Answers
Answer:
The answer:
A. [tex]x= \frac{-5+ \sqrt{-11} }{2}[/tex]
F.[tex]x= \frac{-5- \sqrt{-11} }{2}[/tex]
Step-by-step explanation:
Step 1: Solve with quadratic formula
[tex]x_{1},2 = \frac{-b+- \sqrt{b^2}- 4ac }{2a}[/tex]For [tex]a=1, b=5, c=9\\x_{1},2 = \frac{-5 + \sqrt{5^2 -4 *1 *9} }{2*1}[/tex]Step 2: Simplify
[tex]\sqrt{5^2 - 4 *1 *9} : \sqrt{11} i[/tex]Multiply the numbers: [tex]4*1*9 = 36[/tex][tex]i\sqrt{ 36 -5^2}[/tex] = [tex]\sqrt{-5^2 + 36} = i\sqrt{11}[/tex][tex]5^2 = 25 = \sqrt{-25 + 36}[/tex]Add/subtract the numbers [tex]-25 +36 = 11 = \sqrt{11} = \sqrt{11}i[/tex]Step 3: Separate the solution
[tex]x_{1} = \frac{-5 + \sqrt{-11}i}{2} , x_{2} = \frac{-5 - \sqrt{-11}i}{2}[/tex]Answer:
[tex]\large {\textsf{A and F}}\ \implies \bold{x_1}=\dfrac{-5-\sqrt{-11}}{2},\ \bold{x_2}=\dfrac{-5+\sqrt{-11}}{2}[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Standard Form of a Quadratic Equation: ax² + bx + c = 0, where a ≠ 0.
Given polynomial: x² + 5x + 9
⇒ a = 1, b = 5, c = 9
Step 1: Rewrite to Standard Form.
⇒ x² + 5x + 9 = 0
Step 2: Substitute the values of a, b, and c into the formula.
⇒ a = 1, b = 5, c = 9
[tex]x=\dfrac{-5\pm\sqrt{\bold{5^2}-4\bold{(1)(9)}}}{\bold{2(1)}}\\\\x=\dfrac{-5\pm\sqrt{25\bold{\ - \ 4(9)}}}{2}\\\\x=\dfrac{-5\pm\sqrt{\bold{25-36}}}{2}\\\\x=\dfrac{-5\pm\sqrt{-11}}{2}[/tex]
Step 3: Separate into two possible cases.
[tex]x_1=\dfrac{-5-\sqrt{-11}}{2}\\\\x_2=\dfrac{-5+\sqrt{-11}}{2}[/tex]
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Related Questions
What is another way to write the absolute value inequality p ≤ 12? O-12≤p≤ 12 O-122p≤12 O-12 ≤por p≤ 12 -122P or p≤ 12 958 What is another way to write the absolute value inequality p ≤ 12 ? O - 12≤p≤ 12 O - 122p≤12 O - 12 ≤por p≤ 12 -122P or p≤ 12 958
Answers
Answer:
-12 ≤ p ≤ 12
Step-by-step explanation:
If the absolute value inequality is
|p| ≤ 12,
then the answer is
-12 ≤ p ≤ 12
Which function is the result of vertically stretching f(x) = x ^ 2 - 7 by a factor of 2 and translating downward 5 units?
Answers
The function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)The given function f(x) is needed to be stretched vertically by a factor of 2, therefore, the function can be written as,
g(x) = 2(x² - 7) = 2x² - 14
Now, the function is needed to be translated by 5 units in the downward direction, therefore,
p(x) = g(x)-5 = 2x² - 14 -5
p(x) = 2x² - 19
Hence, the function that is the result of vertically stretching f(x) = x²-7 by a factor of 2 and translating downward 5 units is 2x² - 19.
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3x+2=0 i need the answer quick
Answers
Answer:
[tex]\huge\boxed{\sf x = -2/3}[/tex]
Step-by-step explanation:
Given equation:3x + 2 = 0
Subtract 2 to both sides
3x = 0 - 2
3x = -2
Divide 3 to both sides
x = -2/3
[tex]\rule[225]{225}{2}[/tex]
Which angle refers to the same angle as \angle DAC∠DACangle, D, A, C?
Answers
Answer:
Option
Step-by-step explanation: The way tell what the answer is are the similar lines. The single yellow line helps indicate that it's a similar angle.
