Step-by-step explanation:
x²– 8x - 7 = 0
(x²-8x+16) -7 = 16
(x²-8x+16) = 16+7
(x-4)² = 23
x-4 = √23
so x= 4+√23 or x= -4√23
4. Three hoses are connected end to end. The first hose is
6.25 feet. The second hose is 6.5 feet. If the length of
all 3 hoses when connected is 20 feet, how long is the
third hose?
Answer:7.25 feet
Step-by-step explanation:
6.25+6.5=12.75
20-12.75=7.25
Question 15 of 43
A bag of marbles has 12 red, 7 yellow, 5 blue and 1 white. Find the probability
of selecting 4 marbles from the bag where all 4 are red.
9
A.
o
B.
1
C.
75900
o
D.
Answer:
Option A
Step-by-step explanation:
[tex] \frac{12}{25} \times \frac{11}{24} \times \frac{10}{23} \times \frac{9}{22} [/tex]
we start with 12 red marbles out of 25 marbles, that's the probability for the first.
in the second step we have one red marble less, wich also means one marble less overall
and so on
[tex] \frac{12 \times 11 \times 10 \times 9}{25 \times 24 \times 23 \times 22} [/tex]
[tex] = \frac{11880}{303600} [/tex]
can be reduced by 1320 (step by step) to
[tex] \frac{9}{230} [/tex]
Help needed to solve this
Given:
The expression is:
[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]
To find:
The simplified form of the given expression
Solution:
Formula used:
[tex]x^2-y^2=(x-y)(x+y)[/tex]
We have,
[tex]\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}[/tex]
It can be written as:
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}[/tex]
[tex]=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
Taking LCM, we get
[tex]=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}[/tex]
Using the grouping method factories the numerator.
[tex]=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]
[tex]=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}[/tex]
Cancel out the common factors.
[tex]=\dfrac{1}{b-a}[/tex]
Therefore, the value of the given expression is [tex]\dfrac{1}{b-a}[/tex].
Consider the system of equations given slope intercept form, the soloist ion seems to be about (8, 14) use a graphing calculator to find the exact values for the intersection point what is the solution to the system of equations
Answer:
tienes que pensar
Step-by-step explanation:
put bralinyns
A square is shown below. Which expression can be used to find the area, in square units, of the shaded triangle in the square? A square with a side length of 4 units is shown. A diagonal is drawn with one section shaded inside the figure. (5 points) fraction 1 over 2 ⋅ 4 ⋅ 4 fraction 1 over 4 ⋅ 4 ⋅ 4 fraction 1 over 2 ⋅ 2 ⋅ 2 fraction 1 over 4 ⋅ 2 ⋅ 2
30 points :)
Answer:
again, barely readable.and you didn't provide the picture for this problem.
but if the are of the triangle if just half of the square, it's one of the options that got 1/2 in it as a fraction.
but if it's 1/2 * 2 * 2
or 1/2 * 4 * 4
really depends on the square. either the area of the square is 2*2 or 4*4, and the triangle is just half of it. at least that's most likely.
can't really tell what's going on here without the missing picture
Answer:
A. fraction 1 over 2 ⋅ 4 ⋅ 4 or 1/2 ⋅ 4 ⋅ 4
Step-by-step explanation:
Hope I helped!!
What is the inverse of the function f(x) = 2x + 1?
Answer:
f^1(x)= (1/2)x-(1/2)
hope this helped
mathematics can uh solve this please
Answer:
[tex]a^3 + 1 = 0[/tex]
Step-by-step explanation:
We start with the equation:
[tex]a + \frac{1}{a} = 1[/tex]
We want to find the value of:
[tex]a^3 + 1 =[/tex]
We can start with our previous equation and multiply both sides by a:
[tex](a + \frac{1}{a})*a = 1*a\\a^2 + 1 = a[/tex]
Now we can rewrite our initial expression as:
[tex]a = 1 - \frac{1}{a}[/tex]
Replacing that in the right side, we get:
[tex]a^2 + 1 = a = 1 - \frac{1}{a}[/tex]
Now again, let's multiply both sides by a
[tex]a*(a^2 + 1) = a*(1 - \frac{1}{a} )\\a^3 + a = a - a/a\\a^3 + a = a - 1\\a^3 = -1\\a^3 + 1 = 0[/tex]
So we can conclude that:
[tex]a^3 + 1 = 0[/tex]
38) If AD = 10, find the arc length of DE.
