Question:
Consider the expression [tex]\frac{x^2 + x -10}{x + 3}[/tex]
When using the inspection method the number you would add to (and subtract from) the constant term of the numerator so the polynomial in the numerator will have (x + 3) as a factor is?
Answer:
The constant to add is 4
Step-by-step explanation:
Given
[tex]\frac{x^2 + x -10}{x + 3}[/tex]
First, we need to get an expression that has x + 3 has its factor.
Represent this expression with: [tex](x + 3)(x + k)[/tex]
Expand
[tex]x^2 + 3x + kx + 3k[/tex]
Group like terms
[tex]x^2 + (3 + k)x + 3k[/tex]
Compare the above expression to: [tex]x^2 + x - 10[/tex]
[tex](3 + k)x = x[/tex]
[tex]3k = -10[/tex]
However, we only consider solving [tex](3 + k)x = x[/tex] for k
[tex](3 + k)x = x[/tex]
[tex]3 + k = 1[/tex]
Subtract 3 from both sides
[tex]3 - 3 + k = 1 - 3[/tex]
[tex]k = 1 - 3[/tex]
[tex]k= -2[/tex]
Substitute -2 for k in [tex](x + 3)(x + k)[/tex]
[tex](x + 3)(x + k) = (x + 3)(x -2)[/tex]
[tex](x + 3)(x + k) = x^2 + 3x - 2x - 6[/tex]
[tex](x + 3)(x + k) = x^2 + x - 6[/tex]
So, the expression that has a factor of x + 3 is [tex]x^2 + x - 6[/tex]
To get the constant term to add/subtract, we have:
[tex]Constant = (x^2 + x - 6) - (x^2 + x - 10)[/tex]
Open brackets
[tex]Constant = x^2 + x - 6 - x^2 - x + 10[/tex]
Collect Like Terms
[tex]Constant = x^2 - x^2+ x - x - 6+ 10[/tex]
[tex]Constant = - 6+ 10[/tex]
[tex]Constant = 4[/tex]
-12=4f-24
Solve for f
Answer: f=3
Step-by-step explanation:
The tiles for the bathroom tub makes a rectangular grid consisting of 253 rows and 48 columns. Write an expression that shows the product of the number of tiles in the bathroom.
Answer:
Step-by-step explanation:
Assuming that the tile sizes are an average of 1x1 then the expression would simply be multiplying the number of rows by the number of columns. This would provide us with a product which would be the area of the bathroom as well as the number of individual tiles that the bathroom needs and/or already has installed represented by the variable t. Therefore, the expression would be the following.
253 * 48 = t
12,144 = t
Find the slope of the line that passes through
each pair of points.
(-3, -2), B (5, 4)
Answer:
0.8
Step-by-step explanation:
Estaban is 6 years older than his brother Raoul. The sum of their ages is 38. How old are the brothers?
Answer:
raoul is 16 and estaban is 22
Julie says the most amount of time spent on homework is 1 1\2 times the least amount of time spent on homework
Data for the question :
1 3/4, 2 1/2, 2, 2 3/4, 1, 1 3/4, 1 1/4, 3, 3 1/4, 3 3/4, 2, 2
Answer:
Julie is Incorrect
Step-by-step explanation:
Given the data:
1 3/4, 2 1/2, 2, 2 3/4, 1, 1 3/4, 1 1/4, 3, 3 1/4, 3 3/4, 2, 2
The least amount of time spent is : 1
The most amount of time spent is 3 3/4
According to Julie ; the most amount of time spent is equal to 1 1/2 the least amount of time spent.
That is,
3 3/4 = 1 * 1 1/2
3 3/4 = 15/4
1 * 3/2 = 3/2
Hence, she is incorrect ;
15/4 ≠ 3/2
What is the radius of this circle?
The radius of the circle is 3
(HELP EASY MULTIPLE CHOICE ILL GIVE BRAINLY EVEN THOUGH ITS MULTIPLE CHOICE)
Answer:
3.) -1
Step-by-step explanation:
Distribute the 2.
You would get [tex]3^{2} x^{5(2)} = 9x^{10}[/tex]
a = 9
b = 10
a - b = 9 - 10
= -1
Answer:
3.) -1
Step-by-step explanation:
I NEED HELP ASAP!!!!!!
Answer:
83.3%
Step-by-step explanation:
The probability of rolling a 3 on a 6-sided dice is 1/6
Since you don't want a three, there's a 5/6 chance of not rolling a 3
5/6 (use calculator and divede 5 by 6) = 0.833333 (move decimal 2 to the right) = 83.3%
Therefore, the most reasonable answer would be C, 83.3%
25% of the tickets sold at a water park were child tickets. If the park sold 92 tickets in all,
how many child tickets did it sell?
100 points please help
This painting has?
Answer:
D. Organic shapes
Step-by-step explanation:
Achromatic shapes: shapes with "no color".
Geometric shapes: shapes with straight lines and angles that symbolize structure and order.
Irregular shapes: shapes that have sides and angles of any length and size.
Organic shapes: shapes with a natural look and a flowing and curving appearance. Organic shapes are associated with things from the natural world, like plants and animals.
I hope this helps :)
Answer:
Its the real answer of my inorganic shapes
Step-by-step explanation:
If im wrong im sorry
Find the value of y for the given value of x.
y = -x, x = -18 2
Answer:
y=18.2
Step-by-step explanation:
x=-18.2
-x=18.2
y=18.2
Joseph drives 125 miles in 2.5 hours. At the same rate, how far will he be able to travel in 6 hours
Answer:
300
Step-by-step explanation:
125/2.5=50
50 x 6=300
Joseph will be able to drive 300 miles in 6 hours
hope this helps!
Find -2 - -0.7 model the expression on the number line by drawing an arrow
Answer:
-1.3
Step-by-step explanation:
number line will go all the way to the left and then 7 to the right. which is -1.3
The value of -2 - -7 as modelled in the attached image is; -1.3
According to the question;
We are required to model the expression on the number line by drawing an arrow.The number line model given can be used to evaluate -2 - -0.7 by simply finding the distance between -2 and -0.7 as in the attached image.
Ultimately, the value of -2 - -0.7 is; -1.3
Read more;
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Will give brainliest
Answer:
AC = 4.7 feet
Step-by-step explanation:
cos 20° = x
5
5 · cos 20° = x
4.7 = x
What's the radical of the expression
Answer:
√16 or 4
hope this helps!
simple math, please help, have to turn in soon
Answer:1
Step-by-step explanation:
Does anyone knows how to do that?
I need to solve for x
Answer:
[tex]x=17[/tex]°
Step-by-step explanation:
Because the diagonal lines are marked with arrows, we know that they are parallel. The two angles that are marked with measures are same-side interior angles. Same-side interior angles of parallel lines are supplementary, meaning that the sum of their measures is [tex]180[/tex]°.
Now, with all of this information, we can set up the following equation and solve for [tex]x[/tex]:
[tex]115+4x-3=180[/tex]
[tex]112+4x=180[/tex] (Simplify LHS by combining like terms)
[tex]112+4x-112=180-112[/tex] (Subtract [tex]112[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]4x=68[/tex] (Simplify)
[tex]\frac{4x}{4}=\frac{68}{4}[/tex] (Divide both sides of the equation by [tex]4[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=17[/tex]° (Simplify)
Hope this helps!
Helpppppp pleaseeeee find the angle measurements
Step-by-step explanation:
angle 1 = 50° [ Corresponding Angles]
angle 2 = 130° [ Linear pair]
angle 3 = 110° [ linear pair]
angle 4 = 70° [Corresponding Angles]
angle 5 = 60° [Angle sum property of triangle]
angle 6 = 120° [linear pair]
Oliva buys 6 packs of muffins. She uses a coupon and saves 3$ off the total. which expression represents her total cost?
A. 6m - 3
B. 6 + 3
C. 6 - 3m
D. 6m + 3
Answer:
A. 6m - 3
Step-by-step explanation:
6m represents finding the total cost for the 6 packs of muffins.
When you use PEMDAS or GEMDAS (whichever you know better), they both make you solve 6m first which means you subtract $3 after you find the total amount for the packs of muffins.
After you figure that out, you subtract the $3 from the total since it's a coupon and will save you $3 instead of adding it to the total price.
hope this makes sense and help :)
Answer:
A. 6m - 3
Step-by-step explanation:
Saving 3 dollars off of a coupon lowers the price therefore making it subtraction. 6m is the amount of the muffins cost, m being the unknown price of each muffin.
Maths is hardddddddddd
if Noah finishes the race in 20seconds and Elliot finishes the race in 1/2 the time as Noah, how many seconds does it take Elliot to finish the race?
Answer:
10 seconds
Step-by-step explanation:
Elliot finishes the race in 1/2 of 20 sec or 10 sec
Carly purchased nine one two pints of ice cream for a party. If each guest will be served exactly thee fifths pint of ice cream, what is the greatest number of guests that Carly can serve?
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that Carly purchased 9 1/2 pints of ice cream for a party and that each guest will be served exactly 3/5 pint of ice cream.
The greatest number of guests that Carly can serve will be:
= 9 1/2 ÷ 3/5
= 19/2 ÷ 3/5
= 19/2 × 5/3
= 95/6
= 15 5/6
The greatest number that can be served will be 15
Make a conjecture of what the x-intercepts of the function
f(x) = (2x - 1)(x + 3) will be.
Sally is 140cm tall and Tara is 160cm. What is the ratio of their
heights (in its lowest terms)
Answer:
140:160----simplify by 10
14:16--------simplify by 2
7:8 is the lowest
Step-by-step explanation:
pls help with the image attached
Answer:
2.
Step-by-step explanation:
How much money will Adriano’s online business earn this month
HELP !!!!!!!!!!!!!!!!!!
Answer:
answer is C ( [tex]3^{4}[/tex] )
Step-by-step explanation:
so here is how you do it.
first you need to find out what [tex]3^{8}[/tex] is
which is the same as 3 X 3 X 3 X 3 X 3 X 3 X 3 X 3
the answer to that is 6,561
then you have to square root that
which looks like this
[tex]\sqrt{6,561}[/tex]
which is 81
which means that you have to find the same expression that equals to 81
I then did [tex]3^{4}[/tex] (C) to see if the answer will be 81 and it is. so your answer is C
Carrie needs to take a cab uptown and only has y dollars. The cab company charges a flat fee of $2.25 plus $0.55 per mile.
If Carrie has $12.52 and she finds a cab company with the same flat fee that only charges $0.45 per mile, what is the maximum number of miles she will be able
to travel, to the nearest tenth of a mile?
what is the equation?
The maximum number of miles she will be able to travel, to the nearest tenth of a mile is less than or equals to 22.8 miles.
She needs to take a cab and has y dollars. The company charges a flat rate of $2.25 plus $0.55 per mile. Therefore the equation will be
y = 2.25 + 0.55x
where
x = number of miles travelled.
Now she has $12.52 and she finds a cab company with the same flat rate and only charges $0.45 per mile. The maximum number of miles she will be able to travel to the nearest tenth of mile can be calculated below:
2.25 + 0.45x ≤ 12.52
x = number of miles travelled.
0.45x ≤ 12.52 - 2.25
x ≤ 10.27 / 0.45
x ≤ 22.8222222222
x ≤ 22.8 miles
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which is the product or 11/12 and 4? A 1 1/4 B 3 2/3 C 4 1/3 D 33
Answer:
Step-by-step explanation:
11/12 × 4 = 11/3 = 3⅔
2 sides of a triangle have the following measures. Find the range of possible measures for the third side.
11, 7
NEED HELP!
Answer:
4 < x < 18
Step-by-step explanation:
Given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
11 - 7 < x < 11 + 7
4 < x < 18 ← range of values for third side