A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to $\frac12$. If the original numerator was a 2, what was the original denominator

Answer:

From sin²θ + cos²θ = 1, we have;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ

Step-by-step explanation:

The given equation is (sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ

We have;

(sin⁴θ + cos⁴θ) = 1 - 2 sin²θ·cos²θ gives;

(sin⁴θ + cos⁴θ) + 2 sin²θ·cos²θ= 1

Which is equivalent to sin⁴θ + 2 sin²θ·cos²θ +cos⁴θ  = 1

From which we can get;

(sin²θ + cos²θ)·(sin²θ + cos²θ)  = 1

Given that sin²θ + cos²θ = 1

Therefore;

1 × 1 = 1

To get to the initial equation in the question, we have;

sin²θ + cos²θ = 1

(sin²θ + cos²θ) × (sin²θ + cos²θ) = 1

(sin⁴θ + sin²θ·cos²θ + sin²θ·cos²θ + cos⁴θ = 1

∴ sin⁴θ + cos⁴θ = 1 - sin²θ·cos²θ + sin²θ·cos²θ  = 1 - 2·sin²θ·cos²θ

Therefore;

sin⁴θ + cos⁴θ = 1 - 2·sin²θ·cos²θ.

Answer: g(1) = 9

Step-by-step explanation:

g(x) = 3(1/4)^(x-2) - 3

g(1) = 3(1/4)^(1-2) - 3

g(1) = 3(1/4)^(-1) - 3

g(1) = 3(4) - 3

g(1) = 12 - 3

g(1) = 9

Answer:

Pretty Simple!

Now that you know about ratios and all that, this is pretty tame compared to the last problem.

Now, the problem is talking 2D(2 Dimensions)

The ratio is not going to work because it has only one parameter.

Thus, we need to square it!

[tex](\frac{1}{20})^{2} =\frac{1}{400}[/tex]

Thus, we have your correct ratio.

Now, we only need to do the same thing for the triangle problem. Meaning that, we need to compare the ratios, with x as the thing we are looking for.

[tex]\frac{1}{400}=\frac{219}{x} \\x=87,600[/tex]

See? X is practically handed to us.

Hope this helps!

Answer: 37

Step-by-step explanation:

Given that:

Total number of beads on her necklace = 50

Percentage of blue beads = 26%

Therefore, number of blue beads :

Percentage number of blue beads × total number of beads on necklace

Number of Blue beads = 26% × 50

= 0.26 × 50 = 13

Number of Blue beads = 13

Therefore, number of beads that aren't blue :

Total number of beads - number of blue beads

50 - 13 = 37

Number of beads that aren't blue = 37

Answer:

y=2x-5

Step-by-step explanation:

y=mx+c

mx=slope

In this case, the slope is already given to you which means the m=2.

y=2x+c.

The coordinates are (14, 23) and when you put -5 into c, the line goes through the coordinates (14, 23).

Hope this helps!

Answer:

(b) -m, m + 3

Step-by-step explanation:

x² − 3x − m(m + 3) = 0

x² − 3x = m(m + 3)

x² − 3x + 9/4 = m(m + 3) + 9/4

(x − 3/2)² = m(m + 3) + 9/4

(x − 3/2)² = m² + 3m + 9/4

(x − 3/2)² = (m + 3/2)²

x − 3/2 = ±(m + 3/2)

x − 3/2 = m + 3/2, -m − 3/2

x = m + 3, -m

Answer:

208 cm²

Step-by-step explanation:

First, you take the area of the whole rectangle, to do this you simply multiply 30 by 15, meaning that the big rectangle’s area is 450 cm².

