80 Points, please help!
If using the method of completing the square to solve the quadratic equation x^2-11x-14=0, which number would have to be added to "complete the square"?
Answers
Answer:
±√177/2+11/2
Step-by-step explanation:
Use the formula (b/2)^2 in order to create a new term. Solve for x by using this term to complete the square. Exact Form:x=±√177/2+11/2
x=12.15206734…,−1.15206734…
Answer:
30.25
Explanation:
Quadratic Equation: x² - 11x - 14 = 0
Number added = (b/2)² = (-11/2)² = 30.25
Solving Steps:
x² - 11x = 14[add both sides by 30.25]
x² - 11x + 30.25 = 14 + 30.25[complete square]
(x - 5.5)² = 44.25[exchange sides]
(x - 5.5)² - 44.25 = 0Related Questions
[tex]\sqrt{29-12\sqrt{5}[/tex] simplify this
Answers
[tex] \sqrt{29 \: - \: 12 \sqrt{5} } [/tex]
Factor the indicated expression:[tex] \sqrt{(3 \: - \: 2 \sqrt{5}) ^{2} } [/tex]
Simplified the index the root and also the exponent using the number 2.[tex] \boxed{ \bold{2 \sqrt{5} \: - \: 3}}[/tex]
MissSpanish[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{29-12\sqrt{5}} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{20-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{4\cdot \:5-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(\sqrt{4}\right)^2\left(\sqrt{5}\right)^2-12\sqrt{5}+\left(\sqrt{9}\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{4}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{9}=3 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2\cdot2\cdot3\sqrt{5}=12\sqrt{5} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{2^2\left(\sqrt{5}\right)^2-2\cdot \:2\cdot \:3\sqrt{5}+3^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply\:the\:formula\:from\:binomial\:to\:square:(a-b)^2=a^2-2ab+b^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2^{2}(\sqrt{5})^{2}-2\cdot2\cdot3\sqrt{5}+3^{2}=(2\sqrt{5}-3)^{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(2\sqrt{5}-3\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^{2} }=a \end{gathered}$}[/tex]
[tex]\sqrt{(2\sqrt{5}-3)^{2} } =2\sqrt{5 }-3.[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{=2\sqrt{5}-3 } \end{gathered}$}}} \ \ \red{\Rightarrow} \ \ \bf{\red{Answer}}[/tex]
↓
[tex]\red{\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{MyHeritage}} \end{gathered}$}}}}[/tex]
Type the probability notation for choosing a blue disk or a green disk.
Answers
The probability notation for choosing a blue disk or a green disk is P ( B U G).
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability = (number of blue discs / total number of discs) + (number of green discs / total number of discs)
3/8 + 5/8
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Solve the given inequality and graph the solution on a number line. -X/2 -3/2 = 5/2
No Links:
Answers
Your final answer: X = -8.
A standard die is rolled and a month
of the year is chosen at random.
What is the probability of rolling a
number that is at least
then
choosing a month that does not
begin with the letter M?
200
Answers
Answer:
The probability is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
First we will find the probability of having a roll that is at least 3
1 2 3 4 5 6
this means there is a [tex]\frac{4}{6}[/tex] chance we will roll at least 3
Next we will find which months of the year are applicable
January February March April May June July August September October November December
This means there is a [tex]\frac{5}{6}[/tex] chance we will pick a month that does not begin with the letter M.
Now we can multiply these chances together to see what the total probability is.
[tex]\frac{4}{6} * \frac{5}{6} = \frac{20}{36} \rightarrow \boxed{\frac{5}{9}}[/tex]
That is the answer
- Kan Academy Advance
Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0)
Answers
The x-intercept is (1, 0) and (-0.5, 0).
The correct option is (a)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function is:
f(x)= [tex]-2x^{2}+x+1[/tex]
So, The graph of this equation is attaches below.
The x- intercepts of this graph
[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]
or
X intercepts: (1, 0) and (-0.5, 0)
Hence, the x-intercept is (1, 0) and (-0.5, 0).
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Suppose a charity received a donation of $22.9 million. If this represents 48% of the charity's donated funds, what is the total amount of its donated funds?
Round your answer to the nearest million dollars.
Answers
Hedya is 4 times as old as Hannah, and Hannah is 1.5 times as old as Hadassah. If the sum of their ages is 102, how old is Hadassah?
Answers
Explanation:
x=Hedya
y=Hannah
z=Hadassah
x+y+z=102
x=4y
y=1.5z
z=?
4x1.5z=6z (also x or Hedya's age)
z+1.5z+6z=102
8.5z=102
z=12
PLEASE HELP MEEE ❗‼️‼️❗‼️
Find RS
A) 38
B) 35
C) 37
D) 40
Answers
The interior angles sum to 180°, so the missing angle has measure
180° - 106° - 12° = 62°
Use the law of sines to find RS:
sin(106°)/RS = sin(62°)/34 ⇒ RS = 34 sin(106°)/sin(62°) ≈ 37
Type the correct answer in each box. use numerals instead of words. what are the x-intercept and vertex of this quadratic function? g(x) = -5(x-3)^2 write each feature as an ordered pair: (a,b). the x-intercept of function g is . the vertex of function g is .
Answers
Considering the given quadratic function, we have that:
The x-intercept is (3,0).The vertex is (3,0).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is given by:
g(x) = -5(x - 3)²
Hence h = 3, k = 0, and the vertex is (3,0).
What are the x-intercepts of a function g(x)?They are the values of x for which g(x) = 0, hence:
-5(x - 3)² = 0
(x - 3)² = 0
Applying the root to both sides:
x - 3 = 0.
x = 3.
The x-intercept is (3,0).
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How does the rate of change work
Answers
show how to solve the equation in the picture
Answers
[tex]\left(3\cdot8\cdot x\right)^7\\\\\left(3\cdot2\cdot4\cdot x\right)^7\\\\\left((3\cdot2)\cdot4\cdot x\right)^7\\\\\left(6\cdot4\cdot x\right)^7\\\\6^7\cdot4^7\cdot x^7\\\\[/tex]
In the second step, I rewrote 8 as 2*4. Then after that I regrouped terms so that the (3*2) can pair up together. This of course turns into 6. After that point, we have 6, 4 and x multiplied together as the base.
The last step uses the rule that [tex](a*b*c)^d = a^d*b^d*c^d[/tex], in other words, we apply the exponent d to each term inside the parenthesis. Each term inside gets its own exponent.
An example: [tex](2*4*6)^3 = 2^3*4^3*6^3[/tex]
Betty invests $45,000 into a cd which has an interest rate of 6.3% that compounds monthly for a total of 5 years. how much will betty have after the 5 years? (rount to the nearest dollar)
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45000\\ r=rate\to 6.3\%\to \frac{6.3}{100}\dotfill &0.063\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &5 \end{cases} \\\\\\ A=45000\left(1+\frac{0.063}{12}\right)^{12\cdot 5}\implies A=45000(1.00525)^{60}\implies A\approx 61611[/tex]
The Raymond family is building a pool in their backyard. If the contractor
chargest $2 per cubic foot to excavate, how much money will it cost to dig out
the hole for the pool?
19 ft
14.5 ft
4 ft
5 ft
12 ft
Answers
Answer:
2020
Step-by-step explanation:
(12×5×14.5+7×4×5)×2=
2020
Solve for system of equations. y = x²-3x + 4
x + y = 4
Answers
Answer:
Step-by-step explanation:
x²-3x+4+x=4
x²-3x+x=4-4
x²-2x=0
x²-x=0/2
x²-x=0
x=0
Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination.
If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen?
Answers
Answer:
504 ways
Step-by-step explanation:
We know that since Sonji wants the last digit to be 7 and that numbers don't repeat, there are only 9 possibilities for the first digit, 8 possibilities for the second digit, 7 possibilities for the third digit, and 1 possibility for the fourth digit (which is 7).