Can you answer the question
Answers
Step-by-step explanation:
Hi There! Let me help you :)
[tex] = 8.8.8.8.8.8.8[/tex]
[tex] = ( \text{there \: are \: 7 \:numbers \: eight })[/tex]
[tex] \: [/tex]
So we can rewrite the above equation to be like this.
[tex] = 8.8.8.8.8.8.8[/tex]
[tex] = 8.(1 + 1 + 1 + 1 + 1 + 1 +1)[/tex]
[tex] = 8.7[/tex]
Helen bought 3 books and 2 pencil cases. the pencil case cost $8 less than the book. if helen spent $74, how much did a book cost?
Answers
The cost of book case be $ 11.6.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0.
Here, let the cost of book case be $ x
and the cost of pencil case be $ y
Now, Helen purchased 3 books and 2 pencils in $ 74.
3x + 2y = 74 .......(i)
Cost of pencil case $ 8 less than the book.
y - 8 = x ............(ii)
put the value of x in equation (i), we get
3(y - 8) + 2y = 74
3y - 24 + 2y = 74
5y = 74 + 24
5y = 98
y = 98/5
y = $ 19.6
put the value of y in equation (ii), we get
x = y -8
x = 19.6 - 8
x = $ 11.6
Thus, the cost of book case be $ 11.6.
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Simplify the expression –3(x 3)2 – 3 3x. what is the simplified expression in standard form?
Answers
[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression
The given expression is:
[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]
This is the standard form of the given expression.
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Round 969.991 to the nearest whole number
Answers
Answer:
Round of 969.991
970
Rules of round off
1) If the digit is odd no. the no. will increase to 1
2) if it is even the no. will be same.
What are all the solutions of x² + 3x -4 = 0? Multiple choice
A: -4
B:-2
C:-1
D:0
E:1
F:2
G:4
Answers
Answer :
A and E .
Step-by-step explanation:
2.8 + 32x + 1 =16.6
Answers
Answer:
x = 0.4Step-by-step explanation:
Assuming you are looking for x
2.8 + 32x + 1 = 16.6
32x = 16.6 - 2.8 - 1
32x = 12.8
x = 12.8 : 32
x = 0.4
-----------------------
check
2.8 + 32 * 0.4 + 1 = 16.6
2.8 + 12.8 + 1 = 16.6
16.6 = 16.6
the answer is good
Which table represents a linear function?
Answers
Answer:
The first one (x=1 and y=1/2)
Step-by-step explanation:
The first table is the only one that has a constant rate of change. The x value increases by 1, and the y value increase by 1/2.
Hope this helped :)
Answer:
The first one where x increases by 1 and y increases by 1/2.
Step-by-step explanation:
To find the equation, 1/2=1+b
Solve for b
1/2-1=-0.5
B=-0.5
Now, solve for x
1/2=x-0.5
As you can already see in the table, x increase by 1, so no need to even solve.
The equation would be y=1x-0.5 (I’ll post the graph in the picture to prove it is linear.
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable yy is 1 and the degree of variable x is 1.
15-
4
3+
2H
11
-5-4-3-2-1₁
Mark this and return
2345
-3-
2 3 4 5 x
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to -3
Answers
The question was incomplete. Below you will find the missing graph image.
The range contain all the real numbers greater than or equal to –3 .
Range of function : The set of outputs of a function is called range of that function. Range of a function is also called co-domain of the function.
Example : If f(x) = x² is the function with domain as all real numbers, then the range of that function is the set of all non-negative real numbers.
We have to find the range of the function on the graph.
We can see by the graph minimum value of y of function is -3 and the graph continues to extend upward in the positive direction.
So, the range contain all the real numbers greater than or equal to –3 .
Therefore, the range contain all the real numbers greater than or equal to –3 .
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Mr. Thakuri deposited Rs.2,00,000 in her fixed account at a bank for 3 years. The bank pays her the simple interest at the rate of 10℅ p.a. How much net interest would she get if 5 % of interest in charged as income tax?
Answers
The net interest she would get on the amount deposited is $57,000.
What is the net interest?The net interest is the total interest earned less tax.
Interest = amount deposited x simple interest x time
200,000 x 0.1 x 3 = $60,000
Net interest = $60,000 x (1 - 0.05)
$60,000 x 0.95
$57,000
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please help me its math 10 points
Answers
Answer:
it should be 319
Step-by-step explanation:
Answer:
639 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Follow the steps to find the
area of the shaded region.
Now, use the formula
below to calculate the
area of the triangle.
Triangle Area = bh
h = 10.0708 cm
Triangle Area = [?] cm²
Round to four decimal places.
