Answer:
x > 6
Step-by-step explanation:
2x + 4 > 16
2x > 16 - 4
2x > 12
x > 12/2
x > 6
u and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.
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Work Shown
We'll be using these vector properties
Rule 1: (a,b) + (c,d) = (a+c, b+d)Rule 2: k*(a,b) = (k*a, k*b)To get the following
-2u + v = -2*(-1, 5) + (2,7)
-2u + v = (-2*(-1), -2*5) + (2,7) .... apply rule 2
-2u + v = (2, -10) + (2, 7)
-2u + v = (2+2, -10+7) .... use rule 1
-2u + v = (4, -3)
(8x 2 −15x)−(x 2 −27x)=ax 2 +bxleft parenthesis, 8, x, squared, minus, 15, x, right parenthesis, minus, left parenthesis, x, squared, minus, 27, x, right parenthesis, equals, a, x, squared, plus, b, x If the equation above is true for all values of xxx, what is the value of b-ab−ab, minus, a ?
Answer:
5Step-by-step explanation:
Given the expression (8x² −15x)−(x² −27x) = ax² +bx, we are to determine the value of b-a. Before we determine the vwlue of b-a, we need to first calculate for the value of a and b from the given expression.
On expanding the left hand side of the expression we have;
= (8x² −15x)−(x² −27x)
Open the paranthesis
= 8x² −15x−x²+27x
collect the like terms
= 8x²−x²+27x −15x
= 7x²+12x
Comparing the resulting expression with ax²+bx
7x²+12x = ax²+bx
7x² = ax²
a = 7
Also;
12x = bx
b =12
The value of b - a = 12 - 7
b -a = 5
Hence the value of b-a is equivalent to 5
The value of b minus a is 5
Calculation of the value:Since the expression is
[tex](8x^2 -15x)-(x^2 -27x) = ax^2 +bx[/tex]
Here we have to expand the left-hand side of the expression so it should be like
[tex]= (8x^2 -15x)-(x^2 -27x)\\\\= 8x^2 -15x-x^2+27x\\\\= 8x^2-x^2+27x -15x\\\\= 7x^2+12x[/tex]
Now
[tex]7x^2+12x = ax^2+bx\\\\7x^2 = ax^2[/tex]
a = 7
Also;
12x = bx
b =12
So,
The value of b - a = 12 - 7
b -a = 5
Hence the value of b-a should be 5
Learn more about equation here: https://brainly.com/question/24540444
Ifx= 15t2 and y= 10t2, find dy by
dx
Answer:
2/3
Step-by-step explanation:
dy/dx equals derivative of y by x
dy/dx=20t/30t=2/3
Graph the image of H(-8,5) after a reflection over the x-axis.
Answer ?
Answer: plot a point at (-8, -5)
The y coordinate flips from positive to negative, or vice versa, when we reflect over the horizontal x axis. The x coordinate stays the same.
The rule can be written as [tex](x,y) \to (x,-y)[/tex]
The perpendicular distance of the point from x axis is 2 units and the perpendicular distance from y axis is 3 units.Write the co-ordinates of the if it lies in
Answer:
Step-by-step explanation:
Given that :
the perpendicular distance of the point from x axis = 2 units
the perpendicular distance from y axis is 3 units
The objective is to the write the coordinates of the points if it lies in
(i) | Quadrant (ii) || Quadrant (iii) ||| Quadrant (iv) |v Quadrant
The position of a point in a plane is conveniently specified by the distances fro two perpendicular lines.The lines are called the x-axis and y-axis and their [point of intersection is called the origin.
The perpendicular distance from the y-axis is called the x- coordinate or abscissa and the perpendicular distance from x-axis is called the y-coordinate or ordinate,The coordinate form an ordered pair with the abscissa written as first.
