Answer:
The complete square of the given quadratic equation
( x - 10)² = 67
The solution of the quadratic equation
x = 18.2 and x = 1.8
Step-by-step explanation:
Step(i):-
Given that the quadratic equation
x² - 20 x +33 =0
x² - 2(10) x +(10)²-(10)²+ 33 =0
By using (a-b)² = a² -2ab + b²
( x - 10)² -100 +33 =0
( x - 10)² - 67 =0
( x - 10)² = 67
Step(ii):-
The complete square (x - 10)² = 67
x -10 = ±√67
x -10 = ± 8.1853
x -10 = 8.2 and x -10 = -8.2
x = 10+8.2 and x = 10 -8.2
x = 18.2 and x = 1.8
Which expression is equivalent to 1/2b -15?
A. -1/2 (b + 30)
B. -1/2 (b - 30)
C. 1/2 (b - 30)
D. 1/2 (b + 30)
The expression 1/2b -15 is equivalent to, 1/2(b-30), So option C is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression, 1/2b -15
The expressions are equivalent = ?
So now, we can take 1/2 common from the expressions
⇒ 1/2b -15(2/2)
⇒ 1/2(b -15×2)
⇒ 1/2(b - 30)
Hence, the equivalent expression is, 1/2(b - 30)
To know more about Expressions check:
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Charmaine has 17 cars available to rent. Let C be the number of cars she would have left after renting R of them.
Answer:
C = 17 - R
Step-by-step explanation:
In this scenario, 17 cars would be the initial starting point. While C would be the final number of cars, meaning that our equation would have to equal C. If she rents R number of cars then this number is being subtracted from the initial number of cars because Charmaine would no longer have them in his/her possession. Therefore, it is being subtracted. Using this information we can create the following equation.
C = 17 - R
helpppp meeee plz...
Answer:
3 coefficient po
Step-by-step explanation:
sana maka tulong
At her most recent race, Sue finished in 272 minutes. That is 15% less time than the previous race. What was her time in the previous race?
Answer:
320 minutes was her time on the previous race
Step-by-step explanation:
Let the time spent on the previous race be x minutes.
Given that at her most recent race, Sue finished in 272 minutes which is 15% less time than the previous race then
x - 15% * x = 272
x - 0.15x = 272
0.85x = 272
x = 272/0.85
x = 320 minutes
What additional information would you need to prove
Answer:
A
Step-by-step explanation:
We use the Hypotenuse Leg Theorem
When we know the hypotenuse and a leg of a triangle.
We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.
Decide if the ansewer to 7/5x11 is less than greater than or equal to 11. A.greater than B.less than C.equal to
Answer:
The answer to 7/5x11 is 15.4, so A. Greater than.
Step-by-step explanation:
7/5= 1.4, 1.4x11=15.4.
HELP I NEED HELP ASAP
Answer:
C
Step-by-step explanation:
Answer:
exponential;increase
Step-by-step explanation:
answer is C
What is the slope-intercept equation for the
graph shown below?
A. y = 1/2x - 1
B. y = -1/2x - 1
C. y = -1/2 + 1
D. y = 2x - 1
2/3z=-6
Help please!!
Answer:
z = -9
Step-by-step explanation:
Solve the inequality.
Step-by-step explanation:
subtract the value by placing it in the right side and multiply with 4.
[tex]\sqrt{2x-3} =5[/tex]
f(x) = 4/9x + 7
linear or nonlinear?
Answer:
linear. :)
Step-by-step explanation:
Answer:
It depends on what you meant. See below.
Step-by-step explanation:
What you wrote means this:
[tex] f(x) = \dfrac{4}{9}x + 7 [/tex]
This is linear.
If you meant this
[tex] f(x) = \dfrac{4}{9x} + 7 [/tex]
or this
[tex] f(x) = \dfrac{4}{9x + 7} [/tex]
then it's non-linear.
An x in the denominator makes a function non-linear.
‘Find the value and figure of B’
Answer:
b = 12 in
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + b^2 = c^2
b^2 + 9^2 = 15^2
b^2 = 225 - 81
b^2 = 144
b = 12
Answer: b = 12 in
Back Next
Check
Question 1
Indicate the answer choice that best completes the statement or answers the que
Solve s 3. Graph the solution on a number line.
Ву
+ +
0 1 2 3 4 5 6 7 8 9
-1
Oa
十一
0 1 2 3 4 5 6 7 8 9
Ob.
+
0 1 2 3 4 5 6 7 8 9
Ос.
0 1 2 3 4 5 6 7 8 9
Od
Answer:
C
Step-by-step explanation:
✔️First, solve for r:
r/2 ≤ 3
Multiply both sides by 2
r/2 × 2 ≤ 3 × 2
r ≤ 6
This implies that possible value of r is equal to 6 or less than 6.
Graphing this on a number line, the line with a shaded circle, indicating that 6 is included, starts at 6 and points to the left.
This indicates that value of r ranges from 6 and below.
The graph is C.
which of the given values will make the inequality n-93>175 true?
n=82
n=105
n=268
n=300
n=312
Answer:
n = 300 and n = 312
Step-by-step explanation:
n - 93 > 175
n > 175 + 93
n > 268
Therefore only the two last answers are are possible n values (n has to be more than 268, not equal)
The two numbers 300 and 312 will make the inequality n-93>175 true which are correct option (D)300 and (E)312.
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given inequality as:
n - 93 > 175
n > 175 + 93
n > 268
Therefore, n must be greater than 268 and not equal.
Hence, the two numbers 300 and 312 will make the inequality n-93>175 true.
