Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined
Step-by-step explanation:
According to the dilution law,
[tex]C_1V_1+C_2V_2=C_3V_3[/tex]
where,
[tex]C_1[/tex] = concentration of pure acid solution = 100 %
[tex]V_1[/tex] = volume of pure acid solution = x L
[tex]C_2[/tex] = concentration of another acid solution= 10%
[tex]V_2[/tex] = volume of another acid solution= (72-x) L
[tex]C_3[/tex] = concentration of resulting acid solution = 20 %
[tex]V_1[/tex] = volume of resulting acid solution = 72 L
Putting the values in the equation:
[tex]100\times x+10\times (72-x)=20\times 72[/tex]
[tex]x=8L[/tex]
Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72-liter batch of a 20% acid solution.
If two sides of a triangle are not =, the angle opposite the ___ side is the larger angle. shortest, intermediate, longest?
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
If two sides of a triangle are not equal,
According to Relationship between the angle and side , we know that the angle opposite the shortest side is the larger angle,
And,
The angle opposite the longest side is the shortest angle
So, First option is correct.
what happens to the graph of a line when the slope is negative? Check all that apply. may choose more then 1.
A. As the absolute value of the negative slope gets bigger, the graph of the line gets steeper.
B. As the absolute value of the negative slope gets smaller, the graph of the line gets steeper.
C. The line goes down from left to right.
D. The line shifts down.
E. The line goes up from left to right
How many real solutions does the function shown on the graph have?
Can someone explain?
One, Two, None, or can't be determined?
If the first equation is multiplied by 3 and then the equations are added, the result is _____.
3x + y = 3
x - 3y = -2
10x = 11
10x = 7
8x = 7
Answer: The correct option is (B) [tex]10x=7.[/tex]
Step-by-step explanation: The given equations are :
[tex]3x+y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-3y=-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
We are to select the correct result if the first equation is multiplied by 3 and then added to the second equation.
Now, multiplying equation (i) by 3, we get
[tex]3(3x+y)=3\times 3\\\\\Rightarrow 9x+3y=9~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
adding equation (iii) to equation (ii), we get
[tex](9x+3y)+(x-3y)=9+(-2)\\\\\Rightarrow 9x+3y+x-3y=9-2\\\\\Rightarrow 10x=7.[/tex]
Thus, the required result is [tex]10x=7.[/tex]
Option (B) is CORRECT.
Two workers produced 86 parts during their working shift. The first worker produced 15% more parts than the second one. How many parts did each worker produce?
Answer:
Worker 1: 46 parts
Worker 2: 40 parts
If x=4, then 5x=20 select the property
The property being used when substituting x=4 into the expression 5x to get 5*4=20 is the Substitution Property.
Explanation:When given the statement If x=4, then 5x=20, we are looking at a basic arithmetic operation, specifically multiplication. The property illustrated here is known as the Identity Property of Multiplication, which states that multiplying any number by 1 gives the number itself. However, in the context of this problem, the property being used is actually the Substitution Property, where the value of a variable (x=4) is substituted into an expression (5x) to find its value (5*4=20).
Learn more about Substitution Property here:https://brainly.com/question/12053340
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What is the number of real solutions?
–11x2 = x + 11
cannot be determined
one solution
two solutions
no real solutions
Answer:
no real solutions.
Step-by-step explanation:
-11[tex]x^{2}[/tex] = x+11. Put into standard form of a quadratic equation.
11[tex]x^{2}[/tex] + x + 11 = 0 Find a, b, and c.
a = 11, b =1, c = 11 Write and substitute into the quadratic equation[tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex] .
[tex]\frac{-1 +/- \sqrt{1^{2} - 4(11)(11)} }{2(11)}[/tex] Simplify.
[tex]\frac{-1 +/- \sqrt{1-484} }{2(11)}[/tex]=
[tex]\frac{-1 +/-\sqrt{-483} }{22}[/tex] BUT because the [tex]b^{2} -4ac[/tex] part under the √ is less than 0, THERE IS NO SOLUTION!
If he swim 900m in a day how many kilometers he swim
jamal is 167 cm tall which expression expression finds jamals height in dekametres
A.167 times 100
B.167 times 1000
C.167 divided by 100
D.167 divided by 1000
Jamal's height can be converted to dekametres by dividing his height in centimeters (167 cm) by 1000, because there are 1000 centimeters in a dekametre.
To convert Jamal's height from centimeters to dekametres, we should recall that 1 dekametre equals 10 meters or 1000 centimeters. Since Jamal is 167 cm tall, we need to divide his height in centimeters by the number of centimeters in a dekametre to get his height in dekametres.
Therefore, the correct expression to find Jamal's height in dekametres is:
167 divided by 1000
This is option D: 167 / 1000.
The exponential expression 4^-2 is equal to what fraction value
The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = .
Find the radius of a circle that has a circumference of 16.
Answer: 8 units
Step-by-step explanation:
Given: The formula for the circumference of a circle is [tex]C=2\pi r[/tex], where r is the radius and C is the circumference.
To solve equation for r , we divide [tex]2\pi[/tex] on both sides, we get
[tex]r=\dfrac{C}{2\pi}[/tex]
Now, the circumference of the circle = [tex]16\pi \text{units.}[/tex]
Then, [tex]r=\dfrac{16\pi}{2\pi}=8\ \text{units}[/tex]
Hence, Circumference of the circle = 8 units
Use the polynomial identity to determine which values of x and y generate the values of the sides of the following right triangle.
x = 8, y = 3
x = 3, y = 8
x = 6, y = 4
x = 4, y = 6
(3a2 + 2a - 2) - (a2 - 3a + 7)
What is the mean of 4, 6, 8, 20, 12?
