Answer:
x = 7/4 = 1.75
Step-by-step explanation:
Hello - so you don't seem to have shown what the calculator screen displays, however I can assume it will show a graph of the two lines, and their intersection point. The x-co-ordinate of this intersection point is the solution to the equation.
As I can't see the calculator, I will also show you how to work out the solution for x:
3x - 1 = 6 -x
4x -1 = 6
4x = 7
x = 7/4 = 1.75
Every seat that is sold in the auditorium costs 8 dollars. In addition to that, the auditorium makes 300 dollars as a flat rate. If the auditorium made $2772.00 dollars, how many seats were sold?
Answer:
309
Step-by-step explanation:
8x + 300 = 2772
subtract 300 from both sides of the equal sign
8x = 2472
divide 8 from both sides of the equal sign
x = 309
The total no. of seats that have been sold is 309
What are linear equalities in one variable?
The linear equation in one variable is an equation that is expressed within the form of ax+b = zero, where a and b are integers, and x is a variable and has only one answer.
Conclusion: For example, 2x+3=8 is a linear equation having a single variable in it. therefore, this equation has only one solution, which is x = 5/2.
let the auditorium sell x seats for 8 dollars per seat.
In addition to that auditorium made 300 dollars.
The total money earned by the auditorium by selling x seats and the addition of 300 dollars is 2772 dollars.
8x + 300 = 2772
8x = 2772 - 300
8x = 2472
x = 2472/ 8
x = 309
The above question is an example of linear equalities in one variable.
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The volume of a cylinder is 384 pie. The radius of the base of the cylinder is 4 cm. What is the height of the cylinder?
Answer:
24 cm
Step-by-step explanation:
Using the formula for a right cylinder: V = (pi)(r^2)(h) you can plug in the numbers provided
384(pi) = (pi) × (4^2) × h
<solve for h>
384(pi) = (pi) × (16) × h
<divide by 16pi>
24 = height
Answer:
24 = h
Step-by-step explanation:
V = πr²h
384π = π(4)²h
384π = 16πh
24 = h
Solve for the following equation x^2+9x+14=0
Answer:
R= {-7,-2}
Step-by-step explanation:
divide 14 into 2 and 7 because 2x7=14write the equation as a multiplication of (x+7) and(x+2) =0for the result to equal zero. at least one of the factors must equal zero, therefore we get two solutionsAnswer:
x^2+9x+14=0
x^2+7x+2x+14=0
x(x+7)+2(x+7)=0
(x+7)(x+2)=0
x+7=0
x+2=0
X=-7
x=-2
Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 20 centimeters and the length of B C is 10.5 centimeters. Angle A B C is x. Which is the best approximation for the measure of angle ABC? 27.7° 31.7° 58.3° 62.3°
The best approximation for the measure of angle ABC is 58.3° ⇒ 3rd answer
Step-by-step explanation:
Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle
The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are
[tex]sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}[/tex] [tex]cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}[/tex] [tex]tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}[/tex]In Δ ABC
∵ ∠ BCA is a right angle
∴ The hypotenuse is AB
∵ The adjacent side to ∠ABC is BC
∵ AB = 20 centimeters
∵ BC = 10.5 centimeters
- Use cosine ratio to find the measure of the angle because you
have the adjacent side of the angle ABC and the hypotenuse
∵ m∠ABC is x
∵ [tex]cos(x)=\frac{BC}{AB}[/tex]
∴ [tex]cos(x)=\frac{10.5}{20}[/tex]
- To find x use the inverse of cos(x)
∵ [tex]x=cos^{-1}(\frac{10.5}{20})[/tex]
∴ x = 58.33°
∴ m∠ABC = 58.33°
The best approximation for the measure of angle ABC is 58.3°
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The best approximation for the measure of angle ABC is 31.7°.
To find the measure of angle ABC (x), we can use trigonometric ratios. Since angle BCA is a right angle, we can use the sine function, which relates the opposite side to the hypotenuse in a right-angled triangle.
Let's denote the sides of the triangle as follows:
BC is the opposite side to angle ABC, with a length of 10.5 cm.
AB is the hypotenuse, with a length of 20 cm.
AC is the adjacent side to angle ABC.
Using the sine function, we have:
[tex]\[ \sin(x) = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{BC}{AB} \][/tex]
[tex]\[ \sin(x) = \frac{10.5}{20} \][/tex]
[tex]\[ \sin(x) = 0.525 \][/tex]
Now, we need to find the angle whose sine is approximately 0.525. Using a calculator or trigonometric tables, we can approximate the angle x. The angle whose sine is approximately 0.525 is about 31.7°.
