Which undefined term is used to define a ray?

Answer:

Step-by-step explanation:

Given that Scholastic Aptitude Test (SAT) scores are normally distributed with a mean of 500 points and a standard deviation of 100 points.

If X is the score in SAT, then X is N(500,100)

From std normal table we find 95th percentile as 1.645

i.e. your Z score = 1.645

Convert this to X score by [tex]X =1.645]\sigma + Mean\\= 1.645(100)+500\\=664.5[/tex]

Since expressed as multiples of 10, this equals 660

So points you got = 660

The given equation, cos 65° + cos 55° = cos θ doesn't follow normal trigonometric relationships. Therefore, a value for θ can't easily be computed without further transformations using a cosine formula. Converting θ from degrees to radians also wouldn't directly work due to the equation's specifics.

This question pertains to the field of trigonometry. We have the equation cos 65° + cos 55° = cos θ and we need to find the value of θ in radians. Unfortunately, we cannot resolve this equation directly as the addition of cosines does not equal another cosine. However, one can use cosine formula to transform this equation and solve analytically with a lot of work.

To convert degrees to radians, you would use the formula: θ(radians) = θ(degrees) * π / 180. However, as noted, this task won't work directly for this problem due to the nature of the equation.

This is a particular challenge problem that might not have an easy solution that would fall into the regular high school curriculum.

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The answer is:

vertex: (4,-5); focus: (4,2); directrix: y=-12

The vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.

To determine the vertex, focus, and directrix of a parabola given by the equation y = {1{28}(x - 4)² - 5, we must first identify the standard form of a parabolic equation, which is y = a(x - h)² + k where (h, k) is the vertex of the parabola. In this case, we can see that the vertex (h, k) is (4, -5).

The focus of a parabola is a fixed point from which the distance to any point on the parabola is equal to the distance from that point to the directrix.

The directrix is a fixed straight line. The distance between the vertex and the focus, denoted as 4p, can be determined from the coefficient a in the standard form, where a = {1}/{4p} or p = {1}/{4a}. Thus, p = {1}/{4({1}/{28})} = 7. The focus is then at (h, k + p) = (4, -5 + 7) = (4, 2).

The directrix has the equation y = k - p, so it will be y = -5 - 7 = -12. The parabola opens upwards because the value of a is positive.

In summary, the vertex of the parabola is (4, -5), the focus is (4, 2), and the directrix is the line y = -12.

Answer:

C)18

Step-by-step explanation:

Let Sara present age = x years.

According to question Ralph present  age =3x

Sara age after 6 years =x+6.

Ralph age after 6 years =3x+6.

After 6 years Ralph will be only twice as old as Sara will be then.

3x+6=2(x+6)

Solving for x:

3x+6=2x+12

3x-2x=12-6

x=6.

Ralph present age = 3x=3(6)= 18 years.

Option C.

To convert 0.427 kg to pounds, multiply 0.427 by 2.2, resulting in approximately 0.939 pounds. Thus, the correct answer is Option B.

To convert 0.427 kg to pounds, we use the given conversion factor: 1 kilogram (kg) = 2.2 pounds (lb). Here is the step-by-step explanation:

Write down the value to be converted: 0.427 kg.

Multiply by the conversion factor: 0.427 kg × 2.2 lb/kg.

Perform the multiplication: 0.427 × 2.2 = 0.9394 lb.

So, 0.427 kg is approximately 0.939 lb. Therefore, the correct answer is Option B.

The student buying water and a sports drink to avoid dehydration during soccer practice based on their coach's advice is an example of deductive reasoning, as it applies a general principle to a specific situation.

The scenario described involves a student purchasing fluids to prevent dehydration during soccer practice based on the advice from a coach. This example of reasoning is deductive reasoning. The coach has provided a general principle that drinking a lot of fluids prevents dehydration. The student applies this general principle to a specific situation (soccer practice) and takes action (buying water and a sports drink) to avoid dehydration. This reasoning starts from a general rule and applies it to a particular case, characteristic of deductive reasoning.

Final answer:

To form a polynomial with real coefficients, given non-real zeros 4i and 5i, include their conjugates -4i and -5i. Multiply the corresponding factors to get f(x) = (x^2 + 16)(x^2 + 25), which simplifies to f(x) = x^4 + 41x^2 + 400.

Explanation:

To form a polynomial, f(x), with real coefficients having a specified degree and given zeros, you must use the fact that non-real roots of polynomials with real coefficients come in conjugate pairs. Since 4i and 5i are given as zeros of the polynomial, their conjugates, -4i and -5i, must also be zeros of the polynomial.

The factors of the polynomial that correspond to these zeros are (x - 4i), (x + 4i), (x - 5i), and (x + 5i). To find the polynomial, these factors are multiplied together.

Multiplying the factors that come in conjugate pairs first:

Next, multiply these two results to obtain the polynomial:

(x^2 + 16)(x^2 + 25) = x^4 + 25x^2 + 16x^2 + 400 = x^4 + 41x^2 + 400

Therefore, the polynomial with degree 4 and zeros 4i and 5i is f(x) = x^4 + 41x^2 + 400.

To form the polynomial f(x) with real coefficients and given the zeros 4i and 5i, we use the conjugate pairs and multiply the resulting factors to get x⁴ + 41x² + 400.

To form a polynomial f(x) with real coefficients given the degree and zeros, we start by noting that complex roots always come in conjugate pairs when dealing with polynomials that have real coefficients. Hence, for the zeros 4i and 5i, the polynomial must also include the conjugate roots -4i and -5i.

Thus, the polynomial f(x) is x⁴ + 41x² + 400.

