Mathematics, 31.07.2019 16:50 sophiaroeloffs4348

Apersonal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. a beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. an advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. which statement describes when the plans are based on the same number of aerobic exercise sessions? each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week. each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

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15s + 20a = 90reduces to 3s + 4a = 18
20s + 30a = 130reduces to 2s + 3a = 13

3s + 4a = 18multiply by -2
2s + 3a = 13multiply by 3

-6s - 8a = - 36 (result of multiplying by -2)
6s + 9a = 39 (result of multiplying by 3)
add
a = 3 <=== so there are 3 aerobic sessions

2s + 3a = 13
2s + 3(3) = 13
2s + 9 = 13
2s = 13 - 9
2s = 4
s = 4/2
s = 2 <=== there are 2 strength training sessions

so each plan uses 2 strength training sessions and 3 aerobic sessions

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

Answer from: Quest

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf =

pf = 6,25 u

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step-by-step explanation:

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Apersonal trainer designs exercise plans based on a combination of strength-training and aerobic exe...