Answer:
Step-by-step explanation:
7x - 2y = -3
14x + y = 14
7x - 2y = -3
28x + 2y = 28
35x = 25
x = 25/35= 5/7
14(5/7) + y = 14
10 + y = 14
y = 4
(5/7, 4)
Anjana is riding a motorboat at Katara starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s^2 for 8 s. How far does she ride the boat during this time?
Answer:
96 meters
Step-by-step explanation:
The computation of the distance far from her ride the boat during this time is shown below:
According to the kinematics motion equation
[tex]s = u \times t + \frac{1}{2} \times a \times t^{2}[/tex]
where,
o = 0 m/sec
a = 3.0 m/sec
t = 8.0 sec
Now placing these values to the above formula
So, the distance far from her ride is
[tex]= 0 \times 8 + \frac{1}{2} \times 3 \times 8^{2}[/tex]
= 96 meters
We simply applied the above formula
¡Ayuda!
1. Método del Triángulo: Una embarcación navega a una distancia de 800 km hacia el Oeste y después avanza 1400 km a 135 °. ¿Cuál es la magnitud, dirección y sentido del desplazamiento resultante? R /. 2,080 km, 155 ° NO.
Answer:
La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Step-by-step explanation:
En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:
[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]
[tex]r \approx 2045.463\,km[/tex]
La magnitud del desplazamiento resultante es 2045.463 kilómetros.
La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:
[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]
Se despeja el ángulo correspondiente:
[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]
[tex]\alpha \approx 28.945^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es:
[tex]\alpha' = 180^{\circ}-\alpha[/tex]
[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]
[tex]\alpha' = 151.055^{\circ}[/tex]
La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground.
Answer:
The bird is 2.44km high
Step-by-step explanation:
Hello,
To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.
See attached document for better understanding.
From the first diagram, we understand that the bird is between them and also on top of them.
Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.
But before then, we should know that sum of angles in a triangle is equal to 180°
Therefore,
20° + 50° + b° = 180
70° + b = 180
b = 180° - 70°
b = 110°
Dividing angle b into two equal parts = 55° on each side.
See the last attached document for better illustration.
Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.
We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.
Tanθ = opposite / adjacent
Tan 55° = 3.5 / adj
Adjacent = 3.5 / tan55
Adjacent = 3.5 / 1.43
Adjacent = 2.44km
The height of the bird is 2.44km
Answer:
A. 1.95
Step-by-step explanation:
PLATO
 what is the measure of AC 
Answer:
A
Step-by-step explanation:
The inscribed angle ABC is half the measure of its intercepted arc, thus
arc AB = 2 × 44° = 88° → A
Answer:
A
Step-by-step explanation:
The measure of an inscribed angle is half the measure of it's intercepted arc
Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution. A table titled Ethanol Mixture, showing Gallons, Ethanol Concentration, and Total. The first row shows x percent Ethanol, 20, x, and blank. The second row shows, 12 percent Ethanol, 60, 0.12, and 7.2 The third row shows Mixture, with 80, 0.10, and blank. What is the value of x, the concentration of the unknown ethanol solution? 0.02 0.04 0.05 0.08
Answer:
4%
Step-by-step explanation:
We can write the following equation:
20 * (x / 100) + 60 * 0.12 = 80 * 0.10 (Note that since we're writing the percentages as decimals, x% becomes x / 100 as a decimal.)
x / 5 + 7.2 = 8
x / 5 = 0.8
x = 4%
Answer:
Its B. on edge
Step-by-step explanation:
got it right on my test
need help use the screen shot
Answer:
6.5 < 3rd side < 19.9.
Step-by-step explanation:
For a triangle, the third side must be more than the difference between the given side lengths, but less than the total of the given side lengths.
So, the third side must be more than...
13.2 - 6.7 = 6.5.
The third side must be less than...
13.2 + 6.7 = 19.9.
6.5 < 3rd side < 19.9.
Hope this helps!
Solving Exponential Equations using Logarithms
Answer:
6 weeks
Step-by-step explanation: set the equation to be 1458=2(3^t). Do the division property of equality by 2.
729=3^t
Divide 729 by 3 until you get a 1 as the answer.(Count the number of times that you did it, and that will be your answer)
Rewrite the following radical expression in rational exponent form.