Can u help me here I have more the next one is part 2 for this question
The circumference of the vase is 18.84 inches.
Step-by-step explanation:
The circumference of the cylinder is same as the circumference of its base.
Moreover, the base of the cylinder is actually a circle.
So we need to find the circumference of the circle to find the circumference of the cylinder.
From the given figure, we know that the diameter of the base d= 6 inches.
∴The formula for the circumference of the circle = 2πr or dπ.
⇒ circumference = 6×3.14.
= 18.84.
So the circumference of the circle is 18.84 inches.
∴The circumference of the cylindrical vase is also 18.84 inches.
An inspector must select three tests to preform in a certain order on a manufactured part. He has a choice of seven tests how many different ways can he perform three tests
Answer:
Therefore the inspector can perform three tests in 35 different ways.
Step-by-step explanation:
i) It is given that there is a total of seven tests that the inspector can perform.
ii) it is also given that the inspector needs to select or choose three tests only out of the seven.
iii) therefore this is a Combination problem.
iv) therefore the number of combinations or selections possible is given by
[tex]\binom{7}{3} = \frac{7!}{(3!)(7 - 3)!} = \frac{7!}{(3!)(4!)} = \frac{42 \times 120}{6 \times 24} = \frac{42 \times 20}{24} = \frac{21 \times 10}{6} = \frac{7 \times 10}{2} = 35[/tex]
Therefore the inspector can perform three tests in 35 different ways.
$400,000 is what percent of $2,000,000?
Answer:a
Step-by-step explanation:
a
Answer:
20%
Step-by-step explanation:
x= 400000/2000000*100
x=20
There are 75 students at tryouts for the basketball team. Of this number, about 65% are in the seventh grade. About how many seventh-grade students are trying out for the team?
49 seventh grade students are trying out for the team.
Step-by-step explanation:
Given,
Total students at tryouts = 75
Percent of seventh grade students = 65%
Number of seventh grade students = [tex]\frac{65}{100}*75[/tex]
Number of seventh grade students = 0.65*75
Number of seventh grade students = 48.75
Rounding off to near whole number
Number of seventh grade students = 49
49 seventh grade students are trying out for the team.
Keywords: percentage, division
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Melinda is thinking of two numbers. Each number is greater than 5. If she multiplies one of the numbers by 3 it will be equal to the other number. What could Melindas numbers be?
Douglas is making catnip mice to sell in the craft fair eat catnip mouse calls for 5/6 ounces of catnip how many ounces of catnip does he need to make 96 catnip mice
Final answer:
To make 96 catnip mice, Douglas needs approximately 80 ounces of catnip.
Explanation:
To calculate how many ounces of catnip Douglas needs to make 96 catnip mice, we can set up a proportion using the given information. Since each catnip mouse requires 5/6 ounces of catnip, we can set up the proportion: 5/6 ounces / 1 catnip mouse = x ounces / 96 catnip mice. To solve for x, we cross-multiply and divide: (5/6) * 96 = x. Therefore, Douglas needs approximately 80 ounces of catnip to make 96 catnip mice.
Douglas needs 80 ounces of catnip to make 96 catnip mice.
To determine how many ounces of catnip Douglas needs to make 96 catnip mice,
we can use the given information that each catnip mouse requires 5/6 ounces of catnip.
To find the total amount of catnip needed,
we can multiply the amount of catnip required for one mouse (5/6 ounces) by the number of mice (96).
5/6 ounces/mouse * 96 mice =
(5/6) * 96 = 80 ounces
Therefore, Douglas needs 80 ounces of catnip to make 96 catnip mice.
PLEASE HELP ME PLEASE AND THANK
Answer: OPTION C.
Step-by-step explanation:
You can observe in the picture given in the exercise that [tex]\angle E[/tex] is formed by two secants intersecting outside the circle.
It is necessary to remember that, by definition:
[tex]Angle\ formed\ by\ two\ Secants=\frac{1}{2}(Difference\ of\ Intercepted\ Arcs)[/tex]
You can also identify that the Intercepted Arcs are the following:
[tex]CD=110\°\\\\AB=30\°[/tex]
Then, knowing the measures of the Intercepted Arcs, you can substitute them into the equation shown before and then evaluate, in order to calculate the measure of [tex]\angle E[/tex] , which is the angle formed by the intersection of the secants.
Therefore, you get:
[tex]m\angle E=\frac{1}{2}(110\°-30\°)\\\\m\angle E=40\°[/tex]
Which grades are middle school in, I'm from Australia so I don't know
Step-by-step explanation:
I think up to grade8 are middle school.
but I am not sure about my answer.
Answer:
6th, 7th, and 8th
Step-by-step explanation:
In America this is the standard middle school grades, however some schools diverge and also include 5th, or sometimes 9th. This, however, is VERY uncommon.
line m in xy plane contains the points (2,4) and (0,1) which of the following is the equation of M
Answer:
The equation of line M in slope intercept form is [tex]y=\frac{3}{2}x+1[/tex]
The equation of line M in standard form is [tex]3x-2y=-2[/tex]
Step-by-step explanation:
step 1
Find the slope of line M
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(2,4) and (0,1)
substitute
[tex]m=\frac{1-4}{0-2}[/tex]
[tex]m=\frac{-3}{-2}[/tex]
[tex]m=\frac{3}{2}[/tex]
step 2
Find the equation of the line M in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{2}[/tex]
[tex]point\ (0,1)[/tex]
substitute
[tex]y-1=\frac{3}{2}(x-0)[/tex]
[tex]y-1=\frac{3}{2}x[/tex] ----> equation in point slope form
step 3
Find the equation of line M in slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y in the equation of the line in point slope form
[tex]y-1=\frac{3}{2}x[/tex]
Adds 1 both sides
[tex]y=\frac{3}{2}x+1[/tex]
step 4
Find the equation of the line M in standard form
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y=\frac{3}{2}x+1[/tex]
Multiply by 2 both sides
[tex]2y=3x+2[/tex]
[tex]3x-2y=-2[/tex] ---> equation in standard form
Final answer:
The equation of line m that contains the points (2, 4) and (0, 1) is found by calculating the slope which is 3/2, and using the y-intercept which is 1. The final equation of the line m is y = (3/2)x + 1.
Explanation:
To find the equation of line m in the xy-plane that contains the points (2, 4) and (0, 1), we first need to calculate the slope of the line. The slope m is calculated as the rise over the run. For our points, the slope can be found by the formula:
m = (y2 - y1) / (x2 - x1)
So,
m = (4 - 1) / (2 - 0) = 3 / 2.
Next, we use one of the points and the slope to find the y-intercept (b). Using the point (0, 1), we plug these values into the equation for a straight line y = mx + b:
1 = (3/2) × 0 + b
Therefore, b = 1.
The equation of line m is y = (3/2)x + 1.
Solve a=2x+6xz for x
Answer: x = a/(2 + 6z)
Step-by-step explanation:
a = 2x + 6xz
a = x(2 + 6z)
x = a/(2 + 6z)
Answer:
Step-by-step explanation:
a = 2x + 6xz ....factor out x on the right side
a = x(2 + 6z) ....divide both sides by 2 + 6z
a / (2 + 6z) = x <===
Burt’s parents allow him to watch 10 hours of television per week. This week Burt is planning to watch several two-hour movies and four hours of sports. Solve to find the number of movies Burt is planning to watch this week.
After setting aside 4 hours for sports, Burt has 6 hours left for television. Since each movie is 2 hours, Burt can watch 3 two-hour movies in the remaining time.
Burt's parents allow him a total of 10 hours of television per week. Since he is planning to watch four hours of sports, we subtract this amount from the total to find the time remaining for watching movies. Here's how we solve for the number of movies Burt can watch:
Total TV time allowed: 10 hours per week
Time planned for watching sports: 4 hours
Time remaining for movies: 10 hours - 4 hours = 6 hours
Since each movie is two hours long, we then divide the remaining time by the length of one movie:
6 hours divided by 2 hours/movie = 3 movies
Therefore, Burt is planning to watch three two-hour movies this week.
PLEASE HELP ASAP !!!
Answer:
The answer is A
Step-by-step explanation:
Answer:
The answer is A. 35 degrees
Step-by-step explanation:
The triangle has to measure up to 180 degrees
add the 2 known angles together
105 + 40 = 145
Subtract the total from 180
180-145= 35
the missing angle is 35
Check Answer:
to check your answer add up all the angle measurements
your total should add up to 180
35 + 40 + 105 = 180
The function f is defined by f(x)=2.1x−1.7. Use this formula to find the following values of f. f(x+2)
The value of [tex]f(x+2)=2.1x+2.5[/tex]
Step-by-step explanation:
Given: The function [tex]f(x)=2.1x-1.7[/tex]
Using this formula, we need to find the value of [tex]f(x+2)[/tex]
Hence, we need to substitute [tex]x[/tex] by [tex]x+2[/tex] to find the value of [tex]f(x+2)[/tex]
[tex]f(x+2)=2.1(x+2)-1.7[/tex]
Multiplying the term [tex](x+2)[/tex] by [tex]2.1[/tex], we get,
[tex]f(x+2)=2.1x+4.2-1.7[/tex]
Adding the constant term,
[tex]f(x+2)=2.1x+2.5[/tex]
Thus, the value of [tex]f(x+2)[/tex] is [tex]f(x+2)=2.1x+2.5[/tex]
There are 3x-2 trees planted in each room of a rectangular parecl of land. If there are a total 24x-16 trees planted in the parcel, how many rows of trees are there in the parcel?
