How many gallons of a 70% antifreeze solution must be mixed with 100 gallons of 30% antifreeze to get a mixture that is 60% antifreeze?

Answer:

-(y-3)(x+7)

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

x= -5/2=-2 1/2= -2.5. If you add all of those up you will get x=8

Answer and Step-by-step explanation: There are a number of ways of calculating an area under a curve. The more precise way is to use Definite Integral:

The function is [tex]2x\sqrt{x^{2}+1}[/tex], then the area under, with interval between 0 and 6 is:

[tex]\int\limits^6_0 {(2x\sqrt{x^{2}+1}) } \, dx[/tex]

To solve this integration, use substitution method, in which:

[tex]u=x^{2}+1[/tex]

[tex]\frac{du}{dx}=2x[/tex]

du = 2xdx

Replacing into the integral:

[tex]\int\limits^a_b {\sqrt{u} } \, du[/tex]

Solving:

[tex]\int\limits^a_b {\sqrt{u} } \, du=\frac{2}{3} \sqrt{u^{3}}[/tex]

Replacing it back to x:

[tex]\int\limits^6_0 {2x\sqrt{x^{2}+1} } \, dx =\frac{2}{3}\sqrt{(x^{2}+1)}[/tex]

Substituing limits between 0 and 6:

[tex]= \frac{2}{3}[\sqrt{(6^{2}+1)^{3}}-\sqrt{(0^{2}+1)^{3}} ][/tex]

= 149.37

Area under the curve using Integration is 149.37 square units

Another way of calculating area under the curve is dividing the area into a number of small rectangles and then adding the area of each one. This method is called Riemann Sums and it is an approximation of the area.

The method is done by the following relation:

in which

i is the n, the number of subintervals the area is dividing into

Δx is width of each subintervals.

For the function f(x) = [tex]2x\sqrt{x^{2}+1}[/tex], interval between 0 and 6:

[tex]\Delta x=\frac{6-0}{12}[/tex]

[tex]\Delta x=[/tex] 0.5

[tex]A=\Sigma f(x_{i}).\Delta x[/tex]

[tex]A = f(0)*0.5+f(0.5)*0.5+f(1)*0.5+f(1.5)*0.5+f(2)*0.5+f(2.5)*0.5+f(3)*0.5+f(3.5)*0.5+f(4)*0.5+f(4.5)*0.5+f(5)*0.5+f(5.5)*0.5[/tex]

[tex]A=0+1.12*0.5+2.83*0.5+...+50.99*0.5+61.49*0.5[/tex]

A = 131.575 square units

[tex]\Delta x=\frac{6-0}{5}[/tex]

Δx = 1.2

[tex]A=f(0)*1.2+f(1.2)*1.2+f(2.4)*1.2+f(3.6)*1.2+f(4.8)*1.2[/tex]

[tex]A=0*1.2+3.75*1.2+12.48*1.2+26.90*1.2+47.07*1.2[/tex]

A = 108.24 square units

Comparing results, notice that with less subintervals, the area is far from the exact measure. It occurs because Riemann Sums is an approximation method. So, if there are more subintervals, more approximate is the area, therefore, more precise it will be.

hi

x- 3/5 =  5x/ 6  

6x - 18/5 =  5x

6x -5x =  18/5

     x = 18/5

let's check :      18/5 - 3/5 =  15/5 = 3

                         5 * 18/5   / 6  =    18/6 = 3

result is correct.

Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=1100\hspace{35px}r=0.051\hspace{35px}t=18

P=1100r=0.051t=18

Given values

A=1100e^{0.051(18)}

A=1100e

0.051(18)

Answer: 2,750

Explanation:

Plug in

A=1100e^{0.918}

A=1100e

0.918

Multiply

A=2754.70450683

A=2754.70450683

Use calculator (with e button)

A\approx 2750

A≈2750

Round to nearest ten dollars

please heart!

VVV                   and rate stars! VVV          :D

The amount of money after 18 years nearest to ten will be $2,750.

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

[tex]\rm A=P_o \times e^{r \times t}\\[/tex]

Faith invested $1,100 in an account paying an interest rate of 5.1% compounded continuously.

Then the amount after 18 years is calculated as,

[tex]\rm A = \$1,100 \times e^{0.051 \times 18}\\A = \$1,100 \times e^{0.918}[/tex]

Simplify the equation further, then we have

A = $1,100 x 2.504

A = $2,754.7

The amount of money after 18 years nearest to ten will be $2,750.

More about the continuous compounding link is given below.

https://brainly.com/question/19522540

#SPJ3

Answer:

Step-by-step explanation:

Area of the right angles triangle will be expressed as;

Area of a triangle = 1/2base * height

Let the height of the triangle be 15 units

Get the base;

The base will be the adjacent;

Using the TOA trig identity;

tan 55 = opp/adj

tan 55 = 15/adj

adj = 15/tan 55

adj = 15/7.42

adj = 2.022 units

Area of the triangle = 1/2 * 15 * 2.022

Area of the triangle  = 15 * 1.011

Area of the triangle = 15.165units²

Answer:

0

Step-by-step explanation:

Slop of the line=y1-y2/x1-x2

Where x1,y1 point (-3,-4)

And X2,y2 point (2,-4)

So slop= (-4+4)/(-3-2)

=0/-5

So slop is 0

Answer:

C.

because both of those decimals can be turned into fractions.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

.752 is a rational number and .232323... is a non-terminating repeating number, which is also rational

Answer: What is the value of k in the equation k/3-5=34

Step-by-step explanation: Solution for k/3-5=34 equation: k in (-oo:+oo) k/3-5 = 34 // - 34 k/3-34-5 = 0 1/3*k-39 = 0 // + 39 1/3*k = 39 // : 1/3 k = 39/1/3 k = 117 k = 117

Answer:

k = 117

Step-by-step explanation:

I was just learning this in class...

So basically you need to get the variable k by itself so you add 5 to -5 in the equation and leave k/3 alone and then you add 5 to the other side of the equation also so you add 34+5 and you get 37 so you get k/3=37 and now you multiply 3 by 3 to cancel it out and then you once again do it on the other side of the equation 37 x 3=117 soo that leads you too k=117 YAYYY!!

Answer:

The scale factor of the dilation that transforms the triangle is 1/3

Step-by-step explanation:

9x1/3 is 3. 6x1/3 is 2, etc.

Step-by-step explanation:

you cant add 1 to 5x, so subtract 1 on both sides leaving you with 1 + 5x < 4 that equals 5x < 3 -1 -1

then divide 5 from both sides 5x < 3 This leaves 5 5

you with x < 3/5

X Y

-6 4

-3 1

0 6

3 -9

That’s the real answer

The required table will be:

X      Y

-6     32

-3      17

0       2

3      -13

Since we are not given the x - values, let the x values be -6, -3, 0 and 3

Given the function of y with respect to x;

y = -5x + 2

We need to get all the y-values for the given values of x as shown;

If x  = -6

y = -5 (-6) + 2

y = 30 + 2

y = 32

If x  = -3

y = -5 (-3) + 2

y = 15 + 2

y = 17

If x  = 0

y = -5 (0) + 2

y = 0 + 2

y = 2

If x  = 3

y = -5 (3) + 2

y = -15 + 2

y = -13

Hence the required table will be:

X      Y

-6     32

-3      17

0       2

3      -13

Learn more here: https://brainly.com/question/15011804

Answer:

What is the question?

Step-by-step explanation:

Plz mark brainliest!!!

Answer:

The sample size bedded is   [tex]n =41[/tex]

Step-by-step explanation:

From the question we are told that

   The margin of error is  [tex]E = 0.100[/tex]

    The sample proportion is  [tex]\^ p = 0.45[/tex]

From the question we are told the confidence level is  80% , hence the level of significance is    

      [tex]\alpha = (100 - 80) \%[/tex]

=>   [tex]\alpha = 0.20[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.282[/tex]

Generally the sample size is mathematically represented as  

    [tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]

=> [tex]n = [\frac{1.282}{ 0.100} ]^2 *0.45 (1 - 0.45 ) [/tex]

=> [tex]n =41[/tex]

Answer:

Linear.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 0.5x - 1

Step 2: Compare

y = mx + b

y = 0.5x - 1

m = 0.5

b = -1

The equation is a linear function. It's proportional.

Answer:

Answer is in the screenshot provided.

Step-by-step explanation:

Work is also in the screenshot provided.

Which year group is this question from?

Answer:

25 / 2

Step-by-step explanation:

Find ( D × [tex]\frac{E}{F}[/tex] ) if D = 5, E = 10, F = 4

5 × [tex]\frac{10}{4}[/tex] = 25 / 2

Answer:

1) 5/4 or 1 1/4

2) 9/16

Step-by-step explanation:

3/4+1/2: you multiply 1/2 by 2 to get a common denominator then get 2/4, 3+2=5, 5/4 or 1 1/4

1/3+11/48: you multiply 1/3 by 16 to get common denominator & get 16/48, 16+11= 27/48, divide by 3 & get simplest form of 9/16

Answer:

3/4+1/2= 1 5/8  and 1/3+11/48 is not a mixed number 9/16

Step-by-step explanation:

Answer:x=35

Step-by-step explanation:

Answer:

$6.78

Step-by-step explanation:

Add $10 +$6 +$2.75+$3+$5+$10+$10+$4+$12+$5 =$67.75

Now divide $67.75 by 10 which is the number of values you added up

$67.75/ 10 = 6.775

Now round to nearest cent = $6.78

Answer:

11

Step-by-step explanation:

Answer:

I suppose that you want to find which gym will be cheaper for you.

We have two equations:

• Gym A: 30m + 50

• Gym B: 10m + 100

First, let's find the value of m such that both gyms cost exactly the same:

30*m + 50 = 10*m + 100

Let's solve this for m

30*m - 10*m = 100 - 50

20*m = 50

m = 50/20 = 2.5

now:

for m < 2.5, Gym A will be cheaper, because the y-intercept is smaller.

for m > 2.5, Gym B will be cheaper, because the slope is smaller,

Then depending on the number of months that Martin wants to go to the gym, he can se the info above to pick the one that is cheaper.

Answer: W=V/lh

Step-by-step explanation:

You know that the formula to find the volume is length * width* height.

So l*w*h=V

divide lh on both sides, and you get

W=V/lh, The top right answer

Answer:

Step-by-step explanation:

To create an augmented matrix, we need to transfer the coefficients of each system of equations into its respective place in the matrix. The first row will be the coefficients of the first equation and so on. The number to the right of the equals sign is the last column of the augmented matrix.

[tex]\left[\begin{array}{ccc|c}1&-1&8&8\\3&-9&1&-1\\8&1&0&0\end{array}\right][/tex]

Answer:

what is the question

Step-by-step explanation:

you will not have enough money to pay your car bill though

Answer:

7 - 3 = 4

4 x 4 = 16

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

12-3= 9

9 times 4 =36