1.
Directions:
Factor each expression.
Then find the roots of each equation.
I found all the factors, but not sure the roots of each equation.
Answers
Answer:
a. – 4 or –3
b. –4 or –2
c. 4 or –3
d. 7 or 4
Step-by-step explanation:
To factorize the above expression, multiply the first and last term together, then find two factors of the result such that their sum will result to the middle term of the expression.
Now, we shall give the answers to the question.
a. x² + 7x + 12 = 0
x² + 3x + 4x + 12 = 0
Factorise
x(x + 3) + 4(x + 3) = 0
(x + 4)(x + 3) = 0
x + 4 = 0 or x + 3 = 0
x = 0 – 4 or x = 0 – 3
x = – 4 or –3
Therefore, the roots of the equation are – 4 or –3
b. t² + 6t + 8 = 0
t² + 2t + 4t + 8 = 0
Factorise
t(t + 2) + 4(t + 2) = 0
(t + 4)(t + 2) = 0
t + 4 = 0 or t + 2 = 0
t = 0 – 4 or t = 0 – 2
t = –4 or –2
Therefore, the roots of the equation are –4 or –2
c. 2n² – 2n – 24 = 0
Divide through by 2
n² – n – 12 = 0
n² + 3n – 4n – 12 = 0
Factorise
n(n + 3) – 4(n + 3) = 0
(n – 4)(n + 3) = 0
n – 4 = 0 or n + 3 = 0
n = 0 + 4 or n = 0 – 3
n = 4 or n = –3
Therefore, the roots of the equation are 4 or –3
d. y² – 11y + 28 = 0
y² – 4y – 7y + 28 = 0
Factorise
y(y – 4) – 7(y – 4) = 0
(y – 7)(y – 4) = 0
y – 7 = 0 or y – 4 = 0
y = 0 + 7 or y = 0 + 4
y = 7 or 4
Therefore, the roots of the equation are 7 or 4.
Related Questions
Solve the equation x² = 5. (must show equality properties in work so I can earn full credit)
A. x = 5
B. x = 25
C. x = √5
D. x = ±√5
Answers
take root to both side to clear the square
√x² = ±√5
X = ±√5
What is 5 1/2 is its simple form?
Answers
A dot plot is shown.
Answers
Answer:
C i think but I could be wrong
Step-by-step explanation:
An isosceles triangle has base angles that each measure 69o. Which equation can be used to find x, the measure of the third angle?
a
138 + x = 180
b
69 + x = 180
c
138 + 2x = 180
d
2x + 69 = 180
Answers
Answer:
a. 138 + x = 180
Step-by-step explanation:
Because the angles given are 69+69
which equal 138
and x being the missing angle
finally the total of all angles in a triangle = 180
Prove: An odd times an odd equals an odd.
Answers
Answer:
4mn+2m+2n+1
Step-by-step explanation:
Hope I helped!
Answer: 4mn+2n+1
2(2mn+m+2)+1
Step-by-step explanation:
Consider that AQRS is similar to ALMN and the measure of ZN is 42°. What is the measure of 2S?
A)
42°
B)
48°
56
D)
589
Answers
Answer:
A
Step-by-step explanation:
Solve for the variable A:
-22a = 418
Answers
Answer:
A = -19
Step-by-step explanation:
The answer is a=-19!!
The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. what is the cutoff point?321 474 461 548406 464 517 311534 425 377 505322 435 410 513499 354 307 363The cutoff point is ____minutes( round to the nearest minute)
Answers
Answer:
The answer is "717.25 minutes".
Step-by-step explanation:
In this question first, we arrange the value in ascending order that are:
307,311,321,322,354,363,377,406,425,435,461,464,474,499,505,513,517,534,548
The median is always in an orderly position that is [tex]= \frac{(n+1)}{2}[/tex].
[tex]\to \frac{(n+1)}{2} = \frac{(20+1)}{2} = 10.5[/tex] position orders
[tex]10^{th} \ and \ 11^{th}[/tex] place an average of observations so, the
[tex]Average = \frac{(425 +435)}{2} = \frac{(860)}{2} =430[/tex]
Because as medium stands at 10.5 that median is as below 10 are greater than the level.
[tex]Q_1[/tex] often falls throughout the ordered BELOW average is [tex]= \frac{(n+1)}{2}[/tex] place.
[tex]\to \frac{(n+1)}{2} = \frac{(10+1)}{2} = 5.5^{th}[/tex]ordered position
Average [tex]5^{th} \ and \ 6^{th}[/tex] location findings
[tex]Q_1 = \frac{(354+363)}{2} = \frac{(717)}{2}= 358.5[/tex]
In [tex]= \frac{(n+1)}{2}[/tex] the ordered place, Q3 always falls ABOVE the median.
