Answers
Answer:
Step-by-step explanation:
1). f(x) = x² - 9
g(x) = x - 3
h(x) = f(x) ÷ g(x)
= [tex]\frac{x^2-9}{x-3}[/tex]
= [tex]\frac{(x+3)(x-3)}{(x-3)}[/tex]
= (x + 3)
2). f(x) = x² - 4x + 3
= x² - 3x - x + 3
= x(x - 3) - 1(x - 3)
= (x - 1)( x- 3)
g(x) = x - 3
h(x) = f(x) ÷ g(x)
= [tex]\frac{(x-1)(x-3)}{(x-3)}[/tex]
= (x - 1)
3). f(x) = x² + 4x - 5
= x² + 5x - x - 5
= x(x + 5) - 1(x + 5)
= (x - 1)(x + 5)
g(x) = x - 1
h(x) = f(x) ÷ g(x)
= [tex]\frac{(x-1)(x+5)}{(x-1)}[/tex]
= (x + 5)
4). f(x) = x² - 16
= (x - 4)(x + 4) [Since a² - b² = (a - b)(a + b)]
g(x) = (x - 4)
h(x) = f(x) ÷ g(x)
= [tex]\frac{(x-4)(x+4)}{(x-4)}[/tex]
= (x + 4)
Answer:
Step-by-step explanation:
1). f(x) = x² - 9
g(x) = x - 3
h(x) = f(x) ÷ g(x)
=
=
= (x + 3)
2). f(x) = x² - 4x + 3
= x² - 3x - x + 3
= x(x - 3) - 1(x - 3)
= (x - 1)( x- 3)
g(x) = x - 3
h(x) = f(x) ÷ g(x)
=
= (x - 1)
3). f(x) = x² + 4x - 5
= x² + 5x - x - 5
= x(x + 5) - 1(x + 5)
= (x - 1)(x + 5)
g(x) = x - 1
h(x) = f(x) ÷ g(x)
=
= (x + 5)
4). f(x) = x² - 16
= (x - 4)(x + 4) [Since a² - b² = (a - b)(a + b)]
g(x) = (x - 4)
h(x) = f(x) ÷ g(x)
=
= (x + 4)
Related Questions
Solve -27p²q²+6p³-2p⁴-q³
Answers
Answer:
-27p^2 q^2 +6p^3 -2p^4 -q^3
Step-by-step explanation:
COMBINE LIKE TERMS
Use the function below to find Fl-2).
F(x) = 3x
Answers
explanation
The perimeter of a rectangular field that measures 2 feet by 18 inches is _________ ft. A. 40 B. 7 C. 84 D. 6
Answers
Answer:
B. 7
Step-by-step explanation:
2 - The length of a field, 1.2 km long is represented on a map bye
line 40 mm long. What is the scale of the map,
of
Answers
Answer:
1,000,000 mm:1 kmStep-by-step explanation:
This problem bothers on the conversion of units
to get the scale we need to know how many millimetres are there in one km.
Hence the scale is 1,000,000 mm:1 km
Which of the following linear equations passes through points (-1, 5) and (1, -5)? y = -5x y = 5x + 10 y = -2x + 3 None of these choices are correct.
Answers
Answer:
y = -5x
Step-by-step explanation:
Which of the following linear equations passes through points (-1, 5) and (1, -5)?
y = -5x
y = 5x + 10
y = -2x + 3
None of these choices are correct.
Solution:
First find slope of equation:
slope, m = (y2-y1) / (x2-x1) = (5-(-5) / (-1-1) = 10/(-2) = -5
Now substitute m in the point slope form to find the y-intercept b
y-y1 = m(x-x1)
y-5 = 5(x- -1)
y = -5(x+1) + 5
y = -5x
There are ten people in the Baking Club, including Mark. They choose $3$ people to form an executive committee. How many possible committees can be formed that do not include Mark?
Answers
Answer:
504 committees
Step-by-step explanation:
In this scenario, there are 9 choices to choose the first person (not 10 because the committee should not include Mark), 8 choices for the second person and 7 choices for the last person so the answer is 9 * 8 * 7 = 504.
What is the only solution of 2x^+8=x^-16
Answers
Use SOHCAHTOA for this. Work out 'm' in 3sf, I need the working out.
