a. Find the value of a. b. Find the value of the marked angles.


A)14; 94°

B)16; 106°

C)19; 124°

D)15; 100°

Final answer:

To solve the equation 3ax + 2b / c = 4d for x, isolate x on one side of the equation by multiplying both sides by c, subtracting 2b, and dividing by 3a.

Explanation:

To solve the equation 3ax + 2b / c = 4d for x, we need to isolate x on one side of the equation. Here are the steps:

Therefore, the solution for x is x = (4cd - 2b) / (3a).

Answer:

2,225 years apart

Step-by-step explanation:

A function is a rule that maps each preimage to a unique image.

A rule that maps each preimage to a unique image is called a function. In mathematics, a function is a relation between a set of inputs (preimages) and a set of outputs (images) in which each input is associated with exactly one output.

For example, consider the function f(x) = 2x, where the input x is a preimage and the output 2x is the corresponding image. If we plug in x = 3, the preimage, we get f(3) = 2(3) = 6, the image.

Functions are commonly represented using algebraic expressions, tables, graphs, or diagrams. They are fundamental to many branches of mathematics and have applications in various fields. The phrase 'rule that maps each preimage' refers to the function or transformation that defines how to manipulate a preimage to obtain an image, either by applying a mathematical formula or by executing a geometric operation.

Answer:

Step 1:  Use the straightedge to draw a line k that passes through A and intersects line j. Label the point of intersection as point P.  This is because you must have a point of intersection with the line before you can move forward.

Step 2:  Place the point of the compass on point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R.  This will give us a compass width to move forward.

Step 3:  Place the point of the compass on point Q and open it to width ​ QR.  

Step 4:   Without changing the width of the compass opening, place the point of the compass on point A and draw an arc that intersects line k. Label the intersection as point S.   This gives us the point to use to construct the second point of our parallel line.

Step 5:  With the compass opening set to width QR , place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B.   This is the second point of our parallel line.

Step 6:  Use the straightedge to draw AB←→.  

The steps are shown below:

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.

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By using the formula for the area of a rectangle, we will see that there are 117 square units on the office.

We know that for a rectangle of width W and length L, the area is given by:

A = W*L

In this case, we have a rectangle of width of 13 units, and length of 9 units, replacing that in the area equation:

A = (13 units)*(9 units) = 117 square units.

So the correct option is the second one, there are 117 square units in the office.

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Answer:

-7/6  

Step-by-step explanation:

-2-5/3+3= -7/6

Answer:

Question 1 is B and Question 2 is D

Answer:

Slope of the line passing through the points (1, −5) and (4, 1) is 2 .

Step-by-step explanation:

The equation of the slope is given by

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

As given

line passing through the points (1, −5) and (4, 1) .

[tex]m = \frac{1-(-5)}{4-1}[/tex]

[tex]m = \frac{1+5}{4-1}[/tex]

[tex]m = \frac{6}{3}[/tex]

m = 2

Therefore the slope of the line passing through the points (1, −5) and (4, 1) is 2 .

The formula for Poisson distribution is:

P (x) = e^-k * k^x / x!

We know that:

3P(x = 1) = P(x = 2)

Therefore:

3 [e^-k * k^1 / 1!] = e^-k * k^2 / 2!

Simplifying by cancelling similar terms:

3 / 1! = k / 2!

k = 3 * 2! / 1!

k = 6

So at x = 4:

P (x = 4) = e^-6 * 6^4 / 4!

P (x = 4) = 0.1339 or 13.39%

Answer:

X is the answer.

Step-by-step explanation:

The values of x and y are 4.29 and 90.

Given that ∆ABC and ∆FDE are congruent by a certain criterion, let's denote the corresponding sides as follows:

AB = FD (corresponding side)

BC = DE (corresponding side)

AC = FE (corresponding side)

Let's also denote the angles of ∆ABC and ∆FDE as follows:

∠A = ∠F (corresponding angle)

∠B = ∠D (corresponding angle)

∠C = ∠E (corresponding angle)

Now, if we're given specific values for some sides or angles, we can use that information to find the missing values.

Let's assume we're given that AB = 5 cm, BC = 7 cm, AC = 6 cm, ∠A = 40°, and ∠B = 50°.

First, let's find the missing side FD using the side-length proportion:

[tex]\[ \frac{AB}{FD} = \frac{BC}{DE} = \frac{AC}{FE} \][/tex]

Substitute the given values:

[tex]\[ \frac{5}{FD} = \frac{7}{DE} = \frac{6}{FE} \][/tex]

We can solve for FD by setting up the proportion:

[tex]\[ \frac{5}{FD} = \frac{7}{6} \][/tex]

Cross-multiply to solve for FD:

[tex]\[ 5 \cdot 6 = FD \cdot 7 \][/tex]

[tex]\[ 30 = 7FD \][/tex]

[tex]\[ FD = \frac{30}{7} \][/tex]

[tex]\[ FD \approx 4.29 \text{ cm} \][/tex]

Next, we can find the missing angle measures. Since ∠A = ∠F = 40° and ∠B = ∠D = 50°, we can find ∠C = ∠E using the fact that the sum of angles in a triangle is 180°:

[tex]\[ ∠C = 180° - ∠A - ∠B \][/tex]

[tex]\[ ∠C = 180° - 40° - 50° \][/tex]

[tex]\[ ∠C = 90° \][/tex]

So, we have found that FD ≈ 4.29 cm and ∠C = 90°. Thus, the values of x and y are 4.29 and 90, respectively.

Complete question

∆ABC and ∆FDE are congruent by the

criterion. (Use the three-letter abbreviation without spaces.)

The value of x is

, and the value of y is

.