The speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.
According to the question,
We have the following information:
A boat take 4 hour to travel upstream 30 miles. On the return trip downstream it took 2 hours.
Now, let's take the speed of the boat in still water to be s miles per hour and the speed of the current to be c miles per hour.
Upstream speed = speed in still water - speed of current
Downstream speed = speed in still water + speed of current
Upstream:
s-c = 30/4
s-c = 7.5
s = 7.5+c ...(1)
Downstream:
s+c = 30/2
s+c = 15
Putting the value of s from equation 1:
7.5+c+c = 15
7.5+2c = 15
2c = 15-7.5
2c = 7.5
c = 7.5/2
c = 3.75 miles per hour
Putting this value in equation 1:
s = 7.5+c
s = 7.5+3.75
s = 11.25 miles per hour
Hence, the speed of the boat if it were in still water is 11.25 miles per hour and the speed of the current is 3.75 miles per hour.
To know more about speed of the boat here
https://brainly.com/question/24229194
#SPJ4
Decide whether the equation has no solution, one solution, or infinitely many
solutions. Put an X in the appropriate box in the table.
Infinitely
what is the volume of a solid with a radius of 12 and a height of 24
The volume of a solid of cylinder with a radius of 12 and a height of 24 is
3456[tex]\pi[/tex].
What is volume?Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.
Given that the cylinder with a radius of 12 and a height of 24.
Volume of a cylinder = [tex]\pi[/tex] r² h
Volume of a cylinder = [tex]\pi[/tex] (12)² × 24
Volume of a cylinder = [tex]\pi[/tex] ( 144 × 24)
Volume of a cylinder = [tex]\pi[/tex] (3456)
Therefore, the volume of cylinder is 3456[tex]\pi[/tex].
To learn more about the volume;
https://brainly.com/question/1578538
#SPJ1
Ms. D'Amico bought a car with a 20% down payment, which was 5,750. She will finance the rest of the car payments. What was the price of the car?
Answer:
$28,750
Step-by-step explanation:
To find the price of the car, you need to use the following formula:
price of the car = down payment / (down payment percentage / 100)
Plugging in the given values, you get:
price of the car = 5,750 / (20 / 100)
Simplifying the expression, you get:
price of the car = 5,750 / 0.2
The price of the car is therefore 28,750.
Ayana is making 6 scarves that each require 114 yards of purple fabric and a certain amount of blue fabric. She will use 10 yards in all. Which equation can be used to determine how many yards of blue fabric, b, are needed for each scarf?.
each scarf's 0.4166 yards of blue scarf
What is the basic algebraic formula?
This problem can be solved using a straightforward algebraic equation. For each scarf, Ayana requires many yards of blue cloth.
When solving a straightforward equation, visualize the equals symbol (=) as the fulcrum or center of a balance.
What three sorts of equations are there?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
In order to answer this question, let's say that each scarf needs x square inches of purple fabric and y square inches of blue fabric.
A total of six scarves are reportedly required. It is assumed that a total of 10 yards of fabric—the combined amount of the purple and the blue fabrics—will be utilized.
So that we may solve this equation.
We use x and y as 6x and 6y as 6 scarves are needed.
10 yards of cloth were used in total (6x + 6y).
Next up It goes without saying that 1 yard of purple cloth is required for each and every scarf.
Therefore, a total of 6 * 1(1/4) yards is required for 6 scarves.
As a result, 6x becomes 6 * 1/4 yards.
This equates to 6 yards of purple material
We now solve for the required amount of blue cloth.
6y = 10 -30/4 = 40-30/4 = 10/4
However, the yards are for six scarves, therefore we need to divide it by six to obtain the amount of material for one scarf.
Each scarf needs 0.4166 yards of blue fabric, or y = (10/4)/6 =10/4 *1/6 =10/24 = 5/12 yards.
Visit this link for additional information about the word puzzle: brainly.com/question/13818690
#SPJ4
Find the first five terms of the geometric sequence whose constant ratio is -4 and whose first term is 7.
