Answer:
x=21
Step-by-step explanation:
6-1/3x=-1
-6 -6
-1/3x=-7
__ __
-1/3 -1/3
x=21
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\6-\dfrac{x}{3}=-1 \\\\\text{Move 'x/3' to the right side and '-1 to the other side}\\6+1=\dfrac{x}{3}\\ 7=\dfrac{x}{3} \\\\\text{Multiply 3 to both sides}\\7*3=3*\frac{x}{3} \\x = 21[/tex]
Answer: x = 21
Hope that helps!
50 POINTS
What system of linear inequalities is shown in the graph? Enter your answers in the boxes.
enter your answers in the boxes
□
□
Answer:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
Step-by-step explanation:
Find the equations of the two lines by substituting two points on each line into the slope formula to find the slope, then substituting the found slope and one of the points into the point-slope formula.
Equation of Line 1
Points on the line: (0, 2) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{2-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Equation of Line 2
Points on the line: (0, -3) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-3)}{2-0}=-\dfrac{4}{2}=2[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-3)=2(x-0)[/tex]
[tex]\implies y=2x-3[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.As the line for equation 1 is solid and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y \geq -\dfrac{1}{2}x+2}[/tex]
As the line for equation 2 is dashed and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y > 2x-3}[/tex]
Therefore, the system of linear inequalities shown in the graph is:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
6. What is the constant of proportionality of the linear function?
Time, x 12 3 4
Cost ($), y 25 50 75 100
F. 2 G. 12 H. 25 I. 50
Pls help!!
The table has a constant of proportionality of 25
How to determine what is the constant of proportionality?The table represents the given parameter
On the table, we have the following points
(x, y) = (1, 25)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have
k = 25/1
Evaluate the quotient
So, we have
k = 25
Hence, the constant of proportionality of the table is 25
Read more about constant of proportionality at
brainly.com/question/28413384
#SPJ1
Based on triangle inequality theorem, what are the restrictions on the values of y
The restriction on the the values of y of the triangle is 4 < y < 16
How to find the side of a triangle using the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle.
According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.
Therefore, a triangle x, y and z have the following rule:
x < y + z
y < x + z
z < x + y
Hence, the restriction of the on the values of y, third side of the triangle is as follows:
6 < 10 + y
10 < 6 + y
y < 10 + 6, y < 16
Therefore, the restriction is y > 4 and y < 16.
Hence,
4 < y < 16
learn more on triangle here: https://brainly.com/question/1163433
#SPJ1
a) How much time do people in Bhutan spend watching TV each night?
Answer:
about 2 hours
Step-by-step explanation:
it is the reported average
ANSWER FAST I WILL GIVE BRAINLIEST
Which graph represents the solution to one seventhm ≤ −1 over 22? number line with closed circle on point negative 14 over 11 and arrow shaded to the right number line with closed circle on point negative 7 over 22 and arrow shaded to the right number line with closed circle on point negative 14 over 11 and arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Answer: arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Step-by-step explanation:
Answer:
for easier explanation.... it's D
Step-by-step explanation:
the number of messages that arrive at a web site is a possion distirbuted random variable with a mean of 5 messages per hour. round your asnwers to four decimal places. what is the probaiblity taht 5 messages are received in 1 hour
17.54% is the probability that 5 messages are received in 1 hour.
The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P(X = x) = ([tex]e^{-u}[/tex] × [tex]u^{x}[/tex]) ÷ x!
In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.
In this case, the average message rate is 5 messages per hour.
The probability of receiving 5 texts in one hour.
Determine the value of P for x = 5 and u = 6.
P(X = x) = ([tex]e^{-5}[/tex] × [tex](5)^{5}[/tex]) ÷ 5!
P(X = x) = 21.0560 ÷ 5!
P(X = x) = 0.1754
There is a 17.54% chance that 5 messages will be received in 1 hour.
Learn more about the probability at
https://brainly.com/question/13416734?referrer=searchResults
#SPJ4
Ben's monthly housing costs for his new home will be $2100 per month. What
must his monthly net income be to keep housing as 30% of his budget?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The monthly net income to keep housing a 30% of his budget is $7000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Cost of monthly housing per month = $2100
$2100 = 30%
Monthly income = 100%
30% = 2100
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 2100
100% = 7000
Thus,
The monthly net income to keep housing a 30% of his budget is $7000.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
Please help. See picture attached.
The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.
A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.
t = 1/2ah + 1/2bh
Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.
t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h
2. You are riding your bicycle. It takes you 20 minutes to go 5 miles.
a. Find your average speed per minute.
b.
How long would it take you to cycle 12 miles?
