b^2 + 35 = −12b Solve each equation by factoring
I really need help with understanding this step by step, thank you. I am giving 40 points for this.
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.
Dude help me pleaseeeeeee
Answer: -25/42
Step-by-step explanation: For multiplying fractions, it’s multiplying numerator by numerator and denominator by denominator. 5 x 5 = 25 and 6 x 7 = 42 and then add the - since it’s negative. It can not simplify
Bobby bought the following items at the school store: 10 pencils for $0.21 each, 8 pens for $0.45 each, and 2 posters for $0.55 each. How much money did Bobby spend in all?
Group of answer choices
$5.70
$1.21
$4.70
$6.80
p−1=5p+3p−8
Anyone help. Its due at 11:59 pm :( please help
Answer:
p = 1
Step-by-step explanation:
p - 1 = 5p + 3p - 8(collect like terms)
p - 1 = 8p - 8(add 1 on each side)
p = 8p - 7(subtract 8p on each side)
-7p = -7 (divide by -7)
p = 1
Write a fraction that is equivalent to 3/4
PLEASE I WILL GIVE YOU BRAINLEIST
Answer:
6 / 8
Step-by-step explanation:
Just multiply by 2
Answer:
3/4=6/8=9/12=12/16 and so on
Step-by-step explanation:
Just use the multiples of 3/4
Pls mark me brainliest!!!
Triangle ADB is congruent to triangle ? Please HELP!!
Answer:
CBD
Step-by-step explanation:
Three scoops of whey powder contain 45 grams of protein. How many scoops of whey powder contain 135 grams of protein?
Please help ‼️
The answer is 405 because if you multiply 3 and 135 that would lead you to your answer.
Help pleaseI don’t understand
Answer:
Angle 3 is 65
Angle 8 is 115
Step-by-step explanation:
whats the rate of change?
A weather balloon is launched in Texas from an altitude of 300 feet above sea level. If the balloon is rising at a constant speed of 80 feet per minute, write an equation that can be used to find t, the time in minutes it will take for the balloon to reach an altitude of 10,500 feet?
Question 1 Please. I need help.
Answer:
74.22
Step-by-step explanation:
You are supposed to add 52.39+21.83 because of part whole postulate (PWP) So, now you get 74.22, which is your answer.
Determine the y-intercept of the
equation below. Write your answer as
an ordered pair.
5x + 8y = 40
sporting goods store is offering a 20% discount on shoes. Mariana also has a $5 off coupon that can be applied to her
purchase. She is planning to buy a pair of shoes that originally costs $89. Will the final price be lower if the discount is applied before the
coupon or if the coupon is applied before the discount? Justify your response
The final price be lower if the discount is applied before the coupon.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that sporting goods store is offering a 20% discount on shoes. Mariana also has a $5 off coupon that can be applied to her
purchase.
She is planning to buy a pair of shoes that originally costs = $89.
The discount price is the same either way.
Thus 20 percent of $89.00= 17.80$
Therefore, we have;
$89.00 - ($5.00 x $17.80) = $66.20
$89.00 - ($17.80 x $5.00) = $66.20
Learn more about multiplications;
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please help asap, i will give brainliest
Answer:
1) 110*, 2) 84*, 3) 80*
Step-by-step explanation:
These are intersected parallel lines (with only 1 intersecting line), so having missing angles in the questions 1 and 2 opposite from the shown angle is giving the answer away. However, on answer 3, it is on the same side, so for that angle you will need to subtract the angle of the intersecting line by 100* to get 80*. Check by adding the two. 100* + 80* = 180*. Hope this helps.
Modeling Task 1
A cell phone company charges a monthly rate of $14 and $0.25 a minute per call.
Judy's total cell phone bill is $50. How many minutes, m, was Judy charged for?
Make sure to define your variable, write an equation, solve the equation, and
write a sentence.
Answer:
144 minutes
Step-by-step explanation:
The equation will be 14 + 0.25x = 50
50 - 14 = 36
0.25x = 36
36/0.25 = 144 minutes
Write the income equation for a small business that
begins with $150 and grows by 20% each year. When
will the company's income be $300?
Answer:
in 4 years
Step-by-step explanation:
because you should find the 20% of 150
150×20=3000
3000÷100= 30
so 20% of 150 is 30
then you keep adding 30 to the results till you reach 300
The equation is 150+30x=300 and it takes 3 years for the company to earn $300.
Given that, a small business begins with $150 and grows by 20% each year.
We need to find when will the company's income by $300.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 20% of 150=30
Let x be the number of years.
So, f(x)=150+30x
⇒150+30x=300
⇒30x=150
⇒x=3
The equation is 150+30x=300 and it takes 3 years for the company to earn $300.
