In buffalo, New York, the temperature was -14F in the morning. If the temperature dropped 7F, what is the temperature now?

Answer:

The correct option is D. The image and preimage are congruent.

Step-by-step explanation:

Let us understand the this concept with the help of an example.

Consider the figure 1:

From the figure 1, it is clear that the size of image doesn't change.

Thus, option A and C are invalid.

Or we can say that, the image and preimage remain the same.

Therefore, the correct option is D. The image and preimage are congruent.

We want to find what separates terms in an algebraic expression.

The answer is: The sum and subtraction symbols.

By definition, a "term" can be a signed number, a variable, a constant multiplying a variable, or more complex things, like expressions inside parentheses.

The terms in an algebraic expression are the things we are adding or subtracting.

Thus, what we use to separate them are the sum symbol (+) or the subtraction symbol (+).

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Answer:

Y-axis and y = -x

Step-by-step explanation:

The student's question is about the sequence of rigid transformations that resulted in polygon A'B'C'D' from polygon ABCD. While the reflections lines are unspecified, typically two reflections across intersecting lines equal a rotation around the point of intersection by twice the angle between the lines.

The student's question involves identifying the type of rigid transformations that polygon ABCD underwent to form polygon A'B'C'D'. Unfortunately, there seem to be missing elements in the provided description of the transformations. Normally, a rigid transformation would include details such as the lines across which the reflections occur. That said, a sequence of two reflections across two intersecting lines is equivalent to a rotation around the point of intersection of the lines, with the angle of rotation being twice the angle between the two lines.

If we could infer that the lines of reflection are perpendicular to each other, the overall transformation would be a rotation of 180 degrees. This would mean that polygon A'B'C'D' is the result of this 180-degree rotation of polygon ABCD about the point of intersection of the two reflection lines.

Answer:

The vertex of the function is (h,k)=(3,3)

The axis of symmetry is x=3.    

Step-by-step explanation:

Given : Function [tex]y=2x^2-12x+21[/tex]

To find : Determine the axis of symmetry and the vertex of the given function.

Solution :  

The quadratic function is in the form, [tex]y=ax^2+bx+c[/tex]

On comparing, a=2 , b=-12 and c=21

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

[tex]h=-\frac{b}{2a}[/tex]

[tex]h=-\frac{-12}{2(2)}[/tex]

[tex]h=\frac{12}{4}[/tex]

[tex]h=3[/tex]

For k, The y-coordinate of the vertex is given by,

[tex]k=f(h)[/tex]

[tex]k=2h^2-12h+21[/tex]

[tex]k=2(3)^2-12(3)+21[/tex]

[tex]k=18-36+21[/tex]

[tex]k=3[/tex]

The vertex of the function is (h,k)=(3,3)

The x-coordinate of the vertex i.e. [tex]x=-\frac{b}{2a}[/tex] is the axis of symmetry,

So, [tex]x=-\frac{b}{2a}=3[/tex] (solved above)

So, The axis of symmetry is x=3.    

Answer: Hello mate!

"four times a certain number increased by 6 is equal to 94"

is equivalent to: 4*x + 6 = 94

where x represents the number.

Now we would want to find the value of x.

4*x + 6 = 94

4*x = 94 - 6 = 88

x = 88/4 = 22

then the value of the number x that makes the statment true is x = 22.

The length of GQ is 25/3 units.

To find the length of GQ, we need to equate GQ to GH and solve for x. Since Q is the midpoint of GH, the lengths GQ and QH are equal. Therefore, we have the equation:

2x + 3 = 5x - 5

Subtract 2x from both sides:

3 = 3x - 5

Add 5 to both sides:

8 = 3x

Divide both sides by 3:

x = 8/3

To find the length of GQ, substitute the value of x back into 2x + 3:

GQ = 2(8/3) + 3

GQ = 16/3 + 3

GQ = 16/3 + 9/3

GQ = 25/3 units

Answer:   C.  ΔSQR

Step-by-step explanation:

In [tex]\triangle{STR}[/tex] and [tex]\triangle{SQR}[/tex], we have

[tex]\angle{TSR}\cong\angle{OSR}\\\\\angle{STR}\cong\angle{QRS}=90^{\circ}[/tex]

By AA- similarity postulate , we get

[tex]\triangle{STR}\sim\triangle{SQR}[/tex]

Adam is 4 years old. This conclusion is reached by setting up a system of equations based on the information that Mark and Adam's ages add up to 28 years and Mark is 20 years older than Adam.

The student is asking how old Adam is, given that the total age of Mark and Adam is 28 years, and Mark is 20 years older than Adam. To solve this, we can set up a system of equations. Let Mark's age be represented by M and Adam's age be represented by A. The two equations based on the given information would be:

Now, substituting the second equation into the first one, we get:

A + 20 + A = 28

This simplifies to:

2A + 20 = 28

Subtracting 20 from both sides, we have:

2A = 8

Dividing both sides by 2, we find:

A = 4

So, Adam is 4 years old.

Answer:the answer would be c which is 146

Step-by-step explanation:

The total costs t of the eggs is the dependent variable.

Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.

Thus if variable is taking its values independently of any visible direct cause, then that variable is called independent variable.

The variables that take their values based on some other variables' values are called dependent variables.

Given that the number of eggs e in the carton and the total costs t of the eggs.

Here, we know the number of eggs, e, to know how much it costs.

Hence, it is the dependent variable.

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It is difficult to estimate the mass of an average flat screen computer monitor without specific data.

In order to estimate the mass of an average flat screen computer monitor, you could use the rule-of-thumb approach by mass. This approach involves finding the average mass of similar monitors. However, since we do not have specific data on the mass of an average flat screen computer monitor, it is difficult to provide an accurate estimate.

The mass estimate can also be influenced by factors such as the size, type, and materials used in the construction of the monitor. Therefore, it is recommended to refer to the product specifications provided by the manufacturer for the most accurate information regarding the mass of a specific model of flat screen computer monitor.

Answer:

p>[tex]\frac{8}{7}[/tex]

Step-by-step explanation:

The equation is 6(2 P-1) > 5 P +2

6(2 P-1)> 5 P+2

6×2 P-6×1> 5 P+2

12 P-6> 5 P+2

12 P - 5 P > 2+6

 7 P > 8

P > [tex]\frac{8}{7}[/tex]

P is greater than[tex]\frac{8}{7}[/tex]

Hence, the correct answer is p greater than [tex]\frac{8}{7}[/tex]

Answer:

103 mg.

Step-by-step explanation:

We have been given that the decay of 230 mg of an isotope is described by the function [tex]A(t)=230e^{-0.031t}[/tex], where t is time in years.

To find the amount left after 26 years, we will substitute [tex]t=26[/tex] in our given function as:

[tex]A(26)=230e^{-0.031\cdot 26}[/tex]

[tex]A(26)=230e^{-0.806}[/tex]

Using exponent property [tex]a^{-n}=\frac{1}{a^n}[/tex], we will get:

[tex]A(26)=230\times \frac{1}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{e^{0.806}}[/tex]

[tex]A(26)=\frac{230}{2.2389343}[/tex]

[tex]A(26)=102.72744\approx 103[/tex]

Therefore, 103 mg of isotope will be left after 26 years.