The lengths of the sides of a triangle are 3, 3, 32. Can the triangle be a right triangle?

Answer:

The coordinate of the wells are

[tex] (-4 -\sqrt[]{\frac{53}{2}}, 70+15\sqrt[]{\frac{53}{2}})[/tex]

[tex] (-4 +\sqrt[]{\frac{53}{2}}, 70-15\sqrt[]{\frac{53}{2}})[/tex]

Step-by-step explanation:

The y coordinate of the stream is given by [tex] y = 4x^2+17x-32[/tex]. Also, the y coordinate of the houses are determined by y=-15x+10. We will assume that the houses are goint to be built on the exact position where we build the wells. We want to build the wells at the exat position in which both functions cross each other, so we have the following equation

[tex] 4x^2+17x-32 = -15x+10[/tex]

or equivalently

[tex]4x^2+32x-42=0[/tex] (by summing 15x and substracting 10 on both sides)

Dividing by 2 on both sides, we get

[tex]2x^2+16x-21=0[/tex]

Recall that given the equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are

[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]

Taking a =2, b = 16 and c = -21, we get the solutions

[tex]x_1 = -4 -\sqrt[]{\frac{53}{2}}[/tex]

[tex]x_2 = -4 +\sqrt[]{\frac{53}{2}}[/tex]

If we replace this values in any of the equations, we get

[tex]y_1 = 70+15\sqrt[]{\frac{53}{2}}[/tex]

[tex]y_2 = 70-15\sqrt[]{\frac{53}{2}}[/tex]

Please see attached picture for full solution

Hope it helps

Good luck on your assignment

Step-by-step explanation:

4x+6x-8-12=10

10x-20=10

10x=10+20

10x=30

x=3

Answer:

x=3

Step-by-step explanation:

to find X first find the like terms

like terms: 4x and 6x

like terms: -12 and -8

combine the like the like terms

4x+6x=10x

-12-8=-20

10x-20=10

add 20 on both sides

10x-20+20=10+20

10x=30

divide both sides by 10

10x/10=30/10

x=3

ANSWER CHECK

substitute the variable

4(3) – 8 + 6(3) – 12 = 10

12-8+18-12

4+18-12

22-12 = 10

10=10

Answer:

We want to create sentences that are false (this means that the truth value is F

False ---> true: then the statement is false

true-----> false: then the statement is false.

For the first option we have:

"If the GCD of 5 and 12 is 1,____"

the left side is true, so the right side must be false:

"If the GCD of 5 and 12 is 1, then 12 is less than 5"

this means that the truth value is false, because the left side is true and the right side false.

For the second sentence we have:

The sum of 5 and 12 is 7 if and only if _______

The left side is false, so the right side must be true, the only true option is 12 is greater than 5, so the sentence is:

"The sum of 5 and 12 is 7 if and only if 12 is greater than 5."

Answer:

Step-by-step explanation:

5.) here no. of people represent frequencies, so modal group (the group with the highest frequency) is 0.25-0.50.

Estimated Mode = L + (( fm − fm-1) / ( (fm − fm-1) + (fm − fm+1) ) ) × w

where,

L is the lower class boundary of the modal group = 0.25

fm-1 is the frequency of the group before the modal group = 38

fm is the frequency of the modal group = 67

fm+1 is the frequency of the group after the modal group = 50

w is the group width = 0.25

mode= 0.25 + ((67-38)/((67-38)+(67-50)))* 0.25

= 0.25 + (29/ (29+17))*0.25

= 0.25 + 0.63*0.25

= 0.41

6) mean= total(fx) / total(f)

= 166.25/250

= 0.665

7) standard deviation = sqaure root (( total(fx2) - (total(f)* mean2)) / (total(f)-1))

= sqaure root (( 149.906 - 250* 0.6652)/ 249 )

= square root ( (149.906 - 110.556) /249)

= sqaure root (0.158)

= 0.397

8) The median is the middle value, which in our case is the 125 (250/2) , which is in the 0.5 - 0.75 group.

