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fomenos
7 days ago
9

Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?

Mathematics
2 answers:
babunello [11.8K]7 days ago
7 0
For solutions to exist, the equations need to be equal to one another. Thus, we can represent it as y=y, which implies:

x^2+2x-3=x-1 we subtract x from both sides

x^2+x-3=-1 then, we add 1 to both sides

x^2+x-2=0 proceed by factoring

(x+2)(x-1)=0, leading to two solutions:

x=-2 and 1; to obtain the corresponding y values, we can apply y=x-1

y(-2)=-3 and y(1)=0, so the solutions are represented as the points:

(-2,-3) and (1,0)
lawyer [12.5K]7 days ago
6 0
The intersection points of the given system of equations, y = x² + 2x – 3 and y = x – 1, are B. (–2, –3) and (1, 0). The

Discriminant of a quadratic equation ( ax² + bx + c = 0 ) is determined using the formula:

D = b² - 4 a c. The value of the Discriminant indicates the number of solutions as follows:

D < 0 → No Real Roots

D = 0 → One Real Root D > 0 → Two Real Roots. Now, let's solve the problem!

To find solutions for the above equations, we can apply the substitution method:

y = y Setting each equation to zero gives us (x + 2) = 0 or (x - 1) = 0

. Thus, we find: x = -2 or x = 1. For x = -2:

the result is ( -2, -3 )

. When x = 1:

the outcome is ( 1, 0 )

.

Learn more about Solving Quadratic Equations by Factoring and Determining the Discriminant.
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A psychologist is collecting data on the time it takes to learn a certain task. For 50 randomly selected adult subjects, the sam
zzz [12365]

Response: (15.263,\ 17.537)

Step-by-step analysis:

Based on the information provided, we note

Sample size: n= 50

\overline{x}=16.40

s=4.00

Given that the population standard deviation is not known, a t-test is employed.

Critical value for the 95 percent confidence interval:

t_{n-1,\alpha/2}=t_{49, 0.025}= 2.009575\approx2.010

Confidence interval: \overline{x}\pm t_{n-1, \alpha/2}\dfrac{s}{\sqrt{n}}

16.40\pm (2.010)\dfrac{4}{\sqrt{50}}\\\\=16.40\pm1.13702770415\\\\=16.40\pm1.1370\\\\=(16.40-1.1370,\ 16.40+1.1370)\\\\=(15.263,\ 17.537)

Required 95% confidence interval: (15.263,\ 17.537)

8 0
16 days ago
Max wants to start a farm to grow mussels. He needs to determine the best environment for growing them. He is going to try two d
Leona [12618]

Response:

1.) Subjects = 18 aquariums, each containing mussels

2.) Factors (levels) = temperature (3 levels) and salinity (2 levels)

3.) Treatments include: High salinity at high temperature; High salinity at low temperature; High salinity at medium temperature; Low salinity at low temperature; Low salinity at high temperature; Low salinity at medium temperature.

4.) Response variable = size of mussel produced

5.) Implementing random assignment minimizes the risk of bias and confounding variables.

6.) For replication purposes, every one of the six treatments could be applied to 3 tanks, thus having 3 aquariums designated for each treatment.

7.) This arrangement might introduce a potential location-based effect that could skew the results of our study, thus resulting in a false relationship.

8.) A control experiment with no salt added is not viable since mussels require salt for survival.

Step-by-step explanation:

Responses are explanatory.

4 0
1 month ago
Determine if each scenario is either a permutation or combination. Do NOT solve these scenarios. a) An art gallery displays 125
PIT_PIT [12445]

Answer:

a) Permutaciones

b) combinaciones

Step-by-step explanation:

a)

Dado que el orden de las 15 obras de arte más importantes es relevante, comenzando por la más popular y luego las que ocupan los lugares 2, 3, 4, y así sucesivamente. Cuando nos ocupamos del "orden de colocación", el tema se refiere a permutaciones.

b)

De un total de 320 obras, se deben "seleccionar" 125 para ser exhibidas, el proceso de selección implica combinaciones en las que el orden de la selección no importa.

3 0
1 month ago
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), c
AnnZ [12381]

Answer: F(x) > 0 in the ranges (-0.7, 0.76) and (0.76, ∞).

I hope this is useful:)

5 0
23 days ago
Read 2 more answers
Which statement about the lines below is true?
tester [12383]
I affirm that all of these statements are correct.
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