The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).
What are the values of a variable and the lengths of three line segments associated to it?
In accordance with geometry, three points are collinear if and only if these points lie on the same line. Then, the geometric system is represented by the following model:
AC = AB + BC
If we know that AB = x + 4, BC = 2 · x - 1 and AC = 4 · x - 7, then the value of x and the lengths of the line segments are, respectively:
4 · x - 7 = (x + 4) + (2 · x - 1)
4 · x - 7 = 3 · x + 3
x = 10
AB = 10 + 4
AB = 14
BC = 2 · 10 - 1
BC = 20 - 1
BC = 19
AC = 4 · 10 - 7
AC = 40 - 7
AC = 33
The solution of the geometric system is (x, AB, BC, AC) = (10, 14, 19, 33).
To learn more on collinear points: https://brainly.com/question/1593959
#SPJ1
Mathwatch question please help
Answer:
before 7 = 10%
after 7 = 90
Step-by-step explanation:
percetanges are part/whole
before 7 there are 15 people (the part) and in total there are 150 (the whole) so divide 15 by 150 and miltiply by 100 to get 10
after 7 there are 135 (the part) and the total is still 150 (the whole) so divide 135 by 150 and multiply by 100 to get 90
If two triangle angles are 37 and 69 what is the third angle?
Answer:
37+69=106
180/106= 74
Step-by-step explanation:
its 74
Answer: 74°
Step-by-step explanation:
the two angles are first added
the sum of a triangle is 180° so the third angle equal 180- sum of angles.
37+69=106
180-106= 74°
2. 7th-grade easy math PLEASE Answer this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
PLS
PLEASE Answer correctly this is for a grade
SHOW YOUR WORK AND TAKE A PICTURE
The expression on the table shows that the shelf pace that the books take is 1 inch per book.
How to calculate the value?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It should be noted that from the table, the relationship between the books and the inches is illustrated on the table.
Relationships between two variables that are proportional occur when their ratios are equal. Therefore, this is a proportional relationship and is illustrated as:
= 2/2
= 1
Therefore, there's 1 inch per book.
Learn more about expressions on:
https://brainly.com/question/25968875
#SPJ1
calculate the slope between the two points (6, 5) and (2, 13).
A. zero
B. undefined
C. -2
D. 10
Answer:
M= -2
Step-by-step explanation:
13-5=8
2-6=-4
8/-4= -2
The formula for slope is Y2-Y1/X2-X1.
so in this case it would be 13-5 divided by 2-6.
LESSON 8.2
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Based on the central angle theorem:
1. m<RQS = 100°
2. m<IJH = 70°
3. m<TQR = 100°
What is the Central Angle Theorem?The measure of the central angle of a circle is the same as the measure of the intercepted arc, according to the central angle theorem.
1. m<RQS = measure of arc RS [central angle theorem]
Measure of arc RS = 180 - 80
Measure of arc RS = 100°
m<RQS = 100°
2. m<IJH = measure of arc HI [central angle theorem]
Measure of arc HI = 360 - 140 - 150
Measure of arc HI = 70°
m<IJH = 70°
3. m<TQR = measure of arc TR [central angle theorem]
Measure of arc TR = 360 - 120 - 140
Measure of arc TR = 100°
m<TQR = 100°
Learn more about the central angle theorem on:
https://brainly.com/question/27203912
#SPJ1
The following frequency table summarizes the number of children that dads in Dads Club have.
Number of children Number of members
111 666
222 444
333 888
444 111
555 111
Based on this data, what is a reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children?
The reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children is 50%.
How to illustrate the information?Number of children for 333 = 111 members
It should be noted that the total members is illustrated as:
= 666 + 111 + 111 + 888
= 1776
Therefore, the reasonable estimate of the probability that the next dad to join Dads Club has fewer than 333 children:
= 888 / 1776
= 50%.
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
100 POINTS NEED HELP ASAP
A line passes through point (2,3) and has a slope of -4.
