Winslow plans to grow 12 kinds of vegetables in her garden. She has 34 seeds of each kind of vegetables. A neighbor gives her 10 more packets of seeds. Each packet has 25 seeds. How many seeds does Winslow have in all????

Answers

Answer 1

Answer: 658

Step-by-step explanation:

If Winslow wants to plant 12 vegetables and has 34 seeds of each kind of vegetable, then she has 12*34 seeds.

12*34=408

If a neighbor giver her 10 more packets, each with 25 seeds, she has 10*25 more seeds.

10*25=250

Then we add 408+250 to get 658 seeds


Related Questions

As Rainsford struggles in the water, the boat travels onward without him. Quickly, he retains his wits. Instead of panicking, he decides to head toward the sound of the gunshots. He does so _________ he realizes where there are gunshots, there are people. Hopefully, these people will be willing and able to help him.

Which transition best fills in the blank?

specifically
absolutely
because
later

Answers

Because I don’t hav ba reason

Answer:

the answer is 'because'

what is the solution of this equation
w+9=14

Answers

Answer:

w=5

Step-by-step explanation:

14-9=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{ w + 9 = 14}[/tex]

[tex]\huge\text{SUBTRACT by the \#9 on your sides! }[/tex]

[tex]\huge\text{Like: w + 9 - 9 = 14 - 9}[/tex]

[tex]\huge\text{Cancel out: 9 - 9 because it equals 0}[/tex]

[tex]\huge\text{Keep: 14 - 9 because it helps us solve for w}[/tex]

[tex]\huge\text{w = 14 - 9}[/tex]

[tex]\huge\text{14 - 9 = w}[/tex]

[tex]\huge\text{14 - 9 = 5}[/tex]

[tex]\huge\text{w = 5}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: w = 5}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount? Please help!

Answers

The other degree amount is 90 in a clockwise rotation.

Simplify 6 / (7+3i).


Answers

Answer:

To simplify the following expression: 6 / (7+3i), we're going to multiply and divide the entire expression by (7+3i), as follows:

[tex]\frac{6 (7-3i)}{ (7+3i)(7-3i)} = \frac{42-18i}{58} = 0.72 - 0.31i[/tex]

Now, the denominator has NO imaginary numbers.

Answer:

21/29 - 9/29i

what is the value of the expression g * (g+1)^2 for g=2

Answers

Answer:

18

Step-by-step explanation:

[tex]\text{Put}\ g=2\ \text{to the expression}\ g(g+1)^2:\\\\2(2+1)^2=2(3)^2=2(9)=18[/tex]

Select the correct answer.
A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the
A.
(-7, -1). 36 units
'B.
c.
D.
(7.1). 36 units
(7.1), 6 units
(-7, -1), 6 units
Next

Answers

Answer:

(- 7, - 1), 6 units

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - h)² = r²

where (h, k) are the coordinates of the centre and r is the radius.

Given

x² + y² + 14x + 2y + 14 = 0

Collect x/y terms together and subtract 14 from both sides

x² + 14x + y² + 2y = - 14

To obtain standard form use the method of completing the square

add ( half the coefficient of the x/y terms )² to both sides

x² + 2(7)x + 49 + y² + 2(1)y + 1 = - 14 + 49 + 1

(x + 7)² + (y + 1)² = 36 ← in standard form

with centre (- 7, - 1) and radius = [tex]\sqrt{36}[/tex] = 6

If the quadratic formula is used to find the solution set of 3x2 + 4x - 2 = 0, what are the solutions?

Answers

Answer:

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Step-by-step explanation:

Compare [tex]ax^2+bx+c[/tex] to [tex]3x^2+4x-2[/tex].

We have [tex]a=3,b=4,c=-2[/tex].

The quadratic formula is for solving equations of the form [tex]ax^2+bx+c=0[/tex] and is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So we are going to plug in our values in that formula to find our solutions,x.

If you want to notice it in parts you can.

Example I might break it into these parts and then put it in:

Part 1: Evaluate [tex]b^2-4ac[/tex]

Part 2: Evaluate [tex]-b[/tex]

Part 3: Evaluate [tex]2a[/tex]

------Let's do these parts.

Part 1: [tex]b^2-4ac=(4)^2-4(3)(-2)=16-12(-2)=16+24=40[/tex].

This part 1 is important in determining the kinds of solutions you have. It is called the discriminant.  If it is positive, you have two real solutions.  If it is negative, you have no real solutions (both of the solutions are complex).  If it is 0, you have one real solution.

Part 2: [tex]-b=-4[/tex] since [tex]b=4[/tex].

Part 3: [tex]2a=2(3)=6[/tex].

Let's plug this in:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

or in terms of our  parts:

[tex]x=\frac{\text{Part 2} \pm \sqrt{\text{Part 1}}}{\text{Part 3}}[/tex]

[tex]x=\frac{-4 \pm \sqrt{40}}{6}[/tex]

40 itself is not a perfect square but it does contain a factor that is.  That factor is 4.

So we are going to rewrite 40 as [tex]4 \cdot 10[/tex].

[tex]x=\frac{-4 \pm \sqrt{4 \cdot 10}}{6}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4} \cdot \sqrt{10}}{6}[/tex]

[tex]x=\frac{-4 \pm 2\cdot \sqrt{10}}{6}[/tex]

I'm going to go ahead and separate the fraction like so:

[tex]x=\frac{-4}{6} \pm \frac{2 \cdot \sqrt{10}}{6}[/tex]

Now I'm going to reduce both fractions:

[tex]x=\frac{-2}{3} \pm \frac{1 \cdot \sqrt{10}}{3}[/tex]

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Final answer:

Using the quadratic formula with a=3, b=4, and c=-2, the solution set for the quadratic equation 3x^2 + 4x - 2 = 0 is x = (-4 + 2√(10)) / 6 and x = (-4 - 2√(10)) / 6.

Explanation:

To find the solution set of the quadratic equation 3x2 + 4x - 2 = 0, we can use the quadratic formula:

x = (-b ± √(b2 - 4ac)) / (2a)

Here, comparing with the standard form ax2 + bx + c = 0, we identify a = 3, b = 4, and c = -2. Substituting these values into the quadratic formula gives us:

x = (-(4) ± √((4)2 - 4(3)(-2))) / (2(3))

x = (-4 ± √(16 + 24)) / 6

x = (-4 ± √(40)) / 6

x = (-4 ± 2√(10)) / 6

Which simplifies to two solutions:

x = (-4 + 2√(10)) / 6

x = (-4 - 2√(10)) / 6

These are the two solutions to the given quadratic equation.

What is the measure of E, in degrees?
O A. 1550
O B. 1300
O
C. Cannot be determined
O
D. 125°

Answers

Answer:

B. 130

Step-by-step explanation:

Since both sides of the triangle are 10, given that angle D is 25. We can conclude that angle F is also 25.

Total angle of triangle is equal to 180.

angle D + angle F + angle E = 180

25 + 25 + E = 180

50 + E = 180

E = 180 - 50

angle E = 130

If f(x) = x/1 + x, what is the value of f(x+h)

Answers

Answer:

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Step-by-step explanation:

Given function is:

f(x) = x/1 + x

In order to find f(x+h) we have to put x+h in place of x

[tex]f(x)=\frac{x}{1+x} \\f(x+h)=\frac{x+h}{1+x+h}[/tex]

Therefore,

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Answer: B

Got it right lol

Find the value of x for which line a is parallel to line b. (21)

Answers

X is 20 degrees. Since it says that lines a and b are parallel and angles four and five are right next to each other, it means that when you add the two of them together you’ll get 180. Since it’s replaced with variables with coefficients, add the coefficients to get 9 and divide 180/9 to get 20. 20 is the value for x which is your answer

Find the measure of the indicated arc

Answers

Answer:

m SQ = 95°

Step-by-step explanation:

The measure of the inscribed angle RSQ is one half the measure of its intercepted arc, that is

m RQ = 2 × 95° = 190°

To find the measure of SQ subtract the sum of the measures of SR and RQ from 360

m SQ = 360° - (75 + 190)° = 360° - 265° = 95°

How do you find the base area of a rectangular prism and a cylinder? Please help

Answers

Answer:

See explanation.

