Answer:
119.32 m
Step-by-step explanation:
The circumference of a circle is given by
C = 2*pi*r
C = 2 (3.14) *19
C = 119.32
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.c
Answer:
[tex]\displaystyle y=\frac{1}{4}x^2[/tex]
Step-by-step explanation:
Let (x, y) be a point on the parabola.
By definition, any point on the parabola is equidistant from the focus and the directrix
The distance from the focus is given by:
[tex]\begin{aligned} d&=\sqrt{(x-0)^2+(y-1)^2\\\\&=\sqrt{x^2+(y-1)^2}\end{aligned}[/tex]
The distance from the directrix is given by:
[tex]d=|y-(-1)|=|y+1|\text{ or } |-1-y|[/tex]
So:
[tex]\sqrt{x^2+(y-1)^2}=|y+1|^[/tex]
Square both sides. Since anything squared is positive, we can remove the absolute value:
[tex]x^2+(y-1)^2=(y+1)^2[/tex]
Square:
[tex]x^2+(y^2-2y+1)=y^2+2y+1[/tex]
Hence:
[tex]x^2=4y[/tex]
So, our equation is:
[tex]\displaystyle y=\frac{1}{4}x^2[/tex]
A scale model of a sculpture has a scale of 2:49.
The height of the model is 24 cm.
Find the height of the actual sculpture.
Give your answer in m.
Answer:
ok so if the scale is 2:49 that can be simplified as 1:98
so that means the real one is 98 times bigger then 24
98*24= 2352 cm or 196 feet
quiere cercar con alambre un terreno rectangular que mide 180 m (metros) de largo por 85 m de ancho.¿cuantos metros de alambre necesita? ¿Con qué concepto matemático relacionas esta situación?
You want to wire a rectangular piece of land that is 180 m (meters) long by 85 m wide. How many meters of wire do you need? With what mathematical concept do you relate this situation?
Answer:
The wire required to fence is 530 m.
Step-by-step explanation:
Length, L = 180 m
Width, W = 85 m
The perimeter of the wire is
P = 2 (L + W)
P = 2 (180 + 85)
P = 530 m
So, the wire required to fence is 530 m.
What is the direct variation between x and y when x=7 and y=3 1/2?
Answer:
[tex]{ \tt{y \: \alpha \: x }} \\ { \tt{y = kx}} \\ \\ { \bf{3 \frac{1}{2} = k \times 7 }} \\ { \bf{k = \frac{1}{2} }} \\ \\ { \tt{y = \frac{1}{2}x }} \\ \\ { \tt{y = 0.5x}}[/tex]
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer: x= -7/8
Step-by-step explanation:
Hope it helps you
Rami is solving the equation for x .
–6x – 1 = 5
–6x – 1 Empty square 1 = (5 Empty square 1)
–6x = 6
–6x Empty circle – 6 = 6 Empty circle –6
x = –1
Which operation symbols should Rami write in the Empty squareand the Empty circle?
Answer:
Empty square = +
Empty Circle = ÷
Step-by-step explanation:
In order to eliminate the extra numbers from the equation you have to do the opposite of the problem. So...
-6x-1=5
-6x -1+1 = 5+1 (eliminating the 1 from the -6x side and adding it to the other side)
-6x = 6
-6x ÷ -6 = 6 ÷ -6 ( eliminating the-6 so that one side just has x)
so... x= -1
Answer: Option B is your correct answer.
Anyone know the answer to this ?!?
Answer:
12/25 = 48/100 = .48 = 48%
Step-by-step explanation:
6. The diagram on the right shows right-angled triangles POR
and PRS. Given that tan 0 =
3
4
in em, the length of
(a) PR
(b) RS
Q
9 cm
R
Answer:
The answer is below
Step-by-step explanation:
Trigonometric ratios shows the relationship between the sides of a right angled triangle and its angles. Some trigonometric ratios are:
sinθ = opposite / hypotenuse, cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent.
