Answer:
B. x = the quantity of 3 plus or minus the square root of 29 all over 2Step-by-step explanation:
Given equation
x² - 3x - 5 = 0The roots are
[tex]x=\cfrac{-b+- \sqrt{b^2-4ac} }{2a}[/tex]Substitute values into equation
[tex]x=\cfrac{3+- \sqrt{(-3)^2-4(1)(-5)} }{2(1)} =\cfrac{3+- \sqrt{9+20} }{2} =\cfrac{3+- \sqrt{29} }{2}[/tex]This is matching the option B
Answer:
[tex]x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2-3x-5=0[/tex]
To find the exact solutions of the given equation, use the quadratic formula or complete the square.
Method 1: Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-3, \quad c=-5[/tex]
Substituting these values into the formula:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(-5)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Method 2: Completing the square
Move the constant to the right side by adding 5 to both sides:
[tex]\implies x^2-3x-5+5=0+5[/tex]
[tex]\implies x^2-3x=5[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2-3x+\left(\dfrac{-3}{2}\right)^2=5+\left(\dfrac{-3}{2}\right)^2[/tex]
[tex]\implies x^2-3x+\dfrac{9}{4}=\dfrac{29}{4}[/tex]
Factor the perfect trinomial on the left side:
[tex]\implies \left(x-\dfrac{3}{2}\right)^2=\dfrac{29}{4}[/tex]
Square root both sides:
[tex]\implies \sqrt{\left(x-\dfrac{3}{2}\right)^2}=\sqrt{\dfrac{29}{4}}[/tex]
[tex]\implies x-\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}[/tex]
Add 3/2 to both sides:
[tex]\implies x-\dfrac{3}{2}+\dfrac{3}{2}=\pm\dfrac{\sqrt{29}}{2}+\dfrac{3}{2}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{29}}{2}[/tex]
Learn more about completing the square here:
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It takes 0.5 gallon of cream to make 1 pound of butter. How much cream would you need to make 2.5 pounds of butter?
What is the volume of a sphere with a radius of 14 cm?
Ayuda, por favor (Help please)
Answer:
see below
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi ( 14)^3
V =3658.666666pi
Using 3.14 for pi
V =11488.21333 cm^3
Using the pi button
V =11494.04032cm^3
Step-by-step explanation:
Volume of sphere----> 4/3π r³
4/3 x 22/7 x 14³. r=14(given)
4. x 22. x 14³
3. 7
4 x 22 x 14x14x2
3
88. x 196 x 2
3
88 x 392
3
34496
3
11498.6 answer
hope this helps you
have a nice day
What expression is equivalent to 1-2 sin^2x?
I know the answer is 2cos^2x-1, but unsure how to solve it. Do I use the Pythagorean identity to start?
Thanks!
Answer:
1-2*sin^2 (x) = 2cos^2(x) -1
Step-by-step explanation:
1-2sin^2(x)
= 1-2(1-cos^2(x)) =2cos^2(x)-1; Pythagorean identity, sin^2(x)=1-cos^2(x)
=1-2+2cos^2(x)=2cos^2(x)-1; distribute
= -1+2cos^2(x)=2cos^2(x) -1; collect and rearrange terms
= 2cos^2(x)-1 = 2cos^2(x)-1
Calculate the distance between the points (7, 4) and (-5, -3).
Answer:
D = √193 units
or
D = 13.892 units
Step-by-step explanation:
Given:
(7, 4) and (-5, -3)
Calculate the distance
Solution:
[tex] \rm \: Distance (D) = \sqrt{( x_{2} - x_{1}) {}^{2} + (y_{2} - y_{1) {}^{2} }} [/tex]
Now, substitute the values given:
[tex] \rm \: D = \sqrt{ \{( - 5) - 7 \}^{2} + \{( - 3) - 4 {}^{} \} {}^{2} } [/tex]
[tex] \rm \: D = \sqrt{ \{12 \}^{2} + \{( - 3) - 4 {}^{} \} {}^{2} } [/tex]
[tex] \rm \: D = \sqrt{ 144 + \{( - 3) - 4 {}^{} \} {}^{2} } [/tex]
[tex]\rm D = \sqrt{144 + \{ 7\}{}^{2} } [/tex]
[tex] \rm \: D = \sqrt{144 + 49} [/tex]
[tex] \boxed{\rm \: D = \sqrt{193}} [/tex]
[tex] \boxed{\rm \: D =13 .892}[/tex]
Thus, Distance between the two given points will be √193 or √13.892 units.
Answer:
[tex]\bf \sqrt{193}[/tex] units or 13.9 units is the distance.