Answer:
[tex]x^\frac{3}{7}[/tex]
Step-by-step explanation:
we can write [tex]\sqrt[7]{x}[/tex] as [tex]x^\dfrac{1}{7}[/tex] and we multiply 1 by 3 to get [tex]x^\frac{3}{7}[/tex]
I believe this is pretty easy but it's: solve for x using common denominators 3/4(x+2)=x/(x+3) Answer choices below:
Answer:
x = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{x}{x+2}[/tex]
multiply numerator/ denominator of [tex]\frac{x}{x+2}[/tex] by 4, thus
[tex]\frac{3}{4(x+2)}[/tex] = [tex]\frac{4x}{4(x+2)}[/tex]
Since the denominators are common , equate the numerators, that is
4x = 3 ( divide both sides by 4 )
x = [tex]\frac{3}{4}[/tex]
Unit 6 Test Part B
MCR3U Summer
4. Sophie is riding her bike home when she runs over a nail. It gets stuck to the tire of her bike but does not pop
the tire. As she continues to cycle home, the nail hits the ground every 2 seconds and reaches a maximum
height of 48 cm
Answer:
You did not ask anything, i guess that you want to find the equation of the height of the nail as a function of time.
Data that we have:
The nail is in a circular object.
the nail hits the ground every 2 seconds, then the weel does a full cycle every 2 seconds.
The maximum height of the nail is 48cm, and as the nail is stuck on the weel, the maximum height will be when the nail is on top of the weel.
From this, we can conclude that the diameter of the weel is 48cm.
Now, with this we could write the equation of the height of the nail as a function of time.
We know that this is a periodic function, so let's write it as:
f(t) = A*cos(c*t) + B
where A, B and c are constanst.
At t = 0, when the byke hits the nail, the nail must be in the ground, so we have that:
0 = A*cos(c*0) + B
A + B = 0
A = - B
and we also know that the function is periodic with T = 2s
cos(c*t) = cos(c*(t + 2s) = cos( c*t + 2s*c)
and we know that the period of the cosine function is 2*pi
then:
c*2s = 2*pi
c = (2pi/2s) = pi/s
then our function is:
f(t) = -B*cos(t*pi/s) + B
now, the maximum heightwill be when cos(t*pi/s) = -1, and this happens at t = 1s
f(1s) = -B*cos(pi) + B = 2B
And we know that the maximum height is 48cm
2*B = 48cm
B = 24cm
Then the function of the height of the nail is:
f(t) = -24cm*cos(t*pi/s) + 24cm
Please help ASAP. The question is down below. Thanks
Answer:
B
Step-by-step explanation:
there is three sections to be fenced using 78 m of fence so it would be letter B.
a subway train with 47 people stops at a station and picks up 20 more people at the same station p people get off. there are 52 people left on the train. which equation shows how to find the value of p
Answer:
67 - p = 52
Step-by-step explanation:
the train starts with 47 people: 47
it picks up 20 more: 47 + 20 = 67
p people get off: 67 - p
52 people are left on train: 67 - p = 52
The supply and demand curves for a product line of bicydes are shown. A protimately where is the equilibrium pointe
у
350
Quantity
300
+250
+200
+150
+100
demand
+50
20
80 100 120 140 160 180 200 220 240 250 200 300
Price (dollars)
A (93,268)
B. (132,220)
C.(180,355)
D.(220,115)
Answer:
It's B
Step-by-step explanation:
plato
Mr. Duncan bought a table at a discount if 30% thus saving $42. what was the marked price of the table?
Answer:
$140
Step-by-step explanation:
if 30% of full price = $42 then 100% = 42/0.3 = 140
Answer:
$140
Step-by-step explanation:
1. Set up the equation
[tex]\frac{42}{x}[/tex] = [tex]\frac{30}{100}[/tex]
Percentage is out of 100 this equation says 42 of x number is equal to 30%.
2. Cross multiply
30x = 4200
3. Solve for x by dividing both sides by 30
x = 140
For what values of the following expressions are true: |a−5|=5−a
Answer:
Whenever a-5<0 or a<5
Step-by-step explanation:
So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.
Is y = 75 x + 52 increasing or decreasing.
Answer:
Increasing if X is positive decreasnig if X is negative
Step-by-step explanation:
Answer:
increasing
Step-by-step explanation:
positive slope of 75 so line goes up to the right
Which function is graphed below?
Answer:
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Step-by-step explanation:
The graph represents a second order polynomial function (a parabola), whose axis of symmetry is the x-axis and whose form is presented as follows:
[tex]x - h = C\cdot (y-k)^{2}[/tex]
Where:
[tex]x[/tex], [tex]y[/tex] - Dependent and independent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, dimensionless.
[tex]C[/tex] - Vertex constant, dimensionless. If [tex]C > 0[/tex], then vertex is an absolute minimum, otherwise it is an absolute maximum.
After a quick observation, the following conclusions are done:
1) Vertex is an absolute minimum ([tex]C > 0[/tex]) and located at (-2, 0).