In triangle PQR:
tanθ = QR / PQ
substituting gives:
3/4 = 9 / PQ
PQ = 9 * 4 / 3 = 12 cm
Applying Pythagoras in triangle PQR gives:
PR² = PQ² + QR²
PR² = 12² + 9²
PR² = 144 + 81 = 225
PR = 15 cm
Also in triangle PRS:
PS = (5/3)PR = (5/3)*15 = 25 cm
PS² = PR² + RS²
25² = 15² + RS²
625 = 225 + RS²
RS² = 400
RS = 20 cm
HELP ME!
Line segment EQ consists of the points ____________. ???
Answer:
{F, G, H, I, J, K, L, M, N, O, P}
are the points between segment EQ :)
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of C'be?
5
00
NO
A
D
1
-7 -6 -5
4
-3
1
2
3
4
-2 -1 0
-1
C' = (1, [?])
-2
Given:
The rule of translation is:
[tex](x+3,y-2)[/tex]
The trapezoid ABCD on the graph.
To find:
The coordinates of the point C'.
Solution:
From the given graph, it is clear that the coordinates of point C are (-2,4).
The rule of translation is:
[tex](x,y)\to (x+3,y-2)[/tex]
Using this rule of translation, we get
[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]
[tex]C(-2,4)\to C'(1,2)[/tex]
Therefore, the coordinates of the point C' are (1,2).
If a line has a slope of 3, what is the slope of a line perpendicular to it?
Answer:
- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]
Here m = 3 , then
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{3}[/tex]
solve for x: 3(x-5)+4x-2=4
Answer:
x = 3
Step-by-step explanation:
3(x−5)+4x−2=4
Step 1: Simplify both sides of the equation.
3(x−5)+4x−2=4
(3)(x)+(3)(−5)+4x+−2=4(Distribute)
3x+−15+4x+−2=4
(3x+4x)+(−15+−2)=4(Combine Like Terms)
7x+−17=4
7x−17=4
Step 2: Add 17 to both sides.
7x−17+17=4+17
7x=21
Step 3: Divide both sides by 7.
7x
7
=
21
7
x=3
As a salesperson at Trading Cards Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $500 worth of merchandise in one month, he is paid $410. If he sells $900 of merchandise in one month, he is paid $498.
Answer:
Justin's salary will be $1048 when he sells $3400 worth of merchandise.
Step-by-step explanation:
If the salesperson receives a monthly base pay and the commission on the sales expression that represents his monthly pay,
y = B + C(x)
Here y = Monthly pay
B = Base pay
C = percentage of commission
x = Amount of sales done
If he sells $500 worth of merchandise in a month, he earns $410,
410 = B + C(500) -----(1)
If he sells $900 worth of merchandise in a month, he earns $498,
498 = B + C(900) ------(2)
By subtracting equation (1) from equation (2),
498 - 410 = 900C - 500C
88 = 400C
C = [tex]\frac{88}{400}[/tex]
C = 0.22
From equation (1),
410 = B + 0.22(500)
B = 410 - 110
B = $300
Therefore, expression for the monthly earning will be,
y = 300 + 0.22(x)
Justin's salary when he sells $3400 worth of merchandise in a month,
y = 300 + 0.22(3400)
y = 300 + 748
y = $1048
Therefore, Justin's salary will be $1048.
solve it : -
[tex] \sqrt{27 \times3 } [/tex]
_______
Answer:
9
Step-by-step explanation:
sqrt(27*3)
sqrt(81)
sqrt(9*9)
9
Answer:
9
Step-by-step explanation:
27 * 3 = 81
√81 = 9
Choose the function that is a "parent function". O f(x) = x=3 o f(x) = (x - 3)2 O o f(x)= X O f() = x-31
Answer:
option D is the correct answer I think so
Which equation can you use to solve for the volume of the cake?