Answer:
7, - 28 , 112 , - 448 , 1792
Step-by-step explanation:
to obtain a term in the sequence multiply the previous term by r , so
a₁ = 7
a₂ = a₁ × - 4 = 7 × - 4 = - 28
a₃ = a₂ × - 4 = - 28 × - 4 = 112
a₄ = a₃ × - 4 = 112 × - 4 = - 448
a₅ = a₄ × - 4 = - 448 × - 4 = 1792
has one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
What is eigenvalue?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]
and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]
and the roots of this polynomial is:
[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)
To learn more about eigenvalue visit
https://brainly.com/question/29579848
#SPJ4
Complete Quetion
The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.
divide 4x^3 -x^2 +x - 5 by x^2 +x -1
Answer: 4x^3+1
Step-by-step explanation:
You are starting a new job and are told that your pay will be $3 on the first day. Each day after that, your pay will double until you reach the amount of $96. Starting from the first day, on what day will you reach $96?
6th day
8th day
4th day
10th day
Answer:
A=3, b=2, t=0 to t=5, covering 6 days. $3, $6, $12, $24, $48, $96.
Step-by-step explanation:
A is the starting amount at t=0. b is the base, two because the amount doubles each day. b would be 3 if it tripled every day. t is the final day number, counting from zero.
three sides of a triangle are 3, radical7, and 4. Is the triangle acute, right or obtuse?
Answer: To determine whether a triangle is acute, right, or obtuse, we need to compare the lengths of its sides to the measure of its angles. The triangle is acute if all three angles measure less than 90 degrees, it is right if one angle measures exactly 90 degrees, and it is obtuse if one angle measures more than 90 degrees.
In the case of a triangle with sides 3, radical7, and 4, we can use the Pythagorean theorem to find the measure of its angles. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Since we know that one side of the triangle has length 4, and another side has length radical7, we can use the theorem to find the length of the third side, which is the hypotenuse. We can write this as an equation: 4^2 + radical7^2 = x^2, where x is the length of the hypotenuse. Solving for x, we get x = 5.
Since the length of the hypotenuse is 5, and one of the other sides has length 4, we can conclude that this triangle is a right triangle. Therefore, the triangle is a right triangle and not acute or obtuse.
The equation c = 10.50p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true, based on the equation of the proportional relationship?
A) For $0.50, you can buy 1 pound of shrimp.
B) For $1, you can buy 10.50 pounds of shrimp.
C) For $10.50, you can buy 10.50 pounds of shrimp.
D) For $10.50, you can buy 1 pound of shrimp.
The equation of the proportional relationship is For $10.50, you can buy 1 pound of shrimp.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
c = 10.50p
where total cost (c) and the number of pounds (p) of shrimp at a grocery store.
When p= 1 pounds then the cost is
c= 10.5
Hence, For $10.50, you can buy 1 pound of shrimp.
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ1
Hi, the answer would be D...
For $10.50, you can buy 1 pound of shrimp.
have a nice day! :)
Which is not a valid strategy to use when solving the system of equations? 4x - 3y = 8, 2x + 9y = -3
A. Multiply the first equation by 3.
B. Multiply the second equation by 2.
C. Multiply the first equation by 2 and the second equation by 4.
D. Multiply the first equation by 3 and the second equation by 2
The strategy that does not work to solve the system is the one in option D
"Multiply the first equation by 3 and the second equation by 2"
Which one is not a valid strategy?Here we have the following system of equations:
4x - 3y = 8
2x + 9y = -3
To solve it, we can take a linear combination of the two equations, for example if we do what the first option says and we multiply the first equation by 3 we get:
3*4x - 3*3y = 3*8
12x - 9y = 24
Now we can add this to the other equation to get:
(12x - 9y) + (2x + 9y) = 24 - 3
14x = 21
And the system can be solved.
Now, the option that does not help us to solve the system is the third option:
"Multiply the first equation by 3 and the second equation by 2"
If we do that we will get the equations:
12x - 9y = 24
4x + 18y = -6
If we add these two equations no variable is canceled.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
two sheets of plywood are leaning up against one another, forming a small camping shelter. One sheet of plywood is 7 feet long and makes a 31 degree angle with the ground. The other sheet of plywood is 4 feet long. What is the approximate measure of the angle made between the two pieces of plywood.
