Answers
b≤-7 mean b is "less than or equal to 7"
the arrow to the left of seven is the "less" part and the filled circle is the "equal to" part.
Related Questions
The graph of which of the following equations contains the points (2, 3) and (3, 2)? y = x - 1
y = 5 - x
y= 7 - 2x
Answers
Among all rectangles that have a perimeter of 156, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.
Answers
We have a perimeter of 156, so we have
2L + 2W = 156
Let the length = x
2x + 2W = 156
The width is
2W = 156 - 2x
W = 78 - x
The area of a rectangle is A = LW
A = x(78 - x)
A = 78x - x^2
This is an inverted parabola, so there is a maximum value.
78x - x^2 = 0
x(78 - x) = 0
x = 0 or x = 78
The zeros of the parabola are at x = 0 and x = 78.
Since the parabola is symmetric over its vertical axis, the maximum values occurs at the x-value in the middle of 0 to 78, which is 39.
At x = 39, the area has a maximum value.
L = 39 & W = 39
It's a square with side measuring 39.
The dimensions of the one whose area is largest is 39 by 39
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 156
2L + 2W = 156
L + W = 78
W = 78 - L
The area of the rectangle is expressed as:
A = LW
A = L(78-L)
A = 78L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 78 - 2L
0 = 78 - 2L
2L = 78
L = 78/2
L = 39
Recall that 2(L+W) = 156
2(39 + W) = 156
39 + W = 78
W = 78 - 39
W = 39
Hence the dimensions of the one whose area is largest is 39 by 39
Learn more here: https://brainly.com/question/17229451
I need help asap
the triangles below are congruent. which of the following statements are true
A. a~=d
B. b~=e
C. ab~=de
D. bc~=df
Answers
Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth.
A) JKM is a right triangle because KM = 15.3.
B) JKM is a right triangle because KM = 18.2.
C) JKM is not a right triangle because KM ≠ 15.3.
D) JKM is not a right triangle because KM ≠ 18.2.
Answers
Answer:
C. JKM is not a right triangle because KM ≠ 15.3.
Step-by-step explanation:
We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.
In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].
We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].
Using Pythagorean theorem in triangle JLM we will get,
[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]
[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]
[tex]LM=\sqrt{64-25}[/tex]
[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]
Now let us find length of side KL.
[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]
[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]
[tex]KL=\sqrt{169-25}[/tex]
[tex]KL=\sqrt{144}=12[/tex]
Now let us find length of KM by adding lengths of KL and LM.
[tex]KM=12+6.24=18.24[/tex]
Now let us find whether JKM is right triangle or not using Pythagorean theorem.
[tex]KM^{2}=JK^{2}+JM^{2}[/tex]
[tex]18.24^{2}=13^{2}+8^{2}[/tex]
[tex]18.24^{2}=169+64[/tex]
[tex]18.24^{2}=233[/tex]
Upon taking square root of both sides of equation we will get,
[tex]18.24\neq 15.264337522473748[/tex]
[tex]18.2\neq 15.3[/tex]
We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.
Answer:
I just took the test it is C
The measure of an angle is forty-four times the measure of a supplementary angle. what is the measure of each angle?
Answers
x+44x=180°
x=4
The angle is 4°, supp angle is 176°
Twelve less than negative nine times a number is equal to 8 minus 4 times the number find the number
Answers
Final answer:
The number that satisfies the original equation is -4.
Explanation:
A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.
To solve this, we set up the equation -9x - 12 = 8 - 4x.
Solving for 'x' involves simple algebraic steps.
First, add 9x to both sides to get the variable terms on one side:
-9x - 12 + 9x = 8 - 4x + 9x-12 = 8 + 5xNext, subtract 8 from both sides to isolate the variable term:
-12 - 8 = 5x-20 = 5xFinally, divide both sides by 5 to find 'x':
-20 / 5 = 5x / 5-4 = xThe number that satisfies the original equation is -4.
7n2 + 8n − 12
A) (7n + 6)(n − 2)
B) (5n − 8)(n + 10)
C) Not factorable
D) (7n − 6)(n + 2)
Answers
= (7n - 6)(n + 2)
cause
(7n - 6)(n + 2)
= 7n^2 - 6n + 14n - 12
= 7n^2 + 8n - 12
answer
D) (7n − 6)(n + 2)
A club with 19 members is to choose three officers president vice president and security secretary treasurer. If each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled
Answers
When is a protractor preferred to a ruler when finding a measurement
Answers
A protractor is preferred over a ruler when measuring angles, especially in geometric shapes or when dealing with rotational aspects. While a ruler is great for measuring lengths and distances, it can't accurately measure angles.
For example, let's say you want to measure the angle between two lines on a piece of paper. A ruler can only give you an approximation by comparing lengths, but a protractor will give you an exact measurement of the angle in degrees.
To use a protractor, align the center hole of the protractor with the vertex of the angle. Then, align one side of the angle with the zero-degree mark on the protractor. Finally, read the number where the second side of the angle intersects the protractor scale. This gives you the precise measurement of the angle.
In conclusion, when dealing with angles, a protractor is the preferred tool for accurate measurements, providing exact angles in degrees.
Consider the terms pyramid, line, square, and triangle. The term ____is not defined in Euclidean geometry.
Answers
Answer: Pyramid
Please help me
6 (d+1) - 2d = 54
Answers
6(d+1) -2d=54
distribute the 6
6d+6 -2d=54
subtract 2d from 6d
4d+6 =54
subtract 6 from each side
4d=48
divide both sides by 4 to get d
d=48/4
d=12
A bathtub that holds 32 gallons of water contains 12 gallons of water. begin filling it, and after 5 minutes the tub is filled. write a standard equation
Answers
Answer:
In standard equation format, the condition can be written as [tex]V=5x+12[/tex].
Step-by-step explanation:
The capacity of the bathtub is 32 gallons.
The water already in the tub is 12 gallon.
It takes 5 minutes for the tub to be filled.
Let x be the flow rate of water through tap, in gallon per minutes.
Now, the water filled in the tank in 5 minutes will be [tex]5x[/tex] gallons.
So, in equation, the given condition can be written as,
[tex]V=5x+12\\32=5x+12[/tex]
here V represents the volume of the bathtub.
Therefore, in standard equation format, the condition can be written as [tex]V=5x+12[/tex].
For more details, refer the link:
https://brainly.com/question/22527528?referrer=searchResults
The standard equation for the volume of water in the bathtub at time t is V(t) = 12 + 4t, indicating the tub starts with 12 gallons and fills at a rate of 4 gallons per minute.
Explanation:To write a standard equation for filling a bathtub, we need to find the rate at which the tub fills. Since the tub starts with 12 gallons and ends up holding 32 gallons, it needs an additional 20 gallons to be filled. If it takes 5 minutes to fill these 20 gallons, then the fill rate is 20 gallons per 5 minutes.
The equation for the volume V of water in the tub at any given time t (in minutes) is:
V(t) = 12 + r × t
where r is the rate of filling the tub. We already calculated r to be 4 gallons per minute (20 gallons/5 minutes). Therefore, the equation becomes:
V(t) = 12 + 4t
This equation represents the amount of water in the bathtub at any given time t, assuming it starts with 12 gallons and fills at a rate of 4 gallons a minute.
Juan used the expression 16 – 9 – 12 + 22 to find his profit for days 2 and 3. He rewrote the expression as 16 + (–9) + (–12) + 22. Juan can use the associative and commutative properties to rewrite the expression again. Explain why he had to use the additive inverse before he could use these properties.
Answers
Answer:
Associative property and commutative property true for addition, not true for subtraction.
Step-by-step explanation:
Associative property and commutative property true for addition.
i) a + (b + c) = (a + b) + c ---> Associative property of addition
ii) a + b = b + a --> commutative property of addition.
These properties not true for subtraction.
That's the reason Juan used additive inverse before applying these property.
Hope this will helpful.
Thank you.
[tex]\bold{ a + (b + c) = (a + b) + c } \to[/tex] Associative property of addition
[tex]\bold{a + b = b + a } \to[/tex] commutative property of addition.
As we show above both the property used for the addition and no used for the subtraction, that is why before applying the property Juan applied reverse additives.Learn more:
brainly.com/question/14001628
What is the function rule for the line?
f(x)=2/3x−2
f(x)=3/2x−2
f(x)=−2/3x−2
f(x)=3/2x+2
Answers
The function rule of the line is, f(x)=2/3x-2
What is a straight line?
