please help, seventh grade math problem

Solution :

Given parametric equation for :

\($x=1+2 \sqrt t$\)

\($y=t^3-t$\)

\(z=t^3+t\)

The point is (3, 0, 2)

The vector equation is equal to :

\($r(t) = \left<1+2 \sqrt t, t^3 -t, t^3+t \right>$\)

Solving for r'(t) by differentiating each of the components of r(t) w.r.t. to t,

\($r'(t)= \left< \frac{1}{\sqrt t}, \ 3t^2-1, \ 3t^2+1 \right>$\)

The parameter value corresponding to (3, 0, 2) is t = 1. Putting in t=1 into r'(t) to solve for r'(t), we get

\($r'(1) = \left< \frac{1}{\sqrt 1}, \ 3(1)^2-1, \ 3(1)^2+1 \right>$\)

We know that parametric equation for  line through the point \($(x_0, y_0, z_0)$\)  and parallel to the direction vector <a, b, c > are

\($x=x_0+at$\)

\($y=y_0+bt$\)

\(z=z_0+ct\)

Now substituting the  \($(x_0, y_0, z_0)$\)   = (3, 0, 2) and  <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get:

\($x=3+(1)t$\)

x  = 3 + t

y = (0) + (2)t

y = 2t

z = (2) + (4)t

z = 2 + 4t

Answer:

20 banna slices can be cut from a banna

Step-by-step explanation:

8 divided by 0.4 equals 20

Answer:

0.7692077

Step-by-step explanation:

Number of cards in a standard deck = 52

Number of aces in a standard deck = 4

Number of clubs in a standard deck = 13

Probability = required outcome / Total possible outcomes

P(ace) = 4 / 52 = 0.0769

P(club) = 13 / 52 = 1/4 = 0.25

P(not club) = 1 - p(club) = 1 - 0.25 = 0.75

P(ace and not club) = 3/52 = 0.0576923

P(ace or not club) = p(ace) + p(not club) - p(ace and not club

= 0.0769 + 0.75 - 0.0576923

= 0.7692077

Answer:

The value of y is 216

(and the value of x is 12)

Step-by-step explanation:

The general formula for a geometric sequence is,

\(a_n = a_1(r)^{n-1}\)

Where n represents the nth term, a_1 is the first term and r is the common ratio,

we see that,

r = 6,

the first term is,

a_1 = (x-6)

the 2nd term is,

a_2 = 3x,

the 3rd term is,

a_3 = y, finding y,

first we find x, using the above given formula we have,

\(a_2 = a_1(6)^{2-1}\\3x = (x-6)(6^1)\\3x = 6x -36\\36 = 6x - 3x\\36 = 3x\\x=36/3\\x=12\)

x = 12,

Now, for y we can use the relation between a_3 and a_2,

\(a_3 = a_1(6)^{3-1}\\y = (x-6)(6)^2\\y = (12-6)(6^2)\\y = 6(6^2)\\y = 6^3\\y = 216\)

y = 216

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

706.5 cm²

Step-by-step explanation:

Surface area of the open cylinder with only one base = surface area of cylinder - area of one of the base

= 2πr(h + r) - πr²

Where,

r = 9 cm

h = 8 cm

π = 3.14

Plug in the values into the equation

Area of the open cylinder with one base = 2*3.14*9(8 + 9) - 3.14*9²

= 56.52(17) - 254.34

= 960.84 - 254.34

= 706.5 cm²

The shape of the data that we have here is skewed to the right

A dataset is considered to be right-skewed (sometimes known as excessively positive) when the greater portion of its data points are concentrated on the lower end, forming an asymmetrical distribution that has a long tail to the right.

As such, the mean (average) within these distributions generally surpasses the median in value, with the latter also exceeding the mode.

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Answer:

30: 100

31: -13

32: -45

33: 14

34: -32

35: -22

36: 17

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The amount of salt in the mixture is the sum of the amounts of salt in the constituents. Those amounts are found by multiplying the quantity of solution by the percentage that is salt.

__

Let x represent the quantity of 90% salt solution B, in ounces. Then the number of ounces of salt in the mix is ...

  0.90x +0.65(120 -x) = 0.75(120)

  0.25x = 0.10(120) . . . . . . subtract 0.65(120) and simplify

  x = 48 . . . . . . . . . . . . . divide by 0.25

  120 -x = 72 . . . . . . . amount of 65% solution A

She should use 48 ounces of 90% solution B, and 72 ounces of 65% solution A.

Answer:

x = 8

Step-by-step explanation:

3x^2 + 7 = 199

3x^2 = 199 - 7

x^2 = 192/3

x = sqrt 64

x = 8

Answer:

1/6^8

Step-by-step explanation:

the answer is the one right next to the submit answer

Answer:

-57.6=x

Step-by-step explanation:

-22.3= x/3-3.1
-19.2=x/3
-57.6=x

Answer:

A. The zeroes are -3 and -2/3 because y= (x + 3) (3x + 2)

Step-by-step explanation:

Problem

(6,8) and (-12,-4) put in standard form ​

Solution

The standard form for a line is given by:

y =mx +b

We can calculate the slope with this formula:

Then we can find the intercept using one point given for example x=6 and y=8 and we have:

8= 2/3*6 +b

b= 8- 4= 4

And our standard form would be given by:

y= 2/3 x +4

Answer:

Step-by-step explanation:

Answer: 17

Explanation:

We have a right triangle (a triangle with an angle of 90°). To find the value of c (the hypotenuse of the triangle) we use the Pythagorean theorem:

Where a and b are the legs of the triangle and c is the hypotenuse.

In this case, the value of a and b is:

Substituting these values into the Pythagorean theorem formula:

Solving the operations:

Solving for c:

the result is:

Answer: 17

The area of the shaded portion of the composite figure could be easily 25*25 - 1/2*13*10 that is 625 - 65 = 560 feet

When referring to a two-dimensional space or points, in mathematics, the term "area" is used. It refers to a region's or a flat object's size, such a square or rectangle. The area of a form is determined in geometry by dividing the length by the breadth. For example, the area of a square with a side length of 4 units is 4 x 4 = 16 square units. Square units, such as square inches, square feet, or square meters, are used to measure area. Triangles (1/2 x base x height), circles ( x radius squared), and trapezoids (1/2 x (base 1 + base 2) x height) are other basic geometric forms with associated area calculations.

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Answer:

Line ZL and line LZ.

Step-by-step explanation:

Since it is a line (because a line needs to have two or more points to be able to graph), it can be represented in two ways. The first being ZL, and the second being LZ.

Brainliest please.

Answer:

Step-by-step explanation

Oh

The measure of side length EF in the right triangle is 24.

The Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c²  = a² + b²

From the diagram:

Hypotenuse DE = c = 26

Leg DF = a = 10

Leg EF = b = ?

Plug in the values and solve for b:

c²  = a² + b²

26²  = 10² + b²

676  = 100 + b²

b² = 676  - 100

b² = 576

b = +√576 ( we take the positive value since we are dealing with dimensions)

b = 24

Therefore, the length EF is 24.

Option C)24 is the correct answer.

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Answer: the numbers with the plus sign are positive and the ones with the negative sign are negative

Step-by-step explanation:

The value of the function f'(g(x)) is -10

What is a function?

an expression or rule or law that describes a relationship between one variable  and another variable. i.e. between independent variable and dependent variable is known as function.

We are given f(-6)=-3, f'(-6)=-5, g(2)=-6, g'(2)=2

We are asked to find F'(2) where F(x)= f(g(x))

We will use the algebra of function to solve the given problem and find the required value

We have

\(F(x)=f(g(x))\\F'(x)= f'(g(x))*g'(x)\)

Substituting x=2 in the above equation we get

\(F'(2)=f'(g(2))*g'(2)\\F'(2)=f'(-6)*2\\F'(2)=-5*2\\F'(2)=-10\)

Hence the value of F'(2)= -10 as asked

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Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

The probability that all of them get the same number would be 1/36. Or probability that they will have a chance of  get the same number after 36 throws. And the probability concept that use here is theoretical probability.

        Total out comes in three dice = ( 6 × 6 × 6 = 216 ).

        Probability of getting same number = 6 × 1/6 × 1/6 × 1/6

                                                                     = 6 × 1/6 × 1 × 1/6 × 6

                                                                     = 6/6 × 1/36

                                                                     = 1 × 1/36

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Answer:

Step-by-step explanation:    First, let's call the starting elevation of the plane: e

We can then write an equation representing this problem as:    

e−1.5mi=5.25mi

Now, add 1.5mi  to each side of the equation to solve for e

while keeping the equation balanced:

e−1.5mi + 1.5mi=5.25mi + 1.5mi

e−0=6.75mi

e=6.75mi

The plane's starting elevation was 6.75 miles

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Step-by-step explanation:

the answer is 8q^6r^3 and here are the steps in pic.

Answer:

8q^6r^3

Step-by-step explanation:

As powers in denominator are subtracted from powers of numerator.

8 q^9-3 r^4-1

8q^6r^3.

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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30 divided by 6 gives you the amount of laps which would be 5 laps

Answer:

Area of a rectangle= lenght× width

Dimensions of 1st rectangle: L,W

Dimensions of 2nd rectangle: L+10; W+4

Hence,

LW = 480__________(1)

(L-10)(W+4) = 480_______(2)

LW = LW+4L - 10W - 40

4L = 10W +40

2L = 5W + 20

L = (5/2)W + 10_________(3)

But LW = 480 (from equation one)

So, W = 480/L

substitute as= 480/L into equation (3)

L = (5/2)(480/L)+10

L = 1200/L + 10

L^2 - 10L - 1200 = 0

factorising.

we're have,

(L-40)(L+30) = 0

therefore, since L can't be negative , L = 40

L = 40 cm (length)

Then 480/L = W = 120 cm (width)