Given:
The equation is:
[tex]x^2+5x=2[/tex]
To find:
The solution of the given equation by completing the square.
Solution:
We have,
[tex]x^2+5x=2[/tex]
We need to add the square of half of the coefficient of x on both sides.
Adding [tex]\left(\dfrac{5}{2}\right)^2[/tex] on both sides, we get
[tex]x^2+5x+\left(\dfrac{5}{2}\right)^2=2+\left(\dfrac{5}{2}\right)^2[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=2+\dfrac{25}{4}[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{8+25}{4}[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{33}{4}[/tex]
Taking square root on both sides, we get
[tex]x+\dfrac{5}{2}=\pm \sqrt{\dfrac{33}{4}}[/tex]
[tex]x=\pm \dfrac{\sqrt{33}}{2}-\dfrac{5}{2}[/tex]
[tex]x=\dfrac{\pm \sqrt{33}-5}{2}[/tex]
[tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex]
Therefore, the solutions of the given equation are [tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex].
Answer: d and e
Step-by-step explanation:
edge 2021 :)
3. What is Total Surface Area?
4 in
3 in
10 in
O 82
O 140
O 164
O 120
Answer:
120in. ezy
Step-by-step explanation:
Given the function h(x) = -x2 -X2 – 5x + 8, determine the average rate of change of the function over the interval -4 < x < -2
Hi there!
[tex]\large\boxed{\text{Average rate = 1}}[/tex]
We can calculate the average rate of change using the following:
[tex]ARC = \frac{f(b)-f(a)}{b-a}[/tex]
Thus, we can plug in the endpoints of -4 and -2. Find the corresponding y-values for these x-values:
f(-2) = -(-2)² - 5(-2) + 8 = -4 + 10 + 8 = 14
f(-4) = -(-4)² - 5(-4) + 8 = -16 + 20 + 8 = 12
Plug in the solved for values into the ARC equation:
[tex]ARC(slope) = \frac{14-12}{-2(-4)} = \frac{2}{2} = 1[/tex]
A variable y varies directly with x and the constant of variation is 3. What is the value of y when x = 2?
Answer:
y = 6
Step-by-step explanation:
y varies directly with x
y = k*x
Where,
k = constant of variation
Find y when x = 2 and constant of variation,k =3
y = k*x
y = 3 * 2
y = 6
Check:
if y = 6 and x = 2, find k
y = k*x
6 = k*2
6 = 2k
k = 6/2
k = 3
Lily walks 2 kilometers during each trip to school. Write an equation that shows the
relationship between the number of trips x and the total distance walked y.
Answer:
y = 2x
Step-by-step explanation:
Total distance walked = y
Number of trips = x
Lily walks 2 kilometers during each trip to school
Equation that shows the
relationship between the number of trips x and the total distance walked y:
y = 2x
For example, if the number of trips (x) is 3
Total distance walked,y = 2(3)
y = 6 kilometers
Look at the drawing of a triangle within a rectangle. The
triangle and the rectangle have the same base, b, and
height, h.
If the area of the triangle is 48 square units, what is the
total area of sections 1 and 2?
square units
) Intro
Answer:
48 square. Units
Step-by-step explanation:
Given that :
Triangle and rectangle have the same base, b and height, h
AREA of triangle = 0.5 * base * height
48 = 0.5 bh
bh = 0.5 * 48
bh = 96
Total area of section 1 & 2 :
bh = area of triangle + x
X = bh - area of triangle
X = 96 - 48
Area of se tion 1&2 = 48
Please hurry I’m not looking forward to failing
If the shorter rectangle is 1 unit long, how many units long is the longer rectangle?
Answer: 2 units long
What's the ratio? please help! Urgent!
Answer:
13:5
Step-by-step explanation:
Messy played 65 minutes while the substitute played 25 minutes. This ratio is 65:25 and can be simplified to 13:5.
Heather has a bag of 15 red, 11 orange, 9 yellow, 12 green, 6 blue and 11 purple markers. how many times would you expect heather to pick a red marker if she picked a marker 90 times?
A.about 11 times
B.about 15 times
C.about 21 times
D.about 64 times
Answer:
B should be the correct answer.
