Use synthetic division to determine whether or not (2 – 1) is a factor of (-32% – 2x² – 1).-- Quotient:help (formulas)- Remainder:help (numbers)- Is (2 – 1) is a factor of (-323 – 2x2 - 1)?Yes No
Answer:
Explanations:
From the question, we are to use synthetic division to divide x - 1 by the polynomial function -3x^3 - 2x^2 - 1
Next is to use the synthetic division to carry out the operation as shown below;
From the calculation above, we can conclude the following;
[tex]undefined[/tex]1. ¿Cuántas millas por minuto son 55 millas por hora?
Answer:
0.91
Step-by-step explanation:
Hi guys.I was sick today and I’m still not feeling good.I missed out on class and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = -12
Step-by-step explanation:
these two angles are same side interior angles. These two angles will add up to 180.
so we have the equation:
(x + 142) + (x + 62) = 180
Now just simplify:
(x + 142) + (x + 62) = 180
___-142_________-142
x + (x + 62) = 38
_____-62___-62
x + x = -24
2x = -24
-24/2 = -12
Therefore, x = -12
In ∆VWX, w=680 cm, < X =80° and
1) We know that the sum of the interior angles within a triangle is 180º
So we can state that :
∠X = 80º , ∠V=32º and ∠W = 180º-(80+32), ∠W=68º
2) The area of a triangle can be found by the Heron formula, but before that, we need to find out the other legs. Let's sketch this and use the Law of Sines:
The Law of Sines:
[tex]\begin{gathered} \frac{v}{\sin(V)}=\frac{w}{\sin(W)}=\frac{x}{\sin(X)} \\ \frac{v}{\sin(32)}=\frac{680}{\sin(68)} \\ 680\text{ sin(32) = vsin(68)} \\ \frac{680\text{ }\sin(32_{}}{\sin(68)}=v \\ v\text{ =}388.65 \\ \\ \end{gathered}[/tex]Now let's proceed to find the length of side x:
[tex]\begin{gathered} \frac{w}{\sin(W)}=\frac{x}{\sin(X)} \\ \frac{680}{\sin(68)}=\frac{x}{\sin (80)} \\ x\sin (68)=680\cdot\sin (80) \\ x=\frac{680\cdot\sin (80)}{\sin (68)} \\ x\approx722.26 \end{gathered}[/tex]Now we can add the three sides and find out the Perimeter:
2p: 722.26 +388.65 +680
2p=1790.91
And the semi perimeter is p =2p/2, p =895.455.
2.2) Finally we can find out the area using the Heron Formula:
[tex]\begin{gathered} A=\sqrt[]{p(p-v)(p-w)(p-x)} \\ A=\sqrt[]{895.455(895.455-388.65)(895.455-722.455)(895.455-680)} \\ A=130059.9757\approx130060 \end{gathered}[/tex]3) Hence, the area is 130,060 cm²
10. The value of a new car decreases by 15% each year. The value (D) of the car after t years could be modelled as D = 23000(1 - 0.15) a) Show that the cost of the new car was £23 000. b) What is the cost of the car after 6 years? c) If we drew a graph, what would be the equation of the asymptote? - I just need help with question c
Answer:
y = 0
Step-by-step explanation:
The function has a horizontal asymptote at y = 0 where y is the value of the car
[tex]\text{Since the equation for the value of the car is }[/tex] [tex]23000(1-0.15)^t[/tex]
As [tex]t \rightarrow \infty, \text{the term } (1-0.15)^t \rightarrow 0 \\[/tex]
This is because the term (1-0.15) is < 1 and a nˣ approaches 0 as x → ∞ since the values get smaller and smaller with increasing powers of x
So the equation for the horizontal asymptote is y = 0
Provided graph to illustrate
The coordinates of point T are (0,5). The midpoint of ST is (6,-7).Find the coordinates of point S.S =(
If the midpoint of ST is (6, -7) then its distance from S and T must be the same!
The distance from point T (0,5 ) to (6, -7) is from the Pythagorean theorem:
[tex]d=\sqrt{\left(0-6\right)^2+\left(5--7\right)^2}[/tex]which is
[tex]d=6\sqrt{5}[/tex]Select the correct answer.