The angle made between the two pieces of plywood found using the law of sines is approximately 85°
The law of sines states that the ratio of the sine of an angle to the length of the opposite side is the same for the three angles and sides of the triangle.
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]
The length of one plywood = 7 feet
The angle made by the 7 feet plywood with the ground = 31°
Length of the other sheet of plywood = 4 feet
Using the law of sines, we get;
sin(31)/4 = sin(B)/7
sin(B) = 7 × (sin(31)/4)
∠B = arcsine(7 × (sin(31)/4)) ≈ 64.33°
The angle between the two pieces of wood is therefore;
Angle = 180° - 31° - 64.33° = 85°
The measure of the angle formed between the two plywood is about 85°
Learn more about the law of sines here:
https://brainly.com/question/4372174
#SPJ1
Guadalupe has 15 cups of dough to make dumplings. If she uses 3/4 cup of dough for each dumpling, how many dumplings can Guadalupe make?
Answer: she can make 20 dumplings.
Step-by-step explanation:
15 divided by 3/4 (15/.75) = 20
someone help me solve this
y= x-2
Answer:
See below.
Step-by-step explanation:
There is nothing to solve without some additional information. Does the problem state what is to be done, or does it contain any information on the values of x or y? For example:
1) Rearrange for x:
y= x-2
x = y+2
2) What is the value of x if y is 3?
y= x-2
(3)= x-2
x = 5
12. An antique painting is purchased in 1980 for $995. The value increases by 3.1% every
year. Determine the increase in value of the painting in the 6th year after it was pur-
(3)
chased. You must include an equation with your solution.
An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02
What is increase in value?Increased Value is the amount obtained after deducting the Base Value from the current assessed value.
Given that,
An antique painting is purchased in 1980 for $995 = P
The value increases by 3.1% every = r
r = 3.1%
r = 3.1/100
r = 0.031
As we know,
Value of painting after t years: [tex]P (1+r)^t[/tex]
So, after 6 years:
f(6) = [tex]995 (1+0.031)^6[/tex]
or, f(6) = [tex]995 (1.031)^6[/tex]
or, f(6) = 1195.0197
or, f(6) = 1195.02
Now, at t = 0, f(0) = 995
Thus, value increased by, f(6) - f(0)
= [1195.02 - 995]
= 200.02
Thus, increase in price since it purchased = $200.02
To know more about value increases refer to:
https://brainly.com/question/9258878
#SPJ1
help me with this math question
Answer:
c
Step-by-step explanation:
$55 is what percent of $55?
100%
Step-by-step explanation:$55 = $55. Or in other terms:
100% = 100%
$55 is the maximum number of the problem, which would be 100%. So, they are asking what the maximum is. Which is 100%.
Solution:100%
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer: %100
Step-by-step explanation:
55 is the number you are using and the highest number is 55 so it will be %100
What is the slope of the line that passes through the points (-1, -7)and (1, -13)? Write your answer in simplest form.
Answer:
m=-3
Step-by-step explanation:
use slope formula to solve
m=rise/over=y2-y1/x2-x1
Here is a shaded parallelogram inside a rectangle.
2x
5
12
W
The area of the parallelogram is (10x +50) cm².
Work out the length of the base of the parallelogram.
Answer:
8
Step-by-step explanation:
Will mark 5 stars and give thanks
Answer:
x = 14.56 units
Step-by-step explanation:
In the given figure, two secants of the circle are intersecting outside of the circle.Thus, by the 'Theorem of intersecting secants', we have:[tex]9(9+x)=8(8+19)[/tex][tex]\implies 9(9+x)=8(27)[/tex][tex]\implies 81+9x=216[/tex][tex]\implies 9x=216-81[/tex][tex]\implies 9x=131[/tex][tex]\implies x=\frac{131}{9}[/tex][tex]\implies x=14.55555..[/tex][tex]\implies x\approx14.56\: units [/tex]Graph triangle lmn with vertices l(1,6), m(-2,4), and n (3,2) and its
image after the composition.
