Answer:
11/15
Step-by-step explanation:
First, get a common denominator of 30. 2/5 becomes 12/30. 4/6 becomes 20/30. 1/3 becomes 10/30.
Now we can add and subtract accordingly.
12/30 + 20/30 = 32/30.
32/30 - 10/30 = 22/30.
Finally, simplify the fraction.
22/30 becomes 11/15 when each number is divided by 2.
Answer: [tex]\frac{11}{15}[/tex]
Step-by-step explanation:
The first step is to find the Least Common Denominator of the fractions. Descompose each denominator into its prime factors and muliply the commons and non-commons with the least exponent. Then:
[tex]5=5\\6=2*3\\3=3\\\\LCD=2*5*3=30[/tex]
Divide each denominator by the LCD and multiply this quotient by the corresponding numerator, add the products and then reduce the fraction.
Therefore you get:
[tex]=\frac{(2*6)+(4*5)-(1*10)}{30}=\frac{12+20-10}{30}=\frac{22}{30}=\frac{11}{15}[/tex]
Find an equation for the line perpendicular to y=−15x+3 with x-intercept at x = 3.
Write your answer in the form y=mx+b
bearing in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of the provided line then
[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-15}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-15\implies -\cfrac{15}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{15}}\qquad \stackrel{negative~reciprocal}{+\cfrac{1}{15}\implies \cfrac{1}{15}}}[/tex]
well, we know the x-intercept is at x = 3, recall when a graph intercepts the x-axis y = 0, so this point is (3 , 0). Then we're really looking for the equation of a line whose slope is 1/5 and runs through (3 , 0).
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})~\hspace{10em} slope = m\implies \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{1}{5}(x-3)\implies y=\cfrac{1}{5}x-\cfrac{3}{5}[/tex]
PLEASE HELPP!!
The graph of y = ax^2 + bx + c is shown below. Determine the solution set of 0 = ax^2 + bx + c.
Check the picture below.
something noteworthy to look at is that the graph doesn't cross the x-axis at -2, it simply comes down to it, touches it and it goes back up, it simply bounces off the x-axis, whenever that happens, that zero/solution/root has an even multiplicity.
when 0 = ax² + bx + c, we notice that y = 0, and for the graph that happens there, at x = -2, but that solution has an even multiplicity, and since the equation is a 2nd degree polynomial, thus x = -2 is there twice, namely
x = -2
x - 2 = 0
(x - 2)² = 0 <---- multiplicity of 2.
Answer:
-2
Step-by-step explanation:
:)
Find the equation for the line that passes through the point (−2,0), and that is perpendicular to the line with the equation 2/3x+y=−14/3.
Answer:
y = 3/2 x + 3
Step-by-step explanation:
2/3 x + y = -14/3
y = -2/3 x − 14/3
The slope of this line is -2/3. So the perpendicular slope is the opposite of the inverse:
m = -1 / (-2/3)
m = 3/2
We know the slope of the line and a point on the line, so using point-slope form:
y − 0 = 3/2 (x − (-2))
Simplifying into slope-intercept form:
y = 3/2 (x + 2)
y = 3/2 x + 3
5 ) Fred bought 5 new baseball trading cards to add to his collection. The next day his dog ate
half of his collection. There are now only 31 cards left. How many cards did Fred start with ?
Answer:
Just reverse the order. So double 31 is 62 then subtract 5. 57
what is (7x6)+(4x10)
Answer:
the answer is 82
Step-by-step explanation:
Answer:
82
Step-by-step explanation:
just use a calculator
If f(x) = 5x + 4, which of the following is the inverse of (fx)?
Answer:
see explanation
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = 5x + 4 ( subtract 4 from both sides )
y - 4 = 5x ( divide both sides by 5 )
[tex]\frac{y-4}{5}[/tex] = x
Change y back into terms of x
[tex]f^{-1}[/tex] (x) = [tex]\frac{x-4}{5}[/tex]
prove that cos^2A+sin^2A.cos2B=cos^2B+sin^2B.cos2A
Notice that both sides of the equation have a similar form. If we ignore angle functions we end up with,
[tex]A+A\cdot B=B+B\cdot A[/tex]
That is true if condition [tex]A=B[/tex] is met.