2) Parabola pass through (2, 2).
Then, the value of the vertex constant is obtained after replacing all known values on expression prior algebraic handling: ([tex]x = 2[/tex], [tex]y = 2[/tex], [tex]h = -2[/tex], [tex]k = 0[/tex])
[tex]2+2 = C\cdot (2-0)^{2}[/tex]
[tex]4 = 4\cdot C[/tex]
[tex]C = 1[/tex]
The function is:
[tex]x = -2 + 1\cdot y^{2}[/tex]
[tex]x = y^{2}-2[/tex]
The inverse function of this expression is [tex]y = \pm \sqrt{x+2}[/tex]
The function graphed below is [tex]x = y^{2} - 2[/tex] or [tex]y = \pm \sqrt{x+2}[/tex].
Select all the correct answers. Which statements are correct interpretations of the logarithmic function f(x) = 7 log2 x, with respect to the context? The password is weakest if it uses a single symbol for all 7 characters. The strength of the password increases with a decrease in the number of symbols. The password is stronger with an increase in the number of symbols. The password is strongest if a single symbol is used for all 7 characters. There are 2 possible symbol options per character to produce a password of strength of 7 bits. There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Answer:
The password is weakest if it uses a single symbol for all 7 characters.
The strength of password increases with an increase in the number of symbols.
There are 7 possible symbol options per character to produce a password of strength of 7 bits.
Step-by-step explanation:
The password strength is determined by the usage of symbols and upper case and lower case letters along with a numeric character. The strength of password increases when different symbols are used. It is considered as weak password if only single symbol is used for all the 7 characters. The strong passwords are not easy to break and decode.
Answer:
The three correct options are:
The password is weakest if it uses a single symbol for all 7 characters.
The password is stronger with an increase in the number of symbols.
There are 2 possible symbol options per character to produce a password of strength of 7 bits.
Please help!! Don't anwser if you dont know it :) Brainliest for right anwser
Answer:
D. The graph of g(x) is horizontal stretched by a factor of 3.
Step-by-step explanation:
Multiplying x by 1/3 stretches the graph horizontally by a factor of 3.
Answer:i think its d too
Step-by-step explanation:
Please help me with this question!
Answer: C) 12.2
================================================
Explanation:
We have a known adjacent side (10) and an unknown hypotenuse (x). The cosine rule ties the two sides together.
cos(angle) = adjacent/hypotenuse
cos(35) = 10/x
x*cos(35) = 10
x = 10/cos(35)
x = 12.2077458876146 approximately
x = 12.2
Make sure your calculator is in degree mode.
Answer:
[tex]\boxed{12.2}[/tex]
Step-by-step explanation:
cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]
The hypotenuse of the triangle is x.
cos (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{cos(35)}[/tex]
x = 12.20774588...
x ≈ 12.2
the product of five and a certain number is twelve
Answer:
Step-by-step explanation:
Hello
5 * [tex]\boxed{ }[/tex] = 12
so this number is
[tex]\boxed{ \ } = \dfrac{12}{5}[/tex]
Hope this helps
Answer:
[tex]\frac{12}{5}[/tex] or 2.4
Step-by-step explanation:
→ Form an equation
5 × ? = 12
→ Divide both sides by 5
? = [tex]\frac{12}{5}[/tex] or 2.4
plzzzz answer right away will mark BRAINLIST AND FIVE STARS PLUS THANKS What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFraction StartFraction 8 over 9 EndFraction 1
Answer:
Proportionality Constant = k = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Equation is:
[tex]y = \frac{x}{9}[/tex]
=> [tex]y = (\frac{1}{9} ) x[/tex]
Comparing it with [tex]y = kx[/tex], where k is the proportionality constant, We get:
Proportionality Constant = k = [tex]\frac{1}{9}[/tex]
Answer:
[tex]{\sf \frac{1}{9}}[/tex]
Step-by-step explanation:
y and x are the directly proportional quantities.
[tex]\sf y=kx[/tex]
The constant of proportionality is k.
The equation is:
[tex]\sf y=\frac{x}{9}[/tex]
[tex]\sf y=\frac{1}{9} x[/tex]
The value of k in this equation is:
[tex]\sf k= \frac{1}{9}[/tex]
to solve the equation 3 x + 1 = 4 x + (negative 4)
Answer:
x=5
Step-by-step explanation:
3x+1 = 4x -4
Subtract 3x from each side
3x+1-3x = 4x-3x-4
1 = x-4
add 4 to each side
1+4 = x-4+4
5 =x
Answer: x=5
Step-by-step explanation:
3x+1=4x+(-4)
3x+1=4x-4
3x+5=4x
5=x
among the following, a perfect number a) 6 b)28 c) 625 d) 100
this question comes under more than one correct answer
Answer:
28 and 6
Step-by-step explanation:
List the factors (excluding itself):
6: 1, 2, 3,
28: 1, 2, 4, 7, 14
Add them up!