What is the solution to the equation 41xl - 8 = -8?
O A.
O B.
O C.
O D. No solutions exist.
X=0
X = -16
x = -4 or x = 4
Answer:
A
Step-by-step explanation:
Adding 8 to both sides,
[tex]4|x|=0 \\ \\ |x|=0 \\ \\ x=0[/tex]
Solve for x.Question options:A) 11 B) 13 C) 12 D) 10
Notice that triangles QRS and YRZ are similar, therefore:
[tex]\frac{YZ}{QS}=\frac{YR}{QR}=\frac{1}{2}\text{.}[/tex]Substituting YZ=x+2, QS=3x-8, and solving for x we get:
[tex]\begin{gathered} \frac{x+2}{3x-8}=\frac{1}{2}, \\ 2(x+2)=3x-8, \\ 2x+4=3x-8, \\ x=12. \end{gathered}[/tex]Answer: Option C).
What is the percent of 80 of 62
I need help with the following questions. Please show your work.
1) Find the inverse of f(x)=3 sqrt x-1/2
2) Let f(x)-2/2x-1
Show that this function is one-to-one algebraically.
3) Determine whether f(x)=3x-5 and g(x)=x/3+5 are inverses. Explain how you know.
please help
For the given functions, it is found that:
1) The inverse is: [tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
2) f(a) = f(b) if, and only if, a = b, hence the function is one-to-one.
3) The composite of these two functions is different of x, hence the two functions are not inverses.
Item 1The function is defined by:
[tex]y = 3\frac{\sqrt{x - 1}}{2}[/tex]
To find the inverse, we exchange x and y on the original function and then isolate y, hence:
[tex]x = 3\frac{\sqrt{y - 1}}{2}[/tex]
[tex]3\sqrt{y - 1} = 2x[/tex]
[tex]\sqrt{y - 1} = \frac{2x}{3}[/tex]
[tex](\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2[/tex]
[tex]y - 1 = \frac{4x^2}{9}[/tex]
[tex]y = \frac{4x^2}{9} + 1[/tex]
[tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
Item 2To show that the function is one-to-one, we need to show that f(a) = f(b) if, and only if, a = b, then:
f(a) = -2/(2a - 1).f(b) = -2/(2b - 1).Equaling the functions:
-2/(2a - 1) = -2/(2b - 1).
Applying cross multiplication:
-2(2b - 1) = -2(2a - 1)
2b - 1 = 2a - 1
2b = 2a
b = a.
Hence the function is one-to-one.
Item 3The functions will be inverses if the composition of the functions result in x, hence:
f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.
Hence the functions are not inverses.
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Evaluate the function f(x) = x² + 9x− 7 at the given values
a. f(2) b. f(x+8) c. f(-x)
b. f(x+8)
c. f(-x)
The given values the equation evaluate is:
f(2) = 15,
f(x+8) = x² + 25x + 129,
f(-x) = x² - 9x - 7
What in mathematics is a quadratic equation?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. Since it is a second-order quadratic equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution might be straightforward or difficult.
According to the given data:f(x) = x² + 9x− 7
a) At, f(2)
f(2) = (2)² + 9(2) - 7
f(2) = 4 + 18 - 7
f(2) = 15
b) At, f(x+8)
f(x+8) = (x + 8)² + 9(x + 8) - 7
f(x+8) = x² + 8² + 16x + 9x + 72 - 7
f(x+8) = x² + 64 + 25x + 72 - 7
f(x+8) = x² + 25x + 129
c) At, f(-x)
f(-x) = (-x)² + 9(-x) - 7
f(-x) = x² - 9x - 7
Hence,
The given values the equation evaluate is:
f(2) = 15,
f(x+8) = x² + 25x + 129,
f(-x) = x² - 9x - 7
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find figure 0 for the tile pattern below. write a rule that will give the number of tiles in any figure, record the data for the first six tiles 0-5 in a table, and graph the data
Solution
for this case we can see that for
Figure 0 = 6 tiles
Figure 1 = 7 tiles
Figure 2 = 8 tiles
Figure 3= 9 tiles
Figure 4 = 10 tiles
Figure 5= 11 tiles
Then the table would be given by:
Figure number (x) 0 1 2 3 4 5 x
Number of tiles (y) 6 7 8 9 10 11 6+x
And the line should be like this:
determine if the following are rotations
Answer: D and C are the other rotations
Step-by-step explanation: A is mirrored
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two workers in a holiday boutique are filling stockings with small gifts and candy. Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour. Peter, who just arrived to help, can fill 4 stockings per hour. At some point, Peter will catch up with Katie and they will have completed the same number of stockings. How long will that take? How many stockings will each worker have filled by then?In ____ hours, the workers will each have filled _____ stockings.
