Answers
Answer:
[tex]a. \ \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]b. \ \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Step-by-step explanation:
The question relates with rules of indices
(a) The give expression is presented as follows;
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}[/tex]
By expanding the expression, we get;
[tex]\dfrac{m^3 \times n^{-8} \times 5^4 \times m^4}{\left 3^3 \times m^6 \times n^3}[/tex]
Collecting like terms gives;
[tex]\dfrac{m^{(3 + 4 - 6)} \times 5^4}{ 3^3 \times n^{3 + 8}} = \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
[tex]\dfrac{m^3 \times \left (n^{-2} \right )^4 \times (5 \cdot m)^4}{\left (3 \cdot m^2 \cdot n \right )^3}= \dfrac{625 \cdot m}{27 \cdot n^{11}}[/tex]
(b) The given expression is presented as follows;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \div (x \cdot y^n)^4[/tex]
Therefore, we get;
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n}[/tex]
Collecting like terms gives;
[tex]x^{3 \cdot m + 2 - 4} \times \left (y^{3 \cdot n - 3 -4 \cdot n}} \right ) = x^{3 \cdot m - 2} \times \left (y^{ - 3 -n}} \right ) = x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right )[/tex]
[tex]x^{3 \cdot m - 2} \div \left (y^{ 3 + n}} \right ) = \dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
[tex]x^{3 \cdot m + 2} \times \left (y^{n - 1} \right )^3 \times x^{-4} \times y^{-4 \cdot n} =\dfrac{x^{3 \cdot m - 2}}{y^{ 3 + n}}[/tex]
Related Questions
Find the circumference and the area of a circle with diameter equal to 8.6 inches. Use 3.14 for pi
Please answer it will mean a lot thanks
Answers
Answer: Circumference of circle = 27.004 inches
Area of circle = 58.0586 inches²
Step-by-step explanation:
Diameter of circle = 8.6 inches
Pi ([tex]\pi[/tex]) = 3.14
Circumference of circle (With diameter) = [tex]\pi \\[/tex]d ([tex]\pi[/tex]×diameter)
= 3.14 × 8.6
= 27.004 inches
Area of circle (With diameter) = [tex]\pi[/tex][tex]d^{2}[/tex]/4
= 3.14 × 8.6 × 8.6 / 4
= 3.14 × 73.96 / 4
= 58.0586 inches²
Convert 75 mg into gram
Answers
Answer:
[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]
please help me i will give 20 points for this question
Answers
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?
Answers
The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.
Answer:
Step-by-step explanation:
Given :
45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44
Using technology, the box and whisker plot generated for the data is attached below.
The 5 - number summary is also given below :
Minimum: 39
Median: 45
First quartile: 42
Third quartile: 47
Interquartile Range: 5
Maximum: 49
Outliers: none
Answer:
Step-by-step explanation:
Help solve for the area
Answers
Answer:
B
Step-by-step explanation:
half × base × height
height × length
Answer: B
Step-by-step explanation:
Triangle)
25 - 7 = 18
[tex]A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2[/tex]
Rectangle)
[tex]A=b(h)\\A=7(17) = 119cm^2[/tex]
Total)
[tex]153+119=272 cm^2[/tex]
What is an
equation of the line that passes through the points (-3,-1) and (-4,-4)
Answers
Answer:
y= 3x+8
Step-by-step explanation:
not a 100% sure...
sry if its wrong
(try using Math-way, its rly helpful)
Answer:
Step-by-step explanation:
y=mx+b
To find slope: -4+1/-4+3
Slope=3
y=3x+b
Plug in either points ,as an example, i'll plug in (-3,-1)
-1=3(-3)+b
-1=-9+b
8=b
Finished formula: y=3x+8
Which graph represents the function f(x)=|x−1|−3 ?
Answers
Please Help
Select the correct answer.
What is the slope of a line parallel to line r?
A. A line parallel to line r has an undefined slope.
B. 0
C. -1
D. 1
Answers
Answer:
B 0
Step-by-step explanation:
r is a horizontal line
horizontal lines are of the form y= constant
The slope for horizontal lines are 0
Parallel lines have the same slope.
Answer:
B 0
Step-by-step explanation:
the slope of a line is the rise divided by the run, or the Y increase divided by the X increase. the fact that the Y value does not increase makes the slope 0
find the value of x. give reasons to justify your answer NEED HELP ASAP!!!!
Answers
Answer:
[tex]x = 34^\circ[/tex]
Step-by-step explanation:
Note that ∠TSU and ∠PSR are vertical angles. Hence:
[tex]m\angle TSU = m\angle PSR[/tex]
∠PSR is the sum of ∠PSQ and ∠QSR. Hence:
[tex]\displaystyle m\angle TSU = m\angle PSQ + m\angle QSR[/tex]
We know that ∠TSU measures 4x and ∠QSR measures 3x. Thus:
[tex](4x) = m\angle PSQ + (3x)[/tex]
Solve for ∠PSQ:
[tex]m\angle PSQ = x[/tex]
Next, ∠PQS and ∠RQS form a linear pair. Thus:
[tex]m\angle PQS + m\angle RQS = 180^\circ[/tex]
∠RQS measures 68°. Thus:
[tex]m\angle PQS +(68^\circ) = 180^\circ[/tex]
Solve for ∠PQS:
[tex]m\angle PQS = 112^\circ[/tex]
The interior angles of a triangle must total 180°. So, for ΔPQS:
[tex]\displaystyle m\angle SPQ + m\angle PQS + m\angle PSQ = 180^\circ[/tex]
Substitute in the known values:
[tex](x) + (112^\circ) + (x) = 180^\circ[/tex]
Simplify:
[tex]2x = 68^\circ[/tex]
And divide. Hence:
[tex]x = 34^\circ[/tex]
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answers
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
URGENT ! HELP ME I WILL MARK YOU BRAINLIEST !!!!
pleasee fasterrr !!!!
Answers
Answer:
3b (3a - 4b)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
9ab - 12b² ← factor out 3b from each term
= 3b(3a - 4b) → C
Jo bought a used car for $6000 and paid a 15% deposit. How much did he still have to pay?
Answers
Answer:
900 is the correct awnser
one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2
Answers
Step-by-step explanation:
what to find then??.........
The ratio of girls to boys in grade 6 was 3:2 at Lincoln middle school last year. There were 60 kids in grade 6. How many in grade 6 were girls
Answers
Answer:
40 girls 20 boys i think / guess
Step-by-step explanation:
Answer:
20/40
Step-by-step explanation:
i hope it help
Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST
Answers
Answer:
4x+y=-32
Step-by-step explanation:
given,
slope (m) = -4
point: (-8,0)
as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]
so,
b = 0-(-4)×(-8) = -32
y=mx+b
or, y=-4x-32
or, 4x+y=-32
(this is the standard form of the line)
Using the equation y - y1 = m(x - x1)
y - 0 = -4(x - (-8))
y = -4(x + 8)
y = -4x - 32
pls help me with this question and reply answer
Answers
Step-by-step explanation:
From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.
Write an equation of the line that is parallel to the given line and passes through the given point.
9. y= -2x+6 (0,-4)
10. -2x+3y=12 (3,2)
pls help me!!!!!
Answers
Answer:
9.) y=-2x-4
10.)y=2/3x
Step-by-step explanation:
Parallel lines have the same slope, different intercepts
9.) The slope is -2x
To find the parallel line
y-(-4)=-2(x-0)
y+4=-2x
y-4=-2x-4
y=-2x-4
10.) You must first put the equation in slope-intercept form.
-2x+2x+3y=2x+12
3y=2x+12
Divide by 3
3y/3=2x/3+12/3
Simplify
y=2/3x+4
Slope = 2/3x
y-2=2/3(x-3)
y-2=2/3x-6/3
y-2=2/3x-2
y-2+2=2/3x-2+2
y=2/3x
3. If triangle ABC has the following measurements, find the measure of angle A.
a = 17
b = 21
C = 25
Answers
9514 1404 393
Answer:
(a) 42.3°
Step-by-step explanation:
Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050
A = arccos(777/1050) ≈ 42.3°
The measure of angle A is about 42.3°.
_____
Additional comment
The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.
Answer:
(a) 42.3°
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth. 5 10
Answers
Answer:
[tex]\boxed {\boxed {\sf 8.7}}[/tex]
Step-by-step explanation:
We are asked to find the length of the third side in a triangle, given the other 2 sides.
Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.
[tex]a^2 + b^2 =c^2[/tex]
In this theorem, a and b are the legs of the triangle and c is the hypotenuse.
We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.
b= 5 c= 10Substitute the values into the formula.
[tex]a^2 + (5)^2 = (10)^2[/tex]
Solve the exponents.
(5)²= 5*5 = 25 (10)²= 10*10= 100[tex]a^2 + 25=100[/tex]
We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.
[tex]a^2 +25-25=100-25[/tex]
[tex]a^2=100-25[/tex]
[tex]a^2 = 75[/tex]
a is being squared. The inverse of a square is the square root, so we take the square root of both sides.
[tex]\sqrt {a^2}= \sqrt{75}[/tex]
[tex]a= \sqrt{75}[/tex]
[tex]a= 8.660254038[/tex]
Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 up to a 7 in the tenth place.
[tex]a \approx 8.7[/tex]
The length of the third side is approximately 8.7
Using Pythagorean theorem
[tex]\boxed{\sf B^2=H^2-P^2}[/tex]
Putting values[tex]\\ \sf \longmapsto B^2=10^2-5^2[/tex]
[tex]\\ \sf \longmapsto B^2=100-25[/tex]
[tex]\\ \sf \longmapsto B^2=75[/tex]
[tex]\\ \sf \longmapsto B=\sqrt{75}[/tex]
[tex]\\ \sf \longmapsto B=\sqrt{25\times 3}[/tex]
[tex]\\ \sf \longmapsto B=5\sqrt{3}[/tex]
[tex]\\ \sf \longmapsto B=5\times 1.732[/tex]
[tex]\\ \sf \longmapsto B=8.66[/tex]
[tex]\\ \sf \longmapsto B\approx 8.7[/tex]
Please solve fast. It's really easy!
Answers
Answer:
j = 10.1
Step-by-step explanation:
The difference between 9.5 and 11.3 is
11.3 - 9.5 = 1.8
This is split into 3 divisions, that is
1.8 ÷ 3 = 0.6
Then
j = 9.5 + 0.6 = 10.1
Priya bought a football for £3.50.
She received £1.50 change.
How much money did she give the shop assistant?
£10.00
£4.00
£5.00
Which one £10.00, £4.00 or £5.00?
Answers
Answer:
$5.00
Step-by-step explanation:
$3.50+$1.50=$5.00
£5 - £1.50 = £3.50
find the shaded area ..
Answers
Answer:
39°
Step-by-step explanation:
The angle adjacent to 115° in the lower triangle = 180° - 115° = 65°
angle on circle in lower triangle
= 180° - (65 + 76)° ← angle sum in triangle
= 180° - 141° = 39°
Angles on the circle subtended from the same arc are congruent, then
shaded angle = 39°
[tex](a+b)^{2}[/tex]
Answers
Answer:
[tex] ({a + b})^{2} [/tex]
[tex](a + b)(a + b)[/tex]
[tex] {a}^{2} + 2ab + {b}^{2} [/tex]
hope this help you
Ms. Dawson’s call did a science experiment. The class started out with 650 bacteria cells. The growth rate predicted was 4.5%. Sketch the graph that represents the situation. Label the y-intercept and the point that represents the projected bacteria population 30 h from the start of the experiment. Round to the nearest whole number.
Answers
Answer:
your slope would be 4.5.... so go up 4 and to the right 5. the y-intercept is 650 so that is where your line would start instead of at 0... hope this helped :)
Step-by-step explanation:
The exponential function gotten from the table is given by y = 650(1.045)ˣ
Exponential functionAn exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multipliers.
Let y represent the bacteria population after x hours.
The class started out with 650 bacteria cells.
a = 650Growth rate = 4.5%
b = 100% + 4.5% = 104.5% = 1.045The exponential function gotten from the table is given by y = 650(1.045)ˣ
After 30 hours:
y = 650(1.045)³⁰ = 2434Find out more on exponential function at: https://brainly.com/question/12940982
What’s this topic called
Answers
Answer: MATH
Step-by-step explanation:
Answer:
answer for the question is
x = 1
y = 4
subject is math btw if you are asking about that
(f^3-5f+25)-(4f^2-12f+9)
Answers
Answer:
3−42+7+16
Step-by-step explanation:
if its simplify
State the slope of the line shown below (help ASAP)
Is it a, b, c or d?
Answers
Answer:
D
Step-by-step explanation:
(the above graph depicts a horizontal line that intersects the y axis at -2)
(so, y = -2)
Answer:
0
Step-by-step explanation:
Horizontal line x axis is 0 while the vertical y axis is undefined.
two triangles are similar what is x
Answers
Answer:
x = 10
Step-by-step explanation:
smaller triangle / bigger triangle = 20 / 28
hence,
3x / (4x+2) = 20/28
28(3x) = 20(4x+2)
84x = 80x + 40
4x = 40
x = 10
In the equation $\frac{1}{j} + \frac{1}{k} = \frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$?
Answers
Answer:
Hello,
answer 22
Step-by-step explanation:
[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]
The sum of all possible values for k is 22.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
1/j + 1/k= 1/3
Simplifying the fraction
(k+ j)/ kj= 1/3
3k + 3j = kj
k(3- j) = -3j
k = -3j/ (3- j)
k= 3j/ (j-3)
k = 3j + 9 - 9 / (j-3)
k = 3 + 9/ (j-3)
Since (j-3) must be divisor of 9.
j- 3 = 1---> j=4, k= 3 +9 = 12
j- 3 = 3---> j=6, k= 3 +9/3 = 6
j- 3 = 9---> j=12, k= 3 +9/9 = 4
So, The sum is = 12+ 6 + 4 = 22
Learn more about Fraction here:
https://brainly.com/question/10354322
#SPJ6
The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Answers
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
