Answer:
a+2b-d=1, 3, 5, 7
Step-by-step explanation:
(ax^2+bx+3)(x+d)
ax^3+bx^2+3x+adx^2+bdx+3d
ax^3+bx^2+adx^2+3x+bdx+3d=x^3+6x^2+11x+12
ax^3=x^3, a=1
bx^2+adx^2=6x^2
x^2(b+ad)=6x^2
b+ad=6
b+(1)d=6
b+d=6
------------
3x+bdx=11x
x(3+bd)=11x
3+bd=11
-----------------
b=6-d
3+(6-d)d=11
3+6d-d^2=11
3-11+6d-d^2=0
-8+6d-d^2=0
d^2-6d+8=0
factor out,
(d-4)(d-2)=0
zero property,
d-4=0, d-2=0
d=0+4=4,
d=0+2=2
b=6-4=2,
b=6-2=4.
------------------
a+2b-d=1+2(2)-2=1+4-2=5-2=3
-------------------
a+2(4)-4=1+8-4=9-4=5
-----------------------
a+2(2)-4=1+4-4=5-4=1
-----------------------
a+2(4)-2=1+8-2=9-2=7
Answer:
[tex]a+2b-d=1[/tex]
Step-by-step explanation:
We are given that:
[tex](ax^2+bx+3)(x+d)=x^3+6x^2+11x+12[/tex]
And we want to determine:
[tex]a+2b-d[/tex]
So, we will determine our unknowns first.
We can distribute our expression:
[tex]=(ax^2+bx+3)x+(ax^2+bx+3)d[/tex]
Distribute:
[tex]=ax^3+bx^2+3x+adx^2+bdx+3d[/tex]
Rearranging gives:
[tex]=(ax^3)+(bx^2+adx^2)+(bdx+3x)+3d[/tex]
Factoring out the variable yields:
[tex]=(a)x^3+(b+ad)x^2+(bd+3)x+d(3)[/tex]
Since we know that our expression equals:
[tex]x^3+6x^2+11x+12[/tex]
This means that each of the unknown terms in front of each variable corresponds with the coefficient of the resulting equation. Therefore:
[tex]\begin{aligned} a&=1\\ b+ad&=6\\bd+3&=11\\3d&=12\end{aligned}[/tex]
Solving the first and fourth equation yields that:
[tex]a=1\text{ and } d=4[/tex]
Then the second and third equations become:
[tex]b+(1)(4)=6\text{ and } b(4)+3=11[/tex]
And solving for b now yields that:
[tex]b=2\stackrel{\checkmark}{=}2[/tex]
Therefore, we know that:
[tex]a=1, b=2\text{ and } d=4[/tex]
For the equation:
[tex](x^2+2x+3)(x+4)=x^3+6x^2+11x+ 12[/tex]
Then the expression:
[tex]a+2b-d[/tex]
Can be evaluated as:
[tex]=(1)+2(2)-4[/tex]
Evaluate:
[tex]=1+4-4=1[/tex]
Hence, our final answer is 1.
Ruby has $2.10 in nickels and dimes.
She has three as many dimes as nickels. How many nickels and dimes does she have?
Answer:
$
Step-by-step explanation:
Unit conversion is the conversion of one unit to another unit with its standard conversion.
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
The number of nickels is 5.
The number of dimes is 15.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
20 nickels = $1
10 dimes = $1
1 nickel = 5 cents
1 dimes = 10 cents
Now,
Let,
Dimes = 3x
Nickels = x
Now,
The total number of cents.
10(3x) + 5x = 180
30x + 5x = 180
35x = 180
x = 5.14
x = 5
Now,
3x = 3 x 5 = 15
Thus,
The number of nickels is 5.
The number of dimes is 15.
Learn more about unit conversion here:
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WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!!
Write the equation of the line with a slope of -1.6 and a y-intercept of 4 in slope-
intercept form.
Answer:
y = -1.6x + 4
Step-by-step explanation:
y = mx + b
y = (-1.6)x + (4)
y = -1.6x + 4
The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = - 1.6x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Slope of the line (m) = - 1.6
And, The y - intercept = 4
We know that;
The slope intercept form of an equation of line is,
⇒ y = mx + b
Where, 'm' is slope of the line and 'b' is y - intercept of the line.