Two workers in a holiday boutique are filling stockings with small gifts and candy.
Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour.
3 + x
Peter, who just arrived to help, can fill 4 stockings per hour.
4 x
At some point, Peter will catch up with Katie and they will have completed the same number of stockings.
3 + x = 4x
3 = 4x -x
3 x =3
x = 3/3
x =1 hour How long will that take?
How many stockings will each worker have filled by then?
Katie = 3 + 1 = 4
Peter = 4 x 1 = 4
Robert has 3 more than twice the number of t-shirtsthat Brianne has. Robert has 19 shirts. How manyShirts does Brianne have?** 3x + 219X+ 5 = 16* 2 + 3 =19
1) Considering that we can call t-shirts "x" then we can write out the following equations to express this problem:
Robert: 2x +3
Brianne: x
2) Now, we can write out the following equation to find out how many t-shirts does Brianne have:
[tex]\begin{gathered} 2x+3=19 \\ 2x+3-3=19-3 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]So that's the number of t-shirts Brianne has. And the equation used is:
[tex]2x+3=19[/tex]express your answer as a polynomial in Itandard form.
Answer:
f(x) = x + 5
g(x) = x² - 4x + 8
Find: g(f(x))
The answer to g(f(x)) expressed as a polynomial in Standard form is x² + 6x + 13.
What is the Composition of Functions?The composition of the functions f(x) and g(x), where g(x) acts first, is denoted by f(g(x)) or (fog)(x). A new function is created by combining two or more existing functions. The output of the function inside the parenthesis that is being composed becomes the input for the function outside of the parenthesis. i.e.,In f(g(x)), g(x) is the input to f(x).In g(f(x)), f(x) is the input to g(x).Given the composition of functions g(f(x)),
For which f(x) = x + 5, and g(x) = x² - 4x + 8.
Considering f(x) as input we substitute it in g(x) in place of x.
g(f(x)) = (x+5)²- 4(x+5) + 8
= x² + 25 + 10x - 4x -20 + 8
= x² + 6x + 13
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Which equation represents a line that is perpendicular to Line L on the graph below?A. Y= -1/2x+3B. Y= 1/2x+3C. Y=2x+3D. Y= -2x+3
In this question, we are given a line. The standard equation of line is:
y = mx + b
Here, m is the slope, that is the difference of y values over the x values.
m = (y2 - y1) / (x2 - x1)
b is the y-intercept, where the value of x is zero.
If we see the line, x = 0, when y = -4. Hence, the y-intercept = b = -4
Also,
(x1, y1) = (0, -4)
(x2, y2) = (-4, 4)
m = [4 - (-4)]/ [-4 - 0]
m = 8/-4
m = -2
Hence, the equation of given line is
y = -2x - 4
The rule is: two lines are perpendicular if their slopes are negative reciprocal of each other.
In other words, two lines with slope m1 and m2 are perpendicular if
m1 = -1/m2
Now, the slope (m1) of the given line is -2. Hence, the slope (m2) of the perpendicular line would be m2 = 1/-(-2) = 1/2
Now, just put this value, we get
Y = 1/2 x - 4
As there is no solution closer to this one, I believe the 2nd answer Y = 1/2x + 3 would be correct.
A local salesman receives a base salary of $925 monthly. He also receives a commission of 7% on all sales over $1350. How much would he have to sell in a month if he needed to have a monthly income of $2200?