Answer:

The solution is (–6, 2, 1). (Option A)

Step-by-step explanation:

Given three equations

2x + 4y - 3z = -7  →   (1)

3x + y + 4z = -12  →   (2)

x + 3y + 4z = 4    →   (3)

we have to find the solution of above equations.

By elimination method

Multiply equation (2) by 4 and then subtracting from (1), we get

(2x + 4y - 3z+7)-4(3x + y + 4z + 12)=0

  ⇒  -10x-19z=41 → (4)

Multiply equation (2) by 3 and then subtracting from (3), we get

(x + 3y + 4z - 4)-3(3x + y + 4z + 12)=0

  ⇒ -8x-8z=40 ⇒ x+z=-5 → (5)

Solving (4) and (5), we get

-10x-19z-41+10(x+z+5)=0

 ⇒ -9z=-9 ⇒ z=1

⇒ x+1=-5 ⇒ x=-6

and (3) implies -6 + 3y + 4 = 4 ⇒ y=2

Hence, the solution of above 3 equations will be (x,y,z)=(-6,2,1)

Hence, option (1) is correct.

Answer:

D. Conditional

Step-by-step explanation:

The statement is a conditional statement.

Answer:

statement is true

Step-by-step explanation:

Given  : If triangle RST is congruent to triangle WXY and  area of triangle WXY is 20 square inches, then the area of triangle RST is 20 in.

To find : Statement is true or false .

Explanation :

Yes,if two triangles are congruent then you can place one above the other perfectly and  both cover the same region.

So,we can say that both have the same area.

But the conversion is not true .

Therefore, statement is true .

To find the sum of the first n prime numbers, use a while loop to add each prime number to a total. Use a function is prime to check if each integer is prime. Continue the loop until you've added n primes.

To compute the sum of the first n prime numbers, you would first initialize the total and the count of primes to 0. Then, for each integer starting from 2, you would check if it is prime using the is prime function. If it is prime, you would add it to the total and increment the count of primes. This loop would continue until the count of primes reaches n.

Here is how the code might look in Python:

This code uses a while loop to continue adding prime numbers to the total until it has added the first n primes. The total of the prime numbers is updated inside an if statement that checks whether the current integer i is prime.

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Answer:

0.36

Step-by-step explanation:

One - hundredth =[tex]\frac{1}{100}[/tex]

one hundredth means we have to divide 1 by hundred.

When we  divide one by hundred we get 0.01

To find one-hundredth of 36, than we have to multiply 36 by 0.01

 After multiplying we get

36×0.01=0.36

OR

36×[tex]\frac{1}{100}[/tex]=0.36

Hence, the correct answer is 0.36

One-hundredth of 36 is 0.36.

To find one-hundredth of 36, we simply need to divide 36 by 100. Dividing by 100 means shifting the decimal point two places to the left. Therefore, one-hundredth of 36 is 0.36.

For example, if we have the number 36, we can represent this as 36/1 to show that we have 36 whole parts. When we want one-hundredth of these 36 parts, we are seeking 1 part out of every 100 parts. So, we would write this as (36/1)/ (100/1) which simplifies to 36/100. After simplification, we get 0.36 as the final answer.

This concept is similar to understanding that 1 cm is 1/100th of a meter. By using division or understanding fractions and decimal places, we can easily find one-hundredth of any given number.

Answer:

the answer is 8

Step-by-step explanation:

Answer:

Option (c) is correct.

The interest gained by Gini in 6 years is $ 866.34

Step-by-step explanation:

Given: Gina invests $1,677 in an account paying 8.61% simple interest annually for 6 years.

We have to calculate the interest gained by Gina in 6 years.

Using formula for simple interest

[tex]S.I.=\frac{P\times I\times T}{100}[/tex]

Where,

S.I = simple interest

P is principal

R is interest rate

T is time  

Given : P = $ 1677

R = 8.61%

T = 6 years

Substitute, we get,

[tex]S.I.=\frac{1677\times 8.61\times 6}{100}[/tex]

Simplify, we get,

S.I. = $ 866.3382

Rounding off to nearest hundred  we get, Interest is $866.34

Thus, the interest gained by Gini in 6 years is $ 866.34

Gina has gained $866.34 in interest after six years.

To find the interest gained, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $1,677, the rate is 8.61%, and the time is 6 years. Plugging these values into the formula, we get: Interest = $1,677 * 0.0861 * 6 = $866.34. Therefore, Gina has gained $866.34 in interest after six years.

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the answer is :

1332113

Answer:

Part A) The vertex is the point [tex](0.5,-0.5)[/tex]

Part B) The axis of symmetry is [tex]x=0.5[/tex]

Part C) The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

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

where

(h,k) is the vertex of the parabola

and the axis of symmetry is equal to the x-coordinate of the vertex

so

[tex]x=h[/tex] -----> equation of the axis of symmetry

In this problem we have  

[tex]f(x)=-2x^{2}+2x-1[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+1=-2x^{2}+2x[/tex]

Factor the leading coefficient

[tex]f(x)+1=-2(x^{2}-x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]f(x)+1-(1/2)=-2(x^{2}-x+(1/4))[/tex]

[tex]f(x)+(1/2)=-2(x^{2}-x+(1/4))[/tex]

Rewrite as perfect squares

[tex]f(x)+(1/2)=-2(x-(1/2))^{2}[/tex]

[tex]f(x)=-2(x-(1/2))^{2}-(1/2)[/tex] -----> equation in vertex form

The vertex of the parabola is the point [tex](0.5,-0.5)[/tex]

Is a vertical parabola open downward

The axis of symmetry is equal to

[tex]x=0.5[/tex]

see the attached figure to better understand the problem