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3 years ago

Please help! Quadratic equations!

Mathematics

1 answer:

Alexeev081 [22]3 years ago

7 0

Answer:

$x^2 -2x - 35 =0$

Step-by-step explanation:

Assume that the quadratic term of this equation has no coefficient. One can set the equation up in factored form using the given roots. Then expand the equation and simplify the equation to convert to standard form.

The equation in factored form is the following,

$(x+5)(x-7)=0$

Expand, multiply every term in one of the parenthesis by every term in the other,

$(x+5)(x-7)=0\\\\(x)(x)+(5)(x)-(7)(x)+(-7)(5)=0$

Simplify,

$x^2 +5x -7x -35 =0\\\\x^2 -2x -35=0$

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If a ∝ b and a = 18 when b = 3, then find a when b = 5.

Elden [556K]

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k ⇒ k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

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2 years ago

A tailor used 6 2/3 yards of fabric to make hats. The amount of fabric needed to make each hat is 5/6 yard. How many complete ha

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Answer: The tailor made 8 complete hats

Step-by-step explanation:

Amount of fabrics available to make hat = 6 2/3 yards

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3 years ago

Use a table of values to estimate the value of the limit. Confirm your result graphically by graphing the function with a graphi

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Hello,

$\lim_{x \to 0}\dfrac{ \sqrt{x+25}-5}{x}\\\\$

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3 years ago

Write the equation of the line in slope- intercept and point-slope form.

AnnZ [28]

Answer:

Step-by-step explanation:

As we move from the x-intercept (-2, 0) to the y-intercept (0, 4), x increases by 2 (this is the run) and y by 4 (this is the rise). Thus, the slope of this line is

m = rise/run = 4/2 = 2.

Given the y-intercept (0, 4) and the slope (2), the slope-intercept form of the equation of this line is y = 2x + 4.

From this we get the point-slope form:

y = 2x + 4 becomes y - 4 = 2(x - 0), or just y - 4 = 2x.

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3 years ago

What’s the given m ABC = 70 and m ADC = 46

uysha [10]

Answer:

Step-by-step explanation:

Properties of a kite;

1). A kite has one pair of equal angles.

2). A kite has two pairs of adjacent sides.

3). Diagonals of a kite intersect at 90°.

4). Kite has at least one diagonal that bisects the opposite angles.

It's given in the question,

m∠ABC = 70° and m∠ADC = 46°

By the property number -4,

m∠2 = m∠3 = $\frac{70}{2}$ = 35°

m∠8 = m∠9 = $\frac{46}{2}$ = 23°

By the property number - 3,

m∠4 = 90°

By the property of interior angles in a triangle,

m∠3 + m∠4 + m∠5 = 180°

35° + 90° + m∠5 = 180°

125° + m∠5 = 180°

m∠5 = 55°

Similarly, m∠1 + m∠2 + 90° = 180°

m∠1 + 35° + 90° = 180°

m∠1 = 55°

Now m∠6 + 90° + m∠8 = 180°

m∠6 + 90° + 23° = 180°

m∠6 = 180 - 113 = 67°

Therefore, m∠6 = m∠7 = 67°

3 0

3 years ago