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3 years ago

10

3x-5y=13 x-2y=5 with solution by elimination.

1 answer:

Lisa [10]3 years ago

6 0

X=1 y=-2 I am sure I did it

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Which is the most specific taxonomic level in the classification system above?

scoray [572]

Answer:

Primates

Step-by-step explanation:

It is the most specific because homo, hominidae and O sapiens fall under the catogory of primates

8 0

3 years ago

Please help me with these calculus bc questions

zhannawk [14.2K]

4. Compute the derivative.

$y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1$

Find when the gradient is 7.

$4x - 1 = 7 \implies 4x = 8 \implies x = 2$

Evaluate $y$ at this point.

$y = 2\cdot2^2-2-1 = 5$

The point we want is then (2, 5).

5. The curve crosses the $x$ -axis when $y=0$ . We have

$y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4$

Compute the derivative.

$y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}$

At the point we want, the gradient is

$\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}$

6. The curve crosses the $y$ -axis when $x=0$ . Compute the derivative.

$\dfrac{dy}{dx} = 3x^2 - 4x + 5$

When $x=0$ , the gradient is

$\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}$

7. Set $y=5$ and solve for $x$ . The curve and line meet when

$5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92$

Compute the derivative (for the curve) and evaluate it at these $x$ values.

$\dfrac{dy}{dx} = 4x + 7$

$\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}$

$\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}$

8. Compute the derivative.

$y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b$

The gradient is 8 when $x=2$ , so

$2a\cdot2 + b = 8 \implies 4a + b = 8$

and the gradient is -10 when $x=-1$ , so

$2a\cdot(-1) + b = -10 \implies -2a + b = -10$

Solve for $a$ and $b$ . Eliminating $b$ , we have

$(4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}$

so that

$4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}$ .

5 0

2 years ago

puteri [66]

Answer:

<u>Given:</u>

DC ║ AB
CM = MB as M is midpoint of BC

i) <u>Since DN and BC are transversals, we have:</u>

∠DCM ≅ ∠NBM and
∠CDM ≅ ∠BNM as alternate interior angles

<u>As two angles and one side is congruent, the triangles are also congruent:</u>

ΔDCM ≅ ΔNBM (according to AAC postulate)

So their areas are same.

ii)

<u>The quadrilateral has area of:</u>

A(ADCB) = A(ADMB) + A(DCM)

<u>And the triangle has area of:</u>

A(ADN) = A(ADMB) + A(NBM)

Since the areas of triangles DCM and NBM are same, the quadrilateral ADCB has same area as triangle ADN.

5 0

3 years ago

Read 2 more answers

Write the standard form of the equation of the line passing through the point (-4,1) and perpendicular to the line

notka56 [123]

Answer:

all work is shown/pictured

5 0

3 years ago

In a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man cl

Diano4ka-milaya [45]

Answer:

Step-by-step explanation:

Given that in a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less.

The sample size n = 80

no of wells less than 100 feet deep=27

Sample proportion = $\frac{27}{80} =0.3375$

a) Create hypotheses as

$H_0: p = 0.30\\H_a: p >0.30\\$

(Right tailed test)

p difference $= 0.3375-0.30 = 0.0375$

Std error of p = $\sqrt{\frac{0.3(0.7)}{80} } =0.0512$

b) Assumptions: Each trial is independent and np and nq >5

c) Z test can be used.

Z= p diff/std error = $\frac{0.0375}{0.0512} =0.73$

p value = 0.233

d) p value is the probability for which null hypothesis is false.

e) Conclusion: Since p >0.05 we accept null hypothesis

there is no statistical evidence which support the claim that more than 30% are drilled.

3 0

3 years ago