A triangular bandana has an area of 70 square inches.The height of the triangle is 8 3/4 inches. Write and solve an equation to find the length of the base of the triangle.

Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

Step-by-step explanation:

Given  

Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]

and parabola passes through [tex]\left ( 4,3\right )[/tex]

Let us take a parabola of the form

[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]

And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]

therefore

[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]

Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola

[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]

[tex]a=\frac{25}{4}[/tex]

Thus Equation of parabola is

[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

Answrer

Option (a) is correct .

i.e  take 10% of $85

Reason

As given

15% and 10% on a $100 item i.e first applied 15 % discount on $ 100 and than apply 10% discount .

15 % is written in the decimal form

[tex]= \frac{15}{100}[/tex]

= 0.15

Amount becomes when 15 % discount on$100 = 100 - 0.15 × 100

                                                                              = 100 - 15

                                                                              = $ 85

Now apply 10 % discount on $ 85.

10 % is written in the decimal form

[tex]= \frac{10}{100}[/tex]

= 0.1

Amount becomes when 15 % discount on$100 = 85- 0.1 × 85

                                                                              = 85 - 8.5

                                                                              = $ 76.5

Therefore the option (a) is correct about the  successive discounts of 15% and 10% on a $100 item is $76.5 .

Answer:

B) -7x + 7y= -49

Step-by-step explanation:

Using the general equation for a line

y=mx+b

where m is the slope (positive if the line goes up from left to right and negative is it goes down from left to right)

and b is the point where the line crosses the y-axis

By th graph we can see that the line goes up from left to right, so the slope is positive, and that it crosses the y axis in -7, b= -7 and x is positive.

Solving for y in all the options

A) y = -x

B) y = x - 7

C) y = -x +7

D) y= x+7

the option that describes the line in the graph is B) -7x + 7y= -49 since when clearing for y we get y = x - 7 wich has a positive slope, and has an interception b = -7.

Answer:

the answer is 40 i had it on USATestPrep

Step-by-step explanation:

ion need one lml

Answer:

'a(t)=t^4-3t^(5/2)+2t'

The correct value of x is [tex]\frac{2}{3}[/tex].

To find the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex], follow these steps:

Cross-multiply to eliminate the fractions. Multiply 7 by (18x - 2) and 14 by (6x + 1):

7(18x - 2) = 14(6x + 1)

Expand both sides:

126x - 14 = 84x + 14

Move all terms involving x to one side and constant terms to the other side:

126x - 84x = 14 + 14

Simplify the equation:

42x = 28

Divide both sides by 42 to solve for x:

x = 28 ÷ 42 = [tex]\frac{2}{3}[/tex]

Therefore, the value of x is [tex]\frac{2}{3}[/tex] and the correct answer is option C.

Complete question: What is the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex]?

A. 0

B. 3

C. [tex]\frac{2}{3}[/tex]

D. [tex]\frac{1}{14}[/tex]

Answer:

Step-by-step explanation: 8 inches

Let's consider the equation of parabola, y = a·(x - α)·(x - β)

where α, β are the x-intercepts.

From the given graph, the y-intercept is (0, -3).

From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.

So the equation of parabola would be now, y = a·(x + 1)·(x - 3)

We can plug the y-intercept (0, -3) in the equation to find value of 'a'.

-3 = a·(0+1)·(0-3)

-3 = -3a

a = 1

So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3

Comparing it with y = ax² + bx + c

The x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]

the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.

Hence, vertex would be (1, -4).

a) For a 90% confidence interval: (117.838, 130.056)

b) For a 95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.

To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.

a) For a 90% confidence interval:

Sample mean = 123.947

Sample standard deviation = 11.669

Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]

90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)

b) For a 95% confidence interval:

Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]

95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval:

Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]

99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.

The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.

Answer:

The value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Step-by-step explanation:

It is given that an angle θ with the point (−20, −21) on its terminating side.

It means the right angle triangle is formed in third quadrant where length of the perpendicular is 21 and the base is 20.

According to the Pythagoras theorem,

[tex]hypotenuse^2=base^2+perpendicular^2[/tex]

[tex]hypotenuse^2=(20)^2+(21)^2[/tex]

[tex]hypotenuse^2=400+441[/tex]

[tex]hypotenuse^2=841[/tex]

Taking square root both the sides.

[tex]hypotenuse=\sqrt{841}[/tex]

[tex]hypotenuse=29[/tex]

In a right angled triangle,

[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]

[tex]\cos \theta=\frac{20}{29}[/tex]

θ lie in the third quadrant and cosine is negative in third quadrant.

[tex]\cos \theta=-\frac{20}{29}[/tex]

Therefore the value of cosine is [tex]\cos \theta=-\frac{20}{29}[/tex].

Answer:

the answer is 10

Answer:

The function has

2 real roots and

2 imaginary roots.