Triangle ABC has angle measures as shown.
(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answer:
PLEASE ANSWER AS SOON AS POSSIBLE! 25 POINTS!
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Related Questions
At 9:00 am two cars started from the same town and traveled north on the same road. one ca traveled at a rate of 35 mph and the other at a rate of 40 mph. after how many hours will the cars be 30 miles apart
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40 x 6 = 240
240 - 210 = 30
so after 6 hours the cars will be 30 miles apart
In your math class there are 15 boys and 21 girls. 12 of the boys and 15 of the girls are freshmen. if you randomly choose a student in your class, what is the probability that you'll choose a girl or a freshman?
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Final answer:
The probability of randomly choosing a girl or a freshman from the class is 0.916 or 91.6%. This is calculated by considering the total number of girls and freshmen in the class, while avoiding double-counting freshman girls in the calculation.
Explanation:
To calculate the probability that a randomly chosen student from the class is either a girl or a freshman, we need to consider the total number of students in the class, as well as the number of girls and the number of freshmen. The class consists of 15 boys and 21 girls, totaling 36 students. Out of these, 12 boys are freshmen and 15 girls are freshmen, but we must avoid double-counting the girls who are also freshmen.
First, we calculate the total number of freshmen: 12 boys + 15 girls = 27 freshmen. Next, we calculate the probability of picking a girl: 21 girls / 36 total students = 0.583 (to three decimal places). We then calculate the probability of picking a freshman: 27 freshmen / 36 total students = 0.750. However, since the freshmen include both boys and girls, we must subtract the probability of picking a freshman girl to avoid double-counting: 15 girls who are freshmen / 36 total students = 0.417.
Finally, we add the probability of picking a girl and the probability of picking a freshman, and subtract the probability of picking a freshman girl to obtain the inclusive probability: 0.583 (girl) + 0.750 (freshman) - 0.417 (freshman girl) = 0.916.
Therefore, the probability that a randomly chosen student is either a girl or a freshman is 0.916, or 91.6%.
PLEASE HELP ME ASAP
PLEASE
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Choice D
Company 2 is greater in avg rate of change by $750
=======================================
Explanation:
Average rate of change is the same as slope through two points. The two points are the endpoints of the interval.
The x values we'll use is x = 0 and x = 12 since it constitutes the first 12 years (12-0 = 12)
For company 1, if x = 0 and x = 12, then y = 12000 and y = 30000 respectively. The two points (0,12000) and (12,30000) are on the graph for company 1
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (30000-12000)/(12-0)
m = 18000/12
m = 1500
Over the first twelve years, the average rate of change for company 1 is 1500
For company 2, the points (0,15000) and (12,42000) are on the graph
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (42000-15000)/(12-0)
m = (27000)/(12)
m = 2250
Over the first twelve years, the average rate of change for company 2 is 2250
Now find the difference in the slopes
2250-1500 = 750
Company 2's rate of change is larger by $750
So that's why the answer is choice D. Over this timespan, company 2 is growing faster on average compared to company 1
On a rombus AB=27, m
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PLEASE SOMEONE HELP ME WITH THIS
Hurryyy!!!!
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1st Blank options : +6, +1, +7, +13
2nd blank options: 7,13, 6, 1
3rd blank options: +6 , -1 , +7 , +1
4th blank options: 71 ,59, 69, 61
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[tex]\sf f(1)=7,f(n)=f(n-1)[/tex]
It gives us the first value, which is 7. The second part means that for whatever term we want to find, we plug that in for 'n'. Say we want to find the second term, let's plug in 2 for 'n':
[tex]\sf f(2)=f(2-1)=f(1)[/tex]
We are left with f(1), which is given as 7. So the second term is 7 and then we have the leftover blank. We already know that the second term is 13. 13 - 7 = 6. Therefore, what must be missing from this recursive formula is + 6.
[tex]\sf f(n)=f(n-1)+6[/tex]
For the explicit function, we want to know what will give us these same values if we plugged in which term we want for 'n'. So if we plugged in 1 for 'n', we want to get 7, and if we plugged in 2 for 'n' we want to get 13, and so on. I can spot the similarity that all of these are additions of 1 to the multiples of 6. 6 * 1 = 6 + 1 = 7, 6 * 2 = 12 + 1 = 13, and so on. We could just write this as:
[tex]\sf 6n+1[/tex]
If you tried plugging in 1, you'd get 7, if you plugged 2 in, you'd get 13, and so on. So this is our explicit formula, the 2nd blank should be 6, and the 3rd blank should be + 1.
For the fourth blank, f(10) would just be plugging in 10 for 'n' into our formula, let's do this:
[tex]\sf 6n+1[/tex]
[tex]\sf 6(10)+1[/tex]
Multiply:
[tex]\sf 60+1[/tex]
Add:
[tex]\sf 61[/tex]
So the 4th blank should be 61.
2nd blank: The way we write the generic term of an arithmetic sequence is
a[n] = a[1] +d*(n -1)
You have a[1] = 7 and d = 6, so this is
a[n] = 7 +6*(n -1) = 6 +6n -6 = 6n +1
The appropriate choice for the 2nd blank is "6"
3rd blank: see the discussion for the 2nd blank. The appropriate choice is "+1"
4th blank: a[10] = 6*10 +1 = 61. The appropriate choice is "61"
A baker has three banana muffin recipes. Recipe A uses 3 bananas to make 12 muffins. Recipe Buses 5 bananas to make 24 muffins. Recipe C uses 11 bananas to make 48 muffins.
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Answer:
From least to Greatest: B, C, A
Step-by-step explanation:
For each recipe, dividing the number of bananas needed by the number of muffins will give us the number of bananas per muffin.
A: 3/12 = 0.25B: 5/24 = 0.21C: 11/24 = 0.23As you can see here, Recipe A gives you 0.25 Bananas per muffin, Recipe B gives you 0.21 Bananas per muffin and recipe C will give you 0.23 Bananas per muffin.
Hope this helps!
Answer:
B,C,A
Step-by-step explanation:
Medal will be given to the best answer.
Which of the following is a solution to the equation y = 3x - 1 ?
A. (4,1)
B. (2,5)
C. (4,3)
D. (0, -3)
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For this problem, simply plug in the X values and calculate the Y value and verify that the Y value matches the value given.
A. (4,1); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11. 11 does not match 1.
B. (2,5); X = 2: 3x - 1 = 3*2 - 1 = 6 - 1 = 5. 5 matches 5.
C. (4,3); X = 4: 3x - 1 = 3*4 - 1 = 12 - 1 = 11 does not match 3
D. (0,-3); X = 0: 3x - 1 = 3*0 - 1 = 0 - 1 = -1 does not match -3
And of the above, only option "B. (2,5)" matches.
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.
V(t)=24,500(0.95^t)
Find the initial value of the car and the value after 13 years.
Round answers to the nearest dollar as necessary.
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The value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The dollar value v(t) of a certain car model that is t years old is given by the exponential function.
[tex]\rm V(t)=24,500(0.95^t)[/tex]
The initial value plug t = 0 in the above function:
V(0) = $24500
Plug t = 13 years in the above exponential function
[tex]\rm V(13)=24,500(0.95^1^3)[/tex]
After calculating, we get:
V(13) = 12576.88
V(13) = 12576.9 dollars
Thus, the value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.
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Convert 4 miles to feet.
20,210 feet
21,000 feet
21,120 feet
22,000 feet
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Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each month, how many lunches can she buy at most?
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Final answer:
Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.
Explanation:
The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.
So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.
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Let the function f be defined by f(x) = (x - 1)(x + 7). Which of the following is an equivalent form of f in which the minimum value of f appears as either a coefficient or a constant?
A. f(x) = x^2 - 7
B. f(x) = x^2 + 6x - 7
C. f(x) = (x + 3)^2 - 16
D. f(x) = (x - 3)^2 - 20
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All you have to do is foil
Suppose that x=6 and y=8. If y is inversely related to x, what it y when x=3?
4
5
16
18
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Credit to: Jdoe0001.
C. 16
Look at the figures. How can you prove these triangles are congruent?
∆ABC ≅ ∆DEF by the SAS Postulate.
∆ABC ≅ ∆DEF by the SSS Postulate.
It is not possible to determine if the triangles are congruent.
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by SSS, you need to know AC=DF, but there is no way to know it.
by SAS, you need to know ∠ABC=∠DEF, no way to know as well.
I would like help with the question. It's part of my assigment, but I have trouble with this type of math. If someone understands, can you explain it to me as well? For future reference?
In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in January for Panama City as a function of time (t).,
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Problems where sine or cosine functions are used to model periodic behavior are problems in scaling. You need to match the period and amplitude of your scaled cosine function to the period and amplitude of the phenomenon you are modeling.
Here, high tides are 12 hours apart, so we need to scale x by a factor that turns 12 hours into 2π. That might be x ⇒ 2πx/12 or (π/6)x.
The high tide is 9 ft, and the low tide is 1 ft, so we need to do vertical offset and scaling to make the peak of our transformed cosine function be 9 and its minimum be 1. That difference is 8, so has an amplitude of ±4 around a midline of (9+1)/2 = 5.
