Answer:
The numbers are 19 and 5
Step-by-step explanation:
Given
Let the numbers be [tex]x\ and\ y.[/tex]
So:
[tex]x = 9 + 2y[/tex] --- First statement
[tex]x*y = 95[/tex] --- second statement
Required
Find x and y
Substitute [tex]x = 9 + 2y[/tex] in [tex]x*y = 95[/tex]
[tex](9 + 2y) * y = 95[/tex]
[tex]9y + 2y^2 = 95[/tex]
Rewrite as:
[tex]2y^2 + 9y - 95 = 0[/tex]
Expand
[tex]2y^2 -10y +19y- 95 = 0[/tex]
Factorize
[tex]2y(y -5) +19(y- 5) = 0[/tex]
[tex](2y +19)(y- 5) = 0[/tex]
Solve for y
[tex]2y + 19 =0[/tex] or [tex]y - 5 = 0[/tex]
[tex]2y = -19[/tex] or [tex]y = 5[/tex]
[tex]y = -\frac{19}{2}[/tex] or [tex]y=5[/tex]
Since the numbers are positive, we take only:
[tex]y=5[/tex]
Substitute [tex]y=5[/tex] in [tex]x = 9 + 2y[/tex]
[tex]x = 9 + 2 * 5[/tex]
[tex]x = 9 + 10[/tex]
[tex]x = 19[/tex]
The numbers are 19 and 5
Solve the system of equations.
15x + 31y = -3
X = -y + 3
Answer:
its (6,-3)
Step-by-step explanation:
Look at steps below
Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answer in set-roster notation.) A ∪ (B ∩ C) = (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) = Which of these sets are equal? A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = (A ∪ B) ∩ C (b) Find A ∩ (B ∪ C), (A ∩ B) ∪ C, and (A ∩ B) ∪ (A ∩ C). (Enter your answer in set-roster notation.) A ∩ (B ∪ C) = (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) = Which of these sets are equal? A ∩ (B ∪ C) = (A ∩ B) ∪ C (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (c) Find (A − B) − C and A − (B − C). (Enter your answer in set-roster notation.) (A − B) − C = A − (B − C) = Are these sets equal? Yes No
Answer:
(a)
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)[/tex]
(b)
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
[tex]A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)[/tex]
(c)
[tex](A - B) - C = \{a\}[/tex]
[tex]A - (B - C) = \{a,b,c\}[/tex]
They are not equal
Step-by-step explanation:
Given
[tex]A= \{a,b,c\}[/tex]
[tex]B =\{b,c,d\}[/tex]
[tex]C = \{b,c,e\}[/tex]
Solving (a):
[tex]A\ u\ (B\ n\ C)[/tex]
[tex](A\ u\ B)\ n\ C[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
[tex]A\ u\ (B\ n\ C)[/tex]
B n C means common elements between B and C;
So:
[tex]B\ n\ C = \{b,c,d\}\ n\ \{b,c,e\}[/tex]
[tex]B\ n\ C = \{b,c\}[/tex]
So:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}\ u\ \{b,c\}[/tex]
u means union (without repetition)
So:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
Using the illustrations of u and n, we have:
[tex](A\ u\ B)\ n\ C[/tex]
[tex](A\ u\ B)\ n\ C = (\{a,b,c\}\ u\ \{b,c,d\})\ n\ C[/tex]
Solve the bracket
[tex](A\ u\ B)\ n\ C = (\{a,b,c,d\})\ n\ C[/tex]
Substitute the value of set C
[tex](A\ u\ B)\ n\ C = \{a,b,c,d\}\ n\ \{b,c,e\}[/tex]
Apply intersection rule
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
In above:
[tex]A\ u\ B = \{a,b,c,d\}[/tex]
Solving A u C, we have:
[tex]A\ u\ C = \{a,b,c\}\ u\ \{b,c,e\}[/tex]
Apply union rule
[tex]A\ u\ C = \{b,c\}[/tex]
So:
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{a,b,c,d\}\ n\ \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
