Answer:
[tex]b=-5, -7[/tex]
Step-by-step explanation:
We have the equation [tex]b^2+35=-12b[/tex] and we want to solve it by factoring.
First, let's move all the stuff to one side so that the other side is 0. So, let's add [tex]12b[/tex] to both sides. This yields:
[tex]b^2+12b+35=0[/tex]
Let's review how to factor. If we have an equation in the following form:
[tex]ax^2+bx+c=0[/tex]
Where a, b, and c are the coefficients of the variable (in our example, our variable is b), then we must find two numbers, p and q, such that:
[tex]pq=ac \text{ (p times q equals a times c) and}\\p+q=b \text{ (p plus q equals b)}[/tex]
Our equation can be rewritten as:
[tex](1)b^2+(12)b+(35)=0[/tex]
So, our a is 1, b is 12, and c is 35.
Therefore, we need to find two numbers that when multiplied together yields a(c) = 1(35) = 35 and we added together yields b = 12.
From here, we just have to guess and check. We can start by listing all the factors of 35. There aren't in fact that many:
[tex]35: 1\text{ and } 35, 5\text{ and } 7[/tex]
1 + 35 is 36, not 12. However, 5 + 7 is indeed 12. So, our two numbers p and q are 5 and 7.
Now what we've found our two numbers, we substitute the b term for our two numbers. We have:
[tex]b^2+12b+35=0[/tex]
We will substitute 12b for 5b + 7b:
[tex]b^2+5b+7b+35=0[/tex]
From here, we factor by grouping. From the first two terms, factor out a b:
[tex]b(b+5)+7b+35=0[/tex]
And from the last two terms, factor out a 7:
[tex]b(b+5)+7(b+5)=0[/tex]
Now, notice that both terms have a [tex](b+5)[/tex]. So, by using grouping or the reverse of the distribute property, we can write:
[tex](b+7)(b+5)=0[/tex]
Notice that if we distribute the left term into the right, we get [tex]b(b+5)+7(b+5)=0[/tex], so our equation is indeed equivalent.
So now we. have:
[tex](b+7)(b+5)=0[/tex]
We can now use the Zero Product Property to acquire:
[tex]b+7=0\text{ or } b+5=0[/tex]
Solve for b for each case. Therefore, the solutions of our equation are:
[tex]b=-7\text{ or } b=-5[/tex]
Notes:
If we can't find two numbers p and q that satisfy our conditions, this means that the equation cannot be factored. So, we will use alternative methods to solve our equation.
Kelvin measured the distance from his door to the park. It is 1.5 miles. The distance from Kelvin’s house to the library is twice the distance from Kelvin’s door to the park. How far is it from Kelvin’s to the library?
Answer:
2.25
Step-by-step explanation:
1.5x1.5= 2.25
it is 1.5 mi from kelvins door to the park, it is 2.25 mi from kelvins house to the library.
hope this helps, let me know if you need more explaining
Answer:
3 miles
Step-by-step explanation:
1.5+1.5=3 miles
If Hector is 8 years old and Mary is 3 years old, how old will Mary be when Hector is 16? Can I use proportional reasoning in here
Answer:
Step-by-step explanation:
H=8
M=3
=>difference is 5 years
H=16
=>M=16+5=21
will be nice if you give me brainlies.Good luck!
Answer:
When he is 16 Mary will be 11
Step-by-step explanation:
First subtract 8-3 to see how much older hector is
You will get 5
Now subtract 16-5 to get 11
Can we use proportional reasoning?
NO!!!!!
Reasoning- did we subtract? Yes! You can’t find proportional reasoning if you subtracted or add
You earn $15.25 an hour. Your brother earns $10.25 an hour. You pay $30 a week for lunches, and your brother pays $15 a week. If both of you work the same number of hours in a week, which inequality can be used to find x, the number of hours you will have to work so that the amount of money you have is greater than the amount your brother has after you both pay for lunch?
Answer:
15.25+15.25=20.50+15.25=35.75.
3 hours will give you $35.75
Step-by-step explanation: All you have to do is add till you have enough
Need help on this please Help. I would really appreciate it :)
Answer:
i am not sure but according to me ans is d
Step-by-step explanation:
Ax+By=C
Ax=C-By
A=C-By/x
wendy already spent $10 on a necklace, and each additional charm is priced at $2 each. write a function that shows the relationship between the number of charms purchased, x and the total cost, f( x)
Answer:
f(x) = 2x + 10
Step-by-step explanation:
The amount of charms represents x, or the variable. The price of the charm is represented by 2, or the slope. The necklace is the constant, represented by 10.
7m-3n-4m-7n+3
can someone tell me what is the answer please
Answer:
7m-3n-4m-7n+3 = 3m-10n+3
7-4=3
-3-7=-10
Elisha is paid $280 a week plus commission of $15 per sale. This week, she 2oints wants to earn at least $635. Which inequality represents this inequality??
Answer:
$280 + $15x ≥ $635
Step-by-step explanation
weekly pay (280) + commision per sale (15x) ≥ goal (635)
What percentage of 80 is 67
Answer:
83.75%
Step-by-step explanation:
67/80 = 83.75%
A line passes through the points (–3, –4) and (6, 2). A coordinate plane. What is the x-intercept of this line? –3 –2 2 3
Answer:
D
Step-by-step explanation:
I got it on edge
Answer:3
Step-by-step explanation:
just did it
ANSWER NEEDED ASAP
In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles. angles congruent to ∠1 angles congruent to ∠2 angles congruent to ∠7 angles congruent to ∠6 ∠3,∠7,∠6 arrowRight ∠3,∠7,∠2 arrowRight ∠4,∠8,∠5 arrowRight ∠3,∠6,∠2 arrowRight
Answer:
angles 3, 7, and 6 are congruent to angle 2
angles 3, 7, and 2 are congruent to angle 6
angles 4, 8, and 5 are congruent to angle 1
angles 3, 6, and 2 are congruent to angle 7
Please mark Brainliest
Answer:
∠3,∠7,∠2 congrent to 6
∠3,∠7,∠6 congruent to 2
∠4,∠8,∠5 congruent to 1
∠3,∠6,∠2 congruent to 7
Step-by-step explanation:
To make banana bread, Colin uses 3/4of a cup of brown sugar for every 2 cups of flour. How much brown sugar should Colin use to make a small batch with only 1 cup of flour?
Answer:
The answer is 3/8
Step-by-step explanation:
Set up a table to get one you divide 2 by 2 so then you have to divide 3/4 by 2 and that gets you 3/8
Write the Equation in standard form The line which passes through (1,-4) and (-1, 6)
Is the function g(x)= -2x^2 -2x+7 linear or nonlinear?
HELPP plsss
Answer:
Is non-linear
Step-by-step explanation:
It is a quadratic function
A certain video game console uses 154 watt-hours of energy each hour.
The console used 276 hours last year.
How many watt-hours of energy did the console use?
Use any method to solve this problem. You must show all your work.
Then, explain your reasoning and the steps you took to solve the problem.
Answer:
42,504 watts
Step-by-step explanation:
154x276hours=42,504watts
Answer:
42504
Step-by-step explanation:
As it uses 154 watt-hours per hour, in 276 hours, it would use 42504 as we would multiply the energy usage by the amount of hours used:
154 watt-hours = 1 hour
276 hours = 42504 watt-hours
276*154 = 42504
Please HLEP me
I’ll give u brainlist ♥️
Answer:
9. 1:210. x = 1011. x = 1212. A = 8789 ft²Step-by-step explanation:
see attached image
HAAAAALP PLEASE BRAINLIEST PLEASE TRY
Answer:
D.
Step-by-step explanation:
What is the distance between
(2,3) (8,9)
Answer:
Step-by-step explanation:
in a class of 30 students 60% said they walk to school
Write a proportion that you could use
to determine the number of students in
the class who walk to school.
moan and groan a lot ghjiouygbnjkh
Madyson goes to a restaurant with her best friend, Taylor. The two girls order a meal, Madyson's meal costs $23.75 and Taylor's meal is $15.00. They want to leave a tip of 15% how much money would it cost altogether without tax?
Answer:30.75
$23.75 +$15.00=30.75
5+3=6
21=3
Francisco and Stu were working on simplifying the following polynomial: 4x(2x-3)-5(3x-4). Write the equivalent expression that Francisco and Stu found for the polynomial in standard form?
Answer: 4x + 3x + 2x - 4 - 3
Step-by-step explanation: The numbers that have an X are considered major than normal numbers , when three numbers have the same X you put first the one that is major . Hope this helped.
The equivalent expression that Francisco and Stu found for the polynomial in standard form should be considered as the 4x + 3x + 2x - 4 - 3.
Calculation of the equivalent expression:Since the polynomial is 4x(2x-3)-5(3x-4)
Here the number that should have an X that should be relevant majorly as compared to the normal numbers so here the three numbers should be the similar also X we put first as major.
Therefore, The equivalent expression that Francisco and Stu found for the polynomial in standard form should be considered as the 4x + 3x + 2x - 4 - 3.
Learn more about an expression here: https://brainly.com/question/13424191
a six pack of soda is on sale
Answer:
that is not complete you would need the starting price and the percentage
hope that helps good luck
Answer:
what's the question?
Step-by-step explanation:
i dont know cz u didnt put the question n only a lil bit of information
i need HELP!
Model the following situation with an equation or inequality statement.
The quotient of forty-nine and a number is greater than or equal to seven.
49 ÷ x ≥ 7
hope this helps! :):)
transposing method
+ 21 = 5
how to do ?
[tex]x + 21 = 5[/tex]
[tex]x = 5 - 21[/tex]
[tex]\color{hotpink}x = ( - 16)[/tex]
Let us check whether or not we have found out the correct value of x , by placing -16 in the place of x :-
[tex] - 16 + 21 = 5[/tex]
[tex] 5=5[/tex]
[tex]\color{hotpink}LHS = RHS [/tex]
As the left hand side of the equation is equivalent to the right hand side of the equation, we can conclude that we have found out the correct value of x .
Therefore , the value of :-
[tex]\color{hotpink}x \color{olive}=\color{hotpink} ( - 16)[/tex]
Use deductive reasoning to show that the two triangles are congruent. given that fab is congruent to ged and c is the midpoint of ae prove that abc is congruent to edc
Answer:
ΔABC is congruent to ΔEDC by the Angle-Side-Angle congruency rule
Step-by-step explanation:
The
Statement [tex]{}[/tex] Reason
∠FAB ≅ ∠GED [tex]{}[/tex] Given
C = Midpoint of [tex]\overline {AE}[/tex] [tex]{}[/tex] Given
∠BAC and ∠FAB are supplementary Angles on a straight line
∠DEC and ∠GED are supplementary Angles on a straight line
∠BAC ≅ ∠DEC [tex]{}[/tex] Transitive property
[tex]\overline {AC}[/tex] ≅ [tex]\overline {CE}[/tex] [tex]{}[/tex] Definition of midpoint
ΔABC ≅ ΔEDC [tex]{}[/tex] ASA congruency rule
Where two angles and an included side of one triangle is congruent to the corresponding two angles and an included side of another triangle, both triangles are congruent. [tex]{}[/tex]
Macy estimated a product to be 800. The actual product is 768. Her estimate was an
A. overestimate
B. underestimate
Answer:
Overestimate
Step-by-step explanation:
it would be an underestimate if the number was lower than the actual number but since its larger than it is an overestimation.
hope this helps
what is 5 divided 1/3
Answer:
15
Step-by-step explanation:
basic math.
Answer:
its 15 i believe
Step-by-step explanation:
What is the solution for the equation 6x - 8 = 4x? x =
Answer:
x = 4
Step-by-step explanation:
6x - 8 = 4x
subtract 4x from both sides of the equation
6x - 4x -8 = 4x - 4x
2x - 8 = 0
add 8 to both sides of the equation
2x - 8 + 8 = 0 + 8
2x = 8
divide both sides of the equation by 2
2x/2 = 8/2
x = 4
Answer:
x = 4.
Step-by-step explanation:
6x - 8 = 4x
6x - 4x - 8 = 0
6x - 4x = 8
2x = 8
x = 4.
Solve: sqrt(x+9) = x-3
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[tex] \sqrt{x + 9} = x - 3[/tex]
Sides gets power 2
[tex] ({ \sqrt{x + 9} })^{2} = ( {x - 3})^{2} [/tex]
[tex] |x + 9| = {x}^{2} - 6x + 9 [/tex]
_________________________________
[tex]x + 9 = {x}^{2} - 6x + 9[/tex]
Subtract sides 9
[tex]x + 9 - 9 = {x}^{2} - 6x + 9 - 9[/tex]
[tex]x = {x}^{2} - 6x[/tex]
Subtract sides x
[tex]x - x = {x}^{2} - 6x - x[/tex]
[tex] {x}^{2} - 7x = 0[/tex]
[tex]x(x - 7) = 0[/tex]
[tex]x = 0[/tex]
OR
[tex]x - 7 = 0[/tex]
[tex] x = 7[/tex]
_________________________________
[tex]x + 9 = - ( {x}^{2} - 6x + 9)[/tex]
[tex]x + 9 = - {x}^{2} + 6x - 9[/tex]
Subtract sides 9
[tex]x + 9 - 9 = - {x}^{2} + 6x - 9 - 9 \\ [/tex]
[tex]x = - {x}^{2} + 6x - 18 [/tex]
Subtract sides x
[tex]x - x = - {x}^{2} + 6x - 18 - x [/tex]
[tex] - {x}^{2} + 5x - 18 = 0[/tex]
Multiply sides by -1
[tex] {x}^{2} - 5x + 18 = 0 [/tex]
[tex]x = No \: \: solution[/tex]
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CHECK the roots :
[tex]x = 0[/tex]
[tex] \sqrt{0 + 9} ≠0 - 3[/tex]
[tex] \sqrt{9} ≠ - 3[/tex]
[tex]3≠ - 3[/tex]
Thus (( x = 0 )) is unacceptable.
+++++++++++++++++++++++++++++++++++++++
[tex]x = 7[/tex]
[tex] \sqrt{7 + 9} = 7 - 3[/tex]
[tex] \sqrt{16} = 4[/tex]
[tex]4 = 4[/tex]
Thus (( x = 7 )) is the only solution for x.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Done...
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a) Simplify
7(x - 2)2
7X = 2
Please
Answer:
49 x2 + 28 x + 4
Step-by-step explanation:
someone please answer ASAP