Estimated Median = L + ( ((n/2) − B)/G) × w

where:

L is the lower class boundary of the group containing the median = 0.5

n is the total number of values = 250

B is the cumulative frequency of the groups before the median group = 105

G is the frequency of the median group = 50

w is the group width = 0.25

median = 0.5 + (((250/2)-105)/50)*0.25

= 0.5 + ((125-105)/50)*0.25

= 0.5 + (20/50)*0.25

= 0.6

Complete Question

The complete question is shown on the first uploaded image

Answer:

The angle P is  [tex]P = 26^o[/tex]

Step-by-step explanation:

From the question we are told that

    The angle BD is  [tex]BD = 154^o[/tex]

Now looking at the diagram we can deduce that angle [tex]B \r CD = 180 ^o[/tex]

Now looking at line AD we see that it is tangent to the circle this implies that line CD is perpendicular to line AD

   So  we can also deduce that

            [tex]B \r C A + D \r C A = 180[/tex]

=>       [tex]D \r C A = 180 - 154[/tex]

=>       [tex]D \r C A = 26^o[/tex]

 Now total angle in a triangle is 180 so

        [tex]C\r DA + D\r A C + A \r C D = 180^o[/tex]

Now  [tex]D \r A C = 90^o[/tex]

So  

          [tex]D \r AC = 180 - (90 + 26)[/tex]

=>      [tex]P = D \r AC = 26^o[/tex]

Answer:

1761 square meters

Step-by-step explanation:no, thanks.

Answer:

$360

Step-by-step explanation:

If the company charges $30 for $500 in one month.

The interest they will be changing for a year = 30*12 = $360 interest.

It's just simple, multipling the the interest value by 12 to get it's annual interest value.

Answer:

256

Step-by-step explanation:

since the the path surounds both sides of the garden you have to add 2 x instead of just x

let me show you what i mean. 10=garden width and 3=path width=x

since it is a square, we can calculate the area by taking one side and squaring it so you get (10+2x)^2 which is 16^2 since x is 3, the width of the garden

to do simaler problems just use thei formula (garden length+2path length)^2 or (garden length+2path length)times(garden length+2path length)

Answer:

approximately $95.94375

Answer:

0.234

Step-by-step explanation:

Answer:

0.234

To convert from milliliters to liters, divide by 1,000.

234 ÷ 1,000 = 0.234

Step-by-step explanation:

Complete each statement.

? L = 234 mL

234/1000=0.234

There are 1000 milliliters in a liter, therefore dividing the milliliters by 1000 will give you the amount of liters. Liters = 0.234

RESULT

0.234L

Answer:

A

Step-by-step explanation:

I'm not sure if it's right though

Complete Question:

Football and Cognitive Percentile A recent study1 examined several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Percentile, which gives percentile on a cognitive reaction test. The regression line for predicting Percentile from Years is:

Percentile = 102 - 3.34(years)

1Singh R, et al., "Relationship of Collegiate Football Experience and Concussion with Hippocampal Volume and Cognitive Outcomes", JAMA, 311(18), 2014. Data values are estimated from information in the paper. Predict the cognitive percentile for someone who has played football for 11 years and for someone who has played football for 17 years. Enter the exact answers.

Answer:

cognitive percentile for someone who has played football for 11 years = 65.26

cognitive percentile for someone who has played football for 17 years = 45.22

Step-by-step explanation:

This is a very straight forward question. The regression line for predicting percentile from the number of years has been explicitly given in the question as:

Percentile = 102 - 3.34(years)

Therefore,

the cognitive percentile for someone who has played football for 11 years will be calculated as:

Percentile = 102 - 3.34(11)

Percentile = 102 - 36.74

Percentile = 65.26

the cognitive percentile for someone who has played football for 17 years will be calculated as:

Percentile = 102 - 3.34(17)

Percentile = 102 - 56.78

Percentile = 45.22

Answer:

$1,944.00

Step-by-step explanation:

Interest= Principal x Rate x Time (years)

