Simplify. (In the problems where you combine fractions with unlike denominators leave the denominators in factored form.)
Answer:
[tex] \dfrac{a}{a - 4} [/tex]
Step-by-step explanation:
You are subtracting fractions, so as usual with fraction subtraction, you need a common denominator. To get a common denominator, you need to factor each denominator.
[tex] \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{a^2 - 16} = [/tex]
Factor the right denominator. It is a difference of two squares.
[tex] = \dfrac{3a}{a + 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
The left denominator is (a + 4). The right denominator is (a - 4)(a + 4). The LCD is (a - 4)(a + 4), so multiply the left fraction by (a - 4)/(a - 4).
[tex] = \dfrac{3a}{a + 4} \times \dfrac{a - 4}{a - 4} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a}{(a - 4)(a + 4)} - \dfrac{2a^2 - 16a}{(a - 4)(a + 4)} [/tex]
Be careful when you do the subtraction of the numerators, 3a² - 12a minus 2a² - 16a. 3a² - 12a - (2a² - 16a). The minus of the subtraction changes each sign inside the parentheses, so you end up with 3a² - 12a - 2a² + 16a. Be especially careful with the +16a.
[tex] = \dfrac{3a^2 - 12a - (2a^2 - 16a)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{3a^2 - 12a - 2a^2 + 16a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a^2 + 4a}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a(a + 4)}{(a - 4)(a + 4)} [/tex]
[tex] = \dfrac{a}{a - 4} [/tex]
Which to integers is Sqrt 58
between?
A. 7 and 8
B. -8 and -7
C.-6 and -5
D. 5 and 6
Option A
Solution:First, let's find the square root of 58.The square root of 58 is equivalent to:√58≈7,62 (approximately equal to)Now, which two integers is 7.62 between?Is it between 7 and 8? Yes.Is it between -8 and -7? No. 7.62 is positive.Is it between -6 and -5? No.Is it between 5 and 6? No.Therefore, √58 is between 7 and 8.Hope it helps.
Do comment if you have any query.
h(t)=50− 5th, left parenthesis, t, right parenthesis, equals, 50, minus, start fraction, t, divided by, 5, end fraction
h(35)=h(35)=
Answer:
H(t) = 50 - t/5
h(35)=50-35/5
=50-7
=43
h(35) = 43
In circle K with \text{m} \angle JKL= 82^{\circ}m∠JKL=82 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{JL}. JL⌢ .
Answer:
M< JKL = 82°Solution: UP
The angle measure of the minor arc JL equals 82°.
What is Arc of a Circle?An arc of a circle is defined as the part of the boundary of a circle. The straight line drawn joining the two end points of the arc is called chord of the circle.
If we mark any two points on the circle, by joining those points along the circle, we get two arcs. The smaller arc is called the minor arc and the longer arc is called the major arc. If the length of the arc exactly equals the half length of the circle, then the arc is called semicircular arc.
An arc can be measured in two ways : By finding the measure of the angle of arc and finding the length of the arc.
Here we are asked to find the measure of the minor arc which is the measure of the angle of the arc JL.
Measure of the angle of the arc equals the angle formed at the center of the circle by joining the end points of the arc to the center of the circle.
We have ∠JKL = 82°
∴ measure of arc JL = 82°
Hence, the measure of the minor arc JL equals 82°.
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Complete the calculations so that each shows the correct sum of difference (GIVING 30 POINTS)
Answer:
See below ↓↓↓
Step-by-step explanation:
a) 2 . 1 4 0 b) 2 9 . 9 9 c) 6 . 1 5 7
+ 1 . 7 2 5 + 1 . 4 2 - 1 . 0 0 9
3 . 8 6 5 3 1 . 4 1 5 . 1 4 8
Aiko types at a rate of 50 words per minute.
After typing at the same rate for 3 minutes, he has typed a total of 150
words.
This situation can be represented with a linear equation written in point- slope form, where x represents the number of minutes and y represents the number of words.
Use this information to complete each statement about the linear equation.
Answer:
Slope: 50x
One point will be: (1,50)
Equation: y = 50x
Step-by-step explanation:
Answer:
The slope of the linear equation is *50
One point on the graph of the linear equation will be *(3, 150)
This linear equation can be written as *y – 150 = 50(x – 3)
Step-by-step explanation:
ttm
The cost to mail a package is $8 for the first 4 pounds and 25 cents for each additional ounce. Which of the following functions represents the cost to mail a package if x is the number of ounces over 4 pounds?
f( x) = 32 + 0.25 x
f( x) = 0.25( x + 4)
f( x) = 0.25+ 8 x
f( x) = 8 + 0.25 x
Answer:
f(x) = 8 + 0.25x
Step-by-step explanation:
The minimum cost is $8, for up to 4 pounds.
