By the remainder theorem, if p(x) = x³ - 3x² + kx - 1 and x - 1 is a factor p(x), then the remainder upon dividing p(x) by x - 1 is p (1) = 0.
So we have
p (1) = 1³ - 3 • 1² + k - 1 = 0
Solve for k :
1 - 3 + k - 1 = 0
k = 3
4x + 5y = 10
Ax + By = 16
Find a value for A and B that would make the system above have infinitely
many solutions.
Answer:
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
Step-by-step explanation:
Given equations are:
4x + 5y = 10
Ax + By = 16
The general form of linear equation in two variables is given by:
[tex]ax+by = c[/tex]
Here a, b and c are constants and x,y are variables.
In the given equations, after comparing with the general form
[tex]a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16[/tex]
"In order for a system of equations to have infinity many solutions,
[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex] "
Putting the values we get
[tex]\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8[/tex]
Hence,
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
Are all terminating and repeating decimals rational numbers?
Answer:
Yes they are rational numbers
Step-by-step explanation:
Rational numbers are Any number that can be written in fraction form is a rational number. This includes integers, terminating decimals, and repeating decimals as well as fractions. ... So, any terminating decimal is a rational number.
solve 7(3-y)=5(y+5).
Answer:
-1/3
Step-by-step explanation:
21-7y=5y+25
12y=-4
y=-1/3
find the slope of the line passing through the given points
PLEASEEEE please please help me with thissss ill luv u forever!!
Answer:
Hello,I don't think anyone can help you as your question is not there only the subquestions are. Kindly post the main question for assistance.
Regards
Answer and ill mark u as brainlist with an explaination
Answer:
d
Step-by-step explanation:
Are you in the mood to save a life? if your answer is yes you are in the right place.
PLSSSSSSSSSSSSSSSSSSSSSSSS HELPPPP
Could a design be both translational and glide reflectional symmetry? Explain why or why not.
thank you
Answer:
i think ye
Step-by-step explanation:
because symmetry and wikepedia says yes
6. How many sides has a regular poly- gon when each interior angle is 108°? 144°? 120°? 150°? 140°? 90°? 12870?
Answer:
there are 'n' sides of the regular polygon. Thus, the measure of the angle of the quad, are 36°, 12°, 108° and 144°. Thus, the required number of sides of the regular polygon is 5.
Step-by-step explanation:
Im checking my answers for this question and im wondering if im correct or not
Answer and step-by-step explanation:
Checking what you've done, the first two images you've shown have the correct matching. But the last two are wrong. Reason being:
For the third mage, the table suggests that all the points are on the positive part of the y-axis, this means the curve should open upwards not downwards.
For the last image, the table suggests that the points are on the negative part of the y–axis except (0, 1). This means the curve should open downwards not upwards.
The table in the third image should match the graph in the last image and the table in the last image should match the graph in the third image.
Answer:
oh i had the same question so thanks to the guy who answered
Step-by-step explanation:
Consider the equation y=4x + 2. Write three ordered pairs that would be in the table of values.
Answer:
Step-by-step explanation:
(0,2) (1,6) (2,10) are the three ordered pairs
Max a passé 10% de sa journée à jouer à la console
Julie has $1.50 in quarters. How many quarters does Julie have? A. 3 B. 6 C. 15 D. 30
Answer:
B. 6
hope this helps
Answer:
The answer is b
Step-by-step explanation:
Which cube root function is always decreasing as x increases?
Answer: D
Step-by-step explanation:
Kristen has $850 to put in a savings account that earns 4% simple interest each year. How much will be in her account after 6 years?
Answer:
$1054
Step-by-step explanation:
simple interest = 4% of original amount each time
850/100 = 8.5 = 1%
8.5 x 4 = 34 = 4%
34 x 6 = 204
$850 + $204 = $1054
Please help!!!!!!!!!!!!!!!
Answer:
x = 48.59 degrees
Step-by-step explanation:
Do sin-1(12/16) and put it in a calculator. After that, you will get your final answer as 48.59 degrees. This requires sin because the opposite angle is 12 for x. The adjacent angle is something else.
CAN SOMEONE GIVE ME A SUPER SIMPLE ANSWER TO THIS!!??
How do you recognize if a binomial is a difference of perfect squares and how is the pattern used to factor the binomial?
Answer:
A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
Step-by-step explanation:
A binomial is an expression with only terms where at least one is a term with a variable. When we can factor for difference of squares, we can have two variable terms or just one with a constant.
A difference of squares has the following form . Any two perfect squares connected by subtraction can be factored.
It factors to (a+b)(a-b).
2 lb for $4.98 5 lb for $12.25 8 lb for $18.80 10 lb for $23.70 which is a better buy?
Answer:
8 lb for $18.80 is best buy option
Step-by-step explanation:
Given:
2 lb for $4.98 5 lb for $12.25 8 lb for $18.80 10 lb for $23.70Find:
Best buy option
Computation:
1. 2 lb for $4.98
For 1 lb = $4.98 / 2
For 1 lb = $2.49
2. 5 lb for $12.25
For 1 lb = $12.25 / 5
For 1 lb = $2.45
3. 8 lb for $18.80
For 1 lb = $18.80 / 8
For 1 lb = $2.35
4. 10 lb for $23.70
For 1 lb = $23.70 / 10
For 1 lb = $2.37
is 4 1/4 rational or irrational
Rational my guy. Hope you pass ur exams
Answer:
The number 14 is a fraction, and fractions are ratios, and ratios are ratio-nal numbers!
