Answer:
Step-by-step explanation:
Do you have any options or a graph?
[tex]\{ \frac { ( \sqrt { 3 } ) \times 3 ^ { - 2 } } { ( \sqrt { 5 } ) ^ { 2 } } \} ^ { \frac { 1 } { 2 } }[/tex]solve this equation
Answer:
Step-by-step explanation:
Exponent law:
[tex]\sf \bf a^m * a^n = a^{m+n}\\\\ (a^m)^n = a^{m*n}[/tex]
[tex]\sf a^{-m}=\dfrac{1}{a^m}[/tex]
First convert radical form to exponent form and then apply exponent law.
[tex]\sf \sqrt{3}=3^{\frac{1}{2}}\\\\\sqrt{5}=5^{\frac{1}{2}}[/tex]
[tex]\sf \left(\dfrac{(\sqrt{3}*3^{-2}}{(\sqrt{5})^2}\right)^{\frac{1}{2}}= \left(\dfrac{3^{\frac{1}{2}}*3^{-2}}{(5^{\frac{1}{2}})^2} \right )^{\frac{1}{2}}[/tex]
[tex]= \left(\dfrac{3^{\frac{1}{2}-2}}{5^{\frac{1}{2}*2}}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{1-4}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\left(\dfrac{3^{\frac{-3}{2}}}{5}\right)^{\frac{1}{2}}\\\\=\dfrac{3^{\frac{-3}{2}*{\frac{1}{2}}}}{5^{\frac{1}{2}}}\\\\ =\dfrac{3^{{\frac{-3}{4}}}}{5^{\frac{1}{2}}}[/tex]
40 POINTS PLS HELP PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS /J IM LAZY NO PLS HELP
Answer:
y = -0.5x - 3.5
Explanation:
Take two points: (1, -4), (3, -5)
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]
Equation:
[tex]\sf y- y_1 = m (x - x_1)[/tex]
[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]
[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]
[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]
[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]
The formula of a line is:
[tex]f(x) = kx + b[/tex]
k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.
We can see 2 points:
A (1, -4)
B (3, -5)
We can make a system of equations:
[tex]k*1+b=-4\\k*3+b=-5\\[/tex]
From second equation:
[tex]b = -5 - 3k[/tex]
Let's put b in first equation:
[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]
Now we can find b:
[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]
The answer is:
-0.5x -3.5
Step 3: So, M 12= 60 Degrees
Use the drop-down menus to explain whether or not Stuart is corrrect.
The reasoning that may be used for finding the measure of m∠12, is the
same side interior angles theorem.
The correct options using the drop-down menu are;
The sum of ∠1, ∠7, and ∠8 is 180°
∠8 and ∠12 are the same side interior angles
The measure of ∠12 must be = 120°
Stuart is not correct
The complete question is given below:-
In the diagram, line x is parallel to line y,m21= 65°, and m27 = 55°. Stuart says that m212 = 60°. His reasoning is shown. Step 1: mZ8 = 60°, because m21+ m27 +m28 = 180º. Step 2:28 212, because 28 and 212 are corresponding angles. Step 3: So, mZ12 = 60° Use the drop-down menus to explain whether or not Stuart is correct.
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.
Given parameters;
Line x ║ line y
m∠1 = 65°, m∠7 = 55°
m∠12 = 60°
Stuart states ∠12 = 60°
The reasoning is presented as follows;
Step 1: m∠8 = 60°, because m∠1 + m∠7 + m∠8 = 180°
Step 2: ∠8 ≅ ∠12, because ∠8 and ∠12 are corresponding angles
Step 3: So, m∠12 = 60°
Using the drop-down menu, we have;
The sum of ∠1, ∠7, and ∠8 is 180° (Sum of angles in the triangle)
∠8 and ∠12 are same side interior angles (by definition)
Same side interior angles are supplementary, therefore;
∠8 +∠12 = 180°
∠12 = 180° - ∠8
Which gives;
The measure of ∠12 must be 180° - ∠8 = 180° - 60° = 120°
The measure of ∠12 must be = 120°
Stuart is not correct
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x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is
The Standard form of the equation of circle is (x+21)² + (y+19)² = 849
What is Standard form of circle?To transform general form to a standard form, you can use completing the square method or you can convert this equation
x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
Here, Given: x² + y² + 42x + 38y − 47 = 0
Required: Find the values of h, k, and r using this formula
x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
On comparing we get,
-2h = 42
h = 21
-2k = 38
k = 19
-47 = h² + k² - r²
-47 = 21² + 19² - r²
r² = 849
r = √849
Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849
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6x9(7-3)4+3x36+3
what is the answer
The given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].