1+2+3=6
1+2+4+7+14=28
if they add up to the original number then the number is perfect.
========================================
Explanation:
By definition, a perfect number is one where the factors smaller than itself add to the number in question.
The factors of 6, smaller than 6, are {1,2,3}. We can see that 1+2+3 = 6. Therefore, 6 is a perfect number.
Similarly, 1+2+4+7+14 = 28 showing that 28 is also a perfect number.
------
The factors of 625, that are smaller than 625, are 1,5,25,125. They add to 1+5+25+125 = 156. This isn't equal to 625, so 625 isn't a perfect number.
A similar issue happens with 100 as well. The smaller factors are 1,2,4,5,10,20,25,50, meaning we get a sum of 1+2+4+5+10+20+25+50 = 117, which is too large.
------
The first four perfect numbers are: {6, 28, 496, 8128}
3. The diagram shows a piece of rectangular tile
PQRS. A kite shape TUVW is inscribed in the
rectangle. Given that the perimeter of PQRS is
120 cm, find the area of TUVW.
Answer:
432cm²
Step-by-step explanation:
If the Perimeter is 120cm, PT=8 (120-28-12-12-28-12-12)/2
This means the rectangle is 24x36.
area of a kite is the diagonals divided by 2 (or half of the rectangle).
24x36=864
864/2=
432 cm²
The ratio of figure A to B is 4:1. The volume of figure A is 4,032π in3. What is the volume of figure B?
Answer:
The volume of figure B is 1008π in³Step-by-step explanation:
The ratio of figure A to B is 4:1
That's
[tex] \frac{4}{1} [/tex]
Volume of figure A is 4.023π in³
To find the volume of figure B we compare the volumes of the two figures to the ratio
That's
[tex] \frac{4}{1} = \frac{4032\pi}{B} [/tex]
Cross multiply
That's
4B = 4032π
Divide both sides by 4
B = 1008π
The volume of figure B is 1008π in³Hope this helps you
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.
Answer:
a. (True) Since ∠6 and ∠8 are vertical angles, they are congruent.
b. (False) ∠1 and ∠2 are supplementary but 65 + 125 ≠ 190.
c. True
d. True
e. True
Answer:
The answer is Freddy Kruger
Step-by-step explanation:
Elm Street, duh
Which example illustrates the commutative property of addition for polynomials?
Answer:
The fourth.Step-by-step explanation:
The alternation of addition means you can swap places of components of sum.
(2x²+5x) and (4x²-4x) are polynominal components of the sum: (2x²+5x)+(4x²-4x)
Answer:
D
Step-by-step explanation:
got it right on edge
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m3 of fluffy
material.
0.5 m
? m
1 m
What is the length of the pillow?
Give an exact answer (do not round).
HELP PLEASE
Complete Question
Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy
material. The base is 0.5m² and the height is 1m.
What is the length of the pillow?
Give an exact answer (do not round).
Answer:
1.4m
Step-by-step explanation:
A wedge comes in the shape of a Triangular prism. Hence,
Volume of a wedge(Triangular prism) = 1/2 × B × H × L
b = 0.5m
h = 1 m
l = ??
Volume of a wedge = 0.35m³
0.35 = 1/2 × 0.5 × 1 × L
0.35 = 0.25 × L
L = 0.35/0.25
L = 1.4m
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,100 .2 1,400 .3 1,300 .5 Click here for the Excel Data File What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions. (Round your standard deviation to 2 decimal places.)
Answer:
Variance =10900.00
Standard deviation=104.50
Step by step Explanation:
Admissions Probability for 1100= 0.2
Admissions Probability for 1400=0.3
Admissions Probability for 1300 =0.5
To find the expected value, we will multiply each possibility by its probability and then add.
mean = 1100*0.2 + 1400*0.3 + 1300*0.5 = 1290
To find the variance, we will start by squaring each possibility and then multiplying it by its probability. We will then add these and subtract the mean squared.
E(X^2)=( 1100²*0.2)+ (1400²*0.3 )+ (1300²*0.5) = 1675000
Variance(X)=E(X²)- [E(X)]²
= 1675000 - (1290)²
=10900
Hence, the Variance(X)=10900
Then to calculate the standard variation , we will use the formular below,
standard variation (X)=√ var(X)= √10900
=104.5
Hence the standard variation=104.5