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2 years ago

Consider the quadratic function.

1 answer:

4 0

A standard form for the quadratic function is
f(x) = ax² + bx + c
where the coefficients are a,b, and c.

The given quadratic function is
f(p) = p² - 8p - 5
When this function is compared to the standard form, with p replacing x, we obtain
a = 1 because the leading term is 1*p²,
b = -8 because the linear term is -8*p,
c = -5 because the constant term is -5.

Answer:
Of the answers given the correct one is the 3rd one:
a = 1, b = -8, c = -5.

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Circular tracts of land with diameters 900 meters, 700 meters and 600 meters are tangent to each other externally. There are hou

Rudik [331]

Answer:

$\alpha=69.28^o$

$\beta=61.26^o$

$\gamma=49.46^o$

Step-by-step explanation:

<u>Triangle Solving</u>

If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.

The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are

$x=450+350=800$

$y=450+300=750$

$z=350+300=650$

The internal angles can be computed by using the cosine's law

$x^2=y^2+z^2-2yzcos\alpha$

$y^2=x^2+z^2-2xzcos\beta$

$z^2=x^2+y^2-2xycos\gamma$

Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:

$\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}$

$\displaystyle cos\alpha=\frac{750^2+650^2-800^2}{2\cdot 750\cdot 650}$

$cos\alpha=0.3538$

$\alpha=69.28^o$

Similarly

$\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}$

$\displaystyle cos\beta=\frac{800^2+650^2-750^2}{2\cdot 800\cdot 650}$

$cos\beta=0.4808$

$\beta=61.26^o$

The other angle is computed now

$\displaystyle cos\gamma=\frac{x^2+y^2-z^2}{2xy}$

$\displaystyle cos\gamma=\frac{800^2+750^2-650^2}{2\cdot 800\cdot 750}$

$cos\gamma=0.65$

$\gamma=49.46^o$

The area can be found by

$\displaystyle A=\frac{1}{2}x.y.sin\gamma$

$\displaystyle A=\frac{1}{2}\cdot 800\cdot 750\cdot sin49.46^o$

$A=227980.26\ m^2$

8 0

2 years ago

Consider a set of 7500 scores on a national test whose score is known to be distributed normally with a mean of 510 and a standa

german

$\mathbb P(X>600)=\mathbb P\left(\dfrac{X-510}{85}>\dfrac{600-510}{85}\right)=\mathbb P(Z>1.059)\approx0.145$

So approximately 14.5% of the scores are higher than 600. This means in a sample of 7500, one could expect to see $0.145\times7500\approx10.86$ scores above 600.

5 0

2 years ago

Chester, the dog, loves to eat treats. He has eaten twice as many today as yesterday. He has eaten a total of 15 dog treats in b

stich3 [128]

Answer:

The equations are:

$T = 2Y$ and $T + 2Y = 15$

Step-by-step explanation:

Given

Represent bones eaten Today with T and yesterday with Y

Required

Write the equation

In the first statement, we have that:

$T = 2Y$

Reading further; In the second statement

$T + 2Y = 15$

Hence, the equations are:

$T = 2Y$ and $T + 2Y = 15$

Solving further:

Substitute 2Y for T in the second equation

$2Y + 2Y = 15$

$4Y = 15$

Divide both sides by 4

$Y = \frac{15}{4}$

$Y = 3.75$

Recall that

$T = 2Y$

$T= 2 * 3.75$

$T= 7.5$

7 0

1 year ago

Zucchini plants require 9 square feet around each plant.

MrRa [10]

The area of square TUVW = 3×3 = 9 square units

1 square unit = 4 head lettuces
9 square units = 9×4 = 36 lettuces

Area of plot QRST = length × width = 12×6 = 72 square units

36 vegetables for every 9 square units
We have 72÷9 = 8 lots of 9 square units

Total vegetable = 8 × 36 = 288 vegetables

We can have 8 different vegetables, each type can have 36 vegetables

4 0

2 years ago

23.7 – y when y = 10

sveta [45]

10.7
23.7-10=10
that r the maths

6 0

2 years ago

Read 2 more answers