The given expression is [tex]6x^{9} (7-3).4+3x^{36} +3[/tex].
We need to simplify the given expression.
What is an algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
First, multiply the numbers 6×4=24.
That is, [tex]24x^{9} (7-3)+3x^{36} +3[/tex].
Next, subtract the numbers 7-3=4.
[tex]24x^{9}.4+3x^{36} +3[/tex]
Finally, multiply the numbers 24×4=96.
[tex]96x^{9}+3x^{36} +3[/tex].
Hence, the given expression can be simplified as [tex]96x^{9}+3x^{36} +3[/tex].
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Solve using the factoring method: x2 + 4x - 21 = 0
Answer:
x² + 4x - 21 = 0
x² + 7x - 3x - 21 = 0
x ( x + 7 ) -3 ( x + 7 ) = 0
( x - 3 ) ( x + 7 ) = 0
∴ x - 3 = 0 or x + 7 = 0
x = 0 + 3 x = 0 - 7
x = 3 x = -7
Which of the following equations is equivalent to the logarithm equation below E^x=4 A.x=log(10)^4 B.x=In^4 C.x^4=e D.Inx=4
Solving the exponential function, the resulting logarithmic expression is:
x = ln(4).
How to solve an exponential function?Considering an exponential equation involving Euler number e, the expression is solved applying the natural logarithm ln, which is the inverse function to the exponential function, to both sides of the equation.
Hence:
[tex]e^{x} = 4[/tex]
Applying ln to both sides:
[tex]\ln{e^x} = \ln{4}[/tex]
Since ln and e are inverse, we can isolate x, hence:
[tex]x = \ln{4}[/tex]
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What is the simplified form of this expression? (3 − 13x − 7x2) − (5x2 12x − 10)
Answer:
-12x²-25x+13
Step-by-step explanation:
First open parenthesis.
(3 − 13x − 7x²) − (5x² + 12x − 10)
3 − 13x − 7x² − 5x² - 12x + 10
Now combine like terms.
3 − 13x − 7x² − 5x² - 12x + 10=13-25x-12x²
Now put into standard form, exponents greatest to least.
-12x²-25x+13
Hope this helps!
If not, I am sorry.
Answer:-12x²-25x+13
Step-by-step explanation:
Refer to the attached image
Answer: [tex]\boldsymbol{2(x-2)(5x+7)}[/tex]
========================================================
Work Shown:
[tex](4x^2-16)+3(2x-4)(x+1)\\\\4(x^2-4)+3*2(x-2)(x+1)\\\\4(x-2)(x+2)+3*2(x-2)(x+1) \ \text{ ... difference of squares rule}\\\\2*2(x-2)(x+2)+3*2(x-2)(x+1)\\\\2(x-2)(2(x+2)+3(x+1))\\\\2(x-2)(2x+4+3x+3)\\\\\boldsymbol{2(x-2)(5x+7)}\\\\[/tex]
The answer has been confirmed with WolframAlpha which is basically a calculator app, but does a ton more than any average calculator.
The CAS (computer algebra system) in the app GeoGebra is another tool I use all the time.
Yet another way to confirm the answer is to graph the original expression and the answer as separate functions. You should find they produce the exact same curve. One curve perfectly overlaps the other. This visually verifies the two expressions are the same thing, just written a different way of course.