Answer:
The correct answer is A. 10
4+6+8+20+12=50
50/5 =10
Step-by-step explanation:
Charlie was carrying around the steps to solve Square root of 6x plus 4 = 8. On his way through the Math Factory, Charlie dropped them and they mixed with other steps. Put the correct steps in order to solve Square root of 6x plus 4 = 8.
A. Divide by 2 from both sidesB. Square root both sidesC. Divide by 6 from both sides
D. Subtract 4 from both sidesE. Subtract 8 from both sidesF. Square both sides
Answer:
First F, then D, then C
For Earth Day, the school plans to sell the following buttons to students and the community. The school will have to pay $18 for 15 dozen buttons. How much will the school have to pay for 50 dozen buttons?
The school will have to pay $60 for 50 dozen buttons, by using a proportional calculation based on the known cost of $18 for 15 dozen buttons.
Explanation:The student's question involves calculating the cost of purchasing a larger quantity of buttons based on a known cost for a smaller quantity. To solve this, we will use proportional reasoning.
The school pays $18 for 15 dozen buttons. First, we find the cost for one dozen by dividing the total cost by the number of dozens:
$18 ÷ 15 dozen = $1.20 per dozen
Next, we calculate the cost for 50 dozen buttons by multiplying the cost per dozen by the number of dozens:
$1.20 per dozen × 50 dozen = $60
Therefore, the school will have to pay $60 for 50 dozen buttons.
What is the first step in solving a quadratic equation of the form given below?
(ax + b)2 = c
A.Divide both sides by c
B.Use the zero product rule
C.Factor out a common factor
D.Take the square root of both sides
the answer is d,,,,,,,,,,,,,,,,,
Answer:
Correct option is D.
Step-by-step explanation:
Given the quadratic equation
[tex](ax+b)^2=c[/tex]
we have to define the first step in solving a quadratic equation.
To find the value of x we have make the equation linear i.e taking the square root on both sides as c is any constant.
If c is 0 the we use the zero product rule.
Hence, our first step in solving a quadratic equation of the form
[tex](ax+b)^2=c[/tex]
is to take the square root of both sides.
Correct option is D.
Which pair of angles must be congruent?
A. Supplementary angles
B. Complementary angles
C. Adjacent angles
D. Vertical angles
Randolph has 8 ties, 6 pairs of pants, and 4 dress shirts. how many days can randolph go without wearing the same combination of these three items?
When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using __________.
A. The law of sines
B. The alternative form of the law of sines
C. The alternative form of the law of cosines
D. The Pythagorean Theorem
C. The alternative form of the law of cosines
When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using the alternative form of the law of cosines.
Explanation;From the law of cosines, given that a, b and c are the edges of a triangle and A, B and C are the corresponding interior angles of the the triangle.Then; a² = b² + c² − 2 bc cos A, or b² = a² + c² − 2 bc cos B, or c² = a² +b ² − 2 bc cos CTherefore; when given all the sides or edges of the triangle;
we can use the law of cosines to find one angle, then we use the law of cosines again to find the second angle, and finally,we use the point that angles in a triangle add up to 180 to get the third angle;Is the area between y = 1/x and y = 1/x^2 on the interval from x = 1 to finite or infinite?
The sum of 8 and 7, doubled
A pack of gum costs 75 cents. That is 3 cents less than three times what the pack cost 20 years ago. Which equation could be used to find the cost of the gum 20 years ago?
A)
0.3x - 0.3 = 0.75
B)
3x - 0.3 = 0.75
C)
3x - 3 = 75
D)
3 - 3x = 75
Answer:
C
Step-by-step explanation:
Let the cost of a pack of gum 20 years ago = x cents
Given, present cost of a pack of gum = 75 cents
Given, present cost of a pack of gum is 3 cents less than three times what the pack costs 20 years ago.
So,
[tex]75 + 3 =3x[/tex]
[tex]75= 3x -3[/tex]
[tex]3x-3=75[/tex]
Therefore,
Equation , [tex]3x-3=75[/tex] , can be used to find the cost of the gum 20 years ago.
Three identical coins, labeled A, B, and C in the figure, lie on three corners of a square 10.0 cm on a side. Determine the x coordinate of each coin, xA, xB, and xC.
This is a continuous set of numbers. every real number from the starting value to the ending value is included. it is called an ___.
Solve for y.
7y - 6y - 10 = 13
y = -23
y = -3
y = 3
y = 23
Which of the following are valid names for the triangle below? Check all that apply.
A. KE
B. KMD
C. DKM
D. SKMO
E. MDK
F. SKD
Answer:
KMD,MDK,DKM
Step-by-step explanation:
Write the tangent ratios for P and Q. The figure is not drawn to scale.
Answer:
tan P = 24/7 and tan Q = 7/24
Step-by-step explanation:
tangent of any angle in a right angle triangle is always represented by
tan x = opposite side/ adjacent side = height / base
from the question we have to write tangent of P and Q.
tan P = QR/PR = 24/7
tan Q = PR / RQ = 7/24
So the answers are tangent ratios for P and Q are 24/7 and 7/24.
What is the result if you divide -12x8y8 by 3x4y2? ...?
Answer:
-4x⁴y⁶
Step-by-step explanation:
To divide -12x⁸y⁸ by 3x⁴y², we can apply the rules of division for exponents.
When dividing variables with the same base, we subtract the exponents:
x⁸ / x⁴ = x⁸-⁴ = x⁴
Similarly, y⁸ / y² = y⁸-² = y⁶
Now, let's divide the coefficients:
-12 / 3 = -4
Putting it all together, the result of dividing -12x⁸y⁸ by 3x⁴y² is:
-4x⁴y⁶
Use the elimination method to solve the following system of equations.
2x - y + z = -3
2x + 2y + 3z = 2
3x - 3y - z = -4