Answer:
a= one mile in 4 minutes
b =48 minutes
Step-by-step explanation:
A
t = 20 minutes
d = 5 miles
Average speed = distance ÷ time
5 miles÷ 20 minutes
= 1 mile in 4 minutes
= 0.25 miles in 1 minute
B
0.25 miles in 1 minute
12 miles in g minutes
12 miles in 48 minutes
we get this answer because 0.25 in one minute is 1 ÷4
12÷ 12 × 4
12÷ 48
= 12 miles In 48 minutes
About 30% of people age 50 to 60 suffer from mild depression. A researcher is interested in determining if a vitamin d supplement will increase or decrease the proportion of people that have mild depression. The researcher randomly selects 500 people between the ages of 50 and 60 and ask them to take a vitamin d supplement for 6 months. At the end of the six months, the participants are asked to complete a survey. A psychologist then classifies each participant as either depressed or not. The psychologist classifies 158 people as depressed. Is the proportion of people that are classified as depressed different from 0. 30? what is the null and alternative hypothesis?.
The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.
Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
Mild depression affects about 30% of adults in the 50 to 60 age range.
500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.
The psychologist classifies 158 people as depressed.
The null hypothesis will be:
H₀ : p = 0.30 and;
The alternative hypothesis is,
Hₐ : p ≠ 0.30
Learn more about hypothesis here:
brainly.com/question/606806
#SPJ4
how would i solve this?
FIRST FIND THE EQUATION OF THE LINE
I WILL USE THE POINTS (-94,24) AND (-54,12)
TO FIND THE GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{12 - 24}{ - 54 - ( - 94)} \\ m = \frac{ - 24}{ - 54 + 94} \\ m = \frac{ - 24}{40} \\ m = \frac{ - 3}{5} [/tex]
THE m ABOVE IS THE GRADIENT.
I WILL USE THE POINT (-74,18) TO GET THE VALUE OF C IN THE EQUATION Y=MX+C
[tex]15 = \frac{ - 3}{5} ( - 74) + c \\ 15 = \frac{222}{5} + c \\ c = 15 - \frac{222}{5} \\ c = \frac{ - 147}{5} [/tex]
THEREFORE THE EQUATION NOW IS
[tex]y = \frac{ - 3}{5} x - \frac{147}{5} \\
FOR THE X-INTERCEPT Y=0 SINCE IN THR X-AXIS Y=0..PLUG IN 0 IN THE PLACE OF Y TO GET X-INTERCEPT.
[tex] \frac{ - 3}{5} x - \frac{147}{5} = 0 \\ \frac{ - 3}{5} x = \frac{147}{5} \\ x = \frac{147}{5} \div \frac{ - 3}{5} \\ x = - 49[/tex]
(-49,0)
Answer the questions below to find the total surface area of the can..
The total surface area of the cylinder is equal to 117.8 in^2
Total Surface Area of Cylinder
The total surface area of a cylinder can be calculated using the formula
[tex]TSA = 2\pi rh + 2\pi r^2[/tex]
h = height of cylinderr = radius of cylinderLet's substitute the values and proceed to solve.
[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]
The total surface area of the cylinder is 117.8 squared inch.
The area of each circle is
[tex]A = \pi r^2 \\A = 19.6in^2[/tex]
And there are two identical circle in the diagram and this will have a total area of
[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]
The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2
Learn more on total surface area here;
https://brainly.com/question/22982196
#SPJ1
An empty swimming pool is shaped like a rectangular prism with a length of 18 feet and a width of 9 feet. once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot per hour.
Answer:
volume=length×width×depth
Step-by-step explanation:
Elena received a $25 gift card to a fun center. She drives a race car which costs $4.75. She also wants to use the gift card to play video games. Each game costs $0.75 which of these inequalities describe this situation, where n is the number of games Elena wants to play.
A. 4.75 + 0.75. ≤ 25
B. 4.75 + 0.75. ≥ 25
C. 4.75 - 0.75. ≥ 25
D. 4.75 - 0.75. ≤ 25
Answer: B - 4.75 + 0.75 is greater than 25
Step-by-step explanation:
so, first you have 4.75 and she want to play video games that cost 0.75 each but we don't know how many video games she played.
so, n = how many video games played4.75 + 0.75n =? which is greater than 25divide 4.75 + 0.75n 0.75 0.75after dividing you will get 4,100 + 1n = which equals 4.101 is greater than 25Don’t ignore help pls I think i know it but I’m not sure
Answer:
The y intercept is 0
Step-by-step explanation:
Where the line crosses the y axis that is your y intercept
Check the picture below.
Ron's youth group commits to making a certain number of sandwiches for a local soup
kitchen. They make 132 sandwiches, but then they run out of peanut butter. The group still
has 110 sandwiches left to make to meet their commitment.