Explanation:
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 +(y_2 - y_1)^2}[/tex]
Given points: (7, 4) and (-5, -3)
Identify following:
[tex]\sf x_2= 7[/tex], [tex]\sf x_1 = -5[/tex], [tex]\sf y_2 =4[/tex], [tex]\sf y_1 =-3[/tex]
Find distance:
[tex]\rightarrow \sf \sqrt{(7 - (-5))^2 + (4 - (-3))^2} \quad = \quad \sqrt{144+49} \quad = \quad \sqrt{193} \quad \approx \ 13.9[/tex]
A storage rental company charges $1 for
the first month and $25 per month for the next
two months. After three months, the cost is
$20
per
month. How much would it cost to
rent a unit for 10 months?
A $151
$
B
$171
C$191
D
$211
Answer:
C
Step-by-step explanation:
Jan:1$
Feb and March: 50$
April to Oct: 140$
=>1+50+140=191
-
A road is defined by y = x - 3. A house is
located at the coordinates A(6,5). Determine the
shortest distance from the house to the road.
so x-3=4 you add 3+4=7 and your answer is x=7
In figure below points T,R,X,Y and Z
Answer:
a
Step-by-step explanation:
Which equation represents the polar form of x – y = 0?
Answer:
x means 2 and y means -2
Step-by-step explanation:
Of the 300 fifth graders at Benson Elementary School, 40% signed up for an after-school activity. How many students signed up for an after-school activity?
Answer: 120 students
Step-by-step explanation:
multiply 40 by 300 then divide by 100 = 120
can anyone help me find the area pls ty
Answer:
42 in^2
Step-by-step explanation:
The given is a parallelogram and to calculate the area of a parallelogram we multiply its height and base
The height here is given as 6in and base is 7in
7*6 = 42, the area is presented in square units so the answer is 42 in^2
Find m/H.
126⁰
F G
m/H=
(6x - 1)
H
(5x +17)
Answer:
59 degrees
Step-by-step explanation:
180 - 126 = 54
6x-1 + 5x + 17 +54 =180
11x + 70 = 180
11x = 180 -70
11x = 110
x =10
Therefore
6(10) - 1 = 59 degrees
HELP ME PLEASEEEEE ASAP TYYYY
Step-by-step explanation:
with 2 dice we have 6×6 = 36 possible outcomes.
you know
1, 1
1, 2
1, 3
...
6, 6
from these 36 possible outcomes only the following have a sum of 4 :
1, 3
2, 2
3, 1
so, 3 out of 36.
that mags the probability is
3/36 = 1/12
the first answer option is correct.
Help I can’t figure
Which one represents y as a function of x.
Answer:
the graph
Step-by-step explanation:
The statement "*Remember ..." tells you how to identify the functional relations.
__
In the top diagram, each x-value maps to more than one y-value. Effectively, that means x is repeating (not a function).
In the set of ordered pairs, the value 3 shows up as an x-value more than once. It repeats (not a function).
In the graph, each value of x is shown as corresponding to exactly one value of y. The graph shows y as a function of x.
On the mapping one
0 has two ranges i.e 0 and 12
As it doesn't has unique range it's not a functionWhere as in the graph
Every x has unique y f(x)=yGraph represents a function
Jamie has 9 gallons of paint that she needs to pour into containers that
hold 0.75 gallon. How many containers will she need?
Answer:
12:)
Step-by-step explanation:
This is a program for development that lists what an athlete hopes to do in order to meet their goals.
A. Feedback
B. Action Plan
C. none of these
D. Area for improvement
Answer:
B. Action PlanStep-by-step explanation:
#hope it helps!
Answered by ReyvREYV111
Help!
Simplify: 9log9(4)
Answer:
hope this will help you
Step-by-step explanation:
Let x = 9log9(4)
x = 9[log(4)/log(9)]
x = 9*0.6224
x = 5.6016
Someone help please
Answer:
32
Step-by-step explanation:
ok if it was a normal rectangle =
8 x 6
but the middle part takes 4 from the middle
since there are 2 rectangle
4/2 = 2
since there are lines
6 x 2 = 12 + another 12 since the rectangle on the bottom is the same as the top
24 + ...
6 - 4
2 x 4 = 8
24 + 8 =
32
Determine whether the following situation would produce a random sample. Write Yes or No and explain your answer. Two hundred students at a school basketball game are surveyed to find the students' favorite sport. a. Yes, students preferring different sports may be in the group. b. Yes, this may be the only sporting event occurring that day. c. No, students attending this event are more likely to enjoy basketball. d. No, student attendance may have been required at this event.
Answer:
c.
Step-by-step explanation:
Students who have chosen to attend a basketball game are more likely to like basketball.
19. The area of the square is half the area of the rectangle. Find x.
2(x+4)
Answer:
2x+8
Step-by-step explanation:
WILL GIVE BRAINLIEST 25 POINTS
What is the perimeter of this rectangle?
Answer:
6√17 units
Step-by-step explanation:
A property of rectangles is that their opposite sides are equal in length.
