Complete the square to re-write the quadratic function in vertex form:

y = x2 – 7x + 1

Based on the definition of congruent triangles, we can state that: C. They are not congruent because only one pair of corresponding sides is congruent.

Congruent triangles refer to a pair of triangles that possess identical shape and size. If two triangles are congruent, it implies that their corresponding sides and angles are precisely equal.

The image that is attached below shows the diagram of triangles FGH and FJH. We see that only one pair of sides are congruent (FH = FH).

This is not enough to conclude that both triangles are congruent. Therefore, we can conclude that:

C. They are not congruent because only one pair of corresponding sides is congruent.

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Mrs. Nez will receive $19.16 from the credit card company. A credit card is different from a charge card, which requires the balance to be paid in full each month.

A credit card is a payment card issued to users (cardholders) to enable the cardholder to pay a merchant for goods and services based on the cardholder's promise to the card issuer to pay them for the amounts so paid plus the other agreed charges. The card issuer (usually a bank) creates a revolving account and grants a line of credit to the cardholder, from which the cardholder can borrow money for payment to a merchant or as a cash advance.  In contrast, credit cards allow the consumers a continuing balance of debt, subject to interest being charged.

Mrs. Nez will receive 95.8% of the $20 purchase, which is equal to $20 * 0.958 = $19.16.

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Answer:  " Yes; Kim is  correct."

Explanation:  [refer to the end of this "answer"].

Note: Any "triangle" has 3 sides and 3 angles.

An isosceles triangle has 2 (angles) with the exact same measurements.

We are given the following information:

We have an isosceles angle:
 with one of the angles = 48°
 _______
Does this mean that one of the angles must be:  66 ° ?

If so; then:  either:
       48 + 66 + 48 = 180 ?
or:   48 + 66 + 66 = 180 ?

1)  First: Start with 48 + 66 + 48 ≟ 180 ?

   (48 + 66 + 48) ≟ 180 ?   ;  162 ≟ 180?  No; " 162 < 180 " .

2) Second: Try:  "48 + 66 + 66 = 180 " .

   (48 + 66 + 66) ≟ 180 ? ;  180 ≟ 180 ? ; Yes! "180 = 180".
_______
So:  Kim is correct; because isosceles triangles must have angles with 2 (two) equal measurements.  Note that all triangles have angles that add up to 180° .  
So:  As shown above:
    If one angle of the triangle is 48°; then: **each** of the other angle measurements must be 66°.
  So:  Yes; Kim is correct when he says that one of the other angles must be 66°.
   (48 + 66 + 48) ≟ 180 ?   ;  162 ≟. 180?  No; " 162 < 180 " .
_______
Hope this is helpful to you!  Wishing you well!
_______

Answer:

7/20

Step-by-step explanation:

15/25 * 14/24 = 210/600 = 21/60 = 7/20

the solution to the equation by completing the square is: x = (9/2) ± √(-7k - 47/4).

To solve the given equation by completing the square, we need to rewrite the equation in the form of \((x + a)^2 = b\) , where a and b are constants. This can be done by following these steps:

1. Move all the terms to one side of the equation:

\(5x^2 + 7k + 76 - 9x - 4x^2 = 0\)

2. Combine like terms:

\(x^2 - 9x + 7k + 76 = 0\)

3. Rewrite the equation by completing the square for the x terms. To do this, take half of the coefficient of x (-9/2), square it, and add it to both sides of the equation:

\(x^2 - 9x + (-(9/2))^2 + 7k + 76 - (-(9/2))^2 = (-(9/2))^2\)

4. Simplify:

\((x - (9/2))^2 + 7k + 76 - (81/4) = 81/4\)

5. Combine constants:

\((x - (9/2))^2 + 7k + 47/4 = 0\)

6. Solve for x by taking the square root of both sides:

x - (9/2) = ±√(-7k - 47/4)

7. Add (9/2) to both sides:

x = (9/2) ± √(-7k - 47/4)

Therefore, the solution to the equation by completing the square is: x = (9/2) ± √(-7k - 47/4).

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the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

To find the perimeter of an isosceles trapezoid, follow these steps:

1. Identify the given measurements: In an isosceles trapezoid, know the lengths of the two parallel sides (the bases) and the two non-parallel sides (the legs).

