Answer: 22 kph
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> [tex]\dfrac{5}{2(x-2)}=t[/tex]
Downstream equation: 3 = t(x + 2) --> [tex]\dfrac{3}{x+2}=t[/tex]
Set the equations equal to each other to solve for x:
[tex]\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x[/tex]
Step-by-step explanation:
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> \dfrac{5}{2(x-2)}=t
2(x−2)
5
=t
Downstream equation: 3 = t(x + 2) --> \dfrac{3}{x+2}=t
x+2
3
=t
Set the equations equal to each other to solve for x:
\begin{gathered}\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x\end{gathered}
2(x−2)
5
=
x+2
3
Cross multiply:
5(x+2)=3⋅2(x−2)
Distribute:
5x+10=6x−12
Isolate x:
10=x−12
22=x
I need help on this problem. (-5)^5/(-5)^-6
Answer: (-5)¹¹ of (-5)^11
Step-by-step explanation:
Since the base of the two exponents are teh same at -5, we can subtract the exponents.
5-(-6)=11
Now, we know that the new exponent will be 11, with the base staying the same.
Evaluate the expression when x = 5 and z= 7.
5z +x
Simplify your answer as much as possible.
Answer:
12
Step-by-step explanation:
We are given the expression:
[tex]\frac{5z+x^2}{x}[/tex]
and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.
[tex]\frac{(5(7)+(5)^2)}{5}[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, evaluate the exponent.
(5)²= 5*5= 25
[tex]\frac{(5(7)+25)}{5}[/tex]
Next, multiply 5 and 7.
5*7=35
[tex]\frac{(35+25)}{5}[/tex]
Next, add 35 and 25.
25+25=60
[tex]\frac{60}{5}[/tex]
Finally, divide 60 by 5.
[tex]12[/tex]
The expression (5z+x²)/x when x=5 and z=7 is 12.
Figure A is a scale image of Figure B.
27
Figure A
Figure B
45
35
What is the value of x?
Greetings from Brasil...
According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....
So
BIG/small = BIG/small
or
small/BIG = small/BIG
27/X = 45/35
OR
35/45 = X/27
27/X = 45/35
45X = 27·35
45X = 945
X = 945/45
X = 21The record high temperature in Alabama is 112f and the record low temperature is -27f. What is the difference between the highest and lowest temperature? A. 139 degrees B. 27 degrees C. 85 degrees D. 112 degrees
Answer:
(A) 139°
Step-by-step explanation:
What we are trying to find here is the distance between -27 and 112.
To do this, we have to think of it as a number line.
The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.
So the total distance is [tex]112+27=139[/tex]
Hope this helped!
Find m∠PQR. A. 81 B. 90 C. 77 D. 72
Work Shown:
Angle PQR = (far arc - near arc)/2
Angle PQR = ( (major arc PR) - (minor arc PR) )/2
Angle PQR = ( (2x+252) - (2x+108) )/2
Angle PQR = 144/2
Angle PQR = 72
Notice how we didn't need to find the value of x at all.
solve the equation -3+(1) −3+(1)
Answer:
-4
Step-by-step explanation:
you can just plug this into a calculator.
OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4
Answer:
-4
Step-by-step explanation:
-3 + (+1)= -2
2(-3 + (+1)) = -4
The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14
Answer:
r = 5 cm
Step-by-step explanation:
A = πr²
78.53 = (3.14)r²
divide by 3.14
25 = r²
r = ±5
r = 5
Read the table. 1/2 = 2 gallons 1 = 4 gallons 1 1/2 = 6 gallons. If this goes on. how much gallons is 6 1/2?
Answer:
24 1/2
Step-by-step explanation:
Every 1/2 is 2 gallons.
1/2 x 2 gallons = 4 gallons.
The whole number in 6 1/2 is 6.
1 x 6 = 6.
Now, we multiply 6 by 4 because each 1 = 4 gallons.
6 x 4 = 24.
There is still an 1/2 left in 6 1/2.
You add that.
Your answer is 24 1/2.
Hope this helps you!
You have —1 ounce of whole wheat grains. How many more ounces do you need to 8
make the recipe?
idek
-=-=-=--=-==-=-=-=-=-=-=-=-=-=-=-===========-----------------==============================================------------------------------------------------------====================================-----------==================--===================================--------------------------------------------------==========--------------------========----------------------------------------------------================-------------=====-=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
midpoint of the segment with endpoints A(-5, -2) and B(-7, 6).
(-6,2)
Inbox me on fb for more help with math same name as my brainly
Answer:
(-6,2)
Step-by-step explanation:
step by step explanation pls?
Answer:
x = 34
Step-by-step explanation:
x/3 - 7/3 = 9
Combine like terms
(x-7)/3 = 9
Multiply each side by 3
(x-7)/3 * 3 = 9*3
x-7 = 27
Add 7 to each side
x-7+7 = 27+7
x = 34
what is the difference between -8 to the power of 2 and (-8) to the power of 2?