Use an equation to find the total number of sandwiches the youth group commits to making.
sandwiches
Answer:
242 sandwiches
Step-by-step explanation:
The group wants to make x number of sandwiches.
They have already made 132 sandwiches and still have 110 sandwiches to make.
To find the total, you can add these numbers up, because:
132 + 110 = total sandwiches
This way, you get 242 sandwiches
Name a pair or vertical angles.
Answer:
There are two pairs:
1 and 3
2 and 4
Step-by-step explanation:
Verticle angles are angles opposite to each other when two lines intersect.
Suppose a projectile is fired from a cannon with velocity v0 and angle of elevation θ. The horizontal distance Rθ it travels (in feet) is given by the following. R(θ)=(v0)²sin2θ/32 If v0=80ft/s, what angle θ (in radians) should be used to hit a target on the ground 129 feet in front of the cannon? Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian. (If there is more than one answer, enter additional answers with the "or" button.)
The angle at which the projectile should be launched to hit the target which is 129 feet away is 7/100π.
The projectile fires with a velocity V₀ and angle of elevation θ, then the horizontal distance is given by the R(θ),
R(θ) = V₀²sin2θ/32
The given function in dependent on theta θ,
The angle at which the projectile must be fired so that it reaches the horizontal distance of 129 feet in front of the cannon,
R(θ) = V₀²sin2θ/32
putting R(θ) equal to 129, V₀ = 80ft/s,
129 = (80)²sin2θ/32
sin2θ = (129 x 32)/(80 x 80)
sin2θ = 0.645
Hence,
θ = 7/100π
so, the projectile should be launched at angle of 7/100π.
To know more about projectile, visit,
https://brainly.com/question/12870645
#SPJ9
If a biker travels 380 meters in 20 seconds at that rate how far could he travel in 3 seconds
I think its 57 meters.
Antonio draws a spuare that has 13 centimeters what the perimeter of his spuare
Answer:
52 centimeters
Step-by-step explanation:
A square has 4 sides
Side of square = 13 cm
Perimeter of square = sum of all sides of square
Perimeter of square = 4 x 13 = 52 cm
Calculate the surface area of the can. Area of a circle =
Height = 10cm
Diameter = 7 cm
Please help me thank you!
What is the surface area of the circle?
The surface area of the can is 220cm².
The height of the can is 10cm, and the diameter is 7cm.
height (h) = 10cm
radius(r) = 7/2 cm
The formula to find the surface area of the can = 2πrh
= 2 × 22/7 × 7/2 × 10
= 220cm²
Therefore the surface area of the can is 220cm².
To know more about the surface area refer to the link given below:
https://brainly.com/question/16519513
#SPJ1
Which ordered pairs are on the graph of 7x−y=2?
Select ALL that applies.
A. >>(−3,−19)open paren negative 3 comma negative 19 close paren
B. (−1,−9)open paren negative 1 comma negative 9 close paren
C. (0,−2)open paren 0 comma negative 2 close paren
D. (1, 9)(1, 9)
(3, 23)(3, 23)
The ordered pairs which are on the graph of 7x - y = 2 as required in the task content are; Choices B and C; (-1, -9) and (0, -2).
Which ordered pairs are on the graph of 7x - y = 2 as required in the task content?It follows from the task content that the ordered pairs which are on the graph of 7x - y = 2 be determined.
Hence, by testing each pair as follows; we have;
For (-3, -19); we have; 7(-3) - (-19) = 2; -21 + 19 = 2; -2 ≠ 2. Hence, FALSE.For (-1, -9); we have; 7(-1) - (-9) = 2; -7 + 9 = 2; 2 = 2. Hence, TRUE.For (0, -2); we have; 7(0) - (-2) = 2; 0 + 2 = 2; 2 = 2. Hence, TRUE.For (1, 9); we have; 7(1) - (9) = 2; 7 - 9 = 2; -2 ≠ 2. Hence, FALSE.For (3, 23); we have; 7(3) - (23) = 2; 21 - 23 = 2; -2 ≠ 2. Hence, FALSE.Ultimately, the required ordered pairs are; (-1, -9) and (0, -2).
Read more on ordered pairs;
https://brainly.com/question/24880873
#SPJ1
(-5 -5) (10 4), point-slope
The slope is 5/3, and the point-slope is y = 5(x+2)/3.
Describe point slope.
A linear equation has the general form y-y1=m (x-x1). It highlights the line's slope as well as one of the line's points (that is not the y-intercept).
The formula provided is to find slope, i.e.
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where (-5, -5) for (x1, Y1) and (x2, Y2) (10, 4)
m = (10 + 5) / (4 + 5)
= 15 / 9
= 5 / 3
Now that we have the slope value, we can easily enter it into the supplied equation.
y - y1 = m(x - x1) (x - x1)
y + 5 = 5/3(x + 5)
Upon resolution, we obtain
y = 5x/3 + 10/3
or, y = 5(x + 2)/3
As a result, the slope is 5/3 and the point-slope is y = 5(x+2)/3.
