Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies

Answer:

[tex]\large\boxed{x=-3\pm\sqrt{13}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+6x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2(x)(3)=4\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=4+9\\\\(x+3)^2=13\Rightarrow x+3=\pm\sqrt{13}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{13}[/tex]

The coordinate of the vertex F across y = -x will be (3, -1). Then the correct option is B.

It is the image of the point which is located in the opposite direction of a given point.

The rule of the reflection is given will be

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

Now, the rule for reflecting a point about the line y = -x is;

While reflecting on the line y = -x, we get the reflected points by multiplying '-1' with the swapped coordinates.

The coordinates of the image are given below.

G(-2, -3), F(1, -3), E(-1, -5), and H(2, -5)

The reflection across the line y = -x.

Then the coordinate of the vertex F across y = -x will be (3, -1).

Then the correct option is B.

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Answer:

Explanation:

The graph has the following properties:

        (0.5, 1.6), (0.8, 1), (1.6, 0.5), and (2, 0.4)

The equation represented by the graph is an inverse variation:

From that equation, you can solve for the contstant:

Now, you can take any ordered pair to find the constant:

Thus, you have obtained that the constant is 0.8.

Charlene will need 286 square inches of wrapping paper to cover all six sides of the box with dimensions of 7 inches by 9 inches by 5 inches. This is found by calculating the surface area of each side and then adding them together.

To determine how much wrapping paper Charlene will need to wrap a box with dimensions 7 inches by 9 inches by 5 inches, we calculate the surface area of the box. The box has 6 sides, with each side being a rectangle. The dimensions of the sides are 7x9 inches (two sides), 7x5 inches (two sides), and 9x5 inches (two sides).

To find the total surface area, we calculate the area of each of these rectangles and then sum them together:

Area for two 7x9 sides: 2 * (7in * 9in) = 2 * 63in2 = 126in²

Area for two 7x5 sides: 2 * (7in * 5in) = 2 * 35in2 = 70in²

Area for two 9x5 sides: 2 * (9in * 5in) = 2 * 45in2 = 90in²

Adding these together gives:

Total surface area = 126in² + 70in² + 90in² = 286in²

Charlene will need 286 square inches of wrapping paper to wrap the box.

Answer:

The value x=-5 makes the quotient undefined

Step-by-step explanation:

When we are looking for undefined values, we want values that make the denominator zero

x+5 =0

Subtract 5 from each side

x+5-5 =0-5

x=-5

The value x=-5 makes the quotient undefined

Answer:

Option d. the initial amount of money placed in the savings account

Step-by-step explanation:

we have

[tex]f(x)=3,005(1+0.03)^{x}[/tex]

This is a exponential function of the form

[tex]f(x)=a(1+r)^{x}[/tex]

where

a is the initial value

r is the growth rate

(1+r) is the base

x is the number of years

f(x) is the amount of money in a savings account

In this problem we have

a=$3,005

r=0.03=3%

(1+r)=1.03

therefore

3,005 represent the initial value ( the amount of money for the value of x equal to zero)

Answer:

d. The initial amount of money placed in the savings account

Step-by-step explanation:

Given function that represents the amount of money after x years,

[tex]f(x)=3005(1+0.03)^x[/tex]

Which is an exponential growth function,

Since, in a growth function,

[tex]f(x)=ab^x[/tex]

a represents the initial value,

b is the growth rate per period,

x is the number of periods,

By comparing,

a = 3005,

Hence, 3005 must be represent the initial amount of money placed in the savings account,

Option 'd' is correct.

Answer:

y=3x+3 is slope-intercept form

y-6=3(x-1) is point-slope form

I don't know the form your equation(s) are in. There are other forms.

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

So the slope of y=3x+2 is 3.

Parallel lines have the same slope.  So the slope of the line we are looking for has a slope of 3.

Therefore, our equation his this form y=3x+b.

We need to now find b.

We know a point (x,y) on the line.

y=3x+b using (x,y)=(1,6).

6=3(1)+b

6=3+b

Subtract 3 on both sides:

3=b

So the equation is y=3x+3

Point-slope form is another form we can put our line into

y-y1=m(x-x1)

where m is the slope and (x1,y1) is a point on the line.

We have m=3 and a point (x1,y1) on the line is (1,6).

y-6=3(x-1)

[tex]\huge{\boxed{y=3x+3}}[/tex]

It could also be [tex]\boxed{y-6=3(x-1)}[/tex]

We can use point-slope to find this.  Parallel lines have the same slope, and the given line has a slope of 3 ([tex]m[/tex] in [tex]y=mx+b[/tex]).  This means that the parallel line will also have a slope of 3.

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.