Answer:
0
because -8 powered 2 and -8 powered 2 is same. 64-64=0
Step-by-step explanation:
Graph the function and its parent function. Then describe the
transformation.
g(x) = 1/3x^2
Answer: find the answer in the explanation
Step-by-step explanation:
Given the function and its parent function, to describe the
transformation of g(x) = 1/3x^2
First sketch the graph of the parent function which is g(x) = x^2
For every value of x, g(x) will take the value it would have had at kx, that is, the graph of g(x) = x^2 is stretched by a factor of 1/3 in the x - direction.
Find the attached files for the graph and solution
Pls help answer ASAP I will give Brainlyist
Answer:
Letter B because it is less than. < is less than
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
c < 27.50
The sign < means less than.
Plug the numbers in and you've got:
The cost is less than $27.50
Good luck mate :)
PLZ HELP ME 100 POINT AND BRAINEST Solve the Quadratic Equation X^2 = -8x -7
A. 7, -1
B. -1, -7
C. 8, 1
D. 7,1
E. -8, -1
Answer:
B
Introduction:Given equation: [tex]x^2 = -8x -7[/tex]
To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.
[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]
[tex]\implies 0= -8x -7 - x^2[/tex]
To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.
[tex]\implies 0= -1(8x + 7 + x^2)[/tex]
[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]
Finally, factor the expression on the right hand side.
Factoring a quadratic equation can be done in 2 ways.
1) Splitting methodIn this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.
The product of the suitable terms must be equal to the product of the first and last terms of the expression. The sum of the suitable terms must be equal the middle term.Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.
However, this method follows a condition. If the middle term cannot be split into two suitable terms, then the second method should be followed to determine a solution. 2) The Quadratic FormulaIn this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).
[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.
-----------------------------------------------------------------------------------------------------
Solving for x using the splitting methodWe can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.
[tex]\implies 0= x^2 + 8x+ 7[/tex]
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
Now, factor the first two terms and the last two terms separately.
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]
We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.
[tex]\implies 0= (x + 7)(x + 1)[/tex]
Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.
[tex]\implies x + 7 = 0; x + 1 = 0[/tex]
[tex]\implies x = -7; x = -1[/tex]
Solving for x using the Quadratic formulaNow, let us try to solve using the Quadratic formula.
[tex]0= x^2 + 8x+ 7[/tex]
Tip: Standard form: 0 = ax² + bx + c
Comparing both equations will allow us to determine the a, b, c variables.
⇒ a = 1; b = 8; c = 7
Now, let us plug these values into the quadratic formula and simplify.
[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]
Therefore, in both methods, the answer is -1, -7 (B).
Learn more about quadratic formula: brainly.com/question/22364785
Learn more about splitting method: brainly.com/question/13874704
Which equation is equivalent to 7w – 1 = –15?
A: 1 - 7w = -15
B: 7w = -15 + 1
C: 7w = –15 – 1
D: 7w = 15 - 1
Answer:
i believe the answer is A
Step-by-step explanation:
In each expression below identify the coefficient constant and variable
Answer:
The expression is missing in the question.
The expression is 4x +450
The variable is x and the coefficient is 4
Step-by-step explanation:
In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.
The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.
A dealer sold a painting for $800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.
She paid $640 for the painting
Step-by-step explanation:
her selling price SP = 800
CP+25%of CP = 800
1.25CP=800
CP=640
Answer:
$640
Step-by-step explanation:
paint sold for $800
profit 25%
the price she paid for the painting = $800 / 1.25 = $640
Show that the statement is true. If DF has endpoints D(-1,8) and E(3,-2), then the midpoint M of DE lies
I
in Quadrant I.
The midpoint M is
and the y-coordinate is (select)
). M lies in (select)
since the x-coordinate is (select) v
please help me with my homework
what is the slope of the line shown below? (1,-4) (2,2)
Your question has been heard loud and clear.
Slope formula when two points are given= y2-y1/x2-x1
Here y2= 2
X2=2
Y1= -4
X1= -1
= 2-(-4)/2-(-1)= 2
Slope of line= 2
Thank you.
Answer:
[tex]\huge \boxed{\mathrm{B. \ 2}}[/tex]
Step-by-step explanation:
The line crosses two points.
The two points are (-1, -4) and (2, 2).
The slope of a line can be found through two points.
[tex]\displaystyle \sf slope = \frac{rise}{run}[/tex]
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]y_2=2 \\ y_1 = -4 \\ x_2=2 \\ x_1=-1[/tex]
Plug in the values and evaluate.
[tex]\displaystyle m=\frac{2-(-4)}{2-(-1)}[/tex]
[tex]\displaystyle m=\frac{2+4}{2+1}[/tex]
[tex]\displaystyle m=\frac{6}{3}[/tex]
[tex]m=2[/tex]
The slope of the line is 2.
A contractor purchases 7 dozen pairs of padded work gloves for $102.48. She incorrectly calculates the unit price as $14.64 per pair for the expense report. What is the correct unit price? What is the error?
Answer:
The correct unit price can be calculated by dividing the total price paid by 84 that was the number of pairs of padded work gloves that were bought:
$102.48/84=$1.22
The correct unit price is $1.22.
