A line parallel to a triangle's side splits AB into lengths of x - 7 and x - 3. The other side, AC, is split into lengths of x and x + 12. What is the length of AC?
33
[tex]\frac{x-7}{x} = \frac{2x-10}{2x+12}[/tex] → x = [tex]\frac{21}{2}[/tex]
AC = x + x + 12 = [tex]\frac{21}{2} + \frac{21}{2}[/tex] +12 = 33
George traveled 300 miles in 8 hours. How far could he travel in 4 hours if he traveled at the same rate?
rewrite d= 2r in function notation
The equation d = 2r can be rewritten in function notation by replacing 'd' with 'f(r)', giving the function f(r) = 2r.
Explanation:To rewrite the equation d = 2r using function notation, we first need to understand that function notation is a way to represent a function that is derived from a certain equation. Here, the equation given is d = 2r, where d is in terms of r.
To translate this into function notation, we would change d to f(r). The letter f stands for 'function', and the (r) is the variable that the function is dependent upon. Therefore, the equation d = 2r would be rewritten in function notation as f(r) = 2r.
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An iron fence reacts with the oxygen in the air to form rust. The formation of rust is an oxidation-reduction reaction and a _____ reaction.
A. decomposition
B.combustion
C. synthesis
D. single-replacement
The formation of rust on an iron fence is a synthesis reaction, where iron combines with oxygen in the air to create iron oxide. During this process, iron is oxidized and oxygen is reduced, making it an oxidation-reduction (or redox) reaction.
Explanation:The formation of rust is an oxidation-reduction reaction and a synthesis reaction. Rusting occurs when iron reacts with oxygen in the air, typically in the presence of water, to form iron oxide.
The process can be summarized as iron (Fe) being oxidized to iron(II) ions (Fe2+) which react further with oxygen and water to produce a hydrated iron(III) oxide, commonly known as rust (Fe2O3·xH2O).
This process is classified as a synthesis reaction because it involves the combination of simpler substances - iron and oxygen - to form a more complex compound, namely iron oxide.
In comparison to other types of reactions, decomposition refers to a single compound breaking down into two or more simpler compounds or elements.
Combustion reactions involve fuel (often a hydrocarbon) reacting with oxygen to produce carbon dioxide and water.
Lastly, single-replacement reactions occur when an element replaces another element in a compound. Since the reaction of iron with oxygen adds oxygen to create a new product, rather than decomposing, combusting, or substituting, it is indeed a synthesis reaction.
A map shows the distance between the corner of Cactus Road and 1st Street and the corner of 1st Street and Merle Road as 3 inches. If the scale is 1 in. : 3.7 mi, what is the actual distance? A. 1.3 mi B. 22.2 mi C. 11.1 mi D. 111 mi
If it took 2.5 gallons of paint to cover 282 square feet of wall, how much paint is needed to paint an additional 423 square feet
Is it true that a continuous function that is never zero on an interval never changes sign on that interval? give reasons for your answer?
Yes, It is true that a continuous function that is never zero on an interval never changes its sign on that interval.
What is a continuous function?In mathematics, a continuous function is a function such that a continuous variation of the argument causes a continuous variation of the value of the function. This indicates that there aren't any discontinuities or sudden changes in value.
Unchanged sign is a property of continuous functions that are never zero on an interval, hence this is true. This is due to the perennially significant Intermediate value theorem.
Therefore, It is true that a continuous function that is never zero on an interval never changes its sign on that interval.
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1. Link took out a $160,000, 10-year term policy at age 45. The premium per $1,000 is $4.18. He will be 55 years old next year when the premium per $1,000 will be $6.47. What is the amount of the increase?
What is the solution to 3x+2.4≥3.0
Answer:
A
Step-by-step explanation:
A bag contains 4 red marbles, 5 yellow marbles, and 6 blue marbles. three marbles are to be picked out randomly (without replacement). what is the probability that exactly two of them have the same color
Ben and Josh are in the same physical education class. Ben weighs twelve more pounds than josh. Together their weights add to 144. How much does each one weigh?
What is the scope of government?
I have a math problem
For the geometric sequence 3, 12, 48, 192 find the indicated term
Let f(x) = x2 and g(x) = x − 3.
Evaluate (f ∘ g)(−2).
1
25
−7
20 My guess
Answer:
[tex]25 = f(g(-2))[/tex]
Step-by-step explanation:
[tex]g(-2) = -2 - 3 = -5 \\ \\ f(-5) = {[-5]}^{2} = 25 \\ \\ 25 = f(g(-2))[/tex]
I am joyous to assist you anytime.
The perimeter of a rectangle is 66 m. the length is 1 m more than three times the width. find the dimensions of the rectangle.
Term insurance covers the insured for the stated term of the policy.
True
False
Answer:
it's true
Step-by-step explanation:
When two lines intersect to form a 90 degree angle, these lines are called ________ lines?
Answer:
perpendicular lines.
Step-by-step explanation:
If you know the density and volume of a substance, how could you find its mass?
What is the number of x intercepts of the parabola with equation y=6x^2-4x-3?
The parabola y=6x^2-4x-3 has 2 x-intercepts. This is determined by solving the equation for when y equals zero, using the quadratic formula. Because the discriminant is positive, there are two distinct real solutions, indicating the two x-intercepts.
Explanation:To find the number of x-intercepts of the parabola with equation y=6x^2-4x-3, you need to set y to 0 and solve the equation for x. The solutions for x will be the x-coordinates of the intercepts.
The x-intercept(s) occur where y=0. The quadratic formula, x = [-b ± sqrt(b^2 - 4ac)]/2a is used to find these points.
Substituting the coefficients a=6, b=-4, and c=-3 into the formula, we get:
x = [4 ± sqrt((-4)^2 - 4*6*(-3))]/(2*6)
This simplifies to x = [4 ± sqrt(16+72)]/12 = [4 ± sqrt(88)]/12
Since the value under the square root (the discriminant) is positive, we have two distinct real solutions for x. This means that the parabola crosses the x-axis at two points, so there are 2 x-intercepts.
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y=1/4x+1 Solve for x and show your work
If w||v, solve for x.
Romeo and Juliet headed north at 8.a.m by noon Romeo was 80 miles ahead of Juliet what was romeos speed if Juliet's speed was 30 miles per hour? Will give brainlest for help!!!
The graph of which function passes through (0,4) and has a minimum value at 3pi/2, 3
Answer: f(x) = sin(x)+4
Step-by-step explanation:
Rosa brought d drawings to an art show. After selling 14 of them , she had 34 left . Identify the equation that represents this situation and the correct solution
Answer:
[tex]d-14=34[/tex] shows that when we add sold drawing we get the total drawings.
Step-by-step explanation:
We have been given that Rosa brought d drawings to an art show.
After selling 14 of them, she had 34 left.
We have to form a equation such that when we add 14 in 34 we get the total of drawings.
[tex]d-14=34[/tex] (1)
Equation (1) shows that when we add sold drawing we get the total drawings.
Answer:
d - 14 = 34; d = 48
Step-by-step explanation:
Sakura speaks 150 words per minute on average in Hungarian and 190 words per minute on average in polish she once gave cooking instructions in polish Sakura spent 5 minutes total giving both instructions and spoke 370 more words in polish than Hungarian
100 pts LZ HLP(d) Mrs. Carothers suggested contacting a travel agent to see whether they could get a lower price. The agent found a price that was 30% lower than $2075. What was the price the travel agent found? Explain and Show your work. (Hint: there is more than one step to this problem!)
Answer:$1452.5
Step-by-step explanation:2075*.3=622.5
2075-622.5=$1452.5 is you answer
if im wrong correct me but have a blessed day
answer by:
(DJ)
Two events e and f are __________ if the occurrence of event e in a probability experiment does not affect the probability of event f.
Two events are independent if the occurrence of one event does not affect the probability of the other event.
Explanation:Two events are independent if the occurrence of one event does not affect the probability of the other event. This means that the outcomes of the two events are not related and the probability of one event happening does not change based on whether the other event occurred or not.
For example, if you flip a coin and roll a die, the outcome of the coin flip does not affect the probability of getting a certain number on the die roll. The two events are independent.
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A new car dealer offered to sell his demonstrator model for 80% of the retail price. If the retail price is $30,863, how much did the customer save?
Answer:
The customer saved $6,167.20
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
To begin solving this problem we need to change the percent into decimal form. We can do this by moving the decimal point 2 digits to the left like so...
80.0% ⇔ 0.80
Now that we have the percent in decimal form we can find how much the customer paid by multiplying the percent by the retail price.
[tex]30,836 * 0.80 = 24,668.80[/tex]
Now that we have the amount the customer paid, we can subtract that value by the retail price of the model to calculate how much the customer saved.
[tex]30,836-24668.80 = 6,167.20[/tex]
Finally, we can see that the customer saved $6,167.20
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A trainer gives his horse, Caballo, 7 gallons of water every day from a 57 - gallon container. How many days will Caballo receive his full portion of water from the container? On which number day will the trainer need to refill the container of water?