What type of slope is demonstrated by the line below?
(-1,3)
A. Positive slope
B. Negative slope
C. Undefined slope
D. Zero slope
(0,-2)

Answer: C.

Step-by-step explanation: In a linear function, both numbers rise or fall in a steady way. This means the answer would be c, where the x rises in increments of one, and y increases by multiplying by three each time.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) (x - 5) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{ (x- 5) {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: (x- 5) [/tex]

value x lies between :

[tex]\qquad \sf  \dashrightarrow \: - 5 \leqslant x \leqslant 5[/tex]

if the value of x is taken -5

[tex]\qquad \sf  \dashrightarrow \: - 5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 10[/tex]

if value of x is taken as 5

[tex]\qquad \sf  \dashrightarrow \:5 - 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:0[/tex]

So, the possible values of the required expression lies between ~

[tex]\qquad \sf  \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0[/tex]

I hope you understood the whole procedure. let me know if you have any doubts in given steps ~

Answer:

We are 90% confident that the population mean height of college football players is between 65.6 and 67.1 inches.

Step-by-step explanation:

90% Confidence interval means that out of 100 different samples, for example, 90 out of 100 confidence intervals with include the true mean value (average height).

Answer:

An angle inscribed in a circle is half of the central angle 2 that subtends the same arc on the circle, according to the inscribed angle theorem. As a result, the angle does not change as the vertex of the circle is moved around.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) Opposite angles in a parallelogram are congruent, so angle B measures 82 degrees.

2) Opposite sides of a parallelogram are congruent, so 12=6x. Hence, x=2.

3) Opposite sides of a parallelogram are congruent, so by the alternate interior angles theorem, the answer is 62 degrees.

Answer:

see explanation

Step-by-step explanation:

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 82°

the opposite sides of a parallelogram are parallel and congruent , then

AD = BC , that is

6x = 12 ( divide both sides by 6 )

x = 2

∠ BCA and ∠ DAC are alternate angles and are congruent , then

∠ BCA = ∠ DAC = 62°

The option u1 =/ u2 =/ u3 is correct if the researcher randomly assigns 60 people to 1 of the 3 treatment conditions.

The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.

We have:

A group of researchers wants to determine whether the type of psychotherapy has an effect on the number of PTSD symptoms in refugees.

As we can see in the problem, there are three treatment conditions are given.

Alternative hypothesis H₁: Not all means are equal

[tex]\rm H_0: \mu_1\neq \mu_2\neq \mu_3[/tex]

Thus, the option u1 =/ u2 =/ u3 is correct if the researcher randomly assigns 60 people to 1 of the 3 treatment conditions.

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87.5

25x7=175

175/2=87.5

The critical points for the inequality x²-5x+6 is x= 2 and x = 3.

In calculus, a critical point of a function is a point where the derivative of the function is either zero or undefined.

These points are important in determining the maximum and minimum values of a function, and can also help identify points of inflection and other important features of a curve.

To find the critical points for the inequality x²-5x+6, we need to find the values of x that make the expression equal to zero (i.e., the roots of the quadratic equation).

We can factor the expression as (x-2)(x-3) and set each factor to zero to find the critical points:

x-2 = 0 or x-3 = 0

x = 2 or x = 3

So the critical points are x = 2 and x = 3.

Therefore, the answer is x= 2 and x = 3.

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Answer:

106º

Step-by-step explanation:

Because both the base angles are 74º. The known angles so far are 148º.

The top angles also have to be equal as they are on parallel lines so:

360 - 148 = 212º

212 / 2 = 106º

Answer:

x = 106 degrees

Step-by-step explanation:

74 plus 74 = 148

360 is the interior angle sum of all trapezoids

360-148=212

212 is the sum of both x and y

x and y are the same measure.

212/2 = 106

Answer:

1) (I) 1/4,  2) (B) 11/20,  3) (G) 3/20,  4) (C) 4/5

Step-by-step explanation:

Probability is Desired Outcome/All Possible Outcomes. For the first problem, we want apples, which is 25. Altogether though, there are 100 options. So, we get 25/100 or 1/4. For the second, oranges and grapes together (because either would be a desired outcome) are 55. So, we have 55/100, or 11/20. For the third, apples and oranges, the max can be 15, because that's how many total oranges (the lesser of the two) and you can't have anything other than that. So, we get 15/100 or 3/20. Finally, we're looking for everything but bananas, which is 100-20, or 80. For that, we get 80/100 or 4/5.

Hope this helped!

Answer:
Question 1: The Students favorite fruit is an apple is 1/4
Question 2: 3/20

Question 3: 2/5
Question 4: 4/5

Step-by-step explanation:

* All of the fruits equal up to 100, so 25 percent of 100 is 1/4 or 0.25
* Do 100/55. It should give you 5.8181818181818181818181818181818 which would be at least 3/20 because it is closer to 1.
* 25+15=40. 2/5=0.4 which is 40% of 100.

Answer:

see explanation

Step-by-step explanation:

(a)

∠ XBC = 55° because it corresponds to ∠ AXY

(b)

since XB = XC then Δ XBC is isosceles with base angles congruent, that is

∠ XBC = ∠ XCB = 55°

the sum of the 3 angles in Δ XBC = 180° , then

∠ BXC + 55° + 55° = 180°

∠ XBC + 110° =180° ( subtract 110° from both sides )

∠ XBC = 70°

Answer:

Make use of the fact that as long as [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex].

[tex]\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}[/tex].

[tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex].

Step-by-step explanation:

Assume that [tex]\sin(\theta) \ne 0[/tex] and [tex]\cos(\theta) \ne 0[/tex].

Make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] and [tex]\csc(\theta) = (1) / (\sin(\theta))[/tex] to rewrite the given expression as a combination of [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex].

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}[/tex].

Since [tex]\cos(\theta) \ne 0[/tex]:

[tex]\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

By the Pythagorean identity, [tex]\sin^{2}(\theta) + \cos^{2}(\theta) = 1[/tex]. Rearrange this identity to obtain:

[tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex].

Substitute this equality into the expression:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}[/tex].

Again, make use of the fact that [tex]\tan(\theta) = (\sin(\theta)) / (\cos(\theta))[/tex] to obtain the desired result:

[tex]\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}[/tex].

The equation of a line that is passing through the points (0, 4) and (1, 6) will be y = 2x + 4.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A coordinate plane. The x-axis and y-axis are each scaled by one.

A graph of a line goes through the points (0, 4) and (1, 6) will be

The equation of a line that is passing through the points (0, 4) and (1, 6) will be

y - 4 = [6 - 4 / 1 - 0] (x - 0)

y - 4 = 2x

    y = 2x + 4

The graph is given below.

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Answer:y=x-5

Step-by-step explanation:

khan academy

Probability = option(s) that we want / total number of possibilities

Options that we want = cash or credit card  = 50 + 4 = 54

Total number of possibilities = cash, debit card, credit card = 50 + 2 + 4 = 56

54 / 56 = 0.96

Answer: 0.96

Hope this helps!

Yes

Step-by-step explanation:

Because the sides of this triangle follow the Pythagorean Theorem.

i.e.

[tex]52^{2} = {20}^{2} + {48}^{2} [/tex]

[tex]\boxed{\textbf{Therefore it IS a right triangle}} [/tex]

The option (C)  20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, —, ×, and ÷.

We have:

= (20 x 100)

= 2000

4 times smaller will be:

=2000/4

= 500

A) (20×100) 4 = 4000

B) 204×100 = 20400

C) 20 – 25 = -5

D) 5×25​ = 100

-5 < 500

100 < 500

Thus, the option (C)  20 – 25, and option (D) 5×25 are 4 times smaller than (20 × 100) option (C) and (D) are correct.