Then, you take the area of the small rectangle (the unshaded one), to do this, you simply figure out the sides (they end up being 11 cm and 22 cm, you can find this out through subtracting) and to find the area of this rectangle, you multiply 11 by 22, which gives you 242 cm²

Now all that is left to do is to subtract the unshaded area by the whole rectangles area to find the shaded part! This will look like this: 450-242= 208 cm²

Work Shown:

x^2 - 7x = -12

x^2 - 7x + 12 = 0

(x - 3)(x - 4) = 0 ... see note below

x - 3 = 0 or x - 4 = 0

x = 3 or x = 4

Note: we're looking for two numbers that multiply to 12 and add to -7. Those two numbers are -3 and -4, so that's where the factorization (x-3)(x-4) comes in. After this step, you set each factor equal to zero and solve for x.

Answer:

x=3  x=4

Step-by-step explanation:

x^2 − 7x = −12

Add 12 to each side

x^2 - 7x +12 =0

Factor

What 2 numbers multiply to 12 and add to -7

-3*-4 = 12

-3+-4 = -7

(x-3)(x-4) =0

Using the zero product property

x-3 =0   x-4 =0

x=3  x=4

Answer:

27

Step-by-step explanation:

Since 3^6 is only divisible by 3 and powers of 3(including 1) the gcd of 3^6 and 6^3 mus be a power of 3 hence we need to find the highest powers of 3 that divide 6^3 and that divide 3^6, which are respectively 3^3 and 3^6, hence, taking the smaller one (since we want it to divide both), our answer is 3^3=27.

Answer:

Step-by-step explanation:

Greatest common divisor is the largest positive integer that divides each integer in the given problem

6³ = (2* 3)³ = 2³ * 3³

3⁶ = 3³ * 3³

Greatest common divisor = 3³ = 3* 3* 3 = 27

Answer:

For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Step-by-step explanation:

HOPE THIS HELPS AND PLSSS MARK AS BRAINLIEST]

THNXX :)

What must be true for two polygons to be similar?

Similar polygons: For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.

Answer:

"The probabilities are equal."

Step-by-step explanation:

Since the amount of times the paper cup landed on its open, and closed end is equal, then the answer is "The probabilities are equal."

Answer: the probability’s are equal

Step-by-step explanation:

Answer:  78 ounces of dough was bought.

52 ounces of sauce was bought.

There were 13 guests .

Step-by-step explanation:

Let x = Number of guests

As per given, For each person 6 ounces of dough and 4 ounces of sauce is required.

i.e. Total ounces of dough and sauce together required = 6+4=10

The dough and sauce is 130 ounces all together.

i.e. [tex]10x=130[/tex]

Divide both sides by 10 , we get

x= 13

i.e. there were 13 guests .

Total ounces of dough = 6 x ( Number of guests) = 6 x 13= 78 ounces

hence, 78 ounces of dough was bought.

Total ounces of sauce = 4 x ( Number of guests) = 4 x 13= 52 ounces

hence, 52 ounces of sauce was bought.

The total ounces of dough is 78 ounces

The total ounces of sauce is 52 ounces

The total number of guests is 13

The equation that can be used to represent the question given is:

6a + 4a = 130

Where a represents the number of guests at the party.

The above equation means that the total ounces of dough and sauce bought is a function of the number of guests at the party. These total ounces is equal to 130.

6a + 4a = 130

10a = 130

a = 130 / 10

a = total number of guests = 13

The total ounces of dough = 13 x 6 = 78 ounces

The total ounces of sauce = 13 x 4 = 52 ounces

A similar question was solved here: https://brainly.com/question/16430804?referrer=searchResults

Answer:

Step-by-step explanation:

Equation of the line using point (0, 1) and slope 4/5 is

[tex]y - 1 = \frac{4}{5} (x - 0) \\ \\ 5y - 5 = 4x \\ \\ 5y - 4x = 5[/tex]

Hope this helps you

Answer:

D. [tex]\boxed{5y-4x=5}[/tex]

Step-by-step explanation:

Slope = m = 4/5

y - intercept = b = 1 (As from the point (0,1) , y-intercept is when x = 0)

So, the equation becomes

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{4}{5} x +1[/tex]

=> [tex]y - \frac{4}{5} x = 1[/tex]

Multiplying both sides by 5

=> [tex]5y-4x = 5[/tex]

Answer:

hypotenuse

Step-by-step explanation:

hypotenuse.  The length of the hypotenuse is the distance between the two given points.

Answer:

hypotenuse

Step-by-step explanation:

Answer:

Ok, i will suppose the situation that:

The rocket has a constant speed S (So the acceleration of the rocket is equal in magnitude, but opposite in direction, to the gravitational acceleration)

Here we can remember that:

Velocity = distance/time.

Then if the distance is the height of the rocket, we can write this as:

H = velocity*time

h = S*t

This is a linear model that represents the height of the rocket as a function of time.

Case 2:

The rocket is fired with an initial velocity v0, but no acceleration:

In this case the only acceleration acting on the rocket is the gravitatonal acceleration pulling the rocket down, so the acceleration is:

a = -g

To get the velocity as a function of time, we should integrate:

a = -g*t + v0

To get the height as a function of time, we integrate again:

h(t) = (-g/2)*t^2 + v0*t + p0

Where p0 is the initial position of te rocket, but the rocket starts at the ground, so p0 = 0m.

The height as a function of time is:

h(t) = (-g/2)*t^2 + v0*t

This is a quadratic equation.

Answer:

Step-by-step explanation: I hope it helps :)

1.

[tex]Surface\: area=\:2\pi rh+2\pi r^2\\h = 2ft\\diameter = 2ft\\Radius = d/2=2/2=1ft\\\\A=( 2\times 3.141\times1\times2)+(2\times 3.141 \times 1^2)\\A = (12.564)+(6.282)\\A = 18.846\\A = 18.85ft^2[/tex]

2.

[tex]Area \:of\: square = A=a^2\\A = 3^2\\A=9\\Area\:of \:one \:rectangle\: = (l\times b)\\ A = (8\times 3)\\A = 24cm^2\\\\A = 2(Area\: of\: square)+2(Area\: of \:rectangle)\\A = 2(9)+4(24)\\A = 18+96\\A =114cm^2[/tex]

3.

[tex]Area \: of\: base=?\\ r = 7\:in\\h = 12\:in\\A = \pi \times r^2\\A = 3.141 \times 7^2\\A = 153.909\\\\Height \: of \:the \:cylinder = 12\:inches\\Circumference = 2\pi \times r\\C= 2 \times 3.141 \times 7\\ C =43.98\\\\S.A= 2B+Ch\\S.A = 2(153.909)+43.98(12)\\S.A = 307.818+527.76\\S.A =835.578[/tex]

4.

[tex]Perimeter = a+b+c\\P = 10+8+6\\P = 24\\S.A =2B+Ph\\S.A = 2(24)+24(8)\\S.A =48+192\\S.A = 240\:yd^2[/tex]

Answer:

h=3√3 cm

Step-by-step explanation:

An equilateral triangle has 3 Equal sides

The height of an equilateral triangle with side a =a√3/2

That is,

h=a√3/2

Where,

h=height of the equilateral triangle

a=side length

From the triangle given,

a=6cm

Therefore,

h=6√3/2

=3√3

h=3√3 cm

Answer:

your answer is -35.

Step-by-step explanation:

let the first 7 terms be 1,2,3,4,5,6, and 7.

we have ,

general term t_n = -3n +7 ,then

t_1 = -3*1 +7

= -3+7

= 4

t_2 = -3*2 +7

= -6 +7

= 1

t_3 = -3*3 +7

= -9+7

= -2

t_4 = -3*4 +7

= -12+7

= -5

t_5 = -3*5 +7

= -15+7

= -8

t_6 = -3*6 +7

= -18+7

= -11

t_7 = -3*7 +7

= -21+7

= -14

Now, the sum of first seven terms is

4 + 1 + (-2) + (-5) + (-8) + (-11) + (-14)

= 5 -2 - 5 - 8 - 11 - 14

= -35

Answer:

-35

Step-by-step explanation:

Sum of the first 7 terms of AP is:

As per general formula t_n= -3n +7 we find the first and seventh terms and the sum of the first 7 terms:

Answer is - 35

Answer:

8 more unit of tiles

Step-by-step explanation:

The function is given as;

f(x) = x² - 6x + 1

Now, we want to add more unit tiles to complete the square.