Answer:
8 rows of trees are there in the parcel.
Step-by-step explanation:
The number of trees planted in each row = (3 x -2) trees
The total number of trees planted on the land = (24 x - 16)
Let us assume the total number of rows planted = m
Now,as we know:
The plants in each row x The number of rows = Total trees Planted
⇒ (3 x -2) x (m) = (24 x - 16)
[tex]\implies m = \frac{24x-16}{3x-2}[/tex]
Simplifying for the value of m, we get:
[tex]m = \frac{24x - 16}{3x-2} = \frac{8(3x-2)}{3x-2} = 8\\\implies m = 8[/tex]
Hence, the total number of rows planted = 8
Determine the most precise name for quadrilateral?
a. Parallelogram
b. Rhombus
c. Kite
d. Isosceles trapezoid
Answer:
Parallelogram
Step-by-step explanation:
This diagram shows that the opposite sides of the figure are equal.
The quadrilateral is Parallelogram.
What are types of quadrilateral?A quadrilateral is a polygon having four sides, four points, and four vertices. The Latin words "quad," which means four, and "latus," which means side, are the source of the term "quadrilateral."
There are four basic types of quadrilaterals: parallelograms, squares, rectangles, and rhombuses. Parallelograms include the square, rectangle, and rhombus as well.
Given a quadrilateral,
in which opposite sides are parallel to each other,
the given figure shows opposite side are parallel to each other, so
according to definition of Parallelogram: The opposite sides of a parallelogram are parallel and of equal length. Additionally, opposite angles are equal.
Hence the Given quadrilateral is Parallelogram.
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find the area of the rectangle , i put a pic .
Step-by-step explanation: Notice that the figure shown here is a rectangle so we can find its area by using the formula length x width.
Since the length is 3/7 in and the width is 2/8 in, we can plug this information into the formula to get (3/7)(2/8).
Now multiplying across the numerators and multiplying across the denominators we get 6/56 which can be reduced to 3/28 in².
Could someone please help me with these systems. I have to use substitution.
-7x+2y=18
6x+6y=0
Please show your steps so I can learn too. Thank you.
Final answer:
Using substitution, we solve the equation 6x + 6y = 0 for y, yielding y = -x. Substituting into -7x + 2y = 18 and solving for x gives x = -2. Substituting x back into y = -x, we find y = 2.
Explanation:
To solve the system of equations using substitution, we can isolate one variable in one equation and then substitute it into the other equation. In this case, we've been given the system:
-7x + 2y = 18
6x + 6y = 0
From the second equation, we can isolate y:
6x + 6y = 0
x + y = 0
y = -x
Now, substitute y = -x into the first equation:
-7x + 2(-x) = 18
-7x - 2x = 18
-9x = 18
x = -2
Now that we have the value for x, we can substitute it back into y = -x to find y:
y = -(-2)
y = 2
The solution to the system is x = -2 and y = 2.
Find the measure of x in each figure
Answer:
x = 20
Step-by-step explanation:
The two angle are a linear pair. Their measures has a sum of 180 deg.
2x + 140 = 180
2x = 40
x = 20
7• blank=1 Answer is a fraction
Answer:
1/7
Step-by-step explanation:
if 7 × (?) = 1, just take 1 and divide by 7. Thus, your answer is 1/7
the width of a box is one third of its length. the height of the box is one third of its width. if the length of the box is 27cm, what is the volume of the box?
a. 81cm³
b. 162cm³
c. 243cm³
d. 729cm³
Answer:
d) 729cm^3
Step-by-step explanation:
Length =27cm
Width = 1/3 of length
= 1/3 of 27cm = 1/3 × 27cm = 9cm
Height = 1/3 of width
= 1/3 of 9cm = 1/3 × 9cm = 3cm
Thus, length = 27cm; width = 9cm; height = 3cm
Hence, volume = length × width × height
= 27cm × 9cm × 3cm
= 729cm^3
Volume is a three-dimensional scalar quantity. The volume of the box is 729 cm³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a room or box that is the shape of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
Volume = Length × Width × Height
Given that length of the box is 27 cm. Also, it is mentioned that the width of a box is one third of its length. Therefore, the width of the box is,
Width of the box = (1/3) × 27cm = 9cm
Further, the height of the box is one third of its width. Therefore, the height of the box is,
Height of the box = (1/3) × 9cm = 3 cm
Furthermore, the volume of the box can be written as,
Volume of the box = Length × Width × Height
= 27cm × 9cm × 3cm
= 729 cm³
Hence, the volume of the box is 729 cm³.
