Answer:
12
Step-by-step explanation:
Simplify the expressions. 3p+-q-7r--8p-q+2r
Answer:
=11p-5r
Step-by-step explanation:
3p+(-q)-7r-(-8p)-q+2r=
3p-q-7r+8p-q+2r=
3p+8p-q-q-7r+2r=
11p-5r=
If α and β are the zeroes of the polynomial ax^2 + bx + c, find the value of α^2 + β^2
Answer:
Step-by-step explanation:
α + β = -b/a
αβ = c/a
α² + β² = (α + β)² - 2αβ
[tex]= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}[/tex]
Simplify......................
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{( {a}^{2} + {b}^{2} )}{a} }}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ {a}^{4} - {b}^{4} }{ {a}^{3} - a {b}^{2} } [/tex]
[tex] \\= \frac{ ({ {a}^{2} })^{2} - { ({b}^{2} })^{2} }{a( {a}^{2} - {b}^{2} )} [/tex]
[ ∵ (a²)² = [tex]{a}^{4}[/tex] ]
[tex] \\= \frac{( {a}^{2} + {b}^{2} )( {a}^{2} - {b}^{2}) }{a( {a}^{2} - {b}^{2}) } [/tex]
[tex] \\= \frac{( {a}^{2} + {b}^{2} )}{a} [/tex]
Note:[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{ヅ}}}}}[/tex]
An exam has 20 exercises.For every exercise solved correctly you get 8 points and for every exercise solves wrong are taken off 5 points.Ben had 13 points.How many exercises did he solve?
Answer:
13 exercises
Step-by-step explanation:
The number of exercises in the exam = 20
The points received for questions solved correctly = 8 points
The points taken off for exercises solved wrong = 5 points
The number of points Ben has = 13 points
Let 'c' represent the number of exercises he solved correctly and let 'w' represent the number of exercises he solved wrong, we have;
0 < c + w ≤ 20...(1)
8·c - 5·w = 13...(2)
Given that 5·w has either a 0 or 5 as the unit digit, and x3 = x8 - 5, such as 13 = 18 - 5, we have that the last digit of 8·c is 8, and the last digit of 5·w is 5
The products of 8 with '8' as the unit are, 8 × 6, 8 × 11, and 8 × 16
Therefore, when c = 6, and w = 7, we get;
8 × 6 - 5 × 7 = 13
The number of exercises Ben solved, c + w = 6 + 7 = 13 < 20
When c = 11, we get;
8 × 11 - 5 × 15 = 13
11 + 15 = 26 > 20
The number of exercises Ben solved = 13 exercises
4,-7 -1,5 what’s the midpoint
Answer:
(4, 5) Midpoint
Step-by-step explanation:
Need- What is a midpoint of the line segment?
Solution:
Midpoint: x,m , y,m = ([tex]\frac{x {a +x b } }{2}[/tex]) ,( [tex]\frac{y, a + y b}{2}[/tex])=( [tex]\frac{0 +8 }{2}[/tex] ) , ( [tex]\frac{2 + 8 }{2}[/tex]) = [tex]\frac{8}{2} , \frac{10}{2}[/tex] Midpoint segment - ([tex]x_{m} , y_{m}[/tex]) = (4,5)a bicycle was sold for $285 at a discount of 5% calculate the cost price of that bicycle
Answer:
Cost price = $300
Step-by-step explanation:
Let the cost price be = x
Discount % = 5%
Price after discount = $285
Find Cost price .
[tex]Price \ after \ discount = x - (5 \% \ of \ x)\\\\285 = x - \frac{5}{100}x\\\\285 = \frac{100 - 5 }{100} x\\\\95x = 285 \times 100\\\\x = \frac{28500}{95} = \$ 300[/tex]
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
Answer:
[tex]x =5\sqrt 3[/tex]
Step-by-step explanation:
Given
See attachment for triangle
Required
Find x
To do this, we make use of Pythagoras theorem
[tex]x^2 + 5^2 = 10^2[/tex]
Solve the exponents
[tex]x^2 + 25 = 100[/tex]
Collect like terms
[tex]x^2 =- 25 + 100[/tex]
[tex]x^2 =75[/tex]
Take square roots
[tex]x =\sqrt{75[/tex]
Expand
[tex]x =\sqrt{25*3[/tex]
Split
[tex]x =\sqrt{25}*\sqrt 3[/tex]
[tex]x =5\sqrt 3[/tex]
I need help!!! Parallel lines p and q are cut by two non parallel lines m and n as shown in the figure the value of x is degrees and the value of y is degrees
Answer:
x = 78° , y = 115°
Step-by-step explanation:
The angle adjacent to x on the left side is corresponding to 102° , then
x = 180° - 102° = 78°
----------------------------------------
y and 115° are corresponding angles and congruent, then
y = 115°
35 into binary number
Answer:
35 in binary is 100011.
Step-by-step explanation:
To find decimal to binary equivalent, divide 35 successively by 2 until the quotient becomes 0.
George earned $3,200 for one month of work. He paid $640 in income tax for the month. What percent tax did he pay? (Ignore the percent sign when gridding your answer.
Answer:
He paid $640 out of his total $3,200 for the month.
As a fraction it is (640/3200) which equals (1/5)
We want it as a percentage so we multiply the fraction by 100.
1/5×100=20%
20% is the final answer.
Which radical expression, when simplified, equals -8?
Answer:
Where are the radical expressions?
Step-by-step explanation:
what is the value of the expression below?
Answer:
C
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] , then
[tex]121^{\frac{1}{2} }[/tex] = [tex]\sqrt{121}[/tex] = 11 → C
please help me i have geo finals
Answer:
x = 8
Step-by-step explanation:
Given 2 intersecting chords.
Then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
14(2x + 2) = 12(2x + 5) ← distribute parenthesis on both sides
28x + 28 = 24x + 60 ( subtract 24x from both sides )
4x + 28 = 60 ( subtract 28 from both sides )
4x = 32 ( divide both sides by 4 )
x = 8
In a group of students, every student needs to make a bookmark for each of their groupmates. If the total bookmarks made is 42, how many students are there in this group?
7
Hope this helps! :)
______________
Answer:
very easy there are 42 students because every student needs a bookmark for each of their groupmates
i cant do this lollllllll
Answer:
12
Step-by-step explanation:
first, do the question in parenthesis
then do the questions in the exponent
then do the question with division
then do addition part
(7-4)^2 = (3)^2
9/3 = 3
9+3 = 12
Which table shows a proportional relationship between a and b?
A.
a b
3 9
4 12
5 20
B.
a b
20 25
24 30
32 40
C.
a b
4 12
5 15
6 24
D.
a b
3 4
6 9
12 16
A bus completed a journey of 98 km in 140 minutes. Calculate the average speed, in kilometres per hour, for this journey.
Answer:
hope you like it
Step-by-step explanation:
at first change minutes to hour and calculate by dividing 98 to specific hour
14. A polygon ABCD is inscribed in a circle. Find angle ABC
15. A polygon GHIJ is inscribed in a circle if GHI=76 and HIJ=66 what is IJG
Answer:
m<ABC = 100degrees
m<IJG = 104degrees
Step-by-step explanation:
14. The sum of the opposite angle of the quadrilateral is 180degrees. Hence;
m<ADC + m<ABC = 180
3y+8+4y+4 = 180
7y + 12 = 180
7y = 180 - 12
7y = 168
y = 168/7
y = 24
Get <ABC
m<ABC = 4y+4
m<ABC = 4(24) + 4
m<ABC = 96 + 4
m<ABC = 100degrees
15. Similarly for this;
GHI + IJG = 180
76 + m<IJG = 180
m<IJG = 180 - 76
m<IJG = 104degrees
In the decimal number 3.105, the digit in the hundredths place is a 5?
True
False
Answer:
False cuase 5 is in thousands
what is 11010^2 - 1101^2
Answer:
-120,007,899
Step-by-step explanation:
Given :
[tex]11010^{2} -1101^{2}[/tex]
It can be solved as :
[tex]11010^{2} -1101^{2}[/tex]
121,220,100-1212201
-120,007,899
Therefore, answer will be -120,007,899
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{11,010^2 - 1,101^2}[/tex]
[tex]\mathsf{11,010^2}[/tex]
[tex]\mathsf{= 11,010 \times 11,010}[/tex]
[tex]\mathsf{= \boxed{\bf 121,220,100}}[/tex]
[tex]\mathsf{\bold{121,220,100} - 1,101^2}[/tex]
[tex]\mathsf{1,101^2}[/tex]
[tex]\mathsf{= 1,101 \times 1,101}[/tex]
[tex]\mathsf{= \boxed{\bf 1,212,201}}[/tex]
[tex]\mathsf{121,220,100 - \bf 1,212,201}[/tex]
[tex]\mathsf{= \boxed{\underline{\bf 120,007,899}}}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \underline{\bf 120,007,899}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please help me with this question.
Answer:
[tex]80\text{ square miles}[/tex]
Step-by-step explanation:
Since the map is using a scale of 1 inch : 5 miles, to find the scale of square inches to square miles, square the ratio:
[tex]\implies 1\text{ square inch}:25\text{ square miles}[/tex]
Since the section of land has an area of 3.2 square inches, the actual area of the section of land must be [tex]3.2\cdot 25=\boxed{80\text{ square miles}}[/tex]
Which is equivalent to 80
?