Step-by-step explanation:

The 'base' of a rectangular prism refers to only one side of the rectangular prism, which is a rectangle.

The formula for the area of a rectangle is as follows:

[tex]A=lw[/tex]

Where A = area, l = length, and w = width.

The 'base' of a cylinder refers to only one side of the cylinder, which is a circle.

The formula for the area of a circle is as follows:

[tex]A=\pi r^2[/tex]

Where A = area and r = radius.

Just in case you typed your question incorrectly and were asking for surface area, here is the formula for surface area for both as well:

Rectangular prism: [tex]A=2(wl+hl+hw)\\[/tex]

Cylinder: [tex]A=2\pi rh+2\pi r^{2}[/tex]

help please
1) Which of the following is not a line segment in the drawing?

2) Which of the following does not name the same line?

Answers

The option "KM" does not represent a direct line segment in the drawing as there is no straight path connecting points K and M without passing through another point.

The figure contains various labeled points connected by lines representing different segments except for NK; hence option NK does not name an existing line segment in the drawing.

1) In this case, all options refer to line segments except for "KM." The points K and M are not connected by a straight line; instead, point N lies between them. Therefore, KM is not a direct line segment in this drawing.

It's essential to understand that a line segment is named after its end points and consists of these points and all the points on the line between them. Since there is no direct path from point K to M without passing through another point (N), KM cannot be considered as a single, uninterrupted line segment.

2)The image you provided contains a geometrical diagram with five labeled points: J, K, L, M, and N. Line segments are drawn connecting these points forming an X shape. The options given are JL, MN, JK, and NK.

Upon careful examination of the image, it is evident that line segments JL (from point J to L), MN (from point M to N), and JK (from point J to K) are present in the drawing. However, NK (from point N to K) is not a line segment depicted in this drawing.

Using the linear combaination method what is the solution to the system of linear equations 7x-2y=-20and9x+4y=-6

Answers

Answer:

x=-2  y=3

Step-by-step explanation:

7x-2y=-20

9x+4y=-6

Multiply the first equation by 2

2(7x-2y) = 2 * -20

14x - 4y = -20

Add this to the second equation

14x - 4y = -40

9x+4y=-6

--------------------------

23x = -46

Divide by 23

23x/23 = -46/23

x = -2

Now we solve for y

9x+4y=-6

9(-2) +4y = -6

-18 + 4y = -6

Add 18 to each side

-18+18 +4y = -6+18

4y = 12

Divide by 4

4y/4 = 12/4

y=3

what is the soultion to 40(0.9-x)

Answers

Answer:

Step-by-step explanation:

(40*0.9)+(40*-x)

36-40X

Answer: 36-40X

   Answer:

[tex]\displaystyle =36-40x[/tex]

 Step-by-step explanation:

  Distributive property:

          ↓

[tex]\displaystyle A(B+C)=AB+AC[/tex]

A= 40, B=0.9, and C=x

[tex]\displaystyle 40*0.9-40x[/tex]

Then multiply numbers from left to right.

[tex]40*0.9=36[/tex]

[tex]\displaystyle 36-40x[/tex], which is our answer.

what is the slope of the line shown below? (5, 11) (-5, -1)

Answers

Answer:

-6/-5 is the slope

Step-by-step explanation:

Y2 - Y1 / X2 - X1 so

-1 - 11 / -5 - 5 = -12 / -10 simply it and get -6 / -5

Slope equals rise over run

Answer:

6/5

Step-by-step explanation:

A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 20% salt and
Solution B is 80% salt. She wants to obtain 180 ounces of a mixture that is 30% salt. How many ounces of each solution should she use?

Answers

The answer is 150 oz of solution a and 30oz of solution b. I’m adding in the work please ask if you have any questions

The scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.

To obtain 180 ounces of a 30% salt mixture, the scientist should use 90 ounces of Solution A (20% salt) and 90 ounces of Solution B (80% salt) by solving a system of two equations.

To solve the problem, we need to create a system of equations based on the quantities of salt in each solution and the desired final mixture. We want to mix Solution A (20% salt) and Solution B (80% salt) to get 180 ounces of a mixture that is 30% salt. Let the amount of Solution A be x ounces and the amount of Solution B be y ounces.

The two equations representing the system are:

Equation for total mixture: x + y = 180 (total ounces of the mixture)Equation for salt content: 0.20x + 0.80y = 0.30  *180 (total ounces of salt in the mixture)

Now, we solve this system of equations. Multiplying the second equation by 100 for simplicity, we get:

20x + 80y = 54  * 100

Using the first equation to express y in terms of x, we get y = 180 - x. Substitute y into the second equation:

20x + 80(180 - x) = 5400

Opening parentheses and simplifying gives us:

20x + 14400 - 80x = 5400

Subtract 20x from each side:

-60x + 14400 = 5400

Solving for x, we find that:

x = (14400 - 5400) / 60 = 90

Substituting x into y = 180 - x, we get y = 180 - 90 = 90.

Therefore, the scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.

3^8 a^10 b^-5 c^2 over 3^12 a^7 b^-3 c^-2 when a =4 b= 8 and c= 3

Answers

[tex]\bf \cfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\implies \cfrac{a^{10}a^{-7}c^2c^2}{3^{12}\cdot 3^{-8}b^{-3}b^5}\implies \cfrac{a^{10-7}c^{2+2}}{3^{12-8}b^{-3+5}}\implies \cfrac{a^3c^4}{3^4b^2}~\hfill \begin{cases} a=4\\ b=8\\ c=3 \end{cases}[/tex]

[tex]\bf \cfrac{4^3\cdot ~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 8^2}\implies \cfrac{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1[/tex]

Answer:

1

Step-by-step explanation:

[tex]\dfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=3^{8-12}a^{10-7}b^{-5-(-3)}c^{2-(-2)}=3^{-4}a^3b^{-2}c^{4}\\\\\text{substitute:}\ a=4,\ b=8,\ c=3:\\\\(3^{-4})(4^3)(8^{-2})(3^4)=(3^{-4}\cdot3^4)\bigg(2^2\bigg)^3\bigg(2^3\bigg)^{-2}\\\\\text{use}\ (x^n)(x^m)=x^{n+m}\ \text{and}\ \bigg(x^n\bigg)^m=x^{nm}\\\\=(3^{-4+4})\bigg(2^{(2)(3)}\bigg)\bigg(2^{(3)(-2)}\bigg)=(3^{0})(2^6)(2^{-6})\\\\\text{use}\ x^{-n}=\dfrac{1}{x^n}\ \text{and}\ (x^n)(x^m)=x^{n+m}[/tex]

[tex]=(1)\left(2^{6+(-6)}\right)=2^0=1\\\\\text{Used}\ a^0=1\ \text{for any real value of}\ a,\ \text{except 0}.[/tex]

What was done to the quadratic parent function F(x) = xto get the
function G(X) = x2 - 3? 0
A.Shifted 3 units to the right
B. Vertically stretched by multiplying by 3
C.Shifted 3 units down
D.Shifted 3 units to the left

Answers

Answer:

Step-by-step explanation:

Given the function f(x), the  function g(x) = f(x) + k represents the function f(x) shifted k units downwards.

In this case, given that k=-3 (k<0). The graph is shifted 3 units down. Therefore,  we can conclude that the correct option is Option C.

Myra owns a car service that charges a $5 flat rate and an additional $0.50 per mile, which is represented by the equation y = 0.5x + 5, where x is the number of miles and y is the total cost.

How much is the total cost for a car with 30 miles?
$10
$15
$20
$35

Answers

Answer:

Option C is correct.

Step-by-step explanation:

The equation given is y = 0.5x +5

where x is the number of miles and y is the total cost.

We need to find total cost y if the car has traveled 30 miles

so, x=30

Putting value of x in the given equation:

y = 0.5x +5

y = 0.5(30) + 5

y = 15 + 5

y = 20

So, the total cost is $20

Option C is correct.

Answer:

the answer is $20 i just did that one :))

Step-by-step explanation:

good luck!

Can somebody please help me. I don’t understand it at all.

Answers

Step-by-step explanation:

Just pick a bunch of values of x, and use the formula to find the corresponding value of y.

For example

When x = 0, y = 0+5 = 5 ----> Plot the point (0,5) on graph paper

When x = 1, y = 1+5 = 6 ----> Plot the point (1,6) on graph paper

When x = 2, y = 2+5 = 7 ----> Plot the point (2,7) on graph paper

Then connect the dots to get a linear graph. You should get a graph that looks  like the one attached.

You first make a table with x and y

like this: x      |        y

then you think of possible values for x then solve for y

it needs to be positive , 0, and a negative like:

under x, you do:

2

0

-3

then you take the equation and solve for y.

after, with the y values, create a Cartesian plane and plot the points

so the points would be (2,7), (0,5), and (-3,2)

then you connect the points and draw arrows on both ends.

then label the line w/ the equation

-------------------------------------------------------

hey btw, i learned this just yesterday. lol

great timing

(6x - 9 - 2x)(8 + 5x - 5)

Answers

-27 - 33x + 20x²

Combine like-terms in all sets of parentheses and just FOIL it:

[4x - 9][5x + 3]

F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT

O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT

I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT

L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT

I am joyous to assist you anytime.

!PLEASE HELP!

y + x = 3
Does the line increase or decrease? How do I find this without graphing the line?

Answers

Answer:

Decreasing

Step-by-step explanation:

y=mx+b is called slope-intercept from because it tells you the slope,m, and the y-intercept,b.

If the slope is positive then the line is increasing.

If the slope is negative then the line is decreasing.

If the slope is zero then the line is horizontal or constant.

So let's solve our equation for y:

y+x=3

Subtract x on both sides:

y=-x+3

The slope is -1.

Therefore the line is decreasing.

just a quick addition to @Freckledspots' great reply above.

y + x = 3

y = 3 - x

if we pick any random "x" value, and then pick another value larger than the one before for "x", to get a "y" value, if "y" is decreasing, the the first value of "y" will be larger, else it's increasing, let's do so, say using hmmm x = 2 and x = 7.

x = 2

y = 3 - 2

y = 1

x = 7

y = 3 - 7

y = -4

as "x" moves to the right, from 2 to 7, "y" moved down, from 1 to -4, thus is decreasing.

what is the surface area of the rectangular pyramid

Answers

Answer:

41.74 m²

Step-by-step explanation:

We have:

rectangle 4.8 m × 3.8 m

two triangles with base b = 4.8 m and height h = 2.6 m

two triangle with base b = 3.8 m and height h = 2.9 m.

The formula of an area of a rectangle l × w:

[tex]A = lw[/tex]

Substitute:

[tex]A_1 = (4.8)(3.8) = 18.24\ m^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_2=\dfrac{(4.8)(2.6)}{2}=6.24\ m^2\\\\A_3=\dfrac{(3.8)(2.9)}{2}=5.51\ m^2[/tex]

The Surface Area:

[tex]S.A.=A_1+2A_2+2A_3\\\\S.A.=18.24+2(6.24)+2(5.51)=41.74\ m^2[/tex]

Answer:

GIVE THE OTHER DUDE BRAINLISET

Step-by-step explanation:

how to create an equation with infinitely many solutions.

Answers

Answer:

See below.

Step-by-step explanation:

An equation with infinite solutions is, strictly, an identity.

An example is 2(x + 3) = 4x + 6

Simplifying  we get 4x + 6 = 4x + 6. We can replace by any value of x  and the equation will hold true.

Use dimes, nickels, and pennies to show 42 cents. How many different ways can you show this amount?

Answers

Answer:

Step-by-step explanation:

You Can Use 4 dimes and 2 pennies

Or 42 Pennies, 8 Nickels and 2 pennies.