With that be said, So In the given question,
the perpendicular distance of the point from x axis = 2 units
y coordinate = ±2
the perpendicular distance from y axis is 3 units
x coordinate = ±3
The ordered pair of the coordinates = ( ±3, ±2)
Therefore;
in | quadrant ; we have (3,2) where x and y are both on the positive axis
in || quadrant ; we have (-3,2) x is on the negative axis and y is on the positive axis
In ||| quadrant ; we have (-3. -2) both x and y are on the negative axis
In |v quadrant ; we have ( 3, -2) x is on the positive axis and y is on the negative axis.
A student earned grades of , , , , and . Those courses had the corresponding numbers of credit hours , , , , and . The grading system assigns quality points to letter grades as follows: A4; B3; C2; D1; F 0. Compute the grade point average (GPA) as a weighted mean and round the result with two decimal places. If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list
Answer:
grade point average (GPA) as a weighted mean = 3.14
Yes, student makes the Dean's list.
Step-by-step explanation:
Since the data is not given I will explain the question with a relevant example:
For example
Data:
Students grades are: A, C, B, A, D
The corresponding number of credit hours: 3, 3, 3, 4, 1
The grading system assigns quality points to letter grades as:
A = 4
B = 3
C = 2
D = 1
F = 0
To find:
grade point average (GPA) as a weighted mean
If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list?
Solution:
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]
Here
Using the earned grades of A, C, B, A, D and corresponding quality points to these letter grades we get:
A = 4
C = 2
B = 3
A = 4
D = 1
So the values in x[tex]_{i}[/tex] are:
x
4
2
3
4
1
Now the number of credit hours are represented as weights w[tex]_{i}[/tex] :
w
3
3
3
4
1
In order to calculate weighted mean first multiply x[tex]_{i}[/tex] with w[tex]_{i}[/tex]
x[tex]_{i}[/tex] w[tex]_{i}[/tex]
4 * 3 = 12
2 * 3 = 6
3 * 3 = 9
4 * 4 = 16
1 * 1 = 1
The sum of x[tex]_{i}[/tex] w[tex]_{i}[/tex] is :
Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] = 12 + 6 + 9 + 16 + 1 = 44
Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] = 44
Now compute the sum of w[tex]_{i}[/tex]
Σw[tex]_{i}[/tex] = 3 + 3 + 3 + 4 + 1 = 14
Σw[tex]_{i}[/tex] = 14
Putting the values in the weighted mean formula:
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex]
= 44 / 14
= 3.1429
Weighted Mean = Σx[tex]_{i}[/tex] w[tex]_{i}[/tex] / Σw[tex]_{i}[/tex] = 3.14
Since the Dean's list requires a GPA of 3.00 or greater and the grade point average (GPA) as a weighted mean of the student is 3.14 so the student makes the Dean's list because his/her GPA is higher than 3.00
Pls help me , idk how to do
Answer:
PQRS is a parallelogram with right-angle corners
Step-by-step explanation:
We know that the midsegment of a triangle is parallel to the base.
QR is the midsegment of triangle BCD, so is parallel to BD.
SP is the midsegment of triangle DAB, so is parallel to BD.
QR and SP are both parallel to BD, so are parallel to each other.
RS is the midsegment of triangle CAD, so is parallel to AC.
PQ is the midsegment of triangle ABC, so is parallel to AC.
RS and PQ are both parallel to AC, so are parallel to each other.
__
We have shown that opposite sides of PQRS are parallel to each other, so the figure is at least a parallelogram.
__
By virtue of the congruence of corresponding angles where a transversal crosses parallel lines, each of the so-far named lines can be shown to be perpendicular to any of the lines it meets.* Hence the figure PQRS must be a parallelogram with right angles, a rectangle.
_____
* Transversal BD crosses PQ, AC, and RS at right angles. Hence, transversals RS and PQ cross QR, BD, and SP at right angles. That is, the angles at corners P, Q, R, and S of the parallelogram are right angles.
Hello, a quick question which number is least to greatest 0.359, 0.35, 1
Answer:
0.35, 0.359, 1
Step-by-step explanation:
0.359 = 359 thousandths
0.35 = 0.350 = 350 thousandths
1 = 1.000 = 1000 thousandths
Since 350 < 359 < 1000, then from least to greatest you get
0.35, 0.359, 1
Jack is building a square garden. Each side length measures 777 meters. Jack multiplies 7\times77×77, times, 7 to find the amount of space in his garden is equal to 494949 square meters. Which measurement does 494949 square meters represent?
Answer:
49 square meters represent area of the square garden
Step-by-step explanation:
Each side length=7 meters
He multiplied 7 × 7 times to find the amount of space
=49 square meters
Jack is trying to measure the area of his square garden
Area of the square garden = length^2
=Length × length
Recall,
Length=7 meters
Area of the square garden= 7 meters × 7 meters
=49 square meters
5 diferrent representations of the value 3
Answer:
3
= 15/5
= [tex]\sqrt[3]{27}[/tex]
= 1.5*2
= 3/1
= 3*1
= 3¹
= 1/3⁻¹
= 3⁴ / 3³
= 3⁵ * 3⁻⁴
Given that ΔABC is a right triangle with the right angle at C, which of the following is true?
1. tan A = 1/(tan B)
2. tan A = sin B
3. cos A = 1/(cos B)
4. sin B = 1/(sin A)
Answer:
1. tan A = 1/(tan B)
Step-by-step explanation:
By definition,
tangent A = opposite / adjacent = a / b
and
tangent B = opposite / adjacent = b / a
Therefore tangent A = a/b = 1/tan(B)
Answer: Tan a=tan b
I belive
Step-by-step explanation:
10. In 2005 there were 9 million bicycles in Beijing, correct to the
nearest million.
The average distance travelled by each bicycle in one day was
6.5 km correct to one decimal place.
Work out the upper bound for the total distance travelled by all the
bicycles in one day,
Answer:
Total distance = 6,540,000 km
Step-by-step explanation:
Given
Number of bicycles = 9,000,000
Average Distance = 6.5 km (to 1 d.p)
Required
Calculate the upper bound of all bicycle distance
First, we need to determine the range of the distance traveled by each bicycle;
Since, the average distance is approximated, then the Range is:
[tex]Range = (6.45km\ to\ 6.54km)[/tex]
All number in this range approximate to 6.5km
Note that the upper bound of the range is 6.54km;
Hence, total distance is calculated as thus;
[tex]Total\ distance = Number\ of\ bicycle * upper\ bound[/tex]
[tex]Total\ distance = 1,000,000 * 6.54km[/tex]
[tex]Total distance = 6,540,000km[/tex]
Point E is on line segment DF. Given DE=9 and DF=11, determine the length EF.
Answer:
EF = 2 units
Step-by-step explanation:
Given:
Line segment DF and point E on it.
DF = 11 unit
DE = 9 Unit
Find:
EF
Computation:
We know that,
DF = DE + EF
11 = 9 + EF
EF = 11-9
EF = 2 units
5
What is the equation, in point-slope form, of the line that
is parallel to the given line and passes through the point
(-3, 1)?
4
3
2
(-3, 1)
42.27
1
5 4 3 2 1
2 3 4 5 x
y-1=-{(x+3)
y-1=-{(x + 3)
y-1= {(x + 3)
y-1= {(x + 3)
(-2, 4)
Answer: [tex]y-1=\dfrac32(x+3)[/tex]
Step-by-step explanation:
Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]
In graph(below) given line is passing through (-2,-4) and (2,2) .
Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]
Since parallel lines have equal slope . That means slope of the required line would be .
