Answer:
x ≤ 11/6 or x > 11/3
Step-by-step explanation:
6x - 2 ≤ 9 or 4 + 3x > 15
6x ≤ 11 or 3x > 11
x ≤ 11/6 or x > 11/3
The given inequality is simplified as x≤11/6 or x>4.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, 6x-2≤9 or 4+3x>15.
Here, 6x-2≤9
Add 2 on both the sides of an inequality, we get
6x≤11
Divide 6 on both the sides of an inequality, we get
x≤11/6
Now, 4+3x>15
Subtract 4 on both the sides of an inequality, we get
3x>12
Divide 3 on both the sides of an inequality, we get
x>4
So, x≤11/6 or x>4
Therefore, the given inequality is simplified as x≤11/6 or x>4.
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Solve the following system of equations using matrices:
4x + 5y = 40
X-y=1
You move up 1 unit and down 7 units. You end at (-5, -2). Where did you start?
hi there! heres my answer for you...
Answer:
you started at (-5, 4)
Step-by-step explanation:
do what the instructions given said but in reverse. so move up 7 units and move back down 1 unit and you will find where you started.
hope this helps. have a good one!
The coordinate of the point from where we started will be (1, -2).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
You move up 1 unit and down 7 units. You end at (-5, -2).
Let the initial coordinate be (x, y). Then the transformation is written as,
(-5, -2) → (x + 1 - 7, y)
Compare the abscissa, then we have
- 5 = x + 1 - 7
x = - 5 - 1 + 7
x = 1
Compare the ordinate, then we have
y = -2
Then the coordinate of the point from where we started will be (1, -2).
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The solution to f - (-4) = 12 is f = 8.
True False
Answer:
true
Step-by-step explanation:
as negative takeaway a negative is positive so 8-(-4)= 8+4=12
Answer:
True
Step-by-step explanation:
- * - = +
8 + 4 = 12
so it's true
Solve Please and Thank U
The solution to the systems are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)
How to determine the solution to the system?System 1
In this case, the system of equations is given as
y = -3x + 4
y = 3x - 2
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, 1)
So, the solution is (1, 1)
System 2
In this case, the system of equations is given as
y = x + 2
x = -3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, -1)
So, the solution is (-3, -1)
System 3
In this case, the system of equations is given as
4x + y = 2
x - y = 3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, -2)
So, the solution is (1, -2)
System 4
We have
y = 4x - 9
y = x - 3
Substitute y = 4x - 9 in y = x - 3
4x - 9 = x - 3
Evaluate the like terms
3x = 6
So, we have
x = 2
Recall that:
y = x - 3
So, we have
y = 2 - 3
y = -1
So, the solution is (2, -1)
System 5
We have
x + 7y = 0
2x - 8y = 22
Make x the subject in x + 7y = 0
x = -7y
Substitute x = -7y in 2x - 8y = 22
-14y - 8y = 22
Evaluate the like terms
-22y = 22
So, we have
y = -1
Recall that:
x = -7y
So, we have
x = -7(-1)
x = 7
So, the solution is (7, -1)
System 6
We have
-7x + 2y = 18
6x + 6y = 0
Make x the subject in 6x + 6y = 0
x = -y
Substitute x = -y in -7x + 2y = 18
7y + 2y = 18
Evaluate the like terms
9y = 18
So, we have
y = 2
Recall that:
x = -y
So, we have
x = -2
So, the solution is (-2, 2)
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Consider the number sentence 146 + 7 = 20857, is it true? If not, use what you know about estimation to
determine the correct placement of the decimal point. Justify your solution.
Answer:
No, that number sentence is not true. 146+7 = 153, not 20857
EXCUSE ME WHAT?! I hate my school. They haven’t even said anything about this yet.
Answer:
The first one is acute, the second is right, and the third is obtuse.
Step-by-step explanation:
Hope this helps :)
Have an excellent day!
~sunny~
Answer:
Angle 1 - acute angle
Angle 2 - right angle
Angle 3 - obtuse angle
Step-by-Step Explanation:
The acute angle is smaller than right angles, right angles are 90 degrees, and obtuse angles have larger degree angle than right angles.
XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
The calculated value of k on the line is 9
How to determine the value of kFrom the question, we have the following parameters that can be used in our computation:
XZ is the perpendicular bisector of segment WY
This means that
WX = XY
substitute the known values in the above equation, so, we have the following representation
3k - 4 = 2k + 5
So, we have
3k - 2k = 4 + 5
Evaluate
k = 9
Hence, the value of k is 9
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mark invested a certain amount at 5 % simple interest per year after 10 year he received an interest of 50000 how much did he invest
Step-by-step explanation:
hope it helps u...........
Search Calibri (Body) 11 Å Å Aar to 三三 AL T inter B IU - ab x, X A-D-A Аавьссос Аавьссос Аавьс Аавьсаг АаВ Аавьсаг I Normal 1 No Spac... Heading 1 Heading 2 Title Subtitle Font Paragraph Styles 4. Jacob bought some tickets to see his favorite group, and it cost $76. The relationship between the adult tickets, a, and the student's tickets, s, can be expressed by the equation 10a + 8C = 76. If he bought 4 adult ticket, then how student's tickets did he buy? If he bought 2 student ticket, then how adult's tickets did he buy? Which equation shows the number of student tickets as a function of the number of adult tickets? A. C= 68 – 10a B.C=76 – 10a C. C= -4/5a +38/5 D. C=-5/4a+19/2 Darren works as a truck driver. This graph shows the distance he drove over time during a recent trip. 5
For the first question. Since Jacob bought 4 adult tickets, replace a = 4 in the given equation and solve for s, like this
\(\begin{gathered} 10a+8c=76 \\ a=4 \\ \text{ Replacing} \\ 10(4)+8c=76 \\ 40+8c=76 \\ \text{ Solve for c} \\ \text{ Subtract 40 from both sides of the equation} \\ 40+8c-40=76-40 \\ 8c=36 \end{gathered}\)Which of the following points lie in the solution set to the following system of inequalities?
y > -3x + 3
y > x + 2
(2,5)
(2,-5)
(-2,-5)
(-2,5)
Answer:
not (2,-5)
Step-by-step explanation:
18) What is the slope of the line that contains points (–6, –6) and (–3, 1)?
The slope of the line is 7/9
How to determine the slope of the lineIt is important to note that the equation of a line is represented as;
y = mx + c
Where;
y is a point on the linem is the slope of the linex is a point on the x - axisc is the intercept of the y-axisThe formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/x₂ - x₁
Now, let's substitute the values into the formula from the points given we have;
Slope, m =1 -(-6)/ -3 - (-6)
expand the bracket
Slope, m = 1 + 6/ 3 + 6
add the values
Slope, m = 7/9
Hence, the value is 7/9
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Amy's car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas she needs, in liters, to fill the gas tank.
Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
Please help. Will award brainliest
The dimension of the rectangular of a norman window will be 1.6803*3.3606.
What is the area of Rectangle?
In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.
Let r represents the radius, and b be the breadth.
Then, perimeter = 3.14*r+2r+2b = 12
For the dimension needed for the most light to enter we need to maximize the area.
Hence, area of the window : area of the semicircle + area of the rectangle
= \(\frac{3.14*r^2}{2} + 2rb\)
= \(12r - (\frac{3.14+4}{2}) r^2\)
A'(r) = 0
Therefore, \(r=\frac{12}{3.14+4}\) which is nearly equal to 1.6803m
From this value of r we can calculate the value of b to be;
b= 1.6803m
Thus, a= 3.606m
Thus the required dimension is : 1.6803*33606
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Find an angle θ that is coterminal with an angle measuring −490∘, where 0∘≤θ<360∘. Do not include the degree symbol in your answer. For example, if your answer is 20∘, you would enter 20.
Answer: \(230\)
Step-by-step explanation:
To find coterminal angles, add/subtract integer multiples of \(360^{\circ}\).
\(-490^{\circ}+360^{\circ}=-130^{\circ}\\\\-130^{\circ}+360^{\circ}=230^{\circ}\)
An angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
To find an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘, we can use the concept of coterminal angles.
Coterminal angles are angles that have the same initial and terminal sides when drawn in standard position. To find a positive coterminal angle with a negative angle, we can add 360 degrees to the negative angle until we get an angle within the desired range (0∘ to 360∘).
Let's find the positive coterminal angle:
θ = -490∘ + 360∘
θ = -130∘
So, an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.
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help me? please?????????