Hopefully this helps!

Final answer:

42 cents can be represented in a variety of ways using dimes (10 cents), nickels (5 cents), and pennies (1 cent). Some of the possible representations are 4 dimes and 2 pennies; 3 dimes, 2 nickels and 2 pennies; 8 nickels and 2 pennies, amongst others.

Explanation:

The question is about displaying the number 42 cents using dimes, nickels, and pennies. Each dime is equal to 10 cents, nickel is 5 cents and penny is 1 cent. Here's a few methods:

4 dimes and 2 pennies3 dimes, 2 nickels, and 2 pennies8 nickels and 2 pennies2 dimes, 7 nickels, and 3 pennies1 dime, 6 nickels, and 7 pennies42 pennies

It's a fun exercise to see how many other ways you can come up with!

Learn more about Combinations of Coins here:

https://brainly.com/question/33179317

#SPJ2

A rectangular prism has a base that is 5cm by 7cm and a height of 12cm if all dimensions are doubled what happens to the volume?

Answers

Answer:

The volume increased eightfold.

Step-by-step explanation:

The formula of a volume of a rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have l = 5cm, w = 7cm and h = 12cm.

Substitute:

[tex]V=(5)(7)(12)=420\ cm^3[/tex]

Doubled the dimensions:

l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.

Calculate the new volume:

[tex]V'=(10)(14)(24)=3360cm^3[/tex]

Calculate the quotient [tex]\dfrac{V'}{V}[/tex]

[tex]\dfrac{3360}{420}=8[/tex]

Generalization:

V = lwh - the volume of a prism l × w × h

2l × 2w × 2h - new dimensions

V' = (2l)(2w)(2h) = 8lwh = 8V - new volume

A data set with less variation will have a smaller ____________________.

A. minimum

B. mean

C. interquartile range

D. median

Answers

Answer: Option C

A data set with less variation will have a smaller __ interquartile range__.

Step-by-step explanation:

The datasets that have less variation are those that have smaller dispersion or variation measures.

Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.

Then the answer is the option C

It is c which is the answer

use trigonometric identities cosec²X = 3cot X-1 ​

Answers

Step-by-step explanation:

cosec²x = 1/sin²x = (sin²x+cos²x)/sin²x =1 + cos²x/sin²x = 1 + cot²x.

Therefore:

1+cot²x = 3cot x - 1

cot²x - 3 cot x + 2 = 0

let cot x = t

t²-3t+2=0

t²-2t-t+2=0

t(t-2)-(t-2)=0

(t-1)(t-2)=0

t1=1

t2=2

so:

cot x = 1 then x1 = π/4 + πk

cot x = 2 then x2 = arccot(2) + πk

k is an integral.

Tre determines the solution to the equation 3.57x + 1.61 = 4.71 - 2.63x is x = 0.5. He verifies his solution using the steps below.

Equation: 3.57x + 1.61 = 4.71 - 2.63x
Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5)
Step 2: 1.785 + 1.61 = 4.71 - 1.315
Step 3: 3.395 = 6.025

Which statement most accurately describes Tre’s error?

A. Tre made an error when determining the original solution of x = 0.5.
B. Tre made an error when substituting the solution in for x.
C. Tre made an error when multiplying each coefficient by 0.5.
D. Tre made an error when adding or subtracting.

Answers

Answer:

Option D. Tre made an error when adding or subtracting

Step-by-step explanation:

we have the equation

[tex]3.57x + 1.61 = 4.71 - 2.63x[/tex]

Solve for x

Group terms that contain the same variable and move the constant to the other side

[tex]6.2x= 4.71 - 1.61[/tex]

Combine like terms

[tex]6.2x=3.1[/tex]

[tex]x=0.5[/tex]

Verify

Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5) ---> is correct

Step 2: 1.785 + 1.61 = 4.71 - 1.315  ----> is correct

Step 3: 3.395 = 6.025 ---> is not correct

because

4.71-1.315=3.395 instead of 6.025

therefore

Tre made an error when  subtracting

Answer: The answer is d

Step-by-step explanation:

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