Step-by-step explanation:
well you can distribute the sqrt(15x) to the (√3x + √5) and then combine the radicals using the product property of radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex].
[tex](\sqrt{3x} + \sqrt{5})\sqrt{15x} + 2\sqrt{30}\\(\sqrt{3x} * \sqrt{15x}) + (\sqrt{5} * \sqrt{15x}) + 2\sqrt{30}\\\sqrt{45x^2} + \sqrt{75x} + 2\sqrt{30}\\[/tex]
Now we can simplify the radicals using the same property we used to combine them but instead of combining into one radical we'll separate them into two radicals where one of the radicals simplifies into a number without a radical
[tex](\sqrt{9} * \sqrt{x^2} * \sqrt{5}) + (\sqrt{25} * \sqrt{3x}) + 2\sqrt{30}\\3x\sqrt{5} + 5\sqrt{3x} + 2\sqrt{30}[/tex]
What is the measure of an angle if it is 120 less
than four times its own supplement?
Answer:
120°
Step-by-step explanation:
x = angle supplement = 180-x
x = 4(180-x) -120
x = 720 - 4x - 120
5x = 600°
x =120°
What are the zeros of the quadratic function f(x) = 2x² + 16x - 9?
7
O x = -4 -
-√7
and x = -4 +
+√√2/2
O x=-4- 25
and x = 4 +
-
2
21
0 x = -4-√²/²
and x = -4 +
2
41
Ox=-4-
and x = -4 +
2
|~~
25
2
21
2
41
2
The zeros of the quadratic function f(x) = 2x² + 16x - 9 are given as follows:
[tex]x = -4 + \sqrt{\frac{41}{2}}, x = -4 - \sqrt{\frac{41}{2}}[/tex]
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is given by:
f(x) = 2x² + 16x - 9.
The coefficients are a = 2, b = 16, c = -9, hence:
[tex]\Delta = 16^2 - 4(2)(-9) = 328[/tex]
Then:
[tex]x_1 = \frac{-16 + \sqrt{328}}{2(2)} = -4 + \sqrt{\frac{41}{2}}[/tex]
[tex]x_2 = \frac{-16 - \sqrt{328}}{2(2)} = -4 - \sqrt{\frac{41}{2}}[/tex]
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I need math help. I don’t understand the question.
Answer:
A.) 132.3 mm Hg
B.) 49 years old
Step-by-step explanation:
[tex]P= 0.006y^{2} -0.01y+119[/tex]
P = blood pressure
y = age in years
A.) Solution
To find: P
Given: y = 48
[tex]P= 0.006y^{2} -0.01y+119[/tex]
P = 0.006 x 48 x 48 - 0.01 x 48 + 119
P = 0.006 x 2,304 - 0.48 + 119
P = 13.824 - 0.48 + 119
P = 132.344 ⇒ 132.3
B.) Solution
To find: y
Given: P = 132.92
[tex]P= 0.006y^{2} -0.01y+119[/tex]
[tex]132.92= 0.006y^{2} -0.01y+119[/tex]
[tex]0.006y^{2} -0.01y-13.92[/tex]
.......................................................
Answer: 49 years old
if c = 10 then the value of a is…
5[tex]\sqrt{3}[/tex]
Step-by-step explanation:Special right triangles, such as the one shown, have unique equations that can be used to find missing sides.
30-60-90 Triangles
The angle measurements show us that this is a 30-60-90 triangle. This name refers to the 3 angle measurement. There are 2 types of special right triangles, 45-45-90 and 30-60-90. For most triangles, it would take the law of sine or cosine to find a missing side with only 1 side given. But, with special right triangles, we can use shortcuts to find a.
Formulas
For all 30-60-90 triangles, there are 3 sides: the hypotenuse (c), the long leg (a), and the short leg (b). The shortcuts for 30-60-90 triangles are based on the length of the short leg.
The formulas are as follows (the variables match the variable given in the figure):
c = 2bb = 0.5ca = b[tex]\sqrt{3}[/tex]Solving for a
So, to find a, we must first find b. Since b is equal to half of c, we can divide the value of c by 2.