Hence, The equation of line with a slope of -1.6 and a y-intercept of 4 in slope- intercept form is,
⇒ y = mx + b
⇒ y = - 1.6x + 4
Learn more about the equation of line visit:
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negative 12 minus negative 13
Answer:
jflsnfjclewndlsfjnenqwpcpoop
Step-by-step explanation:
Hehe
The area of a rectangle is 102 cm, if it's breadth is 6 cm find the length.
Need it ASAP
Step-by-step explanation:
A=102cm2
A=Lengthxbreadth
102=Lengthx6
Length=17 cm
this assignment is due tomorrow please help :(
Answer:9
Step-by-step explanation:
I think it’s 9 as the area of a parallelogram is A=bh. The height is 3 as well as the base so times them together equates to 9.
if you have a class with 32 students and 16 of them are boys how many girls are there in the class
Answer: if there are 32 students in the class and 16 are boys so the other half well be 16 girls. 16 + 16 = 32. Sooo the answer is 16 girls
Step-by-step explanation:
PLEASE HELP FASTT!!!!!!!!!!!!!!!!!!!!!!Determine whether each ratio is equivalent to 1/2,3/9, or 5/7.
Write the ratio in the correct box.
the quoitent of two numbers is negative . what must be true about tthe two numbers
What is the domain of this function?
-1>2 3>6 5>8
A (2, 6, 8)
B. (2, 6, 8,3, 5)
C. (-1,3, 5)
D. (3)
It's Letter C. 1 3 and 5
that's the domain
what is the solution to 2/3(9x-6)=4(x+2)+2
Answer:
7
Step-by-step explanation:
Which expression is equivalent to 1/8 - 3/8?
Answer:
2/16-6/16
Step-by-step explanation:
how many ways can 3 yearbooo posters out of a total of 6 posters be displayed across a wall?
Answer:
69
Step-by-step explanation:
Given that a baby is 8month and her elder sister is 4 years old, express their ages as a ratio
Answer:
11.10
Step-by-step explanation:
may be not sure about it
Answer:
1:6
Step-by-step explanation:
1 year = 12 months
4 year = 4 × 12 months
= 48 months
Baby = 8 months
Elder sister = 48 months
B : ES
8 : 48
÷8:÷8
1 : 6
In simplest form, what is the quotient of 1 = ?
Answer:
Do u mind reposting ur question-? I dont quite undersatnd what u're asking ;-;
Step-by-step explanation:
Sarah earned $36.00 mowing lawns. She saved 1/6 of her money. After saving, how much money does Sarah have left?
Subtract. Write your answer as a fraction in simplest form.
5/8 - (-7/8)= ???
helppppp nowwwwwww plsss
Answer:
c!
Step-by-step explanation:
good luck! :)
Please help with math homework!!
Answer:
y = 0.75x + 53.67
Step-by-step explanation:
Answer:
y=53.67+0.75x
Step-by-step explanation:
53.67 is the initial price upon paying to rent the car. 0.75 is for additional mile, so it is multiplying x in order for it to count for the mileage. Finally it is equivalent to Y because Y will be the final cost.
please help me and my mom can't figure it out at all
Answer:
simple
Step-by-step explanation:
p= 30
hahahaha asking how
ok let's go
that 90°is also 90°in those angles around it
for the 140
sum of angles in a straight line =180
180-140
that's 40
90+40 =130
then sum of angles in a triangle=180
therefore 180-130=50
MAGIC/WISDOM
hope it's helpful thank me later
what is the slope of y=45x
Answer:
45/1
Step-by-step explanation:
45x is the rate at which the line goes up
A large tank holds 1.9 x 10^7 gallons of oil. How much oil can be stored in 9 tanks. Write your answer in scientific notation.
Answer:
1.71 × 10^8 gallons
Step-by-step explanation:
1.9 × 10^7 = 19,000,000
19,000,000 × 9 = 171,000,000
171,000,000 in scientific notation is 1.71 × 10^8
2x + y + z = 9
-x-y +z = 1
3x - y +z=9
Answer:
603 hope this helps
Answer:
x = 2
y = 1
z = 4
Step-by-step explanation:
Step 1:
2x + y + z = 9
3x - y = z = 9
5x + 2z = 18 <-- add x and y
Step 2:
-x -y + z = 1
2x + y + z = 9
x + 2z = 10
Step 3:
-(x + 2z = 10) = -x - 2z = -10
5x + 2z = 18
-x - 2z = -10
4x = 8
x = 2
Step 4: solve for z
-x - 2z = -10 <-- Plug x
-(2) - 2z = -10
-2z = -8
z = 4
Step 5: solve for y
2x + y + z = 9
2(2) + y + 4 = 9
8 + y = 9
y = 1
Match the term to its meaning.