Using the Fundamental Counting Principle, there are 9*8*7*1 = 504 ways for the remaining digits to be chosen.
Answer:
B. 504
Step-by-step explanation:
Have a good day!
Name something that you cannot find when looking at a box and whisker plot
Answers
Answer:
how many are of each number
Step-by-step explanation:
because it just shows the range, and the average, and the quarters, you can't really tell how many of the "item" of associated with each number
solution for -4 5/6 +5 1/3
Answers
Answer:
1/2
Step-by-step explanation:
to solve this equation you must find the greatest common factor or gcf to make the denominators the same
that happens to be 6
so
-4 5/6 + 5 2/6
then you add
you can break them up at add them like this
(-4 + 5) + (-5/6 + 2/6)
1 + -3/6
-3/6 is also -1/2
1 + -1/2
1/2
that is your answer
Step 1: Choose a point on the line, such as (2, 5).
Step 2: Choose another point on the line, such as (1, 3).
Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is StartFraction one-half EndFraction.
Step 4: Substitute those values into the point-slope form.
y – y1 = m(x – x1)
y – 3 = y minus y 1 equals m left-parenthesis x minus x 1 right-parenthesis. (x – 1)
Which of Talia’s steps is incorrect?
Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
Answers
The step of Talia that's incorrect is: C. step 3 because the slope ratio she calculated is incorrect.
What is the Slope?The slope of a line (m) = rise/run = change in y / change in x.
Calculating the slope using two points on the line, (2, 5) and (1, 3), we should have:
Slope (m) = (5 - 3)/(2 - 1)
Slope (m) = (2)/(1)
Slope (m) = 2
This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3
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For an upcoming field trip to the science center, the school will allow students to select one extra activity. The school surveys a random sample of 25 students to determine about how many tickets of each kind they will need to buy.
Answers
The total amount that would be spent on all the activities is $1605.40.
What is the total amount?The total amount that would be spent on movies = (14/25) x 1200 x 1.55 = $1041.60
The total amount that would be spent on planetarium tickets = (7/25) x 1200 x 1.05 =352.80
The total amount that would be spent on backstage passes = (4/25) x 1200 x 1.10 =211.20
Total amount = 211.20 + 352.80 + $1041.60 = $1605.40
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Darnell's graduation picnic will cost $12 if it has 6 attendees. If there are 7 attendees, how much will Darnell's graduation picnic cost? Solve using unit rates
Answers
Answer:
$14
Step-by-step explanation:
6 attendees divided by the cost of 12 = $2 per attendee
If 7 attendees are joining times $2 per person =$14
How many cups are equal to 1/2 of a pint ?
Answers
Answer:
0.5 =12.0095
pint U.S Cup
I think im right but I hope this helps! ^^
The lines shown below are parallel. If the green line has a slope of -27, what is
the slope of the red line?
10-
O A.-/7/7
OB.
10
O C. /
OD.
7
3
-10-
5
15
713
B.-
Answers
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The correct option is A.
What is a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.
The slope of the parallel line is always equal. Given the slope of the green line is -3/7, also, it is parallel to the red line. Therefore, the slope of the red line is -3/7.
Hence, the correct option is A.
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The A.M. between two numbers exceeds their G.M. by 2 and the G.M. exceeds the H.M by 1.8. Find the numbers.
Answers
The numbers based on the information will be 4 and 16.
How to compute the numbers?Let the numbers be a and b.
Therefore, a - g = 2
(a + b)/2 - ✓ab = 2 or
(✓a - ✓b( = 4
g - h = 1.8
✓ab = 2ab/a + b = 1.8
5✓ab(✓a - ✓b)² = 8(a + b)
2a - 5✓ab + 2b + 0
✓a = 2✓b
a = 4b
b = 4.
✓a = 2✓b = 4
a = 16
Therefore, the numbers based on the information will be 4 and 16.
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A yardstick measures distance to 1/4, or 0.25, of an inch. What is the most
appropriate way to report a length measured using this yardstick?
Answers
The most appropriate way to report a length measured by using this yardstick is to write the measurement in decimals (0.25) rather than in fraction (¼).