10/2 = 5Thus, b = 5
Next, plug this value into the formula for b
a = 5[tex]\sqrt{3}[/tex]Answer:
Last option
Step-by-step explanation:
cos30° = a/10
a = 10cos30°
[tex]cos30=0.8660=\frac{\sqrt{3} }{2}[/tex]
[tex]a=10(\frac{\sqrt{3} }{2} )=5\sqrt{3}[/tex]
Hope this helps
find the length of AD
The length of AD is 5 units. so, option A is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The length of DC is given as 13 units.
The length of AC is given as 12 units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.
by Pythagoras theorem;
[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]
Hence, the length of AD is 5 units. so, option A is the correct answer.
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Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a .
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a .
Using translation concepts, it is found that the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
From triangle X′Y′Z′ to triangle X′′Y′′Z′′, the rule is given by:
(x,y) -> (x, -y)
Hence the type of transformation that triangle X′Y′Z′ undergoes is a reflection over the x-axis.
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The dimensions of a rectangles are 8cm and 12cm. What is the ratio of its length to its perimeter?
Answer:
Dimensions = 8 CM and 12 CM
length = 12 CM
width = 8 cm
perimeter = 2 ( length + width)
= 2( 12 + 8)
= 2 ( 20)
= 40 CM
ratio = 12/40
= 6/20
= 3/10
= 3 : 10what does [ ] mean in math?
it is a bracket used in maths
Answer:
They are kind of like outer brackets, so if you have some expression like this:
5 + (4 × 6 + (7 - 8)),
it's better to write it like this:
5 + [4 × 6 + (7 - 8)],
so you can read it more easily.
The interest on Rs. 300 for 5 years is Rs. 37.50. What will be the interest on Rs. 100 for the same years?
Answer:
the interest for 100 in 5 years us 12.5
A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of _______.
A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate
What is a rate?
A rate is known as the quantity measured with respect to another measured quantity. It refers to the comparison of a part to a whole.
It is also the measure of a part with respect to a whole or a proportion.
Therefore, a comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate
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8. Find the other endpoint of the segment with a midpoint of (-6, 4) and endpoint of (4, 8).
Answer:
1,3 is the answer... if you look down here↓:
Step-by-step explanation:
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195, how long was the repairman there? answers a: 2 hours b: 2.5 hours c:4 hours d: 3 hours
The time spent by the repairman there will be 3 hours so the correct answer is option D.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.
The time will be calculated as:-
Total amount = $195
Now the fixed consulting cost will be $60 and will be deducted from the
total amount.
Variable cost = 195 - 60 = 135
The $45 per hour charge so for $145 the time will be:-
Time = 135 / 45
Time = 3 Hours
Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.
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Find the derivative of y = x^3/2.
Find the derivative of y = 1/x^3.
Find the derivative of y = 1/√x.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
properties to be used here :
[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]
[tex]\large \textsf{Question : 1} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]
[tex]\large \textsf{Question : 2} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]
[tex]\large \textsf{Question : 3} [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]
[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A bag contains equal numbers of green marbles and blue marbles. You can divide all of the green marbles into groups of 12 and all the blue marbles into groups of 16. Whatis the least number of each color of marble thatcan be in the bag
Answer: 48
Step-by-step explanation:
We need to find the least common multiple of 12 and 16.
Finding the prime factorizations of 12 and 16,
[tex]12=2^{2} \times 3\\\\16=2^{4}[/tex]
Thus, the least common multiple is [tex]2^{4} \times 3=\boxed{48}[/tex]
The radius of the water well is 2r inches. Find the area of the water well.
