Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.

J = 90° J' = 90°

K = 65° K' = 65°

L = 25° L' = 25°

Which statement is true about this transformation?

The next step for the evaluation of the given expression is:

         [tex](3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

We are given an arithmetic expression as follows:

      [tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})[/tex]

Now, in order to solve the given arithmetic expression we need to use the distributive property.

i.e.

[tex](a+b)c=a\cdot c+b\cdot c[/tex]

Now, the expression in the next step is written as follows:

[tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})=(3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

Answer:

Graph 1 has two solutions

Graph 2 has one solution

Graph 3 has no solution

Graph 4 has two solutions

Step-by-step explanation:

* Lets explain the solution of the quadratic equation

- The quadratic equation represented graphically by a parabola

- The solution of the quadratic equation is the intersection point

  between the parabola and the x-axis

- At the x-axis y coordinate of any point is zero, then the solution is

 the value of x-coordinate of this point

- If the parabola cuts the x-axis at 2 points then there are 2 solutions

- If the parabola cuts the x-axis at 1 point then there is 1 solutions

- If the parabola doesn't cut the x-axis then there is no solution

* Lets solve the problem

# Graph 1:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

# Graph 2:

∵ The parabola cuts the x-axis at one point

∴ There is one solution

# Graph 3:

∵ The parabola doesn't cut the x-axis

∴ There is no solution

# Graph 4:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

A quadratic function is given in the general form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
The solutions of a quadratic function are found using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
The number of solutions is determined by the discriminant, which is the expression inside the square root: b² - 4ac.
Here's how the discriminant determines the number of solutions:
1. If the discriminant is positive (b² - 4ac > 0), there are two distinct real solutions.
2. If the discriminant is zero (b² - 4ac = 0), there is exactly one real solution.
3. If the discriminant is negative (b² - 4ac < 0), there are no real solutions (but there are two complex solutions).
Now, let's apply this to the quadratic functions that you've been given. Unfortunately, you haven't provided the specific functions, so I'll give you a generic example for each case. You will be able to use this method to determine the number of solutions for any given quadratic function.
Example 1: One Solution
Consider the equation x^2 - 4x + 4 = 0.
Here, a = 1, b = -4, c = 4.
Discriminant = (-4)² - 4(1)(4) = 16 - 16 = 0.
Since the discriminant is zero, there is exactly one solution.
Example 2: Two Solutions
Consider the equation x^2 - 4x + 3 = 0.
Here, a = 1, b = -4, c = 3.
Discriminant = (-4)² - 4(1)(3) = 16 - 12 = 4.
Since the discriminant is positive, there are two distinct real solutions.
Example 3: No Real Solutions
Consider the equation x^2 + 2x + 5 = 0.
Here, a = 1, b = 2, c = 5.
Discriminant = (2)² - 4(1)(5) = 4 - 20 = -16.
Since the discriminant is negative, there are no real solutions.
Drag and label each quadratic function with the number of solutions based on your calculation of the discriminant:
- If the discriminant is zero, label it "one solution."
- If the discriminant is positive, label it "two solutions."
- If the discriminant is negative, label it "no real solutions."
Remember to apply this method to each of the quadratic functions that you have by calculating their discriminants.

Answer:

Step-by-step explanation:

[tex]\text{The vertex form of an an equation of a quadratic function:}\\\\y=a(x-h)^2+k\\\\(h,\ k)-vertex\\\\\text{We have}\ g(x)=(x-h)^2+k,\ \text{and the vertex in}\ (9,\ 8).\\\\\text{Therefore}\ h=9\ \text{and}\ k=8.\ \text{substitute:}\\\\g(x)=(x-9)^2+8[/tex]

Answer:

The answer is g(x) = (x - 9)^2 + -8

So 9 and -8 are the correct answers

Step-by-step explanation:

The guy above got the first one right but not the second one, it's supposed to be negative.

Answer:

Step-by-step explanation:

If two lines are parallel, their slopes are equal.

Next time, if you are given possible answer choices, please share them.

Answer:

The slopes of the two lines that are parallel, are equal.

Step-by-step explanation:

In order for two or more lines to be parallel their slopes have to be the same.