Then our tide model is
.. water level = 5 +4*cos((π/6)t)
The sum of two numbers is 240. the larger number is 6 less than twice the smaller. find the numbers. the smaller number is , and the larger number is
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----------
Let the smaller be "x" ; Larger is "2x-6"
EQUATION:
x + 2x-6 = 240
3x= 246
x = 82 (smaller)
2x-6 = 158 (larger)
The smaller number is 82 and the larger number is 158.
Given that, the sum of two numbers is 240.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the smaller number be x.
The larger number is 6 less than twice the smaller.
Larger number = 2x - 6
Now, the sum of two numbers is 240.
So, x+2x-6 = 240
⇒ 3x - 6 =240
⇒ 3x = 246
⇒ x = 82
Larger number = 240 - 82
= 158
Therefore, the smaller number is 82 and the larger number is 158.
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which trig functions have a period of 2pi?
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Hi need this done fast, please
Andrea is planting a rectangular garden with a length of 6 feet and a width of 5 feet. Her mother is planting another garden that is 60% of the length of Andrea's garden and 150% of the width of Andrea's garden.
The length of her mother's garden is--- feet, and the width is---- feet.
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60% of 6 is 3.6
3.6 x 6 = 21.6
Width:
150% of 5 is 7.5
7.5 x 5 = 37.5
So her mothers garden should be 21.6 feet in length, and 37.5 feet in width.
Matt is saving to buy a new motorcycle. If he deposits $60 at the end of each month in an account that pays an annual interest rate of 3.5%, how much will he have in 15 months? Assume that the compounding is being done monthly.,
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You need to apply the following formula:
C = P[ [tex] (1+r)^{t} [/tex] - 1]
where:
C = compound interest you need
P = original amount of money deposited
r = is the rate, written as a rational number
t = number of months
Pluggin in numbers:
C = 60[ [tex] (1+0.035)^{15} [/tex] - 1] = 40.52$
Now, you need to add this amunt to the original amunt:
(60+40.52) = 100.52$
Therefore, Matt will have 100.52$ after 15 months.
How do I solve this? Please explain.
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The first candle will have a volume of
.. V = Bh = (21 cm^2)*(8 cm) = 168 cm^3
The second candle will have a volume of
.. V = Bh = (7 cm^2)*(14 cm) = 98 cm^3
The total volume of the two candles is
.. 168 cm^3 +98 cm^3 = 266 cm^3
Josie is 6 cm^3 short of the amount required for the two candles she has in mind.
No, the base area of the second candle cannot be 7 cm^2. There is not enough wax to make a candle with that area 14 cm tall.
The following is an idealized equation representing the world population of Leatherback turtles, where t represents time in years since 1970.
f(t) = 50,000(.92)^t
How would you determine the population in the year 2000?
Is this a growth or a decay function?
How can you tell a growth or decay function just by looking at it?
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so population in 2000 = 50,000 * (0.92)^30 = 4098 Asawer
This is a function of decay.
The function is decay because the number in the parentheses is < 1.
Please help me asap!!!
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-x - 2y = - 9
multiply the (1st) equation by 3
-3x - 6y = -27
now you have
-3x - 6y = -27
3x - 6y = -15
-----------------------add
-12y = -42
y = 3.5
2(3.5) = -x + 9
7 = - x + 9
x = 2
answer
(2 , 3.5)
am i correct?
Which of the following describes how to translate the graph of y = |x| to obtain the graph of y = |x + 1| - 2?
shift right 1 and down 2
shift left 1 and down 2 <<<
shift right 1 and up 2,
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Answer: both of u are wrong its one unit shift up one unit shift down
Taylor is competing in a 30 km race. She has already run 12.35 km through a park and swam 3.75 km. She will bike the rest of the way. Round each distance to the nearest km. About how far does Taylor need to bike to finish the race? A. about 12 km B. about 13 km C. about 14 km D. about 23 km
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12km + 4km = 16km
30km - 16km = 14km
What equation results from completing the square and then factoring x^2-12x=58
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The correct answer is (x - 6)2 = 94
Answer:
A for me
Step-by-step explanation:
If it takes bottling machine to fill 150 bottles per minute, how many minutes will it take the machine to bottle 4500 bottles
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Can someone explain the Pythagorean theorem to me, please?
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Pythagorean theorem is a²+b²=c².
a is the length is the leg, b is also a leg and c is the hypotenuse
A jar made of 3/16-inch-thick glass has an inside radius of 3.00 inches and a total height of 6.00 inches (including the bottom thickness of glass). The glass has a density of 165 lb/ft3. The jar is placed in water with a density of 62.5 lb/ft3.
Assume the jar sits upright in the water without tipping over. How far will the empty jar sink into the water?
What is the volume of the glass shell of the jar? Precision 0.00
What is the weight of the jar? Precision 0.00
What is the weight of water the empty jar will displace? Precision 0.00
What is the volume of water the empty jar will displace? Precision 0.00
How far will the empty jar sink?
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The total volume of the jar is:
[tex]V_t=Bh=\pi h(r+a)^2[/tex]
Where h is the height of the jar, a is the thickness and r is the inner radius.
The volume of empty space, bounded by the jar, is:
[tex]V_e=B(h-a)=\pi r^2(h-a)[/tex]
The volume of a jar shell is the difference between these two:
[tex]V_s=V_t-V_e=\pi h(r+a)^2-\pi r^2(h-a)[/tex]
When we plug in all the number we get:
[tex]V_s=27.17 {$in}^3[/tex]
The weight of the jar is simply its volume times its density. We have to convert density of the glass:
[tex]165 \frac{lb}{ft^3}=\frac{165}{1728}\frac{lb}{in^3}=0.0949\frac{lb}{in^3}[/tex]
Now we can find the mass:
[tex]m_j=V_s\rho_j=27.17\cdot 0.0949=2.58 $lb[/tex]
The volume of water jar would displace depends how far the jar would sink.
There two forces acting on the jar when you put in the water. The first one is gravity and it's pulling the jar down. The second force is the buoyancy the and this force pushes the jar upward. In order for that jar to be stable, these two forces must be the same.
The buoyancy is given with this formula:
[tex]B=\rho gV_{disp}[/tex]
The volume of water that would be displaced by the jar can be expressed by this formula:
[tex]V_{disp}=\pi h'(r+a)^2[/tex]
Where h' is the height of the jar that is submerged in the water.
So the buoyancy force is:
[tex]B=\rho_w g\pi h'(r+a)^2[/tex]
This force must be equal to the force of gravity acting on the jar:
[tex]F_g=B\\ m_jg=\rho_w g\pi h'(r+a)^2\\ m_j=\rho_w \pi h'(r+a)^2\\[/tex]
We solve for h':
[tex] h'=\frac{m_j}{\rho_w \pi(r+a)^2}[/tex]
If we plug in the number we get:
[tex]h'=2.24 $in[/tex]
Now we can calcuate the amount of water discplaced and its mas(keep in mind that we also converted density of water into lb/in^3):
[tex]V_{disp}=\pi h'(r+a)^2=71.50${in}^3\\ m_v=\rho_w\cdot V_{disp}=2.58$lb[/tex]
We get the same mass as the mass of the jar, which makes perfect sense:
[tex]m_jg=\rho_w V_{disp}g\\ m_j=m_{wdisp}[/tex]
The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.
Explanation:To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³
Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.
To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.
Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.
Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)² = 0.18 ft -> convert to inches = 2.2 inches.
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what is the answer too......5(x+9)
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To solve for x in this problem, we need to distribute the 5 using the distributive property and then simplify.
5 * x + 5 * 9
= 5x + 45
So, the most simplified form of this expression would be 5x + 45.
Hope this helps!
5*x + 5*9 =
5x + 45
You have to get the x alone so divide both of them by 5
5x/5 + 45/5 =
x + 9
To get the x alone subtract it.
x - x + 9 =
9 = -x can't leave x a negative so dived both sides by -1
9/-1 = -x/-1 =
-9 = x or x = -9
Hope this Helps!
How do I solve this?
Answers
I find it convenient to draw a graph of a line that represents the ladder. I choose to have the y-intercept be where the ladder touches Catie's head (5.5 feet above the ground), and the x-intercept to be where the ladder touches the ground, 16 inches away from Catie.
Then the wall is 4.5 feet (54 inches) from the ladder's base, or 38 inches in the other direction from Catie. The graph shows the ladder hits the wall at a height of about 18.6 feet.
The graph shows the calculations for the position of the wall and for the equation of the line. (The line is written in "intercept form.") The graphing calculator shows the intercept points, so no "work" is required except to highlight them.
Choose the polynomial that is written in standard form. (1 point)
−3x5y2 + 4x3y + 10x2
−8xy2 + 4x4y2 + 3x3
x4y2 + 4x3y5 + 10x4
x6y2 + 4x3y8 + 10x7
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The only one where this is true is the first one.
The degree goes from 7 to 4 to 2
Answer:
[tex]-3x^5y^2+4x^3y+10x^2[/tex]
Step-by-step explanation:
A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.
For example
[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]
The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]