roberta is 6 times danielles age. in 12 years, roberta will only be 2 times danielles age. how old is danielle now?

Answer: y = 7

Step-by-step explanation:

[tex]\\ \sf\dashrightarrow x^3-y^3+x^2+y^2+3[/tex]

[tex]\\ \sf\dashrightarrow (-2)^3-(1)^3+(-2)^2+(1)^2+3[/tex]

[tex]\\ \sf\dashrightarrow -8-1+4+1+3[/tex]

[tex]\\ \sf\dashrightarrow -9+8[/tex]

[tex]\\ \sf\dashrightarrow -1[/tex]

Answer: -1

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

x = -2

y = 1

Given expression

x³ - y³ + x² + y² + 3

Substitute values into the expression

=(-2)³ - (1)³ + (-2)² + (1)² + 3

Simplify exponents

=-8 - 1 + 4 + 1 + 3

Simplify by simple operation (addition/subtraction)

=-9 + 4 + 1 + 3

=-5 + 1 + 3

=-4 + 3

=[tex]\boxed {-1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x = 1/8

Step-by-step explanation:

[tex]\log _2\left(x\right)=-3\\\\\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c\\\\\log _2\left(x\right)=-3\quad \Rightarrow \quad \:x=2^{-3}\\\\Simplify\\\\x=\frac{1}{8}[/tex]

Step-by-step explanation:

C(x) = 2.50 + 5(0.40x)

<=> C(x) = 2.50 + 2.00 x

The required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

Given that,
A New York City taxi charges $2.50, plus $.40 for each fifth of a
mile if it is not delayed by traffic. To determine an expression for the cost of the ride, if travel x miles in the taxi with no traffic delays to determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the number of miles be x,
The total charge be C(x)
Now accoding to the condition total charge could be the sum of the cost of every fifth mile and $2.40. So, every fifth mile = x / 5
Now,
C(x) = 2.40 + 0.40 * x/5

Thus, the required expression for the taxi charges is C(x) = $2.50 + 0.4  * x/5.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

[tex]\Large \boxed{- \frac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sqrt[3]{-\frac{1}{125} }[/tex]

Distribute the cube root to the numerator and denominator.

[tex]\displaystyle -\frac{\sqrt[3]{1} }{\sqrt[3]{125} }[/tex]

Solve for the cube root.

[tex]\displaystyle - \frac{1}{5}[/tex]

Answer:

25[tex]\sqrt{3}[/tex] +60

Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.

So now we know both sides are 10.

We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.

So the top two angles are 120 degrees and bottom two angles are 60 degrees.

It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.

Wow, these two triangles are special right triangles in the form of

30 - 60 - 90 degrees.

shorter side = n

longer side = n[tex]\sqrt{3}[/tex]

hypotenuse = 2n

So, 2n = 10

n = 5 for the short side

The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]

The longer side is  5[tex]\sqrt{3}[/tex].

The area of trapezoid = (base1 + base2)/2 * height

= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60

So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.

Answer:

  60 +25√3

Step-by-step explanation:

In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...

  DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10

Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...

  Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3

  Area = 60 +25√3 . . . square units

_____

In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.

Answer:

2 3/8

Step-by-step explanation:

First get the LCM (Least Common Multiple) for the denominators so we can subtract them.  The denominators would both be 8 because it is the lowest number that they can have to be able to subtract.  (The LCM).  So is 4 3/4 has a denominator of 8 it'll become:

4 3/4= 4 6/8 because if 4 turned into 8, that means it multiplied by 2.  So, you need to multiply 3 by 2 as well which equals 6.  This is it as a ratio:

3:4 into x:8    

So 4 times 2, which means you need to do 3 times 2 as well.  It equals 6.

So now that we know 4 3/4 is 4 6/8, it is time to subtract.  2 3/8 already has a denominator of 8 so we don't need to do anything with that.  Subtract.

4 6/8-2 3/8= 2 3/8.  4-2=2, so the whole number is 2.  6-3= 3, so the numerator (the top number) is 3.  The denominator (the bottom number) always stays the same so it is the same, which is 8.

Answer:

C

Step-by-step explanation:

The colony will follow an exponential equation. y(x) = 8000*(2)^(t/210). Plug in t=630 and you will get y(x) = 64000

Answer:

x=-2 and x = 5

Step-by-step explanation:

The solutions to the equation are where the graph crosses the x axis

We can see that the graph crosses at x=-2 and x = 5

Answer:

x = -2

x = 5

Step-by-step explanation:

The answer is found when the graph crosses the x-axis

Hope this helps :D

Answer:

5, 12, 13

Step-by-step explanation:

Pythagoras theorem ⇒ Perpendicular² + Base² = Hypotenuse²

5² + 12² = 13²

25 + 144 = 169

Thus 5, 12, 13 is a Pythagorean triple.

r=I × 100÷pxt

8200×100÷ 11406×4

820000÷. 45624

17.97

make me brainliest .

Answer:

[tex]\large \boxed{e^{i\pi}+1=0}[/tex]

Step-by-step explanation:

Hello, please consider the following.

For any x real number,

[tex]e^{ix}=cos(x)+i\cdot sin(x)\text{, right? So}\\\\e^{i\pi}=cos(\pi)+i\cdot sin(\pi)\\\\e^{i\pi}=-1+i\cdot 0=-1\\\\\text{ We add 1 to both sides of the equation.}\\\\\large \boxed{e^{i\pi}+1=0}\\[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

I can't believe I'm doing this for 5 points, but ok!

For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:

[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex]  and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):

[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:

392 + 36 - 192 - [48 + 504 - 112] which simplifies to

236 - 440 which is -204

On to the second one:

[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:

-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to

-417 - 124 which is -541, choice c.

Now for the third one:

[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us

[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:

[tex]-126+48-90-[-280+54-36][/tex] which simplifies to

-168 - (-262) which is 94, choice c again.

Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.

[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.

Find the inverse by:

* finding the determinate

* putting the determinate under a 1

* multiply that by the "mixed up matrix (you'll see...)

First things first, the determinate:

|A| = (-4*-8) - (-6*-5) which simplifies to

|A| = 32 - 30 so

|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:

[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex]  (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:

[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:

[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to

x = 20 - 5 which is

x = 15 and

y = -15 + 4 which is

y = -11

(It works, I checked it)

Answer:

6+4*(5-3)

Step-by-step explanation:

Because of PEMDAS l, we first solve in the parantheses. So 5-3 would be 2, then we multiply 2 by 4 which would be 8 obviously. Then we do the final step, add 6 and 8 which would be 14. Cheers!

Answer: 6 + 4 × (5-3)

Explanation:

6 + 4 × (5-3) = 14

6 + 4 × 2 = 14

6 + 8 = 14

14 = 14

Must click thanks and mark brainliest

Answer:32

Step-by-step explanation:

if selling is 28 and she is 4 years greater than Drake then that is 28-4 which is 32 so Drake is 32 years old

Answer:

The answer is 32.

Step-by-step explanation:

If Celine is 28 and Drake is four years older than her, we do 28+4.

Answer:

Step-by-step explanation:

We will use the addition rule of probability of two events to solve the question. According to the rule given two events A and B;

p(A∪B) = p(A)+p(B) - p(A∩B) where;

A∪B is the union of the two sets A and B

A∩B is the intersection between two sets A and B

Given parameters

P(A)=15

P(A∪B)=1225

P(A∩B)=7100

Required

Probability of event B i.e P(B)

Using the expression above to calculate p(B), we will have;

p(A∪B) = p(A)+p(B) - p(A∩B)

1225 = 15+p(B)-7100

p(B) = 1225-15+7100

p(B) = 8310

Hence the missing probability p(B) is 8310.

[tex]\sf \longrightarrow \: \:Surface \: area \: of \: cylinder \: = \: 2\pi \: r \: h \: + \: 2\pi \: {r}^{2} [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \frac{Diameter}{2} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \frac{12}{2} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \: \cancel\frac{12}{2} \: \: ^{6} \\ [/tex]

[tex]\sf \longrightarrow \: \: r \: = \:6 \: ft[/tex]

[tex]\sf \longrightarrow \: \: h \: = \: 15 \: ft[/tex]

[tex]\sf \implies \: \:2 \: \times \: \pi \times \: 6 \: \times \: 15 \: \: + \: \: 2 \: \times \: \pi \times \: {6}^{2} [/tex]

[tex]\sf \implies \: \:2 \: \times \: \pi \times \: 90 \: \: + \: \: 2 \: \times \: \pi \times \: 36[/tex]

[tex]\sf \implies \: \:180 \: \pi \: + \: \: 72 \: \pi[/tex]

[tex]\sf \implies \: \:252 \: \pi[/tex]

Hence, the surface area of cylinder is 252 π ft²

Answer:

(1) Variance = 4.5 and Standard deviation = 2.121.

(2) Variance = 4.5 and Standard deviation = 2.121.

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged.

Step-by-step explanation:

We are given with the following set of data below;

              X                     [tex]X-\bar X[/tex]                   [tex](X-\bar X)^{2}[/tex]

              5                   5 - 8 = -3                     9

              5                   5 - 8 = -3                     9

              8                   8 - 8 = 0                      0

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

             10                  10 - 8 = 2                     4

              9                   9 - 8 = 1                       1

              9                   9 - 8 = 1                       1

              6                  6 - 8 = -2                    4                

Total    72                                                   36      

Firstly, the mean of the above data is given by;

              Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                              =  [tex]\frac{72}{9}[/tex]  = 8

(1)Now, the variance of the given data is;

            Variance  =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]

                                  =  [tex]\frac{36}{9-1}[/tex]  = 4.5

So, the standard deviation, (S.D.)  =  [tex]\sqrt{\text{Variance}}[/tex]

                                                        =  [tex]\sqrt{4.5}[/tex] = 2.12

(2) Now, each value is added by 2; so the new data set is given by;

              X                     [tex]X-\bar X[/tex]                   [tex](X-\bar X)^{2}[/tex]

              7                   7 - 10 = -3                     9

              7                   7 - 10 = -3                     9

             10                  10 - 10 = 0                     0

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

             12                  12 - 10 = 2                     4

              11                  11 - 10 = 1                       1

              11                  11 - 10 = 1                       1

              8                  8 - 10 = -2                    4                

Total    90                                                   36      

Firstly, the mean of the above data is given by;

              Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                              =  [tex]\frac{90}{9}[/tex]  = 10

(1)Now, the variance of the given data is;

            Variance  =  [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]

                                  =  [tex]\frac{36}{9-1}[/tex]  = 4.5

So, the new standard deviation, (S.D.)  =  [tex]\sqrt{\text{Variance}}[/tex]

                                                                =  [tex]\sqrt{4.5}[/tex] = 2.12

(3) The effect on the measure of dispersion if each value is changed uniformly ​is that it remains unchanged as we see in the case of variance or standard deviation.

Answer:

45

Step-by-step explanation:

c(x)=2x^2-4x-3

Let x= -4

c(-4)=2(-4)^2-4(-4)-3

      = 2(16) +16-3

       =32+16-3

         45

Answer:

45

Step-by-step explanation:

c(-4) = 2(-4)² - 4(-4) - 3

       = 2(16) + 16 - 3

       = 32 + 13

       = 45

Answer:

6 out of the 20 values are below 2.  6/20 = 30%.

Since 30% of the values are below 2, 2 is located at the 30th percentile.

Step-by-step explanation:

Answer:

[tex]z=14.4[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]24=\frac{z}{0.6}[/tex]

Use inverse operations to solve this equation. Multiply both sides of the equation by (0.6) to undo the division of (0.6).

[tex]24=\frac{z}{0.6}[/tex]

[tex](0.6)(24)=z[/tex]

Simplify,

[tex](0.6)(24)=z[/tex]

[tex]z=14.4[/tex]

Answer:

Top left: 6

Bottom left: 8

Top right: 7

Bottom right: 3

Step-by-step explanation:

To solve this problem, we need to look at the table to see what missing information we need to solve for. On the table, it asks us how many students:

On the first intersection (top left), we are asked how many students played an instrument and sport. That is easy to solve because the information they provide us already gives us that number: 6.

On the second intersection (bottom left), things get a little more challenging. The information states that 14 students in total play sports, so that is not the number of people who only play sports. Since 14 people in total play sports and 6 people play both an instrument and sport, we subtract 6 from 14 to get our answer, 8.

On the third intersection (top right), it asks us how many people play an instrument but doesn't play a sport. Let's look at the remaining values first. There is: 6, 8, 3. When we add those together, we get 17, and when we subtract that from the total (24), we get our answer: 7.

On the last intersection (bottom right), the information already provides us with the answer to how many people don't play anything: 3.

Answer:

Step-by-step explanation:

∠HIG and ∠JIK are vertical angles, so:

m∠HIG = m∠JIK

[tex]\dfrac{GI}{IJ}=\dfrac{7.5}3=2.5\\\\\dfrac{HI}{IK}=\dfrac{2.5}1=2.5[/tex]

[tex]\left\{\dfrac{GI}{IJ}=\dfrac{HI}{IK}\quad\ \wedge\quad m\angle HIG=m\angle JIK\right\}\implies \triangle HIG\sim\triangle JIK\ \ by\ SAS[/tex]

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]

And the we know that if the discriminant is

***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning

[tex]\boxed{k>\dfrac{8}{3}}[/tex]

then, there is no real solution.

***** [tex]\Delta = 0[/tex], meaning

[tex]\boxed{k=\dfrac{8}{3}}[/tex]

There is 1 solution.

***** [tex]\Delta[/tex] > 0, meaning

[tex]\boxed{k<\dfrac{8}{3}}[/tex]

There are 2 solutions.

Thank you

PS: To give more details...

[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]

Answer:

b

Step-by-step explanation:

16x10=160

Answer:

The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates.

Step-by-step explanation:

Answer:

[tex]{x, y} = {-\frac{2}{3}, \frac{5}{3}}[/tex]

Step-by-step explanation:

7x + 4y = 2

x + y = 1

// Solve equation [2] for the variable  y  

 [2]    y = -x + 1

// Plug this in for variable  y  in equation [1]

  [1]    7x + 4•(-x +1) = 2

  [1]    3x = -2

// Solve equation [1] for the variable  x  

  [1]    3x = - 2  

  [1]    x = - 2/3  

// By now we know this much :

   x = -2/3

   y = -x+1

// Use the  x  value to solve for  y  

   y = -(-2/3)+1 = 5/3  

Solution :

{x,y} = {-2/3,5/3}

Answer:

6 1/2 ft^3 or 13/2 ft^3 or 6.5 ft^3

Step-by-step explanation:

Use the formula for volume of a rectangular prism (lwh)

(3 1/4)(2) = 6 1/2

(6 1/2)(1) = 6 1/2 ft^3

Answer:

26.5 liters

Step-by-step explanation:

We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78  by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.