Step-by-step explanation:
15 + 11 + 9 + 12 + 6 + 11 = 64
64<90
Answer:
15 red out of 64 total markers
15 / 64 = .234375
90 x .234375 = 21.09375
so she will pick a red marker about 21 times
Step-by-step explanation:
pls help on these and thku
Answer:
the second one
Step-by-step explanation:
Raise 1.00203333 to the negative 360 power
Answer:0.4813042802
Step-by-step explanation:
45 POINTS!! PLEASE HELP
The scatter plot shows the relationship between the test scores of a group of students and the number of hours they study in a week.
Part A: What is the group of points labeled N called? What is the point labeled M called? Give a possible reason for the presence of point M.
Part B: Describe the association between students’ test scores and the number of hours they study.
Answer:
Step-by-step explanation:
m is called an outlier and it is a positive association
Answer:
Part A) Part N.) is called the cluster of the whole chart. Part M.) is called the outlier because it's not with the rest of the group, therefore, it's the outlier of the group.
Part B.)
The association between the students' test scores and the number of hours they've studied is a positive correlation. That means the longer the students spent time studying for their tests... the better grades they got because of it. It's a lot like a cause-and-effect kind of situation.
Step-by-step explanation:
I hope this helps you!!! Brianlyest please!!! And SO sorry this is so late!
Please help me. Very important please show work
Does anyone know how to solve this problem
9514 1404 393
Answer:
∠CBE = 59°
Step-by-step explanation:
Adjacent angles of a parallelogram are supplementary.
∠BCD +∠CDE = 180°
∠BCD +∠CDB +∠BDE = 180°
(21x -5) +34 +(4x+1) = 180
25x +30 = 180
25x = 150
x = 6
∠CBE = ∠CDE = 34 +(4x +1) = 4x +35 = 4(6) +35
∠CBE = 59°
Solve for x and solve for FGI
Answer:
X equals -0.5 in decimal and in fraction it would be negative one half. Im not 100% sure of the answer also I dont know what angle that is...
Please help !!!!!!!!!!!!!!
36 + (12 - 8) + 2 × 5
Answer:
50
Step-by-step explanation:
To answer this we need to use the PEMDAS strategy, first solve any questions in parentheses, next solve all multiplication and division problems from left to right. Next, solve all addition and subtraction problems from left to right.
36 + (12 - 8) + 2 × 5
36 + 4 + 2 x 5
36 + 4 + 10
40 + 10
50
Answer:
[tex]50[/tex]
Step-by-step explanation:
Follow the PEMDAS order of operations:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction.
Calculate the Parentheses- (12-8)
This will equal 4.
[tex]36+4+2x5[/tex]
(x= times)
Multiply and divide, left to right.
[tex]2x5=10[/tex]
[tex]36+4+10=50[/tex]
Please help! Solve the following:
Answer:
n=10.
Step-by-step explanation:
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3}{n-4}[/tex] = [tex]\frac{2}{n+1 }[/tex]
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3(n+1)}{(n+1)(n-4)}[/tex] = [tex]\frac{2(n-4)}{(n+1)(n-4) }[/tex]
[tex]\frac{45}{n^{2}-3n-4 }[/tex] - [tex]\frac{3n+3}{n^{2} -3x-4}[/tex] = [tex]\frac{2n-8}{n^{2} -3x-4 }[/tex]
45-3n-3=2n-8
45-3+8=5n
n=50/5=10
HELP ME PLEASEE Select all of the following that could be classified as a Perfect Square Trinomial.
Son el B el C y el E
Please help me with this !!
Answer:
Step-by-step explanation:
a = 1
b = 6
c = 6
axis of symmetry = -(6) / 2*1
= -6 /2
= -3
vertex = ( -3, -3 ) :)
Answer:
Step-by-step explanation:
a = 1 because if is not written what x^2 multiply, it means that x^2 multiply 1
b = 6 b is the term that multiply x
c = 6 c is the therm without x
axis of symetry = -6/2 = -3
the x of vertex is same of the axis of the symmetry so it is -3
if we subistute x with this value we can find the y of vertex
(-3)^2 + 6(-3) + 6 = 9 -18 + 6 = -3
Vertex (-3, -3)
4y(2 + y) - (3y +3)
HELPPP
Answer:
4y² + 5y - 3
roots are: (-5 ± [tex]\sqrt{73}[/tex]) / 8
Step-by-step explanation:
8y + 4y² - 3y - 3
4y² + 5y - 3
roots are: (-5 ± [tex]\sqrt{73}[/tex]) / 8
Answer:
4^2 + 5 − 3
Step-by-step explanation:
you multiply those numbers, add these and those, combine these and that. and BOOM. you have your answer UwU
(x+y) (x+y) - (x-y) (x-y)
Answer:
4xy
Step-by-step explanation:
(x+y) (x+y) - (x-y) (x-y)
(x² + xy + xy + y²) - (x² - xy - xy + y²)
(x² + 2xy + y²) - (x² - 2xy + y²)
x² + 2xy + y² - x² + 2xy - y²
x² - x² + 2xy + 2xy + y² - y²
4xy
Answer:
that could literally be anything, as long as the first sum is greater then the second.
example;
(2+4) (3+5) - (6+1) (5+2)
(or, 6+8 = 14, 7+7 = 14, 14 - 14 = 0)
hope this helped :)
Kyle is a satellite radio sales representative. He receives 7% commission on all sales. If
the total sales for the year were $345,000, what would his commission be?
Answer:
24,150
Step-by-step explanation:
7% of 345,000 = 24,150
A worker places tape around a rectangular shipping label that is 2 times longer than it is wide. How much tape does the worker need? The width is 74mm
Answer:
444 :) (angel number, haha)
Step-by-step explanation:
it needs 74 times 2 mm which is 148 I think, which will also be the length since 148 is 2 times more than 74
so it's : 74 + 74 + 148 + 148 which is basically just 148 times three, so the answer is 444!
Suppose the function:
f(x) = 2.9646 (1.0170)x
models the world population x years after 1948.
Rewrite the exponential equation given above using base e.
f(t) = 2.9646 e ^(0.0169) t
B.
f(t) = 2.9646 (1.0170) e^t
C.
f(t) = 2.9646 + 1.0170e^t
D.
f(t) = 2.9646 e^(1.0170t)
E.
f(t) = 2.9646 e^ln (1.0170t)
Given:
The function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
To find:
Rewrite the exponential equation given above using base e.
Solution:
The exponential models is:
[tex]f(x)=P(1+r)^x[/tex] ...(i)
Where P is initial values, r is the rate of interest and x is the time period.
The exponential models using base e is:
[tex]f(t)=Pe^{rt}[/tex] ...(ii)
Where, P is initial values, r is the rate of interest and t is the time period.
The given function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
It can be written as:
[tex]f(x)=2.9646(1+0.0170)^x[/tex] ...(iii)
On comparing (i) and (iii), we get
[tex]P=2.9646[/tex]
[tex]r=0.0170[/tex]
Putting [tex]P=2.9646[/tex] and [tex]r=0.0170[/tex] in (ii), we get
[tex]f(t)=2.9646e^{0.0170t}[/tex]
Therefore, the correct option is D.
HELP PLEASE DUE SOON (i got the question wrong 2 tries)
Step-by-step explanation:
Mean number of tickets sold by boys =
Total Number of tickets sold / Number of boys
=
[tex] \frac{(1 \times 4) + (2 \times 3) + (4 \times 1) + (12 \times 1) + (13 \times 1) + (15 \times 3) + (14 \times 2}{4 + 3 + 1 + 1 + 1 + 3 + 2} \\ = \frac{4 + 6 + 4 + 12 + 13 + 45 + 32}{15} \\ = \frac{116}{15} \\ = 7.73(nearest \: hundredth)[/tex]
Which step comes last when using the divide-center method to find the trend line on a scatterplot? Approximate the center of the cluster located on the left side of the line, and repeat for the right side of the line. Connect the two centers to produce the trend line. Disregard all outliers.Draw a vertical line so that each side has the same number of data points.
Answer:
Is there a picture?
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
High blood pressure has been identified as a risk factor for heart attacks and strokes. The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. (a) Is it appropriate to use the normal approximation to find the probability that more than 40% of the people in the sample have high blood pressure? If so, find the probability. If not, explain why not. (b) A new sample of 80 adults is drawn. Find the probability that more than 40% of the people in this sample have high blood pressure. (c) Find the probability that the proportion of individuals in the sample of 80 who have high blood pressure is between 0.23 and 0.32.
Answer:
The National Health and Nutrition Examination Survey reported that the proportion of U.S. adults with high blood pressure is 0.3. A sample of 38 U.S. adults is chosen. a. Is it appropriate to use the normal approximation
can u help please :)
Answer:
z = 8
Step-by-step explanation:
All angles inside a triangle add up to 180 so:
90 + 40 + 5z + 10 = 180
5z + 140 = 180
5z = 40
z = 8
What is the volume, in cubic feet, of the right rectangular
prism shown by the net? Show your work.
i think it’s upside down turn your phone or something pls