Q) 14.5% of 153 = ?
→ 14.5% of 153
→ 14.5/100 × 153
→ 22.185
So, 22.185 is answer.
What is the equation of a line that passes through the point (1,8) and is perpendicular to the line whose equation is y=x/2+3?
Answer:
m=1/2
y-8=1/2(x-1)
y-8=1/2x-1/2
multiply through by 2
2y-16=x-1
2y-16+1-x=0
2y-15-x=0
2y-x-15=0
A rectangle with the dimensions of 2 feet
by 8 feet is similar to a rectangle with the
dimensions of
А 4 feet by 16 feet
B. 6 feet by 12 feet
C 12 feet by 32 feet
D 22 feet by 28 feet
Given rectangle: 2 feet by 8 feet. Similar rectangle: Option A (4 feet by 16 feet).
Use the concept of the rectangle defined as:
Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.
Given that,
Rectangle dimensions: 2 feet by 8 feet
And here are the options provided:
A) 4 feet by 16 feet
B) 6 feet by 12 feet
C) 12 feet by 32 feet
D) 22 feet by 28 feet
To determine if two rectangles are similar,
Compare their corresponding side lengths.
In this case,
A rectangle with dimensions 2 feet by 8 feet.
After simplifying it we can write 1:4
Let's check each option to see if it matches the similarity:
A) 4 feet by 16 feet:
The ratio of the corresponding side lengths is 2:8, which simplifies to 1:4. However, the given rectangle has side lengths of 4:16,
Which simplifies to 1:4 as well.
So, option A is similar to the given rectangle.
B) 6 feet by 12 feet:
The given rectangle has side lengths of 6:12,
Which simplifies to 1:2.
So, option B is not similar to the given rectangle.
C) 12 feet by 32 feet:
The given rectangle has side lengths of 12:32,
Which simplifies to 3:8.
So, option C is not similar to the given rectangle.
D) 22 feet by 28 feet:
The given rectangle has side lengths of 22:28,
Which simplifies to 11:14.
So, option D is not similar to the given rectangle.
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You need to build a box from an 8 inchby 10 inch piece of cardboard. To do this, you cut out squares of length x from the four corners of the box in order to fold the sides up. Verify that the volume of the box is given by the equation:
V= 4x^3â36x^2+ 80x
Answer:
Step-by-step explanation:
From the attached image below, let assume we have a square of diameter x by x which is to be cut from each corner of the cardboard sheet.
Thus, from the diagram
the length = 8 - 2x the width = 10 - 2x and the height = x
So, the volume V = L*w*h
Volume (V) = (8 - 2x) (10 - 2x) x
V = (80 - 16x - 20x +4x²)x
V = 80x -36x² + 4x³
By rearrangement:
V = 4x³ - 36x² + 80x
∫[tex]\frac{x+2019}{x^{2}+9 }[/tex]
Split up the integral:
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \int\frac{x}{x^2+9}\,\mathrm dx + \int\frac{2019}{x^2+9}\,\mathrm dx[/tex]
For the first integral, substitute y = x ² + 9 and dy = 2x dx. For the second integral, take x = 3 tan(z) and dx = 3 sec²(z) dz. Then you get
[tex]\displaystyle \int\frac x{x^2+9}\,\mathrm dx = \frac12\int{2x}{x^2+9}\,\mathrm dx \\\\ = \frac12\int\frac{\mathrm du}u \\\\ = \frac12\ln|u| + C \\\\ =\frac12\ln\left(x^2+9\right)[/tex]
and
[tex]\displaystyle \int\frac{2019}{x^2+9}\,\mathrm dx = 2019\int\frac{3\sec^2(z)}{(3\tan(z))^2+9}\,\mathrm dz \\\\ = 2019\int\frac{3\sec^2(z)}{9\tan^2(z)+9}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = 673\int\frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = 673\int\mathrm dz \\\\ = 673z+C \\\\ = 673\arctan\left(\frac x3\right)+C[/tex]
Then
[tex]\displaystyle\int\frac{x+2019}{x^2+9}\,\mathrm dx = \boxed{\frac12\ln\left(x^2+9\right) + 673\arctan\left(\frac x3\right) + C}[/tex]
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answer: [tex]\dfrac{11}{9}I[/tex]
Step-by-step explanation:
Given
There is [tex]l[/tex] liter of pure alcohol
Suppose [tex]x[/tex] liters of water is added
After addition of water, alcohol becomes 45% in concentration
[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]
Thus, [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.
Determine if f(x, y) = 10 − x^2 − y^2
is increasing or decreasing at (7, −3) if we
take y to be constant and let x vary. Also determine if f(x, y) is increasing at
(7, −3) if we take x to be constant and let y vary.
Answer:
Step-by-step explanation:
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. x is treat any other variable as a constant.
dz/dx=0-2x-0
dz/dx=-2x
Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.
Since this result is negative, it mrans as x increases z decreases.
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. y is treat any other variable as a constant.
dz/dx=0-0-2y
dz/dx=-2y
Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.
