Translate and solve: -5 times b is no less than 35.
Note: Write your solution in interval notation,
The solution in interval notation b ∈ (-∞ , -7)
-5 times b is no less than 35.
5b ≥ 35
n order to isolate the variable in this linear inequality, we need to get rid of the coefficient that multiplies it.
-[tex]\frac{5b}{5} = \frac{-35}{5}[/tex]
This can be accomplished if both sides are divided by .
Notice that the inequality sign has changed.
b ≤ -7
We need to reduce this fraction to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
In our example, this is the common factor:5
b ∈ (-∞ , -7)
We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.
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Luke and Seth each need to buy the same amount of fencing for their gardens. While Seth's garden is square in shape, Luke's garden is rectangular with the length 3 feet longer than Seth's. Luke's width is half of the length of his own garden.
How much fencing did each buy? Need this asap please and thank you.
option
40. 5 feet
81 feet
72 feet
36 feet
Fencing that Luke and Seth did each buy is 72 feet
Using the information given, you can set up and solve the system of equations. Let x be the length of Seth's garden.
Seth's garden is square, so it has four times the perimeter.
The perimeter of Luke's garden is a rectangle of length x + 3 feet and width x/2 feet, so 2(x + 3) + 2(x/2).
We also know that Luke and Seth should buy the same amount of fences. So:
4x = 2(x + 3) + 2(x/2)
Solving this equation for x gives x = 6 feet.
So Seth's yardage is 6 feet and Luke's yardage is 9 feet.
So the fence required for Seth's garden is 46 = 24 feet
and the fence required for Luke's garden is 2(9) + 2(9/2) = 29 + 2*4.5 = 36 + 9 = 45 It's feet.
So the total fencing required is 24 + 45 = 72 feet.
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C. It will
make 18 more parts.
5
Which number line shows the solution set to 1< -49 - 13/9 x <55/3?
The inequality is x 26 and asks for the values of x where the perimeter of the rectangle is smaller than 112.
The definition of inequalityIn mathematics, a link between two terms or values that isn't comparable is referred to as an inequality. As a result, imbalance leads to inequality. A mathematical inequality is a relationship between two non-equal expression . Egality is distinct from inequality. The not common basic is frequently used to denote that two values aren't actually equal (). Various inequalities are used to contrast the values, no matter how small or large. Many simple inequalities can be resolved by switching the two aspects until the variables are the only thing remaining. But a number of things encourage inequality: Values that are negative are divided or added along either side.
Here,
given
A rectangle's perimeter is determined by its length, width, and height.
rectangle's perimeter is calculated as length + length + width + width.
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
In order to find the x value that occur when the rectangle's boundary is less than 112, the inequality is x 26.
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Why infinity is open interval?
The number line is drawn to find the open end point interval is infinity.
Number Line of an Open endpoint to the endpoint of number line =?
Selection of Open endpoint to the endpoint of the number line is fit for the following intervals as such determined below :
basically the intervals are mentioned as follow
( ), [ ], ( ], [ )
An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and
(-a , a) are open intervals.
For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).
Secondly, the definition forgot to add that (−∞,∞) is also open
Take numbers as follows:
Final Answer as followed in intervals
(-2, 2)
[-2, 2]
(-∞, 2]
[2, ∞)
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Are 2 sides of an isosceles triangle?
Yes, the lengths of the two sides of an isosceles triangle are equal.
An isosceles triangle is a type of triangle that has two sides that are equal in length. The other side of the triangle can be either longer or shorter than the two equal sides. The two equal sides are called the legs, and the other side is called the base. The angles opposite the two equal sides are also equal in measure. Because of this, the two equal sides create an angle bisector that divides the base into two equal parts. This angle bisector forms two angles of equal measure as well. Thus, the two equal sides of an isosceles triangle are a defining feature of the shape.
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In altitude BH and angle bisector AL intersect at point M. Given m∠HML = 100° and m∠MLC = 110°. Find angles of △ABC
The angles of triangle ABC are 60 degrees when altitude BH and bisector AL intersect at point M.
What is equilateral triangle?
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides.
Given that:
[tex]\angle HML = 100 \\\\\angle MLC = 110[/tex]
Since, BH is the altitude [tex]\angle MHC= 90[/tex].
The total angle of a quadrilateral is 360, hence:
100 + 110 + 90 + C = 360
C = 60 degrees.
Now consider triangle BHC:
The sum of angle of a triangle is 180, hence:
90 + 60 + B = 180
B = 30
Since the half angle B = 30, the entire [tex]\angle ABC = 60[/tex].
Consider triangle ABC:
Using sum of triangles, we have:
[tex]\angle A + \angle B + \angle C = 180\\\\\angle A + 60 + 60 = 180 \\\\\angle A = 60[/tex]
Hence the measure of angles of triangle ABC is 60 degrees.