A. 60 × 40 × 30 × 10 = V
B. (30 + 60 + 10) + (30 × 60 × 10) = V
C. (40 × 60 × 10) + (30 × 60 × 10) = V
D. (30 × 60 × 10) + (30 × 40 × 10) = V
Answer:
C. (40 × 60 × 10) + (30 × 60 × 10) = V
Step-by-step explanation:
Picture of the cake can be found in the attachment below :
To solve, we resolve the cake into two distinct boxes :
The lower which is lateral sits parallel, whose volume, = (length * width * height) = (60 * 30 * 10)
And the other which sits vertically ;
Volume = (length * width * height) = (10 * 60 * 40)
Then, we add;
Overall volume:
(60 * 30 * 10) + (10 * 60 * 40)
Put these numbers in order from least to greatest.
0.36,7/10, and 0.44
Answer:
0.36,0.44,7/10
Step-by-step explanation:
Answer:
0.36, 0.44, 7/10
Step-by-step explanation:
7/10=0.7=0.70
Tính :
a) (a+b+c)^2
b) (a-b-c)^2
c) (a+b-c)^2
d) (a-b+c)^2
Answer:
a.) a² + b² + c ² + 2ab + 2ac + 2bc
b.) a² + b² + c² - 2ab - 2 ac + 2bc
c ) a² + b² + c² + 2ab - 2ac - 2bc
d.) a² + b² + c² - 2ab + 2ac - 2bc
Step-by-step explanation:
Use ( a + b + c )² = a² + b² + c² + 2 × ab + 2 × ac + 2 × bc to expand all these expressiona) ( a + b + c )²
= a² + b² + c² + 2 × ab + 2 × ac + 2 × bc
= a² + b² + c ² + 2ab + 2ac + 2bc
b.) ( a - b - c )
= a² + ( - b )² + ( - c)² + 2a ( -b ) + 2a(-c) + 2(-b)(-c)
= a² + b² + c² - 2ab - 2 ac + 2bc
c.) ( a + b - c )²
= a² + b² + ( -c)² + 2ab + 2a ( - c) + 2 b( -c)
= a² + b² + c² + 2ab - 2ac - 2bc
d.) (a - b + c ) ²
= a² + ( -b)² + c² + 2a(-b) + 2ac + 2c( -b)
= a² + b² + c² - 2ab + 2ac - 2bc
[tex] \frac{1.107}{123} \times \frac{1.998}{333} = [/tex]
Answer:
45Step-by-step explanation:
[tex]\frac{1.107}{123} \times \frac{1.998}{333} = [/tex]
[tex] = > 9 \times 6[/tex]
[tex] = 45[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{1.107}{123}*\frac{1.998}{333}= 0.009 * 0.006 = 0.000054[/tex]
1107÷ 123 = 9
The dividend has 3 decimal places. So, take 3 decimal places from the right towards left in the result 0.009
1.107 ÷ 123 = 0.0009
0.009 * 0.006
First multiply 9 * 6 = 54
Now, count the number of decimal place in the multiplicands. 0.009 has 3 decimal places and 0.006 has 3 decimal places. So totally, 3+ 3 = 6 decimal places in the result
0.009 * 0.006 = 0.000054
john bought a new game system for $529 how much is he in debt
Answer:
Depending on how much he had before he bought the game system.
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Answer:
C = 20
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Step 1
We solve for C first
6A + 4B + 5C = 390....Equation 1
6A + 4B + 5.75C = 405... Equation 2
We substract Equation 1 from Equation 2
0.75C = 15
C = 15/0.75
C = 20
If f(x) = 2x-5, then f(4) is ___.
Answer:
3
Step-by-step explanation:
f(x) = 2x-5
Let x = 4
f(4) = 2*4 - 5
Multiply
f(4) = 8 -5
Subtract
f(4) = 3
HELP ASAP< BRAINLIEST IF RIGHT
Answer:
Option B.
Step-by-step explanation:
For a general function f(x), a vertical stretch of scale factor K is written as:
g(x) = K*f(x)
Also, for definition, we usually define:
for K > 1, this is an "stretch" or "dilation"
for 0 < K < 1, this is a "contraction"
Here we have:
f(x) = ∛(x + 4)
We want to find an option that is a vertical stretch from this:
So we want something like:
g(x) = K*∛(x + 4)
With K > 1
Then the correct option is B, where we have K = 2, so this is a vertical stretch of scale factor K = 2.
Which of the following are solutions to the quadratic equation? Check all that
apply.
x2 + 8x + 16 = 7
Answer:
x=-9/10
Step-by-step explanation:
2x+8x+16=7
Step 1: Simplify both sides of the equation.
2x+8x+16=7
(2x+8x)+(16)=7(Combine Like Terms)
10x+16=7
10x+16=7
Step 2: Subtract 16 from both sides.
10x+16−16=7−16
10x=−9
Step 3: Divide both sides by 10.
10x/10
=
−9/10
x=-9/10
Answer:
x = - 4 ± [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Given
x² + 8x + 16 = 7 ( subtract 16 from both sides )
x² + 8x = - 9
Using the method of completing the square
add ( half the coefficient of the x- term)² to both sides
x² + 2(4)x + 16 = - 9 + 16
(x + 4)² = 7 ( take the square root of both sides )
x + 4 = ± [tex]\sqrt{7}[/tex] ( subtract 4 from both sides )
x = - 4 ± [tex]\sqrt{7}[/tex]
Then
solutions are x = - 4 - [tex]\sqrt{7}[/tex] , x = - 4 + [tex]\sqrt{7}[/tex]
What is the slope that passes through the points (-9.-8) (-15,-16)
Answer:
Slope/gradient is 4/3
Step-by-step explanation:
Have a nice day
Which of the following steps were applied to ABCD to obtain A'B'C'D
Answer:
B. 3 units right and 4 units up
The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
We have to given that;
Translation applied to ABCD to obtain A'B'C'D.
Now, We get;
Coordinate of A = (2, 3)
Coordinate of A' = (5, 7) = (2 + 3, 3 + 4)
Hence, The correct steps were applied to ABCD to obtain A'B'C'D is,
⇒ 3 units right and 4 units up
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Which describes the
correlation shown in the scatterplot? help pls
Answer:
B
Step-by-step explanation:
There is a negative correlation. The direction of a line if we plot it generally through thi scatter plot would be going down, negative.
Answer:
Negative Correlation
Step-by-step explanation:
Because the graph shows that the y axis is on 4 and then goes down to 2
The two cross sections shown are taken parallel to their respective bases. The cross sections have the same area. If the heights of the two solids are equal, find the volume of the cylinder. Round your answer to the nearest hundredth. A. 465.10cm3 B. Please select the best answer from the choices provided A B C D
Answer:
489.40 cm³
Step-by-step explanation:
Since the cross section is parallel to their respective bases, hence:
Area of the cylinder cross section = area of the circular base = πr²
where r is the radius of the cylinder base.
Area of other cross section = area of rectangle base = 3.8 cm * 8.1 cm
Since both cross sections have same area, hence:
Area of cylinder cross section = Area of rectangle base
πr² = 8.1 * 3.8
r² = 9.8
r = 3.1 cm
Volume of the cylinder = πr²h = π(3.1)²(15.9) = 489.40 cm³
help please on all of these
the answer is on the picture
2. Find the perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2).
Answer:
12 units
Step-by-step explanation:
the perimeter = 3 + 4 + 5 = 12 units
The perimeter of a triangle is 12 cm.
To find the perimeter of the triangle.
What is triangle?
A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.
Use the distance formula to find the length between point A and B, B and C, C and A. Then add all three lengths together to get the perimeter.
Distance = √ ( (x2 - x1)2 + (y2 - y1)2 )
Points A and B:
d = √(-3 +3)2 + (2 - 5)2
d = √ 0 + 9
d = √9
d = 3
Points B and C:
d = √ (1+ 3)2 + (2 -2)2
d = √ 16 + 0
d = √ 16
d = 4
Points C and A:
d = √ (-3 - 1)2 + (2 -5)2
d = √ 16 + 9
d = √ 25
d = 5
Perimeter= 3 + 5 + 4 = 12
So, the perimeter of a triangle is 12 cm.
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