Answers
Anwer:3.537m
STEP BY STEP EXPLANATIOND:using SOH CAH TOA
First find the opposite
Represent the opposite with x
Tan 33° =x\10
x=10Tan 33°
x=6.494
To find m
Sin 33°=m\6.494 Sin 33°
m=3.5368
m=3.537meteres
Find the equation of the given parabola in vertex and standard form. Describe in words all transformations that have been applied to the graph of y=x^2 to obtain the given graph of the transformed function
Answers
Answer: [tex]a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6[/tex]
[tex]b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}[/tex]
c) Transformations: reflection over the x-axis,
vertical stretch by a factor of 3/2,
horizontal shift 1 unit to the left,
vertical shift 6 units up
Step-by-step explanation:
Intercept form: y = a(x - p)(x - q)
Vertex form: y = a(x - h)² + k
Standard form: y = ax² + bx + c
We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.
p = -3, q = 1, (x, y) = (-1, 6)
a(-1 + 3)(-1 -1) = 6
a (2)(-2) = 6
a = -6/4
a = -3/2
a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
b) Input a = -3/2 into the Intercept form and expand to get the Standard form:
[tex]y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}[/tex]
c) Use the Vertex form to identify the transformations:
[tex]y=-\dfrac{3}{2}(x+1)^2+6[/tex]
a is negative: reflection over the x-axis|a| = 3/2: vertical stretch by a factor of 3/2h = -1: horizontal shift left 1 unitk = +6: vertical shift up 6 unitsCaitlyn started collecting shells in 2005. She records how many shells are in her collection each year.
Years since 2005 # shells
0 30
1 39
2 48
3 57
What is the initial value?
0
9
30
57
Answers
Answer:
30.
Step-by-step explanation:
The initial value is the value that she starts out with. This means that she is referring to year 0. According to the chart, on year 0, she collected 30 shells.
The answer is 30.
Help me asap i really need this
Answers
Answer:
3
Step-by-step explanation:
6/2
I hope this is right :)
I really need help pls
Answers
If you add 2 feet to the length
Length = x +2
If you subtract 2 feet to the width
Width = x-2
Area of rectangle = l x w
= (x-2)(x+2)
If the original patio was 10 feet by 10 feet, the new one can be found by inserting x = 10 to the expression above
(10-2)(10+2) = 8 x 12 = 96
96 square feet is the new area
Answer:
D.
Step-by-step explanation:
Original dimensions:
L = x
W = x
Now we reduce the width by 2 ft and increase the length by 2 ft.
L = x + 2
W = x - 2
The area is the product of the length and width.
A = LW = (x + 2)(x - 2)
The original length and width are 10 ft.
L = W = x = 10
A = LW = (10 + 2)(10 - 2) = 12 * 8 = 96
The new area is 96 sq ft.
Answer: D.
Angles C and D are complementary. The ratio of the measure of Angle C to the measure of Angle D is 2:3. What are the measures of both angles?
Answers
Answer:
36° and 54°
Step-by-step explanation:
Complementary angles are angles whose sum equals to 90°
Hence C +D = 90°
The ratio of C &D = 2:3 respectively
Sum of the ratio = 2+3 = 5
Hence we divide each of the ratio by the sum of the entire ratio and then multiply by 90°
For angle C :
2/5 × 90
2×18 = 36°
For angle D :
3/5× 90
3×18 = 54°
Hence the angles are 36° and 54° respectively
To proof that we are actually right
C+D = 90°
36+54 = 90°
Hence the answer is right.
Which of these systems of linear equations has no solution?
2 x + 8 y = 15. 4 x + 16 y = 30.
2 x minus y = 18. 4 x + 2 y = 38.
4 x + 7 y = 17. 8 x minus 14 y = 36.
4 x minus 3 y = 16. 8 x minus 6 y = 34.
Answers
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution
Step-by-step explanation:
Examine the system
2 x + 8 y = 15
4 x + 16 y = 30
We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.
Next, look at the system
2 x minus y = 18
4 x + 2 y = 38
If we divide the second equation by 2, we get the system
2x - y = 18
2x + y = 19
Combining these two equations, we get 4x = 37, which has a solution.
Third, analyze the system
4 x + 7 y = 17 => 8x + 14y = 34
8 x minus 14 y = 36 => 8x - 14y = 36, or 16x = 70, which has a solution
Finally, analyze the system
4 x minus 3 y = 16 => -8x + 6y = -32
8 x minus 6 y = 34 => 8x - 6y = 34
If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible. This system has no solution.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution. the 4th option.