Since this result is positive it mrans as y increases z decreases.
find the solution of the general equation of the differential equation:
(1-cosx)y' - ysinx =0, x ≠ k2π
Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:
(1 - cos(x)) y' - y sin(x) = 0
==> (1 - cos(x)) y' = y sin(x)
==> y'/y = sin(x)/(1 - cos(x))
==> dy/y = sin(x)/(1 - cos(x)) dx
Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.
∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx
∫ dy/y = ∫ du/u
ln|y| = ln|u| + C
exp(ln|y|) = exp(ln|u| + C )
exp(ln|y|) = exp(ln|u|) exp(C )
y = Cu
y = C (1 - cos(x))
Use the vertex
(h, k)
and a point on the graph
(x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−4, −1), (x, y) = (−7, 8)
Answer:
Step-by-step explanation:
Let the quadratic function be
y=a(x+4)²-1
∵(-7,8) lies on it.
8=a(-7+4)²-1
8+1=a(-3)²
9a=9
a=9/9=1
so quadratic function is
f(x)=1(x+4)²-1
or
f(x)=x²+8x+16-1
so quadratic function is
f(x)=x²+8x+15
Find the missing side lengths.
Answer:
x is 18, and y is 9 √ 3
Step-by-step explanation:
Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.
The relationship is listed below:
The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3
So x is 18, and y is 9√3
Find the measure of the missing angles.
Answer:
Step-by-step explanation:
Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
find the surface area of the triangular prism below.
Step-by-step explanation:
At first you need to take its lateral surface area by using the perimeter of base of the triangle and the height of prism.
Then after calculating it you need to find out its total surface area which is asked in the question and that is calculated by adding the area of both triangles of the prism in the lateral surface area.
Then that's your answer.
9514 1404 393
Answer:
544 square units
Step-by-step explanation:
The surface area is the sum of the area of the two triangular bases and the three rectangular faces. The relevant area formulas are ...
A = 1/2bh . . . . area of a triangle with base b and height h
A = LW . . . . . are of a rectangle of length L and width W
__
SA = 2(1/2)(12)(8) + (10 +10 +12)(14)
SA = 96 +448 = 544 . . . square units
We have that 2a+1=1 and b-a=1. What is the value of b?
Answer:
b=1
Step-by-step explanation:
2a+1 =1
Subtract 1 from each side
2a+1-1 = 1-1
2a=0
a=0
Now find b from the second equation
b-a =1
b-0=1
b=1
Answer:
Equation: 2a+1=1
Subtract 1 from both sides: 2a=0
Divide by 2: a=0
Equation: b-a=1
Substitute: b-0=1
Combine: b=1
So, b=1.
Let me know if this helps.
A poll of 2,060 randomly selected adults showed that 89% of them own cell phones. The technology display below results from a test of the claim that 91% of adults own cell phones. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.01 significance level to complete parts (a) through (e).
Test of p=0.91 vs p≠0.91
Sample X N Sample p 95% CI Z-Value p-Value
1 1833
2,060 0.889806 ( 0.872035 , 0.907577 ) ~ 3.20 0.001
a. Is the test two-tailed, left-tailed, or right-tailed?∙
Left-tailed test∙
Two-tailed test∙
Right tailed test
b. What is the test statistic?
The test statistic is _____ (Round to two decimal places as needed.)
c. What is the P-value?
The P-value is _____ (Round to three decimal places as needed.)
d. What is the null hypothesis and what do you conclude about it?
Identify the null hypothesis.
A. H0:p<0.91∙
B. H0:p≠0.91∙
C. H0:p>0.91∙
D. H0:p=0.91.
Answer:
Two tailed test
Test statistic = 3.20
Pvalue = 0.001
H1 : p ≠ 0.91
Step-by-step explanation:
Given :
Test of p=0.91 vs p≠0.91
The use if not equal to ≠ sign in the null means we have a tow tailed test, which means a difference exists in the proportion which could be lesser or greater than the stated population proportion.
The test statistic :
This is the Z value from the table given = 3.20
The Pvalue = 0.001
Since Pvalue < α ;Reject H0
pLEASE help best and right answer gets brainliest
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
CAN SOMEBODY HELP WITH THIS QUESTION ASAP
Answer:
The rectangles are not similar
Step-by-step explanation:
In order to check whether they are similar, we need to take the ratio of their similar sides and ensure they are equal to a constant k.
Hence;
AB/PL = AD/LM = k
32/26 = 18/12 = k
16/13 = 9/6 = k
Since the scale factor is not the same, hence the rectangles are not the same.
Help with this Area question
Step 1: Find the area of the rectangle
A = base x height
A = 39 x 20
A = 780
Step 2: Find the area of the semi-circles
---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.
A = pi x r^2
A = pi x 10^2
A = 100pi = 314
Step 3: Find the area of the figure
Area = area of the rectangle - area of the semi-circles
A = 780 - 314
A = 466 cm^2
Hope this helps!
Answer:
466 cm^2
Step-by-step explanation:
This one is done basically the same as the other.
Rectangle = 20 x 39
Circle = (3.14) x 10^2
Rectangle = 780
Circle = 314
rectangle - circle
780 - 314 = 466
Use the order of operations to simplify the following expression.
