How many distinct pairs of perfect squares differ by 35? (the pair $a, b$ is the same as the pair $b, a$.)?

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

Answer:

We know: 0 Celsius = 32 Fahrenheit.

We can convert the Celsius to Fahrenheit using this formula:

[tex](C\times9/5)+32[/tex]

a. 35° C

= [tex](35\times9/5)+32=95[/tex] degrees Fahrenheit

b. 500° C

= [tex](500\times9/5)+32=932[/tex] degrees Fahrenheit

c. 10° C

= [tex](10\times9/5)+32=50[/tex] degrees Fahrenheit

d. 55° C

= [tex](55\times9/5)+32=131[/tex] degrees Fahrenheit

a. 35°C to Fahrenheit: 95°F

b. 500°C to Fahrenheit: 932°F

c. 10°C to Fahrenheit: 50°F

d. 55°C to Fahrenheit: 131°F

1. Formula:

To convert Celsius to Fahrenheit, you can use the formula:

[tex]\[ F = \frac{9}{5}C + 32 \][/tex]

2. Calculations:

a. For 35°C:

[tex]\[ F = \frac{9}{5} \times 35 + 32[/tex]

= 95°F    

b. For 500°C:

[tex]\[ F = \frac{9}{5} \times 500 + 32[/tex]

= 932°F

c. For 10°C:

[tex]\[ F = \frac{9}{5} \times 10 + 32[/tex]

= 50°F

d. For 55°C:

[tex]\[ F = \frac{9}{5} \times 55 + 32[/tex]

= 131°F

Answer:

Your answer is D :)

Step-by-step explanation:

No explanation :) <3

Answer: First option is correct.

Step-by-step explanation:

Since we have given that

There is a geometric sequence:

where a₁ = 2

r = √2

We need to find a₉:

As we know the formula for "nth term ":

[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]

Hence, First option is correct.

All the given expressions are binomials except the expression in (i) which is a trinomial.

What are binomials in expressions?

Binomials can be defined as the expression that contains two variables that are different in terms.

ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴

= 10x⁵-10x⁴+3x⁵-6x⁵

= 7x⁵+10x⁴ (this is an example of a binominal)

iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)

iv.) 5(a-1)-10(a-1)+100(a-1)

= 5a-5-10a+10+100a-100

= 95a - 95 (binomials)

v.) (2πr-πr²)r-(2πr-πr²)2r

= 2πr²-πr³-4πr²+2πr³

= -2πr²+πr³(binomials)

Perimeter is 30 units

Semi-perimeter is 15 units

The Area is 39.7 square units

Answer:

(x+2)(x+4)

Step-by-step explanation:

Answer:

[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream

Step-by-step explanation:

Using unitary method,  

Unitary method is a method use to find the value of a unit quantity.

[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk

[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream

One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk

                                                        = [tex]\frac{7}{5}[/tex] gallon of milk

                                                         = [tex]1\frac{2}{5}[/tex] gallon of milk

Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.

Answer: The answer is actually 6.

Step-by-step explanation:

The value of x is 6, rounded to the nearest whole number.

To solve for x given the conditions:

1. Define the variables based on the problem:

  - Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]

  - Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]

2. Write the equation for the area of the rectangle:

  - Area [tex](\( A \)) = \( L \times W \)[/tex]

  - Given that the area is 56 cm², we have:

[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]

3. Expand the equation:

[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]

4. Set up the equation:

[tex]\[ 2x^2 - x - 10 = 56 \][/tex]

5. Move all terms to one side of the equation to set it to zero:

[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]

6. Solve the quadratic equation using the quadratic formula:

[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]

7. Calculate the discriminant:

[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]

8. Calculate the roots:

[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]

So, the solutions are:

[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]

and

[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]

Since x must be a positive value in the context of this problem, we have: x = 6

9. Verify the solution:

Length L = x + 2 = 6 + 2 = 8 cm

Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7  cm

Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.

Therefore, ( x = 6).

factor X + 1 is the answer

central angle theta (in radians) = arc length / radius

So theta = 5.6/8 = 0.7 radians

The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.

The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ =  [tex]\frac{5.6}{8}[/tex]

Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.

Answer: ASA

hope that helps have a nice day