Rotation: 90 about the origin
Translation: (x,y) (x-3,y+2)
The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
What is Translation of graph?
A graph can be horizontally translated by moving the base graph to the left or right in relation to the x-axis. Each point on a graph is moved by k units in order to translate it horizontally.
To graph triangle LMN and its image after the composition of a 90 degree rotation about the origin and a translation of (x, y) (x-3, y+2), we can first plot the vertices of triangle LMN on the coordinate plane.
pair L = (1,6);
pair M = (-2,4);
pair N = (3,2);
Next, we can apply the 90 degree rotation about the origin to the vertices of the triangle. The rotation matrix for a 90 degree rotation about the origin is given by:
[cos(90) -sin(90)][x] [y]
[sin(90) cos(90)][y] = [-x]
Substituting the coordinates of the vertices into the rotation matrix, we get:
[cos(90) -sin(90)][1] [6]
[sin(90) cos(90)][-2] = [4]
[3] [2]
Therefore, the image of triangle LMN after the rotation is triangle L'M'N' with vertices L'(-6,1), M'(4,-2), and N'(-2,3).
Finally, we can apply the translation of (x, y) (x-3, y+2) to the vertices of the rotated triangle to get the final image of triangle LMN. The translation matrix is given by:
[tex][1 \ 0][x] [y][-3 \ 2][y] = [x-3][/tex]
Substituting the coordinates of the rotated vertices into the translation matrix, we get:
[1 0][-6] [1]
[-3 2][4] = [-1]
[-2] [3]
Therefore, The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
To know more about Translation of graph visit,
https://brainly.com/question/26238840
#SPJ1
Which ordered pairs lie on the graph of the exponential function ƒ(x) = 5 (1/2) ^x
Which fraction has the same value as 55.5¯%?
Answer: 55.5 as a fraction is 111/2.
Answer:
55.5/100 or 111/200 in its simplest form
Step-by-step explanation:
55.5 (per)cent) - means every 100
55.5/100= 111/200
Complete the similarity statement for the two quadrilaterals
given.
Enter your answer in the box.
quadrilateral PGY X ~ quadrilateral
Answer: loll ok so yes
Step-by-step explanation:
Write an expression equivalent to (2/5)x(2/5)x(2/5)x(2/5) using a positive exponent
Answer:
2/5^4
Step-by-step explanation:
2/5 is being multiplied four times
2x-6y=-18 please help me its due today
Answer:
Assuming you want to convert this to slope-intercept form.
Step-by-step explanation:
y=1/3x+3
Subtract 2x from both sides, then divide both sides by negative 6
if you want to graph it, this is what your graph should look like
** See attached photo**
HELP ASAP PLEASE I NEED THIS QUICK
40 POINTS
Answer: 4/25
Step-by-step explanation:
(2/5)^2 or can write as 2/5 times 2/5
2/5 times 2/5 = 4/25
Answer:
0.08
Step-by-step explanation:
2/5 = 0.4 x 0.4
To make 5 batches , jude need to use blank packages of pre mixed mortar
Answer:
the answer to your question is 20
Step-by-step explanation:
5 batches× 4 quarts
Help me plssssssssssssssssssss
Answer:
Yes, point (2,4) satisfies the system of inequalities.
Step-by-step explanation:
The area of the graph that is the darkest contains all points that satisfy both inequalities. See the attached worksheet for further explanation of the graph and other colors.
PLS HELP ME NEOW PLS
The correct order of sentences to bisect the angle Q is (1) draw a line from Q to where the arc crosses (2) vertex: set the compass to any convenient width (3) from where the arc crosses lag, make an arc.. (4) place the compass point on the angle Q.
How to bisect an angle?We should know that an angle is the intersection of two or more straight lines.
In construction of angles, using the compass, the first thing is to locate a point say Q. The open the leg of the compass to a convinient radius, make an arc at another point say P. From the point P, bisect the initial arc so made then joion to the starting point Q.
Second, from the point where the arcs met on the two lines, make another two arcs above the points, then join them to the starting point Q
Learn more about bisection of angles on https://brainly.com/question/29277802
#SPJ1