Otherwise it is false.
Hope this helps.
r3t40
The sundae bar at Sarah's favorite restaurant has 5 toppings. In how many ways can Sarah top her sundae if she is restricted to at most 2 toppings?
There are 16 different ways Sarah can top her sundae, considering no toppings, 1 topping or 2 toppings out of 5 available at the restaurant.
Explanation:The subject of this question is in the field of combinatorics, a branch of mathematics. We are asked to find the number of ways Sarah can top her sundae with at most 2 toppings out of 5 available. The answer will be the number of ways she can pick no topping, or 1 topping, or 2 toppings.
The number of ways to pick no toppings is 1 (just the ice cream), to pick 1 topping out of 5 is 5 (assuming all toppings are different), and to pick 2 toppings out of 5 is represented by a combination formula '5 choose 2', which means: 5! / ((5 - 2)! * 2!) = 10, where '!' denotes factorial.
So by summing these possibilities (1+5+10), we come to the conclusion that Sarah can top her sundae in 16 different ways if she is restricted to at most 2 toppings.
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Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.
Explanation:To calculate the number of ways or combinations, Sarah can top her sundae with at most 2 toppings, we can consider two cases. In the first case, she chooses 0 toppings. In the second case, she chooses 1 topping.
The total number of ways would be the sum of these two cases.
In the first case, she has only one choice, which is not to choose any topping.
In the second case, she can choose any one of the 5 toppings. So, the total number of ways would be 1 + 5 = 6.
Therefore, Sarah can top her sundae in 6 different ways if she is restricted to at most 2 toppings.
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According to Vinay's model, what is the probability that he will have a male history teacher two years in a row?
1. 3/8
2. (3/8)(2)
3. (3/8)^(2)
4. 3/(8)^(2)
Answer:
(3/8) ^2
Step-by-step explanation:
P ( male history teacher) = Number males/ total
= 3/8
Assuming nothing changes in year two
P ( male history teacher year two) = Number males/ total
= 3/8
P( male, male) = 3/8 * 3/8 = (3/8) ^2
(3/8)^2 would be your answer.
Since there are 3 male and 5 female, that means there are 3/8 male and 5/8 female. We are talking about male and how many times it would happen in 2 years, so (3/8)^2 would be your answer.
Help please. I attempted, but I couldn't succeed.
Answer:
y=(3/2)x+-14
First blank: 3
Second blank:2
Last blank:-14
Step-by-step explanation:
The line form being requested is slope-intercept form, y=mx+b where m is slope and b is y-intercept.
Also perpendicular lines have opposite reciprocal slopes so the slope of the line we are looking for is the opposite reciprocal of -2/3 which is 3/2.
So the equation so far is
y=(3/2)x+b.
We know this line goes through (x,y)=(4,-8).
So we can use this point along with our equation to find b.
-8=(3/2)4+b
-8=6+b
-14=b
The line is y=(3/2)x-14.
Help with substitution! (With pictures-2 separate questions) thanks!
Answer:
Explanation contains answer.
Step-by-step explanation:
Question 1:
I would perfer to solve the first equation for y because there is only one operation to perform on both sides and it is subtraction of 2x on both sides.
The other equation requires two steps to isolate y; subtracting 3x on both sides then multiplying both sides by -1.
So basically solving the first one for y because it has coefficient 1.
Question 2:
They solved the 2nd equation for y and plugged into itself instead of plugging it into 1st equation.
find f(1) if f(x)=2x^3+x^2-3x-1
Answer:
The answer is -1
Step-by-step explanation:
f(x) = 2x³ + x² - 3x - 1
f(1) = 2(1)³ + (1)² - 3(1) - 1
f(1)= 2 + 1 - 3 - 1
f(1)=3-3-1
f(1)=0-1
f(1)= -1
Thus the answer is -1 ....
