Given:
Matrix c =
[tex]\begin{bmatrix}{c} & {0} \\ {0} & {d}\end{bmatrix}[/tex]How many liters each of a 50% acid solution and a 75% acid solution must be used to produce 70 liters of a 70% acid solution? (Round to two decimal places if necessary.)
We can express this as a system of equations.
Let x be the liters of the 50%-acid solution and y the liters of the 75%-acid solution.
We then need 2 equations to solve this.
One equation is the total amount of liters (70 liters) that is equal to the sum of the amount of each solution:
[tex]x+y=70[/tex]The second equation is the final concentration, that is a weighted average of the concentration of each solution:
[tex]0.5\cdot x+0.75\cdot y=0.7\cdot70=49[/tex]Then, we can solve this by substitution:
[tex]x+y=70\longrightarrow y=70-x[/tex][tex]\begin{gathered} 0.5x+0.75y=49 \\ 0.5x+0.75(70-x)=49 \\ 0.5+52.5-0.75x=49 \\ -0.25x=49-52.5 \\ -0.25x=-3.5 \\ x=\frac{3.5}{0.25} \\ x=14 \end{gathered}[/tex]Then, we can calculate y as:
[tex]y=70-x=70-14=56[/tex]Answer: we need 14 liters of the 50% acid solution and 56 liters of the 75% acid solution.
Jonathan's checking balance is -45 dollars. After receiving his allowance he deposits $7 into the account. What is the balance of the account after Jonathan's deposit?
Given,
The initial balance in the account is - 45 dollars.
The amount he deposite in the account is $7.
The balance of the account after Jonathan's deposit is,
[tex]\text{Balance of the account=initial balance+deposite amount}[/tex]Substituting the values then,
[tex]\text{Balance of the account=-}45+7=-38[/tex]Hence, the balance of the account after Jonathan's deposit is $-38.
Student in a limnology class took water from a lake to determine the temperature at different depths. Which of the following techniques for gathering data do you think was used
The Experiment is the best way to determine the temperatures at different depths. This is because to do a measurement of the temperature it's necessary that the student introduce a thermometer into the water by himself, and determine how the temperature is changing while He is go down with the thermometer into the water of the lake.
All the previous description is the description of an Experiment.
to factor the trinomial by grouping, you need to find two integers whose product is -15 and whose sum is which number?
Answer
The answer is -2.
Explanation
In trying to factorize the expression given by grouping,
The volume of a soup can is 125.6 cubic inches the diameter of the can is 8 inches what is the height of the soup can
Okay, here we have this:
Considering the provided information, we are going to calculate the requested height of the cylinder, so we obtain the following:
Then to find the requested height we will clear the height of the formula for the volume of a cylinder, therefore we have:
V=h * π * r^2
h=V/(π * r^2)
Replacing with the given values:
h=V/(π * (d/2)^2)
h= 125.6 in^3/(π * (8in/2)^2)
h= 125.6 in^3/(π * (4in)^2)
h= 125.6 in^3/(π * 16in^2)
h= 125.6 in^3/(3.14 * 16in^2)
h= 125.6 in^3/(50.24 in^2)
h= 2.5 inches
Finally we obtain that height of the soup can is 2.5 inches.
What do they mean to write 5 less than r as an expression
What do they mean to write 5 less than r as an expression?
Explanation:
From the given data,
[tex]r-5[/tex]Thus, the expression is (r-5)
Hey :)
[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Put a minus sign between 5 and r. And put 5 after the minus.
[tex]r-5[/tex]. This is what the expression is. If you do everything correctly, then ur answer should be [tex]r-5[/tex].
So, the calculations showed that the answer is x=5. I hope i could provide a good explanation and a correct answer to you. Thankyou for taking the time to read my answer.
here for service,
silennia[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]
Which equation represents a line which is parallel to y=0?A. y=−2B. y=xC. y=-8D. x=1/4y
We have a line described with the equation
[tex]y=0[/tex]This describes a horizontal line in the plane, at the height of the x-axis, let's remember that
the horizontal line is the one whose trajectory represents the direction of the horizon as we perceive it. We can also say that the horizontal lines are lines with zero slope.
On the other hand, we must remember that parallel lines are those that, while traveling in the same direction, remain separated at exactly the same distance from each other for exactly the same time.
That is to say that for a line to be parallel we must have another horizontal line.
Now let's determine which equations represent parallel lines one by one.
[tex]y=-2[/tex]The above equation represents a slope of zero, i.e. it is a horizontal line so it is a parallel line.
[tex]y=x[/tex]The above equation represents a slope of one, i.e. it is not a horizontal line so it is not a parallel line.
[tex]y=-8[/tex]The above equation represents a slope of zero, i.e. it is a horizontal line so it is a parallel line.
[tex]x=\frac{1}{4}y[/tex]The above equation represents a slope of one, i.e. it is not a horizontal line so it is not a parallel line.
[tex]y=-8[/tex]In conclusion, the answer is that y = -2 and y = -8 are parallel lines.
A translation 1 unit down and 6 units left maps L onto L'. If the coordinatesof L are (-2, 6), what are the coordinates of L'?
Translation
We are given the rule for a translation: 1 unit down and 6 units left. It can be written as:
(x,y) --> (x - 6 , y -1 )
We need to subtract 6 units to the x-coordinate and subtract 1 unit to the y-coordinate.
The point L=(-2,6) will map to L' when applied the translation described above.
The coordinates of L' are:
L' = (-2-6 , 6 - 1 ) = (-8 , 5)
The coordinates of L' are (-8,5)
PRACTICED Make sense of Problems A bus has 15 rows of seats. Each row has 4 seats. At the first stop, 25 people get on the bus. At the second stop, 3 people get off of the bus, and 12 people get on the bus. How many empty seats are there after the second stop? ? ? Building on the Essential Question How can I us 9. equations to model real-world problems?
Given:
A bus has 15 rows of seats. Each row has 4 seats.
So, a total of 60 seats.
At the first stop, 25 people get on the bus.
So, the number of occupied seats is 25 and the number of unoccupied seats is 35.
At the second stop, 3 people get off of the bus, and 12 people get on the bus.
So, the number of occupied seats is 34 and the number of unoccupied seats is 26.
Hence, a number of empty seats are thereafter the second stop is 26.
Carrie and Steve agree to a $149,000 mortgage at 5.5% annual interest for 30 years. They have a monthly payment of $846.01 and the interest paid in month one is $682.92. Assuming they only make the minimum payment in month one, what do you know about their loan?
They make the minimum payment in month one, which is just the interest from the value of the mortgage. That means that the initial $149.000 has no change, if the value of the mortgage has no change, and the interest neither, then the interest in month two will be $682.92.
Find the quotient. 5 3 2 = 7 8 12 3 5 2 = 7 8 12 (Type a whole number, fraction, or mixed number.)
Step 1
Write your question.
[tex]\begin{gathered} 2\frac{3}{8}\text{ }\frac{.}{.}\text{ 7}\frac{5}{12} \\ \end{gathered}[/tex]Step 2
Convert all mixed fractions to improper fractions.
[tex]=\text{ }\frac{19}{8}\text{ }\frac{.}{.}\text{ }\frac{89}{12}[/tex]Step 3
Change division to multiplication and invert the fraction.
[tex]\begin{gathered} =\text{ }\frac{19}{8}\text{ x }\frac{12}{89} \\ =\text{ }\frac{19\text{ x 3}}{2\text{ x 89}} \\ =\text{ }\frac{57}{178} \end{gathered}[/tex]Solve 5c^2 + 5c = 36 by completing the square. If there are multiple answers, list them separated by a comma (e.g. there is no real solution, enter Ø. Enter an exact answer. Provide your answer below:
First, completing the square, we have:
[tex]undefined[/tex]identify the constant of variation.7y-4x=0
We have the following equation given:
[tex]7y-4x=0[/tex]We can solve for y like this:
[tex]7y=4x[/tex][tex]y=\frac{4}{7}x[/tex]And if we compare with the general formula:
[tex]y=kx[/tex]With k the constant of variation we see that the answer is k= 4/7
In the standard equation for a conic section Ax? + Bxy + Cy? + Dx +Ey + F = 0, if B2 - 4AC > 0, the conic section in question is a circle.TrueFalse
If B² -4AC > 0, the conic is a hyperbola. If B² -4AC < 0, the conic is a circle, or an ellipse. If B² - 4AC = 0, the conic is a parabola.
So in this case the conic section in question is a hyperbola. Therefore it is false.
I would like help I will give 5 starPart B and C
Answer:
A. Average rate of change = -30
B. x ≥ 0
Explanation:
Part B.
