Answer:
-13a
Step-by-step explanation:
Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.
Answer:
-13a
Step-by-step explanation:
These two numbers are already like terms, so you can subtract it easily.
First, don't look at the a.
-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.
Now that we now it equals -13, we can add the variable a back onto the answer. We get -13a.
An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 300 miles per hour. The other is 200 miles from the point and has a speed of 400 miles per hour.(a) At what rate is the distances between the planes decreasing?(b) How much time does the air traffic controller have to get one of the planes on a different flight path?
Answer:
The answer to this question can be defined as follows:
In option A, the answer is "- 357.14 miles per hour".
In option B, the answer is "-0.98".
Step-by-step explanation:
Given:
[tex]\frac{dx}{dt} =- 300 \text{ miles per hour}[/tex]
[tex]\frac{dy}{dt} =- 400 \text{ miles per hour}[/tex]
find:
[tex]\frac{ds}{dt} =?[/tex] when
[tex]x= 150 \\y= 200\\s=x+y\\\\[/tex]
[tex]= 150+200 \\\\=350[/tex]
[tex]\to s^2=x^2+y^2\\[/tex]
differentiate the above value:
[tex]\to 2s\frac{ds}{dt}= 2x \frac{dx}{dt}+2y \frac{dy}{dt}[/tex]
[tex]\to 2s\frac{ds}{dt}= 2(x \frac{dx}{dt}+y \frac{dy}{dt})\\\\\to \frac{ds}{dt}= \frac{(x \frac{dx}{dt}+y \frac{dy}{dt})}{s}\\\\[/tex]
[tex]= \frac{(150 \times -300 +200 \times -400 )}{350}\\\\= \frac{-45000+ (-80000) }{350}\\\\= \frac{- 125000 }{350}\\\\= - 357.14 \ \text{miles per hour}[/tex]
In option B:
[tex]\to d=rt\\\\ \to t= \frac{d}{r}[/tex]
[tex]\to \ \ d= 350 \ \ \ \ \ \ r= -357.14\\[/tex]
[tex]\to t= - \frac{350}{357.14}\\\\\to t= - 0.98[/tex]
A stone is thrown downward straightly its speed at speed of 20 second what and it reaches the ground at 40 metre second what will be the height of building
Answer:
[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]
Step-by-step explanation:
A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)
The initial velocity ⇒ 20 m/s
The final velocity ⇒ 40 m/s
We can apply a formula to solve for the height of the building.
[tex](V_f)2 - (V_i)^2 =2gh[/tex]
[tex]V_f = \sf final \ velocity \ (m/s)[/tex]
[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]
[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]
[tex]h = \sf height \ (m)[/tex]
Plugging in the values.
Acceleration due to gravity is 9.8 m/s².
[tex](40)^2 - (20)^2 =2(9.8)h[/tex]
Solve for [tex]h[/tex].
[tex]1600 - 400 =19.6h[/tex]
[tex]1200 =19.6h[/tex]
[tex]\displaystyle h=\frac{1200}{19.6}[/tex]
[tex]h= 61.22449[/tex]
The height of the building is 61.22 meters.
According to data from the U.S. Department of Education, the average cost y of tuition and fees at public four-year institutions in year x is approximated by the equation where x = 0 corresponds to 1990. If this model continues to be accurate, during what year will tuition and fees reach $4000?
Answer:
Graphing Calculator
Step-by-step explanation:
really urgent...i need the working also ...pls help me
Answer:
See below.
Step-by-step explanation:
In each case, you are looking for time. We know speed is distance divided by time. Lets start with the speed formula.
speed = distance/time
Now we solve it for time. Multiply both sides by time and divide both sides by speed.
speed * time = distance
time = distance/speed
Time is distance divided by speed. In each problem, you have a speed and a distance. Divide the distance by the speed to to find the time.
1) speed = 44.1 km/h; distance = 150 km
time = distance/speed = 150 km/(44.1 km/h) =
= 3.401 hours = 3 hours + 0.401 hour * 60 min/hour = 3 hours 24 minutes
2) speed = 120 km/h; distance = 90 km
time = distance/speed = 90 km/(120 km/h) =
= 0.75 hours = 0.75 hour * 60 min/hour = 45 minutes
3) speed = 125 m/s; distance = 500 m
time = distance/speed = 500 m/(125 m/s) =
= 4 seconds
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4) {}^{2} }{4 + 3x - {x}^{2} } [/tex]
pls help me need help asap
Answer:
[tex] { x^2+3x-4} [/tex]
Step-by-step explanation:
Factor top and bottom.