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100 teeth / 20 teeth = 5

5 x 10 rpm = 50 rpm

answer: 50 rpm

The students will colour the 1/8th part of the sheet given to them by their teacher.

The fraction is defined as the division of the whole part into an equal number of parts.

Given that:-

Now the sheet student have =  1 / 2

Students will colour 1/4th of the sheet they have = ( 1/2  x  1/4 )

= 1 / 8

Therefore the students will colour the 1/8th part of the sheet given to them by their teacher.

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Answer:

cupboard is 1.2 m wide.

Will a stick 1m 5cm long fit across the cupboard?

Give reasons for your answer

Answer:

a point

a line

a line segment

a ray

and an angle in a triangle

Step-by-step explanation:

Answer:

8 then 2 and reflection on y axes

For the form [tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k). The vertex is found by (x, y).

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form.

It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

First of all, we used this vertex formula thing since it is visible that there are quadratic functions.

Otherwise, you had to use calculus to get critical points, then a second derivative of functions to find the character of critical points as minima or maxima or saddle, etc to get the location of vertex point.

This point (h,k) is called the vertex of the parabola that the quadratic equation represents.

For the form

[tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k)

Thus, for the obtained form, we get the coordinates of the vertex as:

[tex]h = -b/2a,, \\ k = c - a\times(b/2a)^2[/tex]

Thus, the coordinates of vertex of  [tex]y = ax^2 + bx + c[/tex]is:

[tex](h,k) = (-b/2a, c - a \times (b/2a)^2 )[/tex]

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The triangle PAT is an isosceles triangle because the side lengths PA and AT are congruent

The points are given as:

P = (1,6)

A = (4,5)

T = (5,2)

Calculate the distance between both points as follows:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]PA = \sqrt{(1 -4)^2 + (6-5)^2}[/tex]

[tex]PA = \sqrt{10}[/tex]

[tex]PT = \sqrt{(1 -5)^2 + (6-2)^2}[/tex]

[tex]PT = \sqrt{32}[/tex]

[tex]AT = \sqrt{(4 -5)^2 + (5-2)^2}[/tex]

[tex]AT = \sqrt{10}[/tex]

Because the side lengths PA and AT are congruent, i.e. √10, then the triangle is an isosceles triangle

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If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32

This is the likelihood or chance that an event will occur. Mathematically;

Probability = expected/total

If you toss five fair coins, the total outcome will be:

T = 2^5
T = 32

If all five coins land heads, the expected will 1. The probability that all five coins land heads is 1/32

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Answer:

x-intercept: (4, 0), (-5, 0)

y-intercept: (0, -20)

Explanation:

Their x-intercept:    (at x intercept, y will be 0)

Their y intercept:   (at y intercept, x will be 0)

Answer:

Step-by-step explanation:

Finding x-intercept(s)

Finding y-intercept

Answer:

a

Step-by-step explanation:

raise to five

less than

ten times

Answer:

Step-by-step explanation:

Use the nth tern equation of the AP

We have

Find the value of d

Correct choice is a)

Now

Answer:

96 days. Divide 3072 by 32 and you get 96.

Answer:

2

Step-by-step explanation:

there needs to be qtr with 88 by 779900

Answer: [tex]\displaystyle d=\sqrt{53}[/tex]

Step-by-step explanation:

   We will use the distance formula to solve. See attached and view the work below.

[tex]\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}[/tex]

[tex]\displaystyle d=\sqrt{(5-3)^2 +(11-4)^2}[/tex]

[tex]\displaystyle d=\sqrt{(2)^2 +(7)^2}[/tex]

[tex]\displaystyle d=\sqrt{4+49}[/tex]

[tex]\displaystyle d=\sqrt{53}[/tex]

   Since 53 is prime, this is the simplest form. Since it asks for an exact answer, we are done.