Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.
What is the ground speed?The jet's speed, considering that there is a tailwind, is given by:
J = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 550 knots.Wind: 120 knots.Hence the jet's speed is given by:
J = 550 + 120 = 670 knots.
670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.
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To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? first equation: 4x − 3y = 34 second equation: 3x 2y = 17
To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.
To eliminate the y terms from the equations,
first equation: 4x - 3y = 34, and
second equation: 3x + 2y = 17,
we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).
That is, for :
the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.
the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.
Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
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What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring
to solve.
Answer:
x = ±√7, ±i√2
Step-by-step explanation:
[tex]x^4-5x^2-14=0\\(x^2-7)(x^2+2)=0\\[/tex]
[tex]x^2 - 7 = 0[/tex] or [tex]x^2 + 2 = 0\\[/tex]
x^2 - 7 = 0
x^2 = 7
x = ±√7
or x^2 + 2 = 0
x^2 = -2
x = ±i√2
How do I solve the following system of inequalities graphically on the set of axes below?
y> x-3 y≥− 6/1 x+4
if the exterior angles of a pentagon are x° 2x° (x+30)°,(x-10)° and (x+40)° find x
a) 30
b) 50
c) 60
d) 80
Answer:
[tex]\fbox {b) 50}[/tex]
Step-by-step explanation:
The sum of the exterior angles of any polygon (including a pentagon) is equal to 360 degrees.
Then :
⇒ x + 2x + x + 30 + x - 10 + x + 40 = 360
⇒ 6x + 60 = 360
⇒ 6x = 300
⇒ x = 50
Answer:
[tex]\huge\boxed{\sf x = 50}[/tex]
Step-by-step explanation:
Statement:The exterior angles of a pentagon add up 360 degrees.Given angles:x°2x°(x+30)°(x-10)°(x+40)°Solution:x + 2x + x + 30 + x - 10 + x + 40 = 360
6x + 60 = 360
Subtract 60 to both sides
6x = 360 - 60
6x = 300
Divide 6 to both sides
x = 300/6
x = 50
[tex]\rule[225]{225}{2}[/tex]
True or False? A circle could be circumscribed about the
quadrilateral below.
• A. True
• B. False
Answer:
False
Step-by-step explanation:
m∆A+m∆C=180°
110°+110°=180°
220°(/=) 180°
A circle can be circumscribed about the given quadrilateral, the answer is true.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral is true
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\frac { 6 ^ { n + 2 } - 6 ^ { n } } { 6 ^ { n + 1 } + 6 ^ { n } }
Solve this ...
this is the question of laws of indices(exponent)
Work Shown:
[tex]m = \frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}\\\\m = \frac{6^{n}*6^2-6^{n}}{6^{n}*6^1+6^{n}}\\\\m = \frac{6^{n}*36-6^{n}}{6^{n}*6+6^{n}}\\\\m = \frac{6^{n}(36-1)}{6^{n}(6+1)}\\\\m = \frac{6^{n}(35)}{6^{n}(7)}\\\\m = \frac{35}{7}\\\\m = 5\\\\[/tex]
Therefore,
[tex]\frac{6^{n+2}-6^{n}}{6^{n+1}+6^{n}}=5\\\\[/tex]
Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.
Answer:
Step-by-step explanation:
Equation of the line in slope- intercept form:[tex]\sf \boxed{\bf y = mx +b}[/tex]
Here, m is the slope and b is the y-intercept
Find the slope with the given two points.
[tex]\sf \boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{4-6}{8-5}\\\\=\dfrac{-2}{3}[/tex]
Slope = -2/3 and choose any one the given points.
Substitute m = -2/3 and (5,6) in the above equation and find 'b'
[tex]\sf 6 =\dfrac{-2}{3}*5+b\\\\6 =\dfrac{-10}{3}+b\\\\6+\dfrac{10}{3}=b\\\\\dfrac{6*3}{1*3}+\dfrac{10}{3}=b\\\\\dfrac{18}{3}+\dfrac{10}{3}=b\\\\\boxed{b=\dfrac{28}{3}}[/tex]
Equation of the line:
[tex]y = \dfrac{-2}{3}x + \dfrac{28}{3}[/tex]
The graph of f(x)=x2 is shown. Use the parabola tool to graph the function g(x)=(12x)2. To graph a parabola, first plot the vertex then plot another point on the parabola.
Answer:
Pease check my assumptions.
Step-by-step explanation:
I will assume that f(x)=x2 is actually f(x) = x^2.
Same for g(x)=(12x)^2 [Is it g(x)=12x^2 ???]
See the attached image.
Note that (12x)^2 results in a narrower, steeper graph. That's because (12x)^2 can be rewritten as 144x^2, so every value is multiplied by 144, compared to just x^2.
If * >0 and y > 0, which expression is equivalent to √768x1937?
A. 8r4y6/12r4y
B. 16r4y6√3x¹y
C. 8r9y18/12xy
D. 16r9y18√3xy
Which expression is equivalent to 3^0x3^-3?
Step-by-step explanation:
[tex] = {3}^{0} \times {3}^{ - 3} [/tex]
[tex] = 1 \times \frac{1}{ {3}^{3} } [/tex]
[tex] = \frac{1}{3 \times 3 \times 3} [/tex]
[tex] = \frac{1}{27} [/tex]
Ethan is using 30 cupcakes . he spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the reimagining cupcakes . the rest will get vanilla frosting. how many will have vanilla frosting
Answer:
12 Vanilla Frosted Cupcakes
Step-by-step explanation:
30 Cupcakes.
1/5 Of 30 is 6.
30 - 6 = 24.
24/2 = 12.
a tissue box has a lentgh of 11 inches a width of 5 inches and a height of 4 inches
I want to know the answer quick
Answer:
[tex]\fbox {B. Exponential Decay}[/tex]
Step-by-step explanation:
As the exponent is applied to a number less than 1, the future values of the function f(x) will become smaller and smaller. Hence, it represents exponential decay.
The radius is
cm.
The circumference in terms of is
✓ cm.
7
Using 3.14 for л, the approximate circumference of the
circle is
cm.
The circumference of this circle with a radius of 7 cm is equal to 44 cm.
Given the following data:
Radius of circular rug = 7 cm.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 7
Circumference = 43.96 ≈ 44 cm.
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find lim x->2 for f(x)=
{2x+1, x greater than or equal to 2
{x^2, x>2
a. 5
b. 4
c. 5 or 4
d. dne
LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)
What is the limit of a function ?The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.
It is given that
lim x->2 for f(x)
[tex]\lim_{x \rightarrow 2^-}f(x) = \lim_{x\rightarrow 2^+}f(x)[/tex]
f(x) = 2x+1 x ≤2
f(x)= x² , x >2
When both the function tends to 2
Left Hand Limit
f(x) = 2 *2 +1
f(x) = 5
Right Hand Limit
f(x) = x² ,
f(x) = 4
LHL in not equal to RHL , Therefore the limit does not exists.
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The volume of a cylinder with a height of 4 feet is 144n cubic feet what is the radius of the base of the cylinder V=nr2h
Answer: 6 ft
Step-by-step explanation:
[tex]144\pi =\pi(r^{2})(4)\\\\144\pi=4\pi r^{2}\\\\36=r^{2}\\\\r=\boxed{6 \text{ ft}}[/tex]
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards. Pete walks directly from point A to point C, without passing through point B. What is the direct distance from A to C?
How far would Pete walk if he went from A to B to C? yards
The direct distance from A to C is more than yards.
The inequality w < represents the distance, w, that Pete might save by taking the direct path.
The total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and point C is 25 yards.
Total distance if Pete walks from A to B to C:
= 15 + 25 = 40 yards
As we know in the triangle the sum of the two sides is greater than the third side.
25 + 15 > AC
40 > AC
or
AC < 40
The direct distance from A to C is more than 10(25-15) yards.
The inequality w < 30 represents the distance, w, that Pete might save by taking the direct path.
Thus, the total distance if Pete walks from A to B to C is 40 yards, the direct distance from A to C is more than 10 yards, and an inequality w < 30
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Answer:
40, 10, 30
see picture
Step-by-step explanation:
Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths. C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. Neither the reflection nor the dilation preserves the side lengths and angles of triangle .
Answer: B. The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths.
Step-by-step explanation:
Reflections are congruency transformations, but dilations are similarity transformations.
Prove: 45= m/ZXY
Complete the proof. Number your reasons in the textbox below.
Step-by-step explanation:
since the two angles from a straight line, they make a linear pair and linear pairs are supplementery. by the angle addition postulate, you can determine that the two angles sum to 180. substituting the one angle mearsure that you are guven and using a bit of simple arithmetic and the subtraction property of equality, you can determine that the other angle,angle YXZ, is 45 degrees. I hope this is helpful
whats 10 + 4? i need to know if you answer you get 25 points
On Thursday, the amount of snowfall was 1/8 cm. On Wednesday, the amount of snowfall was 4 1/4 cm. What was the amount of snowfall on the two days combined?
The total amount of snowfall on the two days combined is 4 3/8 cm
Addition of fractionsFrom the question, we are to determine the amount of snowfall on the two days combined
From the given information,
the amount of snowfall was 1/8 cm on Thursday
The amount of snowfall was 4 1/4 cm on Wednesday
Then,
The total amount of snowfall on the two days combined will be
[tex]\frac{1}{8}+4\frac{1}{4}[/tex] cm
= [tex]\frac{1}{8}+\frac{17}{4}[/tex]
= [tex]\frac{1+34}{8}[/tex]
= [tex]\frac{35}{8}[/tex]
= [tex]4\frac{3}{8} \ cm[/tex]
Hence, the total amount of snowfall on the two days combined is 4 3/8 cm
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The average time between accidents in a factory is 5 weeks.
Find the probability that more than 7 weeks pass between accidents.
Answer:
The probability that more than 7 weeks pass between accidents is 4.0551 .
Step-by-step explanation:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes
A Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period.
mean = 5 weeks
rate = 1/5 = 0.2
x = average time
P(x > 7) = e^(0.2×7) = 4.0551
The probability that more than 7 weeks pass between accidents is 4.0551 .
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The local public pool is a rectangle with two semicircles.
The area of the rectangle is
.
Using 3.14 for π and rounding to the nearest meter, the area of each half circle is
m2.
The area of the surface of the pool is
m2.
The area of the surface of the pool is 7322.64 m².
What is Area of rectangle?The area of rectangle is product of length and its breadth.
i.e., length * breadth
Given: Length = 100 m, Width = 52 m and Diameter = 52 m
Area of rectangle,
= 100 × 52
= 5200 m²
Now,
Area of semicircle = 1/2 × πr²
=1/2 × 3.14 × 26²
= 1061.32 m²
Hence, area of the surface of the pool is
= 1061.32 + 1061.32 + 5200
= 7322.64 m²
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5200 square meters, 1061, 7322
X Y
-2 6
0 3.5
2 1
4 -1.5
Which equations represent the data in the table?
Check all that apply.
y-6= =5 (x+2)
y-2=-(x-1)
y + 2 = S(x-6)
y-1=-(x-2)
y-3.5 = -1.25.x
Using the point-slope equation, the equations that represent the data are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
What is the Point-Slope Equation?Given a point (a, b) and slope (m), the point-slope equation is expressed as, y - b = m(x - a).
Find the slope (m) using two pairs from the table of values say, (-2, 6) and (2, 1):
Slope (m) = change in y / change in x = (6 - 1)/(-2 - 2) = 5/-4 = -1.25
Using the point, (a, b) = (-2, 6) and m = -1.25, plug the values into y - b = m(x - a):
y - 6 = -1.25(x - (-2))
y - 6 = -1.25(x + 2)
This cam be rewritten as:
y - 6 = -1.25x - 2.5
y - 6 + 2.5 = -1.25x
y -3.5 = -1.25x
The equations that represent the data in the table are:
y - 6 = -1.25(x + 2)
y -3.5 = -1.25x
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Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets cost $15 for adults and $10 for children under the age of 12.
(AKS 16) What does the solution to the system of equations represent in the context of the problem? Explain.
Answer:
See below
Step-by-step explanation:
The solution will show the NUMBER Of adult and the NUMBER of child tickets purchased .
a = adult tickets cost = 15 a
c = children's tickets <=== this is equal to 20 - a
cost for children's tickets equals 10(20 - a)
15 a + 10c = 225 rememeber c = 20 -a <===put that in
15 a + 10 ( 20 -a) = 225 solve for a
15a + 200 - 10 a = 225
5 a = 25
a = 5 tix then c = 20 - a = 15 tix
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y? y=5.5x; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=5.5x; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5. y=x+5.5; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 5. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5.
Answer:
This situation of the recipe can be represented as y=x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is the equation for this situation?
It is known the total amount of flour (y) is equivalent to the total amount of whole wheat flour (5.5) added to the total white flour (x). Therefore, the equation is:
y = x + 5.5
The possible values are
x = It is expected x is equalthan 0 or greater to it since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Step-by-step explanation:
This situation of the recipe can be represented as equation y = x+5.5 and it is expected that x is ≥ 0 and y is ≥ 5.5.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
For the given expression
y = x + 5.5
The possible values are
x = It is expected x is equal to 0 or greater to it
since the minimum amount of white flour that can be added is 0.
y = It is expected y is equal than 5.5 or greater to it since even if no
white flour is added the minimum total is 5.5.
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Question 3 of 32
Which of the following could be the equation for a parabola that opens to the
left with vertex (-17, 2)?
A. x=-3(y-2)² - 17
OB. x-3(y +17)² +2
OC. y-3(x-2)² - 17
D. y=3(x+17)² +2
Answer:
A
Step-by-step explanation:
The parabola opens to the left, so this eliminates C and D.
Also, the vertex is at (-17, 2), and out of A and B, the only parabola with this vertex is A.
Im in math 2 and I just need help with this to pass please
Answer:
.7 I your answer to your question hope it's help
Answer:
[tex]\frac{7}{10}[/tex]
Step-by-step explanation:
35/50 --> [tex]\frac{7}{10}[/tex]
divide 35 by 5 = 7
divide 50 by 5 = 10
A book seller a book for Rs 70 at a gain of 40 percent find the profit
Answer:
Rs 20
Step-by-step explanation:
140%=Rs 70
100%
(100%×Rs 70)÷140%=50
Rs 70-Rs 50=Rs 20
When 7/11 is written as a decimal, what is the sum of the first 20 digits after the decimal point? Pls Help
There's a neat trick to finding the rational form of a repeating decimal number. Take for instance [tex]x=0.123123123\ldots[/tex]. Then
[tex]x = 0.123123123\ldots \\\\ \implies 1000x = 123.123123\ldots \\\\ \implies 1000x - x = 123.123123\ldots - 0.123123\ldots \\\\ \implies 999x = 123 \\\\ \implies x = \dfrac{123}{999}[/tex]
It's easy to reverse this method to find the repeating decimal form of [tex]\frac7{11}[/tex]. Let
[tex]x = \dfrac7{11}[/tex]
Multiply the numerator and denominator by 9,
[tex]x = \dfrac{63}{99}[/tex]
It follows that
[tex]x = \dfrac{63}{99} \\\\ \implies 99x = 63 \\\\ 100x - x = 63.6363\ldots - 0.6363\ldots \\\\ \implies x = 0.636363\ldots[/tex]
The first 20 digits after the decimal are made up of 10 each of 3 and 6, so the sum is 10 × (3 + 6) = 90.
Answer:
90
Step-by-step explanation:
Using long division, we find that Every group of two digits after the decimal point has a sum of 9 so the sum of the first 20 digits after the decimal point is 10*9=90