Plug in the values. [tex]\boxed{y-6=3(x-1)}[/tex] (point-slope form)

Distribute. [tex]y-6=3x-3[/tex]

Add 6 to both sides. [tex]\boxed{y=3x+3}[/tex] (slope-intercept form)

Answer:

Approximately 0.0294.

Step-by-step explanation:

Assume that there's only one correct choice in each question.

What's the probability that exactly 12 answers are correct?

The probability of getting exactly 12 answers correct is:

[tex]\displaystyle \left(\frac{1}{4}\right)^{12} \times \left(\frac{3}{4}\right)^{28 - 12}\times \left(\begin{array}{c}28\\12\end{array}\right)\approx 0.0182[/tex].

With the same logic, the probability of getting [tex]x[/tex] ([tex]x\in \mathbb{Z}[/tex], [tex]12\le x\le 28[/tex]) correct out of the 28 random answers will be

[tex]\displaystyle \left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}28\\x\end{array}\right)[/tex].

The probability of getting at least 12 correct out of 28 random answers is the sum of

The Sigma notation might help:

[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]}[/tex].

Evaluate this sum (preferably with a calculator)

[tex]\displaystyle \sum_{x = 12}^{28}{\left[\left(\frac{1}{4}\right)^{x} \times \left(\frac{3}{4}\right)^{28 - x}\times \left(\begin{array}{c}x\\28\end{array}\right)\right]} \approx 0.0294[/tex].

[tex]\huge{\boxed{6(3)+6(0.05)}}[/tex]

The distributive property shows that you need to multiply the [tex]6[/tex] separately by each term in the parentheses. This means you multiply [tex]6*3[/tex] and [tex]6*0.05[/tex], then add them together to get [tex]6*3+6*0.05[/tex], or in the terms of your answer choices, [tex]\boxed{6(3)+6(0.05)}[/tex].

Option C is correct. The required equivalent expression will be  6(3)+6(0.05)

Given three values A, B and C expressed as A(B+C)

Using the law of distribution

A(B+C) = AB + AC

Applying this law on the expression 6(3+0.05)

6(3+0.05) = 6(3) + 6(0.05)

hence the required equivalent expression will be  6(3)+6(0.05)

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Answer:

y = 1/16

Step-by-step explanation:

y = 4 • 2^x

Let x = -6

y = 4 • 2^(-6)

The negative exponent puts it in the denominator

y = 4 • 1/ 2^6

y = 4 * 1/64

y = 4/64

y = 1/16  

Answer:

5/3 units  or 1 2/3 units

Step-by-step explanation:

P =2 (l+w)

We know the length = 1/3 and the width = 1/2

P = 2 (1/3+1/2)

Get a common denominator of 6

1/3 *2/2 = 2/6

1/2 *3/3 = 3/6

Therefore

P = 2(2/6+3/6)

  = 2(5/6)

   = 10/6

    =5/3 units

Changing from an improper fraction

  = 1 2/3 units

The correct formula to calculate the circumference of a circle is C = 2πr. To solve for r, the radius, we can rearrange the equation to r = C/(2π), which can be used to find the radius when the circumference is known.

The formula for the circumference of a circle is given by C = 2πr, where 'C' represents the circumference and 'r' is the radius of the circle. The formula has been provided in an errorneous format, it should be 2πr not 2tr.

If we want to solve this equation for 'r', which represents the radius, we would need to isolate 'r' on one side of the equation. We can do this by dividing both sides of the equation by 2π. The resulting equation solved for r would be r = C/(2*π).

This equation can be utilized to find the radius if the circumference is known.

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Answer:

x = - 5, x = 3

Step-by-step explanation:

To find the x- intercepts equate f(x) to zero, that is

x² + 2x - 15 = 0 ← in standard form

Consider the factors of the constant term ( - 15) which sum to give the coefficient of the x- term ( + 2)

The factors are + 5 and - 3, since

5 × - 3 = - 15 and 5 - 3 = + 2, hence

(x + 5)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5 ⇒ (- 5, 0 ) ← x- intercept

x - 3 = 0 ⇒ x = 3 ⇒ (3, 0 ) ← x- intercept

Answer:

left most x intercept : ( -5, 0 )

right most x intercept : ( 3, 0 )

Step-by-step explanation:

Just got it right esketit

Answer:

2 ( 24 ) + 2 a = 215

Step-by-step explanation:

Perimeter of the rectangle is 215 feet, the short sides are 24 feet long and we need to work out the long sides (we will call a long side 'a') so,

24 + 24 + a + a = 215

For this case we have to:

Let "a" be the variable that represents the length of the rectangle and let "b" be the variable that represents the width of the rectangle. Then the perimeter is given by:

[tex]P = 2a + 2b[/tex]

We have as data that:

[tex]P = 215 \ feet\\b = 24 \ feet[/tex]

Then, replacing:

[tex]215 = 2a + 2 (24)[/tex]

Answer:

Option B

Answer:From the box plot, it can be seen that for grade 7 students,

The least value is 72 and the highest value is 91. The lower and the upper quartiles are 78 and 88 respectively while the median is 84.

