ - 8x² + 16 =
(x² - 4)(x² - 4) =
(x - 2)(x + 2)(x - 2)(x + 2) =
(x - 2)²(x + 2)²
In the circle below, segment AB is a diameter. If the length of are ACB is 6pi what is the length of the radius of the circle?
Answers
Answer:
The radius is 6
Step-by-step explanation:
Arc length ACB = 6 pi
The arc length = fraction of a circle times the circumference
6 pi = 180/360 * 2 * pi *r
6 pi = 1/2 * 2 * pi*r
6 pi = pi r
The radius is 6
Next
Unit Pre Test
Submit Test
20
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s)
The equation of a line is 2[v+ 1) = 10x* 3.
The yuntercept of the line is
and the slope of the line is
Answers
Answer:gotta go sorry
Step-by-step explanation:
A sphere has a diameter of 32 ft. What is its surface area?
The surface area of the sphere is
ft?. (Type an exact answer in terms of t.)
Answers
Step-by-step explanation:
the answer is in the above image
======================================================
Explanation:
The diameter 32 cuts in half to 16, which is the radius. So r = 16.
Use this to find the surface area of the sphere in the formula below
SA = 4*pi*r^2
SA = 4*pi*16^2
SA = (4*16^2)*pi
SA = 1024pi
This is the exact surface area in terms of pi.
The area units are in square feet, or ft^2 for short.
determine the equation of the circle graphed below.
( help me please )
Answers
Answer:
(x+5)²+(y-4)²=17
Step-by-step explanation:
I think it's safe to assume that the (-5,4) coordinate is in the center
To find the x and y coordinate just flip the signs
which means it would look like
(x+5)²+(y-4)²=?
the question mark is equal to the raidus squared
to find the radius use the distance formula
√((-4+5)²+(8-4)²)= 4.123106
square this to get 17
the final answer is then
(x+5)²+(y-4)²=17
Which is greater, 2 miles or 1,000 yards? How much greater? Explain. Of 2 miles and 1,000 yards, _____ is greater. Since 2 miles is the same as _____ yards, _____ is __ yards greater than _____ .
Answers
Answer:
yards
Step-by-step explanation:
Answer:
Which is greater, 2 miles
1 mile = 1760 yards
2 miles = 2 * 1760
2 miles = 3,520 yards
How much greater?
3,520 - 1000 = 2520 yards
The quartile deviation and coefficient of quartile deviation of a continuous frequency distribution are 2 and 0.25 respectively. Find lower and upper quartiles.
Answers
Answer:
Lower quartile = 6
Uppwr quartile = 10
Step-by-step explanation:
Coefficient of quartile deviation = 0.25
Quartile deviation = 2
Coefficient of quartile deviation = (Q3 - Q1) / (Q3 + Q1)
Quartile deviation = (Q3 - Q1) / 2
Hence;
Quartile deviation = (Q3 - Q1) / 2 = 2
Q3 - Q1 = 2 * 2
Q3 - Q1 = 4 - - - - (1)
Q3 = 4 + Q1 - - - - (2)
(Q3 - Q1) / (Q3 + Q1) = 0.25
Q3 - Q1 = 4
4 = 0.25(Q3 + Q1)
Q3 + Q1 = 4 / 0.25
Q3 + Q1 = 16 - - - - (3)
Put Q3 = 4 + Q1 in (3)
4 + Q1 + Q1 = 16
4 + 2Q1 = 16
2Q1 = 16 - 4
Q1 = 12 / 2
Q1 = 6
Q3 = 4 + Q1
Q3 = 4 + 6
Q3 = 10
Which are the solutions of the quadratic equation?
x² = 7x + 4
Answers
Answer:
[tex]x = \frac{7 + \sqrt{65}}{2} \ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = 7x + 4 \\\\x^2 - 7x - 4 = 0\\\\ a = 1 \ , \ b = - 7 , \ c \ = \ - 4 \\\\x = \frac{-b \pm \sqt{b^2 - 4ac }}{2a}\\\\Substitute \ the \ values : \\\\x = \frac{7 \pm \sqrt{7^2 - (4 \times 1 \times -4)}}{2 \times 1}\\\\x = \frac{7 \pm \sqrt{49 + 16}}{2 }\\\\x = \frac{7 \pm \sqrt{65}}{2 }\\\\x = \frac{7 + \sqrt{65}}{2}\ , \ x = \frac{7 - \sqrt{65}}{2}[/tex]
In the given figure alongside,prove that
Triangle ABC is simalar to Triangle SRT
Find the length of AC
Answers
Answer:
let's use Pythagoras theorem,
h²=b²+l²
so,
ad²=ac²+dc²
6²=ac²+3²
36-9=ac²=27
√27 can be written as 3√3,
hence ac= 3√3
Hihi , please help if able.