2. Add the lengths of the bases: Add the lengths of the two parallel sides (bases) of the trapezoid.

3. Multiply the sum by 2: Multiply the sum from step 2 by 2 to account for both sides of the trapezoid.

4. Add the lengths of the legs: Add the lengths of the two non-parallel sides (legs) of the trapezoid.

5. Add the results: Add the results from steps 3 and 4 to find the perimeter of the isosceles trapezoid.

Mathematically, the formula for the perimeter (P) of an isosceles trapezoid is:

P = 2 * (base1 + base2) + leg1 + leg2

Alternatively, know the lengths of all four sides of the trapezoid, simply add them together to find the perimeter.

Keep in mind that the measurements used in the formula should be in the same unit (e.g., centimetres, inches) for accurate results.

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Answer:

Step-by-step explanation:

P = a + b + 2c

where a is the top, b is the bottom, and c is a leg of the trapezoid. The perimeter is the sum of the outer edge of the shape, so you just need to add the lengths of the sides.

Answer:

Step-by-step explanation:

slope of line y=4x+12 is 4

slope of line perpendicular to y=4x+12 is -1/4

eq. of perpendicular line or perpendicular linear function is y=-1/4x+b  where b is the y-intercept.

Answer:

Can't be answered, as written.

Step-by-step explanation:

Please check the equations.  As written, they are the same:

y=2x-4 and 6x-3y=12

The second, 6x-3y=12, can be rewritten:

-3y = -6x + 12

y = 2x - 4   is the same as the first equation.

========

I'll do an example based on a different first equation.  Let's try:

y = 4x-4 and 6x-3y=12

There are two equations and 2 unknowns.  We can solve this in either of two ways:  Mathematically and Graphically.  Let's try both.

Mathematically.

Pick either equation and isolate one of the variables (x or y)

I'll chose the first, since the variable y is already isolated.  (the efficient approach)

y = 4x-4

Take the second equation and use the definition of y provided by the first equation in place of y is the second:

6x-3y = 12

6x-3(4x-4) = 12  [Substituted the value of y given in the first equation]

6x - 12x + 12 = 12

-6x=0

  x= 0

Use x = 0 in either equation to find y:

y = 4x-4

y=4*(0)-4

y = -4

The solution (where the lines intersect) is (0,-4)

We can also solve this graphically.  

Plot the two lines and look for their intersection.  The attached graph shows that to be (0,-4).

Answer:

2nd choice

Step-by-step explanation:

Look at the radical, if two radicals can add, they must have the same root. The answer must also have the same root.

Answer:

B on edge

Step-by-step explanation:

Answer:

2x+7

Step-by-step explanation:

3x +(-x) = 3x - x, so it's 2x

12 + (-5) is the same situation, just being 12 - 5, so it's 7.

putting them together leaves you with 2x+7

Answer:

x=1

Step-by-step explanation:

Answer:

eèeeeeeeeeeeeeeeeeeweeeeeee

The inequality that represents the normal temperature range of a dog, where t represents body temperature is given as follows:

|t - 101.8| ≤ 0.7.

The absolute value of a number gives the distance of a number from the origin, hence it basically can be interpreted as the number without the signal, as for example, |-2| = |2| = 2.

The average temperature for a dog is 101.8° F, but it can vary by as much as 0.7° F, hence the absolute value of the difference between t and 101.8 is of at most 0.7, hence the inequality is:

|t - 101.8| ≤ 0.7.

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Answer:

12mn

Step-by-step explanation:

Just multiply 4 by 3

slope:

find two places where the line neatly crosses the grid. As example, we can choose : (-2 , -7) and (2 , 1)

slope = rise/run

so:

slope = change in y/change in x

slope = (-7 - 1) / (-2 - 2)

slope = -8/-4

slope = 2

y-intercept:

this is where the blue line crosses the y (vertical) axis. This occurs when x = 0. y -intercept is: (0 , -3).

equation format: y = mx + b

where m = slope and b = y intercept

so:

y = 2x - 3

By answering the presented question, we may conclude that So Christian  equation spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

What is equation?

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry. Let's start by defining some variables to represent the number of words each student spelled correctly:

Let x be the number of words Christian spelled.

x + (3x - 2) + (2x + 1) = 95

6x - 1 = 95

6x = 96

x = 16

So Christian spelled 16 words correctly, Sarah spelled 3x - 2 = 46 words correctly, and Leonard spelled 2x + 1 = 33 words correctly.

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To find the tangent between two circles, you need to draw a line that is tangent to both circles at the same point. This point of tangency is the point where the two circles meet.

