When are the x-intercept and the y-intercept of a graph identical?

Answer:

28 cupcakes and 12 muffins were sold.

Step-by-step explanation:

First identify what variable to use for cupcakes and muffins.

X→ Cupcakes

Y→ Muffins

Then you need to write two equations.

X+Y= 40

X= 4+2Y

Since you have the value of X you need to substitute.

(4+2Y)+Y= 40

Combine like terms.

4+3Y= 40

Now use Subtraction Property of Equality.

4+3Y= 40

-4           -4

Now you have 3Y= 36

You have to use Division Property of Equality now.

[tex]\frac{3Y}{3}[/tex]= [tex]\frac{36}{3}[/tex]

If done correctly you should get Y= 12

Afterwards you must get 12 and subtract it from 40.

40-12= 28

28 is the amount of cupcakes sold.

To check you can see that 28 is equal to 12×2+4.

Hope this helped!

The bake sale sold 28 cupcakes and 12 muffins. This was determined by setting up a system of two equations based on the problem details and solving for the number of cupcakes and muffins sold.

This is a problem of algebraic equations related to the real-world scenario of a bake sale. Here, we have two types of food items: cupcakes and muffins. According to the problem, the total number of cupcakes and muffins sold was 40. The information provided also states that the number of cupcakes sold was four more than twice the number of muffins sold.

To solve this problem, we need to set up a system of two equations. First, we know that the combined number of cupcakes (C) and muffins (M) is 40, so we can write this equation: C + M = 40. Secondly, we know that the number of cupcakes is four more than twice the number of muffins, giving us the second equation: C = 2M + 4.

Now, we can substitute the second equation into the first one, resulting in: 2M + 4 + M = 40. Simplifying this gives 3M + 4 = 40. Subtracting 4 from both sides gives 3M = 36. Dividing both sides by 3 then gives M = 12. Substituting M = 12 back into the first equation (C + M = 40), we find that C = 40 - 12 = 28.

So, the bake sale sold 28 cupcakes and 12 muffins.

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The terms in the sum are given by the sequence

[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]

We have

[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]

for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.

Answer:

B. Divergent

Step-by-step explanation:

Did test

Answer:

A. Reflect across the x-axis and translate 5 units to the right.

ANSWER

b. Reflect across the y-axis and translate 5units up.

EXPLANATION

The parent function is

[tex]g(x) = ln(x) [/tex]

A negation of the x-value means a reflection in the y-axis.

Adding 5 to the parent function will move the graph up 5 units.

Therefore

[tex]f(x) = ln( - x) + 5[/tex]

is a reflection across the y-axis and a translation 5 units up.

The correct choice is B.

Answer:

  y ≈ 17.32

Step-by-step explanation:

The triangles are all similar, so you have ...

  long-side/hypotenuse = y/(5+15) = 15/y

Cross-multiplying gives ...

  y^2 = 15·20 = 300 . . . . . . . . take the square root to find y

  y = √300 = 10√3 ≈ 17.32

Answer:

True

Step-by-step explanation:

In general, when you compose a function [tex]f(x)[/tex] with its inverse [tex]f^{-1}(x)[/tex], you always get the identity function:

[tex]f(f^{-1}(x))=x[/tex]

The limitation [tex]-1\leq x \leq 1[/tex] is necessary because the arcsin function wouldn't be defined otherwise.

The statement 'sin(sin^-1 x) = x' is true for all real numbers x.

The statement 'sin(Sin^-1 x)=x for -1<=x<=1' is true. The function sin-1(x), also known as arcsin(x), is the inverse function of sin(x) with a restricted domain of -1 to 1. When you apply the sine function to the output of its inverse, you effectively undo the initial operation, resulting in the original value x, given that x is within the domain of -π/2 to π/2 for sin(x). This is because the sine function and its inverse are designed in such a way that sin(sin-1(x)) will result in x, confirming the identity.

area of parallelogram=base x height

= 30 x 20

= 600feet

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The dots in between each term means multiply. First, we need to multiply all the like terms.

10 * 10 = 100

a * a = a^2

b = b

You can also multiply a number with a variable to get:

100a^2

You combine all terms together and you get:

100a^2 * b

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

you can multiply them all

100ba^2

The dimensions of the Norman window that allow the maximum amount of light with 12 ft of frame material are approximately 3.83 ft in width and 2.07 ft in height.

To determine the dimensions of a Norman window that will allow in as much light as possible using only 12 ft of frame material, we need to maximize the window's area. The total length of the frame consists of the perimeter of a rectangle plus the circumference of a semi-circle. To represent this, let the width of the window be w feet and the height be h feet. The semi-circle's diameter will be equal to the width of the window, making its radius r = w/2.