Answer:
23.6 units
Step-by-step explanation:
If we have a circle of radius R, the perimeter of the arc is given by:
P = 2*pi*R
Now, if we only want to find the length of an arc defined by an angle "a", it will be:
L = (a/2*pi)*2*pi*R = a*R
In this case, we know that DA = 10, so we can think that this is a circle of radius R = 10 units
And for the arc DE, we have the angle:
a = 2.36 rad
replacing these two in the formula, we get:
L = 2.36*10 units = 23.6 units
The temperature T of a given mass of gas varies inversely with its volume V. The temperature of 90 cm^3 of a certain gas is 25°C. What will the temperature of the gas be when it is compressed to a volume of 20 cm^3?
a. 112.5°C
b. 6°C
c. 54°C
d. 120°C
Answer:
A. 112.5°C
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Replace y with T, and replace x with V:
T = [tex]\frac{k}{V}[/tex]
Plug in 90 as T and 25 as V, then solve for k:
T = [tex]\frac{k}{V}[/tex]
90 = [tex]\frac{k}{25}[/tex]
2250 = k
So, the equation is T = [tex]\frac{2250}{V}[/tex]
Plug in 20 as V and solve for T:
T = [tex]\frac{2250}{V}[/tex]
T = [tex]\frac{2250}{20}[/tex]
T = 112.5
So, the temperature will be A. 112.5°C
FInd WY Given: Giving brainly.
Answers:
x = 2WY = 28===========================================================
Explanation:
The tickmarks show that WZ and XY are the same length. The arrows show that WX is parallel to ZY. This is an isosceles trapezoid.
For any isosceles trapezoid like this, the diagonals are the same length. We can prove it using the SAS congruence theorem.
So,
WY = XZ
15x-2 = 9x+10
15x-9x = 10+2
6x = 12
x = 12/6
x = 2 .... first answer
Use that value of x to find the length of each diagonal.
WY = 15*x - 2 = 15*2-2 = 30-2 = 28 .... second answerXZ = 9x+10 = 9*2+10 = 18+10 = 28Both diagonals are 28 units long, which helps confirm we have the right x value.
Simplify........................
Answer:
[tex]\frac {x^{3}-4x^{2}-20x+32}{x^{3}+2x^{2}-4x-8}[/tex]
Step-by-step explanation:
make the denominator same
[tex]\frac{(x^{2}-4)(x-2)}{(x^{2}-4)(x+2) }-\frac{(2x+20)(x+2)}{(x^{2}-4)(x+2)}[/tex]
then expand
[tex]\frac {x^{3}-2x^{2}-4x+8}{x^{3}+2x^{2}-4x-8} - \frac {2x^{2}+24x+40}{x^{3}+2x^{2}-4x-8}[/tex]
join
[tex]\frac {x^{3}-4x^{2}-20x+32}{x^{3}+2x^{2}-4x-8}[/tex]
i think but not sure
Answer:
[tex] \frac{x - 2}{x + 2} - \frac{2x + 20}{ {x}^{2} - {2}^{2} } \\ \frac{x - 2}{x + 2} - \frac{2x + 20}{(x + 2)(x - 2)} \\ = \frac{ {(x - 2)}^{2} - (2x + 20)}{(x + 2)(x - 2)} \\ = \frac{ {x}^{2} - 4x + 4 - 2x - 20 }{(x - 2)(x + 2)} \\ = \frac{ {x}^{2} - 6x - 16 }{(x2)(x + 2)} \\ = \frac{(x - 8)(x + 2)}{(x + 2)(x - 2)} \\ = \frac{(x - 8)}{(x - 2)} [/tex]
find the first derivative of the following:
f(x)=e^{x³}
[tex]answer = 3 {x}^{2} {e}^{ {x}^{3} } [/tex]
Answer:
[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]
Step-by-step explanation:
we would like to figure out the first derivative of the following:
[tex] \displaystyle f(x) = {e}^{x ^{3} } [/tex]
to do so take derivative In both sides:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{x ^{3} } [/tex]
to differentiate the above we can consider composite function derivation given by
[tex] \rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dx} f'(g(x)) \times \frac{d}{dx} g'(x)[/tex]
let
g(x)=u
so we obtain:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{u} \times \frac{d}{dx} u[/tex]
substitute back:
[tex] \displaystyle f'(x) = \frac{d}{dx} {e}^{ {x}^{3} } \times \frac{d}{dx} {x}^{3} [/tex]
by using derivation rule we acquire:
[tex] \displaystyle f'(x) = 3x^2 {e}^{ {x}^{3} } [/tex]
and we are done!
Calculate the measure of angle D:
Answer:
The answer is 32
Step-by-step explanation:
A right triangle has a total of 180 degrees. As they give you 58 degrees and 90 degree, you just do 180 degrees - 58 degrees - 90 degrees.
Answer: 32
Step-by-step explanation:
Subtract the angle 58 and 90 since it is a right angle
What is the volume, in cubic ft, of a rectangular prism with a height of 17ft, a width of 11ft, and a length of 18ft?
