Riley has 51/4 cups of chocolate chips, she needs ¾cup of chocolate chips to make one batch of cookies. how many batches of chocolate-chip cookies can Riley make

Answer:

x=24, y=4

Step-by-step explanation:

x=6y

1/x+1/y=7/24,

1/6y+1/y=7/24

1/6y+6/6y=7/24

(1+6)/6y=7/24

7/6y=7/24, then

6y=24

y=24/6

y=4

x=6y=6*4=24

The value of the expression 3f(-2) + f(1) is 45

Piecewise functions are functions that has two or more equations. They can consists of parabola and straight line.

From the equations, the point where x is -2 is f(x) = 3x^2 - 2x

f(-2) = 3(-2)^2 - 2(-2)
f(-2) = 12 + 4

f(-2) = 16

Similarly the point where x = 1 is -2√x - 1

f(1) = -2√1 - 1

f(1) = -2 - 1

f(1) = -3

Substitute

3f(-2) + f(1) = 3(16) +(-3)
3f(-2) + f(1) = 48 - 3
3f(-2) + f(1) = 45

Hence the value of the expression 3f(-2) + f(1) is 45

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The correct value that equates to this expression is 12‐³². Letter A

.

To solve this expression, just: eliminate the parentheses and multiply the exponents among themselves;[tex] \boxed{ \large \sf (a {}^{n} ) {}^{m} \rightarrow a {}^{n \times m} } \\ \\ [/tex]

[tex]{ = \large \sf (12{}^{-4} ) {}^{8} } [/tex]

[tex]{ = \large \sf 12{}^{-4 \times 8} } [/tex]

[tex] \pink{ \boxed{ = \large \sf 12{}^{-32} } } \\ [/tex]

Therefore, the answer will be 12‐³²

Answer:

here you go with your answer

Answer:

y=-x²+8x+16

Step-by-step explanation:

y= -3(x – 4)(x – 4)

We multiply

y=(-3x+12)(x-4)

Expand the bracket

y= x(-3x+12) -4(-3x+12)

y=-3x²+12x

-4(-3x+12)

+12x+48

y=-3x²+24x+48

Divide by 3

y=-x²+8x+16

Answer:

C)

Step-by-step explanation:

Prime factorize.

A) √30 is in its simplest form.

[tex]B) \sf \sqrt{45}= \sqrt{3*3*5} = 3\sqrt{5}\\[/tex]

[tex]C) \sqrt{75}=\sqrt{3*5*5}=5\sqrt{3}[/tex]

So, option C

The simplified expression of 5√3 is √75.

Hence, Option C is correct.

Using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

The given expression is,

5√3

So it can be written as,

⇒√5² x √3

⇒ √25 x √3

Since we know that,

Square roots are multiplied by both the whole number component and the square root component individually.

Therefore,

⇒√(25x3)

⇒√75

Thus,

5√3  = √75

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Step-by-step explanation:

a=110. x,55

y=180-(x+75)=50

w,75

b,110

x,40

y,30

Answer:

[tex]28{cm}^{2} [/tex]

Step-by-step explanation:

we know

area of rectangle=l*b=(7*4)sq cm=28sq cm

Using the unit rate, the missing values that completes the table are:

A = 5; B = 15; C = 40

Unit rate (m) = change in y/change in x.

5 minutes for 8 Blocks (5, 8) and 10 minutes for 16 blocks (10, 16)are given.

Unit rate (m) = (16 - 8)/(10 - 5) = 8/5

An equation that will define the function is, y = 8/5x. Use it to complete the table.

Find A (y) when x is 5:

y = 8/5(5) = 8

The value of A is: 5

Find B (x) when y is 24:

24 = 8/5(x)

5(24) = 8x

120 = 8x

120/8 = x

15 = x

The value of B is: 15

Find A (y) when x is 25:

y = 8/5(25) = 40

The value of C is: 40

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To find the maxima and minima of the function, we need to calculate the derivative of the function. Note, before the denominator is a perfect square trinomial, so the function can be simplified as

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(x) = \frac{x^2 - x - 2}{(x - 3)^2}} \end{gathered}$}[/tex]

So the derivative is:

  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(2x - 1)(x - 3)^2 - 2(x - 3)(x^2 - x - 2)}{(x - 3)^4} } \end{gathered}$}[/tex]

Simplifying the numerator, we get:

                 [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{(x - 3)(-5x + 7)}{(x - 3)^4} = \frac{-5x + 7}{(x - 3)^3} } \end{gathered}$}[/tex]

The function will have a maximum or minimum when f'(x) = 0, that is,

                  [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f'(x) = \frac{-5x + 7}{(x - 3)^3} = 0 } \end{gathered}$}[/tex]

which is true if -5x + 7 = 0. Then x = 7/5.

