Answer: R = (4, 5)
Step-by-step explanation: Midpoint is simply the center of a line. So, the equation for it is ((x1+x2)/2, (y1+y2)/2). Hence for this,
x coordinate- (6+x)/2=5
x=4
y coordinates- (9+y)/2=7
y=5
And therefore R is (4, 5)
what is the discriminant and how many solutions?
Step-by-step explanation:
[tex]\text{Discriminant} =\Delta = b^2-4ac\\
\implies \Delta = 7^2-4(1)(10)=49-40=9\\
\therefore \Delta >0\\[/tex]
Since the discriminant is greater than zero, there are two real solutions.
Also, the solutions are $x=5$ and $x=2$
20. Find the midpoint between the given points.
(3, -8) and (-5, -13)?
I need an answer fast! help if you can!
Hi there! :)
Answer:
[tex]\huge\boxed{(-1, -10.5)}[/tex]
Use the midpoint formula to solve for the midpoint:
[tex](x_{m}, y_{m}) = (\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2}}{2})[/tex]
Plug in the points:
[tex](x_{m}, y_{m}) = (\frac{-5+3 }{2} , \frac{-13 -8}{2})[/tex]
Simplify:
[tex](x_{m}, y_{m}) = (\frac{-2 }{2} , \frac{-21}{2})[/tex]
[tex](x_{m}, y_{m}) = (-1 , -10.5)[/tex]
A container in form of a frustum of a cone is 16 cm in diameter at the open end and 24 cm diameter at the bottom. If the vertical depth of the container is 8 cm calculate the capacity of the container.
Answer:
The capacity of the container is 2546.78 cm³.
Step-by-step explanation:
The volume of the frustum of a cone is:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
The information provided is:
r = 16/2 = 8 cm
R = 24/2 = 12 cm
h = 8 cm
Compute the capacity of the container as follows:
[tex]\text{Volume}=\frac{\pi h}{3}\cdot[R^{2}+Rr+r^{2}][/tex]
[tex]=\frac{\pi\cdot8}{3}\cdot[(12)^{2}+(12\cdot 8)+(8)^{2}]\\\\=\frac{8\pi}{3}\times [144+96+64]\\\\=\frac{8\pi}{3}\times304\\\\=2546.784445\\\\\approx 2546.78[/tex]
Thus, the capacity of the container is 2546.78 cm³.
kind of urgent!! Please describe a real-world scenario in which it would be important to know how to apply scale factors.
One example is that you're given blueprints and you want to find out how large the object is in real life, rather than just on paper. The scale factor will help find those real life measurements. Let's say a house on paper is 2 inches long, and also let's say the scale factor is labeled "1 inch = 20 feet". This means the real life house is 2*20 = 40 feet long.
You could think of it as 1 inch = 20 feet, so 2 inches = 40 feet (multiply both sides by 2).
Scale factors are also used in maps. Look at the bottom corner of any map and it will show you how each distance on paper corresponds to a real life distance (in miles or kilometers maybe). Usually it shows a checkered "ruler" of sorts.
Answer:
everyday living
Step-by-step explanation:
Scale factors are involved in virtually every aspect of the logistics of everyday life. Scale factors of number of units, price per unit, and tax rate are applied to every shopping experience. Scale factors of miles per gallon, or daily rate, or number of travelers are applied to most travel experiences. Scale factors of number of people and/or serving size are applied to food planning--even when ordering pizza.
Scale factors are involved in virtually every aspect of engineering, from specifying or estimating a job, to scheduling, material choice, purchase, and application. Sometimes, these are "rules of thumb", and sometimes they are based on careful calculation.
Much of modern technology is based on the observation that computing power doubles every 2 years or so--a scale factor consistently seen for more than 50 years. This has informed systems planning in many different industries.
Find the exact value of cos A in simplest radical form.