What is measurement?Measurement is a process through which the size, dimensions, or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment.
In Mathematics, a yardstick refers to a graduated measuring stick that has its length equal to one yard.
In this scenario, the most appropriate way to report a length measured by using this yardstick is to write the measurement in terms of decimals (0.25), so as to make easy approximations of the distance possible.
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Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles
Answers
The closest to x the distance between the two poles is gotten as; x = 75 ft
How to utilize trigonometric ratios?
From the Brainly link attached, we can see the diagram and we can say that;
We are given a right angled triangle with;
A known angle of; θ = 20°
Length of the hypotenuse = 80
Now, we want to find the length of the base x. Thus, we will use trigonometric ratio to get;
cos θ = x/hypotenuse
Thus;
cos 20 = x/80
x = 80 cos 20
x = 75.17 ft ≈ 75 ft
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if f(x)=x²+2x-4 and g(x) = -4x+1, what is (g-f)(x)?
A x²+6x-5
B. x2-2x-3
C. x²-6x+5
D.-x²-6x+5
Answers
The (g-f)(x) is option D: - x² - 6x + 5.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Given;
f(x) = x²+2x-4
g(x) = -4x+1,
Then the subtraction of the two function;
g(x) - f(x)
= -4x+1 - (x²+2x-4 )
= -4x+1 - x²- 2x + 4
= - x² - 6x + 5
Hence, the correct option is D: - x² - 6x + 5.
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An adult mamenchisaurus dinosaur was about 24 feet tall . if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches , how tall will the toy dinosaur be
Answers
The height of the toy dinosaur will be 32 inches.
What is scaling?In mathematics scaling is defined as the enlarging or contracting of the size of an object by reducing or increasing the units of the measurements of the object.
Given that:-
An adult mamenchisaurus dinosaur was about 24 feet tall. if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches.
The new height of the dinosaur will be calculated as:-
We know that the size of the dinosaur is scaled as 9 inches to 1 inch the actual height of the dinosaur is 24 feet so the scaled height will be:-
Actual height = 24 ft = 24 x 12 = 288 inches
9 inches → 1 inch
288 inches → 288 / 9 = 32 inches.
Therefore the height of the toy dinosaur will be 32 inches.
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The difference between two numbers is 17 and twice the smaller of these is 26. What are the numbers?
Does anyone know the answer?
Answers
Answer:
13 and 30
Step-by-step explanation:
the smaller of the two numbers is 13.
If there is a 17 number difference, then that means that the second number is 30.
give brainliest, please!
hope this helps :)
The starting line for a race in Cass is 2.4 miles from the finish line. On a map of the course,
the starting and finish lines are 6 inches apart. What scale does the map use?
Write your answer in simplest form using whole numbers.
__ inches = __ miles
Answers
Answer:
5 in. = 2 mi.
Step-by-step explanation:
2.4mi = 6in
1 mi = 2.5in
2.5 inches = 1mile
Convert to whole #'s as the question asks
5 in. = 2 mi
-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)
Answer:
3 inches = 1 miles
Step-by-step explanation:
The first scale you get is with the information that is given:
6 inches = 2.4 miles
Then you simplify, dividing both sides by 2.4:
2.5 inches = 1 miles
Rounding up: 3 inches = 1 miles
Hope it helps!
given f(x)=2/x^2+3x-10.
which of the following is true?
Of(x) is positive for all x < -5
Of(x) is negative for all x < -5
Of(x) is positive for all x < 2
Of(x) is negative for all x > 2
Answers
The function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
[tex]\rm f\left(x\right)=\dfrac{2}{x^2}+3x-10[/tex]
f(x) is positive for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is not true
f(x) is negative for all x < -5
Plug x = -4
f(-4) = -21.875
The above statement is true
f(x) is positive for all x < 2
Plug x = 1
f(1) = -5
The above statement is not true
f(x) is negative for all x > 2
Plug x = 3
f(3) = -0.777
The above statement is not true
Thus, the function f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.
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