Answer:
-5 -√8 or ≈ -7.83
Step-by-step explanation:
Solving the quadratic equation, to find its roots:
x^2 + 10x + 25 = 8 ⇒ The left side is perfect square(x+5)^2=8 ⇒ Getting square root of both sidesx+5 = ± √8 ⇒ There are 2 rootsx = - 5 ± √8The smallest root is:
x= -5 - √8 ≈ -7.83Ben wants to buy a new car stereo and he has already saved some money. He used this inequality to represent the amount he still has to save to be able to buy the stereo, where a represents the amount still left to save. A + 212 greater-than-or-equal-to 365 If Ben saves $15 a week for the next 10 weeks, will he be able to buy the stereo and why? No, because he needs to save at least $153, and he will only save $150 over the next ten weeks. No, because he needs to save $577, and he will only save $150 more. Yes, because he has already saved $365, and the stereo cost $212. Yes, because he has already saved $212, and he will save another $150.
Answer:
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
Step-by-step explanation:
In case when ben wants to save $15 for a week and the total number of weeks is 10 so the total saving amount is $150. Now if the cost of a stereo is less than the total of saving amount so he is confident to purchase the stereo.
Now if the amount that required to be saved is represented by a is more than $150 so he is unable to purchase a stereo
Hence, the correct option is a.
Answer:
Step-by-step explanation:
Using the equation, A + 212 ≥ 365
No, because he needs to save at least $153, and he will only save $150 over the next ten weeks.
Section B
1. In the adjoining figure find out perpendicular, base and
hypotenuse from the given right-angled triangle with a and
B as the reference angles. Also give your reason.
a
nto
B
С
B.
D
Answer/Step-by-step explanation:
Using α as reference angle:
Perpendicular side = BC (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = AB (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AC (the side opposite to the right angle, 90°)
Using β as reference angle:
Perpendicular side = AB (one of the legs that adjoins to form a right angle. It is opposite to the reference angle.)
Base side = BD (The other leg that forms a right angle with the perpendicular side at the adjoining point. It is adjacent to the reference angle)
Hypotenuse = AD (the side opposite to the right angle, 90°)
What is the purpose of multiplying by the conjugate of a complex denominator when finding the quotient of complex numbers?
Answer: To have a real number in the denominator
Step-by-step explanation:
Ok, a quotient between two complex numbers can be written as:
[tex]\frac{A + Bi}{C+Di}[/tex]
Now, when we do these types of divisions, we multiply and divide by the same number (so in essence we are multiplying by one) that is the conjugate of the denominator.
Remember that for a complex number:
Z = A + Bi
the conjugate is = A - Bi.
Then, wen we multiply the denominator by it's conjugate, we have:
(C + Di)(C - Di) = C^2 + D*C*i - D*C*i + (D*i)*(-D*i) = C^2 + D^2
So now we have a real number in the denominator (the imaginary part of this number is equal to zero)
So the answer to the question is:
"To have a real number in the denominator"
PLEase help please help
Answer:
10 m
Step-by-step explanation:
490[tex]\pi[/tex]=[tex]\pi[/tex](7²)h
490[tex]\pi[/tex]/[tex]\pi[/tex]49=h
10=h
What is the coefficient of y in the expression 1 ⋅ 4 + 7y?
Answer:
7
Step-by-step explanation:
The coefficient of a variable is simply the number it's being multiplied by or the number that is in front of it. In this case, the coefficient of y is 7.
A cylinder has a height of 5.3 cm and a diameter of 3.0 cm. What is its volume? (Hint: Volume of a cylinder = r2h ) 25.0 cm3 66.2 cm3 149.9 cm3 37.5 cm3
Answer:
37.5 cm³ .
Step-by-step explanation:
h = 5.3 cm
diameter = 3 cm
r = 3/2 = 1.5 cm
Volume of cylinder = πr²h {Plug in the values of h & r }
= 3.1428 * 1.5 * 1.5 * 5.3
= 37.5399
= 37.5 cm³
Answer:
37.5cm3
Step-by-step explanation:
Diameter = 3cm
Radius = 3cm÷2
= 1.5cm
Volume of cylinder= πr²h
= π(1.5²)+5.3
= 37.5 (3 S.F.)
Square RSTU is inside trapezoid RSVU. What is the measure, in degrees, of angle VSR? R. REN T Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -, -, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or decimal. Your answer
Answer:
135°
Step-by-step explanation:
m<VSR = m<RST + m<VST
Each angle at the vertices of a square is equal to 90°. <RST is one of the vertices of square RSTU, therefore,
m<RST = 90°
also, m<VST = 90 - 45 = 45°
m<VSR = m<RST + m<VST
Thus:
m<VSR = [tex] 90 + 45 = 135 [/tex]
Measure of angle VSR is 135°
The angle VSR will be equal to 135°.