-2 3 + |7| - 4 · 2
-38
-23
-9
-10
Answer:
-9
Step-by-step explanation:
-2 3 + |7| - 4 · 2
I assume -2 3 means -2^3.
-2^3 + |7| - 4 · 2 =
= -8 + 7 - 8
= -1 - 8
= -9
Answer:
-9
Step-by-step explanation:
-2^ 3 + |7| - 4 · 2
Parentheses first and an absolute value is considered parentheses
-2 ^3 + 7 - 4 · 2
Then exponenets
Since the sign is outside of the exponent it is considered multiplication
-1 * (2^3)+ 7 - 4 · 2
-1 *8 + 7 - 4 · 2
Then multiply
-8 +7 -8
Then add and subtract from left to right
-1-8
-9
How many of each coin does he have?
_____nickels
_____quarters
Three jackets cost as much as five shirts. Each jacket costs $16 more
than each shiri. What is the cost of one shirt?
Answer:
$3.20
Step-by-step explanation:
Divide the number 16 (as in the cost per Jacket) by 5. (The amount of shirts you could buy with $16)
Then once you have divided 16 by 5, your answer should be 3.2, so the cost of one shirt is $3.20
What's the dependent variable shown in the table?
A)
The amount of water given to the plant
B)
The color of the flowers
C)
The number of flowers on the plant
D)
The speed at which the plant grows
Answer:
The number of flowers on the plant
Step-by-step explanation:
Answer:
C: Number of flowers on the plant
Step-by-step explanation:
i got it right on my test
Find f such that f'(x) = 8x – 3. f(4) = 0
Answer: y=29 / (4,29)
Step-by-step explanation:
By graphing [tex]f(x)=8x-3[/tex] and [tex]f(4)=0[/tex] on Desmos. You'll be able to find that when x is 4, y is 29.
Similarly, you can plugin 4 into the original equation ([tex]f(x)=8x-3[/tex]) Which looks like:
[tex]8(4)-3\\32-3=29[/tex]
Additionally, you can change [tex]f(x)=[/tex] to [tex]y=[/tex] as it is the exact same thing. With that in mind, you can do the same with [tex]f(x)=0[/tex] and just change it to x=4. As you're wanting to know what the y-value is when x=4.
Answer:
4x²-3x+c is our original equation
Step-by-step explanation:
we have an independent number I called this number c
put 4 from x and try to find c
f(4)=4*(4²)-3*(4)+c=0
we have to be careful about f(4) is 0
64-12+c=0 and c is -52 so our original equation is 4x²-3x-52
Please help! Question and answers are in the pic
So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.
22 hours x $8.50 = $187
Subtract that from the cost of the computer:
899-187 = $712
She needs $712 more.
Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75
Divide what she needs by amount per shift:
712 / 46.75 = 15.22 shifts
She needs to work 16 more shifts.
how far from "0 is the green rectangle
Option 4
3-1/2"
Must click thanks and mark brainliest
Answer:
3 1/2
Step-by-step explanation:
That’s the distance from 0 to the green rectangle
I NEED HELP PLEASE !!!
Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].
Coronado reported the following information for the current year: Sales (44000 units) $880000, direct materials and direct labor $440000, other variable costs $44000, and fixed costs $360000. What is Coronado’s break-even point in units?
a) 32727.
b) 40000.
c) 60923.
d) 36000.
Judy got 27 546 points and 34 668 points in the first two rounds of a
game. How many points did Judy get in all?
Answer:
62 214Step-by-step explanation:
Given,
Points got by Judy in 1st round = 27 546
Points got by Judy in 2nd round = 34 668
Therefore,
Total points Judy got in the first two rounds
= 27 546 + 34 668
= 62 214 (Ans)
A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?
If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.
But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.
That number is 7396 which when square rooted gives 86 soliders on the side.
Subtract 7396 from 7500 and get how many soliders were left out,
[tex]7500-7396=\boxed{104}[/tex]
Hope this helps :)
Line JK passes through points J(–3, 11) and K(1, –3). What is the equation of line JK in standard form?
7x + 2y = –1
7x + 2y = 1
14x + 4y = –1
14x + 4y = 1
9514 1404 393
Answer:
(b) 7x + 2y = 1
Step-by-step explanation:
You don't need to know how to find the equation. You just need to know how to determine if a point satisfies the equation. Try one of the points and see which equation fits. (The numbers are smaller for point K, so we prefer to use that one.)
7(1) +2(-3) = 1 ≠ -1 . . . . . tells you choice A doesn't work, and choice B does
The equation is ...
7x +2y = 1
__
Additional comment
The equations of choices C and D have coefficients with a common factor of 2. If the constant also had a factor of 2, we could say these equations are not in standard form, and we could reject them right away. Since the two points have integer values for x and y, we can reject these equations anyway: the sum of even numbers cannot be odd.
Answer:
b
Step-by-step explanation:
I need help answering this ASAP
Answer:
"D"
if you multiply by Conjugate
the denominator would end up A^2 - b^2
the answer has 25 - 10x
that is D
Step-by-step explanation: