1. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.




2. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.

it was 1091227 on APEX

Answer:

A. x = two over three and x = -5

The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:

[tex]$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]

Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:

[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]

This simplifies to:

[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]

So, the solutions are:

[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]

and

[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]

So, the correct answer is A. x = two over three and x = −5.

Final answer:

The probability of selecting a girl, then a boy, and then another girl from a class with 5 girls and 5 boys is 10.42%.

Explanation:

The probability of a specific sequence of students being selected in a random draw can be calculated by multiplying the probabilities of each event occurring in succession. Since there are five boys and five girls in the class, the probability of drawing a girl first is 5/10, or 1/2. After drawing one girl, there are now four girls and five boys left, so the probability of drawing a boy second is 5/9. Finally, with one girl and one boy already picked, there are three girls and four boys left, making the probability of drawing a girl third 3/8.

To find the overall probability, we multiply these individual probabilities:

Probability = (First girl drawn) × (Second boy drawn) × (Third girl drawn)
Probability = (1/2) × (5/9) × (3/8)
Probability = (1 × 5 × 3) / (2 × 9 × 8)
Probability = 15 / 144
Probability = 0.1042 or about 10.42%

Final answer:

The probability of the teacher randomly selecting a girl, a boy, and another girl from a class of 5 boys and 5 girls is 5/6.

Explanation:

To find the probability of the teacher randomly selecting three different students, we need to consider the number of possible outcomes and the number of favorable outcomes. In this case, there are 10 students to choose from and the teacher needs to select one girl, one boy, and another girl. To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes.

The number of favorable outcomes is 5 for the first girl, 5 for the boy, and 4 for the second girl (since the first girl has already been selected). So the total number of favorable outcomes is 5 x 5 x 4 = 100.

The number of possible outcomes is the total number of ways to choose 3 students from the 10 available. This can be calculated using the combination formula: C(10, 3) = 10! / (3!(10-3)!) = 120.

Therefore, the probability of selecting a girl, a boy, and another girl is 100/120 = 5/6.

answer is 2x+3, x not equal to 6

 see attached pic for steps

Answer:

2x + 3, x ≠ 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

It’s A

The probability of choosing both yellow hats can be obtained as 1/5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The number of yellow, green and blue hats are given as 7, 5 and 3.

Then, the total number of hats is 7 + 5 + 3 = 15.

Now, the probability for both hats to be yellow without replacement can be given as,

P(Both hats are yellow) = 7/15 × 6/14

⇒ P(Both hats are yellow) = 1/5.

Hence, the required value of probability is given as 1/5.

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Final answer:

To find when g(x) = 0 for the function g(x) = 6x² + 23x – 4, the quadratic formula is used, yielding the solutions x = 0.25 or x = −4.

Explanation:

The question asks for the values of x for which the quadratic function g(x) = 6x² + 23x – 4 equals zero. To find the values of x when g(x) = 0, one can use the quadratic formula, which is x = −(b ± √(b² ∔ 4ac)) / (2a) for a quadratic equation ax2 + bx + c = 0.

Here, a = 6, b = 23, and c = −4. Substituting these values into the quadratic formula gives:

x = −(23 ± √(23² ∔ 4 × 6 × (−4))) / (2 × 6)

After calculating the discriminant (√(b² ∔ 4ac)) and simplifying, we obtain the two solutions for x. Therefore, the correct answer is:

So, the correct answer, marked as (d) on Education 2020, corresponds to x = 0.25 or x = −4.

Answer:

(0, 6)

Step-by-step explanation:

Since, when a points is reflected through the line y = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x, -(y-4))[/tex]

While, the points is reflected through the line x = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x-4, y)[/tex]

So, when (4,-2) is reflected over the line y = 2 is,

[tex](4,-2)\rightarrow (4, -(-2-4))[/tex]

Hence, the position of (4,-2) after reflection through line y = 2 is (4,6),

Now,  when (4,6) is reflected over the line x=2 is,

[tex](4,6)\rightarrow (4-4, 6)[/tex]

Hence, the position of (4,6) after reflection through line x = 2 is (0,6),

Third option is correct.

There were 945 girls and 1575 boys respectively.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or a/b

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. The numerator is the upper quantity in the fraction and the denominator is the lower quantity in the fraction). Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.

We have been given that the ratio of the number of girls to the number of boys was 3 to 5.

The ratio girls to boys;

3 to 5

The Total = 8

The number of boys was 3 to 5 . of 2,520, Then;

3/8(2520) = 7560/8

girls = 945  

5/8(2520) = 12600/8

boys = 1575

Therefore, there were 945 girls and 1575 boys respectively.

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There are two correct answers which are not techniques used in geometric constructions with paper folding and these are:

A. Creating arcs and circles work the compass

C. Measuring lengths of line segments by folding the paper and matching the endpoints

In geometric folding, a straight line becomes a crease or a fold. This is achieved by a person by folding a piece of paper and flattening the crease rather than drawing lines to make a guide. Therefore this means that shapes like arcs, curves, circles by using the compass, and measurement of line segments are not used. However, constructions using compass have a long history in Euclidean geometry.

The following are not techniques used in geometric constructions with paper folding:

A. Creating arcs and circles with the compass.

C. Measuring lengths.

A geometric construction can be defined as a process that is used to draw angles, lines, and other geometric figures (shapes), especially through the use of only a compass and straightedge such as a ruler without measurements.

In Geometry, the techniques that should be used in geometric constructions with paper folding include the following:

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the answer is 8.8

that is the answer

The cost of the cell phone is a function of the number of features.

The answer that best represents the situation described is option A. The cost of the cell phone is a function of the number of features.

In this case, as Kurt is buying a new cell phone, he knows that the more features the cell phone has, the more expensive it will be. This implies that the cost of the cell phone is dependent on the number of features it has.

For example, if a cell phone with basic features costs $200, a cell phone with additional features like a better camera, more storage, and waterproof capabilities may cost $400 or more.

Answer:

True

Step-by-step explanation:

All work is shown and pictured

Answer:

C  (1, 1) is the solution to line K but not to line J..

there is 1 gram per 1 milliliter so just divide them

5200/583.1 = 8.91785

you don't say if it needs to be rounded to a certain amount

 so since the mL has one decimal place

 round to 8.9mL

The graph of the inequality 12 - 2x < 16 is represented by an open circle at -2 on a number line, with shading to the right, indicating all values greater than -2.

To describe the graph representing the inequality 12 - 2x < 16, we first need to solve for x. Subtracting 12 from both sides of the inequality, we get -2x < 4. Dividing both sides by -2 (and remembering to flip the inequality symbol when dividing by a negative), we have x > -2.

Graphically, this is represented on a number line with an open circle at -2 and a shaded area to the right of -2, indicating that x can be any number greater than -2.

Answer:

Option 5th is correct

[tex]35x+120y = 500[/tex]

Step-by-step explanation:

Here, x represents only the clients that got a cut and y represent the clients that got a cut and color combo.

As per the statement:

Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo.

" Charges $35 for a cut" translated to 35x

"$120 for a cut and color combo" translated to 120y

It is also given that yesterday she had seven clients and earned $500.

⇒[tex]35x+120y = 500[/tex]

therefore, an  equations could be used to represent this situation is, [tex]35x+120y = 500[/tex]