-3 and 4 cannot be the values of x in the given expression
The expression is given as:
[tex]\frac{(x^2-x-6x^2-8x+16)}{(x^2-x-12)}[/tex]
Start by equating the denominator to 0
[tex]x^2 - x - 12 = 0[/tex]
Expand the above equation
[tex]x^2 - 4x + 3x - 12 = 0[/tex]
Factorize the equation
[tex]x(x - 4) + 3(x - 4) = 0[/tex]
Factor out x - 4
[tex](x + 3) (x - 4) = 0[/tex]
Split
[tex](x + 3)= 0\ or\ (x - 4) = 0[/tex]
Remove brackets
[tex]x + 3= 0\ or\ x - 4 = 0[/tex]
Solve for x
[tex]x =- 3\ or\ x = 4[/tex]
Hence, -3 and 4 cannot be the value of x in the given expression
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24. Solve for x: 3x - 2(x - 4) = 5(2x + 4) -3
x=-1
3x-2x+8=10x+20-3
x+8=10x+17
-9x=9
x=-1
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]x-2\left(x-4\right)=5\left(2x+4\right)-3[/tex]
[tex]-2\left(x-4\right)\\\mathrm{Distribute}\\-2x+8[/tex]
[tex]3x-2x+8=5\left(2x+4\right)-3[/tex]
[tex]\mathrm{Combine\: like\: terms}[/tex]
[tex]x+8=5\left(2x+4\right)-3[/tex]
[tex]\left(2x+4\right)-3\\\mathrm{Distribute}\\10x+20-3\\10x+17[/tex]
[tex]x+8=10x+17[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]x+8-8=10x+17-8[/tex]
[tex]x=10x+9[/tex]
[tex]\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}[/tex]
[tex]x-10x=10x+9-10x[/tex]
[tex]-9x=9[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-9[/tex]
[tex]\frac{-9x}{-9}=\frac{9}{-9}[/tex]
[tex]\bold{x=-1}[/tex]
Lucy borrowed $73,250 to purchase a home. The bank offered her an APR of 3.15% for a term length of 20 years. Excel calculates the monthly payment to be $411.77. If she were to pay only the minimum payment for the lifetime of the loan, how much will Lucy be paying in interest?
Amount Lucy will be paying in interest will be $38,596.2
Using the compound amount formula to get the amount after she will pay back after 20 years expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
A is the amount after 20 yearsr is the rate = 3.15% = 0.0315time in years = 20 yearsn is the compounding time = 12 (monthly)P is the amount borrowed = $73,250Substitute the parameters into the formula;
[tex]A=73,250(1+\frac{0.0315}{12} )^{20(12)}\\A= $73,250 (1.8761)\\A= \$137,421.49[/tex]
If Excel calculates the monthly payment to be $411.77, the amount paid for 20 years will be $411.77 * 240months = $98,824.8
Amount Lucy will be paying interest will be $137,421- $98,824.8 = $38,596.2
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Which equation matches the graph?
Answer:
i think 4x+3y = -24 is answer
The Levine family has 10 gallons of gas in the car. The car uses 1 5/8 of a gallon each hour. How long can they drive on 10 gallons of gas?
Answer:
6.15
Step-by-step explanation:
10 gallons is 80/8
1 5/8= 13/8
80 divided by 13 is 6.15384615385 but rounded 6.15
6.15 hours
if its not that then keep rounding to 6.2 or 6hrs
Convert the following fraction to a decimal.
Share £30 in the ratio 1:5 between Tim and Sam
How do I verify: tan(x)+cot(x)=(2)/sin(2x)?
I always get stuck after writing out (sin^2x+cos^2x)/sin(x)cos(x)
[tex]sin^2(\theta)+cos^2(\theta)=1\qquad \qquad sin(2\theta)=2sin(\theta)cos(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]tan(x)+cot(x)=\cfrac{2}{sin(2x)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{doing the left-hand-side}}{\cfrac{sin(x)}{cos(x)}+\cfrac{cos(x)}{sin(x)}\implies \cfrac{sin^2(x)+cos^2(x)}{\underset{\textit{using this LCD}}{sin(x)cos(x)}}} \implies \cfrac{1}{sin(x)cos(x)}[/tex]
now, let's recall that anything times 1 is just itself, namely 5*1 =5, 1,000,000 * 1 = 1,000,000, "meow" * 1 = "meow" and so on, so we can write anything as time 1.
let's recall something else, that same/same = 1, so
[tex]\cfrac{cheese}{cheese}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{horse}{horse}\implies \cfrac{butter}{butter}\implies \cfrac{25^7}{25^7}=1[/tex]
therefore
[tex]\cfrac{1}{sin(x)cos(x)}\cdot \cfrac{2}{2}\implies \cfrac{2}{2sin(x)cos(x)}\implies \cfrac{2}{sin(2x)}[/tex]
Which of the following word phrases describe the expression y + 3?
A.three less than y
B.the sum of y and 3
C.the product of y and 3
D.three more than y
Make x the subject of the formula
t=
[tex] \sqrt{2(x - ut) \div a}[/tex]
[tex]t = \sqrt \frac{ {2(x - ut)} }{a} \\ = > t = \sqrt{ \frac{2x - 2ut}{a} } \\ = > {t}^{2} = \frac{2x - 2ut}{a} \\ = > a {t}^{2} = 2x - 2ut \\ = > \frac{ { - at}^{2} }{2ut} = 2x \\ = > \frac{ - at}{2u} = 2x \\ = > \frac{ - at}{2u \times 2} = x \\ = > \frac{ - at}{4u} = x[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
3. What is the exact area of triangle ABC? Use special right triangles to help find the base of the triangle. Show your work.
The exact area of triangle ABC is 93.51 cm².
The given parameters;
Height of the triangle, h = 18 cmThe base of the triangle is calculated by using trigonometry ratio as follows;
[tex]tan (30) = \frac{b}{18} \\\\[/tex]
where;
b is the base of the triangle ABC[tex]b = 18 \times tan(30)\\\\b = 10.39 \ cm[/tex]
The area of the triangle ABC with the calculated base and given height is calculated as follows;
[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2[/tex]
Thus, the exact area of triangle ABC is 93.51 cm².
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Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
The cost of each bag of apple is $6.35
Let the cost of a bag of apple be xIf Miguel buys eggs and apples at the store.
• He pays a total of $56.97.
• He pays a total of $6.17 for the eggs.
• He buys 8 bags of apples that each cost the same amount
The correct equation that represents the statement will be given as:
6.17 + 8x = 56.97Make x the subject of the formula
8x = 56.97 - 6.17
8x = 50.8
x = 50.8/8
x = 6.35
Hence the cost of each bag of apple is $6.35
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40x^-4 y^6
________
10x^-5 y^5
Answer:
[tex]4xy[/tex]
Step-by-step explanation:[tex](40/10) *(x^-^4/x^-^5) * (y^6/y^5) \\=4*x*y=4xy[/tex]
130 is what percent of 70?
Answer:
91%
Step-by-step explanation:
hopes this helps
Answer:
185.71%
Step-by-step explanation:
130 / 70 = 1.857142857
(1.857142857)(100) = 185.71%
2 and 5/6 divided by 1 and 2/3 find the solution and write it in simplest form
Thanks for the help!!!!
Answer:
1 7/10
Step-by-step explanation:
= 17/6 ÷ 5/3
= 17 x 3
= 6 x 5
= 51/30
= 1 7/10
The triangles shown bellow must be congruent?
True or False?
find the difderence of 3/4 and 1/28
Answer:
5/7
Step-by-step explanation:
3/4-1/28
21/28-1/28
20/28
simplify
5/7
3.
In parallelogram ABCD, M
m
Answer:
Please send a picture or explain properly
A triangle has sides measuring 7 centimeters and 13 centimeters that form an angle measuring 44°. Which of these is CLOSEST to the length of the third side of the triangle? A) 8.1 centimeters B) 8.7 centimeters C) 9.3 centimeters D) 9.9 centimeters
Answer:
9.3 centimeters
Step-by-step explanation:
A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is
if we can assume the ball is being thrown from the ground upwards, then we can say that the inital height of it is 0, whilst its initial velocity is 80 ft/s, thus
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-16t^2+80t+0\implies h(t)=-16t^2+80t[/tex]
Jose left the airport and traveled toward the mountains. Kayla left 2.1 hours later traveling 35 mph faster in an effort to catch up to him. After 1.2 hours Kayla finally caught up. Find Jose's speed.
========================================================
Explanation:
x = Jose's speed in mph
x+35 = Kayla's speed since she drives 35 mph faster than Jose
Jose gets a 2.1 hour head start and it takes Kayla 1.2 hours to reach him. So this means Jose has been driving for 2.1+1.2 = 3.3 hours when Kayla reaches him. The distance he travels is
distance = rate*time
d = r*t
d = x*3.3
d = 3.3x
while Kayla's distance equation is
d = r*t
d = (x+35)*1.2
d = 1.2x+42
Since Kayla meets up with Jose at the 1.2 hour mark, this means the two distances they travel is the same. Set their distance expressions equal to one another. Solve for x.
3.3x = 1.2x+42
3.3x-1.2x = 42
2.1x = 42
x = 42/(2.1)
x = 20
Jose's speed is 20 mph, while Kayla's speed is x+35 = 20+35 = 55 mph.
Jose's fairly slow speed is probably due to a number of factors such as heavy traffic, icy roads, or poor visibility. Kayla probably got a bit of a break with more favorable conditions.
Since Jose travels at 20 mph and does so for 3.3 hours, he travels d = r*t = 20*3.3 = 66 miles. Kayla travels d = r*t = 55*1.2 = 66 miles as well. We get the same number each time to help confirm the answer.
Martin, his 2 brothers, and his 5 sisters want to fairly share 3 bottles of water. How
much water will Martin get?
Answer:
3/8 bottle
Step-by-step explanation:
Fractions are just division.
Martin + 2sisters + 5bros
= 8 people
3bottles ÷ 8people
= 3/8 bottles per person
Martin is a person, so he gets 3/8 of a bottle, if they all share equally.
Using proportions, it is found that Martin will get 0.375 of a bottle.
This question is solved by proportions, using a rule of three.Martin, his 2 brothers and 5 sisters combine to represent 8 people, which will share 3 bottles equally. How much will Martin, which is one person, get?The rule of three is:
1 person - x bottles
8 people - 3 bottles
Applying cross multiplication:
[tex]8x = 3[/tex]
[tex]x = \frac{3}{8}[/tex]
[tex]x = 0.375[/tex]
Martin will get 0.375 of a bottle.
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QUESTION 19 PLEASE HELP ME ASAP
Answer:
changes over time
Step-by-step explanation: its going up not staying at one spot
Help again please ?? I have 5 more that needs to be answer also ..
Help help help math math math
Answer:
180 - 17 - 14 =149
180 - 149 = 31*
Step-by-step explanation:
Answer: 180 - 17 - 14 =149180 - 149 = 31*
Step-by-step explanation: it’s right
A rectangular garden is 35m long and 25m broad. find the perimeter of the rectangular garden. find the length of wire required to fence with 2 round.
Answer:
The perimeter is the distance all round,
Step-by-step explanation:
perimeter of a rectangle is gotten by the formula
P=2(L+W)
2(35+25)=120m
The wire covers the distance all round
so we use 120m×2=240m
Pls help ASAP
Give the domain and range
Answer:
D: {-2, 0, 2}
R: {-1, 1, 3
Which of these is a ratio table?
A
1
2.
3
o ono
WON
B.
5
6
7
A
1
2
3
chAUD
B
4
5
7
WN
B
A
1
2
3
COA
4
9
А
1
2
3
B
2.
4
6
ANUD
INI
Answer:
The last one
Step-by-step explanation:
A ratio table means that each number in the first column is multiplied by the same number to get the answer in the 2nd column
Find (fog)(x) and the domain
Answer:
(fog)(x) = 2sqrt(x) + 3
Domain: {x | x ∈ R, x>=0}
Step-by-step explanation:
(fog)(x) = f(g(x))
let f(a) = f(g(x))
f(a) = 2a+3 = 2(g(x)) + 3 = 2sqrt(x) + 3
To find domain, pick most restricting domain of the functions that make up the compound function.
At the restaurant, Gordon packed 8 orders with 4 items per order
in the morning. In the afternoon, he packed 6 orders with 7 items
per order.
Answer:
what is the question?
Step-by-step explanation:
Share and Show
MATH
BOARD
Model the product on the grid. Record the product.
1. 3 X 13 =
2. 5 >
Find the product.
Using the grid model, the product of 3 and 13 is 39
Product refers to the result of multiplying two or more numbers or quantities together. It is a fundamental operation in arithmetic and algebra. When multiplying two numbers, the product is obtained by adding together a number of copies of one of the numbers, equal to the value of the other number.
Given, two numbers 3 and 9, and a grid.
To determine the product of 3 and 13 just count all the grids covered in 3 rows up to 13 columns or adding 3 for 13 times will result in 39.
Count the grids covered in a red box attached in the image below.
3+3+3+3+3+3+3+3+3+3+3+3+3=39
So, the product of 3 and 13 is 39.
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