Answer:
Step-by-step explanation:
1. commission
2. percent
3. repeating decimal
4. terminating decimal
5. tip
Factored quadratic equation for (x + 10)(x -2)=0
Pleas help me find the answer and show the work to this question
Answer:
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 15[/tex]
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
In this case:
[tex]17^2 = x^2 + (2x- 1)^2[/tex]
Open Bracket
[tex]17^2 = x^2 + 4x^2- 2x-2x + 1[/tex]
[tex]17^2 = 5x^2 - 4x + 1[/tex]
[tex]289= 5x^2 - 4x + 1[/tex]
Collect Like Terms
[tex]5x^2 - 4x + 1 - 289 = 0[/tex]
[tex]5x^2 - 4x - 288 = 0[/tex]
Solving using quadratic formula:
[tex]x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
So:
[tex]x = 8[/tex] or [tex]x = -7.2[/tex]
Since, x can't be negative, then:
[tex]x = 8[/tex]
One of the leg is:
[tex]Leg\ 1 = x[/tex]
[tex]Leg\ 1 = 8[/tex]
[tex]Leg\ 2 = 2x - 1[/tex]
[tex]Leg\ 2 = 2*8 - 1[/tex]
[tex]Leg\ 2 = 16 - 1[/tex]
[tex]Leg\ 2 = 15[/tex]
The owner of a large fast food chain is considering whether to re-open the dining rooms of his restaurants now that it is legal in the state of Georgia. He is interested to know what percentage of his employees support the re-opening, so he decides to conduct a survey. (a) Which of the following plans would be more likely to produce a sample statistic very close to the true percentage who support re-opening? A simple random sample of 34 employees A simple random sample of 340 employees Both plans are equally likely to get this result, since they are both random samples. (b) He thinks it would be easier to sample employees by randomly selecting franchise locations (individual restaurants) and asking managers to administer surveys to all the workers at the selected restaurants, what kind of sampling method should he use? a) Cluster sample b) Systematic sample c) Convenience sample d) Stratified sample
Answer:
a) A simple random sample of 340 employees
b) a) Cluster sample
Step-by-step explanation:
a) Remember, the sample size of most research work is a factor to consider in other to determine if the data collected represents the true percentage of the entire population.
Hence, a small random sample of 34 employees will not give more precise information than a larger sample of 340 employees because the larger sample contains more representation of the population.
b) A cluster sample is best used in this case because it involves dividing the population into several clusters or groups, then the researcher randomly selects a particular cluster or group in other collect research data for analysis.
Whereas in this case, the randomly selected clusters are the different (individual restaurant) franchise locations.
Skyler has twice as many apples in her grocery bag as her
friends Macy and Janelle combined. Macy has 15 apples
in her bag. Skyler has 50 apples in her bag. How many
apples does Janelle have in her grocery bag?
The equation 2(x+15) = 50 models this situation. Which choice shows the
sequence of operations needed to solve this problem, using both arithmetic
and algebra?
WILL GIVE BRAINLIEST
Answer:
Skyler has 130 apples in her bag
Step-by-step explanation:
well first you have to add 15 and 50 and get 65 then you have to multiply 65 by two and get 130
please give brainliest
the correct answer is to
divide by 2:
2(x+15)/2 =50/2
(x+15)=25
subtract 15:
x+15-15=25-15
x=10
I’m going to continue using up all my points
if you want brainliest, answer at least one of these questions:
What is the most embarrassing thing you’ve done in your life?
or
What is your favorite animal? (If you don’t have one, say your favorite foods or color)
Answer:
My favorite color is purple (any shade of purple) My favorite animal is between birds and dogs. Have an amazing day!
On a factory floor, 65 out of every 140 toy robots is defective. What percent of the toy robots are defective? Round your answer to the nearest hundredth.
Answer:
65/140
as a percentage is 46.43
hundredth rounding
46.4
Step-by-step explanation:
Please help me I appreciate it
Answer:
m∠SRT = 33° ∵ m∠QRT = m∠SRT
Step-by-step explanation:
Given the diagram,
RT bisects ∠SRQ, and m∠QRT = 33°
RT bisecting ∠SRQ means RT will bisect ∠SRQ into two equal angles, which are:
m∠QRT = m∠SRT
as
m∠QRT = 33°
so
m∠SRT = 33° ∵ m∠QRT = m∠SRT