A motorboat travels 464 kilometers in 8 hours going upstream and 644 kilometers in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of boat in still water ______km/h
Rate of current: _______ km/h
Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.
8(b - c) = 464
7(b + c) = 644
b - c = 58
b + c = 92
Adding the two together
2b = 150
b = 75
75 - c = 58
c = 17
The boat's speed is 75 mph and the current's speed is 17 mph.
Write each expression in exponential form
[tex]\sqrt[4]{6^5}[/tex]
Answer:
[tex]4*6^\frac{5}{2}[/tex]
Step-by-step explanation:
Use [tex]\sqrt[n]{a^x}=a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{6^5}[/tex] as [tex]6^\frac{5}{2}[/tex].
[tex]4*6^\frac{5}{2}[/tex]
Which equation is represented by the graph below?
On a coordinate plane, a curve starts at (0, negative 3) in quadrant 4 and then increases into quadrant 1 and approaches y = 3.
y = e Superscript x
y = e Superscript x Baseline minus 1
y = l n x
y = l n x minus 1
The equation represented by the graph will be y = eˣ. Then the correct option is A.
The missing graph is given below.
What is a function?Functions are found all across mathematics and are required for the creation of complex relationships.
The graph is given below.
The exponential graph is always positive and the graph is also positive of the Real value of x.
The equation represented by the graph will be y = eˣ.
Then the correct option is A.
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Please help me find the volume
The formula for calculating the volume of a cube is expressed as V = L³. The volume of the cube is 1/27 cubic meters
How to find the volume of the cube?The formula for calculating the volume of a cube is expressed as:
V = L³
where:
L = 1/3cm
Substitute
V = (1/3)³
V = 1/3³
V = 1/27 cubic meters
Hence the volume of the cube is 1/27 cubic meters
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A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m3. What is the width?
Which steps are correct? Check all that apply.
Substitute the known values into the formula:
140 = 7(w)(5).
Substitute the known values into the formula:
7 = 140(w)(5).
Substitute the known values into the formula:
5 = 7(w)(140).
Solve for the unknown: w = 4 m.
Solve for the unknown: w = 7 m.
Solve for the unknown: w = 2 m.
The question is incomplete because it was not properly and correctly arranged
Complete Question:
A rectangular prism has a length of 7 m, a height of 5 m, and a volume of 140 m³. What is the width? A prism has a length of 7 meters, width of w, and height of 5 meters.
Which steps are correct? Check all that apply.
a) Substitute the known values into the formula: 140 = 7(w)(5).
b) Substitute the known values into the formula: 7 = 140(w)(5).
c) Substitute the known values into the formula: 5 = 7(w)(140).
d) Solve for the unknown: w = 4 m.
e) Solve for the unknown: w = 7 m.
f) Solve for the unknown: w = 2 m.
Answer:
a) Substitute the known values into the formula: 140 = 7(w)(5).
d) Solve for the unknown: w = 4 m.
Step-by-step explanation:
The steps that are correct are Options a) and d). This is because:
Step 1
The volume of a rectangular prism is calculated as:
Volume of a rectangular prism = Length (l) × Width(w) × Height(h)
The unit of the volume or a rectangular prism is in cubic metres (m³)
In the question, we are asked to find the unknown value which is the width and we were given the following known values:
Length = 7 m,
Height = 5 m
Volume = 140 m³
Step 2
Solve for the unknown value( Width)
Volume of a rectangular prism = Length (L) × Width(W) × Height(H)
140m³ = 7m × Width(m) × 5m
140m³ = 35m² × Width(m)
Width(w) = 140m³ ÷ 35m²
Width(w) = 4m
Hence, the unknown Width(w) = 4m
From the above explanation we can see that the correct steps is Option a) and Option d)
Answer:
Step-by-step explanation:
Volume of rectangular prism= Length x width x height
V=L x W x H
140=7 x W x 5
140= 35 x w
W= 140/35
W= 4
If f is a fiction defined by the equation y=f (x), then x is called the ___ variable and y is the ___ variable.
Help please
What is the answer???
The sum of two polynomials is 8d5 – 3c3d2 + 5c2d3 – 4cd4 + 9. If one addend is 2d5 – c3d2 + 8cd4 + 1, what is the other addend?
6d5 – 2c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 4c3d2 + 3c2d3 – 4cd4 + 8
6d5 – 4c3d2 + 5c2d3 – 12cd4 + 8
6d5 – 2c3d2 – 3c2d3 – 4cd4 + 8
By subtracting the given addend to the sum, we see that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
How to get the other addend?
We know that the sum of two polynomials is:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9[/tex]
One of the addends is:
[tex]2d^5 - c^3d^2 + 8cd^4 + 1[/tex]
To get the other addend, we can subtract the given addend to the sum:
[tex]8d^5 - 3c^3d^2 + 5c^2d^3 - 4cd^4 + 9 - (2d^5 - c^3d^2 + 8cd^4 + 1)\\\\6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
Then we can conclude that the other addend is:
[tex]6d^5 - 2c^3d^2 + 5c^2d^3 - 12cd^4 - 8[/tex]
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I honestly am confused on this one
calculates the sum of the first 8 terms of an arithmetic progression starting with 3/5 and ending with 1/4
We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
How to get the sum of the first 8 terms?