The equal sets
We have:
[tex]A\ u\ (B\ n\ C) = \{a,b,c\}[/tex]
[tex](A\ u\ B)\ n\ C = \{b,c\}[/tex]
[tex](A\ u\ B)\ n\ (A\ u\ C) = \{b,c\}[/tex]
So, the equal sets are:
[tex](A\ u\ B)\ n\ C[/tex] and [tex](A\ u\ B)\ n\ (A\ u\ C)[/tex]
They both equal to [tex]\{b,c\}[/tex]
So:
[tex](A\ u\ B)\ n\ C = (A\ u\ B)\ n\ (A\ u\ C)[/tex]
Solving (b):
[tex]A\ n\ (B\ u\ C)[/tex]
[tex](A\ n\ B)\ u\ C[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C)[/tex]
So, we have:
[tex]A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d\}\ u\ \{b,c,e\})[/tex]
Solve the bracket
[tex]A\ n\ (B\ u\ C) = \{a,b,c\}\ n\ (\{b,c,d,e\})[/tex]
Apply intersection rule
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ \{b,c,e\}[/tex]
Solve the bracket
[tex](A\ n\ B)\ u\ C = \{b,c\}\ u\ \{b,c,e\}[/tex]
Apply union rule
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = (\{a,b,c\}\ n\ \{b,c,d\})\ u\ (\{a,b,c\}\ n\ \{b,c,e\})[/tex]
Solve each bracket
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}\ u\ \{b,c\}[/tex]
Apply union rule
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
The equal set
We have:
[tex]A\ n\ (B\ u\ C) = \{b,c\}[/tex]
[tex](A\ n\ B)\ u\ C = \{b,c,e\}[/tex]
[tex](A\ n\ B)\ u\ (A\ n\ C) = \{b,c\}[/tex]
So, the equal sets are:
[tex]A\ n\ (B\ u\ C)[/tex] and [tex](A\ n\ B)\ u\ (A\ n\ C)[/tex]
They both equal to [tex]\{b,c\}[/tex]
So:
[tex]A\ n\ (B\ u\ C) = (A\ n\ B)\ u\ (A\ n\ C)[/tex]
Solving (c):
[tex](A - B) - C[/tex]
[tex]A - (B - C)[/tex]
This illustrates difference.
[tex]A - B[/tex] returns the elements in A and not B
Using that illustration, we have:
[tex](A - B) - C = (\{a,b,c\} - \{b,c,d\}) - \{b,c,e\}[/tex]
Solve the bracket
[tex](A - B) - C = \{a\} - \{b,c,e\}[/tex]
[tex](A - B) - C = \{a\}[/tex]
Similarly:
[tex]A - (B - C) = \{a,b,c\} - (\{b,c,d\} - \{b,c,e\})[/tex]
[tex]A - (B - C) = \{a,b,c\} - \{d\}[/tex]
[tex]A - (B - C) = \{a,b,c\}[/tex]
They are not equal
Pls help need help with answer b
Answer:
Field hockey has a higher variation of heights.
There is more of a difference between the different heights in field hockey.
What is the Area of the right angle
Answer:
141.96
Step-by-step explanation:
The area or solution for the area of a triangle is base* height divided by 2 so what I did was 31.2cm as the base and 9.1 as the height and I multiplied them together and then I divided by 2! Hope this helped!
Find the volume of the cylinder to the nearest tenth
Answer:
1131 m^3
Step-by-step explanation:
Formula is π r^2h
then substitute the values r=6,h=10
1130.97
then round the number by nearest tenth.
which is 1131.
I'm unsure how to solve for w, can someone please help?
Answer:
w = 1/2
Step-by-step explanation:
One of the ways to solve problems using log is to use these two equations that use the same variables and plug in numbers.
log b (a) = c
b^c = a
By plugging in the numbers we get this:
log 16 (4) = w
16^w = 4
w = 1/2
which of the following is a example of a proportional relationship
*photo is down there
show proof for brainliest
Answer:
The third one
Step-by-step explanation:
You multiply x by 6 to get y. 1x6=6, 2x6=12, 3x6=18.
Dr. Lopez gives students 90 minutes to complete the final exam for her course. Most students use almost all the
time allowed, and relatively few students finish early, so the distribution of times that it takes students to finish
the exam is strongly skewed to the left. The mean and standard deviation of the finishing times are 85 and 10
minutes, respectively.
Suppose we took random samples of 40 students and calculated as the sample mean finishing time. We can
assume that the students in each sample are independent.
What would be the shape of the sampling distribution of ??
Choose 1 answer:
Skewed to the left
Skewed to the right
No
Answer:
Approximatly normal
Step-by-step explanation:
Answer:
approximately normal
Step-by-step explanation:
check conditions for constructing a confidence interval about a proportion:
- random sample or randomized experiment?
- 10 % when sampling without replacement, check n≤1/10N (40 students is enough to assume 10%)
- large count
all conditions are met so it is safe to assume distribution will be approximately normal
Can someone help me with these 2 problems pls
Answer:
53.58°
Step-by-step explanation:
SOHCAHTOA
COS (A)= ADJACENT/ HYPOTENUSE
A= acos(19/32(
A= 53.57642°
Answer:
7) horizontal distance = 105.95 m
Step-by-step explanation:
I can't draw. I don't have much use of my hands. but I'll answer #7 for you.
cos 28° = x/120
0.8829 = x/120
x = 105.95 m
The chemical element einsteinium -253 naturally loses its mass over time . A sample of einsteinium-253 had an initial mass of 320 grams when we measured it. The relationship between the elapsed t, in days, and the mass,m(t), in grams left in the sample is modeled by the following function: M(t)=320•(0.125)^t/61.4 complete the sentence: the sample loses 87.5% of its mass every ___ days.
Answer: 61.4
Step-by-step explanation:
A biologist observed a curved relationship between the average heart rates and life expectancies of several
mammal species in a large sample. The biologist took the natural logarithm for the values of both variables,
and they noticed a linear relationship in the transformed data.
Here's the least-squares regression equation for the transformed data, where life expectancy (LE) is in
years and heart rate (HR) is in beats per minute.
In(LE
6.33 – 0.78 In(HR)
According to this model, what is the predicted life expectancy of a mammal species whose average heart
rate is 200 beats per minute?
You may round your answer to the nearest whole year.
years
Show Calculator
Applying the logarithmic function, it is found that the life expectancy of the mammal specie is of 9 years.
The life expectancy(LE) of a specie with heart rate HR is given by the following logarithmic function below:
[tex]\ln{LE} = 6.33 - 0.78\ln{HR}[/tex]
In this problem, heart rate of 200 beats per minute, thus [tex]HR = 200[/tex].
The life expectancy is:
[tex]\ln{LE} = 6.33 - 0.78\ln{HR}[/tex]
[tex]\ln{LE} = 6.33 - 0.78\ln{200}[/tex]
[tex]\ln{LE} = 2.19731245409[/tex]
[tex]e^{\ln{LE}} = e^{2.19731245409}[/tex]
[tex]LE = 9[/tex]
Life expectancy of 9 years.
A similar problem is given at https://brainly.com/question/24286043
I WILL MARK BRAINLIEST The account balance of each of three children at the end of a month is shown below: Kyle has -52.25 Jason has -52.00 Sue has as much savings in her account as the amount Kyle owes the bank. Part A: On a blank paper, draw a number line from -4 to +4. Plot points on the number line to show the account balances of the three children Label the points using the name of each of each child . describe in detail how you created and labeled this number line,and what it looks like in detail Part B: Determine whether Kyle or Jason owes the bank more Use absolute values and inequalities to write statements that justify your conclusion (5 points)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Given:
Kyle's balance is -$2.25
Jason's balance is -$2.00
Sue's balance is: $2.25
Required:
A: plot and label the points on a number line from -4 to +4
describe how you did it
B: determine who owes more
Solution:
Part A: For the attached plot, we used the Desmos graphing calculator utility, giving it the points (-2.25, 0), (-2.00, 0), and (2.25, 0) to plot on x-y coordinates. The y-axis and minor grid lines are suppressed in order to better approximate a number line. The "label" facility is utilized to attach labels to the points.
Part B: Balances are owed to the bank when the balance is negative. The more negative it is, the more is owed. Kyle's point is farthest to the left on the number line (and is left of 0), so Kyle owes more. The ordering is ...
-2.25 < -2.00 < 0
where |-2.25| > |-2.00|. The number -2.25 is Kyle's balance, so he owes more.
Hello! The girl above me is correct :)
Sara uses 9.3 pints of white paint and blue paint to paint her bedroom walls.
3/5 of this amount is white paint, and the rest is blue paint. How many pints of blue paint did she use to paint her bedroom walls?
Answer:2.65
Step-by-step explanation:
The answer is 2.65
find the probability that a point chosen at random on the segment satisfies the inequality
11 & 13 please!
Answer:n h hbuy n gb78
The graph of a function is shown on the coordinate plane below.
Which statement correctly describes the function on a given interval?
Answer: D
Step-by-step explanation:
I did it
The statement that correctly describes the function is:
The function is decreasing and nonlinear from x = 4 to x = 11.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
We see that,
The function is increasing and nonlinear from x = -7 to x = -4.
The function is constant and linear from x = -4 to x = 1.
The function is increasing and nonlinear from x = 1 to x = 4.
The function is decreasing and nonlinear from x = 4 to x = 11.
Thus,
The function is decreasing and nonlinear from x = 4 to x = 11.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
how much greater is 620,000 than 62?
Answer:
10,000
Step-by-step explanation:
620,000/62 = 10,000
The diagonal of the screen of a laptop computer is 19 inches. The width of the screen is 17 inches. What is the helght of the computer screen in inches?
Answer:
Height of computer screen in inches = 8.48 inches (Approx.)
Step-by-step explanation:
Given:
Diagonal of screen of laptop computer = 19 inches
Width of screen of laptop = 17 inches
Find:
Height of computer screen in inches
Computation:
Screen diagonal, width and height makes a right angle triangle
So,
Using Pythagoras theorem;
Perpendicular = √Hypoteneus² - Base²
Height of computer screen in inches = √(Diagonal of screen of laptop computer)² - (Width of screen of laptop)²
Height of computer screen in inches = √(19)² - (17)²
Height of computer screen in inches = √361 - 289
Height of computer screen in inches = 8.48 inches (Approx.)
during a recent period of time compact discs sales have been declining. The sales (billions of dollars) can be modeled by the function (f)t= -9/7t+17.9, where T is the number of years since 2005. Suppose sales decreased at twice the rate. How can you transform F to model the sales?
a. vertically shrink by a factor of 1/2
b. vertically stretch by a factor of 2
c. horizontally shrink by a factor of 1/2
d. horizontally stretch by a factor of 2
pls help me and I will mark u as brainliest plsssss plsssss please answer momoo anyone
Determine if the representation below is an example of a function or not a function (1,3), (3,3), (4,5), (6,5), (7,7), (9,7)
Answer:
Yes.
Step-by-step explanation:
No x value is used twice.
Ian needs to order some new supplies for the restaurant where he works. The
restaurant needs at least 593 spoons. There are currently 161 spoons. If each set on
sale contains 6 spoons, write and solve an inequality which can be used to determine
X, the number of sets of spoons Ian could buy for the restaurant to have enough
spoons
Answer:
72 sets
Step-by-step explanation:
(Easy way)
593 -161=432 spoons needed
432/6 =72 sets
(Harder way)
6= 1
432 =x
432 = 6x
x=72
Answer:
Inequality: 6x + 161 ≥ 593
Answer: x ≥ 72
Step-by-step explanation:
Have a good day :)
PLEASE HELP ASAP!!!! GOING TO GIVE 30 POINTS
Answer:
The second answer option
Step-by-step explanation:
Lmk if you need explanation
Find the sum of these
Step-by-step explanation:
5x² - 8x + 2 + x² - 6x +3
= 6x²- 14x + 5
write a statment about what you think of harry potter
Answer:
DRACO MALFOY- i don't think this needs a further explanation. :)
Step-by-step explanation:
- Malfoy...DRACO Malfoy..
-Scared, Pottah?
-Honestly, Goyle, if you were any slower, you'd be going backwards.
-ItS kiLleD mE
-You and your bLOody ChiCKen
mk im done:)
Class intervals in a grouped frequency distribution are given as 4−11, 12−19, 20−27, 28−35, 36−43. Write the next two class intervals.
i) what is the each class interval?
ii) write the class boundaries of all classes?
iii) what are the class marks of each class?
Answer:
{44-55}{52- 59 } are the last two interval sStep-by-step explanation:
To get the class boundaries deduct 0.5 from the first number and add 0.5 to the second number = 4-0.5 = 3.5 = 11.5 + 0.5 = 11.5 = 3.5 -11.5 as in the fish class boundary .same for all other boundariesEvaluate the following for f(x) = 3(2)^x
1. f (2) =
2. f (-1) =
3. f (10) =
Answer:
1. f (2) = 3 x 2^x-1
2. f (-1) = -3 x 2^x
3. f (10) = 3 x 2^x/10
Step-by-step explanation:
From the choices provided, select all the questions that represent statistical questions,
A What was the temperature at 5:00p.m. today in Boston?
B How many pieces of fruit were used to make Shawn's smoothie today?
How many states are there?
D What types of food do students in your school bring for lunch each day?
E How many books did each student check out at the library last year?
Answer:
all exept c i think
Evaluate the logarithm at the given value of x without using a calculator.
Value
Function
g(x) = log)(x)
х = Vь
9514 1404 393
Answer:
g(x) = 1/2
Step-by-step explanation:
You want to evaluate ...
[tex]g(x)=\log_b(x)=\log_b(\sqrt{b})\\\\g(x)=\log_b(b^\frac{1}{2})=\dfrac{1}{2}\log_b(b)=\dfrac{1}{2}\cdot 1\\\\\boxed{g(x)=\dfrac{1}{2}}[/tex]
write an exponential formula of the form f (t)= a×b^t to represent the following situation. assume t is in years. The beginning population is 27, 000, decreasing by 3.5% annually. f(t)=__________
Answer:
[tex]f(t)= 27000 * 0.965^t[/tex]
Step-by-step explanation:
Given
[tex]a = 27000[/tex] -- initial
[tex]r = 3.5\%[/tex]
Required
The exponential equation
The exponential equation is
[tex]y =ab^t[/tex]
Where
[tex]b=1 -r[/tex]
We used minus, because the rate decreases..
So, we have:
[tex]b=1 -3.5\%[/tex]
[tex]b=1 -0.035[/tex]
[tex]b=0.965[/tex]
So:
[tex]y =ab^t[/tex]
[tex]y = 27000 * 0.965^t[/tex]
Hence:
[tex]f(t)= 27000 * 0.965^t[/tex]
4. Find PQ
N
Р
5x + 16
S
R.
9x - 32
Q
Answer on= 12
Step-by-step explanation:
The value of PQ in rhombus NPQR is 76 units.
The figure above is a rhombus.
Properties of a rhombus:All the sides are equal opposite angles are equalThe diagonal are perpendicular bisector of each other.Therefore,
PQ = NR = NP = RQ
5x + 16 = 9x - 32
5x - 9x = -32 - 16
-4x = -48
x = -48 / -4
x = 12
PQ = 5(12) + 16 = 60 + 16 = 76 units
learn more on rhombus here: https://brainly.com/question/25278931?referrer=searchResults