Answer:

20%

Step-by-step explanation:

step 1

Find 50% of x

we know that

50%=50/100=0.50

so

Multiply the number x by 0.50 to determine 50% of x

(x)(0.50)=0.50x

step 2

Find 40% of 50% of x

we know that

50% of x is equal to 0.50x (see the step 1)

40%=40/100=0.40

so

Multiply the number 0.50x by 0.40 to determine 40% of 0.50x

(0.50x)(0.40)=0.20x

therefore

The percent of x is equal to 0.20*100=20%

Answer:

20%

Step-by-step explanation:

there's really no point of explaining since the other person just explained and I don't wanna copy pasta their explanation

Answer:

10

Step-by-step explanation:

9 1/6 × 1 1/11

Change each number to an improper fraction

9 1/6 = (6*9 +1)/6 = 55/6

1 1/11 = (11*1 +1) /11 = 12/11

55/6 * 12/11

Rearranging

12/6 *55/11

2/1 *5/1

10

Answer:

10

Step-by-step explanation:

[tex]\tt 9\cfrac{1}{6}\cdot 1\cfrac{1}{11}= \cfrac{55}{6}\cdot\cfrac{12}{11}=\cfrac{5}{1}\cdot\cfrac{2}{1}=10[/tex]

Answer:

x=48

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

If f(-x)=f(x), then f is even.

If f(-x)=-f(x), then f is odd.

To determine if f(x)=3x^4+5x^2+1 is even or odd plug in -x like so:

f(x)=3x^4+5x^2+1

f(-x)=3(-x)^4+5(-x)^2+1

f(-x)=3x^4+5x^2+1

f(-x)=f(x)

So f is even.

You should keep in mind the following:

(-x)^odd=-(x^odd)

(-x)^even=x^even

Examples:

(-x)^81=-(x^81) since 81 is odd

(-x)^10=x^10 since 10 is even

Anyways, the student is right and f(-x)=f(x).

Answer:

The student's claim is true, because for any input of x, f(x)=f(−x).

Step-by-step explanation:

If a student says that the function f(x)=3x^4+5x^2+1 is an even function, the student's statement true  because for any input of x, f(x)=f(−x).

f(-x)=f(x) is even.

f(-x)=-f(x) is odd

Answer:

Step-by-step explanation:

Each one of those options is a coordinate point; the first number represents x and the second represents y.  In order for a coordinate point to be a solution to an equation, one side of the equation has to equal the other side when you plug in the number that represents x where x is, and the number that represents y wher y is and then solve.

The first coordinate point filled in looks like this:

If y = 4x + 5, then where x = 0 and y = 10

10 = 4(0) + 5. Solv that to get

10 = 5

Does 10 equal 5?  No.  10 equals 10, not anything else.  So that point doesn't work.

The next point (0, -2) filled in looks like this:

-2 = 4(0) + 5

Does -2 = 5?  No.  Not a solution.

The next point (-4, 0) filled in looks like this:

0 = 4(-4) + 5 and

0 = -16 + 5 and

0 = -11

True?  No.

The next point (-6, 4)

4 = 4(-6) + 5

4 = -24 + 5 and

4 = -19

None of them work. At least according to what you have as your equation and as your points.

Answer:

The angles do not have the same reference angle.  

Step-by-step explanation:

We can answer this question by referring to the unit circle.

The reference angle of 5π/6 is π/6, and the reference angle of 5π/3 is π/3.

B, C, and D are wrong. Tangent is negative in both quadrants

Tan(5pi/6) and tan(5pi/3) are both equal to -sqrt(3), so they are equal.

Tan is a trigonometric function that represents the ratio of the opposite side to the adjacent side of a right triangle. Tan(x) is equal to sin(x) / cos(x).

When we evaluate tan(5pi/6), we find that it is equal to -sqrt(3).

When we evaluate tan(5pi/3), we find that it is equal to -sqrt(3).

Therefore, both tan(5pi/6) and tan(5pi/3) are equal to -sqrt(3), so they are equal.

Answer:

[tex]\Large \boxed{Y=5}[/tex]

Step-by-step explanation:

[tex]\textnormal{First, divide by 90 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{90y}{90}=\frac{450}{90}[/tex]

[tex]\textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle 450\div90=5[/tex]

[tex]\displaystyle y=5[/tex], which is our answer.

