Therefore, any point on the perpendicular bisector of a segment is the same distance from each endpoint. Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
find the nature of the roots of the roots of the equation (x-705)(x-795)+800(x-750)(x-835)=0.
(A) Imaginary roots.
(B) Real and distinct.
(C) Real and equal.
(D) None.
Answer:
B
Step-by-step explanation:
If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.
These roots are real and distinct, or choice B.
If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.
I hope that helps!
3. Find f(5)+j(-2) if f(x)=12-3x and j(x)=x² + 4x - 1.
HELP ME PLEASEEEE
The value of the expression f(5) + j(-2) is -8 where f(x)=12-3x and j(x)=x² + 4x - 1
How to solve the equation?The expression is given as:
f(5) + j(-2)
Where f(x)=12-3x and j(x)=x² + 4x - 1
Calculate f(5) and j(-2)
f(5)= 12 - 3(5) = -3
j(-2) = (-2)² + 4(-2) - 1 = -5
So, we have:
f(5) + j(-2) = -3 - 5
Evaluate
f(5) + j(-2) = -8
Hence, the value of the expression f(5) + j(-2) is -8
Read more about function expressions at:
https://brainly.com/question/13136492
#SPJ1
Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54.
what is the first term of the sequence?
to get to the next term, you would_____
this is a _____ sequence
there are 27 weeks left in this school year for monique. if she continues getting coffee at this rate how much money will she have spent on coffee by the end of the year?
If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
Tₙ = a + (n-1)d
(for all positive integer values of n)
Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,
4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........
Therefore,
The first term of the sequence is 4.54, To get the next term you need to add 4.54. This is an arithmetic sequence.Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,
a₃₆ = 4.54 + (36-1)4.54
a₃₆ = 163.44
Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
Learn more about Arithmetic sequence:
https://brainly.com/question/3702506
#SPJ1
The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334
3
3
4
inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 514
5
1
4
inches apart on the map. The scale on the map is 12
1
2
inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville? Enter your answer in the box.
Answer:
282.7miles
Step-by-step explanation:
334+514=848inch
12inch=4miles
848inch=x
[tex]x = \frac{818 \times 4}{12} = 282.7[/tex]
Total distances in miles
334+514848inchesNow 12 in =4mi
3in=1mi
Total miles
848/3282.7miPlease!!! Help!!! Brainliest of Right! it goes as 50 point in the end but i used 100 point if you help me i will help you!!
Answer:
2. 3.913 kg (3 dp)
3. light cream
4. 240 CoffeeStops
5. 7 CoffeeStops per square mile
6. 2,861 cups of coffee each day
Step-by-step explanation:
Given:
Skim milk density at 20 °C = 1.033 kg/lLight cream density at 20 °C = 1.012 kg/l1 liter = 0.264 gallonsQuestion 2
[tex]\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}[/tex]
Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)
---------------------------------------------------------------------------------------------
Question 3
Given:
Volume of liquid = 9 litersMass of liquid = 9.108 kg[tex]\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}[/tex]
Therefore, the container holds light cream.
---------------------------------------------------------------------------------------------
Question 4
Given:
15 CoffeeStops per 100,000 peoplePopulation of Manhattan ≈ 1,602,000 people[tex]\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}[/tex]
Therefore, there are 240 CoffeeStops.
---------------------------------------------------------------------------------------------
Question 5
Given
Manhattan ≈ 34 square miles[tex]\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}[/tex]
Therefore, the density of CoffeeStops is 7 per square mile.
---------------------------------------------------------------------------------------------
Question 6
Given:
Each person buys 3 cups of coffee per week[tex]\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}[/tex]
Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.
Please answer !!!!!!!
The measure of all the angles is given below:
angle 1= 30
angle 2= 150
angle 3= 30
angle 4= 150
angle 5= 30
angle 6= 150
angle 7= 30
angle 8= 73.5
What is angle?
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
As,
angle 1= 30 (Vertically opposite angle)
angle 7= 30 (corresponding angle)
angle 4+30= 180 (linear pair)
angle 4= 150
angle 4= angle 2= 150 (Vertically opposite angle)
angle 2= angle 6= 150 (corresponding angle)
angle 1= angle 5= 30 (corresponding angle)
angle (2x+3)= angle 4 (corresponding angle)
2x+3= 150
x= 73.5
Lean more about angle here:
https://brainly.com/question/13954458
#SPJ1
|2x -8| < 2
a. 3
b. -5
c. x>5 or x<3
d. x>-3 or x<-5
Answer:
[tex]3 < x < 5[/tex]
Step-by-step explanation:
Given inequality:
[tex]|2x - 8| < 2[/tex]
[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]
[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]
[tex]\implies -2 < 2x-8 < 2[/tex]
Therefore:
[tex]\implies -2 < 2x-8[/tex]
[tex]\implies 6 < 2x[/tex]
[tex]\implies 3 < x[/tex]
And:
[tex]\implies 2x-8 < 2[/tex]
[tex]\implies 2x < 10[/tex]
[tex]\implies x < 5[/tex]
Merge the overlapping intervals: [tex]3 < x < 5[/tex]
Proof
Graph: [tex]y=|2x-8|[/tex]
Add a line at [tex]y=2[/tex]
The interval that satisfies [tex]|2x - 8| < 2[/tex] is the area under the points of intersection (shaded area on the attached graph).
The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.
So
Case-1
2x-8<22x<2+82x<10x<5Case-2
2x-8>-22x>6x>3So solution is
3<x<5How many solutions does the equation below have? 1/(-6-8x) = -3- 1x
Answer:
This equation has 2 solutions.
1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]
2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the given inequality are
–6x + 15 < 10 – 5x
and
A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options
Solving inequalityFrom the question, we are to solve the inequality
The given inequality is
–3(2x – 5) < 5(2 – x)
First, clear the brackets
–6x + 15 < 10 – 5x
NOTE: This is one of the correct representations of the inequality
Collect like terms
-6x + 5x < 10 - 15
-x < -5
Divide both sides by -1 and flip the sign
x > 5
Representing this on a number line, we get a number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right.
Hence, the correct representations of the given inequality are
–6x + 15 < 10 – 5x
and
A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options
Learn more on Inequalities here: https://brainly.com/question/246993
#SPJ1
the table below shows the cost of downloading songs from an online music store.
Answer:
I believe it's c because Greg downloaded 5 song which is 6.45 total then bought certain song at sale price Wich ended at 9.42
Which one of these points lies on the given circle
O (-2.5, -2.5)
O (1, 3)
O (2, - √5)
O (-√3, -√7)
Step-by-step explanation:
every point on the circle has the same distance from the center : r (radius).
we can see that radius right there on the x-axis : the distance of (3, 0) to (0, 0) is simply 3. that is our radius.
the distance formula is applied Pythagoras
distance² = (difference in x coordinates)² +
+ (difference in y coordinates)²
distance = sqrt( ... )
so,
(-2.5, - 2.5)
(-2.5 - 0)² + (-2.5 - 0)² = 6.25 + 6.25 = 12.5
that is not 3² = 9, so the point is NOT on the circle.
(1, 3)
(1 - 0)² + (3 - 0)² = 1 + 9 = 10
that is not 3² = 9, so the point is NOT on the circle.
(2, -sqrt(5))
(2 - 0)² + (-sqrt(5) - 0)² = 4 + 5 = 9
that IS 3² = 9, so, the point IS on the circle.
(-sqrt(3), -sqrt(7))
(-sqrt(3) - 0)² + (-sqrt(7) - 0)² = 3 + 7 = 10
that is not 3² = 9, so the point is NOT on the circle.
Can someone please help me? I put the answer at 47.1 but it says it's wrong.
Answer:
47.14 cm
Step-by-step explanation:
Circumference :
π x diameterπ x 1515π15 x 22/7330/747.14 cm (approximately)Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation?
A. 0.75x = 0.8(x + 10)
B. 0.75(x + 10) + 0.8x = 101
C. 0.75x + 0.8x + 10 = 101
D. 0.75x + 0.8(x + 10) = 101
Jared attempted ____ shots.
Zach attempted ____ shots.
Answer: the other person is correct
20 POINTS + BRAINLY Complete the table.
52, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, 72
Interval Frequency
50-54 2
55-59
60-64
65-69
70-74
The frequency of the data set that matches with the interval stated are:
50 - 54: 2
55 - 59: 6
60 - 64: 7
65 - 69: 3
70 - 74: 2
What is a Frequency?Frequency is the number of times a data point or a set of points within an interval appears often in a data set.
The corresponding frequency to each of the interval given for the data would be as follows:
50 - 54: 2
55 - 59: 6
60 - 64: 7
65 - 69: 3
70 - 74: 2
Learn more about the frequency of a data on:
https://brainly.com/question/15422753
#SPJ1
What are the roots of the equation 9x^2-6x+2=0 in simplest a+bi form?