To determine whether x = 7/5 is a maximum, we can use the second derivative test or the first derivative test. In this case, it is easier to use the first derivative test to avoid calculating the second derivative. For this, we evaluate f'(x) at a point to the left of x = 7/5 and at a point to the right of it (as long as it is not greater than 3). Since 1 is to the left of 7/5, we evaluate:

                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f(1) = \frac{-5 + 7}{(1 - 3)^3} = \frac{2}{-8} < 0} \end{gathered}$}[/tex]

Likewise, since 2 is to the right of 7/5, then we evaluate:

                                   [tex]\large\displaystyle\text{$\begin{gathered}\sf \displaystyle \bf{\frac{-10 + 7}{(2 - 3)^3} = \frac{-3}{-1} > 0} \end{gathered}$}[/tex]

Note that to the left of 7/5 the derivative is negative (the function decreases) and to the right of 7/5 the derivative is positive (the function increases).

The value of f(x) at 7/5 is:

                               [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle f\left(\tfrac{7}{5}\right) = \frac{\tfrac{49}{25} - \tfrac{7}{5} - 2}{\tfrac{49}{25} - 6 \cdot \tfrac{7}{5} + 9} = -\frac{9}{16} } \end{gathered}$}[/tex]

This means that [tex]\bf{\left( \frac{7}{5}, -\frac{9}{16} \right)}[/tex] is a minimum (and the only extreme value of f(x)).

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

[tex]\text{Minimum at }\left(\dfrac{7}{5},-\dfrac{9}{16}\right)[/tex]

Step-by-step explanation:

The local maximum and minimum points of a function are stationary points (turning points).  Stationary points occur when the gradient of the function is zero.  Differentiation is an algebraic process that finds the gradient of a curve.

To find the stationary points of a function:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $y=\dfrac{u}{v}$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=\dfrac{v \dfrac{\text{d}u}{\text{d}x}-u\dfrac{\text{d}v}{\text{d}x}}{v^2}$\\\end{minipage}}[/tex]

[tex]\text{Given function}: \quad \text{f}(x)=\dfrac{x^2-x-2}{x^2-6x+9}[/tex]

Differentiate the function using the Quotient Rule:

[tex]\text{Let }u=x^2-x-2 \implies \dfrac{\text{d}u}{\text{d}x}=2x-1[/tex]

[tex]\text{Let }v=x^2-6x+9 \implies \dfrac{\text{d}v}{\text{d}x}=2x-6[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{(x^2-6x+9)(2x-1)-(x^2-x-2)(2x-6)}{(x^2-6x+9)^2}\\\\& =\dfrac{(2x^3-13x^2+24x-9)-(2x^3-8x^2+2x+12)}{(x^2-6x+9)^2}\\\\\implies \text{f}\:'(x)& =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\\end{aligned}[/tex]

Set the differentiated function to zero and solve for x:

[tex]\begin{aligned}\implies \text{f}\:'(x)& =0\\\\\implies \dfrac{-5x^2+22x-21}{(x^2-6x+9)^2} & = 0\\\\-5x^2+22x-21 & = 0\\\\-(5x-7)(x-3) & = 0\\\\\implies 5x-7 & = 0 \implies x=\dfrac{7}{5}\\\\\implies x-3 & = 0 \implies x=3\end{aligned}[/tex]

Put the x-values back into the original equation to find the y-values:

[tex]\implies \text{f}\left(\frac{7}{5}\right)=\dfrac{\left(\frac{7}{5}\right)^2-\left(\frac{7}{5}\right)-2}{\left(\frac{7}{5}\right)^2-6\left(\frac{7}{5}\right)+9}=-\dfrac{9}{16}[/tex]

[tex]\implies \text{f}(3)=\dfrac{\left(3\right)^2-\left(3\right)-2}{\left(3\right)^2-6\left(3\right)+9}=\dfrac{4}{0} \implies \text{unde}\text{fined}[/tex]

Therefore, there is a stationary point at:

[tex]\left(\dfrac{7}{5},-\dfrac{9}{16}\right)\:\text{only}[/tex]

To determine if it's a minimum or a maximum, find the second derivative of the function then input the x-value of the stationary point.