Hope this helps!

The value of Y in the equation '90 x Y = 450' can be found by isolating Y. This is done by dividing both sides of the equation by 90. Hence, Y equals 5.

In the mathematical equation

90 x Y = 450

, we are being asked to solve for Y. To solve for Y, we can use the basic algebraic principle of isolating the variable on one side of the equation. In this case, since we have 90 multiplied by Y equals 450, we want to isolate Y. We can do that by dividing both sides of the equation by 90. The equation now becomes

Y = 450/90

. By performing the division, we find that

Y equals 5

.

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Answer:

6/16 or 0.375 ..

Step-by-step explanation:

Each time the coin has two possible outcomes so tossing the coin four times

The sample space will be: 2^4 = 16

The sample space is: {HHHH, HTHH, THHH, HTHT , HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT ,HTTT, TTTT, TTHT, THTT}

Let A be the event that there are exactly two heads

A = {HTHT, HTTH, TTHH, THTH, HHTT, THHT}

n(A) = 6

So the probability of exactly two heads is:

P(A) = 6/16 or 0.375 ..

Answer:

3/8

Step-by-step explanation:

The person up there answered it right they just went too high with the numbers.

Answer:

C. There are infinitely many solutions.  

Step-by-step explanation:

3x – 6 < 3x + 13

Subtract 3x from each side

-6 < -13

This inequality is always true.

There are infinitely many solutions.

After simplifying the inequality, it becomes apparent that it holds true for all values of x. Therefore, there are infinitely many solutions to this inequality.

To solve the inequality 3x – 6 < 3x + 13, we need to isolate the variable x on one side. However, when we attempt to subtract 3x from both sides to move the terms involving x to one side, we are left with – 6 < 13 which is a true statement, but no longer contains the variable x. This means that the inequality holds true for all values of x. Therefore, the solution to the inequality is that there are infinitely many solutions. No matter what value of x you choose, the inequality will always be true.

Answer:

its B It gives the number of the kinds of berries needed for the cost to be the same at both bakeries.

Step-by-step explanation:

[tex]V=\dfrac{1}{3}\pi r^2h\\\\h=2r\\V=\dfrac{1}{3}\pi r^2\cdot(2r)=\dfrac{2}{3}\pi r^3[/tex]

Answer:

[tex]V=\frac{2}{3}\pi R^{3}[/tex]

Step-by-step explanation:

The Volume of a cone is by definition 1/3 of the volume of a Cylinder. In this question, the height equals to diameter (2R).

So, We have:

[tex]h_{cone}=2R\\V=\frac{1}{3}\pi R^{2}h \Rightarrow V=\frac{1}{3}\pi R^{2}2R \Rightarrow V=\frac{2}{3}\pi R^{3}[/tex]

We conclude that under this circumstance, a cone with a height equal to its diameter will turn its volume to be equal to 2/3 of pi times the radius raised to the third power.

In other words, when the height is equal to the diameter. The relation between radius, height and Volume changes completely.

The image of Q after QRST has been reflected across the y-axis and then rotated 90 degrees about the origin is (-2,9 ), (2,-9) is correct .

The point Q(-9,2) undergoes a reflection across the y-axis, resulting in Q'(9,2).

Subsequently, two possible 90-degree rotations about the origin are considered.

For a counterclockwise rotation, the coordinates become Q'(-2,9), while for a clockwise rotation, the coordinates become Q'(2,-9).

The process of reflection across the y-axis involves negating the x-coordinate, and the rule for this transformation is (x, y) → (-x, y).

Applied to Q(-9,2), it yields Q'(9,2).

For a counterclockwise rotation of 90 degrees, the rule is (x, y) → (-y, x). Applying this to the reflected point Q'(9,2) results in Q'(-2,9).

Alternatively, for a clockwise rotation of 90 degrees, the rule is (x, y) → (y, -x). Applying this rule to the reflected point Q'(9,2) yields Q'(2,-9).

Therefore, after a reflection across the y-axis followed by a 90-degree rotation (either counterclockwise or clockwise) about the origin, the coordinates of the final image point Q' can be either (-2,9) or (2,-9), depending on the direction of rotation.

