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.
What are 3 words that can be associated with positive numbers?
i will give u brainliest
Answer:
Quotient: 7
Remainder: around .16
Step-by-step explanation:
Answer:
quotient : 7 remainder:1
Step-by-step explanation:
43 / 6 = 7.17
7 x 6 = 42
43 - 42 = 1
hope that helps :)
what is the value of x
Answer:
2.5
Step-by-step explanation:
log8(32^1.5)=2.5
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
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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!!!
Evaluate 2a+7b if a = 5 and b = 3
Answer:
31
Step-by-step explanation:
2(5) + 7(3) =31
2x5 = 10
7x3 = 21
10+21 = 31
Answer:
The answer is 31
Step-by-step explanation:
Plug the numbers for the variables into the equation.
2×5+7×3
Multiply
10+21
Add
10+21 = 31
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.
Select the correct answer from each drop-down menu. Lisa specializes in baking lemon cupcakes. She bakes 3 dozen cupcakes every hour. The cost (in dollars) of making n cupcakes is given by the function C(n) = 60 + 0.45n. The function that models the number of cupcakes Lisa makes in h hours is n(h) = . The cost function in terms of hours, h, is given by . Lisa's cost for making cupcakes for 2 hours is .
Answer:
Step-by-step explanation:
from the question, we are told that Lisa bakes 3dozens cupcakes every hour, to know the amount she makes in h hours, we will use the equality postulate as shown;.
3 dozens = 1hour
n(h) = h hour
Cross multiply
n(h) × 1 = 3×h
n(h) = 3h
Hence the function that models the number of cupcakes Lisa makes in h hours is n(h) = 3h
To get the cost function in terms of hours, we will find the composite function C(n(h))
C(n(h)) = C(3h)
Given C(n) = 60 + 0.45n
C(3h) is derived by substituting n as 3h in the function as shown;
C(3h) = 60+0.45(3h)
C(3h) = 60+1.35h
Hence the cost function in terms of hours, h, is given by 60+1.35h
To get the cost for making cupcakes for 2 hours, we will substitute h = 2 into the expression C(h) = 60+1.35h
C(2) = 60+1.35(2)
C(2) = 60+2.70
C(2) = 62.70
Hence the cost for making cupcakes for 2 hours is $62.70
Answer:
The function that models the number of cupcakes Lisa makes in h hours is n(h) = 36h. The cost function in terms of hours, h, is given by 60 + 16.2h. Lisa's cost for making cupcakes for 2 hours is $92.40
.
Step-by-step explanation:
again my sisters overdue test someone pls just help I’m doing my math and art homework and can’t help her jggvgrcrvgb
Answer:
She should get $23.6 in change
Step-by-step explanation:
You add the two items she bought which makes up $89.94, then you subtract the discount of $13.50, which leaves you with 76.44 to pay. If you pay with a 100 dollar bill, you subtract 76.44 from 100 in order to find out how much change you recieve.
Answer:
Step-by-step explanation:
100-((39.95+49.99)-13.50)=
100-(89.94-13.50)=
100-76.44=
23.56
You have to add the amount she is paying for the total then subtract that by the discount. Then subtract how much she gave them by the cost to get the change!
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.
Solve h+p=7(k -4) for k.
Answer:
k= h/7 + p/7 +4
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.
which term can be combined with 3x? option 1 2xy option 2 2x^2 option 3 -5x option 4 -10
Answer:
3-5x
Step-by-step explanation:
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:
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
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
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:
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?
Triangle ADB is congruent to triangle ? Please HELP!!
Answer:
CBD
Step-by-step explanation:
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.
Dustin surveyed 50 students at his school about their music preferences. The results are shown in the table. There are a total of 722 students at Justin‘s school. Based on the survey results, which is the best estimate of the number of students who prefer hip-hop music?
Answer:240 thank me later -Amanda wlms
Step-by-step explanation:
Answer:
240
Step-by-step explanation:
Solve: Sin(11 pi/2 + x) = -1/2 for [Pi, 2Pi].
StartFraction 4 pi Over 3 EndFraction
StartFraction 5 pi Over 3 EndFraction
StartFraction 7 pi Over 6 EndFraction
StartFraction 11 pi Over 6 EndFraction
Answer: B
The answer above is correct. It would be 5pi/3.
Step-by-step explanation: Edge2021
I just got it right on my quiz.
The value of the x is equal to the 5pi/3.
The expression is
[tex]\sin \left(11\cdot \frac{\pi }{2}+x\right)=-\frac{1}{2},\:\pi \le \:x\le \:2\pi[/tex]
The value of the given expression.
What is the expression?
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
[tex]\sin \left(11\cdot \frac{\pi }{2}+x\right)=-\frac{1}{2},\:\pi \le \:x\le \:2\pi[/tex]
[tex]11\cdot \frac{\pi }{2}+x=\frac{7\pi }{6}+2\pi n,\:11\cdot \frac{\pi }{2}+x=\frac{11\pi }{6}+2\pi n[/tex]
[tex]x=2\pi n-\frac{13\pi }{3},\:x=2\pi n-\frac{11\pi }{3}[/tex]
[tex]x=\frac{5\pi }{3}[/tex]
Therefore, The value of the x is equal to the 5pi/3.
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How many halves are in 19 wholes?
Answer:
38
Step-by-step explanation:
Hope this helps!!
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.
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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
Can someone help Please??????
Answer:
the answer is C, 0
Answer:
C) 0
Step-by-step explanation:
7(x + 2) = 7x - 10
First, we multiply within the parenthesis
7x + 2 = 7x - 10
Add 10 to both sides of the equation
7x + 12 = 7x
Subtract 7x from both sides of the equation
12 = 0
Because the answer is 0, that means there are 0 solutions and the equation can not be solved.
I hope that this helps! :)
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.
whats the slope intercept form of y=3x-2
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