Answer:
2
Step-by-step explanation:
3(2x + 4)=?
6x + 12
6x/6=x
12/6=2
x=2
A car factory takes 6 hours to produce 60 cars. How many hours does the factory take to produce 180 cars?
Final answer:
The factory takes 18 hours to produce 180 cars.
Explanation:
To find out how many hours the factory takes to produce 180 cars, we need to set up a proportion. Since the factory takes 6 hours to produce 60 cars, we can set up the proportion:
6 hours / 60 cars = x hours / 180 cars
Cross-multiplying, we get:
6(180) = 60(x)
Simplifying, we have:
1080 = 60x
Dividing both sides by 60, we find:
x = 18
So, the factory takes 18 hours to produce 180 cars.
Write 651.12 as a mixed number
Answer:
651 and 3/25 is 651.12 as a mixed number.
651.12 can be written as the mixed number 651 3/25.
How to write the mixed fractionTo convert hundredths to a fraction, we write the decimal as the numerator and the place value as the denominator. T
Therefore, .12 can be written as 12/100.
651 + 12/100
= 651 12/100
Simplifying the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
651 12/100 = 651 3/25
Therefore, 651.12 can be written as the mixed number 651 3/25.
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What is the value of the remainder if 10x4 – 6x3 + 5x2 – x + 1 is divided by x – 3?
Answer:
Remainder is 691.
Step-by-step explanation:
Given function is [tex]10x^4-6x^3+5x^2-x+1[/tex].
Now we need to find remainder if we divide given function [tex]10x^4-6x^3+5x^2-x+1[/tex] by (x-3)
(x-3) means plug x=3 into [tex]10x^4-6x^3+5x^2-x+1[/tex] to find remainder.
[tex]10x^4-6x^3+5x^2-x+1[/tex]
[tex]=10(3)^4-6(3)^3+5(3)^2-(3)+1[/tex]
[tex]=10(81)-6(27)+5(9)-(3)+1[/tex]
[tex]=810-162+45-3+1[/tex]
[tex]=856-162-3[/tex]
[tex]=856-165[/tex]
[tex]=691[/tex]
Hence remainder is 691.
Answer:
The remainder = 691
Step-by-step explanation:
Let p(x) = 10x⁴ - 6x³ + 5x² - x + 1
We have to divide p(x) by (x - 3)
To find the remainder we have to find p(3)
To find the remainder
p(x) = 10x⁴ - 6x³ + 5x² - x + 1
p(3) = 10 * (3)⁴ - 6*(3)³ + 5* (3)² - 3 + 1
= (10 * 81 ) - ( 6 * 27 ) + (5 * 9) - 3 + 1
= 810 - 162 + 45 - 3 + 1 = 691
Therefore the remainder is 691
What number represents the same amount as 2 hundreds ++plus 14 tens ++plus 3 ones?
343 is the answer because 14 tens is 1 hundred and 4 tens
The number that represents 2 hundreds, 14 tens, and 3 ones is 343, by adding each place value: 200 + 140 + 3.
Explanation:The student asks how to represent the quantity consisting of 2 hundreds, 14 tens, and 3 ones in a single number.
To solve this, we can convert each quantity to its respective place value in the decimal system and sum them.
Two hundreds is equal to 200 (2 x 100), 14 tens equals 140 (14 x 10), and 3 ones equals 3 (3 x 1).
Adding them together gives us 200 + 140 + 3 = 343.
Match the function with its graph.
1) y= tan x
2) y= cot x
3) y= -tan x
4) y= -cot x
Answer:
Option a. 1C, 2A, 3B, 4D.
Step-by-step explanation:
1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.
2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.
3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.
) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.
If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.
The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.
1) y = tan(x) matches with graph C:
- The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.
- The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.
- It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.
2) y = cot(x) matches with graph A:
- The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.
- The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.
- It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.
3) y = -tan(x) matches with graph B:
- The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.
- The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.
- It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.
4) y = -cot(x) matches with graph D:
- The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.
- The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.
- It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.
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The length of an intercepted arc of a central angle of a circle is 4 cm. If the radius of the circle is 5 cm, what is the measurement of the central angle to the nearest whole degree?
A) 35°
B) 41°
C) 46°
D) 50°
Answer:
C
Step-by-step explanation:
The formula we use here is:
Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]
Where
[tex]\theta[/tex] is the central angle
r is the radius
Putting the given information into the formula we can solve for the central angle:
[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]
rounded to nearest degree, we have 46 degree
C is the right answer.
