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3 years ago

Find the nonpermissible replacement for y in the expression y-3/y+3

Mathematics

1 answer:

Nastasia [14]3 years ago

7 0

Answer:

The nonpermissible replacement of the variable y is -3

Step-by-step explanation:

The nonpermissible replacement of the variable in a certain expression is the value of the variable that will make the denominator of the expression zero.

The expression $\dfrac{y-3}{y+3}$ has the denominator $y+3.$

This denominator cannot be equal zero, thus,

$y+3\neq 0,\\ \\y\neq -3.$

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3 groups of students went to the burger barn for a study break and snack. the first group ordered 4 burgers, 5 fries, and 7 drin

lora16 [44]

Answer:

Cost of one burger, a = $3.35

Cost of one fries, b = $0.9

Cost of one drink, c = $1.1

Step-by-step explanation:

Let

a be cost of one burger

b be the cost of on fry

c be the cost of on drink

So for the 1st group, 4a+5b+7c = $25.60 -----------(1)

for the 2st group, 8a+5b+6c = $37.90 ----------(2)

for the3st group, 12a+10b+11c = $61.30 ----------(3)

Now solving (1) and (2)

That is (1) x 2 - (2) gives,

5b+8c = 13.80 ----------------------(4)

Now, (1) x 3 - (3), we get

5b+10c = 15.5 ---------------------(5)

Solving (4) and (5), we get

c = 1.1

Now putting c in equation (4), we get

b = 0.9

Now from (1), we get

4a+5b+7c = $25.60

4a+5(0.9)+7(1.1) = $25.60

a = 3.35

Cost of one burger, a = $3.35

Cost of one fries, b = $0.9

Cost of one drink, c = $1.1

7 0

3 years ago

Work out the gradient of the straight line that passes through (2,6) and (6,12)

Furkat [3]

Answer:

The gradient of the straight line that passes through (2, 6) and (6, 12) is $m = \frac{3}{2}$ .

Step-by-step explanation:

Mathematically speaking, lines are represented by following first-order polynomials of the form:

$y = b + m\cdot x$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$m$ - Slope.

$b$ - Intercept.

The gradient of the function is represented by the first derivative of the function:

$y' = m$

Then, we conclude that the gradient of the staight line is the slope. According to Euclidean Geometry, a line can be form after knowing the locations of two distinct points on plane. By definition of secant line, we calculate the slope:

$m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}$ (2)

Where:

$x_{A}$ , $y_{A}$ - Coordinates of point A.

$x_{B}$ , $y_{B}$ - Coordinates of point B.

If we know that $A(x,y) = (2,6)$ and $B(x,y) = (6,12)$ , then the gradient of the straight line is:

$m = \frac{12-6}{6-2}$

$m = \frac{6}{4}$

$m = \frac{3}{2}$

The gradient of the straight line that passes through (2, 6) and (6, 12) is $m = \frac{3}{2}$ .

5 0

3 years ago

A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what

Elena L [17]

Answer:

The probability that the pitcher throws exactly 8 strikes out of 15 pitches is approximately 0.199

Step-by-step explanation:

The given probability that the pitcher throws a strike, p = 0.507

The number of pitches thrown by the pitcher = 15 pitches

The probability that the pitcher does not throw a strike, q = 1 - P

∴ q = 1 - 0.507 = 0.493

By binomial theorem, we have;

$P(X = r) = \dbinom{n}{r}p^{r} \cdot q^{n-r}= \dbinom{n}{r}p^{r} \cdot \left (1-p \right )^{n-r}$

When X = r = 8, and n = 15, we get;

The probability that the pitcher throws exactly 8 strikes out of 15 pitches, P(8), is given as follows

P(8) = ₁₅C₈ × 0.507⁸ × (1 - 0.507)⁽¹⁵ ⁻ ⁸⁾ = 6,435 × 0.507⁸ × 0.493⁷ ≈ 0.199

8 0

3 years ago

Find the sum of the first 6 terms in the sequence -5 -25 -125 -625

sashaice [31]

This is a geometric sequence, so use the formula for the sum of a geometric sequence:
Sum = (a(r^n - 1))/(r - 1)
where a is the first term, -5
r is the common ratio, 5
and n is the number of terms

Thus,
Sum = ((-5)(5^6 - 1))/(5-1) = -19530

5 0

3 years ago

Write 1.48 repeating as a mixed number as a mixed number

andrew-mc [135]

$1.48=1+0.48=1+\dfrac{48}{100}=1+\dfrac{48:4}{100:4}=1+\dfrac{12}{25}=\boxed{1\frac{12}{25}}$

4 0

3 years ago