1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ronch [10]
2 years ago
15

Please help me with this!!!!

Mathematics
2 answers:
Ne4ueva [31]2 years ago
5 0

Answer:

\large\text{Slope AB}\ =-\dfrac{3}{2}}

\large\text{R(4, -7)}

Step-by-step explanation:

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points A(-6, 8) and B(-2, 2). Substitute:

m=\dfrac{2-8}{-2-(-6)}=\dfrac{-6}{-2+6}=\dfrac{-6}{4}=-\dfrac{3}{2}

The hypotenuse of triangle QRS is on the same line as the hypotenuse of triangle ABC. Therefore the line QR has the same slope as the line AB.

We have Q(2, -4) and R(x, y). Substitute to the formula of a slope:

\dfrac{-4-y}{2-x}=-\dfrac{3}{2}                   <em>cross multiply</em>

-2(-4-y)=3(2-x)              <em>use distributive property</em>

8+2y=6-3x            <em>subreac 8 from both sides</em>

2y=-2-3x           <em>divide both sides by 2</em>

y=-\dfrac{3}{2}x-1\qquad\boxed{(*)}

The hypotenuse of triangle QRS is one-half the length of AB.

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Calculate the distance between A and B:

|AB|=\sqrt{(-2-(-6))^2+(2-8)^2}=\sqrt{4^2+(-6)^2}=\sqrt{16+36}=\sqrt{52}\\\\=\sqrt{4\cdot13}=\sqrt4\cdot\sqrt{13}=2\sqrt{13}

Therefore

|RQ|=\dfrac{2\sqrt{13}}{2}=\sqrt{13}

Substitute coordinates of the point R(x, y) and Q(2, -4) to the formula of a distance between two points:

\sqrt{(2-x)^2+(-4-y)^2}=\sqrt{13}\to(2-x)^2+(-4-y)^2=13\qquad\boxed{(**)}

Substitute \boxed{(*)} to \boxed{(**)}:

(2-x)^2+\left[-4-\left(-\dfrac{3}{2}x-1\right)\right]^2=13\\\\(2-x)^2+\left(-4+\dfrac{3}{2}x+1\right)^2=13\\\\(2-x)^2+\left(\dfrac{3}{2}x-3\right)^2=13\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\2^2-2(2)(x)+x^2+\left(\dfrac{3}{2}x\right)^2-2\left(\dfrac{3}{2}x\right)(3)+3^2=13\\\\4-4x+x^2+\dfrac{9}{4}x^2-9x+9=13\qquad\text{combine like terms}\\\\\left(\dfrac{4}{4}x^2+\dfrac{9}{4}{x^2}\right)+(-4x-9x)+(4+9)=13\\\\\dfrac{13}{4}x^2-13x+13=13\qquad\text{subtract 13 from both sides}

\dfrac{13}{4}x^2-13x+13=13\qquad\text{subtract 13 from both sides}\\\\\dfrac{13}{4}x^2-13x=0\qquad\text{divide both sides by 13}\\\\\dfrac{1}{4}x^2-x=0\\\\x\left(\dfrac{1}{4}x-1\right)=0\iff x=0\ \vee\ \dfrac{1}{4}x-1=0\\\\\dfrac{1}{4}x-1=0\qquad\text{add 1 to both sides}\\\\\dfrac{1}{4}x=1\qquad\text{multiply both sides by 4}\\\\x=4\\\\\boxed{x=0\ \vee\ x=4}

Put the values of x to \boxed{(*)}

x=0\\\\y=-\dfrac{3}{2}(0)-1=0-1=-1\to(0,\ -1)\\\\x=4\\\\y=-\dfrac{3}{2}(4)-1=-3(2)-1=-6-1=-7\to(4,\ -7)

As the triangle ABC and the QRS triangle are similar, then AB corresponds to QR not RQ. Thus, the coordinates of the R point are (4, -7).

Look at the picture.


Len [333]2 years ago
3 0

Answer:

Slope AB = -3/2

R = (4, -7)


Step-by-step explanation:

AB (-6 , 8) and (-2 , 2)

Slope AB = (8 - 2) /(-6 + 2) = 6/-4 = -3/2

Triangle QRS , QR is half of AB, same orientation and given Q (2 , -4)  so R = (4, -7)


You might be interested in
Convert 6 4/9 into a decimal
Gennadij [26K]
The answer is 6.444 and repeat
8 0
3 years ago
Read 2 more answers
The chamber of commerce of a Florida Gulf Coast community advertises that area residential property is available at a mean cost
Alja [10]

Answer:

a) In the step-by-step explanation.

b)  The null and alternative hypothesis are:

H_0: \mu=125000\\\\H_a:\mu> 125000

c) P-value = 0.015

d) The conclusion, at a level of significance of 0.05, is that there is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.

e) The claim of the chamber of commerce is false. We have statistical evidence against that claim and we can conclude that the mean prices are significantly higher than $125,000.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim, expressed in the alternative hypothesis, is that area residential property is available at a mean cost significantly higher than $125,000 per lot.

Then, the null and alternative hypothesis are:

H_0: \mu=125000\\\\H_a:\mu> 125000

The significance level is 0.05.

The sample has a size n=32.

The sample mean is M=130000.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12500.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12500}{\sqrt{32}}=2209.71

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{130000-125000}{2209.71}=\dfrac{5000}{2209.71}=2.26

The degrees of freedom for this sample size are:

df=n-1=32-1=31

This test is a right-tailed test, with 31 degrees of freedom and t=2.26, so the P-value for this test is calculated as (using a t-table):

\text{P-value}=P(t>2.26)=0.015

As the P-value (0.015) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.

6 0
3 years ago
A circle is centered on point B, Points A, C and D lie on its circumference. if ABC measures 122 degrees, what does ADC measures
iren2701 [21]

Answer:

61°

Step-by-step explanation:

Angle extended to the circumference is half the angle at the centre

ADC = ½ ABC = ½ × 122 = 61

5 0
3 years ago
At a football stadium, 20% of the fans in attendance were teenagers. If there
valina [46]

Answer:cgffffffffh

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Help me pleasseeeee!!! its about algebraic properties of limits!
s2008m [1.1K]

\text{Hello there! :)}

3. \sqrt{2} \\\\\text{4.  0}\\\\\text{5.  dne}

\text{To find the overall limit, they must approach the same y-value from each side:}

\\\\3.  \lim_{x \to \frac{\pi }{4} } 2sinx ={\sqrt{2}

\text{Therefore:}\\\\3.  \lim_{x \to \frac{\pi }{4} } f(x)= {\sqrt{2} }

\text{For this question, evaluate the limit from the RIGHT-HAND side:}\\\\4.   \lim_{x \to \pi +} f(x)\\\\ \text{Use the equation tanx to evaluate since it involves values greater than \pi:}\\\\

\lim_{x \to \pi +} tanx = 0\\\\\text{So:}\\\\ \lim_{x \to \pi +} f(x) = 0

5.  \\\\\text{Evaluate the overall limit. Make sure both sides approach the same y=value:}\\\\ \lim_{x \to \pi } 2cosx= -2\\\\ \lim_{x \to \pi } tanx = 0\\\\ \text{ Therefore:}\\ \lim_{x \to \pi } f(x) = dne \text{ (Does not exist})

5 0
3 years ago
Other questions:
  • I really need help. I don't get this.
    6·2 answers
  • The square root of 128 times r to the power or three​
    6·1 answer
  • Solve the following system of equation graphically 2x+y=-1 and x+2y=4
    5·1 answer
  • A sample of weights of defensive tackles on Big 10 football teams are: Johnson, 202 pounds; Patrick, 215 pounds; Junior, 207 pou
    11·1 answer
  • (3x+4y= 10)<br> (2x+3y=7)<br> Using elimination
    10·1 answer
  • Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor?
    12·2 answers
  • In which place should you write the first digit of the quotient 4,085 ÷ 61?
    10·2 answers
  • Which expression is equivalent to a^m + a^n? A, a^m - n B, a^m+n. C, a^m • n d, a^m (divided by) n
    8·1 answer
  • 5. Which situation is NOT represented by the equation shown below?
    9·1 answer
  • PLEASE ASAP, DONT LIE ABOUT THE ANSWER, I'LL KNOW.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!