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kirill115 [55]
3 years ago
13

Factor 4a2 - 25. A. (2a + 5)(2a + 5) B. (2a - 5)(2a - 5) C. (2a - 5)(2a + 5)

Mathematics
1 answer:
nikdorinn [45]3 years ago
3 0

This is the diference of 2 perfect squares. 4 is a perfect square, x^2 is a perfect square, and 25 is a perfect square. The pattern for this is (ax + b)(ax - b). Our a is 2 since 2*2 = 4, and our b is 5 since 5*5 = 25. So your factors are (2a+5)(2a-5), choice C.

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A large community college has professors and lecturers. the total number of faculty is 136. The school reported that they have 6
ipn [44]
Let's come up with an equation for the numbers. We know that there are 136 faculty members, and there are 6 professors for every 11 lecturers. The equation could look something like this:

(6 * x) + (11 * x) = 136.

First, combine like terms:

6x + 11x = 136
17x = 136

Now, divide both sides by 17.

17x/17 = 136/17
x = 8.

Now, to check, plug in 8 for x in our equation:

(6 * 8) + (11 * 8) = 136
48 + (11 * 8) = 136
48 + 88 = 136

So to answer the question, they have 48 professors! :)
8 0
3 years ago
Alaska is -3 degrees, lowa is 5 degrees, Idaho is - 7 degrees, New York is 9 degrees, and
kirill [66]

Answer:

Idaho

Step-by-step explanation:

3 0
2 years ago
Find the coordinates of S after a rotation of the triangle 90 degrees counterclockwise about the origin
Neko [114]

We first start by finding the actual coordinates of the pre - image's point S.

Assuming the x and y axis count by 1s, as there is no labels, we can conclude that:

The point's x coordiate is 4 to the left from the origin, or -4.

The point's y coordinate is 4 up from the origin, or 4.

So, the coordinates of Point S is (-4, 4).

Next, we apply the translation rule for a 90 degree counterclockwise rotation to the point's coordinates. The rule is (x, y) --> (-y, x). Using this rule on our coordinates, we get:

(-4, 4) --> (-4, -4)

So, the new coordinates of point S prime after a 90 degree counterclockwise rotation are (-4, -4).

4 0
2 years ago
how would you estimate the sum? just like estimate the fractions and then get your estimated answer? Q: 2 1/6 + 3 6/11
denis-greek [22]
I think estimation is terrible. If u want to truly solve it, you just need to get a common denominator on each of the fractions. that means the bottom half of both fractions must be the same in addition or subtraction. so here, the common denominator would be 66. What times 6 = 66? 11. So 1*11/6*11 = 11/66. Then what times 11 = 66? 6. So 6*6/6*11. Your new problem is 2 11/66 + 3 36/66. Now you can just add it up, but the denominators will always stay the same, 66. Your answer would be 5 47/66
4 0
3 years ago
A cash box contains $74 made up of quarters, half-dollars, and one-dollar
Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

0.25q+0.50h+1.00d=74

\displaystyle{h=\frac{3}{5}d+1}

q=4(d+h)

Then, substitute <em>q</em> in the first equation with the expression from the third equation:

0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74

Next, substitute <em>h</em> in that equation with the expression from the second equation:

\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}

2d+0.9d+1.5=74\\2.9d+1.5=74

Solve for <em>d</em>, the number of one-dollar coins:

2.9d+1.5=74\\2.9d=72.5\\d=25

Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{h=\frac{3}{5}(25)+1}

h=15+1\\h=16

Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:

q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164

Then, verify that the coins total $74:

0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{16=\frac{3}{5}(25)+1}

16 = 15 + 1\\16 = 16\\\text{Check.}

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}

6 0
3 years ago
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