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3 years ago

If D=25 use information in the figure below to determine angle F

Mathematics

1 answer:

Sloan [31]3 years ago

8 0

Answer:

130°

Step-by-step explanation:

DEF is an isosceles triangle with base DE and DF = EF.

By definition, base angles of an isosceles triangle are equal.

Hence ∠FDE = ∠DEF = 25°

Angle F = 180° - ∠FDE - ∠DEF

= 180° - 25° - 25°

= 130°

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A scientist has a container of 2% acid solution and a container of 5% acid solution. How many fluid ounces of each concentration

algol [13]

Let 'a' be the number of ounces of 2%-solution in the 25-ounce mixture

and 'b' be the number of ounces of 5%-solution in the 25-ounce mixture.

Since, fluid ounces of each concentration should be combined to make 25 fl oz.

So, a+b=25 (Equation 1)

And, a container of 2% acid solution and a container of 5% acid solution should be combined to make 25 fl oz of 3.2% acid solution.

So, a of 2% + b of 5% = 3.2% of 25

$(a \times \frac{2}{100})+(b \times \frac{5}{100})= 25 \times \frac{3.2}{100}$

$(0.02a)+(0.05b)= 0.8$

Multiplying the above equation by 100, we get

$2a+5b=80$ (Equation 2)

Substituting the value of a=25-b in equation 2, we get

$2(25-b)+5b=80$

$50-2b+5b=80$

$50+3b=80$

$3b=30$

$b=10$

Since, a=25-b

a= 25-10

a=15.

So, 15 fluid ounces of 2% solution combined with 10 ounces of the 5% solution to create a 25-ounce mixture at 3.2% concentration of acid.

7 0

2 years ago

If θ is an acute angle and sin θ = 2 1 , then cos θ =

ss7ja [257]

First of all i think theres a mistakein the question;
i think it is sin θ = $\frac{1}{2}$

and then sin 30° = $\frac{1}{2}$

thus θ= 30° $\frac{ \sqrt{3} }{2}$

3 0

3 years ago

Solve 5x^2-2=-12 by taking the square root

k0ka [10]

Answer:

x = ±i√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra II

Imaginary root i

i = √-1

Step-by-step explanation:

Step 1: Define

Identify

5x² - 2 = -12

Step 2: Solve for x

[Addition Property of Equality] Add 2 on both sides: 5x² = -10
[Division Property of Equality] Divide 5 on both sides: x² = -2
[Equality Property] Square root both sides: x = ±√-2
Rewrite: x = ±√-1 · √2
Simplify: x = ±i√2

7 0

2 years ago

How to solve - 10+5x=7x-4

Triss [41]

10+5x=7x-4
1. simplify 7x - 5x
10=2x-4

2. add four to both sides
10+4=2x
+ 4 4
14=2x

3. divide 14 to both sides
14=2x

x=7

8 0

2 years ago

What is equal to 0/0 0 0 0 none of the above

babunello [35]

Answer:

well um I have to go with 0

6 0

2 years ago