Learn more about inequalities here:
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help me with this question for my homework pls
Answer:
4 1/12 is your answer
Find a common denominator, 12. Multiply the many times you did to the denominator to get 12 to the numerator so 3/4 would be 9/12 and 2/3 would be 8/12 so 9/12 - 8/12 is 1/12 and as you know already 10 - 6 = 4 so 4 1/12 would be your answer.
What is the value of the expression 1/2 divided by 6
Answer: the answer is to divide and you will come up with the answer 1/12
Step-by-step explanation:
Answer:
here is 1/2 divided displayed mathematically
1/2 ÷ 6
1= numerator
2= denominator
3= whole number
to make it fraction from the answer you keep the
numerator by the whole number to make a new
denomiter
___1___ = _1_
2×6 12
thus the answer to 1/2 divided by 6 on fraction form is
1/2 is the answer
pls help me it is important to me
Answer:
no
Step-by-step explanation:
Which of the following ordered pairs is not in the solution set of y < 2x − 5
Answer:
(4,3)
Step-by-step explanation:
Solve the equation:
3<2(4)-5
3<8-5
❌3<3 ❌
3 is not less than three, hence this is the phony
i hope this helps!
What is the additive inverse of -7?
O A. -7
O B. 7
C. -|-7|
D. -(-(-7))
Answer:
B
Step-by-step explanation:
please help me guys!
its blur
how can we read it if your picture is blur
d) What would be the total cost of purchasing the number of shirts needed to use your coupon—after your coupon is applied and a 7.5% sales tax is charged on the purchase?
Answer: Multiply 7.5% by the price after subtracting the coupon's value.
Step-by-step explanation:
Let's assume that the cost of the shirts is x. So the coupon would subtract y from x so that's x-y which gives us z. Then to find z, on a calculator just put in 7.5% x z. I used variables since I don't know the value of the coupon or the original price of the shirts.
please help with this question
==========================================================
Work Shown:
The diagram is below.
In this diagram, we have KN and LM as opposite sides. For any parallelogram, the opposite sides are parallel (as shown by the arrow markers) and they are congruent to each other. In other words, KN and LM are the same length.
This means KN = LM and we can solve for x like so
KN = LM
3x-11 = x+15
3x-x = 15+11
2x = 26
x = 26/2
x = 13
Then we can find side KL
KL = 2x-4
KL = 2*13-4
KL = 26-4
KL = 22
If you borrow $491 for one year at an interest rate of 9%, how much interest will you pay?
Answer:
44.19
Step-by-step explanation:
419*0.09=44.19
Which expression has a value closest to 1? (Use 3.14 as the value of 1.)
A.
77
V10
B. 75-V74
O C.
V37-V26
3V5 – V20
D.
Answer:
C: √37 - √26
Step-by-step explanation:
√37 = 6.083
√26 = 5.1
6.083 - 5.1 = 0.983
Answer:
C
Step-by-step explanation:
please help me with this
Answer:
D. [tex]\sqrt{250}[/tex]
Step-by-step explanation:
First, use prime factorization of 250 to get [tex]\sqrt{2*5^3}[/tex]
Then apply the exponent rule, [tex]a^{b+c} =a^{b}*a^{c}[/tex]
=[tex]\sqrt{2*5^2*5} }[/tex]
Apply radical rule: [tex]\sqrt{ab}= \sqrt{a} \sqrt{b}, a\geq 0, b\geq 0[/tex]
=[tex]\sqrt{5^{2}} \sqrt{2*5}[/tex]
Apply radical rule: [tex]\sqrt{a^{2}} =a, a\geq 0[/tex]
=5[tex]\sqrt{2*5}[/tex]
=5[tex]\sqrt{10}[/tex]
Answer:
D. I did the math on my calculator
Adrianna is two years older than Fernando, while Lucy is triple Fernando's age. If the sum of their ages is eighty-two, how old is Adrianna?
HELPPPP MEEEEE!!!!!!
Answer:
18
Step-by-step explanation:
x + (2+x)+ (3x) =82
x+x+3x= 82-2
5x=80
x= 16
Fernando is 16
Adrianna is 2 years older so she is 18
And Lucy is 3x 16=48
together 82
What is the maximum volume in cubic inches of an open box to be made from a 10- inch by 20-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative.
Answer:
192.5 in³
Step-by-step explanation:
The cardboard is 10 by 20 before removing a square from each end. Assuming that the square is x inches wide. Therefore, the 20 in side gets reduced by x inches on both sides, or say it becomes 20 - 2x inches. On the other hand, the 10 in side is also reduced by 2x. The x value we get happens to be the height of the box when the sides are folded up.
Thus the volume V = lbh =
V = (20-2x)*(10-2x)*(x)
V = 4x³ - 60x² + 200x
On differentiating, we have dv/dx to be
dv/dx = 12x² - 120x + 200
Using general formula to find the roots of this equation, we can solve that x = 7.886 and x = 2.113
This roots we got are possible values of x, the square we cut. Since 7.886 * 2 = 15.772 inches, this is more than the 10 inch side, henceforth x = 2.113 inches.
You cut 2.113 inches from each corner to obtain the maximum volume.
The sizes of the cubes are
20 - (2 * 2.113) = 15.774
10 - (2 * 2.113) = 5.774
2.113
The volume of the cube is 15.774 * 5.774 * 2.113 = 192.5 cubic inches.
what do you observe about the form of the equation of any circle whose center is at the point of origin
Ce clasă ești sa văd daca te pot ajuta
Convert the following quadratic equation to vertex form. 2) 3x2 - 12x - 5
Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
