Use quadrilateral ABCD to find the value of X. The figure is not drawn to scale. Use the following dimensions: mABC=4x, mBCD=3x, mCDA=2x, mDAB=3x

Find the measure of each angle:

mABC=___ mBCD=___ mCDA=___ mDAB=___

To calculate the compound interest, the formula[tex]A=p(1+r)^t[/tex] is used with the principal amount of $2,000, an annual interest rate of 10%, and a time frame of 10 years. The correct calculation results in a future balance of $5,187, when rounded to the nearest dollar. The correct option is d.

The equation [tex]A=p(1+r)^t[/tex] is used to calculate the compound interest on a savings account. To find out how much money will be in the account after a certain number of years, we can follow these steps:

After performing the calculation, we get:

A =[tex]2000(1 + 0.10)^{10[/tex] = [tex]2000(1.10)^{10[/tex] = 2000 ×2.59374 = $5,187.48

Therefore, rounded to the nearest dollar, you will have $5,187 in your account after 10 years. The correct answer is D. $5,187.

In triangle ABC, BD bisects angle ABC into two parts with measures 2y and 5y-12. The measure of angle ABC is the sum of its parts, equating to 7y-12. Without additional information, the exact value of y and thus, the measure of angle ABC, cannot be determined.

The given problem involves a geometrical concept related to triangles, specifically angle bisectors. In triangle ABC, BD is an angle bisector, dividing angle ABC into two angles with measures 2y for angle ABD and 5y-12 for angle DBC. To find the measure of the whole angle ABC, we need to understand that the angle bisector divides the angle into two parts, where their measures are equal to the sum of the parts' measures.

Given:

Since BD is an angle bisector, the sum of the measures of angles ABD and DBC equals the measure of angle ABC. Thus, to find m ABC, we add the measures of angle ABD and angle DBC:

m ABC = m ABD + m DBC = 2y + (5y - 12) = 7y - 12

To solve for y, we note that additional information is required that is not provided in the question. However, the measure of angle ABC in terms of y is 7y - 12, showcasing the relationship between the angle and its bisector.

Answer:

  B.  (f + g)(x) = 6x² – 5x + 12

       (f- g)(x) = 6x² + 5x – 2

Step-by-step explanation:

1) (f +g)(x) = f(x) + g(x) = (6x² + 5) + (7 -5x) = 6x² -5x +12

__

2) (f-g)(x) = f(x) -g(x) = (6x² + 5) - (7 -5x)

  = 6x² +5 -7 +5x . . . the minus sign outside multiplies all the terms inside

  = 6x² +5x -2

In this Mathematics problem, we are asked to add and subtract given functions f(x) and g(x). The sum results in (f+g)(x) = 6x^2 - 5x + 12 and the difference results in (f-g)(x) = 6x^2 + 5x - 2.

The question is asking about finding the sum (f+g) and the difference (f-g) of two functions, f(x) and g(x). To answer this, we add (or subtract) the two given functions together.

For the function (f+g)(x), you simply add f(x) = 6x2 + 5 and g(x) = 7 - 5x together to get (f+g)(x) = 6x2 - 5x + 12. Thus, the sum of the two functions is 6x2 - 5x + 12.

Similarly, for the function (f-g)(x), we subtract g(x) from f(x) to get (f-g)(x) = 6x2 + 5x - 2. Thus, the difference of the two functions is 6x2 + 5x - 2.

So, the correct answer is B, (f+g)(x) = 6x2 - 5x + 12 and (f-g)(x) = 6x2 + 5x - 2.

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Answer:

A) The linear equation is [tex]x=\frac{-1}{15}p+102[/tex]

B) When the rent is raised to $855 the number of units occupied is 45.

C) When the rent is lowered to $795 the number of units occupied is 49.  

Step-by-step explanation:

A) A linear equation for the demand is written as [tex]x=mp+p_{0}[/tex], where [tex]m[/tex] is the slope, [tex]x[/tex] is the number of occupied units, [tex]p[/tex] is the rent.

