First multiply the numbers inside the radicals together.
So √3 · √15 is √45.
So we have 2√45.
Note that the 2 can't be multiplied by anything since
√15 has nothing outside of the radical.
So we have 2√45.
Now, break down your square root.
√45 breaks down as 9 · 5 and 9 breaks down as 3 · 3.
Since we have a pair of 3's, a 3 comes outside of the radical
multiplying by the 2 that was previously outside to get 6.
The 5 doesn't pair up so it stays inside.
So our final answer is 6√5.
Answer:
C) [tex]6\sqrt{5}[/tex]
Arithmetic without explanation:
[tex]2\sqrt{3}* \sqrt{15}\\ = 2\sqrt{3}* \sqrt{3*5} \\ = 2\sqrt{3^2} *\sqrt{5} \\ = 2 * 3\sqrt{5} \\= 6\sqrt{5}[/tex]
Example of radical multiplication:
Take [tex]y\sqrt{x} * a\sqrt{b}[/tex] as an example:
1. Multiple the numbers inside the roots
[tex]\sqrt{x} * \sqrt{b} = \sqrt{x*b} = \sqrt{xb}[/tex]
2. Multiple the numbers outside the roots
[tex]y*a = ya[/tex]
3. Combine them and simplify
[tex]ya\sqrt{xb}[/tex]
Step-by-step explanation:
We are given the expression [tex]2\sqrt{3}*\sqrt{15}[/tex]
1. Identify the roots and multiply them
The roots are [tex]\sqrt{3}[/tex] and [tex]\sqrt{15}[/tex]
[tex]\sqrt{3} *\sqrt{15} \\= \sqrt{45}[/tex]
2. Multiply the numbers outside the root
For [tex]2\sqrt{3}[/tex] it is [tex]2[/tex] and for [tex]\sqrt{15}[/tex] it is [tex]1[/tex]
[tex]2*1 = 2[/tex]
3. Combine and simplify
Combine:
[tex]2* \sqrt{45}\\= 2\sqrt{45}[/tex]
Simplify:
*Note: [tex]\sqrt{n^2} = n[/tex]
1. Find the Prime factorization of 45
[tex]45 = 3^2 * 5[/tex]
2. Simplify the Root
[tex]2\sqrt{45} \\ = 2\sqrt{3^2 * 5} \\= 2\sqrt{3^2} * \sqrt{5} \\= 2 * 3\sqrt{5}\\ =6\sqrt{5}[/tex]
We end up with [tex]6\sqrt{5}[/tex]
Dany scored 93 in physics, 88 in mathematics, and a score in chemistry that is double his score in geography. The average score of all 4 courses is 79. What were his scores in chemistry and geography?
Linda scored a total of 265 point
Answer:
90
Step-by-step explanation:
Let x be Dany's score in geography. His score in chemistry is double his score in geography and it is equal to
2 x
The average of all four scores is 79. Hence
(93 + 88 + x + 2 x) / 4 = 79
Multiply both sides of the equation by 4
4×(93 + 88 + x + 2 x) / 4 = 4×79
Simplify
93 + 88 + x + 2 x = 316
Group like terms
3 x + 181 = 316
Solve for x
3 x = 135
3 x / 3 = 135 / 3
x = 45
score in geography = x = 45
score in chemistry = 2 x = 2 × 45 = 90
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
Answer:
[tex]\huge\boxed{Chem = 90 \ marks , Geo = 45 \ marks}[/tex]
Step-by-step explanation:
Let the score of geography be x
=> Then, the score of chemistry will be 2x
So, the given condition is:
[tex]Average = \frac{Sum \ of \ values}{No. \ of \ values}[/tex]
=> [tex]79 = \frac{93+88+x+2x}{4}[/tex]
=> [tex]79 = \frac{181+3x}{4}[/tex]
Multiplying both sides by 4
=> [tex]79 * 4 = 181+3x[/tex]
=> 316 = 181 + 3x
Subtracting 181 to both sides
=> 316-181 = 3x
=> 135 = 3x
Dividing both sides by 3
=> 45 = x
OR
=> x = 45
So,
Chemistry = 45 * 2 = 90 marks
Geography = 45 marks
Name the intersection of lines a and b
Answer:
W is the point of intersection of the lines 'a' and 'b'.
Step-by-step explanation:
Three points lying on line 'b' are points Y, Z and W.
Similarly, three points on line 'a' are points V, X and W.
Common point lying on both the lines 'a' and 'b' is W.
Therefore, point of intersection of the lines 'a' and 'b' is W.
Which expression is equal to 3 V-75?
15173
15v3i
-15iV3
-1573
न
2
3
4
5
Answer:
15i[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i
Given
3[tex]\sqrt{-75}[/tex]
= 3 × [tex]\sqrt{25(3)(-1)}[/tex]
= 3 × [tex]\sqrt{25}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]
= 3 × 5 × [tex]\sqrt{3}[/tex] × i
= 15i[tex]\sqrt{3}[/tex]
A local radio station is giving away t-shirts to listeners. On
Friday, the radio station gave away 24 shirts and had 212 left over. What equation tells how many shirts (t) the radio
station had to begin with?
A: d – 24 = 212
B: d + 24 = 212
C: d/24 = 212
D: 24d = 212
Answer:
a
Step-by-step explanation:
d - 24 = 212
d +24 = 212 + 24
d= 236
How many factors are there in the algebraic expression −2x(x + 5)? Question 7 options: (a)2 (b)1 (c)4 (d)3
Answer:
d
Step-by-step explanation:
Answer:
THERE R 3 FACTORS SO D
Step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Stretch the graph of f(x) = x + 3 vertically by a factor of 2
Answer:
see below
Step-by-step explanation:
A vertical stretch is accomplished by multiplying the function value by the stretch factor.
g(x) = 2f(x)
g(x) = 2(x +3)
the graph models the projected populations, in thousands, of two towns after x years. both towns experience a 1.9% annual growth rate. which equation represents g(x) as a transformation of f(x)?
a. g(x) = f (x+3/5)
b. g(x) = f (x-5/3)
c. g(x) = f (x) + 3/5
d. g(x) = 5/3 * f(x)
Answer:
d. g(x) = 5/3 * f(x)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a new position. Transforming an object involves transforming all the points in the object. Types of transformation are rotation, reflection, dilation and translation.
From the graph When x = 0, y = f(0) = 30, also when x = 16, y = f(16) = 40
For the graph of g(x), when x = 0, y = g(0) = 50 and when x = 16, y = g(16) = 67
This means that g(x) = 5/3 * f(x), g(0) = 5/3 * f(0) = 5/3 * 30 = 50, also g(16) = 5/3 * f(16) = 5/3 * 40 = 67
Answer:
D.)
Step-by-step explanation:
X2+14x=-7 what number must you add to complete the square
Answer:
49
Step-by-step explanation:
To find the number we add to both sides to complete the square, we do b divided by 2 all squared.
(b/2)²
In this case, we have b = 14
(14/2)²
7²
49
Answer: 49
Step-by-step explanation:
To complete the square, the second leading coefficient divided by 2 squared will give you the number need to add to both sides.
For example,
14 is the second leading coefficient in the so if you divide it by 2 you get 7 and 7 squared is 49.
Which graph shows a proportional relationship?
Answer:
The second option
Step-by-step explanation:
The rate of change needs to stay constant.
The rate of change can be explained by looking at the "rise" (y) over the "run"(x)
The rate of change for the second option is 2. We know this because...
Rise(2)
----------
Run(1)
Try looking at one of the points, now go up 2 and over 1, you should now be at the second point, do it again but twice, you should now be at the third point. A proportional relationship must also go through the origin (0,0)
A retailer buys pairs of shoes for $45.50 each. He marks up all his merchandise 25%. How much will he sell the shoes for? (Round to the nearest cent.) $36.40 $47.99 $56.87 $56.88
Answer:
56.88
Step-by-step explanation:
2 ways to do this
45.50 x 25% = 11.375
45.50 + 11.375 = 56.875
and that rounds to 56.88
for option 2 I recommend a calculater
45.50 + 25% = 56.875
56.88
What is the probability of randomly picking a five-digit number whose leftmost digit is 1 and units digit is 9 from all the odd five-digit numbers that have different digits? 1/80 1/40 1/25 1/20 1/10
Answer:1/25
Step-by-step explanation: do 5 to the second power which will get all combinations then do 1 as the numerator over the denominator which is the number of combinations.
What is the sum of all values of k such that the equation 2x^2-kx+8=0 has two distinct integer solutions?
Answer:
k > 8
Step-by-step explanation:
Step 1: We know in order for a quadratic equation to have 2 distinct solutions the discriminant has to be positive
Important formula: Discriminant = [tex]b^{2}-4ac[/tex]
Step 2: Input information into discriminant
[tex]b^{2}-4ac[/tex] > 0
[tex]k^{2}-4(2)(8)[/tex] > 0
[tex]k^{2}-64[/tex] > 0
[tex]k^{2}[/tex] > 64
[tex]\sqrt{ k^{2}}>\sqrt{64}[/tex]
k > 8
Therefore in order for the equation to have 2 distinct solutions is to have k > 8
(b²-4ac) > 0
where Z is an integer
(-k)²-4(2)(8) > 0
k²-64 > 0
k²>64
k>8
Therefore the sum of all values of k is infinite
Find ST. Help me solve please and thank you
Answer: ST is equal to 12
Step-by-step explanation:
If RU is equal to 24 as a whole and we are given that RS and TU are equal to 6 then we could set up an equation and solve for ST.
6 + 6 +x = 24 where x is the length of ST
12 + x = 24
-12 -12
x = 12
You have a bag of M&M’s with 4 green, 5 yellow, 3 brown, and 8 red M&M’s. What is the probability of selecting 1 yellow followed by a green without replacement?
Answer:
the probability is 5/20 for picking one yellow
and the probability is 4/19 for picking green one right after
The perimeter of a rectangle is 32 cm. The width is 7 cm. What is the area of the rectangle? Will mark brainliest.
Given :
[tex]\begin{lgathered}\bullet\:\:\textsf{Perimeter of reactangle = \textbf{32 cm}}\\\bullet\:\:\textsf{Width = \textbf{7 cm}}\end{lgathered}[/tex]
[tex]\rule{130}1[/tex]
Solution :
[tex]:\implies\sf Perimeter\:of\: rectangle = 2 (Length + Breadth) \\\\\\:\implies\sf 32 = 2 (l + 7)\\\\\\:\implies\sf 32 = 2l + 14\\\\\\:\implies\sf 32 - 14 = 2l\\\\\\:\implies\sf 2l = 18\\\\\\:\implies\underline{\boxed{\sf Length = 9\:cm}} [/tex]
[tex]\rule{170}2[/tex]
[tex]\dashrightarrow\sf\:\:Area\:of\: rectangle = Length \times Breadth\\\\\\\dashrightarrow\sf\:\: Area\:of\: rectangle = 7\:cm \times 9\:cm\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Area\:of\: rectangle = 63\:cm^2}}[/tex]
⠀
[tex]\therefore\:\underline{\textsf{The area of reactangle is \textbf{63}}\:\sf{cm^2}}.[/tex]
Answer:
Area of the rectangle is 63 cm².
Step-by-step explanation:
Given :-
The perimeter of a rectangle is 32 cm.The width is 7 cm.To find :-
The area of the rectangle.Solution :-
Consider,
Length of the rectangle = x cmwidth = 7 cm
Formula used :-
[tex]{\boxed{\sf{Perimeter of rectangle=2(Length+breadth)}}}[/tex]
According to the question ,
2(x+7) = 32
→ x+7 = 32/2
→ x +7 = 16
→ x = 16-7
→ x = 9
★ Length = 9 cm
Area of the rectangle ,
= length × Breadth
= 9 × 7 cm²
= 63 cm²
Therefore, the area of the rectangle is 63 cm².
This is a summary of Mia's pay stub: Gross Pay: $56.00 State Tax Withholding: $1.60 Social Security Tax: $2.35 Federal Tax Withholding: $3.68 Medicare Tax: $.81 Savings Deposit: $35.00 Charity Donation: $1.00 What percent of Mia's gross pay goes for taxes?
Answer: 15.07%
Step-by-step explanation:
Given: Gross Pay: $56
State Tax Withholding: $1.60
Social Security Tax: $2.35
Federal Tax Withholding: $3.68
Medicare Tax: $.81 .00
Total tax = (State Tax Withholding + Social Security Tax + Federal Tax Withholding + Medicare Tax)
= $(1.60+ 2.35+3.68+0.81)
= $8.44
So, the percent of Mia's gross pay goes for taxes = (Total tax ) ÷ (Gross (pay) × 100
=(8.44 )÷ (56) × 100
= 15.07%
Hence, the percent of Mia's gross pay goes for taxes is 15.07%.
How do I rewrite the expression x^3+10x^2+13x+30/x^2+x^2+2x+1
Answer:
A
Step-by-step explanation:
x²+2x+1)x³+10x²+13x+39 (x+8
- x³+2x²+x
+ - -
--------------------
8x²+12x+39
8x²+16x+ 8
- - -
____________
-4x+31
Jaycee Alvarez deposits $425 in a savings account at City Bank. The account pays an annual interest rate of
5.5 percent. She makes no other deposits or withdrawals. After three months the interest is calculated. How
much simple interest does her money earn?
Answer: $5.84
Step-by-step explanation:
Simple interest is calculated using the formula: PRT/100
where P = principal = $425
R = rate = 5.5%
T = time = 3/12 = 1/4 = 0.25
S.I = PRT/100
= (425 × 5.5 × 0.25)/100
= $584.375/1000
= $5.84
I need help solving this i tried and tired but still don’t understand. Factor out the greatest common factor. 6x^5+4x^3+8x=
Answer:
Add and subtract the second term to the expression and factor by grouping.
2
x
3
(
3
x
−
1
)
(
x
−
1
)
Step-by-step explanation:
Answer:
3x⁴+2x²+8
Step-by-step explanation:
[tex]6 {x}^{5} + 4 {x}^{3} + 8x[/tex]
[tex] = 2x(3 {x}^{4} + 2 {x}^{2} + 8)[/tex]
x +12 = 20
can you help me
Answer:
x=8
Step-by-step explanation:
x+12=20
1
What is the solution to the equation 5x + 4 =19
Answer:
x=3
Step-by-step explanation:
5x + 4 = 19
-4 -4
5x = 15
/5 /5
x = 3
What property are these? Associative property of addition, Commutative property of addition, identity property of multiplication, Associative property of multiplication, Commutative property of multiplication. 1. (3 x 7)(8) = 3(7 x 8) 2. (7k)5 = 5(7k) 3.8(x + 15) = (8)(x) + (8)(15)
Answer:
Step-by-step explanation:
1) (3 * 7)(8) =3 (7 * 8)
Associative property of multiplication
It states that product of three or more numbers remains same regardless the way they are grouped
2) (7k)5 = 5(7k)
Commutative property of multiplication
3) 8(x +15) = (8)(x) + (8)(15)
distributive property
3x/5=30 solve the equation
Answer:
Step-by-step explanation:
To solve equations like this you need to to get x by itself.
So, Let's multiply both sides by 5 to get rid of 5.
3x/5 *5 = 30 * 5
= 3x = 150
Now we divide both sides by 3 to get x by itself,
3x/3 = 150/3
x = 50
Answer:
x = 50Step-by-step explanation:
[tex]\frac{3x}{5}=30\\\\\mathrm{Multiply\:both\:sides\:by\:}5\\\\\frac{5\cdot \:3x}{5}=30\cdot \:5\\\\\mathrm{Simplify}\\\\3x=150\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\frac{3x}{3}=\frac{150}{3}\\\\x = 50[/tex]
If f(x) = 7x6cos-1x, find f '(x).
Answer:
F(x)=g'(x)h(X)+g(x)h'(x)
F(x)=90x9tan-1-[9*10/(1+x2)}
The derivative of f(x) is f'(x) = 42x⁵ * cos⁻¹(x) - 7x⁶ / (√(1 - x²))
To find the derivative of the function f(x) = 7x⁶ * cos⁻¹(x), we'll use the chain rule and the power rule of differentiation.
The chain rule states that if we have a function of the form f(g(x)), then its derivative is given by f'(g(x)) * g'(x).
Let's break down the function f(x) into two parts:
u(x) = 7x⁶
v(x) = cos⁻¹(x)
Now, we'll find the derivatives of u(x) and v(x):
u'(x) = d/dx (7x⁶) = 6 * 7x⁵ = 42x⁵
To find v'(x), we differentiate cos⁻¹(x) using the inverse trigonometric differentiation formula:
d/dx [cos⁻¹(x)] = -1 / (√(1 - x²))
Now, applying the chain rule to the function f(x) = 7x⁶ * cos⁻¹(x), we get:
f'(x) = u'(x) * v(x) + u(x) * v'(x)
f'(x) = 42x⁵ * cos⁻¹(x) + 7x⁶ * (-1 / (√(1 - x²)))
So, the derivative of f(x) is:
f'(x) = 42x⁵ * cos⁻¹(x) - 7x⁶ / (√(1 - x²))
To know more about derivative:
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Find the probability of drawing 3 Aces at random from a deck of 52 ordinary playing cards if the cards are:_________
A) Replaced
B) Not Replaced
Answer:
A) 1/2197
B) 1/5525
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome.
Since there are 52 random cards in a deck of card, the total outcome will be 52.
a) Also in a deck of card, there are 4 aces. If we are to select 3 aces with replacement, this means that each time we pick up an ace from the card, it was returned.
Pr(drawing an ace) = 4/52
Pr(drawing 3 aces and replacing it) = 4/52 *4/52*4/52
Pr(drawing 3 aces and replacing it) = 64/140,608
Pr(drawing 3 aces and replacing it) = 1/2197
b) If we pick 3 aces without replacement then each time we pick an ace, the total number cards keeps reducing.
Pr(picking the first ace) = 4/52
Pr(picking the second ace without replacing) = 3/51 (Since we didn't replace the first one, the total ace in the deck of card will reduce to 3 and the total will be 51)
Pr(picking the third ace without replacing) = 2/50 (since we didn't replace the first two aces, the total ace in the deck of card will reduce to 2 and the total will be 50)
Pr(drawing 3 aces without replacement) = 4/52*3/51*2/50
Pr(drawing 3 aces without replacement) = 24/132,600
Pr(drawing 3 aces without replacement) = 1/5525
Given that (y+z), (y+3) and (2y^2-1) are consecutive terms of an arithmetic progression. Find the possible values of y
Answer:
This problem actually says:
(y + 2), (y + 3) and (2*y^2 - 1) are consecutive terms of an arithmetic progression.
Now, the difference between two consecutive terms in an arithmetic progression is always the same, so we have:
(y + 3) - (y +2) = D
(2*y^2 - 1) - (y + 3) = D
From the first equation we have:
y + 3 - y - 2 = 1 = D
Now we can replace it in the other equation:
2*y^2 - 1 - y - 3 = 1
2*y^2 - y - 5 = 0
Now we need to solve that equation to find the possible values of y.
To solve a quadratic equation of the form:
a*x^2 + b*x + c = 0, we can use the Bhaskara's equation:
[tex]y = \frac{-b +- \sqrt{b^2 -4*a*c} }{2*a}[/tex]
in this case, the solutions are:
[tex]y = \frac{1 +-\sqrt[]{(-1)^2 - 4*2*(-5)} }{2*2} = \frac{1 +- \sqrt{61} }{4} = \frac{1+-6.4}{4}[/tex]
Then the possible values of y are:
y = (1 + 6.4)/4 = 1.85
y = (1 - 6.4)/5 = -1.35
Evaluate this expression then round your answer to two decimal places:
7^4 ÷ 7^6 =
Answer:
0.02
Step-by-step explanation:
7⁴ / 7⁶ = 7⁴⁻⁶ = 7⁻² = 1/7² = 1/49 ≈ 0.02
Answer:
.02
Step-by-step explanation:
7^4 ÷ 7^6
We know that a^b ÷ a^c = a^ ( b-c)
7^4 ÷ 7^6
7^(4-6)
7^(-2)
We know that a^ -b = 1/a ^b
1 / 7^2
1/49
.020408163
Rounding to 2 decimal places
.02
(2x +1) -7 (-6x+9) what is the answer if using the Distributive Property?
Answer:
Step-by-step explanation:
Distributive property: a(b +c) = a*b + a*c
(2x + 1) - 7(-6x + 9) = (2x + 1) + (-7)*(-6x) + (-7)*9
= 2x + 1 + 42x - 63 {Combine like terms}
= 2x + 42x + 1 - 63
= 44x - 62
for 10 pts what is 2 1/5 + 1 3/4
Answer:
3 19/20
Step-by-step explanation:
11/5+7/4=
44/20+35/20=
79/20=
3 19/20
Which of the following statements are true about segments in a plane? Choose all that apply. Every segment has infinitely many midpoints Every segment has two bisectors Every segment has one perpendicular bisector Every segment has infinitely many congruent segments Every segment has one line that is perpendicular to it
Answer:
The correct option are;
Every segment has one perpendicular bisector
Every segment has infinitely many congruent segments
Step-by-step explanation:
1) Every segment in a plane has exactly one perpendicular bisector
2) A congruent segment is a segment of equal length as a given segment, given that there can be infinitely many planes that can contain collinear points, whereby two points define a segment, the number of congruent segments that can be formed on infinitely many planes will therefore, be infinite.
Also given that the number of possible segments is infinite, the number of segments of a given size and therefore, the number of possible congruent segments is infinite.