The area of the water well is [tex]4\pi r^2[/tex]
How to determine the area?The radius is given as:
Radius, R = 2r
The area of the water well is calculated using:
[tex]A = \pi R^2[/tex]
This gives
[tex]A = \pi (2r)^2\\\\\\[/tex]
Evaluate the expression
[tex]A = 4\pi r^2[/tex]
Hence, the area of the water well is [tex]4\pi r^2[/tex]
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x + 4y = -10
2x - y = 7
Answer:
(2, - 3 )
Step-by-step explanation:
x + 4y = - 10 → (1)
2x - y = 7 → (2)
multiplying (2) by 4 and adding to (1) will eliminate y
8x - 4y = 28 → (3)
add (1) and (3) term by term to eliminate y
9x + 0 = 18
9x = 18 ( divide both sides by 9 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
2 + 4y = - 10 ( subtract 2 from both sides )
4y = - 12 ( divide both sides by 4 )
y = - 3
solution is (2, - 3 )
The figure shows the letter M and four of its transformed images—A, B, C, and D:
A coordinate grid is shown from positive 8 to negative 8 on the x-axis and from positive 8 to negative 8 on the y-axis. An image of the letter M is shown on ordered pair 1, 2 and 1, 4 and 2, 3 and 3, 12, and 3, 4. Another image of letter M is shown on ordered pair 4, negative 4 and 4, negative 2 and 5, negative 3 and 6, negative 2 and 6, negative 4. This M is labeled as B. Another image of letter M labeled C is shown on negative 4, negative 4 and negative 4, negative 2 and negative 3, negative 3 and negative 2, negative 2 and negative 2, negative 4. An image of the letter W labeled A is shown on 1, negative 2 and 1, negative 4 and 2, negative 3 and 3, negative 2 and 3, negative 4. Another image of the letter W labeled D is shown on negative 2, 4 and negative 2, 2 and negative 3, 3 and negative 4, 2 and negative 4, 4. The letters A, B, C, D are written towards the bottom left of the respective W and M.
Which of the four images was formed by a reflection of the letter M?
A
B
C
D
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x axis, then that leads the graph to go just in the opposite side of the axis as if we're seeing it in a mirror.
If you study it more, you will find that it's symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.
Thus, if you're reflecting a point (x,y) along the x-axis, then its x abscissa will stay the same but y coordinates will negate.
Thus (x,y) turns to (x, -y)
Similarly, if you're reflecting a point (x,y) along the y -axis, the resultant image of the point will be (-x,y).
The image was formed by a reflection of the letter M would be image A in the second quadrant b the reflection on X-axis. The correct option is A.
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The reflection of letter M is (A)
What is reflection?A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure.
According to the graph the reflection of Of letter M is with same coordinates but with x as positive and y as negative.
Hence the reflection is (A).
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Which ordered pair is included in the solution set to the following system?
y > x2 + 1
y < x2 – x + 1
(–3, 4)
(–2, 6)
(0, 2)
(2, 4)
Answer:
The answer is (-2,6)
Step-by-step explanation:
Answer: (-2, 6)
Step-by-step explanation:
An easy way to solve this is to plug in each answer into the system of inequalities to figure out with ordered pair adheres to the rules of both equation.
Let's use the first ordered pair as an example: (-3,4)
Is this true?:
4 > (-3)² +1
4 < (-3)² - (-3) + 1
No, it is not:
4 < 10
4 < 13
Let's try the second answer:
Is this true?:
6 > (-2)² + 1
6 < (-2)² -(-2) + 1
YES, it is!
6 > 5
6 < 7
(-2, 6) is your answer. To check, verify that the last two answer choices are wrong.
which of the following have eight faces
From the observation deck of a skyscraper, Lavaughn measures a 42°
angle of depression to a ship in the harbor below. If the observation deck is 872 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary
By using trigonometry, we conclude that the horizontal distance is 785.15ft
How to find the horizontal distance?We can think of this as a right triangle.
Where the height of the observation deck is one cathetus and the horizontal distance is the other cathetus,
We know that the depression angle when looking from above is 42°. If we step on this angle, the adjacent cathetus is the height of the deck, then the horizontal distance is the opposite cathetus.
Then we can use the relation:
tan(a) = (opposite cathteus)/(adjacent cathetus).
Replacing what we know:
tan(42°) = (distance)/(872ft)
tan(42°)*872ft = distance = 785.15ft
The horizontal distance is 785.15ft
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Help please.. z zzz z Z z z z z z z z z z z z z zz
Consider this function.
ƒ(=) =-3x + 3
Which graph represents the inverse of function??
Answer: The first graph
Step-by-step explanation: A graph’s inverse will have all of their roots inverted as well. If you put the graph f(x)= 3x+3 into a graphing calculator, you’ll be able to see all the roots. From there, just invert (switch) the roots. Since on the original graph the most prominent roots are {(0,3), (-1,0),(-2,-3)}, you just need to invert those roots and find them ALL on one of the graphs, then you have your answer. So, the inverted roots will be {(3,0),(0,-1),(-3,-2)}.