[tex]\to \frac{(n+1)}{2} = \frac{(10+1)}{2} = 5.5^{th}[/tex] ordered At median ABOVE
Consequently [tex]Q_3[/tex] falls between [tex]5^{th} \ and \ 6^{th}[/tex] ABOVE the median position
[tex]15^{th}\ and \ 16^{th}[/tex]place average of observations
[tex]\to Q_3 = \frac{(499+505)}{2}=\frac{(1004)}{2} = 502[/tex]
[tex]\to IQR = Q_3 - Q_1= 502-358.5= 143.5[/tex]
[tex]\to \text{Upper fence} = Q_3 + 1.5 \times IQR= 502 + 1.5 \times 143.5 = 717.25[/tex]
What is the perimeter of ABCD?
Answers
Answer:
360°
Step-by-step explanation:
Based on what I know that the total of degrees has to be 360°. So, two sides of the rhombus have to have two acute angles and two obtuse angles. So, the Image shows that the 63° is an acute angle. So, multiply 63 by 2 which is 126. Then subtract 126 from 360 which is 234. Then, divide 234 by 2 which is 117. Lastly, add 63 with 63 and 117 with 117 which is 360.
Hopefully, you understand.
Isaiah is starting his own gardening business. Isaiah thinks he can charge $15.50 per hour. If he knows he
will only be able to work 140 hours per month (that's 35 hours per week), how much money will he earn
each month?
Answers
Answer:
About $1627.5
Step-by-step explanation:
15.50 x 35 = 542.5
542.5 x 3 (the amount of weeks in a month) = $1627.5
The amount Cami raised during last year’s charity walk, $45.50, is StartFraction 7 over 10 EndFraction of the amount she raised this year. Which equation represents n, the number of dollars she raised this year?
45.50 (StartFraction 7 over 10 EndFraction) = n
45.50 = 0.7 n
45.50 + n = StartFraction 7 over 10 EndFraction
45.50 = 0.7 + n
Answers
Answer:
45.50 (StartFraction 7 over 10 EndFraction) = n
Answer:
the correct answer on edge is B. 45.50=0.7n
Step-by-step explanation:
6y + 25 = 79
can you please help?
Answers
Answer:
y=9
Step-by-step explanation:
6y=79-25
= 6y= 54
= y=54/6
= y= 9
Subtract 25 from both sides
6y=54
Divide both sides by 6
Y=9
If sin theta = -2/3 which of the following are possible?
Answers
Answer:
a
Step-by-step explanation:
The possible trigonometric function is option (C) [tex]sec \theta = \frac{3}{\sqrt{5} }[/tex] and [tex]tan \theta = \frac{-2}{\sqrt{5} }[/tex] is the correct answer.
What is trigonometry?Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The trigonometric function, sin θ = -2/3
We know that [tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
So, opposite = -2, hypotenuse = 3
The other side of the right triangle adjacent side can be found by using the Pythagoras theorem,
[tex]adjacent=\sqrt{hypotenuse^{2} -opposite^{2} }[/tex]
⇒ [tex]adjacent=\sqrt{3^{2} -(-2)^{2} }[/tex]
⇒ [tex]adjacent=\sqrt{9-4 }[/tex]
⇒ [tex]adjacent=\sqrt{5}[/tex]
Now, [tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex] and [tex]tan \theta = \frac{opposite}{adjacent}[/tex]
Then, [tex]cos \theta = \frac{\sqrt{5} }{3}[/tex]
[tex]sec \theta = \frac{1}{cos \theta}[/tex]
⇒ [tex]sec \theta = \frac{1}{\frac{\sqrt{5} }{3} }[/tex]
⇒ [tex]sec \theta = \frac{3}{\sqrt{5} }[/tex]
[tex]tan \theta = \frac{-2}{\sqrt{5} }[/tex]
Hence we can conclude that the possible trigonometric function is option (C) [tex]sec \theta = \frac{3}{\sqrt{5} }[/tex] and [tex]tan \theta = \frac{-2}{\sqrt{5} }[/tex] is the correct answer.
Learn more about trigonometry here
https://brainly.com/question/16965914
#SPJ2
What is the area of this figure?
Enter your answer in the box.
mm²
Answers
Answer:
[tex]84mm^{2} [/tex]
I think this is true
Answer = 84
BECAUSE
8x6/2 for triangles (24)
x2 bc two triangles (48)
6x6 for square (36)
add it all = (84)
Suppose that c is a number for which the equation c÷c = 1 is false. What is c?