Thus, interquatile range of the resting pulse rate of grade 7 students is upper quatile - lower quartle = 88 - 78 = 10

Similarly, from the box plot, it can be seen that for grade 8 students,

The least value is 76 and the highest value is 97. The lower and the upper quartiles are 85 and 94 respectively while the median is 89.

Thus, interquatile range of the resting pulse rate of grade 8 students is upper quatile - lower quartle = 94 - 85 = 9

The difference of the medians of the resting pulse rate of grade 7 students and grade 8 students is 89 - 84 = 5

Therefore, the difference of the medians is about half of the interquartile range of either data set.

Step-by-step explanation: i hope it helps it took a long time to write!

Answer:

I hope this helps

Step-by-step explanation:

Answer:

c. 34.49

Step-by-step explanation:

Note that the nearest tenth place value is directly next to the decimal point (located on the right). Round each number to the nearest tenth. Look at the number in the hundredth place value. If it is 5 or greater round up, if 4 and less, round down.

a. 34.62 rounded to the nearest tenth is 34.6

c. 34.49 rounded to the nearest tenth is 34.5

b. 34.59 rounded to the nearest tenth is 34.6

d. 34.56 rounded to the nearest tenth is 34.6

This makes it so that C. 34.49 is your answer.

~

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

[tex]\huge\text{7*(-3) * (-2)(2) = ?}[/tex]

[tex]\huge\text{7 * (-3) = -21}[/tex]

[tex]\huge\text{-21 * (-2)2 = ?}[/tex]

[tex]\huge\text{-21 * -2 = 42}[/tex]

[tex]\huge\text{42(2) = ?}[/tex]

[tex]\huge\text{42 * 2 = 42 + 42 = 84}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: 84}}}\huge\checkmark[/tex]

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

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

Answer:

C.

Step-by-step explanation:

Your fractions are missing there fraction bars:

3/4 (20y − 8) + 5 = 1/2 y + 1/4 (20y + 8)  

15y − 6 + 5 = 1/2 y + 5y + 2  

15y − 1 = 11/2 y + 2

A. 11/2y and 2 aren't like terms because one contains the variable y and the other contains no variable

B. The distribute property can't be used there because you don't have 15(y-1) you have 15y-1

C. Subtracting 11/2y sounds like a good step because there is a y term on the opposing side.

15y-1=11/2y+2

Subtracing 11/2y on both sides

9.5y-1=2

That looks pretty good because then you would add 1 on both sides giving:

9.5y =3

Last step would get the y by itself which is dividing both sides by 9.5 giving you 6/19.

D. You could actually do this but it doesn't help you get x by itself.  The equation would look like this: 15/2 y-1/2=11/4 y+1

Answer:

C. Subtract 11/2y from each side of the equation.

Step-by-step explanation:

A quadrilateral is a polygon with 4 number of sides and 4 vertices. The correct figure is figure B.

A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.

For the above-given condition,  "If it is a square, then it is a quadrilateral" figure B is correct because, as per the first diagram, not all the squares are quadrilateral, while as per the figure B every square is a quadrilateral.

Hence, the correct figure is figure B.

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Answer:

-1

Step-by-step explanation:

So you are asked to find 3f(1)-4g(-2).

In order to find this you must first find f(1) and g(-2).

So f(1) means what is the value of the expression 3x-2 for when x=1.

f(1)=3(1)-2

f(1)=3-2

f(1)=1

And g(-2) mean what is the value of the expression 5-x^2 for when x=-2.

g(-2)=5-(-2)^2

g(-2)=5-(4)

g(-2)=5-4

g(-2)=1

So both of those function values were 1.

Our problem of 3f(1)-4g(-2) becomes 3(1)-4(1)=3-4=-1.

Answer:

Step-by-step explanation:

=4⁴ · 4³

=4^{7}

=16 384

=2² · 2⁻⁴

=2^{-2}

=1/2^{2}

=1/4

Answer:

565.5 in^3

Step-by-step explanation:

To find the full volume of the tank

V = l*w*h

We know 12 inches high, 14.5 inches long, and 6.5 inches wide.

Substituting in

V = 12 * 14.5*6.5

V =1131 in ^3

He is filling it 1/2 full, that would be 1/2 of the volume

1/2 V = 1131/2 = 565.5 in^3

Answer:

answer is 565.5 in^3

Step-by-step explanation:

Answer:

It is B.