14 cm
hi
46°
14 cm
Answers
The area of the triangle is given as: ≈ 70.50cm²
What is the explanation to the above solution?Area of shaded region = Area of the sector less Area of the Triangle.
This is represented as:
π r² (∅/360) - 1/2 x b x h
= π x 14² x (46/360) - (1/2) x 14 x 10.0708
= 78.6794 - 70.4956
= 8.1838 cm²
Hence, the area of the triangle is (1/2) x 14 x 10.0708
= 70.4956 cm²
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Jack have 34 toy cars, Mike says he have 3 times more than Jack's toy cars. How many toy cars does Mike have?
Answers
Answer:102
Step-by-step explanation:
34 x 3 = 102
Answer:
102
Step-by-step explanation:
Since Jack has 34 toy cars and Mike has 3 times more than Jack's toys, we should multiply 34 with 3 to get the answer.
34 * 3 = 102
So, this means that Mike has 102 toy cars.\
Hope this helps :)
Mikaela and Viktoria both competed in a curling match on opposing teams. Mikaela
said to Viktoria, "2 more than twice my team's score is the
same as three times your team's score reduced by 3." If
Viktoria's team's score was 7, what was Mikaela's team's
score?
Answers
Mikaela's team's score is 8.33
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Viktoria's team's score = 7
According to question,
= 2+ 7*2 = 16
so, Mikaela team score= 16/3+3= 8.33
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What is the value of x in the figure below? In this diagram, ABD ~ CAD.
Answers
Answer:
[tex] \sqrt{30} [/tex]
Step-by-step explanation:
altitude rule
10 / x = x / 3
x^2 = 30
x = sqrt(30)
Work out the values of a, b, c and d.
Answers
Step-by-step explanation:
The are two angles ie. 45 and 80 than find the third angle
80 will be vertically opposite and alternative angle to a
How tall is the tree?
5ft
35°
-20ft-
[? ]ft
Answers
Answer:
19
Step-by-step explanation:
tan35=x/20
20tan35=x
x=14.0041507641942
x+5=19.0041507641942
Nearest foot is 19
What is the answer for the question down below
Answers
Answer:
This is the ray BAStep-by-step explanation:
Ray can be defined as a part of a line that has a fixed starting point but no end point.
The starting point is B and on its way to infinity, it passes through point A.
Correct sign is
[tex]\huge\boxed{\overrightarrow{BA}}[/tex]
Let a be a matrix with 4 columns. What are the possible values for rank(a)?
Answers
The complete question says: Let v, w, be vectors of [tex]\mathbb{R}^4[/tex]. Let A be a matrix with 4 columns v, w, 2v+w, v-w. What are the possible values for rank(A)?
The possible values for rank A = 2
What is a vector space?A vector space is a space that contains vectors as well as the associative including the commutative operation of vector addition and the associative, as well as, distributive operations of vector multiplication by scalars.
From the information given:
If v,w be the vectors in a [tex]\mathbb{R}[/tex]where;
A = matrix with 4 columns v, w, 2v+w, v-w, which are non-independent vectors.However, the vectors 2v+w and v-w can be expressed as a linear combination of the given values of v and w(independent vectors).
We can conclude that the maximum no. of independent rows = 2. Hence, the possible rank of matrix A is 2.
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A shop increases all their prices by 6%
A picture frame increases by £294
Find the new price of the picture frame.
Answers
Answer:
0riginal price = 4900
Step-by-step explanation:
294 = 6%
294/6 = 49 49 = 1%
49 x 100 = 4900
0riginal price = 4900
If the independent variable is in the rows of a cross-tabulation and the dependent variable is in the columns, which percents do we use for comparisons?
Answers
We make use of the row percentage for comparisons
How to determine the percentage of comparison?From the question, we have:
Row ⇒ Independent variableColumn ⇒ Dependent variableThe data represented by the independent variable is always used to make comparison
Since this variable is on the rows, then the row percentage would be used for comparisons
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Partially factored form: f(x) = (x − 3)(x 3)(x2− 4x 5) use the quadratic formula to identify the zeroes of x2 − 4x 5. x =
Answers
Answer:
2 ± i
Step-by-step explanation:
by 5, I assume you mean +5
x² - 4x + 5 = 0
x = (-b±(√(b²-4ac)) / 2a
x = (4 ± (√(16 - 20)) / 2
x = (4 ± (√(-4)) / 2
√-4 = √4√-1 which is 2i
x = (4 ± 2i) / 2
x = 2 ± i
giving 20 points out for this question!