Answer:
The answer is 3366 cubic feet.
Step-by-step explanation:
To find the volume of the rectangular prism, use the formula for a rectangular prism, which is V= LWH. Next, plug in the information given from the question, and the formula will look like V= (18ft) (11ft) (17ft).
Then, solve the equation for the answer, and the answer will be 3366 cubic feet.
Answer:3366
Step-by-step explanation:
which statement would be true if you evaluate the expression (560x70) ÷10
a. the solution is 10 times as small as 560 + 70
b. the solution is 10 times as small as 560-70
c. the solution is 10 times as large as 560+70
d. the solution is 10 times as large as 560-70
Answer:
none
Step-by-step explanation:
No choice is correct.
The original expression has 560 x 70, the product of 560 and 70 inside the parentheses.
(560 x 70) ÷ 10 is 10 times smaller than 560 x 70
None of the choices show 560 x 70. They show 560 + 70 and 560 - 70.
Answer: none
find the measure of an exterior angle of a regular polygon with 9 sides
Answer: 40°
Step-by-step explanation: The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides. So it's 360°÷9=40°
The graph shown below represents the rate at which water drains from a tank once the drain is opened which statement correctly describes the graph
A. The water is draining at constant rate of 1/2 gallon per minute, and the tank contained exactly 14 gallons when the drain opened
B. The water is draining at a constant rate of 2 gallons per minute,and the tank contained exactly 14 gallons when the drain was opened
C. The water is draining at a constant rate of 5 gallons per minute, and the tank contained exactly 14 gallons when the drain was opened
D.the water is draining at a constant rate of 14 gallons per minute, and the tank contained exactly 1/2 gallon when the drain was opened
Answer:
A
Step-by-step explanation:
The slope is -1/2 and the y-intercept is 14
The figure shows ∆ABC with m∠ABC = 90°.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. Match the remaining steps to their correct sequence in the proof.
Statement Reason
1. Draw . construction
2. ∠ABC ≅ ∠BDC Angles with the same measure are congruent.
4. ∠BCA ≅ ∠DCB Reflexive Property of Congruence
4. AA criterion for similarity
5. Corresponding sides of similar triangles are proportional.
6. BC2 = AC × DC cross multiplication
7. ∠ABC ≅ ∠ADB Angles with the same measure are congruent.
8. ∠BAC ≅ ∠DAB Reflexive Property of Congruence
9. AA criterion for similarity
10. Corresponding sides of similar triangles are proportional.
11.
12.
13.
14.
15.
AB2 + BC2 = AC2
Reason: multiplication
AB2 + BC2 = AC × AC
Reason: segment addition
AB2 = AC × AD
Reason: cross multiplication
AB2 + BC2 = AC(AD + DC)
Reason: Distributive Property
AB2 + BC2 = AC × AD + AC × DC
Reason: addition
11
arrowBoth
12
arrowBoth
13
arrowBoth
14
arrowBoth
15
arrowBoth
Answer:
Hello,
Please, see the attached file.
Thanks.
Step-by-step explanation:
The remaining steps can be ∆ABC ∼ ∆DBA AA criterion for similarity Corresponding sides of similar triangles are proportional, AB/AC = AD/AB, and AB2 = AC × AD.
What is triangle?Triangles are closed two-dimensional geometric figures with three straight sides and three angles. The sum of the three angles in any triangle is always 180 degrees.
The first 10 steps to prove that AB2 + BC2 = AC2 are given in the table. The remaining steps to their correct sequence in the proof are:
Draw . construction∠ABC ≅ ∠BDC Angles with the same measure are congruent.∠BCA ≅ ∠DCB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.BC2 = AC × DC cross multiplication∠ABC ≅ ∠ADB Angles with the same measure are congruent.∠BAC ≅ ∠DAB Reflexive Property of CongruenceAA criterion for similarityCorresponding sides of similar triangles are proportional.∆ABC ∼ ∆DBA AA criterion for similarityCorresponding sides of similar triangles are proportional.AB/AC = AD/AB Reason: corresponding sides of similar triangles are proportionalAB2 = AC × AD Reason: cross multiplicationThese steps follow logically from the previous statements in the proof. In step 11, the Pythagorean Theorem is applied to the right triangle ADB.
Thus, this can be the match for the given scenario.
For more details regarding triangles, visit:
https://brainly.com/question/2773823
#SPJ7
Classifique as figuras geométricas em planas ou não planas.
Answer:
São todas planas.
Step-by-step explanation:
São todas planas.
PLS ADD EXPLANATION
Cylinder radius is 2 cm height is 10cm what is the surface area
Answer:
150.83 (cm²).