Let me know if you have any questions about any step. The basic idea I did was to pull out the GCF and then combine like terms.
Tutorial C
A 3-yard roll of aluminum foil costs $4.14. What is the price per
foot?
Answer:
$.46 or 46 cents per foot
Step-by-step explanation:
3 yards = 4.14
1 yard is 3 feet
3 yards is 9 feet
4.14 ÷ 9 = .46
Which value must be added to the expression x2 16x to make it a perfect-square trinomial?
Answer:
16
Step-by-step explanation:
x^2+16x+16
(x+4)(x+4)
x^2+ 4x+4x+16
Answer:
The answer is C.) 64 on edge.
ILL GIVE 5-STAR RATING, A THANKS, 20 PTS AND BRAINLIEST TO FIRST RIGHT ANSWER!!!
Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?
Quadrilateral CDEF is inscribed in circle A. Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _________________, which means that their measures are _________________. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE = 2 ⋅ m∠CDE. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
central angles; equal to the measure of their intercepted arcs
inscribed angles; equal to the measure of their intercepted arcs
central angles; one half the measure of their intercepted arcs
inscribed angles; one half the measure of their intercepted arcs
The missing statements with regard to the mathematical proof are:
It is to be noted that an intercepted arc is the arc that sits inside the inscribed angle. See the attached image.
Thus, it is correct to state that
The missing statements with regard to the mathematical proof are:
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please help mee, (30 points will give brainliest!!!)
Answer:
-4
+3
12
-0.5, 12.25
x = -0.5
Step-by-step explanation:
The x intercepts are the values of x when y = 0 ie the roots of the equation
[tex]-x^2 -x +12 = 0[/tex]
or
[tex]x^2 + x - 12 = 0[/tex]
We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3
y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12
Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x
Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5
Plugging this value of x into the original function gives the vertex y value
[tex]y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25[/tex]
The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5
The graph of the quadratic function shows these values
can't understand tbh anyone willing give a go?
Answer:
nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls
total number on rolls on nr.3 and nr.4= 99
Step-by-step explanation:
Calculate the probability for nr.3
Always try to get 100%
1=13%
2=5%
3=?
4=21%
5=19%
6=30%
Add all the percentage
1+2+4+5+6= 88%
now calculate the percentage for nr.3
100%-88%=12%
give a estimated total number of times the dice will land on nr.3 or nr.4 after 300 rolls
nr.3 300x0.12=36rolls
nr.4 300x0.21=63 rolls
total number on rolls on nr.3 and nr.4= 99
You spent 14 of your allowance on Monday. On Tuesday, you spent 13 of what was left. On Wednesday, you spent 12 of what remains. What fraction of your allowance do you have left? Choose the most reasonable answer.
PLEASE HELP ME WITH THIS
Please help me smart peeps
Determine if the two triangles below are similar and state how you know.
The first and foremost rule for determining if 2 triangles are similar is checking if their angles are the same. Obviously, in this example, the angles are completely different, so the triangles are not similar.
Have a nice day!
And good luck on the assignment!
find 20,21,22,23,24,25,26,27
hello hello hello
Step-by-step explanation:
hi hi hi
A rectangular school yard has a perimeter of 294 meters. Its area is 5,162 square meters. What are the dimensions of the school yard?
The dimensions of the school yard is 58 m and 89 m.
What is rectangle ?A rectangle is a polygon with four sides , It has opposite sides parallel and equal.
It is given that
A rectangular school yard has a perimeter of 294 meters
Perimeter of a rectangle is given by
P = 2(Length +Breadth)
294 = 2( L+B)
147 = L+B
Area of a rectangle is given by
L*B = 5162
B = 5162/L
L + 5162/L =147
L² -147L +5162 = 0
L² -58L - 89L+5162 = 0
L(L-58) -89(L-58)
L = 58 , 89
The dimensions of the school yard is 58 m and 89 m.
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PLEASE HELP ME WITH THIS
Answer:
Vertex
Vertex are the end points of parabola where it opens up
locus are the group of points
latus rectum is the line parallel to it .
Part A
? Question
Enter the correct answer in the box.
Recall that the width is x + 15, and the length is 49 less than 2 times the width. Write a simplified expression for the
length of the garage in terms of x.
(101 0² +
An expression is defined as a set of numbers, variables, and mathematical operations. A simplified expression for the length of the garage in terms of x is 2x-19.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the width is x + 15, and the length is 49 less than 2 times the width. Therefore, a simplified expression for the length of the garage in terms of x is,
Length = 2(x+15) - 49 = 2x + 30 - 49 = 2x-19
Hence, a simplified expression for the length of the garage in terms of x is 2x-19.
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What is 5,435,778 expressed in scientific notation? A. 5.435778 x 10 B. 5.435778 x 10 C. 5.435778 x 10 D. 5.435778 x 10
Answer:
The answer options seem to be missing their exponents for the 10 unit.
Answer is: 5.435778 x [tex]10^{6}[/tex]
Step-by-step explanation:
5,435,778
Move the decimal point to the left until it is between the 5 and 4. Scientific notation means rewriting the number with only one digit to the left of the decimal point and adding the "x [tex]10^{x}[/tex] after to account for the number of positions the decimal point was moved.
Count the number of places required for the move.
5,435,778 0
543577.8 1
54357.78 2
5435.778 3
543.5778 4
54.35778 5
5.435778 6
Each move reduces the number by a factor of 10. This means that the final move to make the number 5.435778 required dividing the original number by 10 a total of 6 times. By multiplying this last number by 10 a total of 6 times, we obtain the original number.
We could write this as: (5.435778)*(10)*(10)*(10)*(10)*(10)*(10)
but that defeats the purpose of scientific notation, which is to simplify the number so that it is 1) easier to read, 2) saves printers paper and ink, and 3) reduces transcription errors.
So scientific notation is the process of writing this as:
5.435778 x [tex]10^{6}[/tex]
Calculate 50% of 684 m.
Give your answer in metres (m).
Answer:
342 mStep-by-step explanation:
Calculate 50% of 684 m.
Give your answer in metres (m).
50% = 1/2
so
684 : 2 = 342 m
Step-by-step explanation:
50% of 684
50/100 × 684
342m ans
What is the length of line segment c d? round to the nearest tenth. 2.3 cm 4.0 cm 10.7 cm 18.6 cm
The value of CD is 10.7 cm , Option C is the right answer.
What is a Line Segment ?A line segment is a line of fixed measure.
From the figure , as Triangle ABC is a right angled triangle
sin 30 degree = (Perpendicular / Hypotenuse)
∠ B = 30° , AB= 10 cm
sin 30 = AC/10
AC = 5 cm.
To determine CD ,
In Triangle ADC ,
tan 25 = Perpendicular / Base
tan 25 = AC / CD
tan 25 = 5 / CD
CD = 5 / 0.4663
CD = 10.7 cm
Therefore the value of CD is 10.7 cm , Option C is the right answer.
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Answer: C
Step-by-step explanation: 10.7 cm
Which is a sum of cubes?
a3 + 18
a6 + 9
a9 + 16
a12 + 8
Answer:
a^12+8
Step-by-step explanation:
let's check all the expressions
1. a^3+18
here 18 is not a perfect cube.
2. a^6+9
here 9 is not a perfect cube.
3. a^9+16
here 16 is not a perfect cube.
4. a^16+8
here 8 is a perfect cube, thus we can write above expression by using laws of exponents as
(a^4)^3+2^3
Thus, is a sum of cubes.
a^12+8
Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
15x²
Name? [?]
Degree? [ ]
Answer:
monomial and degree is 2
Find the variance of the given
data rounded to the nearest
hundredth.
3, 4, 5, 7, 10, 12, 15
Σ (x - mean)²
n
0²
0²
=
=
[?]
Enter
Answer:
17.14
Step-by-step explanation:
You have the data values {3, 4, 5, 7, 10, 12, 15}
To find the mean, [tex]\frac{3+4+5+7+10+12+15}{7} =8[/tex], yay a whole number, my favorite.
Then, [tex](3-8)^2+(4-8)^2+(5-8)^2+(7-8)^2+(10-8)^2+(12-8)^2+(15-8)^2=120[/tex].
Since n=7, σ^2≈[tex]17.14[/tex]
Keiko+has+a+health+insurance+premium+of+$3298+annually. +if+her+employer+pays+90%+of+the+premium,+how+much+does+she+pay+annually?
Answer: $329.8
[tex]3298-(\frac{90}{100} *3298)\\= 3298 - 2968.2\\= 329.8[/tex]
The amount Keiko pays annually is $329.8
To answer the question, we need to know the amount Keiko pays annually
How to calculate how much Keiko pays annually.Since Keiko health insurance premium annually is $3298 and if his employer pays 90% of the premium, we want to know how much Keiko pays.
Since the employer pays 90% of the premium, the employer pays x = 90% of $3298
= 0.9 × 3298
= $2968.2
So, the amount Keiko pays annually is y = premium - amount employer pays, x
= $3298 - $2968.2
= $329.8
So, the amount Keiko pays annually is $329.8
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1. Michael Murphy is employed at Agilent Technologies. He has family medical coverage through the group medical plan that Agilent provides for its employees. The annual premium cost for Michael's family is $5,260. The company pays 70 percent of the cost. How much is deducted from his weekly paycheck for medical insurance? (Note: 52 weeks in a year)
$28.12
$29.74
$30.35
$32.66
None of these choices are correct.
2. Brenda Baker has a group health insurance policy from her job at a bank. Her annual premium is $3,500. The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. If Brenda had medical bills totaling $12,000, how much were her out-of-pocket medical costs, including her premiums?
$5,900
$6,300
$6,700
$6,900
None of these choices are correct.
Addition is one of the four fundamental mathematical operations. The correct option is E, None of these choices are correct.
What is Addition?Addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
1. The annual premium cost for Michael's family is $5,260. The company pays 70% of the cost. Therefore, the cost he needs to may is,
30% of $5,260
= 0.30 × $5260
= $1578
Since the premium is needed to be paid in 52 week, therefore, the premium cost per week will be,
Premium cost = $1578/52 = $30.35
Hence, the correct option is C, $30.35.
2. Brenda annual premium is $3,500. Also, her medical bills is totaling to $12,000. Therefore, the total amount that is paid by the Brenda in purchasing Insurance and paying the bill is,
Amount Brenda spend = $3,500 + $12,000 = $15,500
The policy has a $500 deductible and pays 80% of all medical costs with a stop-loss provision of a limit of $4,000 for out-of-pocket expenses, after the deductible is paid. Therefore, the amount that she can get is,
Amount she can get = $500 + $4,000 = $4,500
Now, the amount that she needs to pay from her pocket is,
Amount = $15,500 - $4, 500 = $11,000
Hence, the correct option is E, None of these choices are correct.
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Does this graph represent a function? Why or why not?
Brian invests £6600 into his bank
account.
He receives 0.6% per year compound
interest.
How much will Brian have after 6 years?
Give your answer to the nearest penny
where appropriate.
O
→ £ 1
Answer:
See Below
Step-by-step explanation:
The equation for this scenario would be ( compounded annually)
6600 ( 1 + .006)^6 = £ 6841.19
Answer:
Brian will have £6841.19 after 6 years.
Step-by-step explanation:
The compound interest formula is:
[tex]A = P( 1 +\frac{r}{100} )^{n}[/tex] ,
where A is the final amount, P is the initial (principal) amount invested (£6600), r is the interest rate (0.6%) and n is the number of years the money is kept for (6 years).
Using the formula:
[tex]A = 6600(1 + \frac{0.6}{100} )^{6}\\\\A = 6841.19[/tex]
