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sergey [27]
3 years ago
8

Can someone please help with these 2 questions? It would mean the world to me. I have attached the image for the questions.

Mathematics
2 answers:
sweet [91]3 years ago
5 0

Answer:

2 \frac{1}{20}

Step-by-step explanation:

for question a)

It would be easier if you converted these to improper fractions (currently it is in the form of a proper fraction)

to convert to improper fraction, you would multiply the denominator (bottom no. of fraction) by the whole number , then add that with the numerator (top no. of fraction) and put the whole thing over the denominator.

E.g.

7 \frac{1}{4} = 7x4 + 1 = 29

Thus, improper fraction would be \frac{29}{4}

do same thing  for other one

thus , \frac{26}{5}

now,

\frac{29}{4} - \frac{26}{5}

however, you can't do this as the denominators are not the same, so multiply them by a number which would give the a common denominator (20 would be the best option for common denominator)

\frac{145}{20} -\frac{104}{20} = \frac{41}{20}

convert back to mixed number

2 \frac{1}{20}

RUDIKE [14]3 years ago
4 0

Answer:

Step-by-step explanation:

a) Step1 : write in improper form

Step 2 : Find least common denominator

Step 3: Find equivalent fractions and then subtract

7\frac{1}{4}-5\frac{1}{5} = \frac{29}{4}-\frac{26}{5}\\

            = \frac{29*5}{4*5}-\frac{26*4}{5*4}\\\\=\frac{145}{20}-\frac{104}{20}\\\\=\frac{145-104}{20}\\\\=\frac{41}{20}\\\\=2\frac{1}{20}

b) Keep Change Flip method

4\frac{1}{4} ÷ 2\frac{1}{5} = \frac{17}{4} ÷ \frac{11}{5}

            =\frac{17}{4}*\frac{5}{11}\\\\=\frac{85}{44}\\\\=1\frac{41}{44}

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42:28
gogolik [260]

Answer:

The statements about arcs and angles that are true in the figure are;

1) ∠EFD ≅ ∠EGD

2) \overline{ED}\cong \overline{FD}

3) mFD = 120°

Step-by-step explanation:

1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)

∠CEG = ∠CDG = 90° (Given)

∠GDE = 60° (Given)

∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)

∠ECD = 360° - (90° + 90° + 60°) = 120°

∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)

120° = 2 × ∠EFD

∠EFD = 120°/2 = 60°

∠EFD ≅ ∠EGD

∠ECD = 120°

∠EGD = 60°

∴∠EGD ≠ ∠ECD

2) Given that arc mEF ≅ arc mFD

Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF

∠ECF = mEF = mFD = ∠DCF (Given)

∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)

\\ \overline{EF}\cong \overline{FD} (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

∠FED ≅ ∠FDE (base angles of isosceles triangle)

∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)

∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°

∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)

2 × ∠FED  = 120°

∠FED = 120°/2 = 60° = ∠FDE

∴ ∠FED = ∠FDE = ∠EFD =  60°

ΔEFD  is an equilateral triangle as all interior angles are equal

\\ \overline{EF}\cong \overline{FD}\cong \overline{ED} (definition of equilateral triangle)

\overline{ED}\cong \overline{FD}

3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)

Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)

60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)

60° = 2 × ∠CFE

∠CFE =60°/2 = 30° = ∠CFD

\overline{CF}\cong \overline{CD} (radii of the same circle)

ΔFCD is an isosceles triangle (definition)

∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)

∠CFD + ∠CDF + ∠DCF = 180°

∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°

mFD = ∠DCF (definition)

mFD = 120°.

5 0
3 years ago
Please help with this I will mark brainliest :)
bixtya [17]

Answer:

Triangles

Step-by-step explanation:

  1. Angle b
  2. Triangle BED
  3. Triangle ABC
5 0
3 years ago
What is the approximate volume of a cylinder with a radius of 3 ft and a height of 4 ft?
Lunna [17]
V≈113.1 ft³ is the answer
5 0
3 years ago
Solve for w.<br>9- w = 224​
Tems11 [23]

Answer:

-215

Step-by-step explanation:

-w = 215

w = -215

hope this helped

8 0
2 years ago
The average cost of tuition and fees at a public four-year college in the United States can be molded by the following formula w
Rudik [331]
T=7556=165x+2771
we need to solve for x, number of years after 1996.
165x=7556-2771=4785
x=4785/165=29
It will be in year 1996+29=2025 that estimated fees and tuition average $7556
3 0
3 years ago
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