Write an equation in Ax + By = C form for this line.
Use integers for A, B, and C.
Answer:
Step-by-step explanation:
Point slope formula y - y1 = m( x - x1)
y - 3 = -4(x - 2)
y - 3 = -4x + 8
y = -4x + 11
check
(2,3)
Y = -4x + 11
3 = -4(2) + 11
3 = -8 + 11
3 = 3
Standard form 4x + y = 11
jimmy had a balance of -$176 in his bank account. After he deposited $500 into his account, what was Jimmy's new balance
The new balance in Jimmy's account is 324.
What does account mean in math?An account is a record that records financial transactions concerning a specific asset, liability, equity, revenue, or expense in an accounting system. As the business events take place throughout the course of the accounting period, these records grow and shrink. The general ledger stores each individual account and is used to create financial statements at the end of an accounting period.
ACCORDING TO GIVEN STATEMENT;
Jimmy had a deposited amount of $500
minus $176, per the information provided;
his new balance is $500 minus $176,
= $324.
The new balance in Jimmy's account is 324.
to know more about account visit;
https://brainly.com/question/22804169
#SPJ9
Help, please! I can't figure out how to solve this problem for my geometry class. Please give me a clear, step-by-step answer to receive 20 points for your brainly score. Thanks!
The equation is 2x - 8 + 11 = x + 10
The value of x is 7
The value of RS is 6
The value of RT is 17
Solving linear equationsFrom the question, we are to write and solve an equation for x
From the given information,
RS = 2x - 8
ST = 11
RT = x + 10
From above, we can write that
RS + ST = RT
Thus,
2x - 8 + 11 = x + 10
Solve the equation for x
2x - 8 + 11 = x + 10
2x - x = 10 - 11 + 8
x = 7
∴ The value of x is 7
Now,
For the values of RS and RT
RS = 2x - 8
∴ RS = 2(7) - 8
RS = 14 - 8
RS = 6
and
RT = x + 10
RT = 7 + 10
RT = 17
Hence,
The equation is 2x - 8 + 11 = x + 10
The value of x is 7
The value of RS is 6
The value of RT is 17
Learn more on Calculating length here: https://brainly.com/question/28308304
#SPJ1
For someone to solve this question for me
The grid above shows the graph of the parent function
f(x)=|x|
and a translated functions graph.
Write the equation for the translated graph.
Ps: please only answer if you can explain it/help me understand it.
The parent function, f(x) = |x|, and the graph of the parent and translated function, gives the equation of the translated graph as; f(x) = |x + 3|
Which equations can be used to represent the given graphs?The given parent function is; f(x) = |x|
From the parent function, we have;
When x = 0, f(0) = 0
The graph of the parent function is therefore the red graph.
The location of the vertex of the translated graph is at (x - 2, y + 1)
Given that the slope of the image of the graph of the parent function is the same as the slope of the graph of the parent function, we have;
(x, y) → (x - 2, y + 1)
Therefore in the image, the coordinates of y = x + 3
Which gives the equation for the translated graph as; y = |x + 3|
Learn more about absolute value functions here:
https://brainly.com/question/21728802
#SPJ1
1.) The function g is related to one of the parent functions
g(x) = x^2 + 6
The parent function f is:
f(x)= x^2
Use function notation to write g in terms of f.
Step-by-step explanation:
if [tex]f(x) = {x}^{2} [/tex]g(x)=f(x) +6 is the solution!
Tamika has 48 pencils and 80 pens that she is dividing up evenly in teacher supply boxes that
will contain both pencils and pens.
(a) What is the greatest number of boxes she can use so that each box contains the same
number of pencils and each box contains the same number of pens? Justify.
Hint: Look at the bold underlined word, that should be a good clue as to what strateg
to use.
(b) Based on your answer to (a), how many pencils and how many pens will be in each b
The Upside Down Birthday Cake/Ladder Method works great here.