To draw the tangent line, you can first draw a line connecting the centers of the two circles. This line will bisect the point of tangency. Next, draw a perpendicular line to this bisecting line passing through the point of intersection of the circles. The intersection of this line with each of the circles will be the points of tangency. Connect these two points of tangency with a line, and you will have drawn the tangent line between the two circles.

The tangent line between two circles is useful in solving problems related to geometry and physics, such as determining the position of a moving object relative to two stationary objects represented by the circles.

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An38

Step-by-step explanation:

The measure of angle B is 93°

Here,

∠A and ∠B are supplementary angles.

∠A = (8x - 25)° and ∠B = (7x - 5)°

We have to find ∠B.

What are Supplementary angles?

Two Angles are Supplementary when they add up to 180 degrees.

Now,

∠A and ∠B are supplementary angles.

Hence, ∠A + ∠B = 180°

Here, ∠A = (8x - 25)° and ∠B = (7x - 5)°

Put in above equation we get;

(8x - 25)° +  (7x - 5)° = 180°

15 x - 30 = 180

15 x = 210

x = 14

So, Measure of ∠B = (7x - 5)° is;

∠B = (7x - 5)° = ( 7 * 14 - 5) = 98 - 5 = 93°

Hence, The measure of angle B is 93°.

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it's easy

Step-by-step explanation:

use the formula for finding a slope and equate it to 7

Answer:

\(\sin C=\frac{28}{35}\)

Step-by-step explanation:

In a right triangle, \(\sin\theta =\frac{\text{opp}}{\text{hyp}}\). In this case, the side opposite to angle \(C\) is 28 and the hypotenuse is 35. Therefore, the exact value of \(\sin C\) is \(\boxed{\frac{28}{35}}\).

Answer:

243

Step-by-step explanation:

Answer:

E Ticket sales are not affected by the number of cloudy days per month.

Step-by-step explanation:

From the scatter plot Given, using visual observation, we can infer that the relationship between theme park ticket sales and the number of cloudy sales is randomly scattered with no defined linear pattern. That is, the plot does not ascertain of the number of ticket sales increases with increasing number of cloudy days, or vice versa. Hence, the relationship will best the described as concluding that ticket sales are not affected by the number of cloudy days per month.

Answer:

ages would no longer get larger as the mouse hovers over them. The transition would happen over 10s, since this is the default duration.

Step-by-step explanation:

If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

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Answer:

I can't currently fully answer, hoping someone can come along and help-

Step-by-step explanation:

separate the shape into 3 triangles and 1 rectangle and then add all the areas together

area of a triangle is 1/2 base times height and area of a rectangle is length multiplied by width

The answer is c. Chi-square test. A Chi-square test is an inferential statistical technique used to analyze the relationship between two categorical variables organized in a bivariate table.

In a chi-square test, the data is organized into a contingency table, also known as a cross tabulation or bivariate tabulation. This table displays the frequency distribution of two categorical variables, showing how they are related or associated with each other.

The chi-square test evaluates whether there is a significant relationship or association between the variables. It calculates a test statistic based on the observed frequencies in the contingency table and compares it to the expected frequencies under the assumption of independence between the variables. If the test statistic is sufficiently large, it indicates that there is a significant relationship between the variables, rejecting the null hypothesis of independence.

The chi-square test is widely used in various fields, including social sciences, market research, and epidemiology, to determine if there is a significant association between categorical variables. It provides valuable insights into the relationship between variables and helps researchers make informed conclusions based on their data.

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Yes, they do form a triangle. This is because the sum of any two sides in a triangle must be greater than the third side. In this case, 4 + 8 is greater than 10, so it meets the criteria for a triangle.

Yes, the side lengths 4 8 and 10 can form a triangle. This is because the sum of any two sides in a triangle must be greater than the third side. In this case, 4 + 8 is greater than 10, so it meets the criteria for a triangle. A triangle is defined as a polygon with three sides and three angles, and is one of the basic shapes in geometry. It is also one of the most studied shapes in mathematics due to its wide range of applications. The three angles of a triangle must add up to 180 degrees, and the three sides must satisfy the triangle inequality, meaning that the sum of any two sides must be greater than the third side. Additionally, the interior angles of a triangle are always equal to the sum of two exterior angles. Knowing this, it can be seen that the side lengths 4 8 and 10 can form a triangle, as the sum of any two sides is greater than the third side.

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Answer:

the final cost is $31.74