Answer:
-1
Step-by-step explanation:
Solve the quadratic equation below by completing the square. What are the
solutions?
x2 + 10x + 22 = 31
Answer:
(x+5)^2=34
Solutions: ≈ -10.831, 0.831
Step-by-step explanation:
First you divide the second term by two to complete the square. The second term divided by two is 5, 5^2 is 25 which means you need a value of 25 to factor. Add 3 to both sides so you have a value of 25 on the left side.
x^2+10x+25=34 Next, factor the left side.
(x+5)^2=34
The solutions to this equation are not rational, you could use the quadratic formula to find the exact answer or put the equation into a graphing calculator to find approximate solutions.
WILL GIVE BRAINSLIEST EASY. Find each product mentally. Show the steps used.
1. 9 x 44 = 2. 4 x 5 1/8 = 3. 7 x 3.8 =
Use the Distributive Property to rewrite each algebraic expression.
4. 8(x + 7) = 5. 6(11 + x) = 6. 8(x + 1) =
Answer:
1) 396
2) 20 1/2
3) 26.6
4) 8x + 56
5) 66 + 6x
6) 8x + 8
Step-by-step explanation:
* Lets explain how to solve the product mentally
# Remember the distributive property can help you to find the product
mentally the distributive property ⇒ a(b + c) = ab + ac
- Lets solve them
1)
- In 9 × 44 we can write 44 as (40 + 4)
∴ 9 × 44 = 9(40 + 4)
∵ 9(40 + 4) = 9 × 40 + 9 × 4
- Now lets multiply 9 by 40 and 9 by 4
∵ 9(40) = 360
∵ 9(4) = 36
∴ 9 × 40 + 9 × 4 = 360 + 36 = 396
∴ 9 × 44 = 396
2)
- In 4 × 5 1/8 we can write 5 1/8 as (5 + 1/8)
∴ 4 × 5 1/8 = 4(5 + 1/8)
∵ 4(5 + 1/8) = 4 × 5 + 4 × 1/8
- Now lets multiply 4 by 5 and 4 by 1/8
∵ 4(5) = 20
∵ 4(1/8) = 1/2
∴ 4 × 5 + 4 × 1/8 = 20 + 1/2 = 20 1/2
∴ 4 × 5 1/8 = 20 1/2
3)
- In 7 × 3.8 we can write 3.8 as (3 + 0.8)
∴ 7 × 3.8 = 7(3 + 0.8)
∵ 7(3 + 0.8) = 7 × 3 + 7 × 0.8
- Now lets multiply 7 by 3 and 7 by 0.8
∵ 7(3) = 21
∵ 7(0.8) = 5.6
∴ 7 × 3 + 7 × 0.8 = 21 + 5.6 = 26.6
∴ 7 × 3.8 = 26.6
- The distributive property ⇒ a(b + c) = ab + ac
4)
- In 8(x + 7) we will multiply 8 by x and 8 by 7 and add them
∵ 8 × x = 8x
∵ 8 × 7 = 56
∴ 8(x + 7) = 8x + 56
5)
- In 6(11 + x) we will multiply 6 by 11 and 6 by x and add them
∵ 6 × 11 = 66
∵ 6 × x = 6x
∴ 6(11 + x) = 66 + 6x
6)
- In 8(x + 1) we will multiply 8 by x and 8 by 1 and add them
∵ 8 × x = 8x
∵ 8 × 1 = 8
∴ 8(x + 1) = 8x + 8
Find the volume, lateral surface area and total surface area of a regular octagonal pyramid of base 6.2cm and perpendicular height of 14.8cm.
Answer:
V ≈ 915.7 cm³
LA ≈ 411.3 cm²
SA ≈ 596.9 cm²
Step-by-step explanation:
Volume of a pyramid is:
V = ⅓ Bh
where B is the area of the base and h is the height.
The base is a regular octagon. The area of a regular octagon is 2(1 + √2) s², where s is the side length.
