Step-by-step explanation:
5 = 5 × 1
9 = 3²
Common Multiple = 1 × 3² × 5 = 45
A Strong wind blows to the west at a speed of 38.7 mph relative to the ground causing a commercial plane to change course. What should be the plane's velocity in order to maintain a southward direction at a constant speed of 452 mph relative to the ground?
The speed of the plane is the rate of change of distance over time
The speed of the plane should be 453.65 mph southwest
The speed of the wind is given as:
[tex]\mathbf{S_w = 38.7mph}[/tex]
The expected speed of the plane is:
[tex]\mathbf{S_s = 452mph}[/tex]
So, the actual speed is calculated using the following Pythagoras theorem
[tex]\mathbf{S_{sw}^2 = S_w^2 + S_s^2}[/tex]
This gives
[tex]\mathbf{S_{sw}^2 = 38.7^2 + 452^2}[/tex]
[tex]\mathbf{S_{sw}^2 = 205801.69}[/tex]
Take square roots of both sides
[tex]\mathbf{S_{sw} = 453.65}[/tex]
Hence, the speed of the plane should be 453.65 mph southwest
Read more about speed at:
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The explicit formula for a sequence is f(n)
What is the value of f(3)?
19 + 6n
Answer:
f(3) = 37
Step-by-step explanation:
If the formula for this arithmetic sequence is f(n) = 19 + 6n, then the value of f(3) is 19 + 6(3), or f(3) = 37
EMERGENCY!! PLEASE HELP ME IMMEDIATLEY PLEASE!!!PLEASE HELP MEEEE!!!!
Answer:
y=1/2-2
Step-by-step explanation:
Solve 47 = -3 + 8y.
Answer:
Answer is y = 25/4
Geometry problem, Fill in the two blanks with the missing angle measures for the triangle shown.
Answer:
A)60°
B)140°
Step-by-step explanation:
Hope it can help you lovelots
#LEARN WITH BRAINLY
7⋅5+42−23÷47⋅5+42−23÷4
49
41
34
9
Answer:
112.765789 ect
Step-by-step explanation:
Solve the expression and find the value of x.
[tex] \frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2[/tex]
[tex]\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2[/tex]
[tex]\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2[/tex]
[tex]\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2[/tex]
[tex]\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2[/tex]
[tex]\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2[/tex]
[tex]\sf\longmapsto - 5x + 7 = 20[/tex]
[tex]\sf\longmapsto - 5x = 20 - 7[/tex]
[tex]\sf\longmapsto - 5x = 13[/tex]
[tex]\sf\therefore x = - \dfrac{13}{5} [/tex]
Hence, the value of x will be -13/5 respectively.
[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex]\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \\ [/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex]\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} [/tex]
Take a look at the denominators. The denominators are 10, 5 & 1. Their LCM is 10. So, multiply the fractions on both the sides of the equation by 10.
[tex]\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \\ \frac{x + 1}{10} \times \frac{1}{1} - \frac{3x - 3}{5} \times \frac{2}{2} = \frac{2}{1} \times \frac{10}{10} \\ \frac{x + 1}{10} - \frac{6x - 6}{10} = \frac{20}{10} [/tex]
Now cancel the denominators (as they have the same value) & take the numerators.
[tex]x + 1 - (6x - 6) = 20 \\ [/tex]
Now, simplify it.
[tex]x + 1 - (6x - 6) = 20 \\ x + 1 - 6x + 6 = 20 \\ x - 6x + 1 + 6 = 20 \\ - 5x + 7 = 20 \\ - 5x = 13 \\ x = -\frac{13}{5} \\ \boxed{ \boxed{ \bf x = - \frac{13}{5} =\: - 2 \frac{3}{5} = - 2.6}}[/tex]
__________________
Hope it'll help you!
ℓu¢αzz ッ
If Heath walks three miles in 30 minutes, how far can he walk in 45 minutes?
Identify whether the expression are equivalent or not. Write YES or NO and justify your answer
Answer:
no.
It is because 5*5=25
Proportions and Percents: solve using a proportion or an equation
Due to inflation, a used Mercedes has gone up 22% from its original price of 48,000 dollars. How much does the car cost now?