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (0,-2) and, (3,0)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+2)/(x-0)=(0+2)/(3-0)
=>3y+6=2x
=>y=2/3x-2
Let, y= f(x)
So, the required function rule of the line is f(x)=2/3x-2
Hence, the required function rule of the line is, f(x)=2/3x-2
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ3
Claire's cousin is now 3 times as old as Claire. in 10 years, her cousin will be twice as old as claire. how old is Claire now?
Answers
Claire is currently 10 years old.
Explanation:Let's assume that Claire's age is x.
According to the given information, Claire's cousin is now 3 times as old as Claire. This can be represented as Cousin's age = 3x.
In 10 years, Cousin's age will be twice as old as Claire's age. So, we can write the equation:
(3x + 10) = 2(x + 10)
Simplifying the equation:
3x + 10 = 2x + 20
Subtracting 2x from both sides:
x + 10 = 20
Subtracting 10 from both sides:
x = 10
Therefore, Claire is currently 10 years old.
Write a proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Answers
A rectangle is defined as having 4 right angles and that the opposite sides are both congruent and parallel to each other. Also, if two numbers are equal, their square roots are equal as well.
I hope this helped you! :)
Answer:
The diagonals intersect each other
Step-by-step explanation:
One of the distinguishing features of triangles is the congruency of the diagonals. The diagonals are bisected into two. Each perpendicular bisector gives a segment of the diagonal that is equal to the other.
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m?
m = 2
m = 3
m = 19
m = 35
Answers
so
27 - 8 = 19
19 - 8 = 11
answer
m = 19
Answer:
m= 19
Step-by-step explanation:
In a linear function the rate of change of y-variable respect x-variable must be constant. In mathematical terms:
Δy/Δx = constant
Given two points of the function: (x1, y1) and (x2, y2), Δy = (y2 -y1) and Δx = (x2 -x1). So,
Δy/Δx = (11 -27)/(12-10) = -8
(m -27)/(11-10) = -8
(m -27) = -8*(11-10)
m = -8 + 27
m = 19
During a sale,Susan grody paid $155 for a clothes dryer.The price paid reflects a 75% discount off the original price. Determine what is the original price of the dryer.
Answers
The original price of the dryer would be; 38.75 dollars.
How to calculate the unit price of something?Unit means 'single entity, the fundamental constructing block. Usually, it is 1 in mathematics and science. Thus, the unit price of something is the price of 1 thing.
Given that Susan grody paid $155 for a clothes dryer.
The price paid by her reflects a 75% discount off the original price.
Required the original price of the dryer.
Thus,
100 - 75 = 25%
Therefore,
155 x 25%
155 x 0.25 = 38.75
Hence, the original price of the dryer would be; 38.75 dollars.
Learn more about unit prices here:
https://brainly.com/question/945712
#SPJ5
if y equals -12 when x equals 9 find y when x equals negative 4
Answers
y/x
-12 / 9 = y / -4
Now, cross multiply:
(-12)(-4) = (9)(y)
48 = 9y
y = 48/9 or 5 8/9 or 5.33
Konnor wants to burn 250 calories while exercising for 45 minutes at the gym. on the treadmill, he can burn 6 cal/min. on the stationary bike, he can burn 5 cal/min. if t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of calories that konnor can burn on the stationary bike?
Answers
Given that b is the number of calories that can be burned using the stationary bike, and the burning rate is 5 cal / min, therefore:
b = 5 t
where t is the time spent on the stationary bike
Answer:
B=5t
Step-by-step explanation:
Explain in detail why the degree of the polynomial below is not 6.
3x^2+6xy-10x^5+y^6-10x^3y^5
Answers
and the degree of the polynomial, is the same as the term with the highest degree, in this case 8.
Compute the requested value. If the cost is $35.96 and the desired markup is 10%, what is the price after markup?
Answers
multiply the cost by 1.10 ( 10% plus cost price)
35.96 *1.10 = 39.556 rounded to $39.56
A dentist is making identical dental care bags for patients using 56 tubes of toothpaste, 112 packets of floss, and 85 toothbrushes. What is the greatest number of identical dental care bags the dentist can make with the least amount of items leftover. Describe the contents of each bag.
Answers
56 tubes of toothpaste, 112 packets of floss and 84 toothbrushes.
The greatest common factor:
GCF ( 56, 112, 84 ) = 28
56 : 28 = 2, 112 : 28 = 4, 84 : 28 = 3