Answer : The number of text messages that will result in the exact same charge from both companies is, 500
Step-by-step explanation :
Let the number of text messages be, 'x'
Cell phone company A charges $20 per month plus $0.05 per text message. Thus, the equation will be:
[tex]20+0.05x=0[/tex] ............(1)
Cell phone company B charges $10 per month plus $0.07 per text message. Thus, the equation will be:
[tex]10+0.07x=0[/tex] ............(2)
Now equating equation 1 and 2, we get:
[tex]20+0.05x=10+0.07x[/tex]
[tex]20-10=0.07x-0.05x[/tex]
[tex]10=0.02x[/tex]
[tex]x=\frac{10}{0.02}[/tex]
[tex]x=500[/tex]
Thus, the number of text messages that will result in the exact same charge from both companies is, 500
Each student wrote a two step equation. peter wrote the equation 4x - 2 =10, and andres wrote the equation 16x - 8 = 40. the teacher looked at their equations and asked them to compare them. describe one way in which the equations are similar
Both equations are two-step equations involving a variable term multiplied by a constant and then subtracting another constant. Peter's is 4x - 2 = 10 and Andres's is 16x - 8 = 40.
One way in which Peter's equation 4x - 2 = 10 and Andres's equation 16x - 8 = 40 are similar is that they both involve a variable term multiplied by a constant and then subtracting another constant.
In Peter's equation, 4x represents four times a variable x, and then subtracting 2 from the result.
Similarly, in Andres's equation, 16x represents sixteen times a variable x, and then subtracting 8 from the result.
This common structure of multiplying a variable term by a constant and then subtracting another constant makes both equations two-step equations, even though the specific values and constants differ.
Mike’s weekly wages are $685.20. What is the amount after a 4.2% Social Security tax and a 15% Federal Withholding income tax are deducted? Round to the nearest cent.
Answer:
553.64 rounded to the nearest cent
or
553.65
Step-by-step explanation:
p=3h+3u solve for h
...?
p=3h + 3u subtract 3u from both sides
p-3u=3h now divide both sides by 3
h = p/3 - u
4. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What angle does each side form with the ground? (1 point)
156°
146°
73°
78°
True or False
5. All right triangles are isosceles. (1 point)
true
false
14. What does CPCTC represent and when would you use it? (4 points)
1) 2x + 35 = 180° so x= 180 - 35 / 2 =73°
the answer is 73°
2)
3) In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other. CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.
If triangles ABC and DEF are congruent, denoted as
Final answer:
Each congruent side of the A-frame house forms a 73° angle with the ground, and the statement that all right triangles are isosceles is false. CPCTC is a geometric theorem that states corresponding parts of congruent triangles are congruent.
Explanation:
Angles in an A-frame house
The given A-frame house forms an isosceles triangle with a peak angle of 34°. Using the theorem that the sum of angles in a triangle is 180°, we can calculate the angles each side forms with the ground. Since the two congruent sides are equal, the angles they form with the ground are also equal. There are two steps to solve this:
Subtract the peak angle from 180° to find the sum of the two base angles: 180° - 34° = 146°.
Divide the sum of the base angles by 2 (since they are equal in an isosceles triangle): 146° / 2 = 73°.
Therefore, each side forms a 73° angle with the ground.
All right triangles are isosceles - True or False?
This statement is false. Not all right triangles are isosceles. A right triangle is defined as having one 90° angle, but it doesn't necessarily have two sides of equal length, which would make it isosceles.
What does CPCTC represent?
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem used in geometry to conclude that the corresponding parts (angles or sides) of two triangles are congruent, given that the triangles themselves are proven to be congruent based on certain criteria like side-angle-side (SAS) or angle-side-angle (ASA).
Intr un oras sunt 235 de blocuri cu 8 etaje si cu 177 mai multe blocuri cu 4 etaje.Formuleaza intrebarea pentru a rezolva problema astfel
Katie cut out a rectangular piece of wrapping paper that was 2 times as long and 3 times as wide as the box that she was wrapping. the box was 5 inches long and 4 inch's wide. what is the perimeter of the wrapping paper that katie cut?
Rewrite the expression below.
-2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8)
Final answer:
The simplified expression is [tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
Explanation:
The expression -2a (a + b - 5) + 3 (-5a + 2b) + b (6a + b - 8) needs to be rewritten by expanding and combining like terms using the distributive property. To expand the expression, multiply each term inside the parentheses by the term outside the parentheses. Then, combine the like terms to simplify the expression.
Let's expand each term as follows:
-2a * a = -2a²
-2a * b = -2ab
-2a * (-5) = +10a
3 * (-5a) = -15a
3 * 2b = +6b
b * 6a = +6ab
b * b = b²
b * (-8) = -8b
Now, combine the like terms:
[tex]-2a^2 - 2ab + 10a - 15a + 6b + 6ab + b^2 - 8b[/tex]
The simplified expression is -
[tex]-2a^2 + 4ab - 5a - 2b + b^2[/tex]
The probability that it will rain today is 0.4, and the
probability that it will rain tomorrow is 0.3. The
probability that it will rain both days is 0.2.
Determine the probability that it will rain today or
tomorrow
Final answer:
The probability that it will rain today or tomorrow, given the individual probabilities and the joint probability for both days, is calculated using the addition rule of probability, resulting in a probability of 0.5 or 50%.
Explanation:
The student is asking how to calculate the probability that it will rain today or tomorrow given the individual probabilities for rain on each day and the joint probability that it will rain on both days. This is a typical question involving the addition rule of probability.
To find the probability of either event A (rain today) or event B (rain tomorrow) occurring, we use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
P(A) is the probability that it will rain today, which is 0.4,
P(B) is the probability that it will rain tomorrow, which is 0.3, and
P(A and B) is the probability that it will rain on both days, which is 0.2.
Substituting the given values, we get:
P(A or B) = 0.4 + 0.3 - 0.2
P(A or B) = 0.5
Therefore, the probability that it will rain today or tomorrow is 0.5, or 50%.
*Need Help??!!
Which table is a probability distribution table?
Photo is attached.
Answer: Hi!
in a probability table, the x represents a given event, and p is the probability of such event.
There are two rules if you have n events; then p₁ + p₂ + ... + pₙ = 1, this is because the probability is normalized.
whit this info you can discard the third option, because there is a probability bigger than 1, and then the addition of al the probabilities is bigger than 1.
The second rule is that there do not exist negative probabilities (because they don't have sense) then you can also discard the second option.
Now we need to check the first and the fourth options, we need to add the 4 probabilites in each and see if the result is 1.
for the first options we have :
0.2 + 0.35 + 0.15 + 0.25 = 0.95
this is not normalized, this is not a probability distribution table.
for the fourth option we have:
0.4 + 0.15 + 0.25 + 0.2 = 1
this is normalized, then this is a probability distribution table.
Then the only right answer is option 4.
1. What is the apparent solution to the system of equations graphed above?
(0,-1)
(0,3)
(1,2)
(2,1)
Answer:
the answer is (,2)
Step-by-step explanation:
the system of solutions is the point that two equations/line cross
the two lines cross at (1,2)
If f(x) = √x + 12 and g(x) = 2√x, what is the value of (f-g)(144)?
-84
–60
0
48
we have
[tex]f(x)=\sqrt{x}+12[/tex]
[tex]g(x)=2\sqrt{x}[/tex]
we know that
[tex](f-g)(144)=f(144)-g(144)[/tex] -------> equation A
Step 1
Find the value of [tex]f(144)[/tex]
For [tex]x=144[/tex]
substitute in f(x)
[tex]f(144)=\sqrt{144}+12[/tex]
[tex]f(144)=12+12[/tex]
[tex]f(144)=24[/tex]
Step 2
Find the value of [tex]g(144)[/tex]
For [tex]x=144[/tex]
substitute in g(x)
[tex]g(144)=2\sqrt{144}[/tex]
[tex]g(144)=2(12)[/tex]
[tex]g(144)=24[/tex]
Step 3
Find [tex](f-g)(144)[/tex]
Substitute the values in the equation A
[tex]24-24=0[/tex]
therefore
the answer is the option
[tex]0[/tex]
How many faces, edges, and vertices does a triangular pyramid have?
A. 3 faces, 4 edges, 4 vertices
B. 3 faces, 3 edges, 3 vertices
C. 4 faces, 6 edges, 3 vertices
D. 4 faces, 6 edges, 4 vertices
The gift shop at manatee mall was having a clearance sale. everything was marked down 30%. the original price of a manatee hat was $18. what is the clearance price?
Answer
Find out the what is the clearance price .
To prove
As given
The gift shop at manatee mall was having a clearance sale.
everything was marked down 30%.
The original price of a manatee hat was $18.
30% is written in the decimal form
[tex]= \frac{30}{100}[/tex]
= 0.30
Than
The clearance price = 18 - 0.30 × 18
= 18 - 5.4
= $12.6
Therefore the clearance price be $12.6 .
What assumption must be made about the sun rays if you use this method of determining the circumference of a large sphere?
How old will Bill be in 10 years if he is x + 2 years old now?
Which expression represents this?
(x + 2) - 10
(x + 2) + 10
10(x + 2)
Solve –2x2 – 16x – 44 = 0
answer please using quadtratic equation ...?
Answer: x=-4 + or - i square root of 6
Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
What is the greatest number of bracelets she could buy?
Answer:
The answer is 63.
Step-by-step explanation:
50-12=38 38/.6 is equal to 63.333 you can't buy .333 of a bracelet so she will be able to buy 63 and have little money left.
The greatest number of bracelets she could buy will be 63.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given data;
The total amount of money in my wallet = $50.00
Cost of shirt = $12.00
Price of bracelet per piece = $0.60
Let x is the no of the bracelet;
The equation obtained as;
⇒The total amount of money in my wallet = Cost of the shirt + Price of the bracelet per piece × No of the bracelet
⇒50 = 12 + 0.60 x
⇒0.60 x = 50-12
⇒x = 38/0.60
⇒x= 63.333 ≈ 63 bracelet
Hence the greatest number of bracelets she could buy will be 63.
To learn more about inequility, refer to https://brainly.com/question/20383699.
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how many 16s go into 57
What is the value of p in the equation x2 = 12y?
Which ordered pairs are solutions to the inequality 2x + y > −4?
Select each correct answer.
A. (−3, 0)
B. (0, 1)
C. (−1, −1)
D. (5, −12)
E. (4, −12)
What is the solution to the equation? 3q 5 = -2q 20
a. q = 3
b. q = 5
c. q = 15
d. q = 25
Which of the following is the expansion of (3c + d2)6?
A) 729c6 + 1,458c5d2 + 1,215c4d4 + 540c3d6 + 135c2d8 + 18cd10 + d12
B) 729c6 + 1,458c5d + 1,215c4d2 + 540c3d3 + 135c2d4 + 18cd5 + d6
C) 729c6 + 1,215c5d2 + 810c4d4 + 270c3d6 + 90c2d8 + 15cd10 + d12
D) 729c6 + 243c5d2 + 81c4d4 + 27c3d6 + 9c2d8 + 3cd10 + d12
E) c6 + 6c5d2 + 15c4d4 + 20c3d6 + 15c2d8 + 6cd10 + d12
Answer: Option A) [tex]729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex] is the correct expansion.
Explanation:
on applying binomial theorem, [tex](a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r[/tex]
Here a=3c, [tex]b=d^2[/tex] and n=6,
Thus, [tex](3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r[/tex]
⇒ [tex](3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6[/tex]
⇒[tex](3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}[/tex]
⇒[tex](3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}[/tex]
⇒[tex](3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}[/tex]
Answer:
Option (a) is correct.
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Step-by-step explanation:
Given : [tex]\left(3c+d^2\right)^6[/tex]
We have to expand the given expression and choose the correct from the given options.
Consider the given expression [tex]\left(3c+d^2\right)^6[/tex]
Using binomial theorem ,
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
We have [tex]a=3c,\:\:b=d^2[/tex]
[tex]=\sum _{i=0}^6\binom{6}{i}\left(3c\right)^{\left(6-i\right)}\left(d^2\right)^i[/tex]
also, [tex]\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}[/tex]
for i = 0 , we have,
[tex]\frac{6!}{0!\left(6-0\right)!}\left(3c\right)^6d^2^0=729c^6[/tex]
for i = 1 , we have,
[tex]\frac{6!}{1!\left(6-1\right)!}\left(3c\right)^5d^2^1=1458c^5d^2[/tex]
for i = 2 , we have,
[tex]\frac{6!}{2!\left(6-2\right)!}\left(3c\right)^4d^2^2=1215c^4d^4[/tex]
for i = 3 , we have,
[tex]\frac{6!}{3!\left(6-3\right)!}\left(3c\right)^3d^2^3=540c^3d^6[/tex]
for i = 4 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=135c^2d^8[/tex]
for i = 5 , we have,
[tex]\frac{6!}{4!\left(6-4\right)!}\left(3c\right)^2d^2^4=18cd^{10}[/tex]
for i = 6 , we have,
[tex]\frac{6!}{6!\left(6-6\right)!}\left(3c\right)^0d^2^6=d^{12}[/tex]
Thus, adding all term together, we have,
[tex](3c+d^2)^6=729c^6+1458c^5d^2+1215c^4d^4+540c^3d^6+135c^2d^8+18cd^{10}+d^{12}[/tex]
Thus, Option (a) is correct.
Complete these ordered pairs for this equation.
Two triangles with the same corresponding side lengths will be congruent.
True
False
Two triangles with the same corresponding side lengths will be congruent - False
False. Two triangles with the same corresponding side lengths are not guaranteed to be congruent. They may still be similar triangles with equal corresponding angles but different sizes.
Which algebraic expression represents “the product of a number and five”?
Answer:
5n
Step-by-step explanation:
group of answer chances below
A. n - 5
B. 5n
C. 5 + n
D. 5/n
At what value(s) of x does f(x)=x^4-18x^2 have a critical point where the graph changes from decreasing to increasing?
The values of x at which f(x) = x^4 - 18x^2 has a critical point and changes from decreasing to increasing are x = 3 and x = -3.
Explanation:To determine at what values of x the function f(x) = x^4 - 18x^2 has critical points where the graph changes from decreasing to increasing, we must find the first derivative of f(x), set it to zero, and solve for x. The first derivative of f(x) is f'(x) = 4x^3 - 36x. Setting the derivative to zero gives us 4x^3 - 36x = 0, which can be factored as 4x(x^2 - 9) = 0. The solutions to this are x = 0, x = 3, and x = -3.
Next, to determine if these points are minima (where the graph changes from decreasing to increasing), we must examine the second derivative, or use the first derivative test. The second derivative f''(x) is 12x^2 - 36. Entering our critical points into this equation, we find that for x = ±3, the second derivative is positive, indicating a minima, whereas for x = 0, the second derivative is negative, which indicates a maxima.
Thus, the values of x at which f(x) has a critical point and the graph changes from decreasing to increasing are at x = 3 and x = -3.
The critical points of the function [tex]f(x) = x^4 - 18x^2[/tex], we need to find the derivative f'(x) and set it equal to zero. The critical points are x = 0, -3, and 3. At x = -3, the graph changes from decreasing to increasing.
The critical points of the function[tex]f(x) = x^4 - 18x^2,[/tex] we need to find the derivative f'(x) and set it equal to zero. Let's find the derivative:
[tex]f(x) = x^4 - 18x^2[/tex]
[tex]f'(x) = 4x^3 - 36x[/tex]
Now, set f'(x) equal to zero and solve for x:
[tex]4x^3 - 36x = 0[/tex]
Factor out 4x:
[tex]4x(x^2 - 9) = 0[/tex]
Now, set each factor equal to zero:
4x = 0 → x = 0[tex]x^2 - 9 = 0[/tex] x = ±3So, the critical points are x = 0, -3, and 3.
To determine whether each critical point corresponds to a minimum, maximum, or an inflection point, we can use the second derivative test. The second derivative is:
[tex]f''(x) = 12x^2 - 36[/tex]
Evaluate f''(x) at each critical point:
At x = 0, f''(0) = -36 (negative), so x = 0 corresponds to a local maximum.At x = -3, f''(-3) = 72 - 36 = 36 (positive), so x = -3 corresponds to a local minimum.At x = 3, f''(3) = 108 - 36 = 72 (positive), so x = 3 corresponds to a local minimum.Therefore, at x = -3, the graph changes from decreasing to increasing.
Identify the explanatory and response variables in the following situation:
There is a strong positive correlation between latitude above the equator and number of hours of daylight on June 21.
A. Explanatory: Latitude
Response: Average temperature
B. Explanatory: Daylight hours
Response: Latitude
C. Explanatory: Time of year
Response: Daylight hours
D. Explanatory: Latitude
Response: Daylight hours
if cos2X=1/3 and 0<=2X<=pi, find cosX ...?
When cos2X=1/3 and 0<=2X<=pi, you can use the double angle formula for cosine to solve for cosX. The result is sqrt(6)/3.
Explanation:To solve for cosX given that cos2X=1/3 and 0<=2X<=pi, you need to use the double angle formula for cosine, which is:
cos2X = 2cos²X - 1
Plugging in 1/3 for cos2X, we get:
1/3 = 2cos²X - 1
Solving this equation for cos²X gives us :
cos²X = 2/3
The square root of this is ±sqrt(2/3), or ±sqrt(2)/sqrt(3). However, since X falls in the range 0<=X<=pi/2 (because 0<=2X<=pi), cosX is positive. Therefore:
cosX = sqrt(2)/sqrt(3) = sqrt(6)/3
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The sum of two numbers is 26. When the second number is subtracted from the first number, the difference is 10. Find the two numbers.
turn 4√5 into an entire radical (unsimplify), the process
To turn 4√5 into an entire radical, the expression is rewritten as a single radical expression, √80, by identifying that 4 is a perfect square (4²), and multiplying it by the number inside the original radical (5) to get the product under one radical sign.
To turn 4√5 into an entire radical, we need to rewrite it as a single radical expression, effectively reversing the process of simplifying radicals. Let's start by recognizing that 4 is a perfect square and can be written as 4². So, we have 4 (the square root of 5), which can be expressed as √(4² × 5).
Here are the steps to convert 4√5 into an entire radical:
Identify the square of the number outside the radical: 4² = 16.
Multiply the square by the number inside the radical: 16 × 5 = 80.
Write the product under a single radical sign: √80.
Now, the expression 4√5 has been turned into an entire radical, √80.