This equation cannot be factorised, at least not easily. It would require decimals and that's not worth the time. Instead you can use the quadratic formula to solve for x, which works for any quadratic equation:
[tex]\frac{-b + or - \sqrt{b^{2} - 4ac} }{2a}[/tex]
a being the x^2 coefficient
b the x coefficient
and c the constant
here a = 21
b = -55
c = -14
let's solve this one:
[tex]\frac{-(-55) + \sqrt{(-55)^{2} - 4(21)(-14)} }{2(21)}[/tex]You can simply input this into a calculator to find the answer, or you can work it out mentally.
= 2.852740993
Now, since this is a quadratic we need to possible values of x. So we just redo the same formula, but this time with a negative square root:
[tex]\frac{-(-55) - \sqrt{(-55)^{2} - 4(21)(-14)} }{2(21)}[/tex]
= -0.2336933736
You can round these answers however you like, but I would recommend doing to either 3 significant figures, either 2 or 3 decimal places.
Answer:
[tex]\displaystyle [7x - 2][3x - 7][/tex]
Step-by-step explanation:
Find two quantities that when summed to 55, they also multiply to 294. Those will be 6 and 49. The TINIER quantity gets the plus sign because the B-value is −55, therefore 49 gets the minus sign, leaving 6 with the plus sign. In extension, sinse we have a leading coefficient greater than one, we need to take extra procedures. Here is how it is done:
[tex]\displaystyle 21x^2 - 55x + 14 \\ \\ [21x^2 + 6x] - [49x + 14] \\ 3x[7x - 2] - 7[7x - 2] \\ \\ \boxed{[7x - 2][3x - 7]}[/tex]
I am joyous to assist you at any time.
**For all you moderatours out there, this user made a typographical errour with the symbol of the C-value. It was supposed to be 14, not −14. BELIEVE ME.
What is the answer -10b-7=9?
i think it should be -1.6
if you add 7 to 9 it'll be 16.
if you divide -10 by 16 it'll give you -16/10.
simplify it and you should get -8/5 or -1.6.
Find the value of x. Then classify the triangle by its angels
Answer:
x=134
Step-by-step explanation:
As angles in a triangle add up to 180 degrees
also angles on a straight line add up to 180
so 180-(64+70)=46
and 180-46=134
PLEASE GIVE BRAINLIEST AND THANKS
Do 2b + b and 3b have the same value for all values of b?
Answer:
Yes
Step-by-step explanation:
2B+B=3b and 3b and 3b are the same.
Thus, they have the same value
answer this question
Answer:
95°
Step-by-step explanation:
all triangles add up to 180 so
19x + 10x + 7x = 180
36x = 180
36 36
x = 5
19(5) = 95°
7(5) = 25°
10(5) = 50°
Answer :8.3
Step-by-step explanation:
i need help n njnkjjknknknknjnjnkn
Answer: 640
All you have to do is Length times Width times Height.
Step-by-step explanation:
4x10x16
4x10=40
40x16=640
So, 640 your answer.
Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below.
Alexandra
Chi
Swim
5 km/hr
6 km/hr
Transition 1
4 minutes
5 minutes
Cycle
15 km/hr
15 km/hr
Transition 2
3 minutes
5 minutes
Run
6 km/hr
7.5 km/hr
Complete question :
Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below.
How long does it take Alexandra to complete the triathlon. Write a linear equation to model total time t in hours.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
SWIM:
Alexandra __5km/hr
Chi _______ 6km/hr
Transition 1:
Alexandra __ 4 minutes
Chi _______ 5 minutes
CYCLE:
Alexandra __15km/hr
Chi _______ 15km/hr
Transition 2:
Alexandra __ 3 minutes
Chi _______ 5 minutes
RUN:
Alexandra __6km/hr
Chi _______ 7.5km/hr
Distances:
swim distance = 1.5km
bicycle ride distance = 40km
run distance = 10km
Time taken by Alexandra :
time = distance / speed
Swim time = 1.5km / 5km/hr = 0.3 hr
Transition 1 = 4/60 = 0.067 hr
Cycle time = 40km / 15km/hr = 2.67 hours
Transition 2 = 3/60 = 0.05 hr
Run time = 10 / 6km/hr = 1.67 hrs
Total time(t) in hours taken by Alexandra :
(0.3 + 0.067 + 2.67 + 0.05 + 1.67) hrs = 4.757 hours
Time taken by Chi :
time = distance / speed
Swim time = 1.5km / 6km/hr = 0.25 hr
Transition 1 = 5/60 = 0.083 hr
Cycle time = 40km / 15km/hr = 2.67 hours
Transition 2 = 5/60 = 0.083 hr
Run time = 10 / 7.5km/hr = 1.33 hrs
Total time(t) in hours taken by Chi
(0.25 + 0.083 + 2.67 + 0.083 + 1.33) hrs = 4.757 hours = 4.416 hours
the select options are: "how many days" "how much money" "how many hours" PLEASE HELP LAST TIME I POSTED THIS QUESTION I GOT A FAKE LINK >:(
Answer:
25
2.5
how many hours
I hope this helps
Help PLEASE! I will make you brainlist!
Answer: proportional
Step-by-step explanation: it is proportional because you can multiply any number by 7
13) through: (0, -1) and (-5,-1)
A) x + 3y = 3
B) x - 3y = 1
C) 5r - 3y = -3
D) y=-1
Answer:
y=-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-(-1))/(-5-0)
m=(-1+1)/-5
m=0/-5
m=0
y-y1=m(x-x1)
y-(-1)=0(x-0)
y+1=0
y=0-1
y=-1
What is the complementary angles, one angle on is 2 degrees larger than the second angle?
Answer:
44 and 46
Step-by-step explanation:
A complementary angle is 90 degrees
90/2 = 45
If 45 + 45 = 90
44 + 2 = 46
44 + 46 = 90
:)
Graph the system of linear inequalities on the coordinate plane.
Shade the solution to the system of inequalities.
Pick a point and show your solution is correct.
The graph can be seen at the end, and by looking at it, you can see that a solution can be (10, 0).
How to graph the system of inequalities?
y ≥ (-1/2)*x + 2 + 1/2
y < (1/5)*x + 6
To graph it, first we need to graph the lines:
y = (-1/2)*x + 2 + 1/2
y = (1/5)*x + 6
Once you have this, we analyze each inequality.
y ≥ (-1/2)*x + 2 + 1/2
Because we use the symbol ≥ we need to use a solid line and we need to shade the region above the line.
For y < (1/5)*x + 6 we need to use a dashed line (the symbol < implies that the points on the line are not solutions) and we need to shade the region below the line.
Then the solution of the system is given by the intersection of the shaded region.
For example, a solution can be the point (10, 0), which you can see that belongs to that region.
If you want to learn more about systems of solutions, you can read:
https://brainly.com/question/9774970
Please help, what is x? This is an exponential function, please show the steps!
(25^x)(5^x+3) = 625^x-7
x = ?
Find the distance between nine and one fourths to seven and one half and four to five
Answer: home / math / distance calculator
Distance Calculator
The calculators below can be used to find the distance between two points on a 2D plane or 3D space. They can also be used to find the distance between two pairs of latitude and longitude, or two chosen points on a map.
2D Distance Calculator
Use this calculator to find the distance between two points on a 2D coordinate plane.
Result
Distance: 7.8102496759067
Steps:
Distance (d) = √
Step-by-step explanation:
Enzo has $20.79 to spend on fruit. If each kiwi costs $0.99, how many kiwis, , can they purchase?
20.79 ÷ 0.99 = k
which number is correct
19
20
21
22
Answer:
21
Enzo can only buy 21 kiwis from the store.
Step-by-step explanation:
We have to divide
But since it's going too be hard for me to show you the long division, I'm just going to use a multiplication trick!
Let's find what is 20x0.99 first, because I feel like this CAN be the answer.
20x0.99=19.8
So this is not the answer
Now, let's try 22x0.99
22x0.99=21.78
So this is also not the answer.
Now, let's try 21, I think only this one can be the answer.
21x0.99=20.79
So hence, 21 is the right answer. Enzo can buy 21 Kiwis
Thanks!
~[tex]FieryAnswererGT[/tex]~
Answer:
21
Step-by-step explanation:
Given;
Enzo has $20.79 to spend on fruit.
Each Kiwis cost $0.99
Note;
20.79 ÷ 0.99 = k
or
20.79 ÷ 0.99 = Solution
Solve;
[tex]\mathrm{Multiply\:the\:numerator\:and\:denominator\:by:}\:100[/tex]
[tex]\frac{2079}{99}[/tex]
[tex]\mathrm{Write\:the\:problem\:in\:long\:division\:format}[/tex]
[tex]\begin{matrix}99\overline{|\smallspace2079}\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
[tex]Divide\;207\;by\;99\;to\;get\;2[/tex]
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 99\overline{|\smallspace2079}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace9\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace9\emptyspace9\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
[tex]Divide\;99\;by\;99\;to\;get\;1[/tex]
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace1\:\:\:\:\:\:\:\:\:\:\:\:\\ 99\overline{|\smallspace2079}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace9\emptyspace8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace9\emptyspace9\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace9\emptyspace9}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
[RevyBreeze]
1 and 4 are congruent because
Answer:
Transitive Property of Congruency;If parallel lines have a transversal, then alternate interior angles are congruent.