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a pentgon has angle of 104,102,115.111 what the angle of the fifth angle
The fifth angle is 108 degrees
Solution:
Given that a pentagon has angle of 104, 102, 115 and 111 We have to find the angle of fifth angle
A pentagon is a five sided polygon
The sum of all the interior angles of a pentagon is 540 degrees
Given that,
Angle 1 = 104
Angle 2 = 102
Angle 3 = 115
Angle 4 = 111
Angle 5 = ?
Let the angle be "x"
So to find the fifth angle, add all the angles and equate to 540 degrees
Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 = 540
104 + 102 + 115 + 111 + x = 540
432 + x = 540
x = 540 - 432
x = 108
Thus the fifth angle is 108 degrees
1. 0.07 = 10m
2. 10.1 = t + 7.2
how would you solve these equations?
Answer: 0.007 and 2.9
Step-by-step explanation:
1) 0.07 = 10m
divide by 10 on both sides
= 0.007
2) 10.1 = t + 7.2
subtract 7.2 from both sides
2.9 = t
The values are;
1. m = 0. 007
2. t = 2.9
How to simply the expressionsFirst, we need to know that algebraic expressions are defined as expressions that are made up of constants, factors, variables and coefficients.
From the information given, we have that;
1. 0.07 = 10m
First, divide both sides by the coefficient of m, we get;
m = 0.07/10
Divide the values
m = 0. 007
2. 10.1 = t + 7.2
collect like terms
't = 10. 1 - 7. 2
subtract the values
t = 2.9
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Whats the answer to -2+(-7/2)
Answer:
-5.5
Step-by-step explanation:
-2 + (-7/2) dividing 7 over 2 to give us -3.5
-2 + (-3.5)
that will give us -5.5
Liana saves $25 every month in her savings account. She took out $100 one
time to Christmas shop. She now has $450 in her account. Write and solve an equation to determine how many months Liana has been saving money. Let m
represent the number of months.
Answer:
Step-by-step explanation:
25m - 100 = 450
25m = 450 + 100
25m = 550
m = 550/25
m = 22 <==== 22 months
someone please answer 28 points please answer with the right facts and the explanation thank you
Describe the sequence of transformations that maps triangle XYZ onto triangle X”Y”Z”
Answer:
The transformation
[tex](x,y) \rightarrow (x-5,-y+1)[/tex]
maps triangle XYZ onto triangle X”Y”Z”.
Step-by-step explanation:
Let us take point Z on the XYZ triangle and see what sequence of transformations we have to apply to map it into the point Z''.
Now Z = (-2, 2) and Z'' = (-7, -1).
The x-coordinate goes from -2 ⇒ -7.
The y-coordinate goes from 2 ⇒ -1.
The x-coordinate is just shifted by -5; thus, [tex]x \rightarrow x-5[/tex], and the y-coordinate first transforms as [tex]y \rightarrow -y[/tex], and is then shifted by 1; thus, it transforms as [tex]y \rightarrow -y+1[/tex].
So we have the full transformation
[tex](x,y) \rightarrow (x-5,-y+1)[/tex]
Ken has 10 red marbles 12 green marbles8 blue marbles 16 yellow marbles in bag
The probability that Mark draws a yellow marble and then a green marble is 1/9.
Explanation:To find the probability that Mark draws a yellow marble and then a green marble, we first need to find the total number of marbles in the bag. The bag contains 4 green marbles, 3 red marbles, and 2 yellow marbles, so the total number of marbles is 4 + 3 + 2 = 9.
Since Mark draws without replacement, the probability of drawing a yellow marble first is 2/9. After drawing a yellow marble, there are now 1 yellow marble and 8 total marbles left in the bag, so the probability of drawing a green marble second is 4/8, or 1/2.
To find the overall probability, we multiply the probabilities of the individual events. Therefore, the probability that Mark draws a yellow marble and then a green marble is (2/9) * (1/2) = 1/9.