Answer:
The coordinates of the image of Δ ABC are:
A' (-2.5, -2.5), B' (10, 0), C' (5, 7.5)
Step-by-step explanation:
Let us revise the rule of dilation
If the point (x, y) dilated by scale factor k centered at the origin, then the image of the point is (k x, k y)
We will use this rule to solve the question
∵ The vertices of triangle ABC are A (-1, -1), B (4, 0), C (2, 3)
∵ The scale factor of a dilation is 2.5
∴ k = 2.5
∵ The center is the origin
→ That means multiply each coordinate of the points by 2.5
∴ A' = (-1 × 2.5, -1 × 2.5)
∴ A' = (-2.5, -2.5)
∴ B' = (4 × 2.5, 0 × 2.5)
∴ B' = (10, 0)
∴ C' = (2 × 2.5, 3 × 2.5)
∴ C' = (5, 7.5)
The coordinates of the image of Δ ABC are:
A' (-2.5, -2.5), B' (10, 0), C' (5, 7.5)
What is 3.4 x 10^-6 in standard notation?
Answer:
The answer is 0.0000034
Step-by-step explanation:
Which of the following has the lowest unit price?
F. 20oz : $9.00
G. 16oz : $7.39
H. 12oz : $5.29
I. 5oz : $2.39
Find the coordinates of the point (x,y) at the given angle θ on a circle of radius r centered at the origin. Show all work. Round decimal to three places. (5 points) θ=215° and r=4 Type equation here. Type equation here. (5 points) θ=-30° and r=1 Type equation here. Type equation here.
Answer:
(i) The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
Step-by-step explanation:
In this exercise we must find the equivalent coordinates in rectangular form from polar form. That is:
[tex](x, y) = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex]
Where:
[tex]r[/tex] - Norm of vector, dimensionless.
[tex]\theta[/tex] - Direction of vector with respect to +x semiaxis, measured in sexagesimal degrees.
(i) ([tex]r = 4[/tex], [tex]\theta = 215^{\circ}[/tex])
[tex](x. y) = (4\cdot \cos 215^{\circ}, 4\cdot \sin 215^{\circ})[/tex]
[tex](x, y) = (-3.277,-2.294)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (-3.277,-2.294)[/tex].
(ii) ([tex]r = 1[/tex], [tex]\theta = 30^{\circ}[/tex])
[tex](x. y) = (1\cdot \cos 30^{\circ}, 1\cdot \sin 30^{\circ})[/tex]
[tex](x, y) = (0.866, 0.5)[/tex]
The equivalent coordinates in rectangular form are [tex](x, y) = (0.866, 0.5)[/tex].
Sara owns a tree farm. Variety A of a pine tree is shipped to her at 12 inches tall and grows at a rate of 14 inches per year. Variety B of a pine tree is shipped to her at 2 inches tall and grows at a rate of 16 inches per year.
Which equation can be used to determine the number of years, x, at which the trees will be an equal height?
14 + 12x = 16 + 2x
14 + 12, x, = 16 + 2, x
16 + 12x = 14 + 2x
16 + 12, x, = 14 + 2, x
12 + 16x = 2 + 14x
12 + 16, x, = 2 + 14, x
12 + 14x = 2 + 16x
12 + 14, x, = 2 + 16, x
Answer:
Step-by-step explanation:
X=5
The recipe says it serves 8 people. By what number should jenny multiply each ingredient to make enough meatloaf for 40 people?
Answer:
5
Step-by-step explanation:
8*5=40 so you multiply the ingredients by 5
Which expression is equivalent to 36 + 54?
A=4(8 + 14)
B=9(4 + 54)
C=12(3 +4)
D=18(2 +3)
Which equation can be used to solve the problem?
750 is 150 percent of what?
Answer:
it would be 750/500
Step-by-step explanation:
150% of 500 is 750
HELP WILL MARK BRAINLIEST!!!
A quadratic function for a parabola has axis of symmetry x = -2, points (-3, 2) and (0,11) and opens upward. What is the value of a? What is the vertex?
Answer:
Let's see what to do buddy..