The added cost is ($0.25/oz)(x), where x is trhe ounces over 4 pounds
The total cost is the sum of these two:
f(x) = 8 + 0.25x
Domain and range for y=x^2+5x-6
Step-by-step explanation:
domain is all real numbers since its quadratic: (-infinity, infinity)
Range is from -6 to positive infinity or [-6, infinity)
Please explain someone!!!
Answer: 1 and 2
Step-by-step explanation: 1 and 2 because if you are graphing this the formula to find the slope / the line is y = x + some number. In the formula x is how much the line goes from the x axis and the number is how much it is from the y axis. On #2 the problem is 3y = 2x + 4 so to follow the formula you need to divide both sides by 3 to get y = 2/3x + 4. For #3 you do the same thing to get y = -3/2x -5. Finally for #1 the equation is 2x + 3y = 7 so to get the slope / line you need to put x on the other side so now it is 3y = 7-2x then you divide both sides by 3 and get y = -2/3x + 7 and on 1 and 2 there x is 2/3 (the negative doesn't matter and the random number) so they are parallel.
which statement uses words to represent 5+8×3-2
Answer:
A
Step-by-step explanation:
You should always multiply before adding or subtracting. By saying "a product of 8 and 3," it means we multiplied them together first.
You should then add and subtract in the order in which they appear. Saying "five more" before "minus 2" means we did it in the right order.
A=2.3,b=3.9,c=5,9 I do not know how to do this
Answer:
put the cords on a chart
Step-by-step explanation:
helppp please been stuck for so long
Answer:
Floating point(Decimal) is 0.1
Fraction is [tex]\frac{1}{10}[/tex]
This is because...10^-1 is going to be 0.1 in this case. This is because 10^-1 is the same as [tex]\frac{1}{10^1}[/tex], which is the same as [tex]\frac{1}{10}[/tex], because anything times 1 remains the same.
[tex]\frac{1}{10}[/tex] is the same as 0.1
We get a 2-in-1 answer, which is perfect for this scenario!
Hence, the correct answers are [tex]\frac{1}{10}[/tex] and 0.1
factor each completely
n^2 - 11n + 10
[tex] {n}^{2} - 11n + 10 = [/tex]
[tex](n - 1)(n - 10)[/tex]
.................................................
Find the missing
information.
Arc length-1.5 ft
Radius-?
Central angle-pie/4 rad
Round to the nearest thousandth.
Answer:
1.91 ft
Step-by-step explanation:
Formula
l = rαwhere :
l = arc lengthr = radiusα = central angleSolving for r
l = rαr = l/αr = 1.5/(π/4)r = 6/πr = 1.90985932 ftr = 1.91 ft (nearest thousandth)Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
By using the Pythagorean Theorem, we will see that the length of the missing side is 4 units.
How to find the length of the third side?
We need to remember the Pythagorean Theorem, the sum of the squares of the cathetus is equal to the square of the hypotenuse.
In this case, the cathetus are x and 3, and the hypotenuse is 5, then we have:
x^2 + 3^2 = 5^2
x^2 = 25 - 9 = 16
x = √16 = 4
So the length of the missing side is 4 units.
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Paul bought 4 DVDs for $9.95 each. What was his total cost?
$39.90
$40.80
$39.80
$38.80
Answer:
$39.80
Step-by-step explanation:
just 9.95 x 4
(4x - 3)
Find the value of 'x'.
(2x + 9)
A. 53
B. 14
C. 16
D. 37
Answer:
please the question is not clear
What is the value of y in the equation 6 + y = −3? (1 point) Group of answer choices −3 −9 3 9
Answer:
y= -9
Step-by-step explanation:
y+6=-3
subtract 6 from both sides
y=-9
y=-9
Solution:First, subtract 6 from both sides.6+y=-3Ory+6=-3Why subtract? Because 6 is added to y, and we need to use the opposite operation. Remember, our goal is to find the value of y.Subtract:y=-3-6y=-9We have found the value of y; it's equivalent to -9.Hope it helps.
Do comment if you have any query.
PLS HELP
1.
Seats in a theater are curved from the front row to the back. The front row has 18 chairs, the second has 26
and the third has 34, and so on.
a.
Write a recursive rule for this series (2 points):
b. Write an explicit rule in simplified form for this series:
Show the steps to simplify. (2 points)
c. Using the explicit formula, find the number of chairs in row 7 (show work) (3 points):
on Voy bob ochote
bu ma'isto
d. The auditorium can hold 12 rows of chairs. Write a sigma notation for this series, and then use either series
formulas to calculate how many chairs can fit in the auditorium. Show all work. (5 points)
The chairs in the auditorium illustrates an arithmetic sequence
The recursive rule is: an = an-1 + 8; a1 = 26The explicit rule is: an = 18 + 8nThere are 74 seats in the 7th row840 chairs can fit the auditoriumThe recursive ruleFrom the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
The explicit ruleIn (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
The number of seats in the row 7This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
The sigma notationWe have the maximum number of rows to be 12.