Step-by-step explanation:
1) the area of the bottom and top is: A₁=π*r²*2=2*3.1415*4≈25.13 (cm²);
2) the length of the circle in the bottom/top side is: l=2*π*r=2*3.1415*8≈12.57 (cm);
3) the area of the side surface of the cylinder is: A₂=l*h=12.57*10=125.7 (cm²);
4) the required area of the cylinder is:
A=A₁+A₂=25.13+125.7=150.83 (cm²).
PLS ANSWER ASAP. ILL GIVE BRAINLIEST. I don’t understand how to do this and need help. It’s due in 10 minutes.
Triangle 1 is a right triangle with one side length of H inches. Triangle 2 is similar to triangle 1 and has one side length of 18 inches. Sketch a possible example of triangle 1 and triangle 2 and label all side lengths.
Answer:162 might be wrong tho so dont mark as brainlyest
Step-by-step explanation:
Factor the algebraic expression: 28a + 12
Answer:
hope it is helpful to you
Answer:
4(7a+3)
Step-by-step explanation:
28a+12
take common
4 is the common number for both the terms because it divides 28 and 12 exactly.
4(7a+3)
what is the result of adding -2.9a t 6.8 and 4.4a - 7.3 if a=2 what is the value of the expression
Answer:
Step-by-step explanation:
2.5
HELP PLS! A boat is heading towards a lighthouse, whose beacon-light is 102 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 13^{\circ}
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22^{\circ}
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.
Answer:
Distance from point AA to point BB = 189.3 feet
Step-by-step explanation:
Let the distance from point AA to the base of the lighthouse be represented by x, and the distance from point BB to the base of the lighthouse be represented by y. So that;
distance from point AA to point BB = x - y
To determine the value of x, applying the required trigonometric function;
Tan θ = [tex]\frac{opposite}{sdjacent}[/tex]
Tan 13 = [tex]\frac{102}{x}[/tex]
x = [tex]\frac{102}{Tan 13}[/tex]
= 441.81 feet
x = 441.8 feet
To determine the value of y;
Tan 22 = [tex]\frac{102}{y}[/tex]
y = [tex]\frac{102}{Tan 22}[/tex]
= 252.46
y = 252.5 feet
Thus,
distance from point AA to point BB = 441.8 - 252.5
= 189.3 feet
Find m-1(x) if m(x) = x+3.
Step-by-step explanation:
m(x) = x+3
y = x+3
=> x = y-3
m`¹(x) = x-3
HELP PLEASE
Work out the size of angle x.
Answer: its 180 , because it dont matter if its up or side .
Answer:
13°
Step-by-step explanation:
the lines are parallel so
the angle above 85° is also 85° (vertical angles)the other angle in the triangle is 82° (180 - 98)82 + 85 = 167
167 - 180 = 13
x = 13°
Evaluate:
10
1° 4(1.5)n-1 = [?]
Answer:
453.3203125
Step-by-step explanation:
I hope it's right just use it. If it's wrong, I'll try again.
Helpppppppppppppp meeeeeeeee
Step-by-step explanation:
Hey there!
From the given figure;
An exterior angle is 127°.
To find: value of"X"
Now;
x+127° = 180°. [Being linear pair]
or, X = 180° - 127°
or, X = 53°
Therefore, the value of "X" is 53°.
Hope it helps!
Answer:
53°
Step-by-step explanation:
the extended line(the base and the line that extends past the triangle) is 180°. With an extended line that is 180°, the inside angle must be 180° - the outside angle, and the outside angle must be 180° - the inside angle. if the angle on the outside is 127°, then the inside angle(x) should be 180° - 127° or 53°.
to verify: all the inside angles must equal to 180°
the angle on the top is 90°( when there is that square thing on an angle it means it is 90°) and the angle on the right is 53°, so the remaining angle is 180 - (90° + 53°) or 37°.
90° + 53° + 37° = 180 °
square in inches, x, and the perimeter of the square in inches, y. What is the constant of proportionality?
Answer:
y/x
Explanation:
The constant of proportionality defines two directly proportional quantities that decrease or increase proportionally/same rate.
Given constant of proportionality= k
Side of the square= x
Perimeter of the square= y
constant of proportionality=k=y/x
For example if perimeter of square is 8 and side of square is 2, constant of proportionality is 8/2=4
PLEASE HELP MEE pleaseee
Answer:
x = 15 and y = 7
Step-by-step explanation:
x = 2y + 1
x + y - 8 = 14
Let's substitute the value of x in the second equation:
(2y + 1) + y - 8 = 14
3y -7 = 14
3y = 14 + 7
3y = 21
y = 21/3
y = 7
And now you substitute the value of y in the first equation:
x = 2•7 + 1
x = 14 + 1
x = 15