-The error is that the person calculated the unit price by dividing the total price paid by 7 but the statement indicates that the contractor purchased 7 dozen pairs, which means: 7*12= 84. According to this, the contractor purchased 84 pairs of padded work gloves.
please help me on this
Answer:
Step-by-step explanation:
coordinate of O(2,1),Y(3,-2),T(-3,-3)
let the reflected points are O',Y',T'
distance of O from y=2 is 1 unit.
∴ ordinate of O' =1+2(1)=3
or O' is (2,3)
distance of Y from y=2 is2+2=4
ordinate of Y'=-2+2(4)=6
so coordinate of Y' is (3,6)
distance of T from y=2 is (2+3)=5
so ordinate of T' =-3+2(5)=7
coordinate of T' is(-3,7)
given the relation y=x+2, if the input is 3, what is the output
Answer:
The output is 5
Step-by-step explanation:
y=x+2,
Let x =3
y = 3+2
y = 5
The output is 5
Answer:
5
Step-by-step explanation:
We are given the relation:
y=x+2
The input is also called "x", and the output is also known as "y". We want to find the output, or y, when x is equal to 3.
Therefore, we must substitute 3 in for x and solve.
y= x+2 at x=3
y=3+2
Add 3 and 2.
y=5
If the relation is y=x+2 and the input is 3, then the output is 5.
8. Laurenpacksanorderofblocksin 2 crates and 7 stacks. How many blocks does Lauren pack?
Answer:
14
Step-by-step explanation:
(multiply 2by7)
2×7
=14
What equation represents a population of 300 animals at the crease and an annual rate of 23%
Answer:
300 + 69xStep-by-step explanation:
Given initial population of animals = 300 animals
If the population increases by 23% annualy, yearly increment will be expressed as:
Yearly increment = 23% of 300
Yearly increment = 0.23*300
Yearly increment for = 69
Let the total number of years of be x
Increment after x years = 69x
Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years
= 300 + 69x
Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x
ifran manages a coffee shop.
The rest of the question is in the screen shot
Answer:
230 capsules.
Step-by-step explanation:
The following data were obtained from the question:
Taste >>>>>>>>>>> Frequency
Volluto >>>>>>>>>> 12
Livanto >>>>>>>>>> 7
Ristretto >>>>>>>>> 23
Cosi >>>>>>>>>>>> 3
Other >>>>>>>>>>> 5
Next, we shall determine the total frequency.
This is illustrated below:
Total frequency = 12 + 7 + 23 + 3 + 5
Total frequency = 50
Finally, we shall determine the number of Ristretto in 500 capsules.
This can be obtained as follow:
Number of Ristretto = Frequency of Ristretto /total frequency x total capsule
Frequency of Ristretto = 23
Total frequency = 50
Total capsule = 500
Number of Ristretto = 23/50 x 500
Number of Ristretto = 23 x 10
Number of Ristretto = 230.
Therefore, the number of Ristretto in the 500 capsules is 230.
What is the value of
3 - x if x = 6?
Answer:
-3
Step-by-step explanation:
3-x if x=6
3-6
-3
Hope this helps ;) ❤❤❤
Answer: -3
Step-by-step explanation: In this case, we are given that x = 6.
So we have 3 - 6 which is -3.
(6x3 + 3x² + 3) + (2x - 5x + 1)
the sum is?
Step-by-step explanation:
(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)
6x^3 + 2x^3 = 8x^3
3x^2 + 0 = 3x^2
-5x + 0 = -5x
3 + 1 = 4
8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.
8x^3 + 3x^2 - 5x + 4
Hope this helped,
Kavitha
Answer:
= 8x³ + 3x² - 5x + 4
Step-by-step explanation:
(6x³ + 3x² + 3) + (2x³ - 5x + 1)
= 6x³ + 3x² + 3 + 2x³ - 5x + 1 remove parentheses
= 6x³ + 2x³ + 3x² - 5x + 1 group like terms
= 8x³ + 3x² - 5x + 3 + 1 add similar elements
= 8x³ + 3x² - 5x + 4
A rectangle is 10 inches smaller than it is wide. The perimeter of the rectangle is 80 inches. Find the length and the width of the rectangle.
Answer:
l = 15 and w = 25
Step-by-step explanation:
[tex]l - w = - 10[/tex]
[tex]l + w = 40[/tex]
Adding both equations
[tex]2l = 30[/tex]
[tex]l = 15[/tex]
subtracting both equation
[tex]2w = 50[/tex]
[tex]w = 25[/tex]
Hope it helps..........
BRAINLIEST PLEASE
Answer:
Length=30 Width=10
Step-by-step explanation:
Riley is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 6 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Answer:
After 6 minutes, the oven temperature will be: [tex]125^o[/tex]
Step-by-step explanation:
If the increase in temperature is [tex]10^o[/tex] per minute, then in 6 minutes, the increase in temperature would be [tex]6\,*\,10^o=60^o[/tex], therefore, since the initial temperature of the oven was [tex]65^o[/tex], its temperature after 6 minutes would be:
[tex]65^o+60^o=125^o[/tex]