Still, I find the simplest thing is to put them into a graphing calc like GeoGebra.
Find the common difference, the 52nd term, and the SIMPLIFIED general term formula.
1) 21, 51, 81, 111, ….
I need this ASAP!!!!! PLEASE I’M begging you!!!!
Answer:
Common difference: 30
General term formula: [tex]a_n=30n-9[/tex]
52nd term: 1551
Step-by-step explanation:
Given sequence:
21, 51, 81, 111
Calculate the difference in terms:
[tex]21 \underset{+30}{\longrightarrow} 51 \underset{+30}{\longrightarrow} 81 \underset{+30}{\longrightarrow} 111[/tex]
The sequence is increasing by 30 each time, so as there is a common difference, this is an arithmetic sequence with a common difference of 30.
General form of an arithmetic sequence
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between consecutive termsGiven:
a = 21d = 30Substitute the given values into the formula to find the general term formula:
[tex]\implies a_n=21+(n-1)30[/tex]
[tex]\implies a_n=21+30n-30[/tex]
[tex]\implies a_n=30n-9[/tex]
To find the 52nd term, simply substitute n = 52 into the found general term formula:
[tex]\implies a_{52}=30(52)-9[/tex]
[tex]\implies a_{52}=1560-9[/tex]
[tex]\implies a_{52}=1551[/tex]
We only have cows and ducks in our garden and know that the animals in the garden have 20 legs and 14 eyes. How many cows and ducks do we have
The number of cows and ducks in the garden are 3 and 4 respectively.
Solve the system of linear equationsLet the numbers of cows be x and the number of ducks is y.
Total number of legs=20
Total number of eyes=14
Linear equation for the total number of legs in the garden,
4x+2y=20 -(1)
Linear equation for the total number of eyes in the garden,
2x+2y=14 -(2)
Solve the system of the two linear equations to find the values of x and y.
Subtract equation (1) from equation (2), and we get,
2x=6
[tex]x=\frac{6}{2}\\[/tex]
x=3
Substitute the value of x in equation (1), and we get,
4(3)+2y=20
12+2y=20
2y=20-12
2y=8
[tex]y=\frac{8}{2}\\[/tex]
y=4
Number of cows=3
Number of ducks=4
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2.
(07.02 LC)
Which statement is true for the equation 4x − 4x − 5 = −5? (5 points)
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
4 hours minus 1 hour, 59 minutes, 58 sec-
onds equals
A. 2 hours, 2 seconds.
B. 3 hours, 1 minute, 2 seconds.
C. 2 hours, 1 minute, I second.
D. 3 hours, 2 seconds.
ircle A has center of (6, 7), and a radius of 4 and circle B has a center of (2, 4), and a radius of 16. What steps will help show that circle A is similar to circle B? (
Answer:
ggggjgfdvhgffgutddfgj
What is the y-value when x equals 23?
y = 460 - 11(x)
If a = 6, then the value of c is...
Answer:
[tex]\boxed{\bf B. \: c = 4 \sqrt{3} }[/tex]
Step-by-step explanation:
Since a = 6, then, b = 3.47 ( opposite of 30°).
By applying the pythagoras theorem..
[tex] \boxed{\bf {h}^{2} = {p}^{2} + {b}^{2}} [/tex][tex]\bf {(c)}^{2} = {(a)}^{2} + {(b)}^{2} [/tex][tex] \bf {c}^{2} = {(6)}^{2} + {(3.47)}^{2} [/tex][tex] \bf {c}^{2} = 36 + 12[/tex][tex]\bf {c}^{2} = \sqrt{48} [/tex][tex]\bf c = 4 \sqrt{3} [/tex]______________________Answer:
4√3 or B
Step-by-step explanation:
Period of y = negative 2 sin x
It has a period of 2pi
the equation to find the period of a sin/cos function is
[tex]period = \frac{2\pi}{b} [/tex]
y = -2 sin(x) has a normal period of 2pi because the b value in this equation isn't stated, making it equal to 1
the basic equation for a sin function is
[tex]y = a \: \sin(b(x - c) ) + d[/tex]