Hence, to find the perimeter :
AB + BC + CD + DA2(AB) + 2(BC)2(AB + BC)Finding AB by applying distance formula :
AB = √(1 + 3)² + (4 - 3)²AB = √4² + 1²AB = √16 + 1AB = √17Finding BC :
BC = √(3 - 1)² + (-4 - 4)²BC = √2² + (-8)²BC = √4 + 64BC = √68BC = 2√17Perimeter :
P = 2(AB + BC)P = 2(√17 + 2√17)P = 2(3√17)P = 6√17 unitsPLEASE HELP ASAP!!! I WILL GIVE BRAINLIEST TO THE RIGHT ANSWER
It is a Part A and Part B Question
Note: please add the answer next to what part it's from so I can know which part was answered
Answer:
Option A is correct.
Step-by-step explanation:
1. solve the inequalities
2. find the intersection :)
Convert 29/30 to a decimal
Answer:
0.97
Step-by-step explanation:
To convert a fraction to a decimal, divide the numerator by the denomiator.
29 ÷ 30 = 0.966666667
= 0.97 (rounded)
hope this helps!
244 people must be split into 4 equal groups. How many people in each group
Answer:
61 people per each group
Step-by-step explanation:
244/4= 61
Answer: 61 people in each group
Step-by-step explanation: 244 divided by 4 is 61
This is a gardener's floor plan of their backyard. Enter the amount of grass, in square yards
needed to completely cover the backyard.
Answer:
39 yd^2
Step-by-step explanation:
First, we must divide the shape into quadrilaterals. The best, and easiest, way to do this is to cut along the line in the middle, below the lower 2 yd mark. This will give us a 1 yard by 3 yard rectangle, 4 yard by 8 yard rectangle, and 2 yard by 2 yard square. The next thing to do is to find the area of each location of the backyard using the A = l x w equation. 1 x 3 = 3, 2 x 2 = 4, 4 x 8 = 32. The final step is to add these individual areas, giving us 39 square yards.
Which equation represents this ellipse?
answer d
y^2/25+x^2/4=1
We can find the equation that represent the equation of ellipse we can identify by the major axis and minor axis, and center.
What is ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have equation of ellipse:
[tex]\rm \dfrac {y^2}{25}+\dfrac{x^2}{4}=1[/tex]
[tex]\rm \dfrac {y^2}{5^2}+\dfrac{x^2}{2^2}=1[/tex]
Here a = 5, and b = 2
Major axis is 2a = 2(5) = 10
Minor axis is b = 2(2) = 4
Here a graph is not given, if
Thus, we can find the equation that represent the equation of ellipse we can identify by the major axis and minor axis, and center.
Learn more about the ellipse here:
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Grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation can he use to find n, the number of gallons of water he should remove?
3.52 (22 minus n) = 0.24
StartFraction 22 minus n Over 3.52 EndFraction = StartFraction 24 Over 100 EndFraction
StartFraction 3.52 Over 22 minus n EndFraction = StartFraction 24 Over 100 EndFraction
3.52 + (22 minus n) = 0.24
The equation that he can use to find n, the number of gallons of water he should remove is; (3.52)/(22 - n) = 24/100
How to Calculate Chemical quantities?Let us first find the amount of ammonia in 22 gallons of 16% ammonia solution.
This gives;
Amount = 16% * 22 gal
Amount = 3.52 gal
Now, the amount of ammonia remains the same after the water evaporates, but the total amount of solution will reduce by the amount of water that evaporates.
Amount of ammonia = 3.52 gal
Amount of water that remains = 22 - n
Desired concentration = 24% = 24/100
Thus, the equation is;
(3.52)/(22 - n) = 24/100
Read more about Chemical Quantities at; https://brainly.com/question/26150306
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2 3/4 miles in 2/3 of an hour enter number of miles she can jog in 3 hours
19
Celeste knows that there are 5,280 feet in 1 mile. What proportion can she use
to find the number of feet in 7 miles?
Answer:
[tex]\frac{1mile}{5,280ft} =\frac{7miles}{"x"feet}[/tex]
Step-by-step explanation:
so there are 5,280 feet in 1 mile
We want to find the number of feet in 7 miles
if we were to set up a proportion it would look something like this :
[tex]\frac{1mile}{5,280ft} =\frac{7miles}{"x"feet}[/tex]
Find an equation for the line that passes through the points (-5,-6) and (1,3).
Answer:
y=3/3x+3/2
Step-by-step explanation:
(-5,-6)(1,3)
x1y1 x2y2
y2-y1/x2-x1
m=3/2
b=3/2
ast year Ryan went to school for 36 out of 52 weeks. Which fraction is
NOT equivalent to 367
52
A
DO
음
76 Els to lo
C
O
26
Answer:
76/26
Step-by-step explanation:
