Answer:
is not a solution to the system of equations.
Step-by-step explanation:
Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:
Substitute the x and y values into the first equation:
y = 1/2x + 6
3 = 1/2(-6) + 6
Simplify the right side of the equation:
3 = -3 + 6
Solve for the value of y:
3 = 3
The first equation is satisfied, so now let's substitute the x and y values into the second equation:
2y = -x - 3
2 * 3 = -(-6) - 3
6 = +6 - 3
Simplify the right side of the equation:
6 = -3
The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.
Solve for x and simplify answer
4
\x=-18
3
The value of the variable is x = -6/9
What is a fraction?A fraction is defined as the part of a whole number.
The different types of fractions are;
Mixed fractionsSimple fractionsComplex fractionsImproper fractionsProper fractionsWe are given the equation:
4/x = -18/3
To make 'x' the subject, cross multiply
-18x = 12
Now, divide both sides by the coefficient of x, we get;
x = 12/-18
x = -6/9
Learn about subject of formula at: https://brainly.com/question/10643782
#SPJ1
K
In 1999 there were 60 million people worldwide who had been infected with a particular disease. At that time the infection rate was 3.5 million people per year.
(a) Write a formula for a linear function that models the total number of people in millions who were infected with the particular disease x years after 1999.
(b) Estimate the number of people who may have been infected by the year 2013.
f(x) = ax + b, where a and b are real values, is the formula for a linear function. In this instance, a denotes the line's gradient, and b denotes the y-axis intercept (which is sometimes called the vertical intercept).
What is linear function?A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y. Look for a steady rate of change to determine whether a table of values depicts a linear function. You are viewing a linear function if there is one!To learn more about linear function, refer to:
https://brainly.com/question/15602982
#SPJ1
A quadratic function has a vertex at the point (-1, 3) and passes through the point (-4, -6).
The quadratic function is of the given question is f(x) = [tex]-2x^{2}[/tex] + 10x + 1.
What is quadratic equation?When a, b, and c are constants and x is an unknown variable, the equation has the form [tex]ax^{2}[/tex] + bx + c = 0, which is known as a quadratic equation. The unknown variable x is solved for using the quadratic equation.
The largest power of the variable in a quadratic equation is two. The variable is now squared, but it may also have a coefficient, often known as a multiplier, in front of it. Two more components in the equation are made up of a constant and a variable with an exponent of 1.
In the given question,
The equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) can be written as:
y = [tex]a(x + 1)^{2}[/tex] + 3
Where a is a constant that determines the shape of the function. To find the value of a we can substitute the coordinates of the vertex and the point into the equation and solve for a.
Substituting (x, y) = (-1, 3) into the equation:
3 = [tex]a(-1 + 1)^{2}[/tex] + 3
Simplifying:
3 = [tex]a(0)^{2}[/tex] + 3
3 = 3
Since both sides are equal, a = 1.
Substituting (x, y) = (-4, -6) into the equation:
-6 = [tex]a(-4 + 1)^{2}[/tex] + 3
Simplifying:
-6 = [tex]a(-3)^{2}[/tex] + 3
-6 = 9a + 3
-9 = 9a
Divide each side by 9:
-1 = a
Since both values of a are equal, a = -1.
Therefore, the equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) is:
y = [tex]-(x + 1)^{2}[/tex] + 3
To know about the quadratic function, visit
brainly.com/question/18958913
#SPJ1
**Image **Find the value of x. Show your steps.
The value of x is 9 by using the concept of corresponding angles.
What are corresponding angles?Corresponding angles are the angles formed when two parallel lines are crossed by any other line. It may also be generated in matching edges(corners) or corresponding corners with the transversal.
From the information given:
(8x + 9) is corresponding to the opposite side of the transversal with an angle of 99 degrees.
Using the sum of angles on a straight line.
Step 1: (8x + 9)° + 99 = 180°
Step 2: 8x + 108 = 180
Step 3: 8x = 72
Step 4: x = 9
Learn more about corresponding angles here:
https://brainly.com/question/11853802
#SPJ1
well asap due today pls
Answer:
96 in²
Step-by-step explanation:
Length of Semiperimeter
[tex]\displaystyle s=\frac{1}{2}(a+b+c)=\frac{1}{2}(12+16+20)=\frac{1}{2}(48)=24[/tex]
Area of Triangle w/Heron's Formula
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-12)(24-16)(24-20)}=\sqrt{24(12)(8)(4)}=\sqrt{9216}=96[/tex]
Hence, the area of the triangle is 96 in².
What is the solution to the system of equations?
{y=5x−10
{y=−3x+14
Enter your answer as the correct ordered pair, like this: (42, 53)
multiply the second equation by -1, you get
y=5x-10
-y=3x-14
add both of the equations together
0=8x-24
then
24=8x
x=3
to find y replace x in one of the original equations
y=5x-10
y=5(3)-10
y=15-10
y=5
(x,y)
(3,5)
A passenger train traveled 240 miles in the same amount of time it took a freight train to travel 160 miles. The rate of the freight train was 20 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
The rate of the passenger's train is given as follows:
60 miles per hour.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
For the passenger train, the equation is given as follows:
v = 240/t.
vt = 240
t = 240/v.
For the freight train, the velocity is 20 miles slower than for the passenger train, hence:
v - 20 = 160/t
v = 160/t + 20.
Replacing the first equation into the second, the rate of the passenger train is obtained as follows:
v = 160v/240 + 20
v = 2v/3 + 20
v/3 = 20
v = 60 miles per hour.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
#SPJ1
The polygons shown are similar. Find the value of each variable.
The value of x is 7.
(Type an integer or a decimal.)
The value of y is.
(Type an integer or a decimal.)
CIT
10.9
5
7.5
3.5
The values of x and y are given as follows:
x = 7y = 7.5.What are similar polygons?Similar polygons are polygons that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.The proportional relationship for the side lengths in this problem is given as follows:
x/10.5 = 5/y = 5/7.5.
Hence the value of x is given as follows:
7.5x = 5 x 10.5
x = 5 x 10.5/7.5
x = 7.
The value of y is given as follows:
5/y = 5/7.5
y = 7.5.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Whats the correct answer answer asap for brainlist
The sentence that uses the word "obstinancy" incorrectly is: if we eat out too often, its result in obstinancy and poor health. The Option C is correct.
Definition of the word "obstinancy", its uses and example:Obstinancy is a noun that refers to the quality of being stubborn or resolutely unyielding. It describes a person's refusal to change their views, opinions, or actions, even in the face of compelling evidence or persuasive arguments. Example of its use: despite the pleas of his family, the man's obstinancy led him to continue his dangerous lifestyle.
We often use the word "obstinancy" for the followings:
to describe someone's persistence in pursuing a particular course of action despite obstacles or challenges.to describe someone's reluctance to change their opinion or attitude in light of new evidence.to describe someone's refusal to give in to the demands or requests of others.Read more about Obstinancy
brainly.com/question/2586563
#SPJ1
A
15
What is the measure of ZA?
B
Enter the correct value.
C
The measure of angle A is given as follows:
<A = 60º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle A, we have that:
The opposite side is of 13.The hypotenuse is of 15.Applying the sine ratio, the angle measure is given as follows:
sin(A) = 13/15
A = arcsin(13/15)
A = 60º.
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and
twice the reciprocal of the larger is 9/10 then find the two integer
Answer:
Step-by-step explanation:
Let the smaller integer be x, then the larger integer is x + 3.
The sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/10:
1/x + 2/(x + 3) = 9/10
Expanding both sides:
10/x + 20/(x + 3) = 90/10
Combining like terms on the left side:
(10 + 20)/(x(x + 3)) = 90/10
30/(x(x + 3)) = 9/10
Cross multiplying both sides:
30 * 10 = 9 * (x(x + 3))
300 = 9x(x + 3)
Expanding the right side:
300 = 9x^2 + 27x
Subtracting 27x from both sides:
273 = 9x^2 + 27x - 27x
273 = 9x^2
Taking the square root of both sides:
√273 = √(9x^2)
√273 = 3x
Dividing both sides by 3:
√273/3 = x
The smaller integer is √273/3 and the larger integer is √273/3 + 3.
(6 points) Here are the data on the age for a random sample of instructors working in three different colleges. Use appropriate
99%
confidence intervals to complete the each of the following questions . Part A We are
99%
confident that the mean age of all instructors in College
A
is College B by between years old and (Round the numeric answers to 5 decimal places) Part B We are
99%
confident that the mean age of all instructors in College
A
is College C by between (Round the numeric answers to 5 decimal places) Part E We are
99%
confident that the mean age of all instructors in College B is College C by between years old and years old. (Round the numeric answers to 5 decimal places)
Part A: We are 99% confident that the mean age of all instructors in College A is between 42.79128 and 51.2088 years old.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 37.36368 and 54.63632 years old.
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
In this question, they are asking to calculate the 99% confidence intervals for the mean age of instructors in three different colleges (A, B, and C). They want to compare the mean age of instructors in College A to College B, College A to College C, and College B to College C. The numeric answers should be rounded to 5 decimal places.
To calculate these confidence intervals, you need to find the sample mean and standard deviation of the data for each college. Then, you can use the formula for a two-sample t-test to calculate the confidence intervals. The formula is (sample mean A - sample mean B) ± t-critical value * (standard deviation of A/√nA + standard deviation of B/√nB), where nA and nB are the sample sizes for Colleges A and B, respectively.
Part A: We are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation of the sample data. The mean age of all instructors in College A is 22.273 and the standard deviation is 1.936.
Next, we must use the t-distribution to calculate the 99% confidence interval. The critical value is 2.228. The confidence interval is calculated as follows:
Lower Bound = 22.273 - (2.228 x 1.936) = 20.81733
Upper Bound = 22.273 + (2.228 x 1.936) = 23.72867
Therefore, we are 99% confident that the mean age of all instructors in College A is College B by between 20.81733 and 23.72867.
Part B: We are 99% confident that the mean age of all instructors in College A is College C by between 17.73173 and 25.71367.
To calculate the 99% confidence interval, we must first calculate the mean and standard deviation
Part C: We are 99% confident that the mean age of all instructors in College B is College C by between 46.24672 and 57.75328 years old.
To learn more about mean age link is here:
brainly.com/question/9244598
#SPJ4
help with this geometry please!
no fake answers :)
The value of x in the given set triangles are:
1) x=17.5
2) x=48
3) x= 8
4) 24.5
5) x=11
6) x=9
What is Triangle Proportionality Theorem?
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides.
1) According to Triangle Proportionality Theorem,
from given fig 1,
[tex]\frac{14}{12} =\frac{x}{15} \\\\\frac{7}{6} =\frac{x}{15} \\\\x= 17.5[/tex]
2) From fig 2,
[tex]\frac{x}{18} =\frac{56}{21} \\\\x=48[/tex]
3) From fig 3,
[tex]\frac{x}{36} =\frac{10}{45} \\\\\frac{x}{36} =\frac{2}{9} \\\\x=8[/tex]
4) From fig 4,
[tex]\frac{6}{21}=\frac{7}{x} \\\\6x=7*21\\\\x=24.5[/tex]
5) From fig 5,
[tex]\frac{30}{x+7} =\frac{25}{15} \\\\\frac{30}{x+7} =\frac{5}{3} \\\\x=11[/tex]
6) From fig 6,
[tex]\frac{6}{21}=\frac{x-1}{3x+1} \\\\ 18xx+6=21x-21\\\\3x=27\\\\x=9[/tex]
To know more about Triangle Proportionality Theorem visit,
https://brainly.com/question/8160153
#SPJ1
Given the following parallelogram, solve for x.
X =
(18x - 79) °
(7x + 9) °
Si en dos horas y media un motociclista ha cubierto una distancia de 320 kilómetros. ¿Ha superado el límite de velocidad previsto, que es de 80 km/h?
La velocidad promedio del motociclista es 128km/h, entonces si, supera el limite de velocidad previsto.
¿Ha superado el límite de velocidad previsto, que es de 80 km/h?Sabemos que podemos definir la velocidad como el cociente entre distancia y tiempo, en este caso sabemos que:
distancia = 320km
tiempo = 2.5 h.
Entonces la velocidad será:
v = 320km/2.5 h = 128 km/h
Podemos ver que claramente, el motociclista supera el limite de velocidad previsto.
Aprende más sobre velocidad en:
https://brainly.com/question/4931057
#SPJ1
An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?
a. 4
b. 16
c. 8
d. 32
16 sample points (possible outcomes as to the classifications) exist.
What is the combination?
Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
Here, we have
Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.
There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.
A total of (4)(4) = 16 sample points.
Hence, 16 sample points (possible outcomes as to the classifications) exist.
To learn more about the combination from the given link
https://brainly.com/question/28065038
#SPJ1
the equation of a curve is given by
y=x^3/3+7x^2/2+10x+d, where d is a
constant. Find the possible values of d
when the x-axis is tangent to the curve
v=x^3/3+7x^2/2+10x+d.
Answer: The x-axis is tangent to the curve when the value of y is equal to 0. So, to find the possible values of d when the x-axis is tangent to the curve, we need to solve the equation:
x^3/3 + 7x^2/2 + 10x + d = 0
To solve this equation, we need to use a method such as the cubic formula or a numerical method such as Newton-Raphson. However, it is not possible to determine a general solution for d without additional information, such as the value of x at which the tangency occurs. The possible values of d will depend on the specific value of x that satisfies the equation.
Step-by-step explanation:
? - 85 ÷ 641 = 650
Need help
Answer:
416,`735
Step-by-step explanation:
Do inverse operations
A mechanic had412 gallons of motor oil at the start of the day. At the end of the day, only 5 pints remained.
How many pints of motor oil did the mechanic use during the day?
Answer:
3,291 pints used
Step-by-step explanation:
There are 8 pints in a gallon
Started with 412 gallons, multiply that by 8 to get 3,296 pints
At the end of day, he only had 5
So we can subtract 5 from the 3,296 that he started the day with, and we get the answer of 3,291 used throughout the day.
Margo borrows $600, agreeing to pay it back with 2% annual interest after 10 months. How much interest will she pay? Round your answer to the nearest cent, if necessary
The amount of interest paid will be $9.6.
What is simple interest?The simple interest is the simple amount paid by the borrower to the bank according to the percentage set by the bank for per year which is a fixed interest rate.
Given that Margo takes out a $600 loan with a 10-month repayment period and a 2% yearly interest rate.
The simple interest will be calculated as:-
SI = ( P x R x T ) / 100
SI = ( 600 x 2 x 0.8 ) / 100
SI = 960 / 100
SI = $9.6
Therefore, $9.6 will be paid in interest.
To know more about simple interests follow
https://brainly.com/question/25793394
#SPJ9
PLS HELP ME DUE TODAY!!!!
Tom is adding soil to his raised garden bed. The depth of the soil is currently 8 inches, and for each bag of soil he adds, the depth will increase by
1/2 of an inch. You can use a function to describe the depth of the soil in the garden bed after Tom adds x bags of soil.
Write an equation for the function. If it is linear, write it in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x.
Answer:
h(x) = 0.5x + 8
Step-by-step explanation:
We are being asked to write an equation where h(x) represents the soil depth in inches and x describes the number of bags. To do this, we need to find b (our y-intercept, ie the value of h(x) or y when x=0) and m (our slope).
"The depth of the soil is currently 8 inches": this means before any bags are added (ie when x=0), the soil depth starts at 8. This makes 8 our y-intercept (b in h(x)=mx+b) as we have to add it on to however much the bagged soil adds in order to get the total depth.
"For each bag of soil he adds, the depth will increase by 1/2 of an inch": this means that the soil depth from added bags is equal to the amount of bags times 0.5, which makes 0.5 our slope (m in h(x)=mx+b).
Therefore our answer is:
h(x) = 0.5x + 8
3m^2 + 4m + 7
4m^2 - 3m + 2
Which of the following is the sum of the above two polynomials?
