x - 2(x + 10) = 12 what's x
How can you use a number line to compare and order numbers?
the "h" value moves the graph up or down true or false ?
Answer:
False
Step-by-step explanation:
Suposse that we are given a function f(x) and a constant value h.
1. Case:
If we take the function g(x)=f(x)+h, then the graph of the function g(x) will be the graph of the funcion f(x) moved up or down.
2.Case:
If we take the function g(x)=hf(x), then the graph of the function g(x) will be the graph of the function f(x) just taller or shorter.
3.Case:
If we take the function g(x)=f(x-h), then the graph of the function g(x) will be the graph of the fuction f(x) moved horizontally.
4. Case:
If we take the function g(x)=f(hx), then the graph of the function g(x) will be tha graph of the function f(x) wither or thiner.
For example:
If we take f(x)=sin(x) and h=2. Then, if we take g(x)=sin(2x) then f(0)=g(0)=0, which means that the graph of the functiction is not moved up or down. However, f(π/2)=sin(π/2)=1 and g(π/2)=sin(π)=0 which gives us a hint that the graph of the function became thiner.
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed)
The required probability that one is right-handed and the other is left-handed is 217/1650.
Given that,
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed) is to be determined.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of left-handed people out of 100 = 7
Total number of right-handed people out of 100 = 100 - 7 = 93
Now,
Probability of picking 2 person(one is right-handed and the other is left-handed) = 7 / 100 (93/99) = 217/1650.
Thus, the required probability that one is right-handed and the other is left-handed is 217/1650.
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A herd of 39 horses has 33 white horses some black horses. What is the ratio of black horses to white horses?
There is 6 black horses, so 6/39.
06.01 LC)
Four graphs are shown below:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D
Answer:
d
Step-by-step explanation:
In a random sample of 75 individuals, 52 people said they prefer coffee to tea. 99.7% of the population mean is between 84/80/74 % and 64/58/54%. (Choose the option closest to your answer.)
rationalize the denominator. write it in simplest terms
3
------
√12x
Simplify
[tex] \frac{ \frac{1}{x+h} + \frac{1}{x} }{x} [/tex]
Hillary age is 3 years greater than 2/3 times Lilly's age if Hillary is 19 years old how old is Lilly
Hillary = 3+2/3X
19=3+2/3X
16=2/3X
X= 16 / 2/3 = 16/1* 3/2 = 48/2
X=24
Lilly is 24
what is the product? 3x^5 (2x^2+4x+1)
Answer:
The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
Step-by-step explanation:
Given: Polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
We have to find the product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Consider the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Apply distributive rule, [tex]a(b+c)=ab+ac[/tex]
Multiply [tex]3x^5[/tex] with each term in brackets, we have,
[tex]=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1[/tex]
[tex]=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5[/tex]
Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex]
Simplify, we have,
[tex]=6x^7+12x^6+3x^5[/tex]
Thus, The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
Are there any rational numbers between 0.4 and 4/9
help help help help help please
The function f(x) = –x2 + 28x – 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Solve the inequality.
Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do you know about this function? B. For what values of l and w will the area of R be greatest? Give an algebraic argument. Give a geometric arguement.
When simplified, the expression (x ^1/8) (x^3/8) is 12. Which is a possible value of x?
find the area of triangle QRS.
Answer: 140 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by
[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]
Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-
[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]
Answer:
the answer is 140. I did the assignment
determine which of the following logarithms is condensed correctly
Find all solutions in the interval [0, 2π).
sin^2 x + sin x = 0
Factor the expression
4b^2+28b+49
He lake is 60 miles away, and rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake
divide distance by speed
60/40 = 1.5
it will take 1 1/2 hours ( 90 minutes)
Which term best describes a proof in which you assume the opposite of what you want to prove?
Answer:
Contradictory Statement
Step-by-step explanation:
In contradictory statement , we basically describes a proof by assuming opposite of what we want to prove .
For example :
Prove that [tex]\sqrt{2}[/tex] is irrational .
Solution :
We will prove this by contradiction .
Let if possible [tex]\sqrt{2}[/tex] is rational .
[tex]\sqrt{2}=\frac{p}{q}[/tex] where p and q are integers and coprime such that [tex]q\neq 0[/tex]
On squaring both sides , we get
[tex]2q^2=p^2\\\Rightarrow 2|p^2\\\Rightarrow 2|p[/tex]
we get ,
p=2r
On squaring both sides, we get
[tex]p^2=4r^2\\\Rightarrow 2q^2=4r^2\\\Rightarrow q^2=2r^2\\\Rightarrow 2|q^2\\\Rightarrow 2|q[/tex]
So, 2 divides p and q which is a contradiction to the fact that p and are coprime .
Therefore, [tex]\sqrt{2}[/tex] is irrational .
An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort’s water rights effectively.
a.)What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.
b.)How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet?
The largest section of the pool is 11307.2 square feet and it seems feasible to add a water slide based on this area. In order to fill the pool, considering that the average depth is 4 feet, approximately 338511.6 gallons of water would be needed.
Explanation:We will first find the area of the circular pool, keeping in mind that the hypotenuse of the triangle serves as the diameter. We will use the formula for the area of a circle, A = πr², where r is the radius of the circle. Here, the radius is half of the hypotenuse so it's 120 feet / 2 = 60 feet.
This makes the area of the circle A = π * 60² = 3600π square feet. This, minus the area of the triangle which can be calculated by (1/2) * base * height = (1/2) * 60 * 103.92 = 3117.6 square feet. So, the largest section of the pool is 3600π - 3117.6 = 11307.2 square feet.
Additional structures such as a water slide could be considered based on the remaining area. Due to size of the pool, it seems feasible to add a water slide without significantly disrupting the swimming space. However, additional calculations considering the base area of the slide would be required for a definitive answer.
The amount of water needed to fill the pool is calculated by multiplying the volume of the pool by the weight of the water. If the average depth of the pool is 4 feet, the volume of the pool (ignoring the central triangle) is 11307.2*4 = 45228.8 cubic feet. As 1 cubic foot of water equals roughly translates to 7.48 gallons, the pool would require approximately 45228.8 * 7.48 = 338511.6 gallons of water.
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A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?
area = 4 x 5.5 = 22 square inches
cost is 0.99 per sq. inch
22 * 0.99 = 21.78
cost is $21.98
To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.
To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.
The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:
Total cost = 22.0 square inches × $0.99/square inch = $21.78.
Therefore, the cost of the glass to cover the picture would be $21.78.
Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?
a tower casts a 450 ft shadow at the same time that a 4 ft child casts a 6 ft shadow. Write and solve a proportion to find the height of a tower
Answer:
[tex]x=300[/tex]
Step-by-step explanation:
Set up the proportion;
[tex]\frac{x}{450} =\frac{4}{6}[/tex]
then cross multiply;
[tex]6x=450[/tex] · [tex]4[/tex]
[tex]6x=1800[/tex]
[tex]x=\frac{1800}{6} =300[/tex]
[tex]x=300[/tex]
9log9(4) =
A. 3
B. 4
C. 9
D. 81
If you place a cup of 210 degree Fahrenheit coffee on a table in a room that is 68 degrees fareinheit, and ten minutes later, it is 200 degrees fareinheit. How long will it be before the coffee is 180 degrees fareinheit? Use newtons law of cooling
Final answer:
According to Newton's Law of Cooling, it will take approximately 10.76 minutes for the coffee to cool from 210 degrees Fahrenheit to 180 degrees Fahrenheit when placed in a room with a temperature of 68 degrees Fahrenheit.
Explanation:
According to Newton's Law of Cooling, the rate at which an object cools is proportional to the temperature difference between the object and its surroundings. We can use this law to determine how long it will take for the coffee to reach a temperature of 180 degrees Fahrenheit.
First, we need to find the temperature difference between the coffee and its surroundings. The initial temperature of the coffee is 210 degrees Fahrenheit and the room temperature is 68 degrees Fahrenheit. Therefore, the initial temperature difference is 210 - 68 = 142 degrees Fahrenheit.We also know that after 10 minutes, the coffee's temperature has decreased to 200 degrees Fahrenheit. So the new temperature difference is 200 - 68 = 132 degrees Fahrenheit.Now we can set up a proportion to find the time it takes to reach a temperature of 180 degrees Fahrenheit. The ratio between the initial temperature difference and the time it takes for the coffee to cool to 180 degrees Fahrenheit is equal to the ratio between the new temperature difference and the total time it takes for the coffee to cool to 180 degrees Fahrenheit. Let's call the total time T: (142 / T) = (132 / 10). Cross-multiplying, we get 1420 = 132T. Dividing both sides by 132, we find that T = 10.76 minutes.Therefore, it will take approximately 10.76 minutes for the coffee to reach a temperature of 180 degrees Fahrenheit.
Draw a graph of the rose curve.
r = 2 sin 3θ, 0 ≤ θ ≤ 2π