Answer:
Step-by-step explanation:
Total amount in cents (unsimplified): 5N +17(10-N)
Simplified: 170-5N
A chemist has a container of 12% peroxide solution and a container of 20% peroxide solution. She needs to mix the two solutions to create 100 mL of a 14% solution. If x represents the amount of 12% peroxide solution and y represents the amount of 20% peroxide solution she needs, which matrix equation can determine the amount of each solution she needs to make the 14% solution?
Answer:
[tex]0.12x+0.2y=14,\:x+y=100\quad :\quad x=75,\:y=25[/tex]
Step-by-step explanation:
.12x + .2y = 14
x + y = 100
Answer:
Its B
Step-by-step explanation:
3y^4/3y^2-6=10 please help I will.mark it as the brainliest answer!
Answer:
y=4
Step-by-step explanation:
you multiply through by 3y^2
3y^4 - 18y^2 =30y^2
Collect like terms
3y^4=48y^2
divide through by y^2
3y^2=48
divide through by 3
y^2=16
take the square root of both sides
y=4
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Y = 1/4 x -3
Step-by-step explanation:
x1 y1 x2 y2
0 -3 -8 -5
ΔY -2
ΔX -8
slope= 1/4
B= -3
Y =0.25X +-3
The length L of the base of a rectangle is 5 less than twice its height H. Write the algebraic expression to model the area of the rectangle.
The length L of the base of a rectangle is 5 less than twice its height H. Then the algebraic expression be, area of rectangle = 2H² - 5H.
What is the algebraic expression to model the area of the rectangle?Let, the given information be "The length L of the base of a rectangle is 5 less than twice its height H".
L be the length of the rectangle
H be the height of the rectangle
By converting the given information into an algebraic expression, we get
Length = 2H - 5
The area of a rectangle is given by the formula;
Area of rectangle = L [tex]*[/tex] H
Where L is the Length.
H is the Height.
Substituting the values into the formula, we have;
Area of rectangle = (2H - 5) [tex]*[/tex] H
Area of rectangle = 2H² - 5H
Therefore, the area of rectangle = 2H² - 5H.
To learn more about algebraic expression of rectangle
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Guided Practice
Which model is most appropriate for the set of points?
(–3, 6), (–1, 0), (0, –1), (1, –1.5)
A.
exponential
B.
quadratic
C.
linear
Answer:
B. quadratic
Step-by-step explanation:
Answer: The model that is most appropriate for the set is: Quadratic
Answer:
exponential
Step-by-step explanation:
Just took the test
Solve for x
Need help asap
Answer:
[tex]x=55[/tex]
Step-by-step explanation:
Corresponding angles of two parallel lines are always equal. The angle on "top" of [tex]2x+6[/tex] corresponds with the angle marked as [tex]x+9[/tex]. Therefore, its measure must also be [tex]x+9[/tex].
Since these two angles form one side of a line which has 180 degrees, we have the following equation:
[tex]2x+6+x+9=180[/tex]
Combine like terms:
[tex]3x+15=180[/tex]
Subtract 15 from both sides:
[tex]3x=165[/tex]
Divide both sides by 3:
[tex]x=\frac{165}{3}=\boxed{55}[/tex]
HELPPPPP
A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?
Answer is : 2,8, and 32
Please show steps because I'm very confused
Let x be the first term in the geometric sequence. Then the next two terms in the sequence are xr and xr ², where r is some constant. (This is the defining characteristic of geometric sequences.)
The sum of the first three terms is 42, so
x + xr + xr ² = 42
x (1 + r + r ²) = 42
The third term is 3.2 times the sum of the other two, so that
xr ² = 3.2 (x + xr )
Solve the second equation for r :
xr ² = 3.2 x (1 + r )
We can divide both sides by x since x ≠ 0. (This is obvious, since if x was zero, then all three terms in the sequence would be 0.)
r ² = 3.2 (1 + r )
r ² = 3.2 + 3.2r
r ² - 3.2r - 3.2 = 0
r ² - 16/5 r - 16/5 = 0
5r ² - 16r - 16 = 0
(5r + 4) (r - 4) = 0
==> r = -4/5 or r = 4
Since there are two possible values of r that might work, there are two possible sequences that meet the criteria.