The average rate of change from x = a to x = b can be calculated as
[tex]\frac{f(b)-f(a)}{b-a}[/tex]In this case, we want to calculate the average rate of change from x = 3 to x = 5, so f(3) = 120 and f(5) = 60. Then
[tex]\frac{f(5)-f(3)}{5-3}=\frac{60-120}{2}=-\frac{60}{2}=-30[/tex]So, the average rate of change is -30. So, from x = 3 to x = 5, when we increase the price by $1, the profit decreases by $30.
Part C.
The domain is the set of values that the variable x can take. In this case, x is the price of the pens, so it has to be greater than or equal to 0.
Therefore, the constraints for the domain are
x ≥ 0
find the axis of symmetry, the max or min, y and x intercepts, the domain, and the range of y=(x+2)^2-9
The quadratic equation is
[tex]y=x^2+4x-5[/tex]The solutions to the question can all be gotten from the graph of the quadratic equation;
The axis of symmetry is the point on the x-axis that divides the vertex of the parabola into two equal parts.
Therefore, the axis of symmetry occurs at x = -2
The graph curves downwards, hence it has a minimum point.
The minimum point occurs at y = -9
The y-intercept is the point where the curve cuts the y-axis when x = 0
Thus, the y-intercept occurs at y = -5
The x-intercept is the point where the curve cuts the x-axis at y = 0. The x-intercept also means the root of the equation
The x-intercept occurs at x = -5 and x = 1.
The domain of the equation is the set of all real values of x that will give real values for y.
Hence, the domain is from minus infinity to plus infinity. All real values of x satisfy the equation.
Domain =
[tex](-\infty,+\infty)[/tex]The range of a quadratic graph is the set of all real values of y that you can get by inputting real values of x
The graph ranges from y greater than or equal to -9
Therefore, the range is ;
[tex]y\ge-9[/tex]Mia by eight apples and four mangoes for $.34 find the cost of single apples
Given:
Isabella bought 2 apples and 4 mangoes for 28 cents. Mia bought 8 apples and 4 mangoes for 34 cents.
Required:
We need to find the cost of single apple.
Explanation:
First of all let assume a as a apple and m as a mango so now the equations are as
[tex]\begin{gathered} 2a+4m=28 \\ 8a+4m=34 \end{gathered}[/tex]now use substitution method
[tex]4m=28-2a[/tex]put this in another equation and we get
[tex]\begin{gathered} 8a+28-2a=34 \\ 6a=6 \\ a=1 \end{gathered}[/tex]Final answer:
So the cost for single apple is 1 cent.
CD is the perpendicular bisects of both XY and ST. match the lengths and the segments below.
Given
Answer
CT = 12
SX= 16-12 = 4
MT = 5
DY = 7
Which of the following values would complete the ordered pair if the point is on the graph of f(x) = -2x + 3?(-1____)-40 15
An ordered pair is a pair of values called the input and output, or just the x and the y on your graph. The input is your x and the output is your y.
When you're given a function, as long as you have a value for your x, you can always easily determine your value of y. Hence, you input -1 and whatever the result is, you have your y value.
The function is given as
f(x) = -2xof y
Which explicit formula can be used to find the account's balance at the beginning of year 4?
Solution
The answer is
A triangular pyramid is sliced by a plane parallel to the base. What is the shape of the cross-section?choice:rectangletrianglestarsquare
Answer:
triangle
Explanation:
The base of a triangular pyramid is a triangle, so if this figure is sliced by a plane parallel to the base, the cross-section will have the shape of the base. Then, cross-section is also a triangle.
So, the answer is triangle
A class has 12 boys and 21 girls. The class as a whole has a GPA (grade point average) of 2.96, and the boys have a GPA of 2.40. What is the GPA of the girls? (Round your answer to two decimal places.)
Given data:
A class has 12 boys and 21 girls.
The GPA of the whole class is 2.96.
The GPA of the boys is 2.40.
to find the GPA of girls,
let x be the GPA of girls.
Then,
(12+21)(2.96) = 12(2.40) + 21x
33(2.96) = 28.8 + 21x
97.68 = 28.8 + 21x
68.88 = 21x
x = 68.88/21
x = 3.28.
Find each new function in simplest form of : g-fWhich of the four options is it? Also please explain why
Need to know how to get the answer in reduced form.
We must solve this divition and write it in reduce form:
[tex]\frac{7}{18}\div\frac{9}{2}=[/tex]Remember that dividing by a fraction is equivalent to multiplying its inverse:
[tex]\frac{7}{18}\div\frac{9}{2}=\frac{7}{18}\cdot\frac{2}{9}[/tex]Now we can multiply both numerators and denominators separately:
[tex]\frac{7}{18}\cdot\frac{2}{9}=\frac{7\cdot2}{18\cdot9}=\frac{14}{162}[/tex]We can simplify that fraction. We can divide both the numerator and the denominator by 2:
[tex]\frac{14\div2}{162\div2}=\frac{7}{81}[/tex]7/81 can't be simplified since 7 is a prime number so this is a fraction in reduced form.
AnswerThen the answer is:
[tex]\frac{7}{81}[/tex]Heather dropped a water balloon over the side of her school building from a height of 80 feet.The approximate height of the balloon at any point it's fall can be represented by the following quadratic equation: h=16t^2+80. About how long did it take for the balloon to hit the groundA. 1.73B.2.24C.2.45D.2.83
Here, we want to know the time it took the ballon to reach the ground from the given height
Now, the height on the ground is at 0 ft
Thus, at this point, h= 0
Kuta Software - Infinite Algebra 2 Name Solving Multi-Step Equations Solve each equation. 2-12=2+5v 1) 4n - 2n = 4
Graph triangle DEF with vertices D(2,4) E(6,4) and F(4,8) and it’s image after a dilation centered at the origin with a scale factor of 3/2. Then, find the difference between the area of the image and the area of the preimage.The graphing part I got correct. I’m just confused on how to find the difference between the area of the image and the preimage.
We have to find the difference between the area of the image and the pre-image.
When we scale a figure with a scale factor k, the the area of the image figure will be k² times the area of the pre-image figure.
We will prove this by calculating both areas with the traditional method: the area of a triangle is equal to half the product of the base and the height.
We can identify the base and the height in the graph of both figures as:
We then can calculate the area of the pre-image as:
[tex]A=\frac{bh}{2}=\frac{4\cdot4}{2}=\frac{16}{2}=8[/tex]and the area of the image as:
[tex]A^{\prime}=\frac{b^{\prime}h^{\prime}}{2}=\frac{6\cdot6}{2}=\frac{36}{2}=18[/tex]Then, the difference in the area between the image and the pre-image is:
[tex]d=A^{\prime}-A=18-8=10[/tex]NOTE: we can now test that the relation between the areas is k²:
[tex]\begin{gathered} k=\frac{3}{2} \\ A^{\prime}=k^2\cdot A \\ A^{\prime}=(\frac{3}{2})^2\cdot8=\frac{9}{4}\cdot8=\frac{72}{4}=18 \end{gathered}[/tex]Answer: the difference of areas between the image and the pre-image is 10 square units.
solve the following variation: interest varies jointly with time and principle of the interest is 1,000 when the time is 10 years and the principle is 6,000. then find the equation of the variable
Interest varies jointly with time and principle
let I = interest
time = t
Principle = P
Mathematically:
[tex]\begin{gathered} I\text{ }\alpha\text{ tP} \\ I\text{ = ktP} \\ where\text{ k = constant of proportionality} \end{gathered}[/tex]when interest = 1000
time = 10 years
Principal = 6000
We will substitute these values in the formula we got above to get k:
[tex]\begin{gathered} 1000\text{ = k}\times10\times6000 \\ 1000\text{ = 60000k} \\ divide\text{ both sides by 60000:} \\ \frac{1000}{60000}\text{ = }\frac{60000k}{60000} \\ k\text{ = 1/60} \end{gathered}[/tex]To get the equation of the variable, we will substitute the value of k in the formula:
[tex]\begin{gathered} I\text{ = }\frac{1}{60}\times t\times P \\ \\ Equation\text{ of the variable:} \\ I\text{ = }\frac{tP}{60} \end{gathered}[/tex]Convert the following radian or degree measures to the other form
Solution
For this case we need to take in count that:
[tex]\pi=180[/tex]Then we can do this:
[tex]\frac{\pi}{5}=36\text{degrees}[/tex]And we can convert -155° on this way:
[tex]\frac{x}{-155}=\frac{\pi}{180}[/tex]Solving for x we got:
[tex]x=-155\cdot\frac{\pi}{180}=-\frac{31}{36}\pi[/tex]How many distinct positive integer factors does 60 have?
The number 60 has the following distinct positive integer factors:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
So we have 12 distinct factors.
