Question 7: Choose the correct simplification of the expression (3x − 6)(2x2 − 4x − 5)
Answer:
C) 6x³ - 24x² + 9x + 30
Step-by-step explanation:
(3x - 6)(2x² - 4x - 5)
3x • 2x² = 6x³
3x • -4x = -12x²
3x • -5 = -15x
-6 • 2x² = -12x²
-6 • -4x = 24x
-6 • -5 = 30
Combine terms.
6x³ - 12x² - 15x - 12x² + 24x + 30
Combine like terms.
6x³ - 24x² + 9x + 30
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Consecutive terms are __________________.
Answer:
Consecutive terms are numbers which follow each other in order, without gaps, from smallest to largest.
Example:
12, 13, 14 and 15
or
2, 24, 26, 28 and 30 (Even Consecutive)
or
40, 45, 50 and 55 (Consecutive Multiples of 5)
SOURCE/GOOGLE
Answer:
Consecutive numbers are numbers that follows one other in their counting order. Each number in the order will be higher than the previous number by 1.
They are always ordered from the smallest to the largest value.
Step-by-step explanation:
Example :
7, 8, 9, 10 are consecutive numbers.
23, 24, 28, 29 are not consecutive numbers.
Hi how to solve this pythagoras theorem
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
Pythagorean Theorem: If x and y are the leg lengths of a right triangle, then r = √(x^2 + y^2) is the length of the hypotenuse. Alternatively, x^2 + y^2 = r^2.
The side lengths 2x, 4x - 1 and 4x + 1 are already arranged in ascending order. Thus, (2x^)2 + (4x - 1)^2 = (4x + 1).
Performing the indicated operations, we get:
4x^2 + 16x^2 - 8x + 1 = 16x^2 + 8x + 1. Simplify this first by combining like terms:
20x^2 - 16x = 16x^2, or
4x^2 - 16x = 0, or
4x(x - 4) = 0. Thus, x = 0 (which makes no sense here) or x = 4.
The perimeter of the rectangle is the sum of the three sides 2x, 4x - 1 and 4x + 1. Substituting 4 for x, we get
P = 8 + 16 - 1 + 16 + 1, or 40.
The perimeter of the triangle is 40.
If the zeros of f(x) are x=-1 and x=2, then the zeros of f(x/2) are
A. -1, 2
B. -1/2, 5/2
C. -3/2, 3/2
D. -1/2, 1
E. -2/4
Answer:
E. -2, 4
Step-by-step explanation:
If the zeroes of a function are given as [tex]\alpha, \beta[/tex], then the function can be written as:
[tex](x-\alpha)(x-\beta) = 0[/tex]
Here, we are given that zeros of [tex]f(x)[/tex] are x=-1 and x=2.
As per above, we can write the function [tex]f(x)[/tex] as:
[tex](x- (-1))(x-2) = 0\\\Rightarrow (x+1)(x-2)=0[/tex]
So, [tex]f(x) =(x+1) (x-2)[/tex]
To find:
Zeroes of [tex]f(\frac{x}2)[/tex].
Solution:
We have found that [tex]f(x) =(x+1) (x-2)[/tex]
Replacing [tex]x[/tex] with [tex]\frac{x}2[/tex]:
[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2)[/tex]
Now, Let us put it equal to 0 to find the zeroes.
[tex]f(\frac{x}2) =(\frac{x}2+1) (\frac{x}2-2) = 0\\\Rightarrow (\frac{x}2+1) = 0 \ OR\ (\frac{x}2-2) =0\\\Rightarrow \frac{x}{2} = -1\ OR\ \frac{x}{2}=2\\\Rightarrow \bold{x =-2, 4}[/tex]
So, the zeroes are -2, 4.
HELPPPP I NEED HELPP ASAPPPP PLEASEE!!!!
Chelsea received $60 for her birthday. She used three fifths of her birthday money to purchase a pair of jeans. She used two thirds of the remaining birthday money to go to the movies. How much money did Brittany have after attending the movies?
Answer:
$8.
Step-by-step explanation:
So, Chelsea started with $60.
