Step 3: Using multi-step equations to solve problems a) You are using the equation 4(p - 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. Describe the operations in the order that you will perform them to solve the equation.​ (no joke answer please)

Answer: Length 132cm, Breadth 48cm

Explanation:

Perimeter = 360cm

Let the length and breadth be x

ATQ

2(11x + 4x) = 360

22x + 8x = 360

30x = 360

x = 360/30

x = 12

Length = 11×12

= 132 cm

Breadth = 4×12

= 48cm

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a) He needs 500 g of sugar to make apple crumble for 16 people.

b) She needs 45 g of flour to make apple crumble for 2 people.

c) 500g of apples is enough to make apple crumble for 6 people.

The amounts for this problem are obtained according to the proportions given in the problem.

For 8 people, the amount of sugar needed is of 250 g. For 16 people, the  number of people doubles, hence the amount of sugar needed will also double, as follows:

2 x 250 = 500 g.

For 2 people, the amount of each item is divided by 4, hence the amount of flour needed is given as follows:

180/4 = 45 g.

The amount of apple needed per people is of:

700/8 = 87.5 grams.

For 6 people, the amount is given as follows:

6 x 87.5 = 525 grams.

Hence 500g of apples is enough to make apple crumble for 6 people.

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Answer:

The answer is:

10a-6b

*Can I have brainliest? I need it for a challenge.*

Step-by-step explanation:

kd      d d d d d .d d d d d d d d d d d d d . d d .d a da a d sa ds d s d  

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

Dear user,

Answer to your query is provided below

Option A is correct

Step-by-step explanation:

3(2m-1)-n

6m-3-n

Answer:

$50

Step-by-step explanation:

Answer:

I know that someone else already answered and got brainliest but I just thought to give some steps to solving because you never know who needs it ;)

The answer is 50 as the person who answered above me said.

Step-by-step explanation:

Now, to get to solving.

I hope this will be helpful to somebody and feel free to comment, ask questions, give feedback, and correct my steps if they are not correct!

Have a great day! :)

All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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The distance Ben travels to get to the park is approximately 2.21 times greater than the distance David travels. This is found by using the distance formula to calculate the distances each person travels and then comparing the results.

To solve this problem, we need to find the distance between each person's house and the park using the distance formula

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For Ben

distance = √((-2 - 4)² + (-2 - 6)²) = √((-6)² + (-8)²) = √(100) = 10

For David

distance = √((-2 - (-7))² + (-2 - (-6))²) = √((5)² + (4)²) = √(41)

So the ratio of Ben's distance to David's distance is

10 / √(41) ≈ 2.21

Therefore, Ben's distance is about 2.21 times greater than David's distance.

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Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

The functions are illustrations of trigonometry ratios

\(\mathbf{(a)\ cos\theta = \frac{\sqrt{15}}{5}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - cos^2\theta}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (\sqrt{15}/5)}}\)

\(\mathbf{sin\theta = \sqrt{1 - (15/25)}}\)

Take LCM

\(\mathbf{sin\theta = \sqrt{\frac{10}{25}}}\)

\(\mathbf{sin\theta = \frac{\sqrt{10}}{5}}\)

\(\mathbf{(b)\ tan\theta = \frac{\sqrt{10}}{2}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{10})^2 + 2^2}\)

\(\mathbf{Hypotenuse^2 = 10 + 4}\)

\(\mathbf{Hypotenuse^2 = 14}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{14}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{\sqrt{14}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{140}}{14}}\)

\(\mathbf{(c)\ csc\theta = \frac{\sqrt{15}}{3}}\)

The sine of the angles is:

\(\mathbf{sin \theta = \frac{1}{csc\theta}}\)

So, we have:

\(\mathbf{sin \theta = \frac{1}{\sqrt{15}/3}}\)

\(\mathbf{sin \theta = \frac{3}{\sqrt{15}}}\)