[tex]m[/tex] is calculated using the problem information. When the rent is [tex]p=$780[/tex] then [tex]x=50[/tex] and when the rent is [tex]p=$825[/tex] then [tex]x=47[/tex].

Using the slope equation we have:

[tex]m=\frac{50-47}{780-825}=\frac{-3}{45}=\frac{-1}{15}[/tex]

Thus the linear equation is:

[tex]x=\frac{-1}{15}p+p_{0}[/tex]

In order to calculate [tex]p_{0}[/tex] we use the problem information, When the rent is [tex]p=$780[/tex] then number of occupied units is [tex]x=50[/tex], thus:

[tex]50=\frac{-1}{15}780+p_{0}  \\\\50=-52+p_{0}  \\\\p_{0}=102  \\[/tex]

Finally, the linear equation is:

[tex]x=\frac{-1}{15}p+102[/tex]

B) The demand equation is plot in the attached file, the number of units occupied when the rent is raised to $855 is 45.

C) In order to predict the number of occupied units lets use the equation:

[tex]x=\frac{-1}{15}p+102[/tex]

where [tex]p=$795[/tex], then:

[tex]x=\frac{-1}{15}795+102\\ \\x=-53+102\\\\x=49[/tex]

Thus, when the rent is lowered to $795 the number of units occupied is 49.  

Answer:

  (x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions

Step-by-step explanation:

Use the first equation to substitute for x in the remaining two equations.

  (-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation

  -7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

__

  2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation

  -7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...

  x = 1 -z

  y = z

  z is a "free variable"

Five friends went to see a movie. Each person paid $5.

This is a total of $40.

$62.50 - $40 = $22.50.

We now have $22.50 to divide by 5 people.

So, $22.50/5 = $4.50.

Each person paid $4.50 for popcorn.

Answer:

B:45 degrees.

Step-by-step explanation:

We are given that a square ABCD .

We have to find the measure of angle BAC.

We know that each angle of square is of 90 degrees.

We know that diagonal AC bisect the angle BAD.

Therefore, measure of angle BAC=Measure of angle CAD.

Measure of angle BAD=[tex]\frac{1}{2}\times 90=45^{\circ}[/tex]

Hence, the measure of angle BAC=45 degrees.

Answer:B:45 degrees.

Answer:

45

Step-by-step explanation:

Answer:

D.The angle between the two vectors must be an acute angle which is less than 90 degrees.

Step-by-step explanation:

We are given that two vectors A and B are added together to form a vector C.

The relationship between the magnitudes of the vectors is given by [tex]a^2+b^2 >c^2[/tex]

We have to find which statement is true about given vectors.

We know that if a triangle is an obtuse triangle then

[tex]c^2 >a^2+b^2[/tex]

If a triangle is an acute triangle then

[tex]a^2+b^2 >c^2[/tex]

If a triangle is right angle triangle then

[tex]c^2=a^2+b^2[/tex]

Therefore,the angle between the two vectors must be an acute angle which is less than 90 degrees.

Option D is true.

Answer:

  373/500 = 0.746

Step-by-step explanation:

373 out of 500 is represented by the fraction 373/500.

This value is easily converted to a decimal number by multiplying numerator and denominator by 2:

  (373×2)/(500×2) = 746/1000 = 0.746

_____

You can also divide 373 by 500 using a calculator to get the decimal result.

The crate contains 24 oranges.

Unitary method is a mathematical technique for first finding the value of a single unit and then deriving the given units from it by multiplying with the single unit.

According to the given question a no. of oranges are in a crate which costs 1.60 dollars also given that per pound of orange costs 0.20 dollars.

∴ The crate contains (1.60/0.20) pounds of oranges which is

= 8 pounds of oranges.

Given 3 oranges are of 1 pound

∴ In 8 pounds of oranges pieces of oranges are (8×3) = 24 oranges.

learn more about unitary method here :

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Answer:

The horizontal speed of the truck is 102.39 km/hr.

Step-by-step explanation:

Given that,

Speed of airplane = 125 km/h

Angle = 35°

We need to calculate the horizontal speed

Using formula of horizontal speed

[tex]u_{x}=u\cos\theta[/tex]

Where, u = speed

Put the value into the formula

[tex]u_{x}=125\times\cos35^{\circ}[/tex]

[tex]u_{x}=102.39\ km/hr[/tex]

Hence, The horizontal speed of the truck is 102.39 km/hr.

Answer:

v = 102.4 km/h

Step-by-step explanation:

Given:-

- The speed of the airplane, u = 125 km/h

- the angle the airplane makes with the ground, θ = 35°

Find:-

How fast must a truck travel to stay beneath an airplane?

Solution:-

- For the truck to be beneath the airplane at all times it must travel with s projection of airplane speed onto the ground.

- We can determine the projected speed of the airplane by making a velocity (right angle triangle).

- The Hypotenuse will denote the speed of the airplane which is at angle of θ from the truck travelling on the ground with speed v.

- Using trigonometric ratios we can determine the speed v of the truck.

                                  v = u*cos ( θ )

                                  v = (125 km/h) * cos ( 35° )

                                  v = 102.4 km/h

- The truck must travel at the speed of 102.4 km/h relative to ground to be directly beneath the airplane.

Answer:

y=-8(x+6)

Step-by-step explanation:

The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,

First we are going to calculate m:

If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],

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

In this case we have A=(-5,-8) and B=(-7,8)

[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]

Replacing in the formula:

[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]

Then [tex]y=-8x+b[/tex].

We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:

Replacing the point (-5,-8):

[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]

Or replacing the point (-7,8):

[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]

The answer is the same with both points.

Then we have:

y=-8x-48

y=-8(x+6)

Answer:

can you elaborate

Step-by-step explanation:

I think you're talking about the slope formula so I'll tell you that y=x+b

y2-y1/x2-x1 (x1,y1) is the first coordinate and (x2,y2) is the second coordinate

Answer:

Step-by-step explanation:

1 ) the slope formula for the line passes by :   A(XA,YA)    B(XB,YB)

the slope is :   (YB - YA)/(XB -XA)

2) y intercept for the line when : x = 0

Answer: true

Step-by-step explanation: x-values are not repeated

Answer:

True

Step-by-step explanation:

For a relation to be a function, each value of x in the domain maps to exactly one unique value of y in the range.

This is the case here, thus this is a function.

Answer: exponential because it's a ratio :)

Step-by-step explanation:

Answer:

Exponential. Because of its cumulative nature (gain of weight) and its growth rate (5%).

Step-by-step explanation:

It's a growth graph given by an exponential function because every gain of weight is cumulative to the earlier week's. This function can be modeled this way since the rate of growth (5%) was given, which is added by 1 then plugged into the formula. [tex]y=90(1.05)^{t}[/tex] Besides, this model is identical to Interest Composite Rate, which follows the same basic structure, namely Cumulative Growth at a given rate.

The first one f(x) = -1/3x + 5

Answer:

f(x)=-1/3+5

Step-by-step explanation:

hope this helps

Answer:

C

Step-by-step explanation:1 kilogram = 1000 grams so if you multiply 0.004 times 1000 you get 4 grams

Answer:

The percentage is approximately 99.7%

Step-by-step explanation:

In order to understand this question you must understand the bell curve. (I would suggest googling a picture of the bell curve)

The mean of the bell curve is 67.5, meaning +1 standard deviation would be 70.9 (67.5+3.4). This would mean that 34% of the sample is between 67.5" and 70.9" (The bell curve % goes 34/14/2/.1 in that order)

When looking at the bell curve of this data, you would find that ±3 standard deviations gives you the range of 57.3" to 77.7". This would represent roughly (2+14+34+34+14+2)% of the sample. This excludes the .2% that are above or below 57.3" to 77.7". Therefore, the only answer that is close would be 99.7%

Using the empirical rule for a normal distribution, the calculation shows that approximately 99.7% of adults in town have heights between 57.3 and 77.7 inches.

The heights of the adults in this town follow a bell-shaped distribution known as the normal distribution. This means that the values are symmetrically distributed around the mean, with most values close to the mean and fewer values farther away. The empirical rule states that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations.

In this case, the mean is 67.5 inches and the standard deviation is 3.4 inches. Thus, one standard deviation away from the mean is a range from 67.5 - 3.4 = 64.1 inches to 67.5 + 3.4 = 70.9 inches. Two standard deviations away from the mean is a range from 64.1 - 3.4 = 60.7 inches to 70.9 + 3.4 = 74.3 inches. Three standard deviations away from the mean is a range from 60.7 - 3.4 = 57.3 inches to 74.3 + 3.4 = 77.7 inches.

Therefore, according to the empirical rule, we would predict that about 99.7 percent of adults in the town have heights between 57.3 and 77.7 inches.

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Answer:

  (a)  domain

  (b)  "argument," or "independent variable"

Step-by-step explanation:

You may want to refer to your notes for terminology related to functions. Different terms are used, depending on the context.

__

The set of valid inputs for a function is called the domain.

__

The input variable x is called the argument, or independent variable.

The set of valid inputs for a function is referred to as the domain, and the variable x is known as the independent variable in a function or an equation.

The set of valid inputs for a function is called the domain (a), and the input variable x is called the independent variable (b).

In the context of the equation of a line, such as y = mx + b, the independent variable x is usually plotted on the horizontal axis. When you select a value for x, it is considered independent because it can be chosen freely, and then you solve the equation for y, which is the dependent variable because its value depends on the chosen x. An example would be setting x to a specific number to see what y would be, demonstrating how the equation represents a straight line on a graph with m representing the slope and b representing the y-intercept.

Answer:

y = - 3x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m = [tex]\frac{-2-4}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

Note the line crosses the y- axis at (0, 4) ⇒ c = 4

y = - 3x + 4 ← equation of line

Time for light A's Flash = 4 seconds

Time for light B's Flash = 6 seconds

Duration between the lights = 6-4=2

Duration to flash again = LCM of 6, 4

2/6,4

2/3,2

3/3,1

/1,1

2x2 x 3

4 x 3

= 12 seconds

Final answer:

The two street lights will flash together again after 12 seconds. This is determined by finding the least common multiple of the intervals at which each street light flashes (4 seconds and 6 seconds), which is 12 seconds.

Explanation:

The question you've posed is about finding the least common multiple (LCM) of two numbers, which in this case are the intervals at which two street lights flash: 4 seconds and 6 seconds. To determine when the street lights will flash together again, we must find the smallest time interval that is a multiple of both 4 and 6. The multiples of 4 are 4, 8, 12, 16, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. The smallest multiple they have in common is 12 seconds.

To arrive at this answer, you can either list out the multiples as above or use a shortcut by calculating the LCM. Here's a step-by-step breakdown:

Write down the prime factors of each number: 4 = 2 x 2 and 6 = 2 x 3.

For each distinct prime factor, take the highest power present in the factorization of either number. Here, this gives us 22 (from 4) and 3 (from 6).

Multiply these together to get the LCM: 22 x 3 = 4 x 3 = 12.

Therefore, the two street lights will flash together again after 12 seconds.

Answer:

l = 10.5 cm and A = 21 cm2

Step-by-step explanation:

Area is w*l

Perimeter is 2(w+l)

Replacing the information known in the problem you can get the length with the perimeter

P = 2(w+l)

25 = 2(2+l)

12.5 = 2 + l

10.5 cm = l

with the length now you can find the area

A = w*l

A = 2*10.5

A = 21 cm2

Answer:

  15 cups

Step-by-step explanation:

To make 15 lattes, Charles will triple his recipe, so use 3×5 = 15 cups of milk.

Answer:

Mutually exclusive, dependent events

Step-by-step explanation:

Two events A and B are mutually exclusive if [tex]P(A\cap B)=0[/tex]

Two events A and B are independent if [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

Remark: All mutually exclusive events are dependent.

Now,

A = the first symptom occurs

B = the second symptom occurs

[tex]P(A)=0.5\ (\text{or } 50\%)[/tex]

[tex]P(B)=0.45\ (\text{or } 45\%)[/tex]

[tex]P(A\cup B)=0.95 \ (\text{or }95\%)[/tex]

Use the rule

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ \\0.95=0.5+0.45-P(A\cap B)\\ \\P(A\cap B)=0.5+0.45-0.95=0.95-0.95=0[/tex]

Thus, the events A and B are mutually exclusive (disjoint) and dependent (accordint to the remark)

Answer:

40 and 70

Step-by-step explanation:

The mode is the most occurring value in a data set. In this data set, the mode is 40 and 70 because

Answer:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD         Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                         Given

BD+CD=AB+BD                            Substitution Property

CD=AB                                         Subtraction Property

AB=CD                                         Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD        Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                          Given

BD+CD=AB+BD                             Substitution Property

CD=AB                                          Subtraction Property

AB=CD                                          Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

The probability of a spyware program breaking into a system depends on the complexity of the password rules. By calculating the total number of possible passwords based on given rules and comparing it to the number of guessing attempts (1,000,000), one can determine the probability for each scenario.

The probability of a spyware program guessing a password correctly can be calculated by determining the total number of possible unique passwords and then seeing how many attempts the spyware has in comparison.

In all cases, the probability of the spyware breaking in is the quotient of the number of attempts made (1,000,000) and the total number of possible passwords for each scenario.

Answer: 2 with the remainder of 200

Step-by-step explanation:

first you are going to times 19 cans by 500 mg of sodium and get 9,500

then you are going to subtract 11,000 by 9,500 and get 1,500

lastly you are going to take 1,500 and divide it by 650.

in the end you will get 2 with the remainder of 200.  

Answer:

Owen bought [tex]9[/tex] cans of soup and [tex]10[/tex] cans of frozen dinners.

Step-by-step explanation:

We can solve this problem by writing the linear equation system that represents the situation.

Let be ''x'' the number of cans of soup purchased and ''y'' the number of frozen dinners purchased.

By reading the question we can write the following linear equation system :

[tex]x+y=19[/tex] (I)

[tex]x.(500)+y.(650)=11000[/tex] (II)

Working with the equation (I) we find that [tex]x=19-y[/tex] (III)

If we replace (III) in (II) :

[tex](19-y).(500)+y.(650)=11000[/tex]

[tex]9500-500y+650y=11000[/tex]

[tex]150y=1500[/tex]

[tex]y=10[/tex]

We find that Owen bought [tex]10[/tex] cans of frozen dinners.

If we replace the value of ''y'' in (I) :

[tex]x+10=19[/tex]

[tex]x=9[/tex]

We find that Owen bought [tex]9[/tex] cans of soup.

Answer:

Part a) 30+m

Part b) $36

Step-by-step explanation:

Part a) Identify an expression that represents the amount Susan spent on the fruits

The complete question in the attached figure

Let

m ------> the number of apples

n -----> the number of oranges

q ----> the amount Susan spent on the fruits

we know that

m+n=15 ----> (in total she needs 15 fruits)

n=15-m -----> equation A

q=3m+2n ----> equation B

Substitute equation A in equation B

q=3m+2(15-m)

q=3m+30-2m

q=30+m -----> expression that represents the amount Susan spent on the fruits

Part b) Identify the amount she spent if she bought 6 apples

we know that

If m=6 apples

substitute the value of m in the expression of Part a)

q=30+m -----> q=30+6=$36

Answer:

y = 2x - 1

Step-by-step explanation:

Note the difference between consecutive terms of y are constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2

Thus the equation is of the form y = 2x ± c ← c is a constant

Substitute values of x to determine the required value of c

x = 0 : 2 × 0 = 0 ← require to subtract 1 for y = - 1

x = 1 : 2 × 1 = 2 ← require to subtract 1 for y = 1

x = 2 : 2 × 2 = 4 ← require to subtract 1 for y = 3, and so on

Thus the required equation is

y = 2x - 1