Step-by-step explanation:
_________________________________
STEP (1)
We know that the quadratic functions form are like this :
[tex]y = a \: {x}^{2} + b \: x + c [/tex]
The quadratic function opens upward so ;
[tex]a > 0[/tex]
The axis of parabolic symmetry passes through the vertex of the parabolic.
So we know that x vertex is equal to -2.
The vertex's x is finding from this equation:
[tex]x = - \frac{b}{2a} \\ [/tex]
So we have :
[tex] - 2 = - \frac{b}{2a} \\ [/tex]
Multiply the sides of the equation by 2a :
[tex]b = 4a[/tex]
_________________________________
STEP (2)
A quota passes through points (-3,2) and (0,11) , so points (-3,2) and (0,11) must be true in the quota equation.
[tex]y = f(x) = a{x}^{2} + bx + c \\ \\b = 4a \\ \\ y = f(x) = a {x}^{2} + 4ax + c [/tex]
[tex]f( - 3) = 2 \\ \\ a ({ - 3})^{2} + 4a( - 3) + c = 2 \\ \\ 9a - 12a + c = 2 \\ \\ - 3a + c = 2 \\ \\ \\ \\ f(0) = 11 \\ \\ a ({0})^{2} + 4a(0) + c = 11 \\ \\ c = 11 [/tex]
[tex] - 3a + c = 2 \\ \\ c = 11 \\ \\ - 3a + 11 = 2 \\ 11 \: goes \: to \: the \: other \: side \: \\ \\ - 3a = 2 - 11 \\ - 3a = - 9 \\ divided \: the \: sides \: of \: the \: equation \: by \: - 3 \\ a = 3[/tex]
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
i need help w this, thanks
Select the construction that guarantees A' is a reflection of point A across line BC
Answer:
Construction B
Step-by-step explanation:
A' is the reflection of point A across line BC
Line BC is the mirror, the distance from point A to line BC and from BC to point A' is same and is the shortest distance.
This is achieved by constructing perpendicular line from the point A to BC and extending same line by same distance from BC.
A truck can be rented from Company A for $80 a day plus $0.40 per mile. Company B charges $40 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
At____miles, the rental costs are the same from either company.
Answer:
200 milesStep-by-step explanation:
Let the required miles be x
Rental for Company A
80 + 0.4xRental for Company B
40 + 0.6xRental costs are equal when:
80 +0.4x = 40 + 0.6x0.6x - 0.4x = 80 - 400.2x = 40x = 40/0.2x = 200 milesWhen converted to speeds, which list is in order from slowest to fastest?
1.) 17 miles in 2 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes;
60 miles in 8 minutes
2.) 17 miles in 2 minutes;
60 miles in 8 minutes;
26 miles in 4 minutes;
33 miles in 6 minutes
33 miles in 6 minutes;
26 miles in 4 minutes;
60 miles in 8 minutes;
3.) 17 miles in 2 minutes
60 miles in 8 minutes;
33 miles in 6 minutes;
26 miles in 4 minutes;
Answer:
2
Step-by-step explanation:
im not 100 percent but i believe it is 2
A 22.5 ounce candle burns at the rate of one ounce every 5 hours. write an equation for the amount of candle left
Answer:
y = 22.5 - 0.2t
Step-by-step explanation:
Given;
total number of candle, n = 22.5 ounce
Rate of candle burn, R = 1 ounce per 5 hours [tex]= \frac{1 \ ounce}{5 \ hours} = 0.2 \ \frac{ounce}{hour}[/tex]
The amount of candle left = total initial value - amount burnt
let the amount let = y
y = 22.5 - 0.2t
where;
t is the time in which the candle is burnt
Thus, the equation for the amount of candle left is given by;
y = 22.5 - 0.2t
At a bicycle shop, all the bicycles are on sale for $25 off the regular price. If p represents the regular price in dollars of a bicycle, which expression gives the sale price in dollars?
The sides of a triangle are as follows:
AB = 10 in
BC = 14 in
AC = 8 in
Order the angles of the triangle from smallest to biggest.
<A, <C, <B
<B, <A, «C
<B, <C,<A
<A, <B, <C
Answer:
<B,<C,<A
Step-by-step explanations:
*Two buses were coming from two different places situated just in the opposite
direction. The average speed of one bus is 5 km/hr more than that of another on
and they had started their journey in the same time. If the distance between
places is 500 km and they meet after 4 hours, find their speed.