Answer:
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Step-by-step explanation:
Since we are finding cos A we have
[tex] \cos(A) = \frac{AC}{AB} [/tex]From the question
AC = √96
AB = 14
Substitute the values into the above formula
That's
[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]We have the final answer as
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Hope this helps you
6 + x is an example of _____.
a formula
an expression
a constant
a variable
Answer:
An expression
Step-by-step explanation:
The constant in this case would be 6 because it never changes.
The variable would be x because the value of x can change.
A formula is a mathematical rule, which 6 +x is not.
Therefore, 6+x is an expression.
Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are (–1, 0). What are the coordinates of B? B( , )
Answer:
-2, 3
Step-by-step explanation:
To find the coordinates of B, we need to understand the translation that has taken place. In a translation, each point of a figure is moved the same distance and in the same direction.
In this case, point A(5, 1) has been translated to point A'(6, -2). To find the distance and direction of the translation, we subtract the coordinates of A from the coordinates of A': Translation Vector [tex]= (6 - 5, -2 - 1) = (1, -3)[/tex] The translation vector represents the change in x and y coordinates between the original figure and its translated image.
Since B' has coordinates (-1, 0), we can apply the translation vector to find the coordinates of B as follows: B = B' - Translation Vector B [tex]= (-1, 0) - (1, -3)[/tex] B [tex]= (-1 - 1, 0 - (-3)) B = (-2, 3)[/tex] So, the coordinates of B are (-2, 3).
To know more about Translation Vector visit:
https://brainly.com/question/29027060
#SPJ2
find the co efficient of m in the expression of ( m/2-3/2) ( m+2/3)
Answer:
Step-by-step explanation:
We will get m when we multiply (m/2)*(2/3) & m *(-3/2)
[tex]\frac{m}{2}*\frac{2}{3}+m*\frac{-3}{2}=\frac{m}{3}-\frac{3m}{2}\\\\\\=m(\frac{1}{3}-\frac{3}{2})\\\\\\=m(\frac{2}{6}-\frac{9}{6})\\\\\\=\frac{-7}{6}m[/tex]
Coefficient of m = -7/6
Bruno is designing his next skateboard. The skateboard store has 3 types of grip tape, 13 types of decks, 7 types of trucks, 4 types of bearings, and 2 types of wheels. How many different skateboards can Bruno create? Assume each skateboard will contain only one type of each component.
Answer:
2184 different combinations
Step-by-step explanation:
To find how many different combinations are possible, multiply all of the values:
3 * 13 * 7 * 4 * 2 = 2184 different combinations
Answer:
2,184 different skateboards.
Step-by-step explanation:
You would have to multiply
3 x 13 x 7 x 4 x 2 = 2184
If it helps you then please mark it as brainliest!
For the following system, if you isolated x in the first equation to use the substitution method, what expression would you substitute into the second equation?
−x + 2y = −6
3x + y = 8
Answer:
x = 2y + 6
Step-by-step explanation:
-x + 2y = -6
-x = -6 - 2y
x= 6 + 2y
x = 2y + 6
what number times itself 3 times go into 343
Answer:
According to an expert your answer is 7.
Step-by-step explanation:
since the unkown number is multiplied by itself what we need to do to get out answer is to work backwards. Thats where we cube root 343 to get 7
HOPE IT HELP!!!!!!!!!!!!IF IT REALLY HELPS SO PLZ MARK ME AS BRAINIESTFind the coordinates of point G that lies along the directed line segment from F(-1, -1) to H(-8, 20) and partitions the segment in the ratio of 5:2.
Answer:
coordinates of point g is ( -6, 14)
Step-by-step explanation:
The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).
