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3 years ago

Which sentence matches the mathematical equation? p-0.40p=0.60p

1 answer:

7 0

P-0.40p = 0.60p

C. Decrease by 40% is the same as multiply by 60%.

Assume that p = 10

10 - 0.40(10) = 0.60(10)
10 - 4 = 6
6 = 6

Based on the above assumption. 40% of 10 is 4 ; and 60% of 10 is 6. So, 10 less 4(40% of 10) is equal to 6 (60% of 10).

Percentage is used because 0.40 and 0.60 will be multiplied with 100% to get the equivalent percentage 0.40 x 100% = 40% ; 0.60 x 100% = 60%

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3 years ago

The partial factorization of x2 – 3x – 10 is modeled with algebra tiles. Which unit tiles are needed to complete the factorizati

baherus [9]

X² - 3x - 10

x² = x * x
10 can be factored:
1 x 10 ⇒⇒⇒ difference between factors = 9
2 x 5 ⇒⇒⇒ difference between factors = 3 ⇒ (The correct pair)

(x-5)(x+2) = x(x+2) - 5(x+2)
 = x² + 2x - 5x - 10
 = x² - 3x - 10

∴ x - 5 = 0 ⇒⇒⇒ x = 5
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I have attached algebra tiles for the given equation.

6 0

3 years ago

Read 2 more answers

Find the missing side. Round your answer to the nearest tenths. X=

Lapatulllka [165]

Answer:

16.5 ≈ x

Step-by-step explanation:

We have a right triangle where we know 1 side, 1 angle and we need to find another side. We can use trigonometric functions to find the missing side.

The tangent function definition is

tan α = opposite side/ adjacent side

In our problem

tan 70° = x/ 6, multiply both sides by 6 to isolate x

6 · tan 70° = x, use the calculator (make sure is set in degrees)

16.4848 ≈ x , round to the nearest tenths

16.5 ≈ x

3 0

2 years ago

F(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, ∞) and g(x) = 2x2 + 8x + 6,

svetlana [45]

Answer:

B) Both functions have the same domain.

C) Both functions have the same x-intercepts.

D) Both functions are decreasing on the interval (−∞, −2).

Step-by-step explanation:

step 1

Find the vertex of f(x)

we know that

The x-coordinate of the vertex is the midpoint of the roots

we have

x=-1 and x=-3

the midpoint is

(-1-3)/2=-2

The y-coordinate of the vertex is -4 (because the range is [−4, ∞))

therefore

The vertex of f(x) is the point (-2,-4)

Is a vertical parabola open upward

The vertex is a minimum

The domain is all real numbers

step 2

we have

$g(x)=2x^2+8x+6$

Find the vertex

Factor the leading coefficient

$g(x)=2(x^2+4x)+6$

Complete the square

$g(x)=2(x^2+4x+4)+6-8$

$g(x)=2(x^2+4x+4)-2$

Rewrite as perfect squares

$g(x)=2(x+2)^2-2$

Is a vertical parabola open upward

The vertex is the point (-2,-2)

The domain is all real numbers

The range is the interval [−2, ∞)

Find the x-intercepts

For g(x)=0

$0=2(x+2)^2-2$

$2(x+2)^2=2$

$(x+2)^2=1\\x+2=\pm1\\x=-2\pm1$

The roots or x-intercepts are

x=-1 and x=-3

Verify each statement

A) Both functions have the same vertex

The statement is false

The vertex of f(x) is (-2,-4) and the vertex of g(x) is (-2,-2)

B) Both functions have the same domain.

The statement is true

The domain is all real numbers

C) Both functions have the same x-intercepts

The statement is true (see the explanation)

D) Both functions are decreasing on the interval (−∞, −2)

The statement is true

Because the x-coordinate of the vertex is the same in both functions, and both functions open upward

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3 years ago

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What is the difference between a centroid, orthocenter, and a circumcenter?

Lisa [10]

Answer:

Take an example in a triangle:

The orthocenter is the intersection point of 3 altitudes.

The centroid is the intersection point of 3 medians.

The circumcenter is the intersection point of 3 bisectors.

Centroid, orthocenter, and circumcenter are collinear.

Hope this helps!

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2 years ago