The local salesman has to sell $19564.3 in a month if he needed to have a monthly income of $2200.
The monthly salary will be the sum of the fixed part or base salary and the commission part.
The base salary of the local salesman is $925.
The salesman commission part is 7% on all sales over $1350.
Let x be the total amount of sales, and x must be greater than $1350.
Then,
The amount of sales over $1350 is x - 1350.
He earns 7% on that amount, so the commission part is 7% of (x - 1350),
or 0.07( x - 1350 ).
So,
monthly salary = fixed part + commission part
monthly salary = 925 + 0.07( x - 1350)
925 + 0.07(x - 1350) = 2200
0.07(x - 1350) = 1275
0.07x - 94.5 = 1275
0.07x = 1369.5
x = 19564.3
He would have to sell $19564.3 in a month if he needed to have a monthly income of $2200.
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Abdul, Beckie, Cynthia and Douglas are making pancakes according to the recipe below:Which person can make the most pancakes?BeckieAbdulCynthiaDouglas
To make 12 pancakes we need 100 g flour, 2 eggs, 300 ml milk
Abdul has 175 g flour, 4 eggs and 500 g milk
The ration between Abdul's amount of each ingredient and the total needed to make 12 pancakes is: (175/100) = 1.75 flour, (4/2) = 2 eggs, (500/300) = 1.67 milk.
So, the total amount of pancakes that Abdul can make is determined by the amount of the less abundant ingredient (milk): 1.67*12 = 20 pancakes
Doing the same steps for Beckie, we got that her less abundant ingredient is milk, with a ratio of 400/300 = 1.33. Then, she can make 1.33*12 = 16 pancakes.
For Cynthia, her less abundant ingredient is flour, with a ratio of 150/100 1.5. Then, she can make 1.5*12 = 18 pancakes.
And for Douglas, his less avundant ingredient is egg, with a ratio of 3/2 = 1.5. Then, he can make 1.,5*12 = 18 pancakes.
Therefore, Abdul is the one who can make the most pancakes
Lucy bought four paint brushes from the Art Supply Store. She had a coupon for 25% off.
How much money does she owe? Each paint brush is 10.50
Answer: $31.50 for the four brushes after using the coupon
Step-by-step explanation:
$10.50 (Amount for EACH brush) * 0.75 (coupon 25% off) = $7.875 (Amount for each after coupon)
$7.875* 4 brushes = $31.5
or
$10.50 (regular price) * 4 brushes = $42 (4 brushes at regular price)
$42 * 0.75(25% coupon) =$ 31.5
If one third of a number is substrates from twice the number the result is 55. What is the number. ?
Let the number be x:
So intepreting the word problem into words we will have:
[tex]2x-\frac{1}{3}x=55[/tex]Simplifying further, we will have:
[tex]\begin{gathered} \frac{5}{3}x=55 \\ \end{gathered}[/tex]Cross multiply:
[tex]\begin{gathered} 5x=165 \\ x=\frac{165}{5} \\ x=33 \\ \text{The number is 33} \end{gathered}[/tex]Segment AB has endpoints A (-5, 7) and B (4, 4). The segment is reflected over the line y =4 to create endpoints A'B' and then rotated 90° CW to form points A"B". Find the location of A" and B".
A(-5,7)
B(4,4)
The segment is reflected over the line y =4
The line y=4 is a horizontal line, coordinate in x doesn't change after reflection.
To find coordinate y after reflection:
Find the distance of each point from y=4
Point A: (-5,7)[tex]\lvert7-4\rvert=3[/tex]As y=4 is below the point A, the point A' will have a coordinate y of: 4-3=1
Point A': (-5,1)Point B: (4,4)[tex]\lvert4-4\rvert=0[/tex]As point B is on line y=4 the point B' will have a coordinate y of 4-0:4
Point B': (4,4)_____________________________then rotated 90° CW:
Rule for a rotation 90º CW:
[tex]P(x,y)\rightarrow P^{\prime}(y,-x)[/tex]Then, you get the next coordinates for A'' and B'':
[tex]\begin{gathered} A^{\prime}(-5,1)\rightarrow A^{\doubleprime}(1,5) \\ B^{\prime}(4,4)\rightarrow B^{\doubleprime}(4,-4) \end{gathered}[/tex]The Cougars scored a total of 84 points in their basketball game last nightagainst the Bears. The Cougars made no one-point shots, and a total of38 two-point and three-point shots. Let x represent the number of two-pointshots and y represent the number of three-point shots.a. How many two-point shots did the Cougars make? How many three-pointshots did the Cougars make? Write and solve a system of equations that canbe used to solve this problem.
Step 1: Write out the values
For Cougars
Total Points = 84
Number of 1 point shot = 0
Number of 3 and 2 points shots = 38
Step 2: Write out the system of equations
[tex]x+y=38---------------------(1)[/tex]Since there are x number of two-point shots, then the total number of points from the two-point shots is 2x
Also, there are y number of three-point shots, then the total number of points from the three-point shots is 3y
Hence, the total number of points is 2x + 3y
Therefore,
[tex]2x+3y=84----------------(2)[/tex]Step 3: Solve the system of equation simultaneously
x + y = 38 ------ equation 1
2x + 3y = 84 ------ equation 2
Using the elimination method to eliminate x
Multiply equation 1 by 2 to get a new equation
2x + 2y = 76 ------ equation 3
Step 4: combine equation 2 and 3 and solve simultaneously
2x + 3y = 84------- equation 2
2x + 2y = 76 ------ equation 3
Subtract equation 3 from 2
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Could you please check this answer for me? Use the following equation to solve Y:2y-6x=18 The answer I got is: y=3(x+3)
The answer is y=3(x+3)
[tex]\begin{gathered} 2y-6x=18 \\ 2y=18+6x \\ y=\frac{2(9+3x)}{2} \\ y=9+3x \\ y=3(3+x) \end{gathered}[/tex]i need help fast as possible and explanation
Answer:
x>0
Step-by-step explanation:
any number less than or equal to zero does not give a negative solution and you need a negative solution so x must be greater than 0
Simplify.10(15 + n)150 n150 + n150 + 10 n50 + n
The Solution:
Given:
[tex]10(15+n)[/tex]We are required to simplify.
[tex]\begin{gathered} 10(15+n) \\ 150+10n \end{gathered}[/tex]Therefore, the correct answer is:
[tex]undefined[/tex]Which fraction divided by 3/6 is equal to -9/10?
A. -3/2
B. -9/20
C. 9/20
D. 9/40
multiply and/ or divide and put into lowest terms
the division of fractions follows the stes
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Applying this into the expression given
[tex]\frac{3\cdot(a-9)}{9\cdot(a^2-81)}[/tex]simplify the coefficients by decomposing 9 into a product and cancelling the common factors
[tex]\frac{3\cdot(a-9)}{3\cdot3\cdot(a^2-81)}[/tex]simplify
[tex]\frac{a-9}{3\cdot(a^2-81)}[/tex]In the denominators there is a difference of squares that can be rewriten as a product, in which by definition the difference of square is described as
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]In the denominator of the expression we can see that a is squared and that 81 has an exact root which is 9, reason why we can write this as a difference of squares, it should look like this:
simplify the expression
[tex]\frac{1}{3\cdot(a+9)}[/tex]distribute the 3
[tex]\frac{1}{3a+27}[/tex]I'm not sure how to find the degrees for angle d
Answer
a° = 58°
b° = 48°
c° = 74°
d° = 122°
Explanation
To answer this, we need to first know
- what alternate angles are.
- that the sum of angles in a triangle is 180°.
- The sum of angles on a straight line is 180°.
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.
We can see that
a° = 58°
b° = 48°
Then, for c°,
48° + 58° + c° = 180° (Sim of angles in a triangle is 180°)
106° + c° = 180°
c° = 180° - 106°
c° = 74°
Then, for d°,
58° + d° = 180° (Sum of angles on a stright line is 180°)
d° = 180° - 58°
d° = 122°
Hope this Helps!!!
4.5 simplified into a fraction is?
4.5 = 45/10 Using GCF
9/2