___________________________________________
given point
F(-1, -1) to H(-8, 20)
ratio : 5:2
the coordinates of point g is
(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)
=> (-2 -40/7 , -2+100/7)
=> (-42/7, 98/7)
=>( -6, 14)
Thus , coordinates of point g is ( -6, 14)
Each packet of the cooking oil weighs 2/5th of a kilogram and one kilogram of the cooking oil costs $6.5. Sara went to the grocery shop to buy some items to stock her kitchen. If she bought 8 packets of the cooking oil, how much money did she spend? A $19.60 B $18.20 C $20.80 D $23.40
Answer:
C) $20.80
Step-by-step explanation:
1 kg of cooking oil = $6.5
1 packet of cooking oil =2/5 kg
If 1 kg of cooking oil = $6.5
2/5kg of cooking oil = $X
Cross Multiply
1kg × $X = 2/5kg × $6.5
$X = 13/5
$X = 2.6
Hence 2/5kg of oil cost $2.6
Since 1 packet of oil = 2/5kg of oil , 1 packet of oil cost $2.6
The amount she spent if she bought if she bought 8 packets of the cooking oil is calculated as:
1 packet of oil = $2.6
8 packets of oil =
$2.5 × 8
= $20.80
Therefore,if Sara bought 8 packets of oil, the amount she would spend = $20.80
Factorize Completely
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Factor [tex]2x^3-3x^2-17x+30[/tex]
[tex]2x^3-3x^2-17x+30[/tex]
= [tex]( x - 2) ( x + 3) ( 2x - 5)[/tex]
So your answer would be : [tex]( x - 2) ( x + 3) ( 2x - 5)[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
HELP!!! Monica measures the number of bacteria that are living on her petri dish. Each day, she measures the amount of change in the number of bacteria. These amounts create a geometric sequence. Use the data in the table to determine the sum of the amounts of change in the bacteria after the seventh day. Day Amount of Change in Bacteria 1 2 2 −8 3 32 4 −128 A) −6553.2 B) −10.8 C)6554 D)11.6
Answer:
The correct option is;
C) 6554
Step-by-step explanation:
The given data are;
Day, Amount of change in Bacteria
1, 2
2, -8
3, 32
4, -128
Given that the data follows a geometric sequence, we have;
The first term of the series = 2, the common ratio = -4, the sum of a geometric progression is given by the following formula;
[tex]S_n = \dfrac{a \times \left (r^n - 1\right )}{r - 1}[/tex]
Which gives;
[tex]S_7 = \dfrac{2 \times \left ((-4)^7 - 1\right )}{(-4) - 1} = \dfrac{2 \times \left (-16384- 1\right )}{-4 - 1} = \dfrac{2 \times \left (-16385\right )}{-5} = 6554[/tex]
Therefore, the correct option is C) 6554.
Kelly bought a crate of floor tiles for $95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles.
Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, to the nearest cent.
Answer:
$1.60 a crate
Step-by-step explanation:
t= 95.94/(6x20)
(6x20)= 60
95.94/60
$1.60
Answer:
Step-by-step explanation:
i) Cost per box = cost of a crate ÷ Number of boxes in the crate
b = 95.94 ÷ 6
b = $ 15.99
ii) Cost per tile = Cost per box ÷ Number of tiles in a box
t = b ÷ 20
t = 15.99 ÷20
t = $ 0.7995
If the product of two matrices is AB=1/-3/5 over 2/5/7, what are the dimensions of Matrix B if A is a 2x3 matrix?
Answer:
Matrix multiplication is associative: ( A B ) C = A ( B C ) \displaystyle \left(AB\right)C=A\left(BC\right) (AB)C=A(BC).
Matrix multiplication is distributive: C(A+B)=CA+CB,(A+B)C=AC+BC. C ( A + B ) = C A + C B , ( A + B ) C = A C +
Find the 9th term of the geometric sequence whose common ratio is 23 and whose first term is 3
Answer:
2.35 x 10^11
Step-by-step explanation:
The formula for finding the nth term in a geometric sequence is ar^n-1.
a = 3, r = 23, and n = 9:
3(23)^9-1 = 3(23)^8 = 2.35 x 10^11.
The perimeter of a rectangle is 10 feet. If twice the width is equal to half of the length , find the dimensions of this rectangle.
WRITE AS AN EQUATION
w = 1ft
l = 4ft
Step-by-step explanation:P =2w + 2l
2w = l/2 => l = 4w
10ft = 2w + 2×4w
10ft = 2w + 8w
10ft = 10w
w = 10ft/10
w = 1 ft
l = 4w
l = 4×1ft
l = 4 ft
Answer:
length = 4 ft
Width = 1 ft
Step-by-step explanation:
Let length = l ft
Width = w feet
[tex]\frac{1}{2}l = 2w\\\\l = 2w*2\\\\l = 4w[/tex]
Perimeter = 10 ft
2*(l +w)= 10
2*( 4w + w ) = 10
2*5w = 10
10w = 10
Equation: 10w = 10
Divide both sides by 10
10w/10 = 10/10
w = 1 ft
Plug in the value of w in l = 4w
l = 4 *1
l = 4 ft
Please answer ASAP!!
plssss
Answer:
86°
Step-by-step explanation:
b = 29× 2 = 58
d= [180-(86+29)]×2 = 130
a=c=x
a+b+c+d = 360
2x+188= 360
2x= 172
x= 86
a = c = 86°
Please Help me with this math question
find the slope between (0, 6) and (-3,9)
Answer:
-1
Step-by-step explanation:
The formula for finding a slope is: m = (change in y)/(change in x)
Find the change in each value
Y: 9 - 6 = 3
X: -3 - 0 = -3
Input the values
m = 3/-3
m = -1
I would start this problem by setting up a table.
In the left column, we will have our x values
and in the right column, we have our y values.
Put our first ordered pair on the top and second on bottom.
We can see the y values go from 6 to 9 so change in y is 3.
The x values go from 0 to -3 so change in x is -3.
The slope is equal to the rate of change or change in y / change in x.
So our slope is 3/-3 of -1.
please solve this fast.
Answer:
- 24 - 70i
Step-by-step explanation:
Given
([tex]\sqrt{5}[/tex] - 7i)²
= ([tex]\sqrt{5}[/tex] - 7i)([tex]\sqrt{5}[/tex] - 7i)
= 5 - 7[tex]\sqrt{5}[/tex] i - 7[tex]\sqrt{5}[/tex] i + 49i² ( note that i² = - 1 )
= 5 - 14[tex]\sqrt{5}[/tex] i - 49
= - 44 - 14[tex]\sqrt{5}[/tex] i
Answer:
Step-by-step explanation:
(a - b)² = a² - 2ab + b²
[tex][\sqrt{5} - 7i]^{2}= (\sqrt{5})^{2} - 2*\sqrt{5}*7i + (7i)^{2}\\\\\\= 5 - 14i\sqrt{5}+7^{2}*i^{2}]]= 5 -14i\sqrt{5} +49 * -1\\\\= 5 -14i\sqrt{5} - 49\\\\= -44 - 14i\sqrt{5}[/tex]
I need the answers for my bro
Answer:
1)He will use 144 squares in his design
2)He will use 36 squares in his design
Step-by-step explanation:
1) There is 12 squares going horizontally and 12 squares going vertically meaning the total amount of squares needed is:
12 x 12 = 144 inch squares
2) If he wants to cover a smaller box that is 1/2 feet big than he would take the square of 1/2 which is 1/4 and multiple it to the original answer to get the answer of the new question
144 x (1/4) = 36 inch squares
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using α = .05.A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = −7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using α = .05.
Answer:
1.734
Step-by-step explanation:
Given that:
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles).
The fitted regression is Time = −7.126 + .0214 Distance
Based on a sample size n = 20
And an Estimated standard error of the slope = 0.0053
the critical value for a right-tailed test to see if the slope is positive, using ∝ = 0.05 can be computed as follows:
Let's determine the degree of freedom df = n - 1
the degree of freedom df = 20 - 2
the degree of freedom df = 18
At the level of significance ∝ = 0.05 and degree of freedom df = 18
For a right tailed test t, the critical value from the t table is :
[tex]t_{0.05, 18} =[/tex] 1.734
Solve the system by substitution.
y = -2
y =
5x + 40
Answer:
x = 8.4
y = -2
Step-by-step explanation:
Step 1: Sub y=-2 into y=5x + 40
-2 = 5x + 40
Step 2: Solve for 'x'
-2 = 5x +40
-42 = 5x
x = 42/5
x = 8.4
Step 3: Solve for 'y'
y is given in the question, y=-2
Which statement about the transformation is true?