Answer: 60 km/hr and 65 km/hr
Step-by-step explanation:
o-----------------------------------←500→-------------------------------------o
Bus 1: rate = r + 5 Bus 2: rate = r
time = 4 time = 4
distance = d distance = 500 - d
Use distance = rate x time
Bus 1: d = 4(r + 5) Bus 2: 500 - d = 4(r)
d = 4r + 20 -d = 4r - 500
d = 500 - 4r
Solve the System of Equations using the Substitution method:
4r + 20 = 500 - 4r
8r + 20 = 500
8r = 480
r = 60
Bus 1: rate = r + 5 Bus 2: rate = r
= 60 + 5 = 60
= 65
Distance between both buses = 500km
Time taken by them to meet each other = 4hr
Let speed of bus A be v km/hr.
ATQ, speed of bus B is 5km/ hr more than that of bus A.
∴ Speed of bus B will be (v + 5) km/hr.
★ Diagram :
[tex]\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,2)\thicklines\put(1,1){\circle*{0.2}}\put(5,1){\circle*{0.2}}\put(1,1){\vector(1,0){1}}\put(5,1){\vector(-1,0){1.5}}\put(0.2,0.9){A}\put(5.5,0.9){B}\put(1.4,1.2){v}\put(3.85,1.2){v+5}\put(2.35,0.4){\sf{500\;km}}\put(2.2,0.5){\vector(-1,0){1.3}}\put(3.55,0.5){\vector(1,0){1.5}}\end{picture}}[/tex]
★ As we know that,
Speed = Distance/Time ... (I)Assuming both buses as point masses,
Relative speed of object A wrt object B when the object B moves in the opposite direction of A is given by
[tex]\boxed{\bf{v_{AB}=v_A+v_B}}[/tex]Relative speed of bus A wrt B :
[tex]:\implies\:\sf{v_{AB}=v_A+v_B}[/tex]
[tex]:\implies\sf\:v_{AB}=v+(v+5)[/tex]
[tex]:\implies\bf\:v_{AB}=2v+5[/tex]
By substituting values in (I), we get
[tex]\leadsto\sf\:v_{AB}=\dfrac{d}{t}[/tex]
[tex]\leadsto\sf\:2v+5=\dfrac{500}{4}[/tex]
[tex]\leadsto\sf\:2v+5=125[/tex]
[tex]\leadsto\sf\:2v=120[/tex]
[tex]\leadsto\sf\:v=60\:kmph[/tex]
Speed of bus A = 60 kmphSpeed of bus B = (v + 5)
Speed of bus B = 65 kmphHope It Helps!Please help me solve this!! If you do think yu so much and have a nice day or night
Answer:
5668
Step-by-step explanation:
What’s there answer for this 4.5x10^-5
Answer:
0.000045
Step-by-step explanation:
-3a+7=22 solve for a show work
Answer:
a = -5
Step-by-step explanation:
-3a + 7 = 22
Subtract 7 from both sides.
-3a = 15
Divide both sides by -3.
a = -5
Answer:
- 5
Step-by-step explanation:
Step 1:
- 3a + 7 = 22 Equation
Step 2:
- 3a = 15 Subtract 7 on both sides
Step 3:
a = 15 ÷ - 3 Divide
Answer:
a = - 5
Hope This Helps :)
What’s -6y + 4x=5 in ymx+b
Answer:
[tex]\boxed {y = \frac{2}{3}x - \frac{5}{6}}[/tex]
Step-by-step explanation:
First you need to solve the expression in order to get the expression in Slop-Intercept Form:
[tex]y = mx + b[/tex]
-The following equation:
[tex]-6y + 4x = 5[/tex]
Solve:
[tex]-6y + 4x = 5[/tex]
[tex]-6y + 4x - 4x = 5 - 4x[/tex]
[tex]-6y = 5 - 4x[/tex]
[tex]\frac{-6y}{-6} = \frac{5 - 4x}{-6}[/tex]
[tex]y = \frac{5 - 4x}{-6}[/tex]
[tex]\boxed {y = \frac{2}{3}x - \frac{5}{6}}[/tex]
Therefore, the expression in Slope-Intercept Form is [tex]y = \frac{2}{3}x - \frac{5}{6}[/tex].
If 7 gift bags cost $6.65 and the price of each bag is the same, how much does each bag
cost
Answer:
$0.95
Step-by-step explanation:
6.65 ÷ 7 = 0.95
0.95
If the function f(x) = (2x - 3) is transformed to g(x) = (-2x - 3), which type of transformation occurred?
OA.
vertical shift
OB.
vertical reflection
O C.
horizontal reflection
OD.
horizontal shift
f (x) = cx + 3
In the function above, c is a constant. If f (1) = 1, what is the value of f (-4) ?
If f(1) = 1 that means c is -2 because when you substitute x = 1 and when c = -2, you'll get f(1) = -2(1)+3 = -2+3 = 1
So the constant c is -2 and that means the value of f(-4) is
f(-4)=-2(-4)+3=8+3=11
Thus, the value of f(-4) is 11.
About why does "c" have to be -2, here's the proof.
Given y = f(x), therefore.
y=cx+3
Since when x = 1 and y = 1, then Substitute x = 1 and y = 1, thus 1 = c+3
1 - 3 = c and therefore, -2 = c #
So this is the proof that c = -2
Line g has an equation of y=-3/2x – 8. Line w, which is parallel to line g, includes the
point (4, -3). What is the equation of line w?
Answer:
y = -3/2x + 3
Step-by-step explanation:
If two lines are parallel to each other the slopes are the same.
So line w's slope would be the same as line g's -3/2
Now all we have to do is pug in the points to find the y-intercept.
-3 = -3/2(4) + b (b represents the y-intercepts)
-3 = -6 + b (add 6 on both sides)
3 = b
y = -3/2x + 3 is the equation for w.
the question is in the picture
Answer:
(x) = 1/2x-3/2
Step-by-step explanation:
The inverse is the opposite of the equation given in this case is 2x+3 and the inverse is when you switch the x and the y and you solve for y.
13.8___13.80 < > = Complete the inequality statement with the symbol that makes it true
Answer:
=
Step-by-step explanation:
because 13.80 equal 13.8 . Because how we know we need to delite 0 snd it will be 13.8
Answer:
13.8 = 13.80
Step-by-step explanation:
13.8 and 13.80 are the same values.
Hope it helped!
in the problem above 2 1/3 is the. answers -> quotient divisor greatest common factor dividend multiple ?
Answer:
I am pretty sure it is 1 because you can divide when it is in inproper for
hint it is 7/3
Step-by-step explanation:
line Y is parallel to line W. what is the measurement of
Answer:
the y-intercept in “y = -3x + 8 (slope-intercept form of the given line),” is 8.
Step-by-step explanation:
to find a parallel line to a given line, you must know how to write an equation of a line. You must also know how to put the equation of a line in slope-intercept form. Additionally, you must know how to identify the slope and the Y-intercept in the equation of a line. It is important to remember that parallel lines have equal slopes. Learn how to be able to find a parallel line.
Look at the equation of the line. Let’s say “3x + y = 8” is the equation of the given line. Put the equation of the given line in slope-intercept form: y = mx + b. Using “3x + y = 8” as the equation of the given line, put the equation in slope-intercept form by solving for "y" (subtracting -3x from both sides). You will get “y = -3x + 8.”
Identify the slope. The slope is the "m" in “y = mx + b.” Therefore, the slope in “y = -3x + 8 (slope-intercept form of the given line),” is -3. Identify the y-intercept. The y-intercept is the b in “y = mx + b.” Therefore, the y-intercept in “y = -3x + 8 (slope-intercept form of the given line),” is 8.
HOPE THIS HELPS HAVE A GREAT DAY!!
HURRYY!!!!! Which algebraic expression means “three more than a number squared”? 2 n + 3 2 n minus 3 n squared + 3 n squared minus 3
Answer: (n+3)^2
Step-by-step explanation:
This is the answer lol
Answer:
C
Step-by-step explanation:
Logx-log(x-3)=1 Como se resuelve?
Answer:
Cant speak spanish
Step-by-step explanation: