Answer:
[tex] {x}^{2} + 5x = - 2[/tex]
arrange the equation according to general formula;
General formula: ax² + bx + c = 0
therefore:
[tex] {x}^{2} + 5x + 2 = 0[/tex]
Using the quadratic equation :
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} \\ [/tex]
a » 1, b » 5, c » 2
substitute:
[tex]x = \frac{ - 5± \sqrt{ {5}^{2} - (4 \times 1 \times 2) } }{(2 \times 1)} \\ \\ x = \frac{ - 5± \sqrt{17} }{2} [/tex]
therefore solutions are;
[tex]{ \boxed{ \boxed{x_{1} = \frac{ - 5 + \sqrt{17} }{2} }}} \: \: and \: \: { \boxed{ \boxed{x_{2} = \frac{ - 5 - \sqrt{17} }{2} }}}[/tex]
x is -0.438 and -4.562
Help pleaseeeeeeeee
Refer to the graphic novel frame below. The brochure says that the rope is 500 feet long. Jacob drew a triangle in the sand that is similar to the actual triangle formed by a parasailer and the boat. Use the properties of similar triangles to determine the parasailer's height above
To solve this problem use the property of similar triangles,
"Corresponding sides of the similar triangles are proportional"
By using this property, height of the parasailer is 160 feet.
From the figure attached,
In ΔPQR, a parasailer is a at point P and a boat is at R.Actual length of the rope PR = 500 ftJacob drew a similar triangle ABC in which parasailer is at A and the boat is at C.Let the height (PQ) of the parasailer = x ft
Height of the parasailer AB = 25 ft.
And the length of the rope AC = 2.5 ft.
Since, both the triangles ΔABC and ΔPQR are the similar triangles, their corresponding sides will be proportional.
[tex]\frac{AB}{PQ}=\frac{AC}{PR}[/tex]
[tex]\frac{2}{x} =\frac{2.5}{200}[/tex]
[tex]x=\frac{200\times 2}{2.5}[/tex]
[tex]x=160[/tex] ft
Therefore, height of the parasailer is 160 feet.
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Closure illustrates that a characteristic of a set is not
necessarily a characteristic of all of its subsets. The real
numbers are closed with respect to multiplication, but the irrational numbers, a subset of the real numbers, are not. Give an example of a set that is not mathematical that has a particular characteristic, but which has a subset without this characteristic.
There are many examples to pick from, but one example is this:
The set of rational numbers (aka any fraction of two integers) is closed under the operation of division. Divide any two rational numbers and we get some other rational number.
However, the set of integers is not closed under division. If we divided 10 over 3, then we get 10/3 = 3.333 approximately which isn't an integer. So just because the set of integers is a subset of the rationals, it doesn't mean that the idea of closure follows suit from superset to subset.
Side note: The term "superset" is basically the reverse of a subset. If A is a subset of B, then B is a superset of A.
I am very confused on this question.
Answer:
A= (-6, 5)
M= (-1.5, -1)
B= (3, -7)
Step-by-step explanation:
*----------------*---------------*
A M B
B has the same distance from M as A from M.
Write the equation of the line described
Step-by-step explanation:
slope = x factor = - 5/2
Perpendicular slopes must be opposite reciprocals of each other: m1 * m2 = –1
New slope = 2/5 = m
y = mx + b
from the point given y = 2 | x = -4
2 = (2/5 × -4 ) + b
2 = - 1.6 + b
b = 3.6
line equation
[tex]y = \frac{2}{5} x + 3.6[/tex]
2. Ifj(x) = x2 + 1, find j(a + 1).
Step-by-step explanation:
if you mean x multiply 2 :
j(x) = 2x + 1
j(a+1) = 2(a+1) + 1
= 2a+ 2 +1
=2a + 3
if you mean x to the power of 2
j(x) = x^2 +1
j(a+1) = (a+1)^2 + 1
= a^2 + 2a + 1 +1
= a^2 + 2a + 2
What are the steps in finding the conditional distribution of a certain category in a dataset. Give an example and solve it.
Answer:
just distribute
Step-by-step explanation:
Just kidding HAHA
PLEASE HELP ASAP WILL GIVE POINTS AND BRAINLIEST
Answer:
option 2 is answerrrrrrrrrr
Pls help! URGENT ONLY DO QUESTION 21 PLS
Answer:
y = x - 8
Step-by-step explanation:
There's no magic method to doing these, and problem 21 makes it harder to see a pattern by using inputs that are not consecutive integers (like problem 20 does)!
Looking at inputs 20 and 21, the outputs are 8 less than the inputs. Check the other inputs and notice that the same pattern holds up.
Let p: A shape is a triangle.
Let q: A shape has four sides.
Which is true if the shape is a rectangle?
O pva
O р а
O p 9
O 9 p
Which of these numbers are divisible by 2? a 45. b 70. c 497. d 2380. e 6678. f 12443.
Answer:
b, d and e
Step-by-step explanation:
Only even numbers are divisible by 2
The only even numbers in the list are
b 70
d 2380
e 6678
help me to solve it
Answer:
plz repost it
Step-by-step explanation:
A line goes through the points (7, 3) and (11, 5). What is the equation of the line? Answer quick pls.
Step-by-step explanation:
slope = ( y2-y1) / (x2-x1)
= (5-3) / (11-7)
= 1/2
y= mx+ b
m = slope
5 = 11/2 + b
5 - 5.5 = b
b = -0.5
the equation y = 1/2(x) - 0.5
The equation of line is x-2y =1
How do you find equation of a line?To find an equation of a line given the slope and a point.Identify the slope.Identify the point.Substitute the values into the point-slope form, y − y 1 = m ( x − x 1 ) . y − y 1 = m ( x − x 1 ) .Write the equation in slope-intercept form.Slope-intercept form: The equation of line with slope m and making an intercept c on the y-axis, is y = mx + c.
Given coordinates are:
(7, 3) and (11, 5)
now, equation of line
(y- y1)= (y2-y1)/(x2-x1) *(x-x1)
y-3 =(5-3)/(11-7) *(x-7)
y-3= 2/4 * (x-7)
y-3= 1/2(x-7)
2y-6= x-7
x-2y =1
Hence, the equation of line is x-2y =1.
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slopes , a few questions I need help on
help me solve this plz
Answer:
sorry but this photo is not clear
Answer:
blur photo cannot answered
Name a pair of vertical angles, a straight angle, and two acute angles
other than
Step-by-step explanation:
While there are no examples available, there is the room to understand each angle type you listed, vertical angles are angles that are opposite from each other, and they are congruent (they have the same angle in degrees) now, imagine that for vertical angles, they are in an X top and bottom are equal, and the two sides are equal. For a straight angle, that is usually two angles that are right angles (90 degrees) back to back, meaning when you add 90 and 90 degrees together, you get a straight line or a 180 degree angle. An example of an acute angle is any angle less than 90 degrees, that is a real number, so imagine 25, 40, and 60 as all acute angles.
Hope this helps you identify them in your problem!
What is the image point of (-8,9)(−8,9) after a translation right 3 units and down 1 unit?
Answer:
(-5,8)
Step-by-step explanation:
The left number represents the x-axis, the right one the y-axis. A translation to the right means in the positive direction on the x-axis, which is why we add 3 to -8 which gives us -5. Down on the y-axis is in the negative direction, which means we have to subtract 1 from 9, giving us 8.
Answer:
the answer is the same since it is the same numeral so in terms of y=mx+c and x1/y1 would be inversely proportional to x2/y2 which is perfectly direct proportional to x3/y3×2 and then dy over dx is the problem of integration so you use (x2/x3÷y2/y3)×x1^y1
(-10) – 48 – (-27)
Can someone help me?
Answer:
I think it's -31
Step-by-step explanation:
I just did it on calculator
Answer:
-31
Step-by-step explanation:
respect BODMAN
open first bracket and its -10, -10-48-(-27)
open second bracket and its - times - is a +
-10-48+27
=-31
Nina can braid 144 inches of rope in 3 hours find her unit rate round your answer to the nearest thousand
Answer:
48 inches
or
0.8 minutes
Step-by-step explanation:
To find the unit rate of inches per hour, divide 144 by 3.
144÷3=48
You don't need to round because there are no decimals.
To find the time to braid 1 inch, first multiply 3 by 60 (because there are 60 minutes in 1 hour).
3×60=180
Then divide 144 by 180.
144÷180= 0.8
You don't need to round because there are no thousandths.
A group of 123 students went on a field trip to
collect seashells. If the students collected 15 shells
each, how many shells did they collect?
Answer:
8.2
Step-by-step explanation:
If each student in the group collected 15 shells, we know that there are 123 students on the field trip, so we can take 123 and divide it by 15 to get 8.2 or 41/5.
How many different 6-digit license plates are possible if the first 3 digits can be any letter and the last 3 digits can be any number?
A. 108
B. 17,576,000
C. 128
D. 15,725,000
Answer:
B
Step-by-step explanation:
every position on the license plate is independent from the others.
so, for each position we have the full choice of all possibilities.
there are 26 letters in the alphabet. and there are 10 different single numeric digits.
so, for the first position we have 26 possibilities. as we have for the second and third positions.
the means for each option for the first position we have 26 choices for the second.
that is 26×26.
then for each given choice of the first 2 positions we have 26 choices for the third position.
that is then 26×26×26 possibilities.
for each of the given choices of the first 3 positions we have 10 choices on the fourth position. and then on the fifth and the sixth positions.
the makes altogether
26×26×26×10×10×10
even without calculator I know it must be B, because the number of possibilities must end with 3 "0"s (due to the 10×10×10).
and the main number block must end with a "6" due to 26×26×26, which means for the last position we only need to consider 6×6×6. 6×6 = 36 ending in a "6". and that again multiplied by 6 is again 36 ending in a "6".
so, 26×26×26 has to end with a "6". that gives us B.
Determine the sum of the first 10 terms of each geometric series.
a) 4 + 12 + 36 + ...
Answer:
I think the sum of the first 10terms of each geometric series is
4x3=12
= 4+12
12x3=36
=4+12+36
36x3=108
=4+12+36+108
108x3=324
=4+12+36+108+324
324x3=972
=4+12+36+108+324+972
972x3=2916
= 4+12+36+108+324+972+2916
2916x3=8748
=4+12+36+108+324+972+2916+8748
8748x3=26244
=4+12+36+108+324+972+2916+8748+26244
26244x3=78732
=4+12+36+108+324+972+2916+8748+26244+78732=the sum of the geometric series which is = 118,096.
hope this helps I am not sure of the answer but I tried my best.
the product of a number and 5
12 The diameter of a circle is 24 cm. Its radius is
Answer:
Radius of circle=24cm÷2
=12cm
Help Please need answer in 10 minutes
Answer:
Answers
Step-by-step explanation:
PLZ HELP (-8x-6)-4 to the 2nd power
Answer:x=-0.75
Step by step: 4 to 2nd power multiple 4 by 4 you get 16 so (-8x-6)16 multiply 16 to -6 and -8x and so on...
How can you use slope to determine whether the parallelogram is a rectangle?
Step-by-step explanation:
To do this we need to calculate the slope of each side. If we can show that the slopes of the opposite sides are the same, then the opposite sides are parallel. The slopes of the opposites were the same, so ABCD is a parallelogram.
Solve the quadratic equation 3x²-5x=7
Give answer to 3 significant figures
Answer:
2.57
Step-by-step explanation:
3x²-5x-7=0
Eqn and u will get the answer
A number tmies two divied by four
Answer:
2
Step-by-step explanation:
2÷2 is 4 because 2×2 is 4 and it is asking that how many times two divided by four so A number 2 times two divided is four
Find the sum
3/4 + 1/2=
Answer: 3/4+1/2= 1¼
Step-by-step explanation:
1/2= 2/4 3/4+2/4=1¼
