The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135
What is completing the square method?Completing the square method is one of the methods to find the roots of the given quadratic equation.
Given equation is:
[tex]x^{2}[/tex]-15x +2 =0
Using Completing the Square method we have
[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0
Now,
[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0
or, [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4
or, [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]
or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135
Thus, the roots of the quadratic equation are: 14.865 and 0.135
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Need help please. Determine whether the statement is true or false.
Answer:
false
Step-by-step explanation:
Find the value of x in the parallelogram below. Enter each line of work as an equation.
Answer: 110
Step-by-step explanation:
Adjacent angles of a parallelogram are supplementary, so [tex]70+x=180 \longrightarrow x=110[/tex]
Pleaseeee helplpppppp
Answer:
Step-by-step explanation:
can someone tell me what letter or variable it is after the = sign, is it an K or R?
Which best describes the three-dimensional figure that can be made from the net shown?
a triangular prism that might not have 4 congruent and equilateral triangles
a triangular pyramid that might not have 4 congruent and equilateral triangles
a triangular prism that must have 4 congruent and equilateral triangles
a triangular pyramid that must have 4 congruent and equilateral triangles
Answer:
Option C
Step-by-step explanation:
See here the net seems like a equilateral triangle
And another equilateral traingle is inscribed in itSo 4 equilateral trianglesHence option C
What is the distance between the two points?
Pyramid A has a volume of 60 mm3 and Pyramid B has a volume of 937.5 mm3. What is the ratio of their heights?
A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. The ratio of the height of pyramid A to pyramid B is 0.064.
What is a pyramid?A pyramid is a polyhedron built by connecting a polygonal base and a point known as the top. A lateral face is formed by the base edge and top of each triangle.
The volume of a pyramid is given by the formula,
Volume of the pyramid = (Length×Width×Height)/3
= (Area of base ×Height)/3
If the area of the base of the two pyramids is the same, then the ratio of the volume of the two pyramids will be,
[tex]\dfrac{\text{Volume of Pyramid A}}{\text{Volume of Pyramid B}} = \dfrac{60\rm\ mm^3}{937.5\rm\ mm^3}\\\\\\\dfrac{3 \times \text{(Area of base})_a \times h_a}{3 \times \text{(Area of base})_b \times h_b}= \dfrac{60}{937.5}\\\\\\\dfrac{h_a}{h_b} = 0.064[/tex]
Hence, the ratio of the height of pyramid A to pyramid B is 0.064.
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Order from least to greatest 7.2 7.04 7.413 7.134
Answer:
7.04, 7.134 ,7.2, 7.413
Step-by-step explanation:
1) If the diameter of a circle is changed from 8 cm to 4 cm, how will the circumference change?
A) increases by a factor of 2
B) decreases by a factor of 2
C) increases by a factor of 4
D) decreases by a factor of 4
Answer:
the answer is B.
Step-by-step explanation:
the formula for circumference of a circle is [tex]\pi[/tex]×diameter=C
[tex]\pi[/tex]·8=25.13
[tex]\pi[/tex]·4=12.56
12.56·2=25.13
Maria bought an open-based pop-up net to put over the plates at the picnic to keep the bugs off of the food. a square pyramid. the square base is 16 inches by 16 inches and the pyramid has a height of 15 inches. how much space is there inside each empty pop-up net? 544 inches cubed 800 inches cubed 1,280 inches cubed 1,920 inches cubed
Based on the height of the pyramid and the dimensions of the square base, the space that Maria has inside the pop-up net is 1,280 in³.
How much space does Maria have?This can be found as the volume of a pyramid which is:
= (Length x Width x Height) / 3
Solving gives:
= (16 x 16 x 15) / 3
= 3,840 / 3
= 1,280 in³
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Does anybody know this? I keep getting the wrong answer. ABC~PRT AC=15 BC=12 and PT=6 find the ares of ABC if the area of PRT=24mm^2
Answer:
The area of triangle ABC is 60 mm^2
Step-by-step explanation:
x = the area of triangle ABC
15/6 * x/24
x=60
Answer:
(d) 150 mm²
Step-by-step explanation:
The scale factor between the triangles is the ratio of the lengths of corresponding sides. The area ratio is the square of the scale factor.
__
scale factorΔABC is larger than ΔPRT by the factor ...
AC/PT = 15/6 = 5/2
areaThe area of ΔABC is the square of this factor times the area of ΔPRT:
area ABC = (5/2)²×area PRT
area ABC = (25/4)×(24 mm²)
area ABC = 150 mm²
I’ll mark brainly if you answer this
Answer:
I'm pretty sure it is (c)
Step-by-step explanation:
bc the angle is not read in the right order
Find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. leave your answer in terms of π.
Answer:
60π
Step-by-step explanation:
Formula for surface area of a cylinder is 2πrh + 2r²π
2πrh: this is the formula to find the area of the cylinder itself (circumference of the base times the height of the cylinder)
2r²π: this is the formula to find the area of the 2 circles at the end of the cylinder (area of a circle times 2)
We can substitute h with 7 and r with 3 to solve:
2πrh + 2r²π
2(3)(7)π + 2π(3²)
42π + 18π
60π
That is your answer
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A cube-shaped aquarium has edges that are 1.75 ft long. the aquarium is filled with water that has a density of 72" lb/f" "t" ^3.
(a) should the aquarium be placed on a table that can support a maximum weight of 150 lb? explain why or why not.
(b) would the density of the water change if the aquarium was only half full? explain.
Answer:
No and the density changes along with the weight.
Answer:
(a) No. The weight is more than 150 lb.
(b) No. Density is not a function of volume.
Step-by-step explanation:
The weight of the aquarium is the product of the volume and the density of the contents.
(a)The volume of the aquarium is the product of its dimensions:
V = LWH = (1.75 ft)(1.75 ft)(1.75 ft) = 1.75³ ft³ = 5.359375 ft³
The weight of its contents, at 72 lb/ft³ will be ...
(72 lb/ft³)(5.359375 ft³) = 385.875 lb
The aquarium should not be placed on the table. The weight of the aquarium is too great for the load limit of the table.
__
(b)The density of water is the ratio of its mass to its volume. Density does not change with depth or volume. It is essentially constant. (Water is considered to be virtually incompressible. Its density changes slightly with temperature,)
No, the density of the water would not change.
_____
Additional comments
The half-full aquarium would weigh about 385.875/2 lb ≈ 194 lb. This is still too heavy for the table.
The density of water is actually about 62.4 lb/ft³. We assume the extra 10 lb/ft³ might take into account the weight of the aquarium and any gravel or other non-water content.
Is this true or false
Answer:
False
Step-by-step explanation:
Range can be calculated by taking the difference of the lower limit and upper limit of the data
The Upper limit here is 8.5 (considering) and lower limit is 4
So,
R= 8.5-4
R=4.5
The given says it is 2.5 so it is false.
the quation is 8=z/6 please help me solve this algebraic equation......
Answer:
to find z
Step-by-step explanation:
8=z/6
z=6 x 8
z= 48
What is the volume of the cylinder 6yd and 11yd
Answer:
Volumer of cylinder
=(πd²/4)×h
=(36π/4)11
99π yd³
What is the volume of a
triangular pyramid that is
12 ft tall and has a base
area of 5 squar & ft?
Answer:
60 ft³
Step-by-step explanation:
Concepts
The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.
Application
In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.
Solution
12 × 560 feet³Which Angle measure must equal 52•
Answer:
c
Step-by-step explanation:
vertically opposite angles are always equal
here, the angle with the measure 52 degree and angle c are vertically opposite angles
so angle with the measure 52 degree = angle c
angle c equals to 52 degree
if you subtract 13 from my number and multiply the difference by -4, the result is -40, what is the number?
Answer:
23
Step-by-step explanation:
let the number = X
subtracting 13 from X = X -13
multiplying the difference by -4= (X -13)×-4
the result is -40 means (X-13)×-4=-40
(X- 13)×-4 = -40
-4 X +52 = -40
collect like term
-4 X = -40-52
- 4X = -92
dividing bothsides by -4
-4 X /-4 = -92/-4
X = 23
[tex]12x ^{2} + 4x + 20[/tex]
I'm really struggling with finding the greatest common factor.
could someone please explain in simple terms?
The GCF is 4
The polynomial factors to [tex]4(3x^2+x+5)[/tex]
==========================================================
Further explanation:
Ignore the x terms
We're looking for the GCF of 12, 4 and 20
Factor each to their prime factorization. It might help to do a factor tree, but this is optional.
12 = 2*2*34 = 2*220 = 2*2*5Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.
We can then factor like so
[tex]12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)[/tex]
The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.
The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).
Sally has just finished her thirty-fifth year with her company and is getting ready to retire. during her thirty-five years, sally’s average annual salary was $45,603. how much can sally expect to receive from social security annually if she were to retire today? (assume she will receive 42% of her average annual salary.) a. $191.53 b. $1,915.33 c. $19,153.26 d. $191,532.60
Using proportions, the amount that Sally can expect to receive from social security annually is given by:
c. $19,153.26.
What is a proportion?A proportion is a fraction of a total amount, and this fraction can also represent a percentage of the total amount.
She is expected to receive 42% of her average annual salary of $45,603, hence, considering 0.42 is equivalent to 42%:
A = 0.42 x 45603 = $19,153.26.
Which means that option C is correct.
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Good evening every one sorry to brother u but can someone answer this
3 - 3 / 1/3 + 1
Thank u very much
Answer:
-5
Step-by-step explanation:
3 - 9 + 1 = -6 + 1 = -5
Hope this helped! I would appreciate a Brainliest!
(BTW, if you can, can you please answer my question? It's due today!)
PLEASE HELP ILL MARK BRAINEST!!!!
Answer:
1, 6, 11, and 16 in that order
Step-by-step explanation:
every time the x value increases by 1, the f(x) value increased by 5
Determine the general solution for sin(x-30°) = cos 2 x
please help me with this math question
Answer:
Min max median and q3 is correct, q2 should be 8.5
Question 11 of 25
Does this table represent a function? Why or why not?
X
y
2
1
4
3
6
3
8
4
10
6
A. Yes, because all of the x-values correspond to one or more
y-values.
B. No, because one x-value corresponds to two different y-values.
C. Yes, because every x-value corresponds to exactly one y-value.
Answer: Let's put the chart into ordered pairs:
(x, y)
(2,1)
(3,4)
(3,3)
(4,2)
(5,5)
In bold, we see that there are two y-values at x=3. This means that this relation fails the vertical line test (two points on the same verticle line). This is not a function.
The answer options may be mis-written.
The answer is no, because one x value corresponds to more than one y-value.
Have a great day!
and night..
;).
Step-by-step explanation:
30 Points if you answer thanks
Answer:
Step-by-step explanation:
Answer:
ok this is pretty simble you just have to subtract the bottom exponents from the top so
3-2=1
2-2=0
a^1=a
a
Hope This Helps!!!
I need the answer for the what if one
so you would ski down the mountain to the nearest foot is 2556.06ft
The volume of the prism is 275 cm³ the area of the base of the prism is 25 square centimeters what is the height of the prism
Answer:
11
Step-by-step explanation:
volume of a prism = area of base × height
plug in what we are given
volume = 275cm³area of base = 25cm²275 = 25 × height
==> divide both sides by 25
11 = height