So, the sigma notation would be:
[tex]\sum\limits^{12}_{n=1} {18 + 8n}[/tex]
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at:
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Classify each polynomial by degree and number of terms. 1. Quartic monomial v 5x? - 7x + 9 2. Cubic binomial 2x3 + 3 < 3. Quadratic trinomial < 8x4 4. Quintic quadnomial
The degree of a polynomial is categorized by its highest power of its leading variable.
Degree and number of terms of a polynomial
Given the following polynomial functions, we are to classify them based on their degrees and the number of terms
For the polynomial function 5x^4 - 7x + 9
The degree is 4 being quartic and there are three terms in the expression
For the polynomial 2x3 + 3 < 3, the degree is 3 (cubic) with three terms in the expression.
For a Quintic quadnomial, the degree of the polynomial is 5.
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What is the multiplier for a 58% decrease
Answer:
A. 0.58
Step-by-step explanation:
please help i need help
Answer:
the answer is 14
Step-by-step explanation:
so first you subtract 8- 2 over 2 then =1 over 8 then subract 2 over 2
8 x 2 - 2 = 16 - 2 = 14 = 2 x 7 = 7
1 x 2 - 2 = 2 = 2 = 2 x 1
then 1 x 2 = 2 = 7 over 1 next add 21 over 3 + 7 = 21 over 3 + 7 over 1 = 21 over 3 + 21 over 3 = 21 +21 over 3 = 42 over 3 = 3 X 14 over 3 x 1 = 14
hope this helps you have a good day
a. Convert 5x^2 + 55x + 140 from standard to vertex form
b. Describe the transformation.
Answer:
The transformation will be 5
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
5x^2 + 55x + 140 ---> required
Coefficients a=5, b=55, c=140 yield
[tex]h=\frac{-h}{2*a} =\frac{-(55)}{2*5} =\frac{-55}{10} =-5.5[/tex]
Thus, the x-coordinate of the vertex is [tex]\boxed{h = -5.5 }[/tex]
Plugging x=-5.5 into the given equation yields:
[tex]k=5*(-5.5)^{2} +55*-5.5+140=-11.25[/tex]
Thus, the y-coordinate of the vertex is [tex]\boxed{k = -11.25 }[/tex]
Altogether, the vertex of the given parabola is
[tex]\boxed{ (h,k)=(-5.5,-11.25) }[/tex]
Plugging (h,k)=(−5.5,−11.25) into the vertex formula
[tex]\boxed{ y=(x-h)^2+k }[/tex]
yields the vertex form of the parabola
[tex]\boxed{ y=(x+5.5)^2-11.25 }[/tex]
To find the vertex of a parabola in standard form, first, convert it to the vertex form y=a(x−h)2+k y = a ( x − h ) 2 + k .On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 270 on the exam.
Answer:
z = -1.5
Step-by-step explanation:
To Find z-score
z = (X - μ) / σX = Test scoreμ = Mean σ = Standard DeviationGiven
X = 270μ = 300σ = 20Solving
z = 270 - 300 / 20z = -30/20z = -1.5The number of students in sixth grade is 1.03 times the number of students in seventh grade. What percent is equivalent to 1.03?
Bella baked a two layer cake.The bottom layer has dimensions of 4 inch x 6inch x 8inch.The dimensions of the top layer are half bottom.What is the volume of the top layer.
Answer:
30 is the answer because you need to multiple 4 and 6
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
See picture for full problem. Please and thank you so very much!
Answer:
Step-by-step explanation:
The Hernandez family built a backyard patio .
Area = 150 square feet
What could be the dimensions of the
patio?
A 100 feet long by 50 feet wide
B
50 feet long by 25 feet wide
15 feet long by 10 feet wide
D
10 feet long by 5 feet wide
Please help pleeaassee!! >_<.
Answer:
Slope intercept form does not dictate whether or not a function is linear. What determines if a function is linear is if there is one independent variable, one dependent variable, and it makes a STRAIGHT line. This function is linear because there are only 2 variables and a horizontal line.
Levi could have determined that the graph was linear by checking the conditions stated above or graphing it out. Then, he would see that y = 2 is a straight horizontal line with an independent and dependent variable.
Hope this helps!
Find the volume of the rectangular prism
Answer:
336
Step-by-step explanation:
V=whl=8·7·6=336
