Answer:
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5\sqrt{10c^3} }{3d^3}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{\frac{250c^3}{9d^6}}[/tex]
Required
Simplify to the simplest form
We start by splitting the square root
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250c^3}}{\sqrt{9d^6}}[/tex]
Expand
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250 * c^3}}{\sqrt{9 * d^6}}[/tex]
Further Split the square root
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{\sqrt{9}*\sqrt{d^6}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*\sqrt{d^6}}[/tex]
From laws of indices;
[tex]\sqrt[n]{a^m} = a^{\frac{m}{n}}[/tex]
This implies that
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*{d^{\frac{6}{2}}}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{250} * \sqrt{c^3}}{3*{d^3}}[/tex]
Expand 250 to 25 * 10
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{25 * 10} * \sqrt{c^3}}{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{\sqrt{25}*\sqrt{10} * \sqrt{c^3}}{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5*\sqrt{10} * \sqrt{c^3}}{3*{d^3}}[/tex]
Combine the square roots
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5*\sqrt{10*c^3} }{3*{d^3}}[/tex]
[tex]\sqrt{\frac{250c^3}{9d^6}} = \frac{5\sqrt{10c^3} }{3d^3}[/tex]
Solved
Answer:
its a
Step-by-step explanation:
i just did it
Here is a sketch of a curve.
YA
The equation of the curve is y = x2 + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.
Answer:
The turning point of the graph is at (3,-16)
Step-by-step explanation:
The general equation of curve is given as:
y = x² + ax + b
The two point for which the equation satisfies is (0,-7) and (7,0).
Substitute (0,-7) in the general equation:
y = x² + ax + b
-7 = 0² + a(0) + b
b = -7
Substitute (7,0) in the general equation:
y = x² + ax + b
0 = 7² + 7a + b
Where b = -7
0 = 49 + 7a - 7
0 = 42 + 7a
a = -6
The equation of the curve is:
a = -6 and b = -7
y = x² + ax + b
y = x² - 6x - 7
Graph of the equation is attached below.
We can see that the the turning point of the graph is at (3,-16)
In ΔCDE, m∠C = (9x+11)^{\circ}(9x+11) ∘ , m∠D = (3x-15)^{\circ}(3x−15) ∘ , and m∠E = (2x+16)^{\circ}(2x+16) ∘ . What is the value of x?
Answer:
x = 12
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180, that is
9x + 11 + 3x - 15 + 2x + 16 = 180, simplify left side
14x + 12 = 180 ( subtract 12 from both sides )
14x = 168 ( divide both sides by 14 )
x = 12
The 8th grade sells popcorn after school.
The 2-cup container is $0.89, the 24-cup
container is $1.10, and the 32-cup
container is $1.75. Which is the best buy?
Answer:
I would say the 2-cup container is the best buy.
Step-by-step explanation:
Value for money and 2 cups are enough.
Someone please help
Answer:
A
Step-by-step explanation:
HOMEWORK HELP! WHY CAN'T ANYONE HELP ME? 1. In Michigan, the sales tax rate is 6%. Suppose that an item costs $50.88 including tax. How can we use algebra to find the price of the item before tax was added? What is the price before tax? Note: Using x = the price before tax, write an equation, and show solving steps to find x. (SOLVE AND CHECK) ($47.83 WON'T BE THE CORRECT ANSWER)
Answer: x + 6/100x = 50.88
Price before tax will be $48
Step-by-step explanation:
The equation will be
x + 6/100x = 50.88
x+0.06x = 50.88
1.06x = 50.88
x = 50.88 / 1.06 = 48
Solve the following system of equations. What is one x-value of a solution?
f(x) = x2 + 4x + 10 g(x) = -32x - 40
a. x = 5
b. x = -5
c. x = 6
d. x = 2
Answer:
There is some mistake in the question, because the solutions are x = -1.445 and x = -34.555
Step-by-step explanation:
Given the functions:
f(x) = x² + 4x + 10
g(x) = -32x - 40
we want to find the points at which f(x) = g(x).
x² + 4x + 10 = -32x - 40
x² + 4x + 10 + 32x + 40 = 0
x² + 36x + 50 = 0
Using quadratic formula:
[tex]x = \frac{-b \pm \sqrt{b^2-4(a)(c)}}{2(a)} [/tex]
[tex]x = \frac{-36 \pm \sqrt{36^2-4(1)(50)}}{2(1)} [/tex]
[tex]x = \frac{-36 \pm 33.11}{2} [/tex]
[tex]x_1 = \frac{-36 + 33.11}{2} [/tex]
[tex]x_1 = -1.445 [/tex]
[tex]x_2 = \frac{-36 - 33.11}{2} [/tex]
[tex]x_2 = -34.555[/tex]
What is the area of the shaded part of the circle that has a diameter of 8 mm? Use 3.14 for
4 mm
8 mm
O 16mm?