Rationalize

\(\mathbf{sin \theta = \frac{3\sqrt{15}}{15}}\)

\(\mathbf{sin \theta = \frac{\sqrt{15}}{5}}\)

\(\mathbf{(d)\ sec\theta =\frac{\sqrt 6}{3}}}\)

The sine of an angle is calculated as follows

\(\mathbf{sin\theta = \sqrt{1 - (1/sec\theta)^2}}\)

So, we have:

\(\mathbf{sin\theta = \sqrt{1 - (3/\sqrt 6)^2}}\)

\(\mathbf{sin\theta = \sqrt{(1 - 9/6)}}\)

\(\mathbf{sin\theta = \sqrt{( - 3/6)}}\)

The sine of the angle does not have a real value

\(\mathbf{(e)\ cot\theta = \frac{\sqrt 6}{2}}\)

Start by calculating the tangent of the angle

\(\mathbf{tan\theta = \frac{1}{cot\theta}}\)

So, we have:

\(\mathbf{tan\theta = \frac{1}{\sqrt 6/2}}\)

\(\mathbf{tan\theta = \frac{2}{\sqrt 6}}\)

Rationalize

\(\mathbf{tan\theta = \frac{2\sqrt 6}{6}}\)

\(\mathbf{tan\theta = \frac{\sqrt 6}{3}}\)

The tangent of an angle is:

\(\mathbf{\ tan\theta = \frac{Opposite}{Adjacent}}\)

Using Pythagoras theorem, we have:

\(\mathbf{Hypotenuse^2 = Opposite^2 + Adjacent^2}\)

So, we have:

\(\mathbf{Hypotenuse^2 = (\sqrt{6})^2 + 3^2}\)

\(\mathbf{Hypotenuse^2 = 6 + 9}\)

\(\mathbf{Hypotenuse^2 = 15}\)

Take square roots

\(\mathbf{Hypotenuse = \sqrt{15}}\)

So, the sine of the angle is:

\(\mathbf{\ sin\theta = \frac{Opposite}{Hypotenuse}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{6}}{\sqrt{15}}}\)

Rationalize

\(\mathbf{\ sin\theta = \frac{\sqrt{90}}{15}}\)

Rewrite as:

\(\mathbf{\ sin\theta = \frac{3\sqrt{10}}{15}}\)

\(\mathbf{\ sin\theta = \frac{\sqrt{10}}{5}}\)

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we are asked to determine the slope of the line that passes through the points (0, 3) and (2, -1). To do that we need to use the formula for the slope of a line:

Where:

Replacing in the formula:

Solving the operations:

therefore, the slope is -2.

To determine the y-intercept we can use the point (0,3), since this means that when x = 0, y = 3. Since the y-intercept is the value of "y" when x = 0, this means that the y-intercept is 3.

To determine the equation of the line we need to use the general form of a line equation:

Where "m" is the slope and "b" the y-intercept. Replacing the value of the slope and "b"

Answer:

a) The vertex of the graph is \((h,k) = (0, 31)\), b) \(a = -16\), c) The equation of the parabola is \(f(t) = -16\cdot t^{2}+31\).

Step-by-step explanation:

a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.

The vertex of the graph is \((h,k) = (0, 31)\).

b) If we know that \((h,k) = (0, 31)\), \(f(t) = a\cdot (t-h)^{2} + k\) and \((t,f(t)) = (1,15)\), then the value of \(a\) is:

\(f(t) = a\cdot (t-h)^{2} + k\)

\(15 = a\cdot (1-0)^{2}+31\)

\(15 = a\cdot 1 + 31\)

\(a = 15-31\)

\(a = -16\)

c) The equation of the parabola is \(f(t) = -16\cdot t^{2}+31\).