Answer:
$58,560
Step-by-step explanation:
First step: set up your proportion equation. Keeping the percents on the bottom, I set it up as $48,000/100% = $x/122%. I'm writing it as 122% rather than 22% so we don't have to add the increase in price to the original price later. You can see that, in order to get from 100 to 48,000, you need to multiply by 480, so you can do this to 122 to get x. Your teacher might, instead, want you to cross multiply. Do what's expected of you. Either way, your result should be $58,560. Check that it makes sense by checking that it's an increase and that it looks reasonable for the amount of the increase and you're done.
-(3x +2) + 2= -5
In simplest form.
Answer:
here is the answer x= 5/3
Step-by-step explanation:
What is the product of −314 and −112?enter your answer as a mixed number,.
Answer: 314 -(112)
-314 -(112)= -314 * -112
Step-by-step explanation:
if the sum of three consecutive intergers is 75, what is the greatest of the integers
Answer:
24,25,26
Step-by-step explanation:
Answer:
Step-by-step explanation:
25
6.
Which of the following describes the parabola with the equation y = 4x^2 − 12x + 9?
A. The axis of symmetry is x = 4 and the vertex is (4, −12).
B. The axis of symmetry is x = −1.5 and the vertex is (−1.5, 36).
C. The axis of symmetry is x = 0 and the vertex is (0, 9).
D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).
Answer:
D. The axis of symmetry is x = 1.5 and the vertex is (1.5, 0).
Step-by-step explanation:
y=4x^2-12x+9:\quad \mathrm{Parabola\:with\:vertex\:at}\:\left(h,\:k\right)=\left(\frac{3}{2},\:0\right),\:\mathrm{and\:focal\:length}\:|p|=\frac{1}{16}
To find the vertex of this parabola, "complete the square:" Rewrite y = 4x2 - 12x + 9 in the form y = 4(x - h)^2 + k:
y = 4x^2 - 12x + 9 => y = 4(x^2 - 3x) + 9.
Now complete the square of x^2 - 3x: Take half of -3 and square the result, obtaining (-3/2)^2, or 9/4. Add 9/4 to x^2 - 3x and then subtract 9/4 from the result: We get x^2 - 3x + 9/4 - 9/4. Substitute this result back into
y = 4(x^2 - 3x) + 9: y = 4(x^2 - 3x + 9/4 - 9/4) + 9
and then rewrite the perfect square x^2 - 3 + 9/4 as the square of a binomial:
y = 4(x - 3/2)^2 - 9/4) + 9. This simplifies to:
y = 4(x - 3/2)^2 + 0.
Thus, the vertex is at (3/2, 0) and the axis of symmetry is x = 3/2. This agrees with Answer B.
Given : equation y = 4x^2 − 12x + 9
To Find :
A) The axis of symmetry is x = 0 and the vertex is (0,9).
B)The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
C)The axis of symmetry is x = 4 and the vertex is (4, -12).
D)The axis of symmetry is x = -1.5 and the vertex is (-1.5, 36).
Solution:
y = 4x² - 12x + 9
=> y = (2x)² - 2(2x)3 + 3²
=> y = (2x - 3)²
=> y = 4(x - 3/2)²
=> y = 4(x - 1.5)²
Axis of symmetry is x= 1.5
Vertex = (1.5 , 0)
The axis of symmetry is x= 1.5 and the vertex is (1.5, 0).
a=8 and b=24 what would ab be?
Answer:
192
Step-by-step explanation:
Given,
a = 8
b = 24
To find : ab = ?
ab
= 8 x 24
= 192
Answer:
192
Step-by-step explanation:
...................
Use order of operations to solve (15 ÷5) + 9 + (14 - 5 ) x 3
Answer:
39.
Step-by-step explanation:
(15 ÷5) + 9 + (14 - 5 ) x 3
= 3 + 9 + 9 x 3
= 3 + 9 + 27
= 39.
Someone plz help me :(
Answer:
B) 5 gallons
Step-by-step explanation:
4 quarts = 1 gallon
multiply each number by 5
20 quarters = 5 gallons
Answer:
5
Step-by-step explanation:
If there are 4 quarts in a gallon and you are given 20 quarts divide 20 by 4 and you get 5
What are the coordinates of point A? (–2, –6) (–6, –2) (–6, –3) (–3, –6)
Answer:
(-3,-6)
Step-by-step explanation:
Answer:
(-3, -6)
Step-by-step explanation:
How do I figure this out
Answer:
x = 21Step-by-step explanation:
Given triangle is equilateral since all three angles marked as congruent.
It means each interior angle measures 60°.
The angle (5x + 15)° is exterior angle.