(a) The greatest number of boxes she can use so that each box contains the same number of pencils and pens is 48.
(b) There will be 48 pencils and pens in each box.
We have given that Tamika has 48 pencils and 80 pens.
So, the greatest number of boxes is 48, because the total number of pencils is 48, in order to share the same number of pencils and pens, the greatest number of boxes would be 48.
And,
Based on above answer and according to question's statement (each box contains the same number of pencils and each box contains the same number of pens), so, there will be one pencil and one pen in each box.
To learn more about Containing visit :
https://brainly.com/question/775226
#SPJ1
Correlation coefficient: If the correlation coefficient for a given scatterplot is r = -0.81, which of the following must be true about the relationship between the explanatory and response variable?
A) The association has a linear form.
B) The association must be positive.
C) The slope must be negative.
D) The association is weakened by outliers.
Answer:
C) The slope must be negative.
Step-by-step explanation:
Correlation coefficient between the explanatory variable x and the response variable y shows whether increases in x will result in an increase or decrease in y
Here correlation coefficient is r = -0.81
Since it is negative, that means the slope of least-squares regression line will be negative
Answer:
C. The slope must be negative.
Step-by-step explanation:
The association has to be negative because if the scattetplot. is 0.81 then the relationship between the exploratory and response variable.
-Solve the equation. Write a reason for each step. 12x = 28 - 16x
How do you do number 10? I got it wrong and is the only one I'm stuck on. PLEASE HELP, thanks!
Answer:
[tex]x=\frac{3\left(-y+6\right)}{7}[/tex]
Step-by-step explanation:
[tex]14x+6y-6y=36-6y\\14x=36-6y\\Divide\\\frac{14x}{14}=\frac{36}{14}-\frac{6y}{14}\\\frac{14x}{14}\\\frac{14}{14}= 1\\\frac{36}{14}-\frac{6y}{14}\\\frac{36-6y}{14}\\36-6y\\6\cdot \:6-6y\\=6\left(6-y\right)\\=\frac{6\left(6-y\right)}{14}\\=\frac{3\left(-y+6\right)}{7}[/tex]
Hope this helps you, and I hope that you get un-stuck! Have a good day.
i hope this helps you
have a nice day
What is the equation of the line that passes through the point (-1,8) and has a slope of −6?
Answer:
y=-6x+2
Step-by-step explanation:
we know the slope is -6
at -1 it should be at 6
to get 6 to 8 add 2
what is the rules of rounding errors
Answer: Rounding error is the difference between a rounded-off numerical value and the actual value. A rounded quantity is represented by a numeral with a fixed number of allowed digits, with the last digit set to the value that produces the smallest difference between the rounded quantity and the actual quantity.
An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. tall, and the initial velocity of the ball is 40 ft per sec. The height s of the ball in feet is given by the equation s equals negative 2.7 t squared plus 40 t plus 6.5s=−2.7t2+40t+6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b. a. After how many seconds is the ball 10 ft above the moon's surface?
The ball when thrown at initial velocity of 40ft/sec is 10 ft above the moon's surface after approximately 0.09 seconds and 14.73 seconds .
When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
The given equation for the height of the ball from the surface after t seconds is given by :
s=-2.7t²+40t+6.5
The initial velocity is 40ft/second.
the height of the ball is 10 ft from the surface.
therefore: s=10
Substituting the value in the equation we get:
10=-2.7t²+40t+6.5
or, -2.7t²+40t-3.5=0
This is a quadratic equation in t . Solving by the quadratic formula we get:
We know that for a equation: ax²+bx+c=0
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
So using the above equation we get:
[tex]{\displaystyle x={\frac {-40\pm {\sqrt {40^{2}-4(-2.7)(-3.5)}}}{2(-2.7)}}}[/tex]
either x=14.726... or x= 0.088...
Therefore x≈14.73 and x≈ 0.09
So the ball will be 10 ft above the moon's surface after approximately 0.09 seconds or 14.73 seconds .
To learn more about velocity visit:
https://brainly.com/question/18084516
#SPJ9
ANSWER ALL WITH THE NUMBER LABELED:))
Think about the function f(x) = 3 - 2x.
What does the notation f(0) mean?
The output value of f(0) in the given function is 3, these form an ordered pair of the y-intercept (0,3).
What is the output value of f(0)?Given the function in the question;
f(x) = 3 - 2xf(0) = ?f(0) equals to the value gotten when 0 replaces all the occurrences of x in the function, this gives an ordered pair of the y-intercept.
f(x) = 3 - 2x
f(0) = 3 - 2(0)
Simplify
f(0) = 3 - 0
f(0) = 3
Therefore, the output value of f(0) in the given function is 3, these form an ordered pair of the y-intercept (0,3).
Learn more about function composite here: https://brainly.com/question/20379727
#SPJ1
Ex.1. Nine counters numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 are placed in a bag One is taken out at random. What is the probability that it is: (a) a 5 (c) less than 5 (b) divisible by 3 (d) divisible by 4.
The probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
Probability = Number of Favorable Outcomes/Number of outcomes
For a) P( getting 5) = 1/10
b) P( getting less than 5) = 4/10 , (Favorable outcomes = 1,2,3,4)
= 2/5
c) P (divisible by 3 ) = 3/10 , (Favorable outcomes = 3,6,9)
d) P( divisible by 4) = 2/10 , (Favorable outcomes = 4, 8)
= 1/5
So, the probabilities for the given situations are:-
a) 1/10
b) 2/5
c) 3/10
d) 1/5
"Learn more about Probability here-
https://brainly.com/question/251701 "
#SPJ9
Trei kilograme de mere si patru kilograme de pere costa 43 de lei,iar cinci kilograme de mere si trei kilograme de pere costa 46 de lei.Cat costa un kilogram de mere si cat costa un kilogram de pere? Repede dau coroana!!!
Answer: ifrkjnvkrhlkv
Step-by-step explanation: yeah
find the smallest number which when doubled will be exactly divisible by 4, 10, 15
Ab’s a midpoint. Find the value of x.
Answer:
b) x=25
Step-by-step explanation:
If B is a midpoint, then segments AB and BC should be equal to each other.
Then you can make an equation making both segments equal to one another:
2x-8=x+17
2x-x=17+8
x=25
If you could exactly afford either 2 units of x and 7 units of y, or 4 units of x and 3 units of y, then if you spent all of your income on y, how many units of y could you buy?
Answer:
11 units of y
Step-by-step explanation:
Let total income be I
We have the two equations
2x + 7y = I (1) (exactly afford 2 units of x and 7 units of y)
4x + 3y = I (2) (exactly afford 42 units of x and 3 units of y)
Multiply (1) by 2
==> 2(2x + 7y) = 2 x I
==> 4x + 14y = 2I (3)
Subtract (2) from (3)
(3) - (2)
==> 4x + 14y - (4x + 3y) = 2I - I
==> 4x + 14y - 4x - 3y = 2I
==> 14y - 3y = I (x terms cancel)
==> 11y = I
This represents an equation where if you buy 11 units of y, it will be your whole income
Answer: 11 units of y
Suppose that between the ages of 22 and 40, you contribute $3000 per year to a 401(k) and your employer contributes $1500 per year on your behalf. The interest rate is 8.3% compounded annually.
a.) What is the value of the 401(k) rounded to the nearest dollar after 18 years?
b.)Suppose that after 18 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money to the nearest dollar, will you have in the plan when you reach 65?
c.) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan?
The value of the 401(k) after 18 years is $173,526 , the value of the 401(k) at the age of 65 is $1,273,424 and the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan is $1,192,724
As per the given information, you contribute $3000 p.a. and your employer contributes $1500 p.a. to a 401(k)
So, the total amount contributed for 401(k) = $3000+$1500 = $4500 p.a.
This is a case of annuity because fixed amount is contributed each year.
Future value of an annuity is given by a formula = a [tex]\frac{(1+i)^{n} -1}{i}[/tex]
Where, a = annuity = $4500
i = rate of interest = 8.3% p.a. or 0.083
n = no. of years or periods = 18
Now, substituting the values in the formula,
FV of Annuity = 4500 [tex]\frac{( 1+ 0.083)^{18}-1 }{0.083}[/tex]
= 4500 [tex]\frac{4.2006 - 1}{0.083}[/tex]
= 4500 × 38.5614
= 173526.3
The future value of 401(K) after 18 years is $173,526
Now, After 40 years no contributions are made to the funds. Therefore, the future value at age 65 (after 25 years):
By applying compound interest formula, the future value = p × [tex](1+i)^{n}[/tex]
Here, p = present value or principal amount = $184,036
i = rate of interest = 8.9% or 0.089
n = no. of years or periods = 25
Substituting the values:
Future value = $173526 × [tex](1+0.083)^{25}[/tex]
= 173526 × 7.34025
= 1273724.22
You will have $1,273,424 in the plan at age 65.
Now, The difference between the amount of money you will have accumulated ate the age of 65 and the amount you
contributed (for 18years) in the plan = $1,550,956 – ($4500×18)
= $1273724 - $81000
= $1,192,724
Hence, the value of the 401(k) after 18 years is $173,526 , the value of the 401(k) at the age of 65 is $1,273,424 and the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan is $1,192,724
To know more about Annuity and Contribution - https://brainly.com/question/14294009
#SPJ1
The length of a Fruity Chew is a normally distributed random variable X with an average width of
1.2 cm and a standard deviation of 0.12 cm (Ms Pitt did a lot of "research").
a.
Find the probability, correct to four decimal places, that the length of a selected Fruity
Chew is
i.
between 0.8 and 1.5 centimetres
The probability that a selected fruity chew length is between 0.8 and 1.5 cm is 0.00578.
A fruity chew's length is normally distributed with random variable X with an average width of 1.2 cm.
The standard deviation is 0.12 cm.
Therefore, mean μ = 1.2 cm and;
Standard deviation, σ = 0.12 cm
Now, the probability is given as:
z = ( x - μ ) / σ
The probability that the length of a selected fruity chew is between 0.8 and 1.5 cm.
P( 0.8 < x < 1.5 )
For, P( X > 0.8)
z = ( x - μ ) / σ
z = ( 0.8 - 1.2 ) / 0.12
z = - 0.4 / 0.12
z = - 3.33
Using the z score table,
P( X > 0.8 ) = 0.99957
For P( x < 1.5),
z = ( x - μ ) / σ
z = ( 1.5 - 1.2 ) / 0.12
z = 2.5
Using the z score table,
P( X < 1.5) = 0.99379
Therefore, the probability is between 0.8 and 1.5 cm will be:
= 0.99379 - 0.99957 = 0.00578
Learn more about probability here:
https://brainly.com/question/13604758
#SPJ9
What is the value of x?
Answer:
x=2
Step-by-step explanation:
All of the dimensions on the Left (hex) = all of the dimensions summed on the Right (tri)
6 (5x) = x+14 + x+17 + 8x+9
30x = 10x + 40
20x=40
x = 2
Answer:
x = 2
Step-by-step explanation:
6(5x) = x + 14+ x +17 + 8x +9
30x = (10x + 40)
Substrate 10x from both sides.
30x-10x = 30x-10x+40
20x = 40
Divide both sides by 20
x = 2
Therefore x = 2
To check out your work
the both sides are equal.
Substitute x for 2.
6(5x) = x + 14+ x +17 + 8x +9
60 = 60
2|x+7|=18
explain steps
Answer:
x=2
Step-by-step explanation:
2x+14=18
2x=18-14
2x=4
x=4/2=2
x=2
hope u understand