Answer: The sum of the two polynomials 3m^2 + 4m + 7 and 4m^2 - 3m + 2 is 7m^2 + m + 9.
Step-by-step explanation:
A bag contains 2 gold marbles, 7 silver marbles, and 29 black marbles. The rules of the game are as follows: you randomly select one marble from the bag. If it is gold, you win $4, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss of you play this game?
Total number of marbles is 5 + 7 + 29 = 41.
Your expected profit or loss of you play this game $0.17 loss?
The given parameters are
2 gold marbles,
7 silver marbles,
and 29 black marbles
Also you win $4, if it is silver, you win $2. If it costs $1 to play
Event P(Event) Net Winnings P(Event) * Net Winnings
Gold 5/41 4 - 1 = 3 15/41
Silver 7/41 2 - 1 = 1 7/41
Black 29/41 -1 -29/41
sum -7/41 = $0.17 loss
Learn more about probabilities on https://brainly.com/question/30034780
#SPJ1
Question 1
What are the coordinates of the x-intercept and y-intercept of the line
4y-4x= -16.
Find the value of X
Please help! Asap
Answer:
Step-by-step explanation:
Suppose we have a bag of jelly beans 82% of the jelly beans orange, 14% are black, and 4% are green. Moreover, 15% of orange are sugar free, 70% of black beans are sugar free, and 90% of green beans are sugar free Suppose we select a jelly bean at random.
1. Construct a tree diagram to represent this situation
2. Find the probability of green bean and sugar free
3. Given the bean is sugar free, what is the probability that it is an orange bean?
Please I need help
Answer:
3/50
Step-by-step explanation:
3 g, 5 r, 2 o
3 + 5 + 2 = 10
Orange = 2 jelly beans
Probability of selecting an orange jelly bean: 2/10 or 1/5
If you put the jelly bean back in, there is still 10 jelly beans.
Green = 3 jelly beans
Probability of selecting a green jelly bean: 3/10\
Multiply the probabilities:
1/5 x 3/10
= 3/50
Consider the line 8x-5y=1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line ?
an actor invests some money at 9% and 29000 more than four times the amount at 11% the total annual interest earned from the investment is 55130. how much did he invest at each amount?
8.The side lengths of the smaller hexagon were increased by a factor of √2 to make the larger hexagon. If the area of the smaller hexagon is 9√3 square units, what is the area of the larger hexagon?
a. 36√3 square units
b. 18√3 square units
c. 18√6 square units
d. 9√6 square units
The area of the larger hexagon in discuss as required in the task content is; Choice B; b. 18√3 square units.
What is the area of the larger hexagon?It follows from the task content that the area of the larger hexagon be determined.
Recall from the concept of similar shapes; if the ratio of side lengths of two similar shapes is; k, therefore the ratio of their perimeters is k and the ratio of their areas is; k².
On this note, since the larger hexagon is √2 times the side length of the smaller hexagon;
It follows that the area of the lager hexagon is (√2)² times the area of the smaller one.
Therefore, Area of larger hexagon = √2² × 9√3
= 18 √3.
Read more on ratio of areas in similar shapes;
https://brainly.com/question/9217675
#SPJ1
3. Explain how "a" affects the graph of a parabola. (f(x) = ax²)
The effect of "a" in the graph of parabola is value from the quadratic function.
How to determine the standard equation of the parabola?In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:
y = a(x – h)2 + k or x = a(y – k)2 +h
Where:
(h, k) - The vertex of the parabola.
p - Least distance between the vertex and the focus of the parabola.
Given that;
The equation of parabola is f(x) = ax².
Now, Let's look at the graph of f(x) = x^2 + 3x + 1, which is below. The b-value in this equation is 3.
We see that our graph is indeed a parabola. Our parabola is curving up. The x-value of the vertex, the tip of the parabola, is -3 / 2 or -1.5. We can actually calculate this x-value by evaluating the expression -b / 2a, where a and b are the values from the quadratic function.
Therefore, the role of a in parabola is stated.
To learn more on parabolas:
brainly.com/question/4074088
#SPJ9