To read more about point-slope
https://brainly.com/question/24907633
#SPJ10
7. A crate of soft drinks contains 9 bottles of coke, 6 bottles of pepsi and 4 bottles of limca. Ademola picks one bottle of soft drink and thereafter Adedeji picks another bottle. Find the probability that: (a) They both. picked limca (b) Ademola only picked pepsi (c) They both picked the same brand (d) They picked different brands.
The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
Total possible outcome of the event of picking drinks contained in the crate = 19
Hence, we can compute the following as follows;
(a) The probability they both picked Limca = (4/19)×(3/18)
Limca = 12/342
Limca = 0.04
(b) The probability Ademola only picked pepsi = 6/19
pepsi = 0.32
(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)
=(72+29+12)/342
= 114/342
= 0.33
(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)
The probability they picked different brand = (54+36+54+24+36+24)/342
The probability they picked different brand = 228/332
The probability they picked different brand = 0.67
Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.
Know more about probability here: https://brainly.com/question/24830485
#SPJ1
PLEASE HELP ME THANK YOU
The area of half circle is 14.13 sq.unit
The total area of the figure is 86.13 sq.unit
Given,
The figure is combined by a triangle, rectangle and a half circle.
The area of triangle = 18 sq.units
The area of rectangle = 54 sq.units
We have to find the area of half circle to get the total area of the figure;
Here,
Area of circle = π r²
Then,
Area of half circle = π r² / 2
Here,
r = 6/2 = 3 units
Now,
Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units
That is,
The area of half circle is 14.13 sq.unit
Then,
The total area of figure = Area of [triangle + rectangle + half circle]
The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units
Therefore,
The total area of the figure is 86.13 sq.unit
Learn more about area of half circle here;
https://brainly.com/question/16734739
#SPJ1
12. Triangle ABC has vertices A(-4, 0), B(-4, 5) and C(1, 5) along line AC. Which are the
coordinates of another slope triangle along the same line?
A. D(-2,-2), E(-2, 1) F(-1,0)
B₁6
B. D(-3, 0), E(-3, 1) F(-2, 1)
C. D(-5, -1), E(-5, 0) F(-4, -1)
D. D(-6, -2), E(-6, -1) F(-5, -1)
Please help will mark brainliest
Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)
What is slope?Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.
How to calculate slopeThe given information from the question include
A(-4, 0), B(-4, 5) and C(1, 5)
The slope of the given triangle is calculated as follows
slope = ( 0 - 5 ) / ( -4 - 1 )
slope = -5 / -5
slope = 1
The domain of the line is -4 ≤ x ≤ 1
The range of the line is 0 ≤ y ≤ 5
options C and D values do not satisfy the domain and range conditions
Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.
Learn more on slope of line: https://brainly.com/question/24820338
#SPJ1
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Answer:
D. Undefined
Step-by-step explanation:
[tex]m=[/tex] ∞
Hope this helps
Is it possible to have a series of true conditional statements that lead to a false
conclusion? Explain.
It is possible to have a series of true conditional statements that lead to a false conclusion.
How to illustrate the information?Making decisions based on particular situations is made easier with conditional statements.
A conditional statement's truth value can be either true or false. Simply demonstrate that the conclusion is true whenever the hypothesis is true to establish the truth of a conditional.
Simply demonstrating that the conclusion is wrong each time the hypothesis is true suffices to demonstrate that a conditional is untrue.
Learn more about conditional statement on:
https://brainly.com/question/11073037
#SPJ1
NEED HELP ASAP - 100 Points (Operations with Polynomials)
In multiple sentences, create your own real-world application problem for either adding or subtracting polynomials. Include a description of how the problem can be solved.
Answer: Well we can look at whether or not cubes may or may not equal the same by using volume and surface area, where the volume can be used as x^3 and the surface area x^2, but the reason why polynomials can help us a great deal in world problems is whether or not measurements are accurate, or just in general for solving big math equations. Hope this helps.
Jennie drew a scale drawing of her family's game room. The pool table is 4 feet wide in real life. Using a scale of 1 inch: 2 feet, how wide is the pool table in her drawing?
Please answer ASAP.
(Will give brainliest)
When Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
The width of the pool table in real life = 4 feet
The scale of width in drawing to real life = 1 inch : 2 feet
Therefore the equivalent ratio is
1 inch : 2 feet :: x inches : 4 feet
1 / 2 = x / 4
x = (1/2) × 4
= 2 inches
Hence, when Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
Learn more about ratio here
brainly.com/question/13419413
#SPJ1