Step-by-step explanation:
Ruby is visiting San Francisco. From her hotel she walks 1 block west and 3 blocks south to a coffee shop. Then she walks 4 blocks east and 4 blocks south to a museum. Where is the museum in relation to her hote
Answers
Answer:
The Museum is 7 blocks south and 3 blocks east
Step-by-step explanation:
Since from the hotel Ruby went 1 block west (left) during the whole time traveled, you would go 3 east (from hotel to museum).
Then in total Ruby went south 7 blocks.
Plz help I’m trying to solve for the indicated variable
Answers
Hey there! :)
Answer:
a. b = y - mx
b. x = y - b /m
c. t = I/ pr
d. t = A - p/pr
Step-by-step explanation:
a. y = mx + b (for b)
Isolate the b variable by subtracting both sides by mx:
y - mx = b.
Therefore:
b = y - mx.
b. y = mx + b (for x)
Subtract 'b' from both sides:
y - b = mx
Divide 'm' from both sides:
y - b / m = x
c. I = prt
Divide both sides by pr:
I /pr = t.
d. A = p + prt
Subtract p from both sides:
A - p = prt
Divide both sides by pr:
A - p / pr = t
Bettina is measuring the food for her farm animals. She has 265 grams of corn, 500 grams of hay, and 495 grams of oats. What is the total weight in kilograms?
Answers
Answer
260 kilograms
Step-by-step explanation:
the correct answer is 260 kg
Answer: 12.6 kg
Step-by-step explanation: add the amounts of food for her farm, and just search for how many kg are in 1,260 grams
A system of linear equations contains two equations with negative reciprocal slopes. Select all of the correct statements. A. The system may have no solution B. The system will have one solution C. The system will have two solutions D. The system may have infinitely many solutions
Answers
Answer:
B.
Step-by-step explanation:
"negative reciprocal slopes" means the lines are perpendicular, so they will always intersect.
Hence there will be exactly one solution.
B. The system will have one solution.
What is a negative reciprocal slope?The slopes of perpendicular strains, or bisecting strains, are continually terrible reciprocals of each other. For instance, if the slope of a line is -five, then the slope of a line perpendicular to this line will be the negative reciprocal of -five.
What is the system of two linear equations that have different slopes?If the 2 traces have exclusive slopes, then they'll intersect as soon as. consequently, the gadget of equations has exactly one answer. If the two traces have the equal slope however of kind y-intercepts, then they're parallel strains, and they'll by no means intersect.
Learn more about the system of linear equations here: https://brainly.com/question/14323743
#SPJ2
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that apply.
Answers
Answer:
y = -[tex]\frac{2}{5}[/tex]x - 1
Step-by-step explanation:
First, we can put the equation into y = mx + b form:
2x + 5y = 10
5y = -2x + 10
y = -[tex]\frac{2}{5}[/tex]x + 2
Now, we know the slope is -[tex]\frac{2}{5}[/tex]. A parallel line will have the same slope.
So, we can plug in the point (-5, 1) into the equation y = -[tex]\frac{2}{5}[/tex]x + b to find b:
1 = -[tex]\frac{2}{5}[/tex](-5) + b
1 = 2 + b
-1 = b
So, the equation will be y = -[tex]\frac{2}{5}[/tex]x - 1
SOMEONE PLEASE HELP ME IM CONFUSEDDD PLEASEE
A negative number raised to an exponent is positive. Which of the following is not true?
A. The number could be even
LB. The number could be odd
C. He exponent could be even
D. The exponent could be odd
Answers
Answer:
D. the exponent can be odd
Step-by-step explanation:
A. (-4)² = 16 ⇒ -4 is even and the product is positive.
B. (-5)² = 25 ⇒ -5 is odd and the product is positive.
C. (-5)⁴ = 625 ⇒ The exponent 4 is even and the product is positive.
D. (-5)⁵ = -3125 ⇒ The exponent 5 is odd and the product is negative.
So, the answer is D.
Hope this helps.
PLEASE HELP ME WITH THIS
Answers
Explanation:
Figure 1:
Angle x = angle 1
And angle 4 = 4x
Angle 4 + angle 1 = 180
4x + x = 180
5x = 180
x = 36
Figure 2:
Angle 1 = 68 degree
Angle 2 = 55 degree
Find angle 3:
180 - (68 + 55)
= 180 - 123
= 57 degree
But angle 3 = angle 4 = 57 degree
But: angle 4 + x = 180
57 + x = 180
x = 180 - 57
x = 123
X is equal to 28
Hope this helps......
y = 5x + 2 3x = –y + 10 What is the solution to the system of equations
Answers
Answer:
x = 1 , y = 7
Step-by-step explanation:
Solve the following system:
{y = 5 x + 2 | (equation 1)
3 x = 10 - y | (equation 2)
Express the system in standard form:
{-(5 x) + y = 2 | (equation 1)
3 x + y = 10 | (equation 2)
Add 3/5 × (equation 1) to equation 2:
{-(5 x) + y = 2 | (equation 1)
0 x+(8 y)/5 = 56/5 | (equation 2)
Multiply equation 2 by 5/8:
{-(5 x) + y = 2 | (equation 1)
0 x+y = 7 | (equation 2)
Subtract equation 2 from equation 1:
{-(5 x)+0 y = -5 | (equation 1)
0 x+y = 7 | (equation 2)
Divide equation 1 by -5:
{x+0 y = 1 | (equation 1)
0 x+y = 7 | (equation 2)
Collect results:
Answer: {x = 1 , y = 7
Answer:
D) (1,7)
Step-by-step explanation:
just took the test
Valentino sells ice cream cones and ice cream tubs. The ice cream flavours are chocolate, strawberry and vanilla. On Sunday, 120 people each bought one ice cream from Valentino. The two-way table shows some information about these ice creams. One of the 120 people is picked at random. Find the probability that this person bought a vanilla ice cream cone.
Answers
Answer:
11/60
Step-by-step explanation:
hello
in total there are 120 ppl
22 are vanilla cones
so the probability that this person bought a vanilla a ice cream cone is 22/120=11/60
hope this helps
Help Please again ;-;
Answers
Answer:
Graph 1 shows a negative correlation, and graph 2 shows a positive correlation. This is because in graph one, as x increases, y decreases, and in graph two as x increases, y also increases.
44. The length of a road is 380 m, correct to the nearest 10 m. Maria runs along this road at an average
speed of 3.9 m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria
Answers
Answer:
Time = distance/speed
max distance = 380+10 = 390 m
Max Time = 390/3.9 = 100 s
Which of the following is true?
A.
A ABC DEC by SAS
B. ABC EDC by SSS
C. BCA DCE by SAS
D. ABC DEC PLEASE HURRYYYYY
Answers
80 inches of snow over 10 days
Answers
Answer:
8-in of snow each day
Step-by-step explanation:
Answer:
8 inches of snow each day
Step-by-step explanation:
hope this helps :)
show that the straight line x+y does not intersect the curve x^2-8x+y^2-12y+6=0 if k^2-20k+8>0
Answers
Need help with this ASAP (just ordered pairs!)
Answers
Answer:
Step-by-step explanation:
You have all your x values to the left. Just take 2 and multiply one by one.
Then in order to graph it, you would take (x,y) and plot it.
For example:
y=2x
y=2(5) = 10
(5,10) - you would plot this on the graph.
1. y = 2x
x | y = 2x | y
5 | y = 2(5) | 10
3 | y = 2(3) | 6
0 | y = 2(0) | 0
-1 | y = 2(-1) | -2
-5 | y = 2(-5) | -10
2. y = 1 + 5x
x | y = 1 + 5x | y
-2 | y = 1 + 5(-2) | -9
-1 | y = 1 + 5(-1) | -4
0 | y = 1 + 5(0) | 1
2 | y = 1 + 5(2) | 11
Pleaseee hellllpp!!!!
How many grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl?
Answers
Answer:
105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.
Step-by-step explanation:
We are given that the compound has 6.3 x10^23 atoms of Cl.
To find how many molecules of AuCl3 are in the given compound, we divide the compound by 3, i.e;
[tex]\frac{6.3 \times 10^{23} }{3}[/tex] = [tex]2.1\times 10^{23}[/tex] molecules of AuCl3.
Now, as we know that 1 mole of AuCI3 has [tex]6.022 \times 10^{23}[/tex] molecules.
So, the moles that our compound has is given by;
= [tex]\frac{2.1 \times 10^{23} }{6.022 \times 10^{23} }[/tex] = [tex]\frac{2.1}{6.022}[/tex] = 0.349 mole AuCI3
Also, the molar mass of AuCI3 = 303.33 g/mole
So, the molar mass of 0.349 moles AuCI3 = [tex]303.33 \times 0.349[/tex]
= 105.86 g
Hence, 105.86 grams of AuCl3, if the compound has 6.3 x10^23 atoms of Cl.