QUESTION 1
The given binomial is;
First terms are multiplied: 
Outside terms are multiplied: 
Inside terms are multiplied: 
Last terms are Multiplied: 
This gives us;
QUESTION 2
We want to factor
The HCF is 
We factor to get;
QUESTION 3;
Split the middle term;
Factor
The solutions are;
and 
These are the x-intercepts of the graph of the function
The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).
<h3>What is sentence correction?</h3>
Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.
Now,
- When 'not only' is used, 'but also' must come after it. When utilizing a correlative conjunction like "not only," "but also," the goal should be parallelism, meaning that the words that come after both sides of the conjunction should be from the same part of speech.
- Here, using 'and' after 'not only...' distorts the structure of the sentence.
Hence, Option D is the right response, i.e., The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).
To learn more about sentence correction, refer to the link: brainly.com/question/14632568
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Answer:
x = 2
Step-by-step explanation:
AB is given as 3(3x-1) multiply inside the parenthesis with 3
AB = 9x - 3
AC is given as 5(2x+2) multiply inside the parenthesis with 5
AC = 10x + 10
if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values
9x - 3 + 9x - 3 = 10x + 10 add like terms
18x - 6 = 10x + 10 transfer like terms to the same side of the equation
18x - 10x = 10 + 6
8x = 16 divide both sides by 8
x = 2 replace x with 2 in given expressions to find the value of each component
18=3(x-1)
18=3x-3
18-3=3x
15=3x
15/3=x
x=5
Answer:
Step-by-step explanation:
To start calculating, we first need to make some proof.
Firstly, since AB = AC, we know that ΔABC is isosceles, which means that ∠ABC = ∠ACB.
Now, looking only to ΔBDE and ΔCDF, we can see that they are similar, because the two of its angles are congruent:
∠BED=∠CFD
∠DBE=∠DCF
To make it easier to visualize which are the corresponding vertexes, we can draw them like this:
And we need to remember that BC is 24, so:
BD+CD=24
Since the triangles are similar, their corresponding sides have constant ratio, which we can calculate from the corresponding sides DE and CF:
This ratio is the same for the other corresponding sides, so we can apply that for BD and CD:
Thus, the measure of CF is approximately 13, alternative D.