Triangle ABC has coordinates A(2, -5), B(1, -3), and C(6, 1). If the triangle is rotated 90° counterclockwise about the origin, what are the coordinates of A'?
Answer:
A(5,2)
Step-by-step explanation:
A 90 degree rotation counterclockwise is
(x , y) -> (-y , x)
Therefore the coordinates of A changes from
A(2 , -5) to A(-(-5) , 2)
A(5,2)
what is the value of y?
Answer:21
Step-by-step explanation:
Answer:
y = 3
Step-by-step explanation:
9 - y = 2y
Step 1: Add y to both sides
9 - y + y = 2y + y
9 = 3y
Step 2: Divide both sides by 3
9 / 3 = 3y / 3
3 = y
Answer: y = 3
I NEED to answer this correctly. Can I get some help?
Answer:
C., F.
Step-by-step explanation:
Vertices in the same position are congruent angles.
There are 3 pairs of congruent angles:
<T, <W
<U, <X
<V, <Y
There are 3 pairs of congruent sides:
TU, WX
UV, XY
TV, WY
Now pick the correct statements from the list:
C., F.
5x-8 3x+16
Find X
Answers are; 12, 43/2, 52, 4
Answer:
Step-by-step explanation:
Those angles are vertical angles, so their measure are equal, so we can set them equal to each other to solve this problem.
5x - 8 = 3x + 16
2x - 8 = 16
2x = 24
x = 24 / 2
x = 12
Which ratio is equivalent to the ratio 6/14
Answer: 6:14 or 3:7 can be equivalent ratios
I haven't been on here for a while, what's new brain.ly?????!!!!
Answer:
nothing
Step-by-step explanation:
Find in the table for any missing values. Please help!!!
Answer:
1:3
2:6
3:9
5:15
Step-by-step explanation:
Ask yourself: What times 3 equals my number?
As you can see 1x3=3 then 2x3=6, 3x3=9, and lastly 5x3=15
This is how you solve the chart.
Maggie buys a dress and a pair of shoes at The Home Store. Before adding the sales tax, she pays $48 for a dress that normally sells for $62 and she pays $34 for a pair of shoes that normally sells for $46. a) Before the sales tax, how much does Maggie save on her purchases by buying at the sale price? Show all work. b) To the nearest percent, what percent discount did Maggie get on her total purchase? Show all work. c) Including a 15% sales tax, what total amount will Maggie pay?
Answer:
a) $26
b) 24.07%
c) $94.3
Step-by-step explanation:
Given that:
Before tax:
Normal price of dress = $62
Discounted price of dress = $48
Normal price of a pair of shoes = $46
Discounted price of a pair of shoes = $34
a) Before the sales tax, total savings = ($64 - $48) + ($46 - $34) = $26
b) Total percentage discount on total sales.
Total bill for original price = $62 + $46 = $108
Percentage discount can be found by the formula:
[tex]\dfrac{\text{Total discount}}{\text{Total bill for original price}}\times 100\\\Rightarrow \dfrac{26}{108} \times 100 = 24.07\%[/tex]
c) Total amount paid if the sales tax is 15%.
Amount paid with tax = Amount after discount + 15% of amount after discount
Amount after discount = $48 + $34 = $82
15% of $82 = $18.29
Amount paid with sales tax = $82 + $12.3 = $94.3
Been stuck on this equation !! The answer isn’t 45 !
Answer:
The correct answer is 3
Step-by-step explanation:
Order of operation
PLEASE HELP!! WILL GIVE BRAINLIEST!!!
Answer:
120
Step-by-step explanation:
GIVE ME THE BRAINLEST POINTS NOW
Answer:
x = 120
Step-by-step explanation:
All three angles are marked as equal. There are two ways to find x.
Method one
Find the supplement to x
Let the supplement to x be y
y + y + y = 180
3y = 180 Divide by 3
y = 180/3
y = 60
=================
A straight line has an angle of 180 degrees.
x + y = 180 Substitute y = 60 into the equation
x + 60 = 180 Subtract 60
x = 180 - 60
x = 120
Method 2
The two angles not connect to x are called remote interior angles. These two angles are equal to x.
x = 60 + 60
x = 120
There are 144 total members at the meeting witch is 90%
Evaluate I5| - |-5|.
Answer:
| 5 | - | -5 | = 0
Step-by-step explanation:
For this problem, the absolute value operator creates the positive value of whatever is contained in it.
This expression can be rewritten as follows:
| 5 | - | -5 |
= 5 - 5
= 0
Hence, the expression simplifies to 0.
Cheers.
Answer:
0
Step-by-step explanation:
This is the answer because:
1) I I = Absolute Value
Absolute Value means that whatever number is inside it, is positive.
2) The I-5I = 5:
5 - 5 = 0
Therefore, the answer is 0.
Hope this helps! :D