Plug either of these solutions into the first equation:
r = -4/5 ==> x (1 + (-4/5) + (-4/5)²) = 42
… … … … … … 21/25 x = 42
… … … … … … x = 50
r = 4 ==> x (1 + 4 + 4²) = 42
… … … … … 21x = 42
… … … … … x = 2
Then the two possible answers would be
• if r = -4/5, then the three terms are {50, -40, 32}
• if r = 4, then they are {2, 8, 32}
Answer:
Step-by-step explanation:
A geometric series means that we multiply one number by a common ratio to get the second number. Let's say our first number is x, and our common ratio is y. We can write the first term is x, and to get the second number, we multiply x by our common ratio, y. For example, if 5 was the first number and 2 was the common ratio, the second number would be 5*2 = 10, and the third would be 10 * 2 = 20.
For our question, the first number is x, the second is x*y, and the third is x*y*y = x*y²
The sum of these three terms is 42, so we can say
x + x*y + x*y² = 42
Next, the third term is equal to 3.2 times the sum of the other two. First, we have 3.2 times something. That something is the sum of the other two, so we must prioritize calculating the sum of the first two numbers, and then multiply that by 3.2 to get the third. We can write this as
(x + x*y) * 3.2 = x*y²
factor out x
x * 3.2(1 +y) = x*y²
divide both sides by x
3.2(1+y) = y²
expand
3.2 + 3.2y = y²
subtract (3.2 + 3.2y) from both sides to make this a quadratic equation
y²-3.2y-3.2 = 0
use the quadratic formula to solve for y (note that +- here stands for "plus or minus")
[tex]y = \frac{-(-3.2) +- \sqrt{3.2^{2}-4(-3.2)(1)} }{2} \\= \frac{3.2+-\sqrt{10.24+12.8} }{2} \\= \frac{3.2+- 4.8}{2}[/tex]
= -0.8 or 4
With these two possibilities, we can try each in our other equation to see what works.
x + x*y + x*y² = 42
for y = -0.8
x + -0.8x + 0.64x = 42
x - 0.16x = 42
0.84x = 42
multiply both sides by 1/0.84 to isolate the x
x=50
This works, with x (the first number) =50, the second number being 50 * -0.8 = -40, and the third being -40 * -0.8 = 32. 50+(-40) = 10, 10*3.2=32, and 50-40+32 = 42
Next, for y=4, we have
x+4x + 16x= 42
21x = 42
divide both sides by 21 to isolate the x
This works as well, with x=2, the second value being 2*4 = 8, and the third value being 8*4 =32. 2+8=10, 10*3.2 = 32, and 2+8+32 = 42
Instructions: Fill in the last step of solving the quadratic equation by factoring. 3x2−2x−5=0 Step 1: Rewrite middle term. 3x2−5x+3x−5=0 Step 2: Group terms together and find GCF. (3x2−5x)+(3x−5)=0 x(3x−5)+1(3x−5)=0 (3x−5)(x+1)=0 Step 3: Apply the Zero Product Property. 3x−5=0 or x+1=0 Step 4: Solve. x= or x=
Answer:
x = (5/3)
x = -1
Step-by-step explanation:
[tex]3x^2 -2x - 5 =0\\\\(3x^2+3x) + (-5x - 5) = 0\\\\(3x-5)(x+1)=0\\\\\left \{ {{3x-5=0} \atop {x+1=0}} \right.\\\\===========\\\\3x - 5 = 0\\\\3x - 5 + 5 = 0 + 5\\\\3x = 5\\\\\frac{3x=5}{3}\\\\x = \frac{5}{3}\\\\===========\\\\x + 1 = 0\\\\x + 1 - 1 = 0 - 1\\\\x = -1 \\\\===========\\\\\boxed{\text{Therefore:}}\\\\\boxed{ x = \frac{5}{3} \text { or } x = -1}[/tex]
You would just need to solve the two equations from step three for 'x'.
Hope this helps you.
If b = -1, which one is the value of b^3?
Answer:
b=-1Put the value of b in b^3[tex] \\ \sf \longmapsto \: b {}^{3} \\ \\ \sf \longmapsto \: { - 1}^{3} \\ \\ \sf \longmapsto \: 1 \times - 1 \\ \\ \sf \longmapsto \: - 1[/tex]
Hence b^3=-1
1. Una empresa realizó una encuesta a 250 personas para saber qué programa de televisión prefieren ver en domingo. Se les dieron 3 opciones: deportes, películas o musicales. El resultado de la encuesta fue: 130 personas prefieren deportes; 80 prefieren ver películas; 40, musicales; 25 prefieren deportes y películas; 20, películas y musicales; 10, deportes y musicales; y sólo a 6 personas les gustan los tres tipos de programas. a) ¿Cuántas prefieren ver sólo deportes? b) ¿Cuántas prefieren ver sólo un programa de televisión? c) ¿Cuántas prefieren ver películas o musicales?