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(6b+ 2) - (4b + 3)
Help pls I don’t know how to do this
Answer:
2b - 1
Step-by-step explanation:
To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:
1(6b + 2) - 1(4b + 3)
We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:
6b + 2 - 4b - 3
Then, we group our like terms:
6b - 4b + 2 - 3
Then, we subtract, giving us:
2b - 1
So the most simplified version is 2b - 1.
Hope this helped!
Answer:
Step-by-step explanation:
You begin by distributing the negative so -4b -3
then you will multiply (6b+2) by (-4b -3)
24b^2 - 18b - 8b - 6
answer = 24b^2 - 26b - 6
..Solve multi step problems
Help me.....
Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards
What is MultiplicationMultiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.
In this problem, we may require the use of some mathematical operators to find the solution to the problem.
1.
He currently has 216 cards, but he needs 15 sets of cards.
1 set of card = 72 cards
Let's calculate the number of sets he currently has.
1 set of card = 72 cards
x set = 216 cards
cross multiply both sides and solve for x.
x * 72 = 216 * 1
x = 216 / 72
x = 3 sets
He currently has 3 sets of cards.
Since he wants 15 sets of cards, we will need 12 more set of cards.
The number of cards can be calculated by multiplying 12 by 72
Number of cards = 12 * 72 = 864
He needs 864 more cards.
2.
1 set of card = $27
1 set = 72 cards
But she's bringing $9 to join, we can calculate the ratio of cards she will get.
1 / 27 = x / 9
x = 9 / 27
x = 1/3
She will get 1/3 of the cards bought which will be
72 * 1/3 = 24 cards
She will get 24 cards
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Please help me plssss
Explanation
Check the picture below.
a. Complete the table to show the length of the field for each given width.
Width (feet) Length (feet) 0 50 100 150 200 250 300
b. Define the function (w) to represent the length of the field as
The length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that a table for showing the relation between length and width of a field;
Width (w) Length (l)
0 50
100 150
200 250
300 350
We see, that, width is 50 less than the length.
Therefore, the function (w) to represent the length of the field will be =
w = l-50
Hence, the length of the field for the missing width is 350 ft. and the function (w) to represent the length of the field is w = (l-50)
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Angle A and Angle B are complementary angles. The measure of Angle A is twice the measure of Angle B.
Write and equation to represent the complementary angle relationship between Angle A and Angle B. Use the equation to find
the measure of Angle A and B. Show all of your work.
Answer:
Acc.to question,
A+B=90° (since,they are complementary angles)
or,A+ A/2=90°(since,A is. twice the measure of B)
or,3A/2=90°
or,A=(90°×2)/3
:.A=60°
Also,
B=A/2=60/2=30°
Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
i got 2/4 of the marks pls help
Answer:
Step-by-step explanation:
Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled
Help me pls I’m struggling and I can’t solve it
The perimeter of the rectangle is 4y + 6 (cm).
How can the perimeter equation be found?All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.
The diagram shows a rectangle. All measurements are in centimetres an expression in terms of y, for the perimeter of the rectangle.
The perimeter of the rectangle is
2(y+3)+24
=2y + 6 + 2y = 4y + 6 (cm)
{ the perimeter:
2 * width + 2 * Length}
The perimeter of the rectangle is 4y + 6 (cm).
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The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?
48
39
57
Answer:
39
Step-by-step explanation:
Find the point(s) on the surface at which the tangent plane is horizontal.
z = xy + 1 x + 1 y
The point(s) on the surface at which the tangent plane is horizontal are (0, 0, 1).
To find the point(s) on the surface at which the tangent plane is horizontal, we need to find the points at which the partial derivatives of z with respect to x and y are both equal to 0. This means we need to solve the system of equations:
∂z/∂x = 0 ∂z/∂y = 0Solving this system of equations yields x = 0, y = 0, and z = 1. Therefore, the point(s) on the surface at which the tangent plane is horizontal is (0, 0, 1).
To understand why solving the system of equations yields the points for which the tangent plane is horizontal, it is important to understand what the partial derivatives represent. The partial derivative of z with respect to x is the rate of change of z with respect to x, and similarly for y.
When the partial derivatives are both equal to 0, it means that the rate of change of z with respect to x and y is 0, which implies that the tangent plane is horizontal.
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F(x)=\begin{cases}-2 & \text{ for }\hspace{10px} -6< x <-1\phantom{\frac{1}{1}} \\ -x-3 & \text{ for }\hspace{10px} -1< x <5\phantom{\frac{1}{1}}\end{cases} f(x)={ −2 −x−3 for −6
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
what is function ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
We note that x=7 is on 1<x< 9 so we use the second piece. Replace x with 7 and
evaluate to find f(7):
f(7)=2(7)
f(7)=14
so f( 7 ) = 14
f(7) = 14 is calculated. Each function is given a domain and a codomain, or scope.
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Find the values of x and y
The values of x and y, given the angles in the diagram, can be found to be :
x = 11y = 17How to find the value of x and y ?The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.
This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to ( 7y - 34 )°.
The value of x is :
8 x + 7 = 9 x - 4
9x - 8x = 7 + 4
x = 11
The value of y is :
5 y = 7y - 34
7y - 5y = 34
2 y = 34
y = 34 / 2
y = 17
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Find the surface area, volume, and radius and select all the correct measurements,
Answer:
surface area ---> i
volume ---> b
radius ---> d
Step-by-step explanation:
surface area= 4πr² =4x3.14x14²=2461.76cm²
volume= (4÷3)πr³= (4÷3)x3.14x14³=11488.21cm³
radius = half the diameter = 14cm
dividing decimals up to 2 decimal places
1.0.2÷6.11
Answer:
its 6.11
6.11 ÷ 1 = 6.11
Calculated to 2 decimal places.
6. 1 1
1 6. 1 1
− 6
0 1
− 1
0 1
− 1
0
Does (1, 10) make the inequality y ≤ 5x + 4 true?
yes
no?
Answer:
No, it is not true
Step-by-step explanation:
y ≤ 5x + 4
We know a point is (1,10), we need to put the 1 in for x and the 10 in for y to see if the inequality is true or not!
10 ≤ 5(1) + 4
10 ≤ 5 + 4
10 ≤ 9
This is not True!
Answer: nope
Step-by-step explanation:
knowing the difference between an experimental group and a control group is most relevant to understanding the nature of: group of answer choices random sampling. replication. hindsight bias. independent variables.
The experimental group is given the experimental treatment, and the comparison group is statistically significant.
Which three attitudes are the basis of the scientific viewpoint?Curiosity, scepticism, and humility are described by historians of science as the three attitudes that form the bedrock of the scientific viewpoint. Larger, more representative sample sizes aid in the production of accurate and valid data.When random sampling is used, every member of the population has an equal chance of being chosen, resulting in the collection of a representative sample. The odds of generalising the study's findings to the population increase with the use of a random sample. The study's margin of error is reduced with higher study sample sizes.) Researcher control over the possibility of reporting false-negative or false-positive findings is made possible by larger sample sizes. Results will be more precisely predicted with a larger sample size.To learn more about random sampling refer to :
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HEEELLP me PLEASE!!!
Answer:
T=(I/p)/r
Step-by-step explanation:
I = Prt is the same thing as: I = P*r*t
We want the answer to be as:
T = ???
The only thing you need to do is the get T to one side.
1. [tex]I = P*r*t[/tex]
2. [tex]I/p=r*t[/tex]
3. [tex](I/p)/r=t[/tex]
4. [tex]t=(I/p)/r[/tex]
Ben wants to buy a binder and some penicals from the school store.binders coast 2.25 each of the pencials coast 0.75 each.how much will it coasg ben to buy 1 binder and P penicals
The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Cost of a binder = 2.25
Cost of a pencil = 0.75
We have to find the total cost for Ben to buy 1 binder and P pencils.
Cost of 1 binder = 2.25
Cost of P pencils = 0.75 × P = 0.75 P
Total cost of 1 binder and P pencils = 2.25 + 0.75 P
Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.
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Reggie made a scale drawing of a house. In real life, the garage is 3 meters wide. It is 6 millimeters wide in the drawing. What is the drawing's scale factor?
Answer:
1:50
Step-by-step explanation:
The drawing's scale factor is
1:50
Explanation:
In drawing, width of the garage is 6 cm and in actual width of the garage is 3m or 3×100=300 cm.
Hence, the drawing's scale factor is 6:300 and dividing by 6, it is 1:50
Reflect shape A in the line y = -x. (See picture)
Answer:
See picture below
Step-by-step explanation:
Additive Relationships
What is the value of y when x=100y=?
The value of y in the equation is y = x / 100.
How to make a variable the subject of the formula?Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.
Therefore, let's make y the subject of the formula in the equation x = 100y.
Hence, we will find y in terms of x.
Therefore,
x = 100y
divide both sides of the equation by 100
100y / 100 = x / 100
y = x / 100
Therefore,
y = x / 100
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What is the greatest common factor of 24,40,32 A.1 B.2 C.4 D.8
Answer:
D. 8
Step-by-step explanation:
8*3=24
8*5=40
8*4=32
Can you help me with this
The linear function that passes through (3,1) and has a slope of -1/2 is defined as follows:
y = -0.5x + 2.5.
The graph of the linear function is given by the image presented at the end of the answer.
How to define the linear function?The linear function for this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value assumed by the output variable y when the input variable x assumes a value of zero.The slope of the function in this problem is given as follows:
m = -1/2 = -0.5
Hence:
y = -0.5x + b.
The line passing through point (3,1) means that when x = 3, y = 1, and thus the intercept b is obtained as follows:
1 = -0.5(3) + b
1 = -1.5 + b
b = 2.5.
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Using the five digits 7, 7, 8, 8, and 8 once each, how many positive five-digit integers can be formed?
Answer:
There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.
Type the correct answer in each box. The coordinates of the point that corresponds to an angle of radians in the unit circle are (, ).
On solving the provided question, we can say that coordinates of the point in the unit circle S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
S = (0, -1 )
coordinates of the point in the unit circle
S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )
S= ( 0 , -1 )
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