Answers:
a = 1
b = 14
c = 65
===========================================================
Explanation:
Let's focus on the root x = -7+4i
Add 7 to both sides, then square both sides. Then get everything to one side so 0 is on the other side.
x = -7+4i
x+7 = 4i
(x+7)^2 = (4i)^2
(x+7)^2 = 16i^2
(x+7)^2 = 16(-1)
(x+7)^2 = -16
(x+7)^2+16 = 0
If you were to follow those steps for the other root -7-4i, then you should get the same result. Solving (x+7)^2+16 = 0 leads to the two complex roots -7+4i and -7-4i.
Expand out that expression to get it into standard form
(x+7)^2+16
(x+7)(x+7)+16
x^2+7x+7x+49+16
x^2+14x+65
The equation is now in y = ax^2+bx+c form
a = 1
b = 14
c = 65
If you were to plug those a,b,c values into the quadratic formula, you'll find that it leads to the two given roots -7+4i and -7-4i.
Write the equation from the line whose slope and the point through which it passes are given. Express the equation in point-slope form. (8,-1) and slope m=-3
Answer:
y + 1 = 3(x - 8)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3 and (a, b ) = (8, - 1 ) , then
y - (- 1) = 3(x - 8) , that is
y + 1 = 3(x - 8)
Three consecutive integers add up to 30. Which integers are they?
Answer:
30 31 33 are the three integer consective
im having a mental breakdown can someone please just do this for me
Answer:
it only changes the magnitude.
for any general a let f(x) be =a|x| , a>0
so for any x say ±3 your function will throw out a×3.
What is an equivalent expression to 14x^2 + 4y^3 - 3x^2 - 5 + 2y^3
Answer:
It’s C :)
Step-by-step explanation:
The solution is Option C.
The value of the equation is simplified as A = 6y³ + 11x² - 5
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 14x² + 4y³ - 3x² - 5 + 2y³ be equation (1)
On simplifying the equation , we get
Adding the similar terms in the equation , we get
A = ( 4y³ + 2y³ ) + ( 14x² - 3x² ) - 5
Now , the value of A is
A = 6y³ + 11x² - 5
Therefore , the value of A is 6y³ + 11x² - 5
Hence , the equation is 6y³ + 11x² - 5
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on a coordinate plane, triangle a b c is shown. point a is at (negative 1, 1), point b is at (3, 2), and points c is at (negative 1, negative 1)if line segment bc is considered the base of triangle abc, what is the corresponding height of the triangle?
Answer:
The corresponding height of the triangle is [tex]1.2[/tex]
Step-by-step explanation:
We have[tex]\Delta ABC[/tex]
Here [tex]AD[/tex] is the height
We need to draw perpendicular from [tex]A[/tex] to [tex]BC[/tex]
The distance from the point [tex](m, n)[/tex] to the line [tex]A x+B y+C=0[/tex] is given by:
[tex]d=\frac{|A m+B n+C|}{\sqrt{A^{2}+B^{2}}}[/tex]
First let us calculate equation of [tex]BC[/tex]
[tex]y-y_1=m(x-x_1)\\\\y-2=\frac{2--1}{3--1} (x-3)\\\\y-2=\frac{3}{4} (x-3)\\\\4y-8=3x-9\\\\3x-4y=1[/tex]
Now distance from [tex](-1,1)[/tex] to [tex]3x-4y-1=0[/tex] is
[tex]d=\frac{|A m+B n+C|}{\sqrt{A^{2}+B^{2}}}\\\\=\frac{|3 \times1+-4\times-1-1|}{\sqrt{3^{2}+(-4)^{2}}}\\\\=\frac{6}{5}\\\\=1.2[/tex]
The staff at Aretha's Furniture built 60 chairs and stools in one day. It takes one person 3 hours to produce a chair and 2hours to build a stool. How many of each were made if the staff of 12 people worked 8 hours each? x+y= 60; 3x + 2y = 96 x + y = 96; 2x + 3y = 60 You can use a system of equations to find the answer. Let x = the number of chairs, and y = the number of stools. x + y = 60; 2x + 3y = 12 x+y= 60; 3x + 2y = 12 +
Answer:
Number of chairs = 24
Number of stools = 12
As about the question number 2, I think you should check whether the question you copied is correct are not.
Step-by-step explanation:
1. One person,
Three hours for a chair and two hours for a stool
Therefore, 12 people working for 8 hours;
Per person produced two chairs and one stool as 3+3+2=8 hours
12×2= 24 chairs and 12×1=12 stools.
Make y the subject of the formula
12m + 24y = 20
Answer: m=5/3-2y or if your solving for y y=-m/2+5/6
Step-by-step explanation:
Answer:
y = 5/6 - m/2
Step-by-step explanation:
4(3m + 6y) = 20
3m + 6y = 5
6y = 5 - 3m
y = 5/6 - 3m/6
y = 5/6 - m/2
1
The blue print of Vanessa's new home was drawn with a scale factor of 1 foot = 0.33 inch. The
actual length of the living room was to measure 12 feet. Determine the length of the living
room shown in the blueprint.
The length of the living room in the blue print is 3.96 inch
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
According to the given question
We have,
1foot = 0.33 inch
The actual length of the living room =12feet.
Therefore,
The length of the living room in the blue print = 12 × 0.33 = 3.96inch
Hence, the length of the living room in the blue print is 3.96 inch.
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I need help with A-G,I,L,N
I hope yall have a merry Christmas
Format of my answer:
[Problem letter] Parallel Lines
- Converse / Reason
!! I am not sure which / what converses you are using, but I gave the reasoning for it. If you see something similar, use the converses you know !!
[a] j & k
- If two lines intersected by a transversal form congruent alternate interior angles, then the lines are parallel
[b] m & n
- If angles are supplementary in this placement, the lines are parallel
[c] l & n
- If angles are equal when they are corresponding, the lines are parallel
[d] l & m
- If two angles that are congruent are vertical, the lines are parallel
[e] j & k
- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel
[f] l & n
- If angles are supplementary in this placement, the lines are parallel
[g] l & n
- If two angles that are congruent are vertical, the lines are parallel
[h] -------
[i] l & n
- If two angles that are congruent are vertical, the lines are parallel
[j] -------
[k] -------
[l] j & k
- If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel
[m] -------
[n] j & k
- If angles are supplementary in this placement, the lines are parallel
[o] -------
-> See attached for more information
Have a nice day! - hopefully these are mostly correct, been awhile since I've done this
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Help please
Pleasssssse
Answer:
a) Draw a line horizontally on 4 on the y axis
b)x=2,y=3
State the y-coordinate of the yintercept for the function below.
f(x) = 4x^3-12x^2-x+15
Answer:
15
Step-by-step explanation:
let y = f(x)
substitute x = 0
y = 4(0)^3-12(0)^2-(0)+15 = 15
Gravitational force acts on all object in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Answer:
[tex]\huge\color{pink}\boxed{\colorbox{black}{Answer♡}}[/tex]
The reason that a heavy body doesn't fall faster than a light body is because the greater gravitational force on the heavier body (its weight), acts on a correspondingly greater mass (inertia). The ratio of gravitational force to mass is the same for every body—hence all bodies in free fall accelerate equally.
hope helpful~
~Be Brainly!~ExhaustedZombieThe computer monitor to the right has a length of 44 inches and
a width of 38 inches. Find the length of the diagonal. Round your
answer to the nearest hundredth.
Answer:
58.14 inches
Step-by-step explanation:
Pitagoras:
Diagonal² = length² + width²
Diagonal² = 44² + 38²
Diagonal² = 1936 + 1444
Diagonal² = 3380
√Diagonal² = √3380
Diagonal = 58.137 = 58.14inches
Sally wants to buy themselves a beautiful, scrumptious, delightful cake but they don't know how money works. If Sally has $50.00, and the cake is $54.99, how much more do they need? literally just made this question off the top of my mind xD
Answer:
$4.99
Step-by-step explanation:
$54.99-$50.00=$4.99
Answer:
Step-by-step explanation:
cake: $54.99
sally money: $50.00
54.99-50= $4.99 lol
id like some help please!
im confused
Answer:
Angels D and G
Step-by-step explanation:
Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located "outside" the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles. Although in this case angels D and G dont have opposite angels so in this cade their is only 2 alternate exterior angels.
I hope this helps have a great day and happy holidays (｢•-•)｢
Answer:
∠D and ∠G
Step-by-step explanation:
Think about what alternate exterior angles are:
"Alternate" means on either side of each other"Exterior" means outside (the transversal BI).Putting these two elements together, we can clearly see the alternate exterior angles are ∠D and ∠G.
Write the equation of the line that passes through (0,5) and is perpendicular to the line x = 3.
Answer:
(0,5)x3=(15,5)
Step-by-step explanation:
A jar is filled with pennies, nickels, and dimes. The probability of picking a penny is
1
4
, and the probability of picking a dime is
1
3
. What is the probability of picking a nickel?
Answer:
1
3 maybe
Step-by-step explanation:
what is 12/3/5 simplified?
Answer:
1/4
Step-by-step explanation:
Divide both the numerator and denominator by the GCD 9 ÷ 9
36 ÷ 9
Reduced fraction: 1/4 Therefore, 9/36 simplified to lowest terms is 1/4.
How can probability be applied to decision making?
Answer:
ANSWER============================You can calculate the probability that an event will happen by dividing the number of ways that the event can happen by the number of total possibilities. Probability can help you to make better decisions, such as deciding whether or not to play a game where the outcome may not be immediately obvious.============================#CarryOnLearningAnswer: Using Probability to Increase the Odds of success
PLEASE HELP QUESTION IN PIC.
Answer:
21.8
Step-by-step explanation:
evaluate the expression when p = 4. p^2+5 no links pls
Answer:
21
Step-by-step explanation:
when p is 4
p² + 5 = 4² + 5
16 + 5 = 21
Which of the following expresses in sigma notation?
Answer:
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .
Simplify. Dividing radicals
Answer:
[tex]\frac{\sqrt[4]{15} }{16}[/tex]
Step-by-step explanation:
You cannot leave a radical in the denominator, so the first step is to get rid of it. The way you do that is by multiplying the radical in the denominator by itself over itself because anything over itself is equal to 1. So, for example in this problem:
[tex]\frac{\sqrt{15}}{\sqrt{16} } *\frac{\sqrt{16}}{\sqrt{16} }[/tex]
From here you multiply straight across. The numerator will be equal to [tex]\sqrt{240}[/tex] and the denominator will be 16 because any radical multiplied by itself cancels the radical out and just equals the number inside of the radical. The last step is to simplify the numerator. You do this by finding factors of 240 which are:
1 * 2402 * 1203 * 804 * 605 * 486 * 408 * 3010 * 2412 * 2015 * 16You want to use the greatest factor you have so you can break it down easier which in your case is (15 * 16). From here you simplify each of those numbers until you have a duplicate of something. The greatest factor of 15 is 3 * 5, so that won't simplify because there are no duplicate numbers. The greatest factor of 16 is 4 * 4 which means that it will simplify. When you are simplifying the duplicate (4) always goes outside of the radical and the non-duplicate (15) always goes on the inside of the radical. Your answer should look like this:
[tex]\frac{\sqrt[4]{15} }{16}[/tex]
Blair worked for 4 2/5 hours and earned $36.30. How much would she earn if she worked for 5 4/5 hours? Enter your answer in the box.
PLEASE HELP ASAPPPPP!!! I WILL GIVE BRAINLIEST AND 50 POINTS!!!
Answer:
$47.85
Step-by-step explanation:
4 2/5 in decimal form is 4.4
Using the equation hrs/money=x, 36.30/4.4=8.25
So, she gets $8.25 per hour
Then, 5 4/5 in decimal form is 5.8
So, 5.8*8.25=47.85
She gets $47.85 for working 5 4/5 hours
Answer:$47.85
Step-by-step explanation:
(Will give 1,000 points!) Look at the two 3s in this number:
89.033
Which of these statements is true? Choose all that apply.
A
The blue 3 on the left is 300 times the value of the orange 3 on the right.
B
The blue 3 on the left is 100 times the value of the orange 3 on the right.
C
The blue 3 on the left is 10 times the value of the orange 3 on the right.
D
The blue 3 on the left is equivalent to the orange 3 on the right.
E
The orange 3 on the right is 1/10 of the value of the blue 3 on the left.
(And yes there are multiple answers!)
The only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"
This question bothers on place values.
Given the decimal value 89.033, the place value of the blue 3 on the left is the hundredth place (1/100) while the place value of the orange 3 is in the thousandth place(1/1000).
We need to check which of the statement is correct.
For the first option, the blue 3 on the left is 300 times the value of the orange 3 on the right;
1/100 = 300(1/1000)1/100 = 3/10Since 0.01≠0.3, hence the first option is wrong
For the second option, the blue 3 on the left is 100 times the value of the orange 3 on the right;
1/100 = 100(1/1000)1/100 = 1/100.01≠0.1, hence the second option is wrong.
The blue 3 on the left is equivalent to the orange 3 on the right is also wrong since they are positioned in a different place
The orange 3 on the right is 1/10 of the value of the blue 3 on the left, is expressed as;
1/1000 = 1/10(1/100)0.001 = 0.001Hence the only true statement is "the orange 3 on the right is 1/10 of the value of the blue 3 on the left"
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A man owns a store. One week he sells 100 loaves of bread. If he sells twice as many loaves the next week, how many loaves did he sell in total
Each week, the price of oranges at the farmer's market increases by 20%.
The price of oranges this week is $4.50.
What was the price last week?
Answer:
3.6? I don't really know
12 for every 2 male birds in a bird cage there are 5 females. What is the ratio of the males to females
What's the answer to the picture I cant figure it out...
Answer:
(p.s area is [tex]a[/tex])
To find the area of a rectangular prism you multiply [tex]l*w*h[/tex]
So then we multiply [tex]4*2*3[/tex] to get 24 the answer is
[tex]a=24[/tex]
brainliest pls
If you walked for 5 minutes, what would the ratio of feet to minutes be? Use your steps to minutes ratio from Task 1 to determine a ratio of feet to minutes. Show your calculation.
Answer:
2:1 RATIO
Step-by-step explanation:
If you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
How did we get the value?To determine the ratio of feet to minutes, we can use the steps to minutes ratio from Task 1. Let's find the steps-to-feet ratio first:
Steps:Feet
4:10
6:15
12:30
30:40
Now, let's calculate the steps-to-feet ratio by finding the average of the steps-to-feet ratio from all the given data points:
Average Steps-to-Feet Ratio = [(10/4) + (15/6) + (30/12) + (40/30)] / 4
Average Steps-to-Feet Ratio = (2.5 + 2.5 + 2.5 + 1.333) / 4
Average Steps-to-Feet Ratio = 2.1665
Now, for the question at hand, if you walked for 5 minutes, the ratio of feet to minutes would be approximately 2.1665 feet per minute.
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