Step-by-step explanation:
Nicole accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Nicole's salary will be $100000 and after working for the company for 5 years, she will have a salary of $110000. Write an equation for S,S, in terms of n,n, representing Nicole's salary after working nn years for the company.
Answer:
S=2000n+100000
Step-by-step explanation:
Since Nicole will have a salary of $110000 after working 5 years for the company, we know that S = 110000 when n = 5.
Find the slope using the two points.
110000 - 100000 10000
m = ------------------------ = ---------- = 2000
5-0 2
The slope shows how much the salary increases each year, which is the same thing as saying that Nicole got a raise of $2000 every year.
What is the perimeter of trapezoid jklm? startroot 2 endroot startroot 5 endroot units 2 startroot 2 endroot startroot 5 endroot units 9 2 startroot 2 endroot units 9 startroot 2 endroot startroot 5 endroot units
The perimeter of the trapezoid is 9 + √2 + √5 units. then the correct option is D.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
The points are J(-7, 4), K(-4, 4), L(-2, 3), and M(-8, 3).
We know that distance between two points will be given as
[tex]\rm D= \sqrt{(x_2 - x_1 )^2 + (y_2 - y_1)^2}[/tex]
The distance between JK will be
[tex]JK = \sqrt{(-4+7)^2 + (0)^2 } = 3[/tex]
The distance between KL will be
[tex]KL = \sqrt{(-2+4)^2 + (3-4)^2 } = \sqrt5[/tex]
The distance between LM will be
[tex]LM = \sqrt{(-8+2)^2 + (0)^2 } = 6[/tex]
The distance between JK will be
[tex]MJ = \sqrt{(-7+8)^2 + (4-3)^2 } = \sqrt2[/tex]
Then the perimeter will be
Perimeter = JK + KL + LM + MJ
Perimeter = 3 + √5 + 6 + √2
Perimeter = 9 + √2 + √5
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
Answer:
the correct answer would be D
Step-by-step explanation:
Is the relationship between the time spent swimming and the number of weeks proportional? Complete the statements
Answer:
lie on goes
Step-by-step explanation:
answer is Lie On For First And Goes For Second
hurry due today, help, please
Use the graph or table to write a linear function that relates y to x
An example for #5 is y=-8x+2, and an answer for 6. is y=6x+9. The formula is y=mx+b so the b is the y-int/y and the m is the slope/x. The x is the variable(the one beside the m).
What is 2.1 x 10^4written in standard form is
Answer:
21000
Step-by-step explanation:
You move the decimal point over that many times as the power of 10.
IT is found that [tex]2.1 \times 10^4[/tex] can be written in standard form as 21,000.
Since Scientific notations have some of the profits are Better readability due to compact representation
The value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
To convert from scientific notation to standard form, we simply move the decimal point to the right by the number of places indicated by the exponent (4 in this case).
Starting with [tex]2.1 \times 10^4[/tex] , we move the decimal point four places to the right to get 21,000.
Hence, [tex]2.1 \times 10^4[/tex] in standard form is 21,000.
Learn more about scientific notation here:
https://brainly.com/question/3112062
#SPJ6
Please help!
A building is constructed on top of a cliff that is 300 meters high. A person standing on level ground below the cliff observes that the angle of elevation to the top of the building is 72° and the angle of elevation to the top of the cliff is 63°.
a. How far away is the person from the base of the cliff?
b. What is the building’s height?
The distance from the person to the base of the cliff is 269.78 meters.
The height of the building from the base of the cliff is 829.37 meters
The situation forms right angle triangle.
The building is constructed on top the cliff that is 300 meters high.
Right angle triangle:Right angle triangle has one of its sides as 90 degrees. Therefore, the sides can be found using trigonometric ratios.
The height of the building from the cliff is 300m. let's find the hypotenuse side of the angle of elevation formed to the cliff.
Using sin rule,
300 / sin (72 - 63) = y / sin (180 - 162)
300 / sin 9 = y / sin 18
300 sin 18 = y sin 9
y = 300 sin 18 / sin 9
y = 92.7050983125 / 0.156
y = 594.230769231
Therefore, how far the person to the base of the cliff can be calculated as follows;
cos 63 = adjacent / hypotenuse
cos 63 = x / 594.2307
x = 594.2307 cos 63
x = 269.775092454
x = 269.78 meters
Therefore, the distance from the person to the base of the cliff is 269.78 meters.
height of the cliff / 269.78 = tan 63
height of cliff = 269.78 tan 63
height of cliff = 529.37493165
height of cliff = 529.37
The height of the building = 300 + 529.37 = 829.37493165 = 829.37 meters
learn more on right triangle here: https://brainly.com/question/14806301
Whitney calculated that the circular clock on her wall has a circumference of 18.84 inches. What is the clock's area?