Answer:
\(\huge\boxed{\tt{\frac{8}{63} }}\)
Step-by-step explanation:
\(\displaystyle \frac{8}{9} * \frac{1}{7} \\\\= \frac{8*1}{9*7} \\\\= \frac{8}{63} \\\\\rule[225]{225}{2}\)
Hope this helped!
~AH1807Kermit's favorite iced tea is made with 151515 tea bags in every 222 liters of water. Peggy made a 121212-liter batch of iced tea with 909090 tea bags. What will Kermit think of Peggy's iced tea?
A. It is too strong.
B. It is too weak.
C. It is just right.
Answer:
C. It is just right
Step-by-step explanation:
Kermit's Favorite iced tea:
Tea bags = 15
Water = 2 liters
Ratio of tea bags to water = 15 : 2
= 15/2
= 7.5
Peggy:
Tea bags = 90
Water = 12 liters
Ratio of tea bags to water = 90 : 12
= 90/12
= 7.5
C. It is just right
Kermit would think of Peggy's iced tea is just right
Answer:
c
Step-by-step explanation:
Kyle drives 32.2 miles one way each day during his commute to work. He drives to and from work 5 days a week. If you round the one way trip to the nearest ones place, approximately how many miles does Kyle commute each week?
Answer:
160
Step-by-step explanation:
round 32 to 30
then 30 x 5 =150
150 miles
In the following diagram, ABCDABCD is a square. The coordinates of the vertices A,B,CA,B,C and DD are (3,3),(8,3),(8,8)(3,3),(8,3),(8,8) and (3,8)(3,8) respectively.
The square is dilated from the origin by a factor of 1111 to give A′B′C′D′A′B′C′D′.
What are the coordinates of point C′C′? (NEED THIS ASAP)
Answer:
Step-by-step explanation:
To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.
The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:
x-coordinate of C' = 1111 * 8 = 8888
y-coordinate of C' = 1111 * 8 = 8888
Therefore, the coordinates of point C' are (8888, 8888).
What is the fraction for 9 copies of 1/12
Answer:
9 x 1/12 = 4 1/2
Im needing help please Find all real zeros of the function Please see attached picture
We must find the zeros of the following function:
\(f(x)=4\cdot(x+3)^2\cdot(x-3)\cdot(x^2-49).\)Now, the zeros of a function are the values of x when f(x) is equal to 0. So we must find all the values of x that makes f(x) = 0. To do that, it is convenient to rewrite the function f(x) as:
\(f(x)=4\cdot(x+3)\cdot(x+3)\cdot(x-3)\cdot(x+7)\cdot(x-7)\text{.}\)Where we use the fact that:
• (x + 3)² = (x + 3) (x + 3),
,• (x² + 49) = (x + 7) (x - 7).
From the previous equation, we see that if we replace x with the following values, we get f(x) = 0:
• x = -3,
,• x = 3,
,• x = -7,
,• x = 7.
Answer
All the real zeros of the function are -3, 3, -7, 7.
Write the expression for the following statement without
any spaces:
the sum of 64y and 3, cubed can be expressed as
The expression of the statement that is given above can be written as follows: 262144y³ + 27.
How to determine a way to express the given statement?To determine how to express the given statement the following should be carried out.
When a number is said to be cubed, it means that the number should be times by itself three consecutive times.
That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,
= 64×64×64(y)³ + 3×3×3
= 262144y³ + 27.
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What is the length of the sink using the red line on the tape measure?
Answer:
A.
Step-by-step explanation:
help please need it adap
Answer:
supplementary angle to x = 180 - 31 - 43 - 32 = 74°
x = 180° - 74° = 106°
(Algebra 2)
C(x) = (12,000x - 0.02x^3) - (3000x - 0.002x^3)
Write a simplified expression for C(x).
A. C(x) = -0.022x^3 + 9000x
B. C(x) = -0.018x^3 + 9000x
C. C(x) = -0.022x^3 + 15,000x
Answer:
B
Step-by-step explanation:
C(x) = (12,000x - 0.02x^3) - (3000x - 0.002x^3)
C(x) = 12,000x - 0.02x^3 - 3000)x + 0.002x^3
C(x) = (12,000 - 3,000)x + (-0.02 - 0.002)x^3
= 9000x - 0.018x^3
The following table presents the temperatures measured on a heat plate:
Using linear interpolation find the temperature at x=4, y=3.2.