O 32mm?
O 34 24 mm
50.24 mm?
Answer: 34.27 sq. mm.
Step-by-step explanation:
Area of a triangle = hb / 2
= 8 x 4 / 2
= 32 / 2 = 16 mm
Area of the circle = πr^2
= π x 4^2
= 50 27 sq. mm.
Area of the shaded part
= 50.27 - 16
= 34.27 sq. mm
Answer: the answer is c, 34.24 mm
Step-by-step explanation: I just did the test
Find the value of the expression 8x↑3 if: x=3
Answer:
216
Step-by-step explanation:
8x³
Put x as 3 in the expression.
8(3)³
Solve the power.
8(27)
Multiply.
= 216
What is the value of the function y = 2x + 3 when x = -1?
5
2
1
-5
Answer:
1
Step-by-step explanation:
y = 2(-1)+3
y= -2+3
y= 1
3x + 2 = x + 4(x+2) I really need help
Answer:
x=-3
Step-by-step explanation:
3x+2=x+4x+8
3x+2=5x+8
-2x+2=8
-2x=6
x=-3
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
[tex]3x + 2 = x + 4(x+2)[/tex]
Expand the brackets.
[tex]3x + 2 = x + 4x+8[/tex]
[tex]3x + 2 = 5x+8[/tex]
Subtract [tex]-5x[/tex] and [tex]-2[/tex] from both sides of the equation.
[tex]3x-5x=8-2[/tex]
[tex]-2x=6[/tex]
[tex]\frac{-2x}{-2}=\frac{6}{-2}[/tex]
Divide [tex]-2[/tex] on both sides of the equation.
[tex]x=-3[/tex]
Find the slope of the line that passes through (72, 60) and (73, -5).
Answer:
-65
Step-by-step explanation:
We can use the slope formula
m= (y2-y1)/(x2-x1)
= (-5-60)/(73-72)
= -65/1
= -65
Answer:
The slope of the line that passes through (72, 60) and (73, -5) is -65.
Step-by-step explanation:
The formula for finding the slope of a line is (y₂₋y₁) / (x₂-x₁).
Substitute the points into the formula and solve.
(-5 - 60) / (73 - 72) =
(-65) / (1) = -65
The slope of the line is -65.
What is the slope of the line shown?
Answer:
1/2
Step-by-step explanation:
Pick two points on the line
(2,0) and (4,1)
Use the slope formula
m= (y2-y1)/(x2-x1)
= (1-0)/(4-2)
= 1/2
Please help Summer homework C:
Answer:
x = 4
Step-by-step explanation:
multiply both sides by six to get rid of the fractions: -5 x = - 20
divide both sides by -5: x = 4
Pls help don’t know how to do this one
Answer:
150 m
Step-by-step explanation:
Since we have a dome inscribed in a rectangle, and are given the width of the rectangle, we can,
1. Find the diameter of the circle, which is also 150m
2. Find the length of the rectangle, which is 75m (the length of the rectangle is the same as the radius of the circle)
If we are to find the perimeter of the shaded region, we add the length and half the width of the rectangle. So,
75 + 75 = 150m
Which expression is equivalent to this expression? x(2x + 3) A) 2x2 + 3 B) 2x2 + 3x C) 2x2 - 3x Eliminate D) 3x + 3
Answer:
B
Step-by-step explanation:
x(2x + 3)
Expand the brackets.
x(2x)+x(3)
Multiply the terms.
2x² + 3x
The answer is 2x² + 3x.
Answer:
I believe it is B. 2x2 + 3x
Step-by-step explanation:
Because x will go into 2x like 2x^2 and if you multiply x * 3 which it would equal 3x. That's the best I can explain it.
Hope my answer has helped you and if not I am sorry.
Given that points A, B, and C are the midpoints of their respective sides, which of the following is true about the figure? ANSWERS: A) ZX || XY B) BC || AB C) 2BC = XY D) YZ = AC
Answer:
C) 2BC = XY
Step-by-step explanation:
A) ZX || XY
No, sides of the triangle, not same size
B) BC || AB
No, sides of triangle
C) 2BC = XY
Yes, as BC║XY and YA= AX
D) YZ = AC
No, YZ║AC but is twice a length
The graph of y=-3x+ 2 is:
Answer:
A
Step-by-step explanation:
This is a linear function whose slope is -3 and whose y-intercept is (0, 2). Answer A is correct.