Substituting:
V = ⅔ (1 + √2) s² h
Given that s = 6.2 and h = 14.8:
V = ⅔ (1 + √2) (6.2)² (14.8)
V ≈ 915.7 cm³
The lateral surface area is the area of the sides of the pyramid. Each side is a triangular face. We know the base length of the triangle is 6.2 cm. To find the area, we first need to use geometry to find the lateral height, or the height of the triangles.
The lateral height and the perpendicular height form a right triangle with the apothem of the octagon. If we find the apothem, we can use Pythagorean theorem to find the lateral height.
The apothem is two times the area of the octagon divided by its perimeter.
a = 2 [ 2(1 + √2) s² ] / (8s)
a = ½ (1 + √2) s
a ≈ 7.484
Therefore, the lateral height is:
l² = a² + h²
l ≈ 16.58
The lateral surface area is:
LA = 8 (½ s l)
LA = 4 (6.2) (16.58)
LA ≈ 411.3 cm²
The total surface area is the lateral area plus the base area.
SA = 2(1 + √2) s² + LA
SA = 2(1 + √2) (6.2)² + 411.3
SA ≈ 596.9 cm²
The volume is 915.7 cm³
The lateral surface area is 411.3 cm²
The total surface area is 596.9 cm²
If one term of a proportion is not known, what can be used to find the value of that term? a. substitution c. cross-multiplication b. graphing d. adding all the numbers together
Answer:
cross multiplication
Step-by-step explanation:
what is the value of x?
x= 2.25
x= 11.25
x= 13
x= 22
For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees.
Then, according to the figure we have:
[tex][180- (6x + 1)] + 79+ (2x + 10) = 180[/tex]
We operate parentheses:
[tex]180-6x-1 + 79 + 2x + 10 = 180[/tex]
We add similar terms:
[tex]-4x + 268 = 180\\-4x = 180-268\\-4x = -88\\x = \frac {-88} {- 4}\\x = 22[/tex]
Thus, x has a value of 22 degrees.
Answer:
Option D
Answer:
(D) x= 22
Step-by-step explanation:
Five liters of water were poured from tank A into tank B. and ten liters of water were then poured into tank C. If tank A originally had 10 more liters of water than tank C, how many more liters of water does tank C now have than tank A?
Answer:
It would be 5 liters because you gave 5 liter to C
Step-by-step explanation:
Hope this helped! :3
Tank C now has 5 more liters of water than tank A.
Assume the initial amount of water in tank C is "x" liters.
Given that:
Tank A originally had 10 more liters of water than tank C,
The initial amount of water in tank A is "x + 10" liters.
When five liters of water were poured from tank A into tank B,
The amount of water in tank A is reduced to "(x + 10) - 5" liters,
The amount of water in tank A = "(x + 5)" liters.
When ten liters of water are poured into tank C
So, the amount of water in tank C= "x + 10" liters.
The amount of extra water in tank C is calculated as;
Difference = (Amount of water in tank C) - (Amount of water in tank A)
Difference = (x + 10) - (x + 5)
Difference = x + 10 - x - 5
Difference = 10 - 5
Difference = 5
Tank C now has 5 more liters of water than tank A by 5 liters.
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Pablo generates the function f(x) = 3/2(5/2)^x-1 to determine the x'th number in a sequence.
Which is an equivalent representation?
A: f(x+1) = 5/2 f(x)
B: f(x) = 5/2 f(x+1)
C: f(x+1) 3/2 f(x)
D: f(x+1) = 3/2 f(x+1)
Answer:
A.
f(x+1)=5/2f(x) with f(1)=3/2
Step-by-step explanation:
So we are looking for a recursive form of
[tex]f(x)=\frac{3}{2}(\frac{5}{2})^{x-1}[/tex].
This is the explicit form of a geometric sequence where [tex]r=5/2[/tex] and [tex]a_1=\frac{3}{2}[/tex].
The general form of an explicit equation for a geometric sequence is
[tex]a_1(r)^{n-1} \text{ where } a_1 \text{ is the first term and } r \text{ is the common ratio}[/tex].
The recursive form of that sequence is:
[tex]a_{n+1}=ra_n \text{ where you give the first term value for } a_1[/tex].
So we have r=5/2 here so the answer is A.
f(x+1)=5/2f(x) with f(1)=3/2
By the way all this says is term is equal to 5/2 times previous term.
Answer:
A
Step-by-step explanation:
Edge 2021
A veterinarian assistant has a 20 pound bag of cat food if he feeds each cat 2/5 pounds how many cats can he feed
Answer:
50
Step-by-step explanation:
20 / (2/5)
To divide by a fraction, multiply by the reciprocal.
20 × (5/2)
50
He can feed 50 cats.
50 cats
20 pounds is 100/5 pounds when written with a denominator of 5. Then you divide 100 by 2 and get 50.
Winslow plans to grow 12 kinds of vegetables in her garden. She has 34 seeds of each kind of vegetables. A neighbor gives her 10 more packets of seeds. Each packet has 25 seeds. How many seeds does Winslow have in all????
Answer: 658
Step-by-step explanation:
If Winslow wants to plant 12 vegetables and has 34 seeds of each kind of vegetable, then she has 12*34 seeds.
12*34=408
If a neighbor giver her 10 more packets, each with 25 seeds, she has 10*25 more seeds.
10*25=250
Then we add 408+250 to get 658 seeds
Circle O is represented by the equation (x + 7)^2 + (y + 7)^2 = 16. What is the length of the radius of circle O?
Answer:
4
Step-by-step explanation:
The standard form of a circle is:
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and
r is the radius.
You compare your equation to mine you should see that:
-h=7 implies h=-7
-k=7 implies k=-7
r^2=16 implies r=4 since 4^2=16
The center is (-7,-7).
The radius is 4.
For this case we have that by definition, the equation of a circle in standard or canonical form is given by:
[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]
Where:
(h, k) is the center
r: It's the radio
We have the following equation:
[tex](x + 7) ^ 2 + (y + 7) ^ 2 = 16\\(x + 7) ^ 2 + (y + 7) ^ 2 = 4 ^ 2[/tex]
Thus, the radius is 4.
Answer:
4
Please answer this correctly
Answer:
Step-by-step explanation:
If we divide 9,795 by 7 we get:
=1399.28571429
Rounding to the nearest hundredth:
Underline the hundredths place: 1399.28571429
Look to the right. If it is 5 or above 5 then we give it a shove.
If it is 4 or less than 4, we let it go.
In our case it is 5. We will add 1 in 8, then it will become 9. 28 will be rounded off as 29.
Therefore the answer after rounding off to the nearest hundredth is 1399.29....
Michael goes to a theme park and rides two different roller coasters that both begin on a raised platform. His height while on the first roller coaster, measured in feet from the platform height, can be modeled by the following graph, where t is the number of seconds since the ride began. His height while on the second roller coaster, measured in feet from the platform height, can be modeled by a trigonometric function, shown in the following table, where t is the number of seconds since the ride began. t 0 20 40 60 80 100 120 140 160 g(t) 0 50 100 50 0 -50 -100 -50 0 Which of the following best describes Michael's height while on the two roller coasters? A. While on the first roller coaster, the function modeling Michael's height switches from positive to negative every 60 seconds, meaning he changes from being at a height above the platform to below the platform every 60 seconds. While on the second roller coaster, this change occurs every 20 seconds. B. While on the first roller coaster, the function modeling Michael's height switches from positive to negative approximately every 40 seconds, meaning he changes from being at a height above the platform to below the platform approximately every 40 seconds. While on the second roller coaster, this change occurs every 80 seconds. C. While on the first roller coaster, the function modeling Michael's height switches from positive to negative every 40 seconds, meaning he changes from being at a height above the platform to below the platform every 40 seconds. While on the second roller coaster, this change occurs every 20 seconds. D. While on the first roller coaster, the function modeling Michael's height switches from positive to negative approximately every 80 seconds, meaning he changes from being at a height above the platform to below the platform approximately every 80 seconds. While on the second roller coaster, this change occurs every 40 seconds.
Answer:
on plato the answer is B, it reads the same as the answer c does on this example. Please make sure that you read the answers and match them up with the correct one on your side.
Step-by-step explanation:
Using the information provided, Michael's height changes from above to below the platform every 40 seconds for the second roller coaster. However, without more concrete information regarding the first roller coaster, a definitive answer for that cannot be provided.
Explanation:The topic in discussion here is the modeling of Michael's height changes on two different roller coasters using functions and graphs. Given the question, we can observe that the second roller coaster's height variations follow a pattern corresponding to a trigonometric function, changing from 0, to 50, to 100, and so forth, then repeating. From this pattern, we can infer that Michael's height on the second roller coaster oscillates from a positive value (above the platform) to a negative value (below the platform) and back every 40 seconds since the value of g(t) changes from positive to negative (or vice versa) at each 40-second interval.
However, without the details of the first roller coaster's function or graph, we cannot accurately determine how often Michael's height on the first coaster changes from positive to negative. Therefore, based on the given information, we cannot definitively choose between the provided answer options.
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Find a ⋅ b. a = 4i - 4j, b = 4i + 5j
Answer:
value of a.b = -4
Step-by-step explanation:
We need to find a.b
a= 4i-4j
b = 4i+5j
We know that i.i =1, j.j=1, i.j =0 and j.i=0
a.b = (4i-4j).(4i+5j)
a.b = 4i(4i+5j)-4j(4i+5j)
a.b = 16i.i +20i.j-16j.i-20j.j
a.b = 16(1) +20(0)-16(0)-20(1)
a.b = 16 +0-0-20
a.b = 16-20
a.b =-4
So, value of a.b = -4
ANSWER
[tex]a \cdot \: b = - 4[/tex]
EXPLANATION
The dot product of two vectors
[tex]a = xi + yj[/tex]
and
[tex]b = mi + nj[/tex]
is given by
[tex]a \cdot \: b = mx + ny[/tex]
The given vectors are:
[tex]a = 4i - 4j[/tex]
[tex]b = 4i + 5j[/tex]
Applying the above definition of dot products, we obtain:
[tex]a \cdot \: b = 4 \times 4 + - 4 \times 5[/tex]
[tex]a \cdot \: b = 16 - 20[/tex]
[tex]a \cdot \: b = - 4[/tex]
What is true of the function g(x)=-2x^2+5?
A) g(x) is the multiplication of g and x.
B) -2x^2+5 is the input of the function.
C) The variable x represents the independent variable.
D) The variable g represents the input of the function.
Answer:
C) The variable x represents the independent variable.
Step-by-step explanation:
The given function is [tex]g(x)=-2x^2+5[/tex].
g(x) is NOT the multiplication of g and x because g is a function of x.
[tex]x[/tex] is the input of the function.
[tex]-2x^2+5[/tex] is the output of the function.
The variable [tex]x[/tex] is called the independent variable because we plug in values of x to find g.
The variable g represents the output of the function NOT the input.
The correct choice is C
Number 28 is the only question I need please help, with steps
Answer:
f (gx) = 1/ -2(1/x^2+6x+10) + 9
Step-by-step explanation:
f (gx) = 1/ -2(1/x^2+6x+10) + 9
Answer:
The domain is all real numbers where
[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]
Step-by-step explanation:
[tex](f \circ g)(x)=f(g(x))[/tex]
So g(x) must exist before plugging it into f(x).
Let's find where g(x) doesn't exist.
[tex]x^2+6x+10[/tex] is a quadratic expression.
[tex]b^2-4ac[/tex] is the discriminant and will tell us if [tex]x^2+6x+10=0[/tex] will have any solutions. I'm trying to solve this equation because I want to figure out what to exclude from the domain. Depending on what [tex]b^2-4ac[/tex] we may not have to go full quadratic formula on this problem.
[tex]b^2-4ac=(6)^2-4(1)(10)=36-40=-4[/tex].
Since the discriminant is negative, then there are no real numbers that will make the denominator 0 here. So we have no real domain restrictions on g.
Let's go ahead and plug g into f.
[tex]f(g(x))[/tex]
[tex]f(\frac{1}{x^2+6x+10})[/tex]
I replaced g(x) with (1/(x^2+6x+10)).
[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9}[/tex]
I replaced old input,x, in f with new input (1/(x^2+6x+10)).
Let's do some simplification now.
We do not like the mini-fraction inside the bigger fraction so we are going to multiply by any denominators contained within the mini-fractions.
I'm multiplying top and bottom by (x^2+6x+10).
[tex]\frac{1}{-2(\frac{1}{x^2+6x+10})+9} \cdot \frac{(x^2+6x+10)}{(x^2+6x+10)}[/tex]
Using distributive property:
[tex]\frac{1(x^2+6x+10)}{-2(\frac{1}{x^2+6x+10})\cdot(x^2+6x+10)+9(x^2+6x+10)}[/tex]
We are going to distribute a little more:
[tex]\frac{x^2+6x+10}{-2+9x^2+54x+90}[/tex]
Combine like terms on the bottom there (-2 and 90):
[tex]\frac{x^2+6x+10}{9x^2+54x+88}[/tex]
Now we can see if we have any domain restrictions here:
[tex]b^2-4ac=(54)^2-4(9)(88)=-252[/tex]
So again the bottom will never be zero because [tex]9x^2+54x+88=0[/tex] doesn't have any real solutions. We know this because the discriminant is negative.
The domain is all real numbers where
[tex](f \circ g)(x)=\frac{x^2+6x+10}{9x^2+54x+88}[/tex]
3x- 5=1 what does x represent
Answer:
x= 5/3
Step-by-step explanation:
3x- 5 = 1
first you have to move the constant or in this case the 5 to the other side to isolate x so to do that you have to ad 5 from both sides, that way itll cancel out from the left and add on the right
3x= 5
now, to isolate x, we have to divide by 3, that way you get
x= 5/3
The system of equations y = 2x - 1 and y = - 1/4 x + 3 is shown on the graph below.
Answer:
Choose something close to (1.8,2.6)
Choice A
Step-by-step explanation:
Without the graph provided, I would prefer to do this algebraically.
y=2x-1
y=-1/4x+3
Since both are solved for y, I'm going to replace the first y with what the second y equals.
-1/4x+3=2x-1
I don't really like to deal with fractions quite yet so I'm going to multiply both sides by 4.
-1x+12=8x-4
I'm going to add 1x on both sides.
12=9x-4
I'm going to add 4 on both sides.
16=9x
I'm going to divide both sides by 9
16/9=x
This is the same as saying x=16/9.
Now to find y, just choose one of the equations and replace x with 16/9.
y=2x-1
y=2(16/9)-1
y=32/9-1
y=32/9-9/9
y=(32-9)/9
y=23/9
So the exact solution is (16/9,23/9).
Round these numbers to the nearest tenths you get:
(1.8, 2.6) .
To get this I just typed into my calculator 16 divided by 9 and 23 divided by 9
16 divided by 9 gave me 1.777777777777777777777777777
23 divided by 9 gave me 2.5555555555555555555555555
So choose something close to (1.8, 2.6).
So your ordered pair (1.75,2.5) is pretty close to that so choice A.
Triangle JKL is translated using (x, y) --> (x + 1, y - 3) after it is reflected across the x-axis. What are the
coordinates of the final image of point under this composition of transformations?
help please
Answer:
(1, - 6 )
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
The point J has coordinates (0, 3 ), hence
J'(0, - 3 ) ← after reflection in x- axis
A translation (x, y ) → (x + 1, y - 3 )
Means add 1 to the x- coordinate and subtract 3 from the y- coordinate
J'(0, - 3 ) → J''(0 + 1, - 3 - 3 ) → J''(1, - 6 ) ← final image