To learn more about the equations visit:
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What is the slope of a line perpendicular to the line graphed below?
Answer:
-3
Step-by-step explanation:
Original slope: 1/3
Perpendicular slopes are the negative reciprocals of the original slope.
What is the value of (-5)^4?
Answer:
-20
Step-by-step explanation:
Answer:
-625
Step-by-step explanation:
-5× -5 = 25
25 × 25= 625
What are 3 words that can be associated with positive numbers?
Which number produces a rational number when added to 0.5?
A. –1.73205081…
B. 1/4
C. 0.54732871…
D. √3
Answer:
Option B is correct 1/4.
Step-by-step explanation:
To find : Which number produces a rational number when added to 0.5?
Solution :
A rational number is defined as number written in simple fraction or in p/q form.
An irrational number is defined as number which cannot be written in p/q form.
We know that,
A rational number adding a rational number gives you a rational number.
A rational number adding an irrational number gives you a irrational number.
Now we take each option and check.
Option A : -1.73205081…
Number has no end and have infinite number of digits so it is irrational number.
No, this number not produce a rational number.
Option B : 1/4=0.25
Number is in form p/q so it is rational number.
Yes, this number produce a rational number.
0.25+0.5=0.75 a rational number.
Option C : 0.54732871…
Number has no end and have infinite number of digits so it is irrational number.
No, this number not produce a rational number.
Option D : \sqrt{3}
\sqrt{3} cannot be written in ratio so it is irrational number.
No, this number not produce a rational number.
If f(x) = 3x + 2, then find the value of x such that f(x) = -4.
Answer:
See Below
Step-by-step explanation:
Solve by substituting
-4 = 3x + 2
-2 -2
-6 = 3x
3x/3 = -6/3
x = -2
Answer:
x = -2
Step-by-step explanation:
So we are given the function f(x) = 3x + 2 and we are asked to find the value of x that makes f(x) = -4. To do this, we can replace f(x) with -4 in the given function and solve for x.
-4 = 3x + 2
Swap sides.
3x + 2 = -4
Subtract 2 from both sides.
3x = -6
Divide both sides by 3.
x = -2
So we have found that x = -2 when f(x) = -4. This means that when x = -2, f(x) = -4.
I hope you find my answer and explanation to be helpful. Happy studying.
A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled.
A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled.
A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled.
A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.
Answer:
i think option D
Step-by-step explanation:
Answer:the man above me
Step-by-step explanation:
Gina's family goes to a theme park. The family pays a $12 fee to park their car and buys admission tickets for all 5 family members. Her family pays a total of $132 . Which equation can be used to solve for t , the price of one admission ticket?
A.
5(12+t)=132
B.
5t+12=132
C.
5(12)+t=132
D.
5+12+t=132
Answer:
B
Step-by-step explanation:
5t + 12 = 132
We know the price of parking and we know what they paid in total. There are 5 members with the unknown price.
Answer:
B
Step-by-step explanation:
You're trying to find how much a ticket, which is t. you need 5 tickets for the family, plus the twelve dollar fee which is there anyways for the car, and it add up to 132. subtract 12 from 132 and you get 120. 120 divided by 5 is 24. so 24 dollars for a ticket, but the equation you would need is 5t+12=132
whats the slope intercept form of y=3x-2
Ten is no less then a number q multiplied by 6.
Answer:
10 > 6q
Step-by-step explanation:
Assuming you are asking what this word problem looks like as an equation, then it would be:
10 > 6q
What is the first step in solving the equation 3.5n+6.4= 42.5?
0 Add 6.4 to each side of the equation.
O Subtract 6.4 from each side of the equation.
O Multiply each side of the equation by 3.5.
O Divide each side of the equation by 6.4.
Answer add 6.4 to each side explanation:
what is the value of x
Answer:
2.5
Step-by-step explanation:
log8(32^1.5)=2.5
Solve h+p=7(k -4) for k.
Answer:
k= h/7 + p/7 +4
A yellowfin tuna weighs about 380 pounds. A bluefin tuna weighs 620 about pounds. If one fish of each species were caught per day, about how many more pounds of bluefin tuna than yellowfin tuna would be caught in a week? Solve the problem two different ways.
Answer:
1680 pounds
Step-by-step explanation:
Given that :
Weight of yellow fin tuna = 380 pounds
Weight of bluefin tuna = 620 pounds
If one fish of each species were caught per day
about how many more pounds of bluefin tuna than yellowfin tuna would be caught in a week?
Total pound of bluefin tuna caught in a week:
7 * 620 = 4340
Total pound of yellow tuna caught in a week:
7 * 380 = 2660
(4340 - 2660) = 1680 pounds
How many halves are in 19 wholes?
Answer:
38
Step-by-step explanation:
Hope this helps!!