Answer:

17

Step-by-step explanation:

The answer is 17 because the operation PEMDAS

Answer:

17

Step-by-step explanation:

20/ 4+6x2 can be simplified. First, you can divide 20 by 4 because of the order PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction) 20 divided by 4 is 5. You can then multiply 6 and 2 which gives you 12. Therefore, your equation is down to 5+12. You can add those two and you get 17 :) Hope this helps!! :D ~Happy Halloween~

Answer:

44 mm

Step-by-step explanation:

radius = 22 mm

diameter = 2 * radius = 44 mm

Area of circle of diameter with 13cm is 132.74

What is area of circle?

Given :

Diameter of circle, d = 13cm

Radius of a circle, r = d/2

=13/2

=6.5

Area of circle = πr²

= 3.142 * 6.5 * 6.5

= 132.74

Hence, the Area of circle of diameter with 13cm is 132.74.

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Answer:

- 7 feet (a)

Step-by-step explanation:

Answer:

Step-by-step explanation:

-14

The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN

Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.

Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.

We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.

Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.

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Answer & Step-by-step explanation:

To prove ∆BAM ≅ ∆CAN:

1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.

2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.

3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.

4. Similarly, ∠BMA and ∠CNA are congruent.

5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.

To prove ∆AMN is an isosceles triangle:

1. From the given information, we know that BM = CN.

2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.

3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.

4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.

Answer:

i dont speak...that language can u translate to english?

Step-by-step explanation:

Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

Answer:

Slope intercept: y = -3/2x + 1

Point slope: y + 2 = -3/2 * (x - 2) [Forgot to add the work for this, I will add it if you need it, feel free to ask.]

Step-by-step explanation:

m = (change in y)/change in x)

But also

m = y_2 - y_1/x_2 - x_1

So lets substitute

m = 1 - (-2)/0 - (2)

Lets find the slope

m = 3/0 - (2)

m = 3/-2

m = -3/2 (Moved the negative)

Now we find the value of b using the equation of a line.

y = mx + b

y = (-3/2) * x + b

y = (-3/2) * (2) + b

-2 = (-3/2) * (2) + b

Now we find the value of b

Lets rewrite

-3/2 * 2 + b = -2

Cancel the CF of 2

-3 + b = -2

Move the terms without b to the right

b = -2 + 3

b = 1

Now we substitute our values of the slope and y-int into y = mx + b to find the equation.

y = -3/2x + 1

Answer:

\(y=\frac{-3}{2}x-1\)

Step-by-step explanation:

Given the two points, we can use the slope formula to get the slope of our equation.

\(\frac{y_2-y_1}{x_2-x_1}=m\)

Plug in what we know

\(\frac{(1)-(-2)}{0-2}=m\)

\(m=\frac{-3}{2}\)

\(y=\frac{-3}{2}x-b\)

Plug in one of the points given and solve to find our y-intercept [b]

\(-2=\frac{-3}{2}(2)-b\)

\(b=1\)

(we already know our y-intercept since we're given what y is when x is 0 [hence (0,1)], but this is how it is done if we did not know it initially)

Final equation

\(y=\frac{-3}{2}x-1\)

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

\(x = y = 3\sqrt{ 2\)

Step-by-step explanation:

Given

The attached triangle

Required

Find x and y

The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.

For this kind of parameter, the opposite = the adjacent

i.e. x = y

Apply Pythagoras theorem

\(x^2 + y^2= 6^2\)

Substitute x for y

\(y^2 + y^2= 6^2\)

\(2y^2= 36\)

Divide by 2

\(y^2 = 18\)

Take square root

\(y = \sqrt{18\)

\(y = \sqrt{9 * 2\)

Split

\(y = \sqrt{9} *\sqrt{ 2\)

\(y = 3*\sqrt{ 2\)

\(y = 3\sqrt{ 2\)

\(x = y = 3\sqrt{ 2\)

Answer: b is the answer maybe i don't know

Step-by-step explanation:

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

S(-2,12)

y= -2(x+2)²+12

Location of coordinate axes:

y=0 → x= -2±√6 (-2-√6,0) (-2+√6,0)

x=0 → y=4 (0,4)