She spend 3/5 of it to buy jeans. Therefore, the jeans' price were 3/5 of 60. In other words, the jeans were 3/5(60)=$36. Since she spend $36 to buy jeans, this means that she has 60-36=$24 left.
And she used 2/3 of $24 to go to the movies. 2/3 of 24 is 2/3(24)=$16. In other words, she spend $16 to go to the movies. This means that she has 24-16=$8 left.
Thus, after buying the jeans and going to the movies, she has $8 left.
Answer:
8 dollars left
Step-by-step explanation:
60 devided by 5 = 12
60 - 36 (three fifths) = 24
24 devided by 3 = 8
24 - 16 ( two thirds) = 8
Sofia tem 52 triângulos retângulos isósceles iguais. Ela quer fazer quadrados usando alguns desses triângulos. Ela pode fazer quadrados de quantos tamanhos diferentes?
Answer:
Portanto, o Sofia pode fazer 6 tamanhos diferentes
Step-by-step explanation:
A fim de sermos capazes de determinar efetivamente quantos quadrados de diferentes tamanhos podem ser formados a partir do triângulo isósceles 52, resolvemos isso usando a fórmula
2 (n + 1) Onde n = 0 e todos os inteiros positivos
em outro para obter um tamanho diferente para os quadrados, temos que adicionar mais triângulos para aumentar o tamanho
a) quando n = 0
2 (0 + 1) = 2 × 1 = 2 triângulos isósceles iguais
A união de 2 triângulos isósceles forma um quadrado. Este é o primeiro quadrado
= 1 quadrado
b) quando n = 1
2 (1 + 1) = 2 × 2 = 4 triângulos isósceles iguais = 1 quadrado
c) quando n = 2
2 (2 + 1) = 2 × 3 = 6 triângulos isósceles iguais = 1 quadrado
d) quando n = 3
2 (3 + 1) = 2 × 4 = 8 triângulos isósceles iguais = 1 quadrado
e) quando n = 4
2 (4 + 1) = 2 × 5 = 10 triângulos isósceles iguais = 1 quadrado
f) quando n = 5
2 (5 + 1) = 2 × 6 = 12 triângulos isósceles iguais = 1 quadrado
Adicionamos o número total de triângulos usados
2 + 4 + 6 + 8 + 10 + 12 = 42 triângulos
42 triângulos de 52 triângulos formariam 6 quadrados com tamanhos diferentes
Vamos fazer mais um, onde n = 6
g) quando n = 6
2 (6 + 1) = 2 × 7 = 14 triângulos isósceles iguais = 1 quadrado
2 + 4 + 6 + 8 + 10 + 12 + 14 = 56 triângulos
Isso já excedeu o número dado de triângulos em questão.
Portanto, o Sofia pode fazer 6 tamanhos diferentes de quadrados usando 42 triângulos isósceles iguais
What is the approximate value of 2 -3
Assuming you are doing x minus y, the value would be -1.00
The number line can help - go left three times from 2 and you get an answer.
Assuming you are doing x times (-y), the value would be -6.00
Add -3 to itself 2 times
Use exterior angle of triangle theorem to find the missing measure of an angle in a polygon.
Answer:
[tex]\boxed{x=60}[/tex]
Step-by-step explanation:
The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles of the triangle.
[tex]130=70+x[/tex]
Subtract 70 from both sides.
[tex]130-70=70+x-70[/tex]
[tex]60=x[/tex]
Answer:
x = 60°
Step-by-step explanation:
Exterior angle is equal to the sum of opposite interior angles
x + 70 = 130
Subtract 70 from both sides
x = 130 - 70
x = 60°
what are some words that relate to geometry but are difficult to precisely define?
Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
find the value of x please
Answer:
A. 40°Step-by-step explanation:
AO = CO = radius
AO = CO ⇒ AB = BC and m∠AOB = m∠BOC = ¹/₂m∠AOC
From BDOE:
m∠EOB + m∠OBC + m∠CDE + m∠DEO = 360°
(65° + 75°) + 90° + x + 90° = 360°
140° + 180° + x = 360°
x = 40°
complete the square to solve
f(x)=x^2+6x-7
Solve y=x2-5 for x.
The expansion of (1 + 4x)5 is
Answer:
5+20x
Step-by-step explanation:
multiply 5 to 1 and 4x respectively
If x3 + ax2 – bx + 10 is divisible by x2 – 3x + 2,
find the values of
1) a-b
2) 2a-b
Which polynomial has factors of 4x – 7 and x + 4?
3x2 + x – 3
4x2 + 9x – 28
3x2 – 7x – 3
4x2 – 23x – 28
Answer:
B. 4x2 + 9x – 28
Step-by-step explanation:
Multiply out the factors and see what polynomial you end up with.
(4x – 7)(x + 4) = 4x^2 + 16x - 7x - 28 = 4x^2 + 9x - 28
The polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
To determine which polynomial has factors of 4x – 7 and x + 4, we can use the fact that if a polynomial has a factors.
So, if a polynomial has factors of 4x – 7 and x + 4, then it can be written as:
(4x – 7)(x + 4)
Multiplying these factors together using the distributive property, we get:
4x²+ 16x - 7x - 28
Simplifying, we get:
4x² + 9x - 28
Hence, the polynomial with factors of 4x – 7 and x + 4 is 4x² + 9x - 28, Option B is correct.
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Round 5.9496 to the nearest thousandth
Answer:
5.95
Step-by-step explanation:
that is because 96 is rounded too 100
so its 5.9500 = 5.95
Answer:
5.950
Step-by-step explanation:
5.9496
ones . tenths hundredths thousandths ten thousandths
5 . 9 4 9 6
We are rounding to the thousandths place
so we look at the ten thousandths place
6 > 5 so we round up the the thousandths place
9 will go up so that forces the hundreds place up
4 becomes 5 in the hundreds place
5.950
Joaquin used two types of flour in a muffin recipe. How much flour did he use in all? Solve any way you choose.
Answer:
3 1/6 cups of flour.
Step-by-step explanation
Let f and g be inverse functions. Find f(g(8)).
Answer:
8
Step-by-step explanation:
If f and g are inverse functions , they undo each other
f(g(8))= 8 when f and g are inverses
Answer:
8
Step-by-step explanation:
I have no further information so this is the only answer.
Show how the greatest common factor of the numbers 10 and 15 can be used to reduce the fraction 10/15.
Answer:
2/3
Step-by-step explanation:
The greatest common factor is 5 because it can divide two of them. When you divide 10/15, it becomes 2/3.
look at image and solve
dac=90-(30+45)
=90-75
=15
hope it helps
It is complementary
Answer:
it is complementary angle.
15degrees
Step-by-step explanation:
complementary angle is when the sum of angles is equal to 90degrees.
45+30+<DAC=90
75+<DAC=90
<DAC=90-75
<DAC=15 degrees.
Factor 75 - 95. a. 5(15 - 19) b. 5(19 - 15) c. 25(3 - 4) d. 25(4 - 3)
Answer:
a. 5(15-19)
Step-by-step explanation:
to factor out this expression you need to find the greatest common factor (GCF) in order to fully factor out the expression
the GCF of the number 75 and -95 is 5
divide both numbers by 5 to get 15 and -19
to finish out with the fully factored expression put 15-19 inside parenthesis and put a 5 outside of the parenthesis as shown below:
5(15-19)
Answer:
a. 5(15 -19)
Step-by-step explanation:
15*5 = 75
-19*5 = -95
Factor is:
5(15 -19)
a quadrilateral with two right angles must be an a trapezoid a square a rectangle or no classification guaranteed
Answer:
No classification guaranteed
Step-by-step explanation:
A parallelogram is a quadrilateral with 2 pairs of parrallel sides.
A rectangle has 4 right angles
A square has all 4 sides being congruent
A trapezoid only needs 1 pair of parrallel lines. However some trapezoids have no right angles but some do. In the context of your question it is probably a trapezoid. However, it is no classification guaranteed.
Is through BYU IS?
The correct option is Option A: a quadrilateral with only two right angles is a trapezoid.
What is a trapezoid?The quadrilateral whose one pair of opposite sides are parallel is called the trapezoid.
So, if one side of the trapezoid touches the parallel side at right angles then it will form 90° with both of the parallel lines. Then two right angles will be formed in the quadrilateral.
A trapezoid is only required quadrilateral to have a pair of parallel sides. However, a trapezoid can have one of the sides connecting the two parallel sides and perpendicular to the parallel sides which would give two right angles. The picture is given below.
Therefore quadrilateral with only two right angles is a trapezoid.
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At a carnival game, there is a 35% probability of winning a prize. What is the probability of not winning a
prize?
70%
65%
35%
50%
The two percentages (for winning and not winning) must always add to 100%, which you can think of 100% of a pie. So 100-35 = 65 showing that 35+65 = 100.
Answer:
There is a 65% probablility of not winning a prize.
Step-by-step explanation:
The 35% chance of winning a prize is taken out of a total percentage of 100. If you subtract 35 from 100, the remaining number, 65, is the probability of not winning, since there are only two possible outcomes.
Find all solutions to the following equation
Answer:
x = -1
Step-by-step explanation:
-2/ ( x * (x+2)) = ( x+3) / ( x+2)
Using cross products
-2 ( x+2) = ( x+3) x* (x+2)
Divide each side by (x+2) This means x cannot equal -2 because we are dividing by 0
-2 = x ( x+3)
Distribute
-2 = x^2 +3x
Add 2 to each side
0 = x^2 + 3x+2
Factor
0 = ( x+2) (x+1)
Using the zero product property
x+2 = 0 x+1 = 0
x = -2 x = -1
But above we said x cannot equal -2
so x = -1
The solution we said x cannot equal -2so x = -1
Step-by-step explanation:
-2/ ( x * (x+2)) = ( x+3) / ( x+2)
Using cross products
-2 ( x+2) = ( x+3) x* (x+2)
Divide each side by (x+2) This means x cannot equal -2 because we are dividing by 0
-2 = x ( x+3)
Distribute
-2 = x^2 +3x
Add 2 to each side
0 = x^2 + 3x+2
Factor
0 = ( x+2) (x+1)
Using the zero product property
x+2 = 0 x+1 = 0
x = -2 x = -1
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b) Factor the expression completely. (1 point)
20b - 16
Answer:
20b - 16
=> 4 (5b - 4)
or
20b - 16
=> 20b/16 - 16/16
=> 1.25b - 1
Answer:
4(5b-4)
Step-by-step explanation:
To factor this you need to find a number, that 20 and 16 are divisible by. You can divide 4 from both of these.
It becomes 4(5b-4)
Happy D's Playland charges a $100 flat
fee for parties plus $1.50 per person.
Marta has $125 to spend. Which
inequality could help Marta find the
number of people she can invite?
Answer:
$16.66
Step-by-step explanation:
$125-$100 = $25
since its $1.50 per person, we do $25 DIVIDED by $1.50 = $16.66.
i hoped this helped :)
can someone please help me with this
f(x)=2x^3-x^2+5 / x-1
f(3)=2(3)^3-3^2+5 / 3-1
f(3)=54-9+5 / 2
f(3)=50 / 2
f(3)=25
Find the solutions to $x^2 + 64 = 0.$[tex]Find the solutions to $x^2 + 64 = 0.$[/tex]
Answer:
x=8i,\:x=-8i
Step-by-step explanation:
x^2+64-64=0-64
x^2=-64
x=\sqrt{-64},\:x=-\sqrt{-64}
x=8i,\:x=-8i
The subject is operations on rational expressions.
The instructions are add or subtract the following expressions. Remember to find a common denominator when necessary. Reduce all answers to lowest terms.
Answer:
[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]
Step-by-step explanation:
[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]
= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
Now we have done the denominators of each term of the expression equal.
Further we add the terms,
[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]
= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]
= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]
Now factorize the numerator of the fraction.
4x² + 14x - 18 = 2(2x² + 7x - 9)
= 2(2x² + 9x - 2x - 9)
= 2[x(2x + 9) - 1(2x + 9)]
= 2(x - 1)(2x + 9)
Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.
you need 3 sticks of butter for every 24 cookies how many cookies can you bake with 5 sticks of butter?
Answer:
40
Step-by-step explanation:
The first box is 2--> 16*3 divided by 24= 2
Second box is 40--> 5*24 divided by 3= 40
Hope it helps.