Answer: OPTION C
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- Use the following formula for calculate the measure fo the central angle:
[tex]\theta=\frac{s}{r}[/tex]
Where s is the arc length and r is the radius.
- Know the lenght of the arc and the radius, you can substitute values.
Therefore, you obtain;
[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]
Convert to degrees:
[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°
HELP!!!
An equal inch is equal to about 2.54 centimeters . Write an expression which estimate the numbers of centimeters in x inches. Then estimate the number of centimeters in 12 inches
Answer: The answers are 2.54x and 30.48 cm.
Step-by-step explanation: The formula to determine the number of centimeters in x inches is 2.54x. To solve for the number of centimeters in 12 inches the formula is 2.54 x 12 = 30.48 cm.
What is the length of the missing side of the triangle in simplest radical form? The figure is not drawn to scale.
Answer:
4√34
Step-by-step explanation:
the question asks for the value of the hypotenuse
Applying the Pythagorean equation
a²+b²=c² where a=12cm, b=20cm and c?
substituting values to equation
12²+20²=c²
144+400=c²
544=c²
√544=c
√16 × √34 =c
4×√34
4√34
ANSWER
[tex] 4 \sqrt{34} cm[/tex]
EXPLANATION
The missing side is the hypotenuse of the right triangle.
According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.
Let the hypotenuse be x.
Then,
[tex] {x}^{2} = {20}^{2} + {12}^{2} [/tex]
[tex]{x}^{2} = 400 + 144[/tex]
[tex] {x}^{2} = 544[/tex]
Take positive square root of both sides.
[tex]x = \sqrt{544} [/tex]
[tex]x = 4 \sqrt{34} [/tex]
Please help - will mark brainlest
Answer:
C 294
Step-by-step explanation:
We can use proportions to solve. Put number of miles over gallons
202 miles x miles
--------------- = ----------------
11 gallons 16 gallons
Using cross products
202*16 = 11 x
Divide by 11 on each side
202*16/11 = 11x/11
293.81818181818 =x
To the nearest whole number
294 miles =x
Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy must determine c, the amount of change in dollars he should give the customer. Which equation represents c? 20-0.75c=9 20-0.75=9c 0.75(9)+c=20 0.75c+9=20
Answer:
Step-by-step explanation:
You need to multiply .75 and 9 you'll get 6.75 .. then you need to take 20 and subtract 6.75 and you'll get 13.25
Answer:
C is the correct choice.
A number is divided by 3 and then 5 is subtracted from the quotient the result is 1. Whats the number?
ANSWER
The number is 18.
EXPLANATION
Let the number be x.
When this number is divided by 3, we obtain the quotient,
[tex] \frac{x}{3} [/tex]
When 5 is subtracted from this quotient, we get,
[tex] \frac{x}{3} - 5[/tex]
If the result is 1, then we have;
[tex] \frac{x}{3} - 5 = 1[/tex]
We group similar terms to get,
[tex] \frac{x}{3} = 1 + 5[/tex]
This gives us,
[tex] \frac{x}{3} = 6[/tex]
Multiply both sides by 3.
[tex]x = 6 \times 3[/tex]
[tex]x = 18[/tex]
Therefore the number is 18.
The function f(x)=x^2-4x+4 is shifted 3 units to the right to create g(x). What is g(x)
Answer:
g(x) = x² - 7x + 16Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
===================================
f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):
g(x) = (x - 3)² - (x - 3) + 4 use (a - b)² = a² - 2ab + b²
g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4
g(x) = x² - 6x + 9 - x + 3 + 4 combine like terms
g(x) = x² + (-6x - x) + (9 + 3 + 4)
g(x) = x² - 7x + 16
Sadie made a rectangular cake. If she wants to cut it into 1/8 portions,how many portions can she cut?
Answer:
8
Step-by-step explanation:
If each portion is 1/8 of the cake, there are 8 equal-size portions. That is what the denominator of the fraction means.
Sadie can cut the rectangular cake into 8 portions if each portion is 1/8 of the whole cake.
To determine how many portions Sadie can cut the rectangular cake into if each portion is 1/8, we need to understand that she is essentially dividing the cake into 8 equal parts.
Here's a step-by-step explanation:
Whole Cake: The entire rectangular cake represents one whole (1).
→ Portion Size: Each portion is 1/8 of the whole cake.
→ Calculation: We divide 1 by 1/8. Mathematically, this is the same as multiplying by the reciprocal,
so 1 ÷ (1/8) = 1 × 8
= 8.
Therefore, Sadie can cut the rectangular cake into 8 portions of size 1/8 each.
SureFire Distribution Company sells phone systems to businesses. On September 1, they began with a balance of 193 digital phones. It received shipments of 23 and 45 phones on September 15 and 30 respectively. It sold 45 phones on September 8 and 100 phones on September 19. How many were on hand as of September 30?
146
145
165
116
I think 145 but I’m not quite sure
Answer:
116. add all and subtract respective to the date.
Step-by-step explanation:
Ken ate 2?7 of the chocolate bar one day and 8?14 the next day. How much of the chocolate bar did Ken eat?
Answer:
6/7
Step-by-step explanation:
8/14 simplified is 4/7.
So 2/7+4/7=6/7.
Can someone help on 3 vertex, parabola questions real quick?
1. Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.
y = 1/28x^2
x = 1/28y^2
-28y = x^2
y^2 = 14x
2. Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -4).
y = -1/4x^2
y^2 = -4x
y^2 = -16x
y = -1/16x^2
3. Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.
y = -1/9x^2
y^2 = -36x
y = -1/36x^2
y^2 = -9x
Answer:
lol
Step-by-step explanation:
Nakesha’s Sporting Goods is running a sale on golf shoes this week. The sale price is $95.98. The shoes cost Nakesha’s $63.45. What is the markup rate based on cost?
Answer:
Markup rate = 0.512 or 51.2%
Step-by-step explanation:
Mark up rate is the increase amount added to the original price.
Sales Price = $95.98
Original Price= $63.45
Gross profit margin = Sales Price - Original cost
= $95.98 - $63.45
= $ 32.53
Mark up Rate = Gross profit margin/ original price
= 32.53 / 63. 45
= 0.51
converting into percentage by multiplying with 100
Mark up Percentage = 0.512 * 100
= 51.2 %
Can you help me with this question?
Sure. To make an equilateral triangle we make any segment AB, which is already done, then we draw one circle (or an arc from the circle) with center A and radius AB, and one circle with center B and radius AB. The two circles intersect at two points; we call either one of them C and ABC is equilateral.
Answer: C
2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale. (2 points)
Answer:
The distance from the plane to SCCA is 34,203.0 feet approximately, and the horizontal distance is 32,708.5 feet approximately.
Step-by-step explanation:
You can draw a right triangle like the one shown in the figure attached, where:
x: horizontal distance.
y: distance from the plane to SCCA.
You can calculate x as following:
[tex]tan\alpha=\frac{opposit}{adjacent}[/tex]
Where:
[tex]\alpha=17\°\\opposite=10,000\\adjacent=x[/tex]
Substitute and solve for x:
[tex]tan(17\°)=\frac{10,000}{x}\\\\x=\frac{10,000}{tan(17\°)}\\\\x=32,708.5ft[/tex]
You can calculate y as following:
[tex]sin\alpha=\frac{opposit}{hypotenuse}[/tex]
Where:
[tex]\alpha=17\°\\opposite=10,000\\hypotenuse=y[/tex]
Substitute and solve for y:
[tex]sin(17\°)=\frac{10,000}{y}\\\\y=\frac{10,000}{sin(17\°)}\\\\y=34,203.0ft[/tex]
Find the annual interest rate I equals $562.50 P equals to $1500 T equals five years
Answer: The rate is 7.5%.
Step-by-step explanation: The formula to calculate simple interest is:
Interest = Principal x Rate x Time
So, we need to plug our information into the formula:
$562.50 = $1,500 x R x 5
Now, perform the multiplication that you can:
$562.50 - $7,500R
Next, divide both sides by $7,500:
.075 = R
Therefore, the rate is 7.5%.
Johnny wants to buy a 60" LED Smart TV, so he opened a savings account and added money to it every month. The chart below shows the relationship between the number of months Johnny has been saving and the total amount of money in his account.
Find sec x if tan^2 x= 1/2
(picture provided)
Answer: option d.
Step-by-step explanation:
Based on the information given in the problem, you know that:
[tex]tan^2x=\frac{1}{2}[/tex]
You also know that:
[tex]sec^2(x)=tan^2(x)+1[/tex]
Substitute values. Then, you obtain:
[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]
Apply square root to both sides. Therefore, you obtain:
[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]
Answer:
D
Step-by-step explanation:
Please help!! Double points! write the ratios for sin X and cos X (Image attached)
Will give BRAINLIEST to the person correct answer and please please show your work :))
Answer:
The ratio for sin(X) is [tex]\frac{\sqrt{119} }{12}[/tex]
The ratio for cos(X) is [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
- The ratio of the sine of a right triangle is:
[tex]sin(\alpha)=\frac{opposite-side}{hypotenuse}[/tex]
Since we need the ratio for angle X, [tex]\alpha =X[/tex]. From the picture we can infer that the opposite side of X is [tex]\sqrt{119}[/tex]. The hypotenuse (the side opposite to the right angle) is 12, so replacing the values:
[tex]sin(X)=\frac{\sqrt{119} }{12}[/tex]
- The ratio of the cosine is:
[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]
Similarly, [tex]\alpha =X[/tex], adjacent side = 5, and hypotenuse = 12, so
[tex]cos(X)=\frac{5}{12}[/tex]
Answer:
Sin X =√119/12
Cs X = 5/12
Step-by-step explanation:
It is given a right angled triangle.
Points to remember
Sin θ = Opposite side/Hypotenuse
Cos θ = Adjacent side/Hypotenuse
To find the value of Sin X
Here X is an angle
Opposite side = √119
Hypotenuse = 12
Sin X = Opposite side/Hypotenuse = ZY/XY = √119/12
To find the value of Cos X
Adjacent side of X = 5
Cos X = Adjacent side/Hypotenuse = XZ/XY = 5/12
Can someone help please?!? ):
Answer:
5, 6, 11, 17, 28Step-by-step explanation:
[tex]a_1=5,\ a_2=6,\ a_n=a_{n-1}+a_{n-2}\\\\a_3=a_2+a_1\\a_4=a_3+a_2\\a_5=a_4+a_3\\\\\text{first term:}\ 5\\\text{second term:}\ 6\\\text{third term:}\ 6+5=11\\\text{fourth term:}\ 11+6=17\\\text{fifth term:}\ 17+11=28[/tex]
Identify the area of the rhombus. PLEASE HELP! I'm desperate!!
Area = 1/2(diagonal) * √4*side^2 - diagonal^2
Area = 1/2(16)*√(4*17^2 - 16^2)
Area = 8 * √(4*289-256)
Area = 8 *√900
Area = 8 * 30
Area = 240 m^2
What is the common factor of the numerator and denominator in the expression [tex]\frac{(2x+3)(x-4)}{(x-4)(x+4)}[/tex]
Enter your answer as a binomial, like this: x + 7
Answer:
Step-by-step explanation:
(x - 4)
What you are being asked to do is find the exact same binomial in the top as is in the bottom.
But there's a small catch. You must stipulate that x cannot equal 4. If it does, then you will get 0/0 which is undefined. You can't have that happening -- not at this level.
Any other value for x is fine.
A survey of eating habits showed that approximately 4% of people in a certain city are vegans. Vegans do not eat meat, poultry, fish, seafood, eggs, or milk. A restaurant in the city expects 350 people on opening night, and the chef is deciding on the menu. Treat the patrons as a simple random sample from the city and the surrounding area, which has a population of about 600,000. If 17 vegan meals are available, what is the approximate probability that there will not be enough vegan mealslong dashthat is, the probability that 18 or more vegans will come to the restaurant? Assume the vegans are independent and there are no families of vegans.
The approximate probability that there will not be enough vegan meals is 94.88%.
Explanation:To calculate the approximate probability that there will not be enough vegan meals, we need to find the probability that 18 or more vegans will come to the restaurant. Since the survey showed that approximately 4% of people in the city are vegans, we can use this information to estimate the probability.
First, we find the number of vegans in the city and surrounding area by multiplying the total population by the percentage of vegans: 600,000 * 0.04 = 24,000.
Next, we calculate the probability of 18 or more vegans showing up out of 24,000 by using a binomial distribution with n = 350 (the number of people expected on opening night) and p = 0.04 (the probability of a person being vegan). We then sum the probabilities for 18, 19, 20, ..., 350 vegans.
Using a calculator or statistical software, we find that the approximate probability is 0.9488, or 94.88%.
Can somebody please help me with my hw
Answer:
Each base is 40
Step-by-step explanation:
An isosceles triangle has a total of 180. An isosceles has two sides that are the same and one different. Think of “sos” in the word isosceles to help. If one is 100, then you have 80 left. 80 divided by 2 is 40.
a cube has a side length of 4 feet what is the volume of the cube
Answer:
V=64
Step-by-step explanation:
What you do is go based off the volume formula of a cube which is V=a^3.
You have a side length of 4.
V=4^3.
V=64.
Write an inequality to represent "7 less than the product of a number, n, and 16 is at most 45."