When 21 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
Ok if I directly write the equation it will become difficult to understand , so I am dividing into small parts. :)
[tex] \\ \\ [/tex]
Let :-
number be x.
[tex] \\ [/tex]
Part 1 :-Statement :-
21 is subtracted from the square of a number.
x² ← square of number
Equation :-
x² - 21
[tex] \\ \\ [/tex]
Part 2 :-Statement :- the result is 4 times the number.
4 times a number means 4 × x = 4x.
Equation :-
x² - 21 = 4x
[tex] \\ \\ [/tex]
Part 3 :-So we got our equation i.e x² - 21 = 4x , now we can finally find negetive value of x.
→x² - 21 = 4x
→x² -21 - 4x = 0
→x² - 4x - 21 = 0
→x² + 3x - 7x - 21 = 0
→x(x + 3) - 7x - 21 = 0
→x(x+3) - 7(x + 3) = 0
→(x - 7) (x + 3) = 0
Comparing:-
x - 7 = 0x = 7 ← possitive valuex + 3 = 0x = - 3 ←negetive value[tex] \\ [/tex]
Required answer :-
[tex]\boxed{\pmb{\sf -3}}[/tex]
Grace had a maturity value of $6,682.50 on an original investment of $6,000. She earned 6.5% annual simple interest. What was the duration of Grace’s investment?
Answer:
A = p(1 + rt)
Step-by-step explanation:
6682.50 = 6000(1 + 0.065t)
Find the 5th term in the sequence a,= 8-2(n-1)
Answer:
0
Step-by-step explanation:
a₅ = 8 - 2(5 - 1) = 8 - 2(4) = 0
2. Vince is a member of a card club. He pays a fixed fee of $55 annually
He must pay $9 for every game he attends. He attended 12 games this year.
What is the total amount that he paid this year?
The equation computed shows that the total amount that Vince paid this year is $263.
How to solve an equation?From the information given, Vince pays a fixed fee of $55 annually and must pay $9 for every game he attends.
The equation to solve the question will be:
= 155 + 9x
= 155 + 9(12)
= 155 + 108
= $263
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(18) What is the equation for a line perpendicular to the line described by the equation -3x + 12y – 7 = 0?
Answer:
Two lines are perpendicular if the product of their slopes equals -1.
In general form, this means that you reverse the coefficients of x and y and negate one of the two.
So the general form of this perpendicular line becomes: 12x + 3y + C = 0, or simplified: 4x + y + C’ = 0.
Now fill in the desired point to find C’: 4*(-2)+5+C’=0 so C’= 3.
The general form of the line becomes 4x + y + 3 = 0
Hope it helps!!!!!!Brainliest pls!!!!!!!MATH QUESTION SCREEN SHOT DOWN BELOW BRAINLIEST!
Answer:
its b bc im smart
Step-by-step explanation:
Answer:
The actual correct answer to this is A
Step-by-step explanation:
Direction: Opens Up
Vertex:
(1,−2)
Focus:
(1,−7/4)
Axis of Symmetry:
x=1
Directrix:
y=−9/4
Hope this helps mark brainliest please :)
Unit 3 - Task 3 - (10 points)
Your job is as an administrative assistant for factory operations for a company producing
Whatchamacallits. Your boss hands you the production information for the factory's
production of Whatchamacallits: 3 Whatchas in the first hour, 7 total after hour 2, 11
total after 3 hours and 15 after 4 hours. You are tasked to produce an equation that
models the number of Whatchas produced given the hours worked, and to find the
predicted number of Whatchas produced if the factory can run for 50 hour
uninterrupted.
Find an explicit formula that models the production for the nth term of the sequence
and use the equation to find the 50th term in the sequence. Show your reasoning for
the equation.
The 50th term in the sequence is 199
Arithmetic sequence
The nth term of an arithmetic sequence is expressed as:
Tn = a+ (n - 1)d
where:
a is the first termn is the number of termsd is the common differenceThe sequence formed by the amount of Whatchamacallits produced as;
3, 7, 11, 15...
a = 3
d = 11-7 = 7-3 = 4
Substitute
Tn = 3 + (n-1) * 4
Tn = 3 + 4n -4
Tn = 4n - 1
Hence the explicit formula that models the production for the nth term of the sequence is Tn = 4n - 1
If n = 50
T50 = 4(50) - 1
T50 = 199
Hence the 50th term in the sequence is 199
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Please help!!!!!!!!!!!!!!!!!!!
Answer:
54 cm²
Step-by-step explanation:
The net of the 3 cm cube has 6 squares, each of which is 3 cm on a side. The area of each is (3 cm)² = 9 cm², so the total area is ...
6×9 cm² = 54 cm²
If y=16 when x=4 find y when x=6
Step-by-step explanation:
Hi! An easy way to find an answer to questions like this is to do a table
y=16 : x=4
Now, add up X and Y together until X reaches 6
y=16 x=4
y=17 x=5
y=18 x=6
As you can see, when x is 6, y is 18.
Hope this helps!
If I have 53 shirts and have to get 100 shirts in 37 days, how many shirts do I have to get in less 37 day?
Answer:
67
Step-by-step explanation:
Total shirts = 53
Have to get = 100
Remaining shirts:
= 100 - 53
= 67
Find the GCF of the terms of each polynomial. 108f to the third power minus 54
Answer:
GCF is the Greatest Common Factor
I this Process you need to find HCF (Highest Common Factor) and Write the Common Number which is Greater among all.
choose the sentence that complete the fact family like 56÷7=8 7×8=56 56÷8=7 is it a 8×7=56 b 56×1=56 c 1×56=56 d 2×28=36 is it abc or d
Answer:
A
Step-by-step explanation:
Flip the previous answers around and you will get it right!!
Have an amazing day!!
PLEASE RATE AND MARK BRAINLIEST!!
Answer:
A) 8 x 7 = 56
Step-by-step explanation:
Let's look at the information we have.
This is the part of the family we are given:
56 ÷ 7 = 8
7 x 8 = 56
56 ÷ 8 = 7
We can see that we have one equation that's multiplying, but two equations that are dividing.
That means we probably need another equation with multiplying.
For the division equations, we have one with the 7 in front of the 8, and one with the 8 in front of the 7.
That means we should have the same for the multiplication ones.
We have one with 7 x 8, so we should have another with 8 in front of the 7
The answer is A.
8 x 7 = 56
what is the most important thing in life
Answer: yourself
Step-by-step explanation:
because there is nothing more important than you
Dani wants to spend less than $25 on a birthday present for her friend. If she buys a necklace for $9.50, how many pairs of earrings, e, can she buy for $3.75 each without exceeding her budget? Enter your answer in the box.
Answer:
4
Step-by-step explanation:
Since it costs $3.75 for every earring, multiply e by 3.75 like this: 3.75e
Add 9.5 on top of that since Dani already bought the necklace for $9.50
3.75e + 9.5
This sum has to be less than or equal to 25 because the budget is $25
3.75e + 9.5 ≤ 25
To find e subtract 9.5 from both sides
3.75e + 9.5 ≤ 25
- 9.5 - 9.5
3.75e ≤ 15.5
Divide both sides by 3.75
3.75e/3.75 = 15.5/3.75 = 4.133...
You can't buy 0.133 of an earring, so the max amount of earrings she can buy is 4.
If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then P(X⏐Y) =
Using conditional probability, it is found that P(X⏐Y) = 0.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, we have that X and Y are mutually exclusive events, hence [tex]P(X \cap Y) = 0[/tex], hence:
[tex]P(X|Y) = \frac{P(X \cap Y)}{P(Y)} = \frac{0}{0.32} = 0[/tex]
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NEED HELP ASAP!! Which expressions are equivalent to the one below? Check all that apply.
21x/7x
The equivalent expressions [tex]$\frac{21^x}{7^x}[/tex] is [tex]$3^{x}$$[/tex].
What is an equivalent expression?Equivalent expressions exist as expressions that work exactly even though they look different. If two algebraic expressions exist as equivalent, then the two expressions contain the exact value when we plug in the same values for the variables.
Given: [tex]$\frac{21^x}{7^x}[/tex]
Factor [tex]$21^{x} = 7^{x} \cdot 3^{x}$[/tex]
[tex]$=\frac{7^{x} \cdot 3^{x}}{7^{x}}$$[/tex]
Cancel the common factor: [tex]$7^{x}$[/tex]
[tex]$=3^{x}$$[/tex]
Therefore, the correct answer is option B. [tex]$3^{x}$$[/tex].
To learn more about equivalent expressions
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27. The diagonals of a rectangle have lengths AC = 4 + 2x and BD = 6x - 20. Find the value of x
Answer:
6
Step-by-step explanation:
Diagonals of a rectangle are congruent
4 + 2x = 6x -20 Add 20 both sides. Subtract 2x both sides
24 = 4x
x = 6
here a subtraction problem that has been solved incorrectly what is the right way 74-25=59
Answer:
Answer:
the equation is wrong
Step-by-step explanation:
=> 74-25=59
since 74 - 25 equals to 59 in order to find the addition sentence that will check the subtraction problem is true and 59 and 3/5 or you can add add 59 and 25 to check if the problem was solved correctly
=> 59+25
add 59 to 25
=> 84
this means the question is wrong
Joseph bought a can in the shape of a cylinder. He wanted to paint the outside of the can but not the top and bottom. The can has a radius of 5 inches and is 10 inches tall. What is the lateral surface area of the can? 314.2 in2 157.1 in2 212.5 in2 471.3 in2
The shape of the can is cylindrical, by employing the formula for lateral surface area and plugin in our data the answer was gotten as
14.2 square inches
Mensuration of solids (Cylinder)Given Data
Radius of can = 5 inches
Height of can = 10 inches
We know that the expression for the lateral surface area of a cylinder is given as
Lateral Surface area = 2πrh
Substitute our given Data
Lateral Surface area = 2*3.142*5*10
Lateral Surface area = 314.2 square inches
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How many 1/12 parts are in 9/12
Answer:
Nine
Step-by-step explanation:
Given the following question:
12/12 = 12 parts or 1 whole unit
1/12 = 1 part of that unit
9/12 = 9 parts of that unit
If 12 parts are needed to create one whole unit or 12/12, that means they're 9, 1/12 parts in the fraction 9/12.
Your answer is "nine."
Hope this helps.
helppp!
a. box 1: always, sometimes , never / box 2: remain ,do not remain
b. box 1: always, sometimes , never/ box 2: always, sometimes , never
c. box 1 : always, sometimes , never/ box 2: remain, not remain/ box 3: remain, not remain
d. box 1 : awlays, sometimes, never/ box 2 : an equal distance, different distance/ box 3 : some, all, no
e. box 1 : awlays, sometimes, never/ box 2 : would, would not / box 3 : all, no.
Answer:
a. always, remain
b. always, remain
c. never, not remain, not remain
d. always, an equal distance, all
e. never, would not, all
Step-by-step explanation:
They are all correct, hope this helps -w-
How many different license plates are possible if each plate contains a group of 6 letters and/or numbers?
Assume the letters can only be uppercase letters.
Answer:
click the image
Step-by-step explanation:
hope it's helpful
The equation 22.5 + x = 42.3 can be used to find the measure of
Answer:
x = 21.8
Step-by-step explanation:
x = 42.3 - 22.5
19. Which statement describes the value of the expression below?
57 X1/6
Answer:
9/1/2
you multiply the exact form and decimal form
Brainliest if correct
Answer:
[tex]24w^3 - 6 + 36y^2[/tex]
Step-by-step explanation:
[tex]-6(-4w^3+1-6y^2)\\\\-6(-4w^3) + -6(1) + -6(-6y^2)\\\\24w^3+-6+36y^2\\\\24w^3-6+36y^2[/tex]
Hope this helps!
24w^3 - 6 +36y^2 is it
Step-by-step explanation:
Expand by distributing terms.
-(-24{w}^{3}+6-36{y}^{2})
−(−24w
3
+6−36y
2
)
2 Remove parentheses.
24{w}^{3}-6+36{y}^{2}
24w
3
−6+36y
2
HELP
Tickets for a dance recital cost $16 for adults and $12 for children. The dance company sold 340 tickets, and the total
receipts were $4,800. How many adult tickets and how many child tickets were sold?
Answer:
adult tickets: 180
child tickets: 160
Step-by-step explanation:
adult tickets =x
child tickets =y
1. create a function
x+y=340
16x + 12y = 4800
2. solve
3. x = 180, y = 160 which also means 180 adult tickets were sold and 160 child tickets were sold
someone pls help i need help with my math question
Answer:
21 units
Step-by-step explanation:
select the correct word form for 444,404 a four hundred forty four thousand four hundred zero tens four b four hundred forty four thousand four hundred four c four hundred forty four thousand and four hundred four
Answer:
is four hundred forty-four thousand four hundred four
Step-by-step explanation:
you need to know the first 4 in 444,404 is in the hundred thousands. then forty thousand, then thousands, then hundreds and lastly four. ;-;7
The expression (x-y)(x2+xy+y2) is equivalent to which of the following?
A. X2-y2
B. X3-y3
C. X3-xy2
D.x3-x2y+y2
Answer:
x^3-y^3
Step-by-step explanation:
(x-y)(x^2+xy+y^2)
Multiply the terms,
x^3 + x^2y + xy^2- x^2y - xy^2 - y^3
Simplify the terms,
x^3 - y^3
This is also the formula for difference of two cubes.
1x -8 < 2x + 1
What is the largest integer value that makes this inequality true
Answer:
The largest integer value that makes the inequality true is 9.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
1x - 8 < 2x + 1
Step 2: Solve for x
Simplify: x - 8 < 2x + 1[Subtraction Property of Equality] Subtract x on both sides: -8 < x + 1[Subtraction Property of Equality] Subtract 1 on both sides: -8 < xRewrite: x > -8∴ we see that any number x greater than -8 would work as a solution to the inequality. That would mean the next largest integer, 9, would be our answer.
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Topic: Algebra I