80
4
V80*
O 809
80
o
what is equivalent to 80 1/4?
-x^2 = - 36 (solve using inverse operations)
Answer:
x = ±6
Step-by-step explanation:
-x^2 = - 36
Divide each side by -1
x^2 = 36
Take the square root of each side
sqrt(x^2) = sqrt(36)
x = ±6
Help me plssss? Thanks
Answer:
B
Step-by-step explanation:
helppp plsss 1 hr left
Answer:
the first one should be correct
The equation 3x² - 4x + 6 = 0 has the roots α and β . Find the new equation with the roots (α/β²) and (β/α²) .
Answer:
[tex]{ \tt{sum = \alpha + \beta = \frac{4}{3} }} \\ { \tt{product = \alpha \beta = \frac{6}{3} = 2}} \\ \\ new \: roots : \\ { \bf{sum = \frac{ \alpha }{ { \beta }^{2} } + \frac{ \beta }{ { \alpha }^{2} } }} \\ \\ { \bf{ = \frac{ { \beta }^{2} \alpha + { \alpha }^{2} \beta }{ { (\alpha \beta )}^{2} } }} \\ \\ = { \bf{ \frac{ \alpha \beta ( \alpha + \beta )}{ {( \alpha \beta )}^{2} } }} \\ \\ = { \tt{ \frac{2( \frac{4}{3}) }{2 {}^{2} } }} \\ \\ sum = \frac{2}{3} \\ \\ { \bf{product = \frac{1}{ \alpha \beta }}} \\ = \frac{1}{2} \\ \\ { \boxed{ \tt{equation : {2x}^{2} + \frac{4}{3} x + 1 }}}[/tex]
HELPPP ME PLEASEEEE asappp
Answer:
B.) √3/2
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
For questions like this I recommend memorizing the Unit Circle, but for the sake of calculations here's how I do it using a calculator
cos(30) = 0.866025.....
So now I'll just go through the answers and see which is equivalent
A= 1.73...
B= 0.866025....
C=0.57735....
D=0.5
E=0.7071.....
F=1
You can see that B is equivalent.
Ramesh went from place A to place B and then from place B to place CA is 10.8 km from B and place B is 15.5 km from place C, Rahul went from place A to place D and then place D to place C, distance between place A and D is 11.7 km and distance between place D and place C is 18.2 km, Who travelled more distance and by how much, also calculate the total distance between place A and place D and express the total distance in M,CM and KM.
Answer:
Part A
Rahul by 3.6 km
Part B
The distance between A and D, through place C, d are;
The distance between A and D in meters, m = 44,500 m
The distance between A and D in centimeters, cm = 4,450,000 cm
The distance between A and D, in kilometers, km = 44.5 km
Step-by-step explanation:
Part A
The details of the journeys are;
The distance of A from B = 10.8 km
The distance of B from C = 15.5 km
The total distance Ramesh traveled, d₁ = The distance of A from B + The distance of B from C
Therefore;
d₁ = 10.8 km + 15.5 km = 26.3 km
The total distance Ramesh traveled, d₁ = 26.3 km
The distances of the journey of Rahul is as follows;
The distance between place A and D = 11.7 km
The distance between place D and C = 18.2 km
The total distance Rahul traveled, d₂ = The distance between place A and D + The distance between place D and C
d₂ = 11.7 km + 18.2 km = 29.9 km
The total distance Rahul traveled, d₂ = 29.9 km
Therefore, given that d₂(29.9 km) > d₁(26.3 km), Rahul travelled more distance than Ramesh
The difference between the distance Rahul travelled and the distance Ramesh travelled, d₂ - d₁ = 29.9 km - 26.3 km = 3.6 km
Therefore;
Rahul travelled more distance than Ramesh by 3.6 km
Part B
The total distance from place A to place D through place C, d₃, is given as follows;
d₃ = The distance from A to B + The distance from B to C + The distance from C to D
∴ d₃ = 10.8 km + 15.5 km + 18.2 km = 44.5 km
The total distance from place A to place D, d₃ = 44.5 lm
The total distance from place A to place D in meters, m = 1000 m/km × 44.5 km = 44,500 m
The total distance from place A to place D in cm = 100 cm/m × 44,500 m = 4,450,000 cm
April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs.
What is the complement of April choosing five pop CDs?
choosing five CDs where none of them are pop
choosing five CDs where not all of them are pop
choosing five CDs where at least one of them is pop
choosing five CDs where all of them are pop
Answer:
Choosing five CDs where not all of them are pop.
Step-by-step explanation:
Answer:
B) choosing five CDs where not all of them are pop
Step-by-step explanation:
E2020
I need help in this (￣▽￣)
Answer:
Step-by-step explanation:
a=-2.9
b=-2 5/8=-21/8=-2.625
c=-7/3=-2.333333