Answer:
28.25in
Step-by-step explanation:
Please help me asappppp
Answer:
<5 ~= <1 - Corresponding Angles Theorem
<1 ~= <7 - Alternate Exterior Angles Theorem
<5 ~= <7 - Vertical Angles Theorem
line I || line m - Transitive Property
What is the value of 532x13
Answer:
the value of 532×13=6,916
Find the coordinates of the midpoint of segment GH with endpoints: G(-2, -8) and H(-3, -12).
Step-by-step explanation:
from midpoint formula p(x,y)= -2 +(-3)÷2 ,-8+(-12)÷2
=-5÷2 , -20÷2
= -2.5 , -10
What is (f - g)(x)?
f(x) = -3x2
g(x) = -5x + 3
Write your answer as a polynomial or a rational function in simplest form.
Work Shown:
(f - g)(x) = ( f(x) ) - ( g(x) )
(f - g)(x) = ( -3x^2 ) - ( -5x+3 )
(f - g)(x) = ( -3x^2 ) - ( -5x) - ( 3 )
(f - g)(x) = -3x^2 + 5x - 3
A triangle has vertices (1,4), (1,-2), and (-3,-2). what is the approximate perimeter of the triangle
Answer:
Perimeter of Traingle is 10 + 2√5[tex]\\[/tex]
Step-by-step explanation:
Let,
A = (1,4)B = (1,-2) C = (-3,-2)[tex]\\[/tex]
To find the perimeter of the traingele with vertices of A (1,4), B(1, -2) and C(-3,-2). We have to first find the distance between each pair of points, which will give length of the sides.
[tex]\\[/tex]
Using distance formula,
[tex]\\[/tex]
[tex] \dashrightarrow \sf \: \: AB = \sqrt{( x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \: AB = \sqrt{{ {(1 - 1)}^{2} } + {( - 2 - 4)}^{2} } \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \: AB = \sqrt{0 + {( - 6)}^{2} } \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \: AB = \sqrt{36} \\ \\ [/tex]
[tex]\pink{ \dashrightarrow\sf \: \: {\underline{AB = 6 }}}\\ \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \: BC = \sqrt{{ {( - 3 - 1)}^{2} } + {( - 2 + 2)}^{2} } \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \:BC = \sqrt{ {( - 4)}^{2} + 0} \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \:BC = \sqrt{16} \\ \\ [/tex]
[tex] \pink{ \dashrightarrow \sf \: \:{ \underline{ BC = 4 }}}\\ \\ \\ [/tex]
[tex]{\dashrightarrow { \sf \: \: {AC = \sqrt{{ {( - 3 - 1)}^{2} } + {(2 - 4)}^{2}}}} } \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \:AC = \sqrt{ {( - 4)}^{2} + {( - 2)}^{2} } \\ \\ [/tex]
[tex] \dashrightarrow\sf \: \: AC = \sqrt{16 + 4} \\ \\ [/tex]
[tex] \dashrightarrow \sf \: \:AC = \sqrt{20} \\ \\ [/tex]
[tex] \pink{ \dashrightarrow \sf \: \: { \underline{AC = 2 \sqrt{5} }}}[/tex]
[tex]\\[/tex]
Now,
[tex]\\[/tex]
[tex] \dashrightarrow\sf \: \: Perimeter = AB + BC + AC \\ \\ [/tex]
[tex] \dashrightarrow\sf \: \: 6 + 4 + 2√5 \\ \\ [/tex]
[tex] \dashrightarrow\sf \: \: {\pink{ \underline{ \boxed { \pmb{ \sf{ \: 10 + 2√5 \: \: }}}}}}[/tex]
[tex]\\[/tex]
Hence,
Perimeter of Traingle is 10 + 2√5Carlos found a nice suit with a price tag of $300. It was on a rack that said take 25% off the price. At the register he got another 10% off of the discounted price of the suit. How much did the suit cost after both discounts were taken off? (Please help)
pls help ASAP this is due in 1 hour and i can't figure it out! HELPPP
the area of the surface of this design is 31 in long
Answer:
392 inches²
Step-by-step explanation:
10 inches × 6 inches = 60 inches²
60 inches² × 2 = 120 inches²
----------------------------------------------------------------------------------------------------------
(6 inches + 4 inches) × 6 inches = 10 inches × 6 inches = 60 inches²
60 inches² × 2 = 120 inches²
----------------------------------------------------------------------------------------------------------
(10 inches × 6 inches) + (4 inches × 4 inches) = 60 inches² + 16 inches² = 76 inches²
76 inches² × 2 = 152 inches²
----------------------------------------------------------------------------------------------------------
Add them all together ~
120 inches² + 120 inches² + 152 inches² = 392 inches²
(12x^2+50x+32)/ (2x+7)
Need the quotient & reminder
Answer:
Quotient: 6x+4
Remainder: 4
Step-by-step explanation:
Hope this helps!