Which best describes the range of the function f(x) = 2(3)*?
Answer:
y > 0 best describes the range of the function f(x) = 2(3)x.
A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
If b is any number such that and then an exponential function is a function in the form, where b is called the base and x can be any real number.
Please vote brainiest!
Instructions: Find the angle measures given the figure is a rhombus.
Answer:
Angle ABC =70
Step-by-step explanation:
Divide 140 by 2 and apply the rule of alternante interior angles
In the given rhombus the unknown measure of ∠ABC is 70 degrees.
A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other.
This means that the two interior opposite angles are equal to each other.
The opposite angle of ∠B is 140 degrees.
So the angle at ∠B is also 140 degrees because the opposite angles of rhombus are equal.
As we finding the half of angle ∠B.
Divide 140 degrees by 2.
∠ABC=140/2
=70 degrees.
Hence, the angle measure given in the figure is 70 degrees.
To learn more on Quadrilateral click here:
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1/3x+4=10
What is x?
Answer:
[tex]x = 18[/tex]
Step-by-step explanation:
[tex] \frac{1}{3} x + 4 = 10 \\ \frac{1x}{3} = 10 - 4 \\ 1x = 6 \times 3 \\ 1x = 18 \\ x = 18[/tex]
Each equation given below describes a parabola. Which statement best compares their graphs? X=2y^2 X=8y^2
A. Both parabolas open upward, and x=8y^2 is wider than x=2y^2.
B. Both parabolas open upwards, and x=2y^2 is wider than x=8y^2.
C. Both parabolas open to the right, and x=8y^2 is wider than x=2y^2.
D. Both parabolas open to the right, and x=2y^2 is wider than x=8y^2.
Answer:
D)Both parabolas open to the right, and [tex]x=2y^2[/tex] is wider than [tex]x=8y^2.[/tex]
Step-by-step explanation:
Standard equation of parabola :
[tex]y=a(x-h)^2+k.[/tex]
If a < 0, then the parabola open downwards and if a > 0, then the parabola open upwards.
[tex]x=a(y-k)^2+h[/tex]
If a < 0, then the parabola open left and if a > 0, then the parabola opens right
Given equations : [tex]X=2y^2[/tex] and [tex]X=8y^2[/tex]
[tex]x=2(y-0)^2[/tex] and [tex]x=8(y-0)^2[/tex]
in both the equations a>0
So, Both parabolas are open to the right.
Refer the attached graph
[tex]x=2y^2[/tex] ---- Red
[tex]x=8y^2[/tex] --- blue
So, [tex]x=2y^2[/tex] is wider than [tex]x=8y^2.[/tex]
So, Option D is true
Need some help Appreciate any help Take a look at the screenshot
Answer:
y = -1/2x+2
Step-by-step explanation:
Two points on the line are (0,2) and (4,0)
We can find the slope
m = (y2-y1)/(x2-x1)
= (0-2)/(4 -0)
= -2/4
- 1/2
We know the y intercept is 2 since it crosses the y axis at 2
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -1/2x+2
Answer:
See below.
Step-by-step explanation:
First, from the graph, we can already pick out two points: (0,2) and (4,0). Note that (0,2) is the y-intercept.
Therefore, we can use slope-intercept form or [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
We already know the b, so:
[tex]y=mx+2[/tex]
Now, we can plug in the ordered pair (4,0) to help us determine the slope (or you can just use the slope formula for the two ordered pairs):
[tex]0=m(4)+2[/tex]
[tex]-2=4m[/tex]
[tex]m=-1/2[/tex]
Thus, the entire equation is:
[tex]y=-\frac{1}{2} x+2[/tex]
help somebody please please im begging you due in 20 minutes
Answer:
a) -7
b) -13.5
c) no
d) (-∞, -27/2)
Step-by-step explanation:
a) substitute the variable into the equation and simplify
b)simplify both sides then isolate the variable
c) -7 is not greater than 0
d) isolate the variable by dividing each side by the factors that don't contain the variable
AX and EX are secant segments that intersect at point X. What is the length of DE?
Answer: 3 units
Step-by-step explanation:
6\8 + 9/32
Show answer
Answer: 1 1/32 or 33/32
Step-by-step explanation:
6 * 4 = 24
8 * 4 = 32
6/8 = 24/32
24/32 + 9/32 = 33/32
33/32 = 1 1/32
Answer:
1 1/32
Step-by-step explanation:
6/8 + 9/32
the common denominator is 32
6/8 *4/4 + 9/32
24/32 + 9/32
33/32
32/32 + 1 /32
1 1/32
Use △XYZ, in which ∠X is a right angle and tanY=815.
Answer:
8/17
Step-by-step explanation:
The correct and complete question is:
Use △XYZ, in which ∠X is a right angle and tanY=8/15. What is the ratio for sinY?
From definition:
tan(Y) = opposite/adjacent
From the graph and the question:
tan(Y) = XZ/XY = 8/15
Then:
XZ = 8 and XY = 15. Using pytaghorean theorem:
XZ² + XY² = YZ²
8² + 15² = YZ²
√289 = YZ
17 = YZ
From definition:
sin(Y) = opposite/hypotenuse
From the graph:
sin(Y) = XZ/YZ
sin(Y)= 8/17
Oscar and Kim have $22.00 each to spend at
both want to purchase a copy of the same book, which normally sells for $28.
enough to purchase the book, Oscar takes 30% of $28.50 and subtracts that
10% of the discounted selling price and adds it back to find the purchase am
price and then computes 110% of the reduced price. Is Oscar correct? Is Kim
purchase the book? Explain your answer using complete sentences, and show your work? Plssssssss
Answer:
21.95
Step-by-step explanation:
They are both correct.
By multiplying the original price of the book by 30%. Oscar is finding the amount of the discount. He then takes the discount off of the original price by subtraction. 28.50 * .30 = 8.55; 28.50-8.55 = 19.95; After he finds the new price he calculates the tax and adds it to the book price. 19.95 * .10 = 2.00 = $21.95
Instead of finding the amount of the discount, Kim found the amount she would have to pay after the 30% was subtracted from the 100%. This left 70% that had to be paid. 28.50 * .70 = 19.95; Then Kim knew that she had to pay this entire amount which was 100% plus another 10% for tax which is 110% so 19.95 * 1.10 = $ 21.95
Both Oscar and Kim got the same amount and they both had enough money to buy the book
khan Academy sucks help plz
Answer:
14
Step-by-step explanation:
sqrt(49*t)
Let t = 4
We know sqrt(ab) = sqrt(a) sqrt(b)
sqrt(49) sqrt(4)
7 * 2
14
Answer:
Step-by-step explanation:
[tex]\sqrt{49*4}\\\sqrt{196}\\=14[/tex]
Which segment is the perpendicular bisector of XY¯¯¯¯¯¯¯¯? options : CD, FH, DH, FG
Answer:
CD
Step-by-step explanation:
CD is perpendicular to XY and also cuts XY into two equal halves.
FH is not perpendicular to XY even though it cuts XY into two equal halves.
DH is not a line.
FG is perpendicular to XY but it does not cut XY into equal halves.
CD segment is the perpendicular bisector of XY¯.
The perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to the segment. It intersects the segment at its midpoint and divides the segment into two segments with equal lengths.
Of the given options, only CD intersects XY at its midpoint and divides the segment into two segments with equal lengths. Therefore, CD is the perpendicular bisector of XY.
The other options do not intersect XY at its midpoint or do not divide the segment into two segments with equal lengths. For example, FH intersects XY at point H, but point H is not the midpoint of XY. Additionally, the segments HF and FH do not have equal lengths.
Therefore, the answer is CD.
Learn more about perpendicular bisector here: brainly.com/question/29132624
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Rewrite in radical form PLEASE HELP
Answer:
b)7c∛d⁵
or
c) 7c∛d⁵
Both options are the same
Step-by-step explanation:
In the above diagram, we are asked to simplify this:
= ∜c × 2d⁴/³ ×1/2c¾ ×7∛d
Collect the like terms
= ∜c × 1/2c³/⁴ × 2d⁴/³ × 7∛d
= c¹/⁴ × 1/2c³/⁴ × 2d⁴/³ × 7d¹/³
= [1 × 1/2c(¹/⁴ + ³/⁴)] × [2 × 7d(⁴/³ +¹/³)
= 1/2c(¹) × 14d(⁵/³)
= 1/2c× 14d(⁵/³)
Collect the whole number together
= 1/2× 14 [C × d(⁵/³)]
= 7cd⁵/³
Writing it in a radical form
= 7c∛d⁵