Rate: 18%= 0.18

Interest= 5,400 x 0.18 x 2= $1,944

Answer:

19.9

Step-by-step explanation:

d = sqrt(6^2+19^2) = sqrt( 397) =. 19.9

Answer: 3:2

Step-by-step explanation:

Answer:

3/2 = 3:2

Step-by-step explanation:

15:10 = 15 /10 = 3/2. { dividing both numerator and denominator by 5}

Answer:

6 miles

Step-by-step explanation:

From the information given you can write the following equation:

x+y= 16 (1), where

x= April's distance

y= Blake's distance

You also have that Blake ran 4 miles farther than April which means that y= 4+x and you can replace this in the first equation and isolate x:

x+(4+x)= 16

x+4+x=16

2x=16-4

x=12/2

x= 6

According to this, the answer is that April ran 6 miles.

Answer:

Step-by-step explanation:

Answer: The constant of proportionality is r = 5.

Step-by-step explanation:

O, we know that x and y are proportional, this means that:

y = r*x

where r is the constant of proportionality.

we also have the table

x    y

7    35

12   60

20   100

Now, we can replace those values in our equation and get, for the first pair:

35 = r*7

r = 35/7 = 5

for the second pair:

60 = r*12

60/12 = 5 = r

So we can conclude that the constant of proportionality is 5.

Answer:

5

Step-by-step explanation:

It was right for me on khan

Answer:

Step-by-step explanation:

Hello!

To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:

Group 1: Ate healthy breakfast

X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.

n₁= 26

Group 2: Did not eat healthy breakfast

X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.

n₂= 20

After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:

p'₁= 0.50

p'₂= 0.40

The parameters of study are the population proportions, if the claim is true then p₁ > p₂

And you can determine the hypotheses as

H₀: p₁ ≤ p₂

H₁: p₁ > p₂

α: 0.05

[tex]Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }[/tex]≈N(0;1)

pooled sample proportion: [tex]p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46[/tex]

[tex]Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67[/tex]

p-value: 0.2514

The decision rule is:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.

At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.

So having a healthy breakfast doesn't seem to improve the grades of students.

I hope this helps!

Answer:

Inequalities are,

y ≥ 4x + 2

y ≥ 2

Step-by-step explanation:

Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).

Let the equation of this line is,

y = mx + b

Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

                      m = [tex]\frac{2+2}{1-0}[/tex]

                      m = 4

Y-intercept 'b' = -2

Equation of the line will be,

y = 4x - 2

Since shaded area is on the left side of this solid line so the inequality representing this region will be,

y ≥ 4x - 2

Another line is a solid blue line parallel to the x-axis.

Shaded region (blue) above the line will be represented by,

y ≥ 2

Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.

Answer:

Hence, the system of equation does not have solution.

Step-by-step explanation:

You have the following 2x2 system:

[tex]x-2y=1\ \ \ \ (1)\\\\-4x+8y=-4\ \ \ \ (2)[/tex]

You can obtain the solution to the system by using substitution method.

You solve the first equation for x:

[tex]x=1+2y[/tex]       (3)

Next, you replace (3) in the equation (2), and you solve for y:

[tex]-4(1+2y)+8y=-4\\\\-4-8y+8y=-4\\\\0=0[/tex]

The last result is the trivial solution. This means that the equation (2) is a multiple scale of the first equation. In fact, if you multiply equation (1) by -4, you obtain the equation (2).

Hence, the system of equations does not have solution.

Answer:

(3)(x+7)(x-1)

Step-by-step explanation:

3x^2+18x-21

Let's start by taking 3 out of the equation.

3(x^2+6x-7)

Now, when we factor, we need to find two numbers that add up to 6 and multiply to -7.

The numbers would be 7 and -1.

So the factored form of this would be:

(3)(x+7)(x-1)

Answer:

(2.4, -1)

Step-by-step explanation:

To find the midpoints of two points in the format (x,y), we find the mean for the values of x and y.