The numerator is a difference of two squares, and the denominator is a quadratic.
[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]
= [tex]\frac{ (3x+x^2-4)(3x-x^2+4) }{(1+x)(4-x)}[/tex]
= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]
If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give
= [tex] { (x-1)(x+4)} [/tex]
= [tex] { x^2+3x-4} [/tex]
Answer:
The answer is
x² + 3x - 4Step-by-step explanation:
[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]
To solve the expression first factorize both the numerator and the denominator
For the numerator
9x² - ( x² - 4)²
Expand the terms in the bracket using the formula
( a - b)² = a² - 2ab + b²
(x² - 4) = x⁴ - 8x² + 16
So we have
9x² - (x⁴ - 8x² + 16)
9x² - x⁴ + 8x² - 16
- x⁴ + 17x² - 16
Factorize
that's
(x² - 16)(-x² + 1)
Using the formula
a² - b² = ( a + b)(a - b)
We have
(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)
For the denominator
- x² + 3x + 4
Write 3x as a difference
- x² + 4x - x + 4
Factorize
That's
- ( x - 4)(x + 1)
So we now have
[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]
Simplify
[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]
Reduce the expression by x + 1
That's
-( x + 4)( 1 - x)
Multiply the terms
We have the final answer as
x² + 3x - 4Hope this helps you
What is the answer??
c — 10 ≥ 15
Answer:
Step-by-step explanation:
c - 10 ≥ 15 =
c ≥ = 15 + 10
c ≥ = 25
c = 26 ( or numbers above 26)
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The two inequalities that show the solution to these equations are n ≥ 55 and y ≥ 6
Step-by-step explanation:
We are given two inequalities that we have to solve. We can solve these inequalities as if we are solving for the variable.
n/5 ≥ 11
Multiply by 5 on both sides.
n ≥ 55
Now, let's do the second one.
-3y ≤ -18
Divide by -3 on both sides. When we divide by a negative in inequalities, then the sign is going to flip to its other side. So, this sign (≤) becomes this sign (≥)
y ≥ 6
Consider line A which is defined by the equation:
y=5/6x-5/2
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answer:
y = -6/5x +12/5distance from P to A: (66√61)/61 ≈ 8.4504midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
40. Which families of plane figures given below are NOT always similar?
A. Squares
C. Equilateral triangles
B. Circles
D. rectangle
Answer:
Rectangle
Explanation:
Rectangles can be oblong, and square is also a rectangle.
Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m
Answer:
x = 2√41 mStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
a² = b² + c²
where a is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]Find the square root of both sides
We have the final answer as
x = 2√41 mHope this helps you
Answer:
2 sqrt(41) =c
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 10^2 = c^2
64+ 100 = c^2
164 = c^2
take the square root of each side
sqrt(164) = sqrt(c^2)
sqrt(4*41) = c
2 sqrt(41) =c
One hundred people, ages 11-15, were randomly surveyed to find their opinion of their favorite leisure time activity. Sixty-four percent of them said they liked to spend time watching TV. If there are 1500 students in your school, about how many of them would you predict would enjoy watching t.v. A.2343 B.960 C.640 D.500
Answer:
If there are 1500 students in your school then 960 students would enjoy watching TV
Step-by-step explanation:
Step 1: We know that 64% of kids aged from 11 to 15 enjoy watching TV and there is 1500 students in your school
Step 2: We now want to find 64% of 1500, we can rewrite 64% as 0.64. We multiple 1500 by 0.64 to find out how many students enjoy watching TV
0.64 x 1500 = # of students who like watching TV
960 = # of students who like watching TV
Therefore out of 1500 students, 960 would enjoy watching TV
Given an angle of a triangle and the opposite side length; which trigonometric function would you use to find the hypotenuse? a TAN b COS c SIN d Not enough information
Answer:
Sin
Step-by-step explanation:
Sin < = opposite/hypotenuse
need help...!!ASAP..!! plz....
the answer for this is A
Answer:
Correct option is A
Step-by-step explanation:
3x - 7
Three times a number x minus 7
Or
The difference of there times a number and 7
Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?