In an arithmetic sequence, the difference between any two consecutive terms is a constant.
Here we know that:
[tex]a_1 = 3/5\\a_8 = 1/4[/tex]
There are 7 times the common difference between these two values, so if d is the common difference:
[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]
Then the sum of the first 8 terms is given by:
[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]
So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
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Given u = −8i − 3j and v = −12i − 7j, what is projvu?
−4.845i − 1.819j
−7.275i − 4.244j
−7.886i − 2.957j
−11.828i − 6.900j
Answer:
(b) -7.275i -4.244j
Step-by-step explanation:
The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.
__
The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.
[tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]
Example
In rectangle PRST, ST and RT are extended as shown.
What is mLUTV?
Since LPTS is a right angle, LPTR and
LRTS are complementary angles.
x + (2x-57) = 90
3x - 57 = 90
3x = 147
X = 49
So, m/UTV = 41°.
(2x-57)
T
LRTS and LUTV are vertical angles,
so m/UTV = m/RTS.
m/UTV = (2x - 57)°
= [2(49) - 57]⁰°
= 41°
S
Name another pair of complementary angles and another pair of vertical angles
Find m
Nani wait what I don't know
Kendra is researching the lowest recorded temperatures in four different cities. She wants to plot the lowest temperatures on a vertical number line. The lowest recorded temperatures of the cities are shown in the table below.
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
On a vertical number line, the point representing Morgantown's lowest recorded temperature should be plotted above the point representing
lowest recorded temperature.
On a vertical number line, the point representing Huntsville's lowest recorded temperature should be plotted below the point representing
lowest recorded temperature.
The attached number line represents points of the lowest recorded temperatures
How to represent the points on a number line?The table is given as:
City Lowest Recorded Temperature
Morgantown 7°F below 0
Charlotte 6°F above 0
Huntsville 4°F above 0
Bluefield 8°F below 0
To rewrite the table, we use the following representations:
Above 0 means positiveBelow 0 means negativeSo, we have:
City Lowest Recorded Temperature
Morgantown -7
Charlotte 6
Huntsville 4
Bluefield -8
See attachment for the number line that represents the above points
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12 is what percent of 24? What percent of 35 is 7? What percent of 90 is 9? 20 out of 60 is what percent?
Answer:
12 is 50% of 24
7 is 20% of 35
9 is 10% of 90
20/60 is 33.33%
evaluate 20÷(5 X 2/5 )+ 3 pls help
(05.03 LC)A polygon is shown:
The area of polygon MNOPQR = Area of a rectangle that is 9 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
The figure is the combination of the rectangle and square. Then the area of the figure will be 13 square units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Then the area of the geometry will be
The figure is the combination of the rectangle and square.
Then we have
Area = 3 x 3 + 4 x 1
Area = 9 + 4
Area = 13 square units
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What is the solution for x in the equation?
-3x+7x-8 = 34+9x-2
OA =
8
OB.
OC. * = -8
OD. = 8
*
118
Answer:
10
Step-by-step explanation:
-3x+7x-8=34+9x-2
(Combine like terms)
4x-8=32
(Add 8 to each side)
4x=40
(Divide by 4)
X=10
similarities between the Product Rule and Quotient Rule?
Step-by-step explanation:
Use the product rule for finding the derivative of a product of functions. Use the quotient rule for finding the derivative of a quotient of functions.
Workers need to know the area of a park to determine how much grass seed to order. A worker drew a sketch of the park to find its area. Which is the area of the park?
The area of the park is 1640 square meters.
What is a quadrilateral?A quadrilateral is a plane shape with four sides and four angles.
The above figure is made up of two quadrilateral; a square and a trapezium.
Analysis:
Area of park = area of square + area of trapezium
Area of park = 1/2(a + b)h + s x s
where a = length of smaller parallel side of the trapezium = 40m
b = length of the larger parallel side = 48m
h = height of trapezium = 35m
s = length of side of square = 10m
Area of park = 1/2(40 + 48)x35 + 10 x 10 = 1640 square meters
In conclusion, the area of the park is 1640 square meters
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Question 16 (5 points)
Find the domain of the function y = 5/3 tan(³/4^x).
A) All real numbers except 0 and odd integer multiples of 4
/3
B) All real numbers except odd integer multiples of 2/3
C) All real numbers except 0 and odd integer multiples of 2/3
OD) All real numbers except odd integer multiples of 4¹
/3
The domain is All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.
What is a function ?A function is defined as a mathematical statement that identifies the relation between a dependent and an independent variable.
A function has a defined range and domain.
In the given function
y = (5/3)tan(3x/4)
Domain is the all the value at which the function is defined .
Tan x is defined for every value except at
x = (2n+1)π/2
The domain of the function y = (5/3)tan(3x/4) is
3x/4 = (2n+1)π/2
x = (2n+1)2π/3
Therefore the domain is All real numbers except odd integer multiples of 2π/3 , Option B is the correct answer.
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(15 pts) Help me out with this please!
Answer:
18
Step-by-step explanation:
my answer is correct,try to read the question,
if the length of larger triangle is 6 times so it means 6 ×5= 30 and you will times 3 to 6=18
so that's why it has lenght of 30
because the. larger triangle is 6 times bigger than smaller rectangle
100%✓sure answer
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use mathematics to calculate [tex] Ilan \ ang \ asawa \ ni \ Sheryl [/tex]
[tex] 4x² - 12x + 9 = 0 [/tex]
[tex]~~~~~~~4x^2-12x+9=0\\\\\implies (2x)^2-2 \cdot 2x \cdot 3+3^2 = 0\\\\\implies (2x-3)^2 = 0\\\\\implies 2x -3 = 0\\\\\implies x =\dfrac 32[/tex]
Please help me with this math problem and I will help you.
In a survey, 60% of those questioned chose winter as their favorite season.
If 48 people chose winter, then how many people were surveyed?
A.29
B.32
C.80
D.128
Answer:
C. 80Step-by-step explanation:
Let the number of people were surveyed is x.
We have 60% of x is 48 people.
Set this as equation and solve:
60% of x = 48x*60/100 = 480.6x = 48x = 48/0.6x = 80Correct choice is C.
Answer:
C. 80
Step-by-step explanation:
Given:
60% = 48 peopleLet x be the total number of people surveyed.
Set up a ratio of people to percentage and solve for x:
[tex]\implies \sf 48 : 60 = x : 100[/tex]
[tex]\implies \sf \dfrac{48}{60}=\dfrac{x}{100}[/tex]
[tex]\implies \sf x=100 \cdot \dfrac{48}{60}[/tex]
[tex]\implies \sf x=\dfrac{4800}{60}[/tex]
[tex]\implies \sf x=\dfrac{480}{6}[/tex]
[tex]\implies \sf x=80[/tex]
Therefore, the total number of people who were surveyed was 80.
3x – 2y = -4
4x + 2y = 25
Answer:
(-21, 54.5)
Step-by-step explanation:
Hello there!
We have two methods to solve this problem.
Substitution methodElimination method.We will limit ourself to Substitution method.
3x – 2y = -4.................... 1.
4x + 2y = 25................... 2.
First lets manipulate eq.2 in terms of y.
4x + 2y = 25
2y = 25 - 4x
y = 25/2 - 2x .............. eq.3
Substitute eq.3 into eq.1
3x – 2(25/2 -2x) = -4
Solve for x.
Opening the brackets
3x - 25 - 4x = -4
-x = 21
x = -21
Substitute x into equation 3
y = 25/2 - 2x
=> y = 25/2 - 2(-21)
= 54.5
In terms of x and y; (x,y)
= (-21, 54.5)
I hope this helps.
Have a nice studies.
Find area in square units
Step-by-step explanation:
please mark me as brainlest
» Solve the equation 9(k − 2) = −6.
-
k = 1
Answer:
False
Step-by-step explanation:
9(k-2)=-6 and k=1
9(1-2)=-6
9(-1)=-6
-9=-6
No, -9 doesn't equal -6.
So this system of equations is false.
Hope this helped! :)
Find the value of x so that (x,-2) satisfies 3y - 4x = 6, x=
Step-by-step explanation:
please mark me as brainlest
Which of the following is a linear equation?
a. 4x² +9y² = 25
b. 2+6= 15
c. 2x-3y=7
d. 4x+6=30
2x - 3y = 7 can be rewritten as y = 2/3x - 7/3, therefore, the equation that is a linear equation is: C. 2x - 3y = 7.
What is a Linear Equation?A linear equation is expressed in the slope-intercept form as y = mx + b.
2x - 3y = 7, rewritten in slope-intercept form would be:
-3y = -2x + 7
y = -2x/-3 + 7/-3
y = 2/3x - 7/3
m = 2/3 and b = -7/3
Therefore, the equation that is a linear equation is: C. 2x - 3y = 7.
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A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has
a y intercept of 6.
What is the equation of the function described?
The equation for the sinusoidal function described is given as follows:
[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]
What is a sinusoidal function?We want a function with a y-intercept at it's maximum value, hence we use the cosine equation, given by:
[tex]y = A\cos{\left(\frac{2\pi}{B}x\right)} + C[/tex]
In which:
2A is the amplitude, which is the difference between the largest and smallest value.B is the period.C is the vertical shift, considering that the standard cosine function has range between -A and A.The amplitude is of 8, hence 2A = 8 -> A = 4. This would represent a function between -4 and 4, but we want between -2 and 6, hence the vertical shift is of C = 2.
As for the period, we have that:
[tex]B = 4\pi[/tex]
Then, the equation is given by:
[tex]y = 4\cos{\left(\frac{1}{2}x\right)} + 2[/tex]
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Which is an x-intercept of the continuous function in the table ? (0, - 6); (3, 0); (- 6, 0) O (0, 3)
An x-intercept of the continuous function in the table is (-1, 0)
Intercept of a lineThe x-intercept of a line is the point where the line crossed the x-axis or the point where the value of y is zero.
From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)
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