Differentiate f'(x) using the Quotient Rule:

Simplify f'(x) before differentiating:

[tex]\begin{aligned}\text{f}\:'(x) & =\dfrac{-5x^2+22x-21}{(x^2-6x+9)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{\left((x-3)^2\right)^2}\\\\& = \dfrac{-(5x-7)(x-3)}{(x-3)^4}\\\\& = -\dfrac{(5x-7)}{(x-3)^3}\\\\\end{aligned}[/tex]

[tex]\text{Let }u=-(5x-7) \implies \dfrac{\text{d}u}{\text{d}x}=-5[/tex]

[tex]\text{Let }v=(x-3)^3 \implies \dfrac{\text{d}v}{\text{d}x}=3(x-3)^2[/tex]

[tex]\begin{aligned}\implies \dfrac{\text{d}^2y}{\text{d}x^2} & =\dfrac{-5(x-3)^3+3(5x-7)(x-3)^2}{(x-3)^6}\\\\& =\dfrac{-5(x-3)+3(5x-7)}{(x-3)^4}\\\\\implies \text{f}\:''(x)& =\dfrac{10x-6}{(x-3)^4}\end{aligned}[/tex]

Therefore:

[tex]\text{f}\:''\left(\dfrac{7}{5}\right)=\dfrac{625}{512} > 0 \implies \text{minimum}[/tex]

Answer:

X=62 degrees

Step-by-step explanation:

The solution is in the image

Answer:

62°

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Therefore,

68.5° + 49.5° + x = 180°

118° + x° = 180°

x = 180° - 118°

x = 62°

Answer:

[tex]\fbox {D. 3,200.4 mm}[/tex]

Step-by-step explanation:

Given :

[ 1 inch = 2.54 centimeters ]

Unit conversions to keep in mind :

Solving

The option that best describes the experiment is accurate and reproducible.

All the values from the experiment are close in value to the accepted value. This indicates that the experiment is accurate. Two experiments yield the same values. This indicates that the experiment is reproducible.

Here is the table used in answering the question:

Accepted Value: 130

Experiment 1 129

Experiment 2 131

Experiment 3 129

Experiment 4 132

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Answer:

(A)They are precise and reproducible

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Add \:\: -6 \hat i - 6\hat j \:\:with \:\; Vector \:\; c[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Vector d can be represented as :

[tex]\qquad \tt \rightarrow \: - 2 \hat i - 2 \hat j[/tex]

Vector c can be represented as :

[tex]\qquad \tt \rightarrow \: 4 \hat i + 4\hat j[/tex]

we have to create vector d from vector c

So, let's assume a vector x, such that sum of vector x and vector c equals to vector d

[tex]\qquad \tt \rightarrow \: x + ( 4 \hat i + 4 \hat j) = - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = - ( 4 \hat i + 4 \hat j) - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = (- 4 \hat i - 2 \hat i) + ( - 4 \hat j - 2 \hat j)[/tex]

[tex]\qquad \tt \rightarrow \: x = - 6 \hat i -6 \hat j[/tex]

Henceforth, in order to get vector d, we need to add (-6i - 6j) in vector c

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

An equation is formed of two equal expressions. The estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the system of equation is the point at which the two lines will intersect as shown below. Therefore, the solution will be,

Solution = (5/2, 4/3)

Hence, the estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.

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Answer:

C

Step-by-step explanation:

Answer C is correct.  The absolute value of 10 is 10 and that of -10 is 10.  Same result.

The ordered pair (7,2) is viable and Option B is the correct answer.

Relationship between variables defines the way one variable is dependent upon the other variable.

It is given that x is the number of visitors and y is the number of winners,

It has to be seen and chosen that which ordered pair makes sense

The ordered pair is viable if the no. of visitor is positive and more than the number of winners.

Therefore ordered pair (7,2) is viable and Option B is the correct answer.

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Answer:

An equilateral triangle is a triangle with all 3 sides the same in size.
If one side is 8cm, then 8x3=24 cm
The perimeter is possibly 24 cm.

The area of the triangle will be 24912 sq. units. Square units and other similar units are used to measure area.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area.

For:

(X1, Y1) = (1, 15)

(X2, Y2) = (-2, 1)

d = 14.317821

For:

(X₂, Y₂) = (-2, 1)

(X₃, Y₃) = (4, 5)

d = 7.211103

For applying the pythogorous them we need the right angle triangle obtained by bisect from the mid point.

The value of the base is;

⇒7.2 / 2

⇒3.6

apply the pythogorous theorem for finding the height;

h² = p² + b²

14.31² = p² + 3.6²

p = 13.84

The area of the triangle is;

[tex]\rm A = \frac{1}{2}\times b \times h \\\\ A= \frac{1}{2} \times 3.6 \times 13.84 \\\\ A = 24.912[/tex]

Hence, the area of the triangle will be 24912 sq. units.

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The unconditional probability of the event A, regardless of which subgroup it comes from is 38%

Let the events be represented as:

So, we have:

P(B) = 60%

P(C) = 40%

P(A | B) = 30%

P(A | C) = 50%

The probability is then calculated as:

P = P(A | B) * P(B)  + P(A | C) * P(C)

Substitute known values

P = 30% * 60% + 50% * 40%

Evaluate the product

P = 38%

Hence, the probability is 38%

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Answer:

1630

Step-by-step explanation:

In words you are looking for 6% of what number is 97.80, turn that into an Algebra equation .06x = 97.80 so x = 97.80/.06 so x = 1630

Step-by-step explanation:

the slope is the factor of x in an equation

y = ax + b

we have here

3y = -5x + 21

to get to the general format above we need to divide everything by 3 :

y = -5/3 x + 7

so, we see, the slope is -5/3.

the perpendicular (angle of 90°) slope is the original slope turned upside-down and with flipped sign :

3/5

so, I guess the correct answer option is c.

but it is not clear what you wrote there, as there is a "-" sign somehow in all 4 answers.

The segment length is 14 (square root)2

Given that Triangle ABC is right angle triangle

The vertex marked is B where side AC is the hypotenuse

The side of AC is at Vertex B is 14

The dash segment from vertex B to point D on side AC

Angle BDA is marked right angle .

Angles A and C both marked 45 degrees.

As shown in diagram

Triangle ABC is drawn according to the statement where B is vertex

The side lengths are 14  

Now to find Another side length that is x

So , the equation formed is

x*cos45 = 14

x/√2 = 14

x = 14√2

Hence the length of the segment is 14√2

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Answer:

Step-by-step explanation:

The segment length is 14 (square root)2

Given that Triangle ABC is right angle triangle

The vertex marked is B where side AC is the hypotenuse

The side of AC is at Vertex B is 14

The dash segment from vertex B to point D on side AC

Angle BDA is marked right angle .

Angles A and C both marked 45 degrees.

As shown in diagram

Triangle ABC is drawn according to the statement where B is vertex

The side lengths are 14  

Now to find Another side length that is x

So , the equation formed is

x*cos45 = 14

x/√2 = 14

x = 14√2

Hence the length of the segment is 14√2

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Answer:

complete this

Step-by-step explanation:

yeah do it

Answer:

Range: (-10 , 14)

Step-by-step explanation:

Given information:

Range: (x , y)?

Plug in domain of x = -4 and x = 4 into equation to find range.

f(-4) = 3 * -4 + 2 = -10

f(4) = 12 + 2 = 14

Range: (-10 , 14)

Answer:

w = -1/5

OR

w = -3

Step-by-step explanation:

Given equation:

−16w-3 = 5w²

Solution:

Subtracting 5w^2 from both sides,we get

Factor the LHS of this equation using middle term factor:

Now,

Solving for equation 1:

Solving for equation 2:

[tex] - 16w - 3 = 5 {w}^{2} \\ \\ 0 = 5 {w}^{2} + 16w + 3 \\ \\ 5 {w}^{2} + 16w + 3 = 0 \\ \\ 5 {w}^{2} + w + 15w + 3 = 0 \\ \\ (5 {w}^{2} + w) + (15w + 3) = 0 \\ \\ w(5w + 1) + 3(5w + 1) = 0 \\ \\ (w + 3)(5w + 1) = 0. [/tex]

The value of w is -3 and -1/5 .

If the value of the z-score is 1. Then the probability that a cat will weigh less than 11 pounds will be 0.84134.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The weight of a cat is normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds.

Then the probability that a cat will weigh less than 11 pounds will be

The value of z-score will be

z = (11 – 9) / 2

z = 1

Then the probability will be

P(x < 11) = P(z < 1)

P(x < 11) = 0.84134

Thus, the probability that a cat will weigh less than 11 pounds will be 0.84134.

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