Answers
what is the equivalent property of 8(4x - 3)
Answers
Answer:
=32x−24
Step-by-step explanation:
50 points if its correct with brainliest!! How many times smaller will a number become if you decrease it by 20%.
Answers
Answer:
1/5 because 20% is equivalent to 20/100
Step-by-step explanation:
or 0.2 Thats what I got- sorry if I am wrong.
Answer: 0.8
Step-by-step explanation:
Decreased by 20percent is multiplying by 80 percent, or 0.8
Are these teams?
5x + 8
lik teams?
Answers
Answer with explanation, one doesn’t have a variable
Lily charges $60 for 5 tutoring sessions. What is the cost PER session?
Answers
$60 divided by 5 = $12
$12 per session.
Pls mark me brainliest!
Answer:$12 per session
Step-by-step explanation: divide 60 by 5 you get 12.
Write formula for the following mathematical statement.
The force acting on a body is equal to the product of the mass of the body and the acceleration produced by it
Answers
Answer:
F=ma
Step-by-step explanation:
F is force and its measured in Newtons (N)
m is mass measured in kg
a is acceleration measured in metres per second per second
The half life of a radioactive kind of cesium is 30 years. How much will be left after 120 years, if you start with 960 grams of it
Answers
Answer:
60 grams
Step-by-step explanation:
120 years / half-life of 30 years = it will grow half the size 4 times
960 * 1/2 ^ 4 = 960 * 1/2 * 1/2 * 1/2 * 1/2 = 60 grams
Help with all 3 ASAP
Answers
Answer:
The second one is right
The third one is wrong.
5. If the cost of two tires is $130,56, how much will it cost to buy ten tires?
A. $1305.60
Tires
B. $652.80
C. $326.40
Cost
Answers
it would be A
Step-by-step explanation:
I'm good at math
Hope this helps
Need help with math who is uppppp brainlest and points pls hurry
Answers
Answer:
[tex]The~triangles~AED~and~ABC~are~similar.\\So,\\\frac{AD}{AB} = \frac{DE}{BC} [Corresponding~sides~of~similar~triangles~are~proportional.]\\or, \frac{30}{15} = \frac{34}{x} \\or, x = \frac{15(34)}{30} = 17inches[/tex]
Shape p is translated to shape Q using vector (a b).
Write down the values of a and b.
Photo attached.
Answers
Answer:
the answer is:
a=-2
b=-4
Step-by-step explanation:
Shape P is translated to shape Q using vector [tex]\left[\begin{array}{ccc}2\\4\end{array}\right][/tex].
What is translation of a graph?"A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other."
Given, the shape P is mentioned on the graph.
Now, shape P is translated to shape Q.
Therefore, in order to reach Q from P, the shape needs to shift to the left 2.
After that the shape needs to shift downwards 4 places.
Therefore, the required vector is [tex]\left[\begin{array}{ccc}2\\4\end{array}\right][/tex].
Learn more about translation of a graph here: https://brainly.com/question/14753556
#SPJ3
please help, thanks if you do :)
Answers
Answer: (4,-2)
Step-by-step explanation: step1.- -1/2x=-x+2 (solving for x) x=4
Step 2- y=-1/2x4(substitute the value of X)
Step 3- y=-1/2x4 (solve the equation for y) =2
Step 4- (x,y)=(4,-2) simplify —>(x,y)=(4,-2)
solve the inequality. Graph the solution on a number line. 7<_2
Answers
Help please i have no idea how to do this please help
Answers
Answer:
pretty sure its d
Step-by-step explanation:
y= 1/2x+ 2 to make the x the subject.
Answers
Answer:
[tex]x=2y-4[/tex]
Step-by-step explanation:
[tex]y=\frac{1}{2} x+2[/tex]
"To make x the subject" means to have the equation with all the terms in x on one side. As of now, y is the subject of the equation.
You start by subtracting 2 from both sides, you should get the following.
[tex]y-2=\frac{1}{2} x[/tex]
Then you multiply by 2 from both sides, you should end up with the following.
[tex]2(y-2)=x[/tex]
Therefore, you get the following.
[tex]x=2(y-2)[/tex]
Finally, you distribute and get the answer.
[tex]x=2y-4[/tex]
Please help due tmr. Find c.
Round to the nearest tenth:
Answers
Answer:
c = 14.9 cm
Step-by-step explanation:
Applying the Law of Sines, we would have the following:
c/sin(C) = b/sin(B)
c = ??
C = 180 - (150 + 12) = 18°
b = 10 cm
B = 12°
c/sin(18) = 10/sin(12)
Multiply both sides by sin(18)
c = (10*sin(18))/sin(12)
c = 14.9 cm (nearest tenth)