Answer:
A) 89 personas prefieren ver sólo deportes.
B) 122 personas prefieren ver sólo un programa de televisión
C) 33 personas prefieren ver películas o musicales.
Step-by-step explanation:
Dado que una empresa realizó una encuesta a 250 personas para saber qué programa de televisión prefieren ver en domingo, y se les dieron 3 opciones: deportes, películas o musicales, donde el resultado de la encuesta fue: 130 personas prefieren deportes; 80 prefieren ver películas; 40, musicales; 25 prefieren deportes y películas; 20, películas y musicales; 10, deportes y musicales; y sólo a 6 personas les gustan los tres tipos de programas; para determinar A) cuántas prefieren ver sólo deportes, B) cuántas prefieren ver sólo un programa de televisión; y C) cuántas prefieren ver películas o musicales, se deben realizar los siguientes cálculos:
A)
130 - 25 - 10 - 6 = 89
B)
80 - 25 - 20 - 6 = 29
40 - 20 - 10 - 6 = 4
89 + 29 + 4 = 122
C)
29 + 4 = 33
the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.
Answer:
Smaller factor/larger figure = 3/6 = ½
Step-by-step explanation:
Scale factor of similar figures is usually the ratio of one to the other.
In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.
Length of smaller figure = 3
Corresponding length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = ½
a.) Where does the turning point of the curve Y= 6- 4x - x^2 occur?
b.) Differentiate with respect to x, [tex]\frac{cos x}{sin 2x}[/tex]
Answer:
Have you gotten the answer. if yes Hmu... Aihs I sit beside you
Step-by-step explanation:
Which of the following equations correctly represents the law of sines?
Answer:
Option c is correct
Step-by-step explanation:
From the screenshot I attached.
sinA/a=SinC/c
a/c=SinA/SinC
Thus a=cSinA/SinC
Emily says that the lengths of the sides of her prism are 6 inches 5 inches
and 3 inches. Is Emily correct? Use words and numbers to explain why or
why not.
− 10x− 6y = 12
4x+ 7y =− 14
x=0, y=-2
tell me if u need the explanation
6.7.35
Question Help
As(t)
800-
A toy rocket is launched from the top of a building 360
feet tall at an initial velocity of 112 feet/second. The
height of the rocket t seconds after launch is given by
the equation s(t)= - 16t2 + 112t+ 360. When does the
rocket reach its greatest height? What is the greatest
height?
600-
400-
200-
0-
0 1
8 9 10
The rocket reaches its greatest height at
feet after
second(s)
Answer:
Step-by-step explanation:
This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!
The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.
If:
[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:
v(t) = -32t + 112 and solve for t:
-112 = -32t so
t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.
Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:
[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and
s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.
Evaluate in 7
0.51
1.95
0.85
1.61
Answer:
We may log in directly in our scientific calculator the given value ln 7 and get an answer of 1.9459. On the other hand, we can rewrite the expression as,
log to the base e or 7 = x
which can be written as,
e^x = 7
The value of x from this is still equal to 1.9459.
Step-by-step explanation:
Which is enough information to prove that U|| V?
Answer:
∠4 = ∠8
Step-by-step explanation:
the lines are parallel if a pair of corresponding angles are congruent
work out the length of ab
Answer:
AB = 2√137
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
a = 22 cm
b = 8 cm
Step 2: Solve for c
Substitute in variables [Pythagorean Theorem]: (22 cm)² + (8 cm)² = c²Evaluate exponents: 484 cm² + 64 cm² = c²Add: 548 cm² = c²[Equality Property] Square root both sides: 2√137 cm = cRewrite: AB = 2√137Answer:
AB= 2√137 cm
Step-by-step explanation:
because we have a right triangle we apply the Pythagorean theorem
hypothenuse² = side² + side²
AB² = BC² + AC², substitute the given sides BC=8 and AC=22
AB² = 8² + 22² , square the numbers and apply the square root to both side
AB = √(64 + 484), add the numbers
AB = √548, simplify the square root
AB= 2√137 cm
please help me out i need this answer very fast! 20points!!!!
Graph the system of equations on graph paper to answer the question.
{y=2/5x+4
y=2x+12
What is the solution for this system of equations?
Enter your answer in the boxes.