Consider the transformation.
It is isometric because the side lengths remained the
same.
It is isometric because all angle measures remained the
same.
It is not isometric because the side lengths did not remain
the same.
It is not isometric because the angle measures did not
remain the same.
The image of the transformation is missing so i have attached it;
Answer:
Option C - The transformation is not isometric because the lengths did not remain the same.
Step-by-step explanation:
Transformation means that it preserves the length of the original figure which means that it is a distance preserving transformation.
Now, from the image of the question attached, the two figures can be said to be isometric if they are congruent.
Now, for the figure displaying the transformation we can see that the size of the original figure has changed.
We can see that the figure is dilated by a scale factor of 2 as each of the sides of the polygon which is a trapezoid is increased by a factor of 2.
Due to the fact that the lengths of sides of the original figure and transformed figure are are not same, we can say that the lengths are not preserved.
Thus, the transformation is not isometric because the lengths did not remain the same.
Answer:
C : It is not isometric because the side lengths did not remain the same.
Credits go to the person above me.
;)
Step-by-step explanation:
EDGE 2021
A delivery truck company just bought a new delivery truck and they need to know the maximum volume it can carry. In the front of the truck, there is an extra ledge that sticks out over the driver's cab for extra storage space. What is the maximum amount of cargo that can fit into the new truck?
Answer:
The answer is below
Step-by-step explanation:
To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.
Volume = length × width × height.
Firstly 1 feet (1') = 12 inches (12"),
For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet
Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³
For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet
Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³
The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³
convert 0.129 into a percentage
Answer:
12.9%
Step-by-step explanation:
Answer:
0.129%
Step-by-step explanation:
Just add the percent sign
Consider the equation: x 2 − 6 = 2 − 18 x x 2 −6=2−18xx, squared, minus, 6, equals, 2, minus, 18, x 1) Rewrite the equation by completing the square. Your equation should look like ( x + c ) 2 = d (x+c) 2 =dleft parenthesis, x, plus, c, right parenthesis, squared, equals, d or ( x − c ) 2 = d (x−c) 2 =dleft parenthesis, x, minus, c, right parenthesis, squared, equals, d. 2) What are the solutions to the equation? Choose 1 answer: Choose 1 answer: (Choice A) A x = 9 ± 89 x=9±89x, equals, 9, plus minus, 89 (Choice B) B x = − 9 ± 89 x=−9±89x, equals, minus, 9, plus minus, 89 (Choice C) C x = 9 ± 89 x=9± 89 x, equals, 9, plus minus, square root of, 89, end square root (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Answer:
1. (x+9)^2 = 89
2. (Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
Step-by-step explanation:
x^2 - 6 = 2 - 18x
1) rewrite the equation by completing the square
x^2 - 6 = 2 - 18x
x^2 + 18x = 2+6
x^2 + 18x = 8
Find the half of the coefficient of x and square it
18x
Half=9
Square half=(9)^2
=81
Add 81 to both sides
x^2 + 18x = 8
x^2 + 18x + 81 = 8 + 81
x^2 + 18x + 81 = 89
(x+9)^2 = 89
Check:
(x+9)(x+9)=89
x^2 + 9x + 9x + 81=89
x^2 + 18x +81 =89
2) (x+9)^2 = 89
√(x+9)^2 = √89
x+9=√89
x=√89 - 9
It can be rewritten as
x= -9 ± √89
(Choice D) D x = − 9 ± 89 x=−9± 89 x, equals, minus, 9, plus minus, square root of, 89, end square root