Equation of a line passing through (a,b) and has slope m is given by :_
(y-b)=m(x-a)
Then, Equation of a line passing through(-3, 1) and has slope = is given by
[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]
Required equation: [tex]y-1=\dfrac32(x+3)[/tex]
can u help me. where do u plot it. what is x and what is y
Answer:
Step-by-step explanation:
for the first equation x= -2 and y=-7
the second equation x=3 and y is 3 now just plot x and y from the same equation on the same line
Answer:
[tex]\huge\boxed{x = -4; y = 7}[/tex]
Step-by-step explanation:
By plotting the points, we see that both of the lines intersect at (-4, 7)
Which means (X,y) = (-4,7)
So,
x = -4
y = 7
See the attached file so that you can know how would it be graphed.
Find the derivative of f(x) = -2x2 + 11x at x = 9.
Answer:
The value of the derivative at x = 9 is -25
Step-by-step explanation:
Here in this question, we are told to find the derivative of the given equation at the point where x = 9
What we need to do here is simply, differentiate f(x), then substitute that value x = 9 into the differentiated equation
In notation form, what we are to find is f’(9)
So;
f(x) = -2x^2 + 11x
f’(x) = -4x + 11
So therefore;
f’(9) = -4(9) + 11
f’(9) = -36 + 11
f’(9) = 11-36
f’(9) = -25
This event is independent, true or false?
There are eight shirts in your closet, four blue and four green. You randomly select one to wear on Monday and then a different one on Tuesday.
Answer:
False
Step-by-step explanation:
Because the question says you pick a different shirt on Tuesday than on Monday, that means you have one less shirt you can select, so the event is dependent.
What is the area of this composite figure?
Answer:
C.) 7.14 in²
Step-by-step explanation:
The figure is made up of a square and a circle. The circle is divided in half and each piece is set on one side of the square. This means that the diameter of the circle is equal to the length of the sides of the square, 2 inches.
The area of the square can be found by multiplying length times the width:
[tex]2*2=4[/tex]
The area of the square is 4 inches, and since we multiplied two lengths, we square the value:
A=4in²
Now find the area of the circle using the formula:
[tex]A=\pi r^2[/tex]
The radius is half of the diameter, so the radius is 1. Insert values and solve:
[tex]A=\pi *1^2\\\\A=\pi *1\\\\A=\pi[/tex]
The area of the circle is equal to π. Add the values together:
[tex]4+\pi =7.14[/tex]
The area of the figure is 7.14 in²
:Done
a zookeeper has both flamingos and alligators in his zoo there are 78 feet and 27 heads how many flamingos and aligators are there
Answer:
15 flamingos and 12 alligators
Step-by-step explanation:
Because there are 27 heads, that means there is a total of 27 flamingos and alligators. Flamingos have 2 feet and alligators have 4 feet.
1. Set up a system of equations
(x = number of flamingos, y = number of alligators)
1x + 1y = 27 heads
2x + 4y = 78 feet
2. Multiply to get the same coefficient
2(1x + 1y = 27) → 2x + 2y = 54
3. Subtract
2x + 2y = 54
- 2x + 4y = 78
0x + -2y = -24
4. Solve for y
-2y = -24
y = 12
5. Plug in y to solve for x
1x + 1(12) = 27
x + 12 = 27
x = 15
5 - (4 - 3x) = 10
how would u distubute in this problem
Answer:
x = 3
Step-by-step explanation:
Given
5 - (4 - 3x) = 10 ← distribute the terms in the parenthesis by - 1
5 - 4 + 3x = 10, that is
1 + 3x = 10 ( subtract 1 from both sides )
3x = 9 ( divide both sides by 3 )
x = 3
4. The rental for a television set changed from $80 per year to $8 per month
What is the percentage increase in the yearly rental?
Answer:
16%
Step-by-step explanation:
rental charge per year = $80
rental charge at the rate $8 per year = 8 * 12 = 96
the increased amount = 96 - 80 = 16
% = 16 / 100 = 16%
What is the volume of this rectangular prism?
4/3
4/3
4/3
Answer:
[tex]\frac{64}{27}[/tex] cm³
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = lbh ( l is length, b is breadth and h is height ), thus
V = [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] × [tex]\frac{4}{3}[/tex] = [tex]\frac{4^3}{3^3}[/tex] = [tex]\frac{64}{27}[/tex] cm³
Answer:
64/27 would be your answer.Step-by-step explanation:
I am more than happy to answer anymore questions. If needed an explanation I can put one in the comments.
Point Q is on line segment PR. Given QR=11 and PQ=3, determine the length PR.
Answer:
[tex]\huge \boxed{14}[/tex]
Step-by-step explanation:
Q is a point on the line segment PR.
PQ = 3
QR = 11
PR = PQ + QR
PR = 3 + 11 = 14
Answer:
[tex]\huge\boxed{PR = 14}[/tex]
Step-by-step explanation:
QR = 11
PQ = 3
Given that Q is on line segmant PR
So,
PR = PQ + QR
PR = 3 + 11
PR = 14
Please answer this question now
Step-by-step explanation:
Hi, there!!!
Here, the question is about the volume of cone,
given that,
diameter = 12m
radius of a circle= 12m/2= 6m
height (h)=9 m
now, we have,
volume of a cone= 1/3×pi× r^2×h
or, v= 1/3×3.14×(6)^2×9
After simplifying it we get,
v= 339.12 m^3
Hope it helps....
An octagonal pyramid ... how many faces are there, how many vertices and how many edges? A triangular prism ... how many faces are there, how many vertices and how many edges? a triangular pyramid ... how many faces are there, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Answer:.
Step-by-step explanation:.
Please give me the correct answer
Answer:
Area= 452.23 ft²
Step-by-step explanation:
Angle at U = 180-48-20
Angle at U = 112°
UT/sin 112=46/sin 48
UT= 0.9272*46/0.7431
UT=57.4 ft
UV= sin 20*46/sin48
UV= 0.3420*46/0.7431
UV= 21.2 ft
S=( 21.2+57.4+46)/2
S=124.6/2
S= 62.3
Area= √((62.3)(62.3-21.2)(62.3-57.4)(62.3-46))
Area= √((62.3)(41.1)(4.9)(16.3))
Area= √204509.5311
Area= 452.23 ft²
Three-fourths of the voters supported the bond measure. If there were
8000 voters, how many supported the bond measure?
Answer:
6000
Step-by-step explanation:
Divide top and bottom by the common factor.
[tex]\dfrac{3 }{4} \times 8000 = 3 \times 2000[/tex]
Simplify
3 × 2000 = 6000
Given: -1/2x > 6. Choose the solution set. A {x | x R, x > -12} B{x | x R, x > -3} C{x | x R, x < -3}D {x | x R, x < -12}
Answer:
D
Step-by-step explanation:
-1/2x > 6 (you have to flip the sign when you multiply or divide by negative
x < -12
Rami goes running in Central Park every Sunday. He runs at a constant speed. He can run 6 3/5 miles in 1 2/3 hours.what is his speed In miles?
Answer:
3 24/25 MPH
Step-by-step explanation:
We know Rami runs 6 3/5 miles in 1 2/3 hrs --> Convert into an improper fraction
--> 6 3/5 = 33/5
--> 1 2/3 = 5/3
Speed = Distance divided by Time
Distance = 33/5
Time = 5/3
33/5 / 5/3 = 33/5 x 3/5
33/5 x 3/5 = 99/25
1/25 less than 4 = 3 24/25
Thus, our answer is 3 24/25 MPH
Hope this helps!
The perimeter of a rectangle is 62 cm. The diagonal and width of the rectangle are 25 cm and x cm respectively.
Form a quadratic equation in terms of x based on the situation.
Step 1:
62cm - (25*2)=12cm
62-25=37cm
Length for both sides 25
Width=37cm=x