1.Find the first five terms of the recursive sequence.
Answer:
4.5, - 27, 162, - 972, 5832
Step-by-step explanation:
Using the recursive rule and a₁ = 4.5 , then
a₂ = - 6a₁ = - 6 × 4.5 = - 27
a₃ = - 6a₂ = - 6 × - 27 = 162
a₄ = - 6a₃ = - 6 × 162 = - 972
a₅ = - 6a₄ = - 6 × - 972 = 5832
The first 5 terms are 4.5, - 27, 162, - 972, 5832
pls answer correctly and explain
thx
Answer:
36n = 360
Step-by-step explanation:
A dozen is 12
3 dozen is 3*12 = 36
36 * n boxes = 360
36n = 360
find the missing length
Answer: x = 120
Step-by-step explanation:
Okay so you have three similar right triangles. To find x, you can set up an proportion [tex]\frac{shorter leg}{long leg} = \frac{64}{x} = \frac{x}{225}[/tex] since similar figures are in proportion. By cross multiplying and finding the square root of x^2, you result in x equaling 120.
If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number.?
Answer:
5:3
Step-by-step explanation:
40% = 2/5
If the numbers are x and y, then
2/5 x = 2/3 y
Divide both sides by 2/5
x = (2/3 * 5/2)y
x = 10/6 y
x = 5/3 y
So the required ratio is 5 : 3.
Checking this result:
10% of 5 = 2
2/3 of 3 = 2 also.
50 points. Please explain each step
Solution given:
Cos[tex]\theta_{1}=\frac{10}{17}[/tex]
[tex]\frac{adjacent}{hypotenuse}=\frac{10}{17}[/tex]
equating corresponding value
we get
adjacent=10
hypotenuse=17
perpendicular=x
now
by using Pythagoras law
Hypotenuse ²=perpendicular²+adjacent ²
substituting value
17²=x²+10²
17²-10²=x²
x²=17²-10²
x²=189
doing square root
[tex]\sqrt{x²}=\sqrt{189}[/tex]
x=[tex]3\sqrt{21}[/tex]
now
In I Quadrant sin angle is positive
Sin[tex]\theta_{1}=\frac{perpendicular}{hypotenuse}[/tex]
Sin[tex]\theta_{1}=\frac{3\sqrt{21}}{17}[/tex]Answer:
sin theta = 3 sqrt(21)/17
Step-by-step explanation:
cos theta = adj / hyp
We can find the opp by using the Pythagorean theorem
adj^2 + opp ^2 = hyp^2
10^2 +opp^2 = 17^2
100 + opp^2 = 289
opp^2 = 289-100
opp^2 = 189
Taking the square root
opp = sqrt(189)
opp = 3 sqrt(21)
Since we are in the first quad, opp is positive
sin theta = opp /hyp
sin theta = 3 sqrt(21)/17
Find the measure of angle BAC.
Answer:
[tex]\angle 72=BC-86/2[/tex]
[tex]144+86=BC[/tex]
[tex]BC=230[/tex]
[tex]BC=230/2[/tex]
[tex]\angle BAC= 115[/tex]°
~OAmalOHopeO
Corine needs 4 pieces
each a foot long to make one
friendship bracelet. She has a total of 144 inches of string. How many friendship bracelets can Corina make?
[?]friendship bracelets
Answer:
Corina can make 3 friendship bracelets.
Step-by-step explanation:
Solve for how much string is needed for one friendship bracelet:
4 pieces × 1 foot
4 feet
Convert feet into inches (1 foot = 12 inches):
4 feet × 12 inches
48 inches
Divide the total string by each bracelet's string:
144 inches ÷ 48 inches
3 friendship bracelets
Answer:лаксдкннйд
Step-by-step explanation:
Which equation represents the graph?
y=3x²-4
y=-3x²-4
y=-3x²+4
y=3x²+4
Find the equivalent percent for ¾
3/4 is equivalent to 75%.
To find the percentage of a fraction, you simply just divide the numerator by the denominator. 3/4=0.75, which is 75%.
Answer:
75%....3/4 expressed as a percentage is just multiplying 3/4 and 100
Polygon D is a scaled copy of Polygon C using a scale factor of 6.
How many times as large is the area of Polygon D compared to the area Polygon C?
Answer:
The area of D is 36 times bigger than C
Step-by-step explanation:
The scale factor is 1:6
We know the ratio of the areas is the ratio of the scale factor squared
1^2 : 6^2
1:36
The area of D is 36 times bigger than C