We know exterior angle measure is same as the sum of non-adjacent interior angles:
5x + 15 = 60 + 605x + 15 = 1205x = 120 - 155x = 105x = 105/5x = 211. Identify the equation that has the same slope as the points (0, -3) and (-1, 1)
1. y= 3x+2
2. y= -4x-3
3. y= x+1
4. y= -x+2
Answer:
2. y= -4x-3
Step-by-step explanation:
y=mx+b
slope :m
(0,-3) : m.0+b=-3 => b=-3
(-1,1) : m.1+b= 1 => m=-4
Evaluate the expression for x =-2 and y=-3 and choose its value.
x2 - y2
Step-by-step explanation:
x = -2
y = -3
= x² - y²
= (-2)² - (-3)²
= 4 - 9
= -5
Write down the equation of a line whose slope is 5 and crosses the y-axis at -6. Express in slope-intercept form.
Answer:
Y= 5x-6
Step-by-step explanation:
The slope intercept form is y=mx+b. The m stands for your slope. The b stands for the y-intercept. So, plug in the slope of 5 for m, then plug in -6 of b and then your equation should end up as y=5x-6. Hope this helps :)
Ezra enjoys gardening Every Sunflower plant he waters requires 0.7 liters of water, and every lily plant he waters requires 0.5 liters of water. He graphs
the number of surfower plants (S) and number of lily plants (L) to determine how many of each plants he can water with at most 11 liters
Which type of boundary line she he use in his graph?
Answer:
the answer is 8
Step-by-step explanation:
yes Ezra can plant 8 sunflowers
hope this helpsss :)
For the piecewise defined function f (x)=
3x-1 x<3
1/2 x + 7. x>3
what is the following is the value of f (6) ?
Answer:
10
Step-by-step explanation:
f(x)=f(6) means x=6
Now, as 6>3 we use the formula for x>3
Substituting 6 into 1/2x+7 we get,
1/2(6)+7
=3+7
=10
The value of function at x= 6 is 10.
What is Piecewise function?A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.
We have,
f(x) = 3x -1 , x<3
1/2x + 7, x>3
Now, for x = 6 which falls in condition x>3
f(6) = 1/2(6)+ 7
f(6) = 3 + 7
f(6)= 10
Learn more about Piecewise function here:
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can u get the limit of this !!
No my brain hurts from looking at that, maybe tomorrow...
what is 15^{2} as a decimal point
Answer:
the answer is.... 0.133
Step-by-step explanation:
hope it helps :D
Pls hurry I will give brainliest if answered in the next ten minutes
Answer:
[tex](2 + \sqrt{3}) - (1 + \sqrt{3})i[/tex]
Answer:
(b) (2+√3) -(1+√3)i
Step-by-step explanation:
Add like terms. Real terms are added; imaginary terms are added.
(√3 -i) + (2-√3i) = (√3 +2) +(-i -√3i)
= (√3 +2) -i(1 +√3) . . . . . the common factor of -i can be factored out
= (2 +√3) -(1 +√3)i
PLEASE HURRY
Explain what pattern or patterns do you see when you are subtracting a negative number as the subtrahend? For example: 8 – (-2) ?
Answer:
8 - (-2) = 10 there you go!
Step-by-step explanation:
Answer:
When you subtract a negative numbe, it is the same as adding the number. For example, 8-(-2) can be written as 8+2. Two negatives make a positive.
:)
Which equation matches the graph
Give me answers plz
Answer:
D: [tex]5x-8y=40[/tex]
Step-by-step explanation:
At a glance: Last one, it's the only one with different signs for x and y coefficient, and the graph is growing.
Some more reasoning: Write all of them in slope-intercept point:
[tex]A: y= -\frac58x +\frac52\\B: y= -\frac85x+4\\C: y= -\frac85x+8\\D:y=-\frac58x-5[/tex]
The only one with a compatible slope and intercept is D
Number crunching: replace the coordinates of either [tex](8;0)[/tex]or[tex](0;-5)[/tex]. As soon as the equality stops holding, that option isn't valid anymore.
Example: A w/ [tex](0;-5)[/tex]: [tex]\frac 52(0) +4(-5) = 10 \rightarrow -20 = 10[/tex] which isn't true, so A is out.
Can you solve this inequality? -4x-5>1/4(x+31)
Answer:
x < -3
Step-by-step explanation:
its correct that the answer.
Step-by-step explanation:
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