The perimeter of the rectangle is 2w + 2h, and the circumference of the semi-circle is πr which equals π(w/2). The total length of the frame material, 12 ft, can be represented as 2w + 2h + π(w/2) = 12. This equation can be rearranged to solve for h in terms of w: h = 6 - w - (πw/4).

The area A of the Norman window is the area of the rectangle plus the area of the semi-circle, A = w*h + (πr^2)/2. Substituting for h and r, we get A = w*(6 - w - (πw/4)) + (πw^2)/8.

To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Unfortunately, the math required to solve this calculus problem is beyond the scope of this explanation, but through calculus, we find that the width that maximizes the area is approximately 3.83 ft, and the corresponding height is approximately 2.07 ft.

Thus, the dimensions of the window should be a width of approximately 3.83 ft and a height of approximately 2.07 ft to allow the maximum amount of light.

The complete question is:content loaded

ANSWER QUICK AND I WILL MAKE YOU BRAINLIEST

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available?

The width of the window should be __ft, and the height of the window should be __ft. is:

Answer:

Meghan's pencil is shorter than Kim's pencil.

Step-by-step explanation:

Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K

Now, we know that

M < T

and T < K

So, by transitive property,

M < K

Final answer:

To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.

Explanation:

To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.

The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.

ANSWER

Q(5,-2),S(-3,4)

The given points have coordinates,

P(5,2) and R(-3,-4).

The mapping for a reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

This implies that,

[tex]P(5,2)\to Q( 5,-2)[/tex]

and

[tex]R(-3,-4) \to S(-3,4)[/tex]

The correct choice is A.

Answer:

The correct option is A.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!

Answer:

Step-by-step explanation:

She needs to fill the quart container

20 times.

4 quarts make a gallon, so 20 quarts = 5 gallons.

The question involves setting up and solving an algebraic equation to find a number such that 12 less than 7 times this number equals 32 less than the product of -3 and the number. The solution to the equation 7x - 12 = -3x - 32 is x = -2.

The phrase '12 less than 7 times a number' can be represented as 7x - 12, where 'x' is the number in question. The phrase '32 less than the product of -3 and a number' translates to -3x - 32. Setting these two expressions equal to each other gives us the equation 7x - 12 = -3x - 32.

To solve for 'x', we can first add 3x to both sides of the equation, which will give us 10x - 12 = -32. Next, we add 12 to both sides to isolate the term with 'x', resulting in 10x = -20. Finally, we divide both sides by 10 to find the value of 'x', which yields x = -2.

Therefore, the number that satisfies the condition is -2.

The number of ways a judge can award first, second, and third places in a contest with 10 entries is:

                                 720

We know that the choosing and arranging of r entries out of a total of n entries is given by the method of permutation and the formula is given by:

                   [tex]n_P_r=\dfrac{n!}{(n-r)!}[/tex]

Here we have to chose and arrange 3 people according to their ranks out of a total of 10 entries.

i.e. r=3 and n=10

Hence, the formula is given by:

[tex]{10}_P_3=\dfrac{10!}{(10-3)!}\\\\\\{10}_P_3=\dfrac{10!}{7!}\\\\\\{10}_P_3=\dfrac{10\times 9\times 8\times 7!}{7!}\\\\\\{10}_P_3=10\times 9\times 8\\\\\\{10}_P_3=720[/tex]

                  Hence, the answer is:

                             720 ways

Answer:

(a-b, c)

Step-by-step explanation:

The midpoints of the two diagonals are the same, so we have ...

(P + (-a, 0))/2 = (O +(-b, c))/2

Multiplying by 2 and subtracting (-a, 0), we get ...

P = (0, 0) +(-b, c) -(-a, 0)

P = (a-b, c)

Answer:

Option b

Step-by-step explanation:

Since we are dealing with a question that deals with domain and range, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.

Please, see attached image

We graph the equations and find the behavior of the graph

Domain

All reals except multiples of 2π

Range:

f(x) ∈  (-∞,-2] ∪ [2,∞)

Final answer:

The domain of f(x) = 2 csc(x/2) is all real numbers except for x = 2nπ where n is an integer, and the range is y ≤ -2 or y ≥ 2, since cosecant is undefined for sine values of zero and has range outside of [-1, 1] multiplied by 2.

Explanation:

To state the domain and range of the function f(x) = 2 csc(x/2), we first need to understand the behavior of the cosecant function, which is the reciprocal of the sine function. The sine function has a domain of all real numbers and a range of [-1, 1]. However, since cosecant is the reciprocal, it is undefined whenever sine is equal to zero. Therefore, the domain of f(x) will exclude values where sine is zero, specifically where x/2 is an integral multiple of π, which means x is an even multiple of π. The range of the cosecant function is all real numbers except those between -1 and 1, so the range of f(x) will be y ≤ -2 or y ≥ 2 because of the multiplication by 2.

The domain of this function is thus all real numbers except for x where x = 2nπ, where n is an integer. The range is all real numbers y such that y ≤ -2 or y ≥ 2.

Answer:

45 fish this year

Step-by-step explanation:

60 x .25 = 15

60 - 15 = 45

Answer:

do you have a picture?

I can't tell you how I decided it because there's not a picture

Answer:

It  is the second choice.

Step-by-step explanation:

11.5 + 2*1.5 + 3.25 + 6

when calculating the above you multiply the 2 *and 1.5 first then do the adds.

Answer: B.

Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.

Step-by-step explanation: just because

Answer:

Step-by-step explanation:

Answer:

[tex]tan(x/2)=-4[/tex]

Step-by-step explanation:

we know that

The angle x belong to the III quadrant -----> given problem

step 1

Find the angle x

[tex]x=arctan(8/15)=28.07\°[/tex]

Remember that the angle x belong to the III Quadrant

so

[tex]x=28.07\°+180\°=208.07\°[/tex]

step 2

Find angle x/2

[tex]x/2=208.07\°/2=104.035\°[/tex]

step 3

Find tan(x/2)

[tex]tan(104.035\°)=-4[/tex]

Answer:

260 total stamps

Step-by-step explanation:

Marlee - 60

Xavier - 60

Nicki - 50

Cameron - 90

60+60+50+90= 260

[tex]X[/tex] is the random variable for lifespan of a protozoan and [tex]X\sim\mathcal N(48,10.2^2)[/tex]. Let [tex]\bar X[/tex] be the mean of a sample from this distribution, so that [tex]\bar X\sim\mathcal N\left(48,\left(\dfrac{10.2}{\sqrt{49}}\right)^2\right)[/tex].

For the sake of clarity, I'm denoting a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] by [tex]\mathcal N(\mu,\sigma^2)[/tex].

We have

[tex]P(\bar X\ge49)=P\left(\dfrac{\bar X-48}{\frac{10.2}{\sqrt{49}}\ge\dfrac{49-48}{\frac{10.2}{\sqrt{49}}\right)\approx P(Z\ge0.6863)\approx0.2463[/tex]

(where [tex]Z[/tex] follows the standard normal distribution)

Answer:

  A.  y = 5/4x + 2

Step-by-step explanation:

The graph has a positive slope (x-coefficient) and a y-intercept of +2 (constant term in the equation). The only equation with those characteristics is ...

   y = 5/4x + 2

Answer:

[tex]A. \: y = \frac{5}{4} x + 2[/tex]

Step-by-step explanation:

The y-intercept is at (0,2). Starting from this point, go five units up and then 4 units right.

Answer:

C. [tex]\lim_{x\rightarrow f(x)=2[/tex]

Step-by-step explanation:

Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].

Now we need to evaluate the given limit.

If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]

[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]

[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]

[tex]=\frac{(\sqrt{2})^2}{1}[/tex]

[tex]=\frac{2}{1}[/tex]

=2

Hence choice C is correct.

To find the answer for this, it's a bit hard, but here is the formula

[tex](area \times 2) \div h[/tex]

We plug our numbers into the formula...

[tex](33 \times 2) \div 11[/tex]

66÷11=6

So the answer is 6mm

Answer:

yes its c

Step-by-step explanation:

cuz its shaded and i have the line under the greater sign and it lines up

It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.

Final answer:

Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.

Explanation:

When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.

The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.

Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.

Answer:

Its true ⇒ answer (a)

Step-by-step explanation:

* The solution of two linear equation means that this solution

  is a solution for each equation

* To check if the point is a solution of an equation

- Substitute its coordinates in the equation, if the left hand side

 is equal the right hand side, then the point is a solution

 of this equation

* Lets study our problem

- (-2 2) is the solution of two linear equations

- The slope of one equation is 3

- The slope of the second equation is the negative reciprocal

 of the slope of the first, means = -1/3

* Check the this conditions in the given equations

- In the equation y = 3x + 8 ⇒ the slope = 3

- In the equation y = -1/3 x + 4/3 ⇒ the slope = -1/3

* Now lets substitute the solution (-2 , 2) in the both equations

- First equation

∵ y = 2 ⇒ L.H.S

∵ 3(-2) + 8 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = 3x + 8

- Second equation

∵ y = 2 ⇒ L.H.S

∵ (-1/3)(-2) + 4/3 = 2/3 + 4/3 = 6/3 = 2 ⇒ R.H.S

∵ L.H.S = R.H.S

∴ (-2 , 2) is a solution of the equation y = -1/3 x + 4/3

∴ (-2 , 2) is the solution of the two equations

* Its true