The given function(f(x)) is of the order 2 due to the highest power of 2 attached to x, but the side of the square will be of the order 1.

Now, Let's make a general order 1 expression ax + b to be the side of the square.

From the function forming the square after adding some p unit tiles, we have;

f(x) + p = (side of square)²

Thus;

x² - 6x + 1 + p = (ax + b)²

x² - 6x + 1 + p = a²x² + 2abx + b²

Comparing both sides of the equation, we have;

a² = 1

2ab = 6

b² = 1 + p

From a² = 1, a = 1

From 2ab = 6,putting 1 for a, we have;

2(1)b = 6

b = 6/2

b = 3

From b² = 1 + p

Putting 3 for b, we have;

3² = 1 + p

9 = 1 + p

9 - 1 = p

p = 8

Thus, 8 more unit of tiles are required to complete the square.

Answer:

15

Step-by-step explanation:

Opposite sides in a parallelogram are equal.

2x - 5 = x + 10

Subtract x and add 5 on both sides.

2x - x = 10 + 5

Combine like terms.

x = 15

Answer:

[tex]\boxed{\red {x= 15}}[/tex]

Step-by-step explanation:

We know that opposite sides in a parallelogram are equal.

So, in this sum value of the sides in a parallelogram

[tex]x + 10 \: \: \: and \: \: \: 2x - 5[/tex]

So now let's create an equation

[tex]x + 10 = 2x - 5[/tex]

Now let's solve for x

[tex]x + 10 = 2x - 5 \\ 10 + 5 = 2x - x \\ 15 = x[/tex]

Answer:

[tex]\large \boxed{\sf \ \ g(x)=3|x| \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's follow the instructions !

Step 1

g(x)=k*f(x)=k*|x|

We know that the point (2,6) is on the graph so 6=g(2) meaning:

6=k*|2|=k*2

*** divide by 2 both sides ***

k = 6/2 = 3

Step 2

g(x)=3*|x|

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                           = [tex]\frac{3-1}{-2+3}[/tex]

                       m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{4-1}{-1-0}[/tex]

               = -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

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

x = [tex]-1\frac{1}{5}[/tex]

From equation (1),

y = 2x + 7

y = [tex]-\frac{12}{5}+7[/tex]

  = [tex]\frac{-12+35}{5}[/tex]

  = [tex]\frac{23}{5}[/tex]

  = [tex]4\frac{3}{5}[/tex]

Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].

Option (B) will be the answer.

Answer:

B. (-1 1/5, 4 3/5)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Here, we have a grain silo having 2 shapes fused together to make it.

A cylinder and then a hemisphere ( half sphere)

Now, we want to calculate the volume of grain that could completely fill the silo.

Mathematically, to do that, we will need to add the volume of the cylinder to the volume of the hemisphere.

Mathematically,

Volume of cylinder is;

pi * r^2 * h

From the question, r = 6 ft and h = 168 with pi = 22/7

Substituting these values, we have

Volume of cylinder= pi * 6^2 * 168 = 6,048 pi

The volume of the sphere will be;

4/3* pi * r^3= 4/3 * pi * 6^3 = 288 pi

So the total volume of the silo will be;

288 pi + 6,048 pi = 6336 pi

So to have the final result, let’s multiply by value of pi

6336 * 22/7 = 19,193 ft^3

The closest answer here probably due to previous approximations is 19,008 ft^3

Answer:

Step-by-step explanation:

Given the expression after 4 has been subtracted from both sides as

1/2 x = - 1/2 x, the original expression will be gotten by adding back 4 to both sides of the resulting expression as shown;

1/2 x + 4 = - 1/2 x + 4

x/2 + 4 = -x/2 + 4

Find the LCM of both equation;

(x+8)/2 = (-x+8)/2

Multiplying both sides by 2 will give;

x+8 = -x+8

Collecting the like terms;

x+x = 8-8

2x = 0

x = 0/2

x = 0

Hence, the value of x is 0

Answer:

0

Step-by-step explanation:

Answer:

Janine=12.6(repeating) Samantha=15.6(repeating) Lucy=19.6(repeating)

Step-by-step explanation:

Lets concentrate on one person, Janine.

Janine = Lucy - 7

Janine = Samantha - 3

If the averae of the 3 people's ages is 16, then we should multiple that by three to get 48, the number of their ages combined.

Janine + Lucy + Samantha = 48

The differences between Janine to Lucy and Janine to Samantha combined is 10, so we can subtract that from 48 to get 38, which is 3 times Janines age.

38/3=12.6(repeating)

That is Janine's age. We can use that to find both Lucy's and Samantha's ages respectively by using their equations. Lucy's is 19.6(repeating) and Samantha's is 15.6(repeating). I hope you can give me brainliest, and that this helped!

Answer:

where is the dot plot also describe if it increases or decreases

Answer: 3 x minus 3 + 4 = 2 minus x minus 3

              3 x + 1 = negative x minus 1

Step-by-step explanation:

             A and D. Edge 2020

The required equation that Samuel used is 3x -3 + 4 =2- x -3. option A is correct.

Samuel is solving the equation 3 (x minus 1) + 4 = 2 minus (x + 3). Which equivalent equations might Samuel use, is to be determined.

The equation is the relationship between variables and represented as[tex]y = ax +b[/tex]  is an example of a polynomial equation.

Given equation is [tex]3(x-1) +4 =2 -(x+3)[/tex]
Simplification of the above equation,
opening the parenthesis on both sides
step 1⇒ 3x - 3 + 4 = 2 - x - 3
step 2⇒ 3x + 1 = -x - 1
Transposition of -x to the left side and +1 to the right side
step 4 ⇒ 3x +x = -1 -1
                  4x = -2
Transposition of 4 to the denominator of -2.
step 5⇒ x = -2/4
               x = -1/2

Thus , Step 1 3x -3 + 4 =2- x -3 is the equivalent equation used by the samuel.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ5

Answer:

Step-by-step explanation:

Given,

Area of square ground = 42025

Now, let's find the length of square ground

Area of square = [tex] = {l}^{2} [/tex]

plug the values

[tex]42025 = {l}^{2} [/tex]

Swipe the sides of the equation

[tex] {l}^{2} = 42025[/tex]

Squaring on both sides

[tex] \sqrt{ {l}^{2} } = \sqrt{42025} [/tex]

Calculate

[tex]l = 205[/tex] meters

The length of square ground = 205 meters

Now,Let's find the perimeter of square

Perimeter of square [tex] = 4l[/tex]

plug the value of length

[tex] = 4 \times 205[/tex]

Multiply the numbers

[tex] = 820[/tex] meters

Hope I helped.

Best regards!!

Answer:

The answer is 1/5 + z = 3/5

Step-by-step explanation:

Answer:

1/5+z=3/5

Step-by-step explanation:

As an approximate decimal, this is 0.5556 which converts to 55.56%

======================================================

Explanation:

Let's say there are 100 households (just for the sake of simplicity). We are told that 90% of them have answering machines. So that means 90 households have answering machines. In addition, 50 households have answering machines and call waiting. Those 50 households are part of the 90 mentioned previously.

We then select a house at random. Someone tells us (or we have some kind of prior knowledge) that whichever house is selected, they have an answering machine. We can ignore the 10 households that don't have an answering machine. Out of those 90 households, 50 have both features. So 50/90 = 5/9 is the probability of getting a household with both features.

The answer would be 1/2 or 50% if we didn't have the prior knowledge of the household having an answering machine. But with this prior knowledge, the conditions change and so does the probability.

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

You could also compute 0.50/0.90 to get the same answer.