Answers
Answer:
9(9m + 3t) = 81m + 27t
Step-by-step explanation:
With brackets with more than one term inside multiplied by a number;
The rule of thumb to know is that with brackets, everything inside must be multiplied by everything outside;
So, in this case, the number 9 must be multiplied by each term inside the brackets:
9 × 9m = 81m
9 × 3t = 27t
So to expand, opening the brackets, you get:
81m + 27t
Please solve with explanation
Answers
Step-by-step explanation:
total wood= 45½=22.5 units
cut wood= 8⅞= 7 units
wasted wood= 1/16=0.06
now wood left is,
total wood -cut wood-wasted wood
22.5-7-0.06
15.44 units
What is the common solution for the equations y = 2x + 1 and y = x + 3?
Write your answer an ordered pair!
Answers
Answer:
y^2 = 2x^2+x = x(2x+1) = xy => y^2 = xy => either y=0 or x = y
If y=0 then from y-2x=1, x=-1/2
If X=y then from y-2x = -x = 1 => x=y=-1
Step-by-step explanation:
answer=1
Answer:
(2,5)
Step-by-step explanation:
This is the graph for both equations and the solution is where both lines cross each other.
Hope this helps
Find the value of x in the triangle shown below
Answers
Answer:
x = 48°
Step-by-step explanation:
Two sides of the triangle are equal, both 7, Then the 2 base angles are congruent, both 66°
The sum of the 3 angles in the triangle sum to 180° , so
x = 180° - (66 + 66) = 180° - 132° = 48°
Answer:
[tex]{ \tt{x + 66 + 66 = 180}} \\ x = 48 \degree \\ \\ { \boxed{ \bf{or : }}} \\ { \bf{ from \:lamis \: theorem : }} \\ { \tt{ \frac{5.7}{ \sin(x) } = \frac{7}{ \sin(66 \degree) } }} \\ \\ { \tt{x = { \sin }^{ - 1}( \frac{5.7 \times \sin(66 \degree) }{7} ) }} \\ x = 48 \degree[/tex]
f(x)=15x³+22x²-15x+2
Write f(x) as a product of linear factors.
Answers
Answer:
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
Step-by-step explanation:
[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]
Apply Rational Root Theorem, our possible roots will be
plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).
I
I tried root -2 and it work so
If we apply synthetic dividon, we would be left with
[tex]15 {x}^{2} - 8x + 1[/tex]
We can factor this regularly.
Apply AC method that a number
AC will multiply to 15 but add to -8.
The answer are -5 and -3 so we write this as
[tex]15 {x}^{2} - 5x - 3x + 1[/tex]
Factor by grouping
[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]
[tex]5x(3x - 1) - 1(3x - 1)[/tex]
So our factor are
[tex](5x - 1)(3x - 1)(x + 2)[/tex]
Solve the equation below :
7/8 = q + 1/2
A : q = 3/8
B : q = 1 3/8
C : q = 7/16
D q = 1 3/4
Answers
Answer:
q = -3/8
Step-by-step explanation:
Clearing out the fractions first simplifies this problem. The LCD here is 8, so we multiply all three terms of 7/8 = q + 1/2 by 8 and simplify the result:
7 + 8q = 4.
Combining the constants, we get: 8q = 4 - 7, or 8q = -3.
Finally, solve for q:
q = -3/8
Is Mercury is a gas giant, and because it is hot, it is named after the mercury in a thermometer.
Please give real answers with explaination. I will follow + I will give brainliest. No Docs/No Files/No Links only answer with explaination.
Answers
Mercury is the smallest and fastest planet in the solar system. It is also the closest planet to the sun. It is named after the Roman messenger god Mercury, the fastest Roman god.