Step-by-step explanation:

x^2+x-6 /  x^2-x-6 = 0

The numerator equates to zero:

x^2 + x - 6 = 0

(x + 3)(x - 2) = 0

the zeroes are {-3, 2).

The zeroes of the function f(x) = (x² + x - 6)/(x² - x - 6) are -3, 2.

Hence, option B. is the right choice.

A function (say f(x)) is defined over x, when an expression in x, gives only one value f(x) for all the x in its domain.

A zero of a function (say f(x)) is the value x, where f(x) = 0.

We are asked to find the zeroes of the function

f(x) = (x² + x - 6)/(x² - x - 6).

To find the zeroes, we put the value of f(x) = 0, in the above equation to get:

(x² + x - 6)/(x² - x - 6) = 0

or, (x² + 3x - 2x - 6)/(x² + 2x - 3x - 6) = 0

or, {x(x + 3) -2(x + 3)}/{x(x + 2) -3(x + 2)} = 0

or, {(x - 2)(x + 3)}/{(x - 3)(x + 2)} = 0

Zeroes are where the numerator = 0, as the denominator can not be 0.

∴ (x + 3)(x - 2) = 0

∴ Zeroes of the function x + 3 = 0 ⇒ x = -3, and x - 2 =0 ⇒ x = 2, that is

-3, 2. Hence, option B. is the right choice.

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Answer:

1. W(5,1),X(1,7),Y(9,9) and Z(11,7).

2.A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).

3. E(5,6) ,F(1,12),G(9,14) and H(11,12).

4.O(10,1),P(6,7),Q(14,9) and R(16,7).

Step-by-step explanation:

We are given that a quadrilateral JKLM with vertices J(8,4),K(4,10),L(12,12) and M(14,10)

We have to match a quadrilateral with its correct transformation of given quadrilateral JKLM

1.a transformation 3 units down and 3 units left

By using transformation rule [tex](x,y)\rightarrow (x-3,y-3)[/tex]

The new  vertices  of quadrilateral is (5,1), (1,7),(9,9) and (11,7).

Hence, the quadrilateral WXYZ with vertices W(5,1),X(1,7),Y(9,9) and Z(11,7).

2.A sequence of reflection across x- axis and y-axis in order

Reflection across x- axis

The transformation  rule [tex](x,y)\rightarrow (x,-y)[/tex]

By using this rule

The vertices of quadrilateral are  (8,-4),(4,-10),(12,-12) and (14,-10).

After the reflection across y- axis

The transformations rule

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

By using this rule

We get the new vertices of quadrilateral are (-8,-4),(-4,-10),(-12,-12) and (-14,-10).

Hence, the quadrilateral ABCD with vertices A(-8,-4),B(-4,-10),C(-12,-12) and D(-14,-10).

3.a translation 3 unit left and 2 units up

The transformation rule [tex](x,y)\rightarrow (x-3,y+2)[/tex]

By using this rule

The new vertices are (5,6),(1,12),(9,14) and (11,12).

Hence, the quadrilateral EFGH with vertices E(5,6) ,F(1,12),G(9,14) and H(11,12).

4.a translation 2 units right and 3 units down

The transformation rule

[tex](x,y)\rightarrow (x+2,y-3)[/tex]

By using this rule

The new vertices are (10,1),(6,7),(14,9) and (16,7)

Hence, the quadrilateral OPQR with vertices O(10,1),P(6,7),Q(14,9) and R(16,7).

Answer:

We have a geometric series in which:

a = 20

r = 1/2

Now, we know that: S2 = 20(1-r^2)/(1-r)  and S12 = 20(1-r^12)/1-r

Therefore:  sigma(3,12) = S12-S2  = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)]  =5115/512  = 9.99023438

Therefore, the answer is: 9.99

Answer: Is D

Step-by-step explanation:

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

It tells us that the slope (m) is -3 and the y-intercept (b) is 5. Plug this into the formula given above:

y = -3x + 5

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

Step-by-step explanation:

we know that

2 is a zero of multiplicity 3 of the polynomial

so

we have that

x=2  is a solution of the polynomial

A factor of the polynomial is

[tex](x-2)^{3}[/tex] ----> is elevated to the cube because is a multiplicity 3

and the other solution is x=-2

since the polynomial  is fifth degree, x=-2 must have a multiplicity 2

so

the other factor of the polynomial is  

[tex](x+2)^{2}[/tex] ----> is squared because is a multiplicity 2

therefore

The polynomial is equal to multiply the factors by the leading coefficient

so

[tex]f(x)=2(x-2)^{3}(x+2)^{2}[/tex]

Answer:

Step-by-step explanation:

Answer: 12.3 seconds.

Step-by-step explanation: Hope It Helps :)

ANSWER = 270,000

MARK BRAINLIST

Answer:

478,387.0000

Step-by-step explanation: