Answer:
The rate at which the distance between the two cars is increasing is 30 mi/h
Step-by-step explanation:
Given;
speed of the first car, v₁ = 24 mi/h
speed of the second car, v₂ = 18 mi/h
Two hours later, the position of the cars is calculated as;
position of the first car, d₁ = 24 mi/h x 2 h = 48 mi
position of the second car, d₂ = 18 mi/h x 2 h = 36 mi
The displacement of the two car is calculated as;
displacement, d² = 48² + 36²
d² = 3600
d = √3600
d = 60 mi
The rate at which this displacement is changing = (60 mi) / (2h)
= 30 mi/h
ulwazi's Father offered to pay for Ani's wedding ring, which cost R1349 excluding 14%VAT calculate the selling price
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Answer:
₹1537.86
Step-by-step explanation:
With the 14% tax added, the final cost is ...
₹1349 × (1 +14%) = ₹1349×1.14 = ₹1537.86
Write as an algebraic expression and simplify if possible: A number four more than 45% of d.
Answer:
0.45d + 4
Step-by-step explanation:
45% of d => 0.45d
Then a number 4 more is gonna be 0.45d + 4
ba xạ thủ độc lập bắn vào một mục tiêu. xác suất bắn trúng tương ứng là 0,8; 0,7; 0,6. mỗi xạ thủ bắn một viên. gọi X là số viên bắn trúng.
a) lập bảng phân phối xác suất.
b) tính E(X) và VAR(X)
Answer:
well I don't know
Step-by-step explanation:
your speaking vietnam
Answer:
Step-by-step explanation:
please help !!!!
i would really appreciate it
Answer: A
Step-by-step explanation: x=-2, y=3, z=-3
Answer:
A. -2, 3, -3
Step-by-step explanation:
x = 7 - 2y + z
y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =
= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z
13y = 63 + 8z
y = (63 + 8z)/13
2x + 2y - 3z = 11
2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11
2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11
14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11
-2×(63 + 8z)/13 - z = -3
-2×(63 + 8z) - 13z = -39
-126 - 16z - 13z = -39
-29z = 87
z = -3
y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3
x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for .
4 in.
6 in.
O A = 38.13 square inches, P = 32.84 inches
O A = 80.52 square inches, P = 32.84 inches
O A = 38.13 square inches, P = 23.42 inches
O A = 80.52 square inches, P = 23.42 inches
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Answer:
(c) A = 38.13 square inches; P = 23.42 inches
Step-by-step explanation:
The radius of the circle is half the diameter, so is 3 inches. This means the entire figure will fit in a rectangle 6 inches wide and 4+3 = 7 inches high. The perimeter of such a rectangle is ...
P = 2(L+W) = 2(7+6) = 26 inches
The area of that rectangle is ...
A = LW = (7)(6) = 42 square inches
Then area of the given figure is less than 42 square inches, and the perimeter is less than 26 inches. The only answer choice that matches these bounds is ...
A = 38.13 square inches; P = 23.42 inches
Find the greatest common factor of the
following monomials:
39c^2
9c^3'
Answer:
3c^2
Step-by-step explanation:
a cookie recipe calls 3 1/4 cups of flour. the recipe makes 3 dozen cookies. how much flour us needed to make 144 cookies
1 dozen = 12
144 / 12 = 12 dozen
12 dozen/ 3 = 4
They need 4 times the amount of flour:
3 1/4 x 4 = 13
They need 13 cups of flour
THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13
1. What is a conic ? How would you be able to model different conic sections at home(how would you slice a 3D shape to create the conic sections)?
2. How does the equation for the ellipse compare to the equation for a hyperbola? How can you determine the difference?
3. What is the difference between a vertex, a focus, and a directrix?
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Explanation:
1.A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.
A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.
a circle - the plane of intersection is perpendicular to the axisan ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.Producing these at home can be an interesting project. A circle can be made using a compass.
An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.
A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.
A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.
__
2.The general form equation for a conic is ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0
Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,
In standard form, the equations for figures centered at the origin are ...
ellipse: x²/a +y²/b = 1hyperbola: x²/a -y²/b = 1 (opens horizontally)hyperbola: y²/a -x²/b = 1 (opens vertically)__
3.The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.
Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
perpendicular to
7y = x − 4
and passes through the point
(−2, 1)
Answer:
[tex]y = -7x -13[/tex]
Step-by-step explanation:
Given
Perpendicular to
[tex]7y = x -4[/tex]
Passes through
[tex](-2,1)[/tex]
Required
The equation
First, we calculate the slope of:
[tex]7y = x -4[/tex]
Divide through by 7
[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]
A linear function is:
[tex]y=mx + c[/tex]
Where;
[tex]m \to slope[/tex]
So:
[tex]m = \frac{1}{7}[/tex]
For the perpendicular line; the slope is:
[tex]m_2 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_2 = -\frac{1}{1/7}[/tex]
[tex]m_2 = -7[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = -7(x - -2) + 1[/tex]
[tex]y = -7(x +2) + 1[/tex]
Open bracket
[tex]y = -7x -14 + 1[/tex]
[tex]y = -7x -13[/tex]
find the missing side length below brainly
Let it be x
[tex]\\ \sf\longmapsto \dfrac{3}{5}=\dfrac{x}{x+4}[/tex]
[tex]\\ \sf\longmapsto 3(x+4)=5x[/tex]
[tex]\\ \sf\longmapsto 3x+12=5x[/tex]
[tex]\\ \sf\longmapsto 5x-3x=12[/tex]
[tex]\\ \sf\longmapsto 2x=12[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{12}{2}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
Make
x
the subject of the formula
x
+
4
=
q
Answer:
x = q-4
Step-by-step explanation:
x+4 = q
Subtract 4 from each side
x+4-4 = q-4
x = q-4
Answer:
x + 4
Step-by-step explanation:
x + 4 = q
4 = x + q
4 = x
x + 4
I need help with that, if you can, plz. I ty it I think is a not sure
Answer:
-5≤x <1
Step-by-step explanation:
sqrt( x+5) / sqrt(1-x)
The numerator must be greater than zero since it is a square root
sqrt(x+5) ≥0
Square each side
x+5≥0
x≥-5
The denominator must be greater than zero (the denominator cannot be zero)
sqrt(1-x)> 0
Square each side
1-x > 0
1>x
Putting these together
-5≤x <1
A rectangular painting is to have a total area (including the frame) of 1200 cm2. If the painting is 30 cm long and 20 cm wide, find the width of the frame
Answer:
5 cm
Step-by-step explanation:
Let x = width of frame.
The width of the frame is added all around the painting, so you must add 2x to the length of the painting and 2x to the width of the painting to find the total length and width including the frame.
painting length: 30
total length: 2x + 30
painting width: 20
total width: 2x + 20
total area = LW
total area = (2x + 30)(2x + 20)
total area = 1200
(2x + 30)(2x + 20) = 1200
(x + 15)(x + 10) = 300
x^2 + 10x + 15x + 150 = 300
x^2 + 25x - 150 = 0
(x - 5)(x + 30) = 0
x - 5 = 0 or x + 30 = 0
x = 5 or x = -30
The width of the frame cannot be a negative number, so we discard the solution x = -30.
Answer: 5 cm
Which of the following graphs is described by the function given below?
y = x2 - 6x-7
Answer:
A
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y = x^2 - 6x - 7[/tex]
And we want to determine its graph.
One of the most important features of a quadratic is its vertex. So, we can start by finding the vertex using the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -6, and c = -7.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = -\frac{(-6)}{2(1)} = 3[/tex]
Substitute this back into the equation to find the y-coordinate:
[tex]\displaystyle y(3) = -16[/tex]
Therefore, our vertex is at (3, -16).
The only graph whose quadratic's vertex is at (3, -16) is Graph A. Thus, our answer is A.
Find the value of this expression
Answer:
[tex] \frac{(3) ^{2} + 3}{3 - 1} [/tex]
[tex] \frac{9 + 3}{3 - 1} [/tex]
[tex] \frac{12}{2} [/tex]
= 6
A randomized study compared two drugs that are designed fo lower a person's serotonin level. It was found that over a 1-year period, those receiving Drug A decreased their serotonin level by a mean of 36 nanograms per millimeter. Those receiving Drug B decreased their serotonin level by a mean of 20 nanograms per millimeter. To determine whether the results are significant, the data are randomized and the difference of the means is shown in the dot plot. What is the best conclusion to make based on the data?
A. The difference of the means is significant because the rerandomizations show that it is outside the range of what likely happens by chance.
B. The difference of the means is not significant because the rerandomizations show that it is outside the range of what likely happens by chance.
C. The difference of the means is not significant because the rerandomizations show that it is within the range of what likely happens by chance.
D. The difference of the means is significant because the rerandomizations show that it is within the range of what likely happens by chance.
The best conclusion to make based on the data is: The difference of the means is significant because the re-randomizations show that it is outside the range of what could happen by chance.
Difference of meansGiven:
Drug A= Decrease serotonin level by means of 36 nanograms per millimeter
Drug B= Decrease serotonin level by means of 20 nanograms per millimeter
Hence,
When we take a look at the difference of means data that was given, we would see that the different of means is significant between the means of Drug A and Drug B due to chance or random variation.
Based on the fact that the re-randomizations indicate that it is outside the range of what could happen by chance.
Therefore the correct option is A.
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Answer:
The difference of the means is NOT significant because the rerandomizations show that it is within the range of what likely happens by chance
Step-by-step explanation:
Took the test and this is 100% the answer. Hope it helps.
Given:
AD
diameter of Circle P.
Dec
B
A
If m < 1 = 30°, then m AB
15
30
60
Answer:
The measure of an arc is the size of the corresponding central angle, so angle 1 for AB,
Answer: B 30
Two numbers total 31 and have a difference of 11. Find the two numbers
Answer:
let 2 no. be x and y
x+y=31 ..... (1)
x-y=11 .........(2)
from (1)
x=31-y ..........(3)
putting (3) in (2)
31-y-y=11
-2y=11-31
-2y=-20
2y=20
y=10
Write the equation of the line for a line that passes through (-2,-4) and (-1, -1).
Answer:
y = 3x+2
Step-by-step explanation:
First find the slope using the slope formula
m= (y2-y1)/(x2-x1)
= ( -1 - -4)/(-1 - -2)
= (-1 +4)/ (-1 +2)
= 3/1
= 3
The slope intercept formula is
y = mx+b where m is the slope and b is the y intercept
y = 3x+b
Using the point (-1,-1) and substituting into the equation
-1 = 3(-1)+b
-1 = -3+b
-1+3 = b
2 = b
y = 3x+2
What is the slope, m, and the y-intercept of the line that is graphed below?
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Answer:
Slope: 1
Y-intercept: (0,3)
Step-by-step explanation:
The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.
Y intercept: (0, 3)
For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]
From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.
Slope: 1
Hope this helped.
Answer: 1
Step-by-step explanation: got it right on edge
Find the slope and the y-intercept of the line with the given equation.
f(x) = 7 -4/5x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is
(Type an integer or a simplified fraction.)
B. The slope is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept is
(Simplify your answer. Type an ordered pair, using integers or fractions.)
B. There is no y-intercept.
Answer:
The slope is -4/5
The y intercept is (0,7)
Step-by-step explanation:
f(x) = 7 -4/5x
Rewriting
y = -4/5x +7
This is in slope intercept form
y = mx+b where m is the slope and x is the y intercept
The slope is -4/5
The y intercept is (0,7)
Lainey is looking for a new apartment and her realtor keeps calling her with new listings. The calls only take a few minutes, but a few minutes here and there are really starting to add up. She's having trouble concentrating on her work. What should Lainey do? a) Tell her realtor she can only receive text messages O b) Limit the time spent on each call O c) Turn off her phone until she is on a break O di Call her realtor back when customers won't see her on the phone
a...cause she's having trouble concentrating,for her to work she needs to tell her realtor she can only receive text messages it enables her to know the process of the house hunt
construct the truth table (p ∧ q) =⇒ [(q ∧ ¬p) =⇒ (r ∧ q)]
[tex]\begin{array}{c|c|c|c|c|c} p & q & r & p\land q & q\land \neg p & r \land q \\&&&&\\ T & T & T & T & F & T \\ T & T & F & T & F & F \\ T & F & T & F & F & F \\ T & F & F & F & F & F \\ F & T & T & F & T & T \\ F & T & F & F & T & F \\ F & F & T & F & F & F \\ F & F & F & F & F & F\end{array}[/tex]
An implication A => B is true if either A is false, or both A and B are true. So
[tex]\begin{array}{c|c|c}p\land q & (q\land\neg p) \implies (r\land q) & (p\land q) \implies \big[(q\land\neg p) \implies (r\land q)\big] \\&&\\T & T & \mathbf T\\T & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & F & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\end{array}[/tex]
and the given statement is a tautology.
Which expression is equivalent to the following complex fraction?
-25
245 5
+
y
3 2
у
Step-by-step explanation:
[tex] \longrightarrow \sf{ \dfrac{ \cfrac{ - 2}{x} + \cfrac{ 5}{y}}{\cfrac{ 3}{y} -\cfrac{ 2}{x} }} \\ \\ \longrightarrow \sf{ \dfrac{ \cfrac{ - 2y + 5x}{xy}}{\cfrac{ 3x - 2y}{xy} }} \\ \\ \longrightarrow \sf{ \cfrac{ - 2y + 5x}{xy}} \times{\cfrac{ xy}{3x - 2y} } \\ \\ \longrightarrow \boxed{ \sf{ \cfrac{ - 2y + 5x}{3x - 2y}}}[/tex]
Option A is correct!
The expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
[-2/x + 5/y] / [3/y - 2/x]
This expression could also be given by;
[-2y + 5x /xy] / [3 x- 2y /xy]
Now, we know that x would cancel out;
[-2y + 5x ] / [3 x- 2y]
Hence, the expression into an equivalent form would be; A [-2y + 5x ] / [3 x- 2y]
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155 ° 35 ° x °
x = ? °
x=35
vertical opposite angles are equal.
HELP NEEDED PLEASE :(
Identify the center and the radius of a circle that has a diameter with endpoints at (5, 8)
and (7,6).
Answer:
Centre is,
((5+7)/2,(8+6)/2)
or, (12/2,14/2)
or, (6,7)
radius is,
[√{(5-7)²+(8-6)²}]/2
= [√(2²+2²)]/2
= [√(4+4)]/2
= [√8 ]= [2√2]/2 = √2
The center of a circle = (6, 7)
the radius of a circle = [tex]\sqrt{2}[/tex] units
What is the distance formula?"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]"
What is midpoint formula?"The coordinates of the midpoint of the line segment having endpoints [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] "
What is diameter of circle?"It is the line segment through the center and touching two points on its edge. "
For given question,
The diameter of circle has endpoints at (5, 8) and (7,6).
Let [tex](x_1,y_1)=(5,8),(x_2,y_2)=(7,6)[/tex]
First we find the length of the diameter of the circle.
Using the distance formula,
[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} \\\\\Rightarrow d=\sqrt{(7-5)^2+(6-8)^2} \\\\\Rightarrow d=\sqrt{2^2+(-2)^2}\\\\\Rightarrow d=\sqrt{4+4}\\\\\Rightarrow d=2\sqrt{2}~units[/tex]
We know that the diameter = 2 × radius
⇒ radius (r) = [tex]\frac{2\sqrt{2} }{2}[/tex]
⇒ r = [tex]\sqrt{2}[/tex] units
We know that the midpoint of the diameter is the center of the circle.
Using midpoint formula the center of the circle would be,
[tex]\Rightarrow O=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\\Rightarrow O=(\frac{5+7}{2} ,\frac{8+6}{2} )\\\\\Rightarrow O=(\frac{12}{2} ,\frac{14}{2} )\\\\\Rightarrow O=(6,7)[/tex]
Therefore, the center of the circle is (6,7)
Hence, the center of a circle = (6, 7)
the radius of a circle = [tex]\sqrt{2}[/tex]
Learn more about the distance formula and mid-point formula here:
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Solve the inequality
Answer:
hope this helps buddy, please mark the brainliest.
Step-by-step explanation:
The bell tower of the cathedral in Pisa, Italy, leans 5.6° from the vertical. A tourist stands 107 m from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be 28.6°. Find the length of the tower to the nearest meter. m
Answer:
[tex]l=56m[/tex]
Step-by-step explanation:
From the question we are told that:
Angle from vertical [tex]\theta =5.6[/tex]
Horizontal Distance [tex]d=107m[/tex]
Angle of elevation [tex]\gamma=28.6[/tex]
Generally the Trigonometric equation for exterior angles is mathematically given by
[tex]Exterior\ angles=\sum of\ two\ interior\ angles[/tex]
Where
[tex]Exterior angles=90 \textdegree +5.6 \textdegree[/tex]
Therefore
[tex]90 \textdegree +\theta \textdegree=\omega+\gamma[/tex]
[tex]90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree[/tex]
[tex]\omega=67 \textdegree[/tex]
Generally the equation for The Sine rule is mathematically given by
[tex]\frac{sin \omega }{d}=\frac{sin \gamma}{l}[/tex]
[tex]l=\frac{107 sin 28.6}{sin 67 \textdegree }[/tex]
[tex]l=56m[/tex]
Can I get some help
Please!!
Answer:
option D is the answer
Step-by-step explanation:
using the HH,ll,ha and la,
where h is the hypotenuse and l is the leg