What is an angle?
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
m∠VSR = m∠RST + m∠VST
Each angle at the vertices of a square is equal to 90°. ∠RST is one of the vertices of square RSTU, therefore,
m∠RST = 90°
also, m∠VST = 90 - 45 = 45°
m∠VSR = m∠RST + m∠VST
Thus:
m∠VSR = 135
Therefore the measure of angle VSR is 135°
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Josh is at the airport and calls for a Uber. He knows the driver will charge $10 to pick
him up and $3 per mile he will drive from the airport to home . if T(x) is the total cost
which equation models this situation
T(x) = 10 + 3x
The answer is not
here
T(x) =13x
T (X) = 10x + 3
Answer:
the answer is 10 +3x
Step-by-step explanation:
"the answer is not here" what do you mean
3/5 + (-1/5)
A. -2/5
B. 4/5
C. 2/5
Answer:
C
Step-by-step explanation:
3/5 + (-1/5) =(3-1)/5=2/5
(3x2+2x+ 4)- (x2+ 2x+1)=
A video game was discounted and now costs two thirds of its original
price. If it originally cost $45, how much does it cost now?
The original price is 45.
It now costs 2/3 of 45.
[tex]\frac{2}{3} * \frac{45}{1} = \frac{90}{3}[/tex] or 30
♡ Hope this helps! ♡
❀ 0ranges ❀
Answer:
The video game will now cost $30
Step-by-step explanation:
Original price: $45
45 ÷ 3 = $15
15 x 2 = $30
Hope this helps!
Miguel Rodriguez borrowed $300 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.5%.
Answer:
Simple Interest = 9.75
Total Amount needed to payback = 309.75
Step-by-step explanation:
SI = P x R x T / 100
SI = Simple Interest
P = Principal
R = Rate in years
T = Time
SI = 300 x 1/2 x 6.5 /100
=> SI = 3 x 1/2 x 6.5
=> 1.5 x 6.5
=> 9.75
Total Amount needed to payback = Principal + Simple Interest
=> Total Amount needed to payback = 300 + 9.75
=> Total Amount needed to payback = 309.75
Solve these two equations using the Addition Method (also known as the elimination method).
3/4x + 1/3y = -1/2
1/2x - 5/6y = -7/2
Answer:
(-2, 3)
Step-by-step explanation:
5/2(3/4x + 1/3y = -1/2)
1/2x - 5/6y = -7/2
15/8x + 5/6y = -5/4
19/8x = -19/4
x = -2
1/2(-2) - 5/6y = -7/2
-1 -5/6y = -7/2
-5/6y = -5/2
y = 3
what is the change in each term of the sequence? 1,4,13,40,121,....
three signals that beep.
signal a beeps every 25 seconds
signal b beeps every 30 seconds
signal c beeps every 100 seconds.
The three signals start beeping at the same time.
How many times in one hour will the three signals beep?
Answer:
The number of times signal a beeps in 1 hour = 144 times
The number of times signal b beeps in 1 hour = 120 times
The number of times signal c beeps in 1 hour = 36 times
The number of times three signals bee in one hour = 12 times
Step-by-step explanation:
The given parameters are;
The period for each signals beep are;
Signal a beeps every 25 seconds
Signal b beeps every 30 seconds
Signal c beeps every 100 seconds
Therefore, in one hour, signal a will beep 1× 60 × 60/25 = 3600/25 = 144 times
In one hour, signal b will beep 1×60×60/30 = 3600/30 = 120 times
In one hour, signal c will beep 1×60×60/100 = 3600/100 = 36 times
Therefore, we have;
The number of times signal a beeps in 1 hour = 144 times
The number of times signal b beeps in 1 hour = 120 times
The number of times signal c beeps in 1 hour = 36 times
From Excel, we can see that the three signals beep the same time at 300, 600, 900, 1200, 1500, 1800, 2100, 2400, 2700, 3000, 3300, and 3600
The number of times three signals bee in one hour = 12 times
signal a beeps every 25 seconds
signal b beeps every 30 seconds
signal c beeps every 100 seconds.
Answer to the above questions is 300,600,900 if the signal beep at the same time 12 times
Explanation to the above questions
One hour contains 3600 secondsSignal a beep 3600/25=144Signal b beep 3600/30=120signal c beep 3600/100=36At the same time all the signal beep than 144+120+36=300we conclude that it will beep 12 times because 300,600,900,1200,1500,1800,2100,2400,2700,3000,3300,3600
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what is the answer to this exponent 6*6*6*6*6
Answer:
6^5 or 7776
Step-by-step explanation:
6^5 because 6 is multiplied with 6, 5 times. So, it is 6^5.
We can also simplify this number.
=> 6 x 6 x 6 x 6 x 6
=> 36 x 36 x 6
=> 36 x 216
=> 7776
b)[3x-7)2 by using identities note:the 2 is a square
Answer:
9x² - 42x + 49
Step-by-step explanation:
Given
(3x - 7)² = (3x - 7)(3x - 7)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(3x - 7) - 7(3x - 7) ← distribute both parenthesis
= 9x² - 21x - 21x + 49 ← collect like terms
= 9x² - 42x + 49 ← in expanded form
2. What is the area of the shaded region below? Notice
that the angle is 120 degrees and the radius of the
circle is 8 inches.
8
120
Answer:
Approximately 67 square inches.
Step-by-step explanation:
The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]
And the sector area of a circle is given by the formula:
[tex]A=\frac{x\textdegree}{360\textdegree}(\pi r^2)[/tex]
Where x is the degree measurement of the sector.
We want to find the sector of the circle with a radius of 8. The degree measurement of the sector is 120. Therefore, plug 8 in for r and 120 for x:
[tex]A=\frac{120\textdegree}{360\textdegree}(\pi(8)^2)[/tex]
The fraction reduces to 1/3. 8^2 is 64:
[tex]A=\frac{1}{3}(64\pi)[/tex]
This is equivalent to:
[tex]A=\frac{64}{3}\pi\\ A\approx67.0206 \text{ in}^2[/tex]
Which is 65% of 35??
Answer:
22.75 .
Step-by-step explanation:
65 x 35 / 100 = 22.75.
The percentage expression 65% of 35 is 22.75
How to evaluate the percentage expressionFrom the question, we have the following parameters that can be used in our computation:
65% of 35
Express as products
So, we have the following representation
65% of 35 = 65% * 35
Express 65% as 0.65
So, we have the following representation
65% of 35 = 0.65 * 35
Evaluate the products
So, we have the following representation
65% of 35 = 22.75
Hence, the solution is 22.75
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Simplify the following Questions. (IMPORTANT NOTE!!! #'s 2 AND 7 MUST BE IN SCIENTIFIC NOTATION!!!!!) 1.) (x)²(2xy³)^5 2.) (4x10^8)^2 3.) (-h^4)^5 4.) (3xy³)²(xy)^6 5.) (p^9)^-2 6.)(5k²)³ 7.)(7x10^5)² 8.)(x)³(-x³y)² 9.)w^5(w²)^-4 10.) (2x^5)^4
Answer:
Step-by-step explanation:
Hint :
[tex](a*b)^{m}= a^{m}b^{m}\\\\\\(a^{m})^{n}=a^{mn}\\\\\\a^{m}*a^{n}=a^{m+n}\\[/tex]
[tex]1)x^{2}(2xy^{3})^{5}=x^{2}*2^{5}*x^{5}*(y^{3})^{5}\\\\\\=x^{2}*2^{5}*x^{5}*y^{3*5}\\\\=x^{2}*2^{5}*x^{5}*y^{15}\\\\=2^{5}*x^{2+5}*y^{15}\\\\=2^{5}x^{7}y^{15}[/tex]
[tex]2) (4x10^{8})^{2}=4^{2}*x^{2}*(10^{8})^{2}\\\\=16*x^{2}*10^{8*2}\\\\=1.6*10*x^{2}*10^{16}\\\\=1.6x^{2}*10^{16+1}\\\\=1.6x^{2}10^{17}[/tex]
[tex]3)(-h^{4})^{5}=(-h)^{4*5}=-h^{20}\\\\\4)(3xy^{3})^{2}(xy)^{6}=3^{2}x^{2}(y^{3})^{2}x^{6}y^{6}\\\\=9x^{2}y^{3*2}x^{6}y^{6}\\\\\\=9x^{2}y^{6}x^{6}y^{6}\\\\=9x^{2+6}y^{6+6}\\\\=9x^{8}y{12}\\\\\\[/tex]
[tex]5) (p^{9})^{-2}=p^{9*-2}=p^{-18}\\\\\\6)(5k^{2})^{3}=5^{3}(k^{2})^{3}=625k^{6}\\\\7)(7x10^{5})^{2}=7^{2}x^{2}(10^{5})^{2}\\\\=49x^{2}10^{5*2}\\\\=4.9*10^{1}x^{2}10^{10}\\\\=4.9x^{2}10^{10+1}\\\\=4.9x^{2}10^{11}[/tex]
[tex]8)x^{3}(-x^{3}y)^{2}=x^{3}*(-x^3})^{2}y^{2}\\\\\\=x^{3}*(-1)^{2}*x^{2*3}y^{2}\\\\=x^{3}*1*x^{6}y^{2}=x^{3+6}y^{2}\\\\=x^{9}y^{2}\\\\\\9)w^{5}(w^{2})^{-4}=w^{5}w^{2*-4}\\\\=w^{5}w^{-8}\\\\=w^{5-8}=w^{-3}\\\\=\frac{1}{w^{3}}\\\\\\10) (2x^{5})^{4}=2^{4}x^{5*4}\\\\=2^{4}x^{20}\\\\=16x^{20}[/tex]
A box contains 4 red pencils, 3 blue pencils, and
3 yellow pencils. What is the probability that a
student randomly selects a blue pencil, keeps it,
and then a second student randomly selects a
yellow pencil? *
Step-by-step explanation:
Red=4
Blue=3
Yellow=3
Total=10
Pr(BY) without replacement= 3/10 *3/9
=6/90
=1/15
When two fair 6-sided dice are tossed, the numbers $a$ and $b$ are obtained. What is the probability that the two digit number $ab$ (where $a$ and $b$ are digits) and $a$ and $b$ are all divisible by 3?
=================================================
Explanation:
If either a or b (or both) are multiples of 3, then so is a*b
Consider 'a' being a multiple of 3. This means a = 3k for some integer k. Multiply both sides by b to get ab = 3k*b, and we see that 3 is a factor of ab, making ab to be a multiple of 3.
----------
There are six sides to the dice and those sides are {1,2,3,4,5,6} of which only {3,6} are multiples of 3.
If we want both dice to be multiples of 3, then the possible outcomes are
(3,3)(3,6)(6,3)(6,6)There are four outcomes. This is out of 6*6 = 36 total outcomes overall.
Dividing the values gives 4/36 = 1/9 as the probability we want
----------
Side note: for a roll like (a,b) = (6,3) we see that a*b = 6*3 = 18, which is a multiple of 3. The same happens with the other three (a,b) pairings mentioned above.
20 POINTS! A book sold 39,200 copies in its first month of release. Suppose this represents 7.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
Solve using the Addition Method.
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Answer:
x = 2
y = - 1
Step-by-step explanation:
5x/6 + y/3 = 4/3
2x/3 - y/2 = 11/6
Multiply the above equation by 6 to express in linear form
6 × (5x/6 + y/3 = 4/3)
5x + 2y = 8.... (1)
6 × (2x/3 - y/2 = 11/6)
4x - 3y = 11.... (2)
Thus, the equation are:
5x + 2y = 8.... (1)
4x - 3y = 11.... (2)
Next, multiply equation (1) by 3 and equation (2) by 2. This is illustrated below:
3 × (5x + 2y = 8)
15x + 6y = 24 ..... (3)
2 × (4x - 3y = 11)
8x - 6y = 22 ... (4)
Next, add equation 3 and 4 together. This is illustrated below:
.. 15x + 6y = 24... (3)
+ 8x - 6y = 22 .... (4)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
23x = 46
Divide both side by 23
x = 46/23
x = 2
Next, substitute the value of x into any of the equation. Here, we shall substitute the value of x into equation (3). This is illustrated below:
15x + 6y = 24... (3)
x = 2
15(2) + 6y = 24
30 + 6y = 24
Collect like terms
6y = 24 - 30
6y = - 6
Divide both side by 6
y = - 6/6
y = - 1
Therefore, the value of x and y is
x = 2
y = - 1
is this a rhombus? see attachment
Answer: No, it is not a rhombus
Why not? This is because we do not have all four sides the same length.
DE is longer than EF, due to the opposite angles being larger. The rule is: the larger the angle, the longer the opposite side will be.
Will Give Brainliest. Answer ASAP please
Answer:
1) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 15 (120/360)
= 44/7 × 15 (1/3)
= 44 × 5/7
= 31.428 in
2) Arc length = 2πr ( Ф/360)
= 2 × 22/7 × 14 (90/360)
= 44/7 × 14 ( 1/4)
= 616/7 × (1/4)
= 88 (1/4)
= 22 yards
Hope it helps!!!
f(2)= can someone let me know what the answer is
Answer:
-2
Step-by-step explanation:
f(2) is the value of the function when x = 2.
Look in the graph. When x = 2, the point on the graph has coordinates (2, -2).
f(2) = -2
the expression 12xyz-45 is a a. monomial b. binomial c. trinomial d. constant
Answer:
Hey there!
12xyz-45 is a binomial. A binomial contains two terms.
Let me know if this helps :)
Using the equation F = ma, find the acceleration (a) of a 15 kg mass (m) that is acted on by 3 Newtons of Force (F). Group of answer choices
Answer:
Step-by-step explanation:
Yes
Answer:
a = 0.20 m/s²
Step-by-step explanation:
F = 3 N
m = 15 kg
F = m * a
find mass m:
3 = 15 * a
a = 3 / 15
a = 0.20 m/s²
what is the density of carbon dioxide gas if 0.196 g occupies a volume of 100ml?
Answer:
The answer is 2Step-by-step explanation:
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