Answer:
The answer is 3%Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]
To find the change subtract the smaller quantity from the bigger one
From the question
original price = $24,600
Current price = $ 25,338
Change = $25,338 - $ 24,600
Change = $ 738
So the percentage increase is
[tex] \frac{738}{24600} \times 100[/tex]
[tex] = \frac{3}{100} \times 100[/tex]
We have the final answer as
Percentage increase = 3%Hope this helps you
Please explain and help
Answer:
y=-x+2
Step-by-step explanation:
it is linear equation y=mx+b two points (0,2),(1,1)
find m ( slope)=y2-y1/x2-x1 ⇒1-2/1-0⇒-1
y=mx+b choosea point from graph :(0,2)\when x =0 the y=b=2
y=-x+2
If a and b are acute angles such that tan (a+b)= 1.73 and tan(a-b) =1/1.73, find a and b
[tex] \LARGE{ \underline{ \boxed{ \orange{ \rm{Solution:)}}}}}[/tex]
Given,tan (a + b) = 1.73 [tex]\approx[/tex] √3tan (a - b) = 1 / 1.83 [tex]\approx[/tex] 1 / √3To find:Value of a and b in degrees....?Solution:☃️ Refer to the trigonometric table....
Then, proceeding
⇛ tan 60 ° = √3
⇛ tan 60° = tan (a + b)
⇛ 60° = a + b
Flipping it,
⇛ a + b = 60° --------(1)
And,
⇛ tan 30° = 1 / √3
⇛ tan 30° = tan (a - b)
⇛ 30° = a - b
Flipping it,
⇛ a - b = 30° ---------(2)
Now adding eq.(1) and eq.(2),
⇛ a + b + a - b = 60° + 30°
⇛ 2a = 90°
⇛ a = 90° / 2
⇛ a = 45°
Putting value of a in eq.(1),
⇛ 45° + b = 60°
⇛ b = 15°
☄ So, Our Required answers:
a = 45°b = 15°━━━━━━━━━━━━━━━━━━━━
If PR = 4X - 2 AND RS = 3X - 5 which expression represents PS?
Answer:
7x - 7
Step-by-step explanation:
If PR, RS, and PS are line segments then the equation below will work.
PR + RS = PS
(4x-2) + (3x-5) = 7x - 7
Michael is using a number line to evaluate the expression –8 – 3. A number line going from negative 12 to positive 12. A point is at negative 8. After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Answer:
move to the left 3 more spaces
Step-by-step explanation:
you are at -8 already. Therefore, you (-3) more spaces, so you go to the left three more spaces. Use the saying keep change change to help with this.
Keep the first number sign, change the next sign, and the next sign.
Answer:
d
Step-by-step explanation:
Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4
Answer:
[tex]\frac{1}{9^4}[/tex].
Step-by-step explanation:
[tex]9^{-4}[/tex]
= [tex]\frac{1}{9^4}[/tex]
= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]
= [tex]\frac{1}{81 * 81}[/tex]
= [tex]\frac{1}{6561}[/tex]
= 0.0001524157903.
Hope this helps!
Why the answer question now correct
Answer:
461.58 in²
Step-by-step explanation:
The surface area (A) is calculated as
A = area of base + area of curved surface
= πr² + πrl ( r is the radius of base and l is slant height )
= 3.14 × 7² + 3.14 × 7 × 14
= 3.14 × 49 + 3.14 × 98
= 3.14(49 + 98)
= 3.14 ×147
= 461.58 in²
Vanessa uses the expressions (3x2 + 5x + 10) and (x2 – 3x – 1) to represent the length and width of her patio. Which expression represents the area (lw) of Vanessa’s patio?
To get the area simply multiply the length by the width.
(3x^2+5x+10)(x^2-3x-1) = 3x^4 - 4x^3 - 8x^2 - 35x - 10
Answer:
the answer is A
Step-by-step explanation:
got it right on edge
First Question The following table shows the length and width of a rectangle: Length Width Rectangle A 4x + 5 3x − 2 Which expression is the result of the perimeter of rectangle A and demonstrates the closure property? A.14x + 6; the answer is a polynomial B.14x + 6; the answer may or may not be a polynomial C.2x + 6; the answer is a polynomial D.2x + 6; the answer may or may not be a polynomial
Answer: A.14x + 6; the answer is a polynomial
Step-by-step explanation:
Since all of the variables have integer exponents that are positive this is a polynomial.
PLEASE HELP!! It’s for a math class and I can’t figure it out been trying every website nothing has helped!
Answer:
11.6%
I hope this helps!
Multiply and simplify. (1 − 5i)(1 − 2i) A) 1 + 7i B) 9 − 7i C) 1 − 7i D) − 9 − 7i
Answer:
The product renders: [tex]-9-7\,i[/tex]
Step-by-step explanation:
Recall that the product of the imaginary unit i by itself renders -1
Now proceed with the product of the two complex numbers using distributive property:
[tex](1-5\,i)\,(1-2\,i)=1-2\,i-5\,i+10\,i^2=1-7\,i-10=-9-7\,i[/tex]
the sum of 35 and one fifth part of itself is added to the sum of one seventh of 11 and 8
Answer:
313/7
Step-by-step explanation:
Here, we are interested in turning the wordings of the statement to numeric values.
We take it one at a time.
Sum of 35 and 1/5(35) = 35 + 7 = 42
This is added to 1/7(11 + 8)
= 1/7(19) = 19/7
So we have;
42 + 19/7 = (294 + 19)/7 = 313/7
Triangle A' B' C' is a dilation of a triangle ABC. The scale factor is [tex]\frac{3}{4}[/tex]. Point B is 11 inches away from the center of dilation is point B'?
Answer:
None of the options are correct
Step-by-step explanation:
Let us assume point B is at (x, y) and the center of dilation is at (a, b). Therefore the distance between the two points is:
[tex]Distance =\sqrt{(b-y)^2+(a-x)^2}=11 \\\\\sqrt{(b-y)^2+(a-x)^2}=11[/tex]
If Triangle ABC is then dilated by 3/4, the new coordinate is B'(3/4 (x-a) + a, 3/4 (y - b) + b). The distance between B' and the center of dilation would be:
[tex]Distance =\sqrt{(b-[\frac{3}{4}( y-b)+b])^2+(a-[\frac{3}{4} (x-a)+a])^2}[/tex]
Therefore the distance cannot be gotten until the center of dilation is given
Need to find the Domain and Range
Answer:
D: {x∈R | -2 ≤ x ≤ 2 }
R: {y∈R | 0 ≤ y ≤ 4 }
Step-by-step explanation:
The domain ranges between -2 and 2
The range ranges between 0 and 4
ux=x+y/k, solve for x
Answer:
x = y/( ku-1)
Step-by-step explanation:
Here in this question, we are asked to solve for x.
we have;
Ux = x+ u/ k
cross multiply;
k * Ux = x + y
kUx = x + y
kUx- x = y
x(KU-1) = y
x = y/( ku-1)
when the point ( k, 3 ) lies on each of these lines, find the value of k y= 3x+1 , y= 4x-2 , y=1/2x - 1 and 2x+3y=4
Answer:
see explanation
Step-by-step explanation:
Since (k, 3) lies on each of the lines, the point satisfies the equations.
Substitute x = k, y = 3 into each and solve for k
y = 3x + 1
3 = 3k + 1 ( subtract 1 from both sides )
2 = 3k ( divide both sides by 3 )
k = [tex]\frac{2}{3}[/tex]
-------------------------------------------------------
y = 4x - 2
3 = 4k - 2 ( add 2 to both sides )
5 = 4k ( divide both sides by 4 )
k = [tex]\frac{5}{4}[/tex]
--------------------------------------------------------
y = [tex]\frac{1}{2}[/tex] x
3 = [tex]\frac{1}{2}[/tex] k ( multiply both sides by 2 to clear the fraction )
k = 6
---------------------------------------------------------
2x + 3y = 4
2k + 3(3) = 4
2k + 9 = 4 ( subtract 9 from both sides )
2k = - 5 ( divide both sides by 2 )
k = - [tex]\frac{5}{2}[/tex]
What is the rule for the transformation below?
=================================================
Explanation:
The translation notation T(-5, 3) looks like an ordered pair point, but it is not. Instead, it is a rule to tell you how to shift any point left/right and up/down. The first number is the left/right shifting as its done along the x axis. The negative value means we shift left, so we shift 5 units to the left. The positive 3 in the y coordinate place means we shift 3 units up.
We see this shifting happen when we go from
A = (-1, -1) to A ' = (-6, 2) B = (2, 3) to B ' = (-3, 6)C = (5, -3) to C ' = (0, 0)The translation notation T(-5, 3) is the same as writing [tex](x,y) \to (x-5, y+3)[/tex] which may be a more descriptive notation to use, and it would avoid confusion with ordered pair point notation.