Answer:
Step-by-step explanation:
In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen to the number of sophomores (F:S), and what ratio compares the number of sophomores to the number of freshmen (S:F)
Answer:
Freshmen to sophomores - (17:19)
Sophomores to freshmen - (19:17)
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
(72 divided by 8-x2x3+1 plese help
Answer:
[tex]\frac{72}{-x^{5} +9}[/tex]
Step-by-step explanation:
Let me know if that is not the same equation you wrote and if you have any questions !!
somebody please help me
Answer:
66°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in a triangle is 180°.
__
79° +x +35° = 180°
x = 180° -114° . . . . . . . . subtract 114° from both sides
x = 66° . . . . . simplify
Question 9 of 9
Which of the expressions are equivalent to the one below? Check all that
apply.
(15.3)-20
A. (3.15)-20
B. 20-(3.15)
C. 6 (15-20)
D. (3-20) (15-20)
Daniel has read 10% of a book. He has 45 more pages to finish. How many pages are there in the book?
Answer:
He read 10% of the book, so 90% remains to be read. That 90% consists of 45 pages, so
45=0.90n
n= 45/0.90
n=50
There are 50 pages total in the book
Step-by-step explanation:
Simplify the expression |1/12 - 5/6| - (2/5 + 1/10)
Answer:
x+2
Step-by-step explanation:
x^2+x-7 = x+2
Answer:
The answer is 1/4!!
<3 love
if f(x)= 3x -2, find f-1(x)
Answer: 1/3x + 2/3
Step-by-step explanation:
f(x)= 3x - 2 =>
y= 3x - 2 =>
x= 3y - 2 =>
3y - 2= x =>
3y= x + 2 =>
y= 1/3x + 2/3 =>
f-1(x)=1/3x + 2/3
What is the name of the red dot located on the curve of the parabola below?
O A. Center
B. Focus
C. Vertex
D. Directrix
C. Vertex (x,y). The vertex is right in the middle of the quadratic graph.
BRAINLIEST if correct + small explanation
Find the area of this rectangle.
11M 9M
Answer: 99M
Step-by-step explanation:
Rectangle area
A=LW
A = 11 x 9
A = 99
Mark as brainliest please TT. Thank you :D
Answer:
99 m
Step-by-step explanation:
width times length = area
11 ×9= 99m
12. Round 2,870 to the nearest hundred.
Answer:
2900
Step-by-step explanation:
2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.
Help help help help help help help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Help
Answer:
-2
Step-by-step explanation:
For a straight-line graph, pick two points on the graph.
The gradient of the line = (change in y-coordinate)/(change in x-coordinate)
(x, y)
Point 1: (2, 0)
Point 2: (3, 2)
Gradient = (change in y)/(change in x)
= (2 - 0) / (3 - 2)
= 2 / 1
= 2
Note: gradient is basically slope where slope = rise / run
Answer:
help has arrived its -2
Step-by-step explanation:
m=p-2b/2
p=57.4
b=8.7
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
What is the value of m?Given that;
m = ( p-2b ) / 2p = 57.4b = 8.7Value of m = ?First, we substitute the value of p and b into the equation.
m = ( p-2b ) / 2
m = ( 57.4 - 2(8.7) ) / 2
m = ( 57.4 - 17.4 ) / 2
m = 40 / 2
m = 20
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
Learn more about equations here: brainly.com/question/14686792
#SPJ1
A teacher has a large container of blue, red, and green beads. she reports to the students that the proportion of blue beads in the container is 0.30. the students feel the proportion of blue beads is lower than 0.30. a student randomly selects 60 beads and finds that 12 of the beads are blue. the p-value for the test of the hypotheses, h0:p=0.30 and ha:p<0.30, is 0.045. what is the correct interpretation of this value?
The interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.
What is a null hypothesis?It should be noted that the null hypothesis simply means a statical theory that suggests that there's no relationship between the variables given in the data set.
From the information given, it was stated that the proportion of blue beads in the container is 0.30. Here, the interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.
Learn more about hypothesis on:
brainly.com/question/11555274
#SPJ1
How many inches are in 12 feet?
Answer:
144 inches in 12 feet.
Step-by-step explanation:
There are 12 inches in 1 foot.
Find inches when you have 12 ft.
[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]
Feet cancel out leaving inches.
There are 144 inches in 12 feet.