The graph of the quadratic parent function, y = x^2, is indeed a parabola and lies in quadrants I and II. It is not a straight line and doesn't occupy quadrants I and III.

The graph of the quadratic parent function, which is y = x^2, has specific characteristics, namely:

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Answer:

-2

Step-by-step explanation:

Let's plug your functions f(x)=x^2-2x and g(x)=6x+4 into (f+g)(x)=0 and then solve your equation for x.

So (f+g)(x) means f(x)+g(x).

So (f+g)(x)=x^2+4x+4

Now we are solving (f+g)(x)=0 which means we are solve x^2+4x+4=0.

x^2+4x+4 is actually a perfect square and is equal to (x+2)^2.

So our equation is equivalent to solving (x+2)^2=0.

(x+2)^2=0 when x+2=0.

Subtracting 2 on both sides gives us x=-2.

Answer:

x=-2

Step-by-step explanation:

f(x) = x^2 - 2x

g(x) = 6x + 4

Add them together

f(x) = x^2 - 2x

g(x) =       6x + 4

-----------------------

f(x) + g(x) =x^2 +4x+4

We want to find when this equals 0

0 =x^2 +4x+4

Factor

What two numbers multiply together to give us 4 and add together to give us 4

2*2 =4

2+2=4

0=(x+2) (x+2)

Using the zero product property

x+2 =0    x+2=0

x+2-2=0-2

x=-2

Answer:

Interquartile Range = 90.5

Step-by-step explanation:

We are given the following data set for which we have to find its interquartile range:

[tex]120,140,150,195,203,226,245,280[/tex]

Since we have an even number data set here so dividing the data set into two halves and taking the average of two middle values for each date set to find [tex]Q_1[/tex] and [tex]Q_3[/tex].

[tex]Q_1=\frac{140+150}{2} =145[/tex]

[tex]Q_3= \frac{226+245}{2}=235.5[/tex]

Interquartile Range [tex](Q_3-Q_1) = 235.5-145[/tex] = 90.5

Answer:

Option C (2556.1 meters).

Step-by-step explanation:

This question can be solved using one of the three trigonometric ratios. The height of the airplane from the ground is 1200 meters and the angle of depression is 28°. It can be seen that the required distance is given by x meters. This forms a right angled triangle, as it can be seen in the diagram. The perpendicular is given by 1200 meters, the hypotenuse is unknown, and the angle of 28° is given, as shown in the attached diagram. Therefore, the formula to be used is:

sin θ = Perpendicular/Hypotenuse.

Plugging in the values give:

sin 28 = 1200/x.

x = 1200/sin 28.

x = 2556.06536183 meters.

Therefore, the airplane is 2556.1 meters (to the nearest tenths) far away from the building!!!

The distance from the airplane to the building is approximately 2256.6 meters, rounded to the nearest tenth.

To find the distance d from the airplane to the building on the ground, we can use trigonometry, specifically the tangent function.

Given:

- Altitude of the airplane h = 1200 m

- Angle of depression [tex]\( \theta = 28^\circ \)[/tex]

The tangent of the angle of depression [tex]\( \theta \)[/tex] is defined as the ratio of the opposite side altitude h to the adjacent side (distance d from the airplane to the building):

[tex]\[ \tan(\theta) = \frac{h}{d} \][/tex]

Substitute the given values:

[tex]\[ \tan(28^\circ) = \frac{1200}{d} \][/tex]

Now, solve for d:

[tex]\[ d = \frac{1200}{\tan(28^\circ)} \][/tex]

Calculate [tex]\( \tan(28^\circ) \)[/tex]:

[tex]\[ \tan(28^\circ) \approx 0.5317 \][/tex]

Now, plug in this value:

[tex]\[ d = \frac{1200}{0.5317} \][/tex]

[tex]\[ d \approx 2256.6 \][/tex]

Answer:

x∈ (11, +∞)

x∈ (-∞, 7)

Step-by-step explanation:

6|x-9|>12 :Split into possible cases

6(x-9)>12, x-9≥0 : solve the inequalities

x>11, x≥9

x<7, x<9 : find the intersections

x∈ (11, +∞)

x∈ (-∞, 7)

Answer:

First part:

Set h(t) = 17and solve for t.

-16t²+ 58t + 7= 17

-16t² + 58t - 10 = 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

Answer:

z=312 if you meant x=26

Step-by-step explanation:

Direct proportional means there is a constant k such that z=kr. k is called the constant of proportionality. The constant k will never change no matter your (x,z).

So using our equation z=kr with point (18,216) we will find k.

216=k(18)

Divide both sides by 18

216/18=k

k=216/18

Simplify

k=12

So we now know the equation fully that satisfies the given conditions of directly proportion and goes through (x,z)=(18,216).

It is z=12x.

Now we want to know the value of z if x=26.

Plug it in. z=12(26)=312

z=312

The two chords on top of each other are the same length as the single vertical chord.

The vertical chord is  2 + 4 +2  = 8 units long.

Z = 8-2 = 6

The answer is A.

Length of chord z is 6.

It is defined as the line segment joining any two points on the circumference of the circle, not passing through its center. Therefore, the diameter is the longest chord of a given circle, as it passes through the center of the circle.

From the figure we can write,

[tex]z+2=2+4+2[/tex]

[tex]z+2=8[/tex]

[tex]z=8-2=6[/tex]

Length of chord z is 6.

Find out more information about chord length here

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Answer:

The quotient is 1/4

Step-by-step explanation:

1/3 ÷ 4/3

The first step you have to do is change the division sign into multiplication. So that the denominator of 2nd term will become numerator and the numerator will become denominator.

Like:

1/3 * 3/4

Now you can cancel out 3 by 3

1 * 1/4

1/4

Thus the quotient is 1/4 ....

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {1} {3}} {\frac {4} {3}}[/tex]

If we apply double C we have:

[tex]\frac {3 * 1} {3 * 4} =[/tex]

We cancel similar terms in the numerator and denominator and finally we have the quotient is:

[tex]\frac {1} {4}[/tex]

Answer:

[tex]\frac {1} {4}[/tex]

Multiply the total number of slices by the fraction he ate:

12 slices x 1/6 = 12/6 = 2

He ate 2 slices.

Answer:

2

Step-by-step explanation:

1/6 of 12 =

= 1/6 * 12

= 1/6 * 12/1

= (1 * 12)/(6 * 1)

= 12/6

= 2

Answer:

(5,1)

(5,0)

Step-by-step explanation:

Vertical lines contain the same x-coordinate per any point on it's line.

So the x-coordinate of (5,-2) is 5.

We are looking for points that have the x-coordinate being 5.

(5,1)

(5,0)

Actually the equation for this line is x=5.

[tex]\huge{\boxed{\text{(5, 1)}}}\ \huge{\boxed{\text{(5, 0)}}}[/tex]

[tex]\text{A vertical line is a line where all of the x values (the first values) are the same.}[/tex]

[tex]\text{In this case, all answers with an x value of 5 are correct.}[/tex]

Final answer:

To calculate vector AB from points A=(-2,5) and B=(3,1), subtract the coordinates of A from B to get AB = (5, -4). Then, use the Pythagorean theorem to find the magnitude |AB|, which is the square root of 41 units.

Explanation:

The question asks for the calculation of the magnitude of the vector AB, given two points A and B with coordinates A=(-2,5) and B=(3,1), respectively. To find vector AB, we subtract the coordinates of point A from point B. This results in AB = (Bx - Ax, By - Ay) = (3 - (-2), 1 - 5) which simplifies to AB = (5, -4). The magnitude of vector AB, often denoted as |AB|, can then be found using the Pythagorean theorem: |AB| = √((5)2 + (-4)2) = √(25 + 16) = √41 units.

Answer:

Isaac traveled 12.8 miles by taxi for $27.46.

Step-by-step explanation:

The formula required here is

$2.50 + ($1.95/mile)x = $27.46.

We need to solve this for x, the number of miles traveled:

Subtract $2.50 from both sides, obtaining:

($1.95/mile)x = $24.96

Now divide both sides by ($1.95/mile):

   $24.96

------------------ = 12.8 miles

($1.95/mile)

Isaac traveled 12.8 miles by taxi for $27.46.

Answer: