Answer:
[tex]4x ^{2} - 2x - 42 \\ 2(2 {x}^{2} - x - 21) \\ 2(2 {x}^{2} + 6x - 7x - 21) \\ 2(2x(x + 3) - 7(x + 3) \\ 2(2x - 7)(x + 3)[/tex]
Answer:
2x - 7
Step-by-step explanation:
4x² - 2x - 42 ( factor out 2 from each term )
= 2(2x² - x - 21) ← factor the quadratic
consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 21 = - 42 and sum = - 1
the factors are+ 6 and - 7
use these factors to split the x- term
2x² + 6x - 7x - 21 ( factor the first/second and third/fourth terms )
= 2x(x + 3) - 7(x + 3) ← factor out (x + 3) from each term
= (x + 3)(2x - 7)
then
4x² - 2x - 42 = 2(x + 3)(2x - 7) ← in factored form
with 2x - 7 as a factor
What is the area of the shaded region of the figure pictured? Round your answer to the nearest tenth.
Answer:
use Pythagoras to find diameter of circle.
use half of diameter as radius to find area of circle.
subtract area of square from area of circle.
the steps are very simple so I didn't want to waste time drawing it out. added a photo outlining each step for you. feel free to ask if you need a step explained
Which of the following represents a nonlinear function?
A server makes $200 a week working at a local restaurant. The server saves 35% of the $200 weekly earnings each week for 4 weeks.
If the server saves 78 of the 5th week’s $200 earnings, how much money will the server have saved in total after the 5 weeks?
please i need help and i taking a test
Answer:
He would of saved 455$
Step-by-step explanation:
Because for 4 weeks he saved 35% of 200$ which would be 70 and 70+70+70+70 is 280$ and then he saved 175 dollars on the 5th week because 7/8 of 200 is 175 so 280+175= 455
I hope this helps!
Factor x^2 + 9 in the complex numbers.
Answer:
Multiply
3
by
−
1
.
(
x
+
3
i
)
(
x
−
3
i
)
Janelle plans to paint her bedroom, which is the shape of a
rectangular prism. Its length is 10 feet, its width is 12 feet, and the
ceilings are 9 feet tall. She does not need to paint the floor or ceiling. How many square feet of wall space will she be covering?
Answer:
19 feet tall
Step-by-step explanation:
(PLS HELP ASAP ⚠️⚠️)
ITS IXL
find the centrroid of the triangle with the given vertices F(1, 5), G(-2, 7) and H(-6, 3)
[tex]\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} F(\stackrel{x_1}{1},\stackrel{y_1}{5})\\\\ G(\stackrel{x_2}{-2},\stackrel{y_2}{7})\\\\ H(\stackrel{x_3}{-6},\stackrel{y_3}{3}) \end{cases} \\\\\\ \left( \cfrac{1-2-6}{3}~~,~~\cfrac{5+7+3}{3} \right)\implies \left( \cfrac{-7}{3}~~,~~\cfrac{15}{3} \right)\implies \left( -2\frac{1}{3}~~,~~5 \right)[/tex]
Help me please
Mr. Kim randomly divides his class into groups. Each group has 5 students and each group is randomly assigned 1 of 6 projects to do. Which simulation best models the outcomes of the sets up?
A rolling 2 number cubes, each with the numbers 1-6 on it
B. spinning a spinner divided into 5 equal sections, and flipping a coin 3 times
C.flipping a coin 5 times, and spinning a spinner divided into 6 equal sections
D. drawing 1 of 5 numbered papers out of a bag, and rolling a number cube with the numbers 1-6 on it one time
Answer:
D
Step-by-step explanation:
Because neither Mr. Kim nor anyone else is picking the people of a specific group when the paper is drawn from the bag. And rolling a cube with numbers 1-6 you almost never get the number you want so it is really random. And then after the groups are picked they roll the die and then that number is crossed off so it is not used again with the other groups.
Solve for x and y.
y
6
X
2
X=
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answer:
How to solve your problem
Step-by-step explanation:
1.1 x2 multiplied by x1 = x(2 + 1) = x3
Final result
y6x3
A shark can swim at a speed of 172 miles per hour. At this speed, how far does it travel in 5 hours? 2
Answer:
860 miles
Step-by-step explanation:
172 miles per hour x 5 hours = 860 miles
Answer:
860 miles
Step-by-step explanation:
172 x 5 = 860
the shark has moved 172 miles in one hour, so to figure out how far it has traveled in 5 you can multiply the speed by the time.
PLEASE HELP!
In the drawing, the symmetries of the sides AB and AC of triangle ABC intersect at point O and <MAN = 84°. Find the magnitude of:
A) <BOC B) <MON
Answer:
∠BOC = 96°∠MON = 48°Step-by-step explanation:
Kenny made a scale drawing of a house and its lot. In real life, the front lawn is 10 meters wide. It is 5 centimeters wide in the drawing. What is the scale factor of the drawing? Simplify your answer and write it as a fraction.
Answer: 1/2
Step-by-step explanation:
Scale factor:
model/real-life = 5/10 = 1/2
50 points HELPP QUICK which picture shows the line of reflection?
Answer:
D
Step-by-step explanation:
it reflects
Answer:
D
Step-by-step explanation:
i think the answer is D.it is just guess
Amy and Jack have candies in a ratio of 1:3. Together, they have a total of 40 candies. How many candies does Amy have?
Amy has 10 candies.
Jack has 30 candies.
1 out of 4 is Amy's
3 out of 4 is Jack's
Amy's = 1/4×40=10
Jack's = 3/4×40=30
Find the slope between the two points given. Then, use the slope and one of the points to write the equation of the line in slope intercept form. State the slope and y-intercept. (1,-3) (0,-1)
Answer:
Step-by-step explanation:
Solve the system of equations algebraically using substitution and elimination
Answer:
my answer is 2x+ 3y=22 because that the answer
help please i beg you!!
Answer:
Step-by-step explanation:
-x + 3y =9
substitute y with 2/3x as mentioned in the question
so,
-x+3 (2/3x) = 9
cancelling 3 we get..
-x+2x=9
x=9
hope it helps
thanks
Answer:
y = 6
Step-by-step explanation:
- x + 3y = 9 ( add x to both sides )
3y = 9 + x → (1)
y = [tex]\frac{2}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )
3y = 2x → (2)
substitute 3y = 2x into (1)
2x = 9 + x ( subtract x from both sides )
x = 9
substitute x = 9 into (1)
3y = 9 + 9 = 18 ( divide both sides by 3 )
y = 6
my question is what is 1.679091 / 67
plsssss help me i need help so bad
Answer:
0.0250610597014925
Step-by-step explanation:
Put the following into standard form.
y=1/2x - 9
Answer:
x - 2y = 18
Step-by-step explanation:
The ratio of the number of pears to the number of oranges in a basket
is 5:3. The rest of the fruits are apples. There are 54 more pears than
oranges and 3 more apples than oranges.
(a) How many pears are there in the basket?
(b) What percentage of the fruits are apples?
Answer:
(a) 135
(b) 28%
Step-by-step explanation:
We can write equations relating pears to oranges, solve them, and then find the number of apples. Let p, o, and 'a' represent the numbers of pears, apples, and oranges.
p/o = 5/3 . . . . . the ratio of pears to oranges is 5:3
p -o = 54 . . . . . there are 54 more pears than oranges
a -o = 3 . . . . . . there are 3 more apples than oranges
__
a)Multiply the first equation by 3/5o to get ...
3/5p = o
Substitute that into the second equation:
p -(3/5)p = 54
2/5p = 54 . . . . . . simplify
p = 54(5/2) = 135 . . . . multiply by 5/2 to get the number of pears
There are 135 pears in the basket.
__
b)a = 3 +o = 3 +3/5p = 3 +3/5(135) = 3 +81 . . . . solve for the number of apples
a = 84
The percentage of fruits that are apples is ...
apples/total = 84/(135 +81 +84) = 84/300 = 28/100 = 28%
28% of the fruits are apples
Consider a game board that has 49 squares. You place 1 grain of wheat on the first square, 2 on the next, 4 on the next, 8 on the next, and so on to the 49th square. How many total grains of wheat will there be? Write your answer using scientific notation.
Approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.
Describe Geometric Series?A geometric series is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant. This constant is called the common ratio, and it is denoted by the letter "r".
The formula for the sum of the first n terms of a geometric series is:
S_n = a(1 - rⁿ)/(1 - r)
where S_n is the sum of the first n terms, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the series.
The number of grains of wheat on each square of the board can be found by raising 2 to the power of the square number minus 1. For example, the number of grains of wheat on the first square is 2⁰ = 1, the number on the second square is 2¹ = 2, the number on the third square is 2² = 4, and so on.
So, the total number of grains of wheat on the board is the sum of 2⁰ + 2¹ + 2² + ... + 2⁴⁸. This is a geometric series with first term 1 and common ratio 2. Using the formula for the sum of a geometric series, the total number of grains of wheat is:
2⁰ + 2¹ + 2² + ... + 2⁴⁸ = (2⁴⁹ - 1)/(2 - 1) = 2⁴⁹ - 1
This is approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.
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what is the volume of 5cm 2cm 8cm.
Answer:
80 cm
Step-by-step explanation:
(5 x 8) x 2
40 x 2
80 cm
Answer:
80cm
Step-by-step explanation:
5x8=40x2=80cm
A triangle is equilateral if
sides are the same length.
what’s the answer? its due in 5h
Answer:
Andre scored 14 points
Step-by-step explanation:
We make an equation describing the problem:
x + 9 = 5 + 9
x = 14
We compare Noah and Andre by doing:
2x + 10
and x = 5
This means Diego scored 5 points.
What is the result of adding -2.9x + 6.8 and 4.4x - 7.3
1.5x-0.5 should be the answer
I need help with this one too
Answer:
10 1/2x + 126 sq. feet
Step-by-step explanation:
Area = length × width
length = 12 + x
width = 10 1/2
(12 + x)(10 1/2)
126 + 10 1/2x
Find the area of a triangle
Answer:
½*b*h
Step-by-step explanation:
½*base*height
you can use the above formula to answer the following questions.Points J and K are midpoints of the sides of triangle FGH.
Triangle F G H is cut by lines segment J K. Point J is the midpoint of side G H. Point K is the midpoint of side H F. Line segments G J and J H are congruent. Line segments H K and K F are congruent. The Length of J K is 2 y + 5 and the length of G F is 5 y + 3.
What is the value of y?
2
5
7
8
Answer:
C. 7
Step-by-step explanation:
Points J and K are midpoints of the sides of triangle FGH.
=> JK = 1/2FG
2y + 5 = 1/2(5y + 3)
4y + 10 = 5y + 3
5y - 4y = 10 - 3
y = 7
The value of y is 7 for the given triangle.
What are the properties of Triangle?The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
We know that GJ = JH, and HK = KF.
Also, J and K are midpoints of GH and HF, respectively.
Therefore, we can say that:
GJ + JH + HK + KF = GF
2(GJ + HK) = GF
2(2y + 5) = 5y + 3
4y + 10 = 5y + 3
y = 7
Therefore, the value of y is 7.
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A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
A convex pentagon has interior angles that measure 60, 80, 120, and 140. What is the measure of the fifth interior angle?
Explanation -:Given -
First interior angle = 60°Second interior angle = 80°Third interior angle = 120°Fourth interior angle = 140°To Find -
Fifth interior angleSolution -
Let us assume fifth interior angle as x
We know,
Sum of interior angles of a pentagon is 540°
60° + 80° + 120° + 140° + x° = 540°
→ 400° + x° = 540°
→ x° = 540° - 400°
→ x = 140°
Fifth interior angle of a pentagon = 140°
[tex] \rule{185pt}{7pt}[/tex]
The quotient of (x4 – 3x2 4x – 3) and a polynomial is (x2 x – 3). what is the polynomial?
The polynomials [tex](x^{2} +x-1)[/tex] and [tex](x^{4} -3x^{2} +4x-3)[/tex] has a quotient of[tex](x^{2} +x-3)[/tex]. The polynomial is [tex](x^{2} +x-1)[/tex].
What is Euclid's division lemma?
Euclid's division lemma states that for any positive integers, let's say a and b the condition [tex]\rm a=bq+r[/tex], where [tex]\rm 0\leq r\leq b[/tex].
Mathematically, we can say that
Dividend = divisor × quotient + remainder
P(x) = g(x) × q(x) + r(x)
To find the divisor g(x)
[tex]x^{4} -3x^{2} +4x-3= \rm g(x)\times (x^{2} +x-3) + r(x)\\[/tex]
On dividing P(x) by q(x) we get,
[tex]x^{4} -3x^{2} +4x-3 \div (x^{2} +x-3) = \rm g(x)+0[/tex][tex](x^{2} +x-3) \times (x^{2} +x-1)\div (x^{2} +x-3) = \rm g(x)\\(x^{2} +x-1) = \rm g(x)\\[/tex]
Hence, the polynomials [tex](x^{2} +x-1)[/tex] and [tex](x^{4} -3x^{2} +4x-3)[/tex] has a quotient of [tex](x^{2} +x-3)[/tex]. The polynomial is [tex](x^{2} +x-1)[/tex].
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