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astraxan
2 months ago
15

What is the length of EF in the right triangle below?

Mathematics
2 answers:
babunello [11.8K]2 months ago
8 0
The result is √217. The step-by-step solution follows: (19)² = (12)² yields 361 - 144 + 217, leading to √217.
Leona [12.6K]2 months ago
8 0

Answer:

\sqrt{217}units

Step-by-step explanation:

Provided : A right triangle EFD

Hypotenuse = ED = 19 units

Base = DF = 12 units

Perpendicular = EF

Solution:

To determine the length of EF, the Pythagorean Theorem will be applied:

(Hypotenuse)^{2}=(Perpendicular)^{2}+(Base)^{2}

ED^{2}=EF^{2}+DF^{2}

19^{2}=EF^{2}+12^{2}

361=EF^{2}+144

361-144=EF^{2}

217=EF^{2}

\sqrt{217} =EF

Consequently, the length of EF is \sqrt{217}units

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A recipe for salsa uses 65% tomatoes. If a batch contains 5.2 cups of tomatoes, how large is the batch of salsa.
AnnZ [12381]

The salsa consists of 65% tomatoes, which amounts to 5.2 cups.

Let’s denote the total salsa as "x" cups, representing 100%. Given that 5.2 cups makes up 65%, we have:

\bf \begin{array}{ccll} cups&\%\\ \cline{1-2} 5.2&65\\ x&100 \end{array}\implies \cfrac{5.2}{x}=\cfrac{65}{100}\implies \cfrac{5.2}{x}=\cfrac{13}{20}\implies 104=13x \\\\\\ \cfrac{104}{13}=x\implies 8=x

3 0
2 months ago
Which of the following is true regarding the solutions to the logarithmic equation below? 2 log Subscript 6 Baseline (x) = 2. lo
zzz [12365]
Regarding the logarithmic equation, option c is correct: x=6 is a valid solution, while x=-6 is considered an extraneous solution. Explanation: The equation requires dividing both sides by 2, simplifying further until each step can be logically followed based on logarithmic definitions, from which we affirm that both sides equal when substituting back the values, confirming that x=6 is the true solution.
4 0
2 months ago
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The angle by which AB turns clockwise about point B to coincide with BC is ? degrees. If from point B, a point E is drawn direc
Zina [12379]
A) AB rotates clockwise to align with BC

= ABD + DBC

= 33.3° + 30.6°

= 63.9°


b) If E is positioned directly opposite C.

EBC forms a straight line, thus the angle sums to 180°

ABE + ABD + DBC = 180°

ABE + 33.3° + 30.6° = 180°

ABE + 63.9° = 180°

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Hope this clarifies things.
3 0
2 months ago
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A billfold holds one-dollar, five-dollar, and ten-dollar bills and has a value of $210. There are 50 bills total where the numbe
AnnZ [12381]

Answer:

25 one-dollar bills, 13 five-dollar bills, and 12 ten-dollar bills.

Step-by-step explanation:

The equations that can be formed are:

x+y+z=50 (1)

x+5y+10z=210 (2)

x= 2y-1 (3)

where x = number of one-dollar bills,[tag_20] y = number of five-dollar bills,

z = number of ten-dollar bills

Substituting (3) into (1) and (2) gives:[

2y-1+y+z= 50

3y+z=51

2y-1+5y+10z= 210

7y+10z=211

You will then derive the following equations:

3y+z=51 (4)

7y+10z=211 (5)

Next, isolate z using (4) and substitute it into (5):

z= 51-3y

7y+10(51-3y)=211

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-23y=-299

y= 13

After substituting the value of y into z= 51-3y, we find:

z=51-3(13)= 51-39= 12

Now, replace y's value in (3):

x=2(13)-1= 26-1= 25

Thus, the final result indicates there are 25 one-dollar bills, 13 five-dollar bills, and 12 ten-dollar bills.

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I believe it’s numerical data
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