Answers
Answer: £20 doubling at the end of each year for 5 years
From the question, Stephen would want to select one option which gives the highest amount of profit. I mean, even if you were to select one, you would obviously try calculating all the 4 choices to see which one makes you earn the most money. Now let's conduct the workout and see which one will earn us the most £ in 5 years:
Option 1:
[tex](500*\frac{5}{100} ) + 500 ---- > 1yr\\= 25 + 500 \\ = 525\\\\(525*\frac{5}{100} ) + 525 ----- > 2yrs\\= 26.25 + 525\\= 551.25\\\\(551.25 * \frac{5}{100}) + 551.25 - - - > 3yrs\\ = 27.563 + 551.25\\= 578.813\\\\(578.813 * \frac{5}{100}) + 578.813 - - > 4 yrs\\ = 28.941 + 578.813\\ = 607.754 \\\\(607.754 * \frac{5}{100}) + 607.754 - - > 5 yrs\\ = 30.388 + 607.754\\ = 638.142 \\[/tex]
ans: £ 638.142
Option 2:
[tex]1 year = 12 months\\5 years : 5*12 = 60 months\\\\10*60 = 600[/tex]
ans: £ 600
Option 3:
[tex](550*\frac{3}{100}) + 550 - - - - > 1yr\\= 16.5 + 550\\= 566.5 \\\\(566.5 * \frac{3}{100}) + 566.5 - - - > 2 yrs\\ = 16.995 + 566.5\\= 583.495\\\\(583.495 * \frac{3}{100}) + 583.495 - - > 3 yrs\\ =17.505 + 583.495\\= 601\\\\(601 * \frac{3}{100}) + 601 - - - - - - > 4 yrs\\= 18.03 + 601\\= 619.03\\\\( 619.03* \frac{3}{100}) + 619.03 - - - - > 5 yrs\\= 18.571 + 619.03\\= 637.601[/tex]
ans: £ 637.601
Option 4:
[tex]20*2= 40 - - - - > 1yr\\40 * 2= 80 - - -- > 2 yrs\\80*2 = 160 - - - > 3 yrs\\160*2 = 320 - - - > 4 yrs\\320*2= 640 - - - > 5yrs[/tex]
ans: £ 640
Out of all the calculated answers, you can see that option 4 has the highest amount. So that's it. By the way, I might do some incorrections in some calculations because I am not good at long maths, but yes i hope I did it all right!
∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
hope it helped
┗━━━━━━━┛
I require assistance.
Answers
Answer:
its 3.348 - crown pls
Step-by-step explanation:
easiest way of doing this is multiplying the total by the known number then put that number on top. After that divide and check if its right
Kimberly loves science and just subscribed to KiwiCo, a company that delivers STEAM kits to students to build and create
things at home! KiwiCo charges a subscription fee of $16.99 for each of its members. KiwiCo had 300 subscribers in March.
In April, 50 new people subscribed to KiwiCo, and 23 people canceled their subscriptions. How much more money did
KiwiCo earn from subscriptions in April?
Answers
The KiwiCo earn money from subscriptions in April would be $5555.73.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
KiwiCo charges a subscription fee of $16.99 for each of its members.
$16.99 per 1 person
KiwiCo had 300 subscribers in March.
In April, 50 new people subscribed to KiwiCo, and 23 people canceled their subscriptions.
300 + 50 = 350 - 23 = 327
So,
327×$16.99= 5555.73
Hence, The KiwiCo earn money from subscriptions in April would be $5555.73.
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Sandhu lights a candle at 6 pm. It is 30 cm high. At 7pm, the candle is 27 cm high. At 8pm, it is 24cm high. a) How many cm does the candle burn down every hour? b) How high is the candle at 11 pm?
Answers
Your final answer: A) The candle burns down 3 centimeters every hour. B) At 11 pm, the candle is 15 centimeters high.
Rotate the given triangle 90 degrees
CLOCKWISE about the origin.
0
0
07
0
-
-3 -4
0 -3
[?]
Answers
The value is [tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
what is clockwise and counterclockwise?Clockwise Rotations (CW) mimic the path of a clock's hands.
Negative numbers are used to represent these rotations. Counterclockwise rotations (CCW) follow the path of a clock's hands in the opposite direction.
Now, rotating 90 degree clockwise we get
[tex]\left[\begin{array}{ccc}0&3&4\\0&7&-1\end{array}\right][/tex]
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