Alinethatincludesthepoint(2, 7)has slope of 5 . what isitsequationin slope -intercept form

Adjust point D so the measure of angle BAD is equal to the measure of angle CAD. Which statements are true? Check all that apply

Otrada [13]

Answer with explanation:

it is given that ,in ΔABC,

∠BAD=20°, and ∠CAD=54°

We have to adjust point D,so that measure of angle BAD is equal to the measure of angle CAD.

that is, if point D is moved to right of B,then ∠BAD increases from 20° to (20+x)° and ∠CAD decreases from 54° to (54-x)°.

→20 +x=54-x

⇒ 2 x= 54 -20

⇒2 x=34

x=17°

Using angle bisector theorem, if AD bisects ∠B AC.

$\frac{BA}{AC}=\frac{BD}{DC}$

so,

If, ∠BAD=∠CAD=37°, then

1. AD bisects ∠B AC.→→→Option A

8 0

2 years ago

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a paint store has 35 gallons of paint in storage, 2/5 of which are for outdoor use. if each gallon cost $22, what is the total c

Likurg_2 [28]

$462
3/5 of 35 gallons = 21 gallons
21 gallons x $22 = $462

3 0

2 years ago

What is the multiplicative rate of change of the function described in the table ?

Vadim26 [7]

The answer to the question is B.

6 0

2 years ago

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A consumer is considering two different purchasing options for the car of their choice. The first option, which is leasing, is d

AVprozaik [17]

Answer:

y=250x+4000
y=400x+400

Step-by-step explanation:

Given that:

x represents the number of months of ownership; and
y represents the total paid for the car after ‘x' months.

First Option (Leasing)

250x - y + 4000 = 0

Expressing the equation in the Slope-Intercept Form y=mx+b, we have:

y=250x+4000

Second Option (Financing)

$400 for 0 months of ownership, (0,400), and $4400 for 10 months of ownership, (10, 4400).

First, we determine the slope of the line joining (0,400) and (10,4400)

$Slope, m= \dfrac{4400-400}{10-0}= \dfrac{4000}{10}=400$

We have:

y=400x+b

When y=400, x=0

400=400(0)+b

b=400

Therefore, the Slope-Intercept Form of the second option is:

y=400x+400

Significance

In the first option, there is a down payment of $4000 and a monthly payment of $250.
In the second option, there is a down payment of $400 and a monthly payment of $400.

Part B

We notice from the graph that after 24 months, the cost for leasing and financing becomes the same ($10,000). Therefore, a consumer will be better off financing since the downpayment for leasing is higher.

i.e

When x=0, y=$4000 for leasing
When x=0, y=$400 for financing

4 0

2 years ago

Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

astra-53 [7]

Answer:

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

Step-by-step explanation:

This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:

$x^{2} - 24 = 1$

Given that resulting expression is a second order polynomial of the form $x^{2} - a^{2}$ , there are two real and distinct solutions. Roots of the expression are:

$x_{1} = -5$ and $x_{2} = 5$ .

Now, it is also required to determine which part of the interval $(x_{1}, x_{2})$ is equal to a number greater than zero (positive). That is:

$x^{2} - 24 > 0$

$x^{2} > 24$

$x < -4.899$ and $x > 4.899$ .

Therefore, exists two sub-intervals: $[-5, -4.899]$ and $\left[4.899,5\right]$ . Besides, $x^{2} - 24 > y = 1$ in each sub-interval. The definite integral of the region between the two curves over the x-axis is:

$A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx$

$A = \int\limits^{-4.899}_{-5} {25-x^{2}} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} {25-x^{2}} \, dx$

$A = 25\cdot x \right \left|\limits_{-5}^{-4.899} -\frac{1}{3}\cdot x^{3}\left|\limits_{-5}^{-4.899} + x\left|\limits_{-4.899}^{4.899} + 25\cdot x \right \left|\limits_{4.899}^{5} -\frac{1}{3}\cdot x^{3}\left|\limits_{4.899}^{5}$

$A = 2.525 -2.474+9.798 + 2.525 - 2.474$

$A = 9.9\,units^{2}$

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

4 0

1 year ago