The temperature at x = 4, y = 3.2, estimated through linear interpolation from the given data points, is approximately 46.744.
How to Use Linear Interpolation to find the Temperature?To find the temperature at x=4, y=3.2 using linear interpolation, first of all, determine the values at the surrounding grid points and interpolate between them.
From the given table, we can identify the following surrounding points:
Point A: (x=4, y=3)
Point B: (x=4, y=4)
Point C: (x=6, y=3)
Point D: (x=6, y=4)
Next, interpolate along the x-axis at y=3 to find the temperature at x=4:
Temperature at x=4, y=3 = Interpolate(A, B)
Also, we have to interpolate along the x-axis at y=4 to find the temperature at x=4:
Temperature at x=4, y=4 = Interpolate(A, B)
Next, we'll interpolate between the temperatures obtained above along the y-axis at y=3.2:
Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)
Let's calculate these values step by step:
Interpolate along the x-axis at y=3:
Temperature at x=4, y=3 = Interpolate(A, B)
= 80.00 + (4-4)/(4-4) * (80.00 - 80.00)
= 80.00
Interpolate along the x-axis at y=4:
Temperature at x=4, y=4 = Interpolate(A, B)
= 38.43 + (4-4)/(4-4) * (35.03 - 38.43)
= 38.43
Interpolate between temperatures along the y-axis at y=3.2:
Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)
= 80.00 + (3.2-3)/(4-3) * (38.43 - 80.00)
= 80.00 - 0.8 * 41.57
= 80.00 - 33.256
= 46.744
Therefore, the temperature at x=4, y=3.2 is approximately 46.744.
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If r = 8 units and h = 8 units, what is the volume of the cylinder shown above? Use 3.14 for.
PLEASE SHOW ME HOW YOU GOT THE ANSWER
The volume (V) of a cylinder is π (r^2) (h). Substituting in the known values, you get V = 3.14 times 64 times 8, which is 1607.68 cubic units.
7Consider the line y= 5x+5.$*+5.Find the equation of the line that is parallel to this line and passes through the point (-9, 2).Find the equation of the line that is perpendicular to this line and passes through the point (-9, 2).Note that the ALEKS graphing calculator may be helpful in checking your answer.
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equation is expressed as
y = 7x/3 + 5
By comparing both equations, slope,m = 7/3
Recall, if two lines are parallel, it means that they have the same slope. This means that the slope of the line parallel to the given line is 7/3. Since the line passes through the point(- 9, 2), to find the y intercept of this line, we would substitute m = 7/3, x = - 9 and y = 2 into the slope intercept equation. We have
2 = 7/3 * - 9 + c
2 = - 21 + c
c = 2 + 21 = 23
The equation of the parallel line is
y = 7x/3 + 23
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. This means that the slope of the line perpendicular to the given line is - 3/7. Since the line passes through the point(- 9, 2), to find the y intercept of this line, we would substitute m = - 3/7, x = - 9 and y = 2 into the slope intercept equation. We have
2 = - 3/7 * - 9 + c
2 = 27/7 + c
c = 2 - 27/7
c = - 13/7
The equation of the perpendicular line is
y = - 3x/7 - 13/7
Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5
1. Construct a histogram for the data.
Answer:
Step-by-step explanation:
This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.
A jar of peanut butter contains 50 tablespoons of peanut butter.
How many sandwiches can you make from the jar of peanut butter, assuming you have plenty of bread and jelly?
A. 25 sandwiches
B. 9 sandwiches
C. 10 sandwiches
D. 50 sandwiches
Answer:
the correct answer is A. 25 sandwiches.
Step-by-step explanation:
Assuming you have plenty of bread and jelly, you can make 25 sandwiches from the jar of peanut butter.
Each sandwich typically requires 2 tablespoons of peanut butter, one slice of bread with peanut butter and one slice of bread with jelly.
So, if you have 50 tablespoons of peanut butter, you can make 25 sandwiches with it, because 50 / 2 = 25.
Therefore, the correct answer is A. 25 sandwiches.
Answer: 25
Step-by-step explanation:
We have 50 tablespoons of peanut butter and we know that it requires 2 tablespoons to make a single sandwich. In order to find how many sandwiches we can make with our 50 tablespoons, we would have to do 50 divided by 2.
2+2...=50
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle. Use words, numbers, or models to justify your answer.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.
Step-by-step explanation:We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.
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