In this question:

(3.2, 2.5) and (1.6, -4.5)

Mean for the values of x:

(3.2 + 1.6)/2 = 2.4

Mean for the values of y:

(2.5 - 4.5)/2 = -1

Midpoint:

(2.4, -1)

Answer:

0.965925826

Step-by-step explanation:

Answer:

(pi6 + pi2)/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

g(6) = 3(6) + 3

      = 18+3

      = 21

Answer:

Confidence interval

[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]    

[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex]  

And the margin of error would be:

[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]

Step-by-step explanation:

For this case we have the followig dataset:

DATA: 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5

We can calculate the mean and the deviation with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 8.98[/tex

[tex]s = 1.29[/tex]

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=12-1=11[/tex]

The Confidence level is 0.95 or 95%, the value of significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.20[/tex]

Repplacing the info we got:

[tex]8.98-2.2\frac{1.29}{\sqrt{12}}=8.16[/tex]    

[tex]8.98+2.2\frac{1.29}{\sqrt{12}}=9.80[/tex]    And the margin of error would be:

[tex] ME=2.2\frac{1.29}{\sqrt{12}}=0.819[/tex]

The 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81

The dataset is given as:

[tex]\mathbf{x= 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5}[/tex]

Start by calculating the sample mean

This is calculated as:

[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]

[tex]\mathbf{\bar x= \frac{8.2+ 9.1+ 7.7+ 8.6+ 6.9+11.2+ 10.1+ 9.9+ 8.9+ 9.2+ 7.5+ 10.5}{12}}[/tex]

[tex]\mathbf{\bar x= \frac{107.8}{12}}[/tex]

[tex]\mathbf{\bar x= 8.98}[/tex]

Next, calculate the sample standard deviation

This is calculated as:

[tex]\mathbf{\sigma_x = \sqrt{\frac{\sum (x - \bar x)^2}{n-1}}}[/tex]

[tex]\mathbf{\sigma_x= \sqrt{\frac{(8.2 - 8.89)^2 +.......... + (10.5- 8.89)^2}{12 - 1}}}[/tex]

[tex]\mathbf{\sigma_x= 1.29}[/tex]

Calculate the degrees of freedom

[tex]\mathbf{df = n - 1}[/tex]

[tex]\mathbf{df = 12 - 1}[/tex]

[tex]\mathbf{df = 11}[/tex]

Calculate the significance level

[tex]\mathbf{\alpha /2=\frac{1 - 95\%}2 = 0.025}[/tex]

The critical value at [tex]\mathbf{\alpha/2 = 0.025}[/tex]  and df = 11 is:

[tex]\mathbf{t_{\alpha/2} = 2.20}[/tex]

Calculate the margin of error

[tex]\mathbf{E = t_{\alpha/2} \frac{\sigma}{\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{E = 2.20 \times \frac{1.29}{\sqrt{12}}}[/tex]

[tex]\mathbf{E = 0.81}[/tex]

The confidence interval is then calculated as:

[tex]\mathbf{CI =\bar x \pm E}[/tex]

So, we have:

[tex]\mathbf{CI = 8.98 \pm 0.81}}[/tex]

Split

[tex]\mathbf{CI = (8.98 - 0.81,8.98 + 0.81)}[/tex]

[tex]\mathbf{CI = (8.17,9.79)}[/tex]

So, the 95% confidence interval is [tex]\mathbf{ (8.17,9.79)}[/tex], and the margin of error is 0.81

Read more about confidence intervals and margin of errors at:

https://brainly.com/question/19426829

Answer: choice A

Step-by-step explanation:

the transposed matrix would be

5 3

2 -1

so

5*5+2*2=29

3*5+2*-1=13

5*3-2*-1=13

3*3+-1*-1=10

which gives us the answer

29 13

13 10

Range of data = [tex]\boxed{\sf{\red{Highest-lowest}}}\\[/tex]

Data = 1, 3 , 5 , 7 , 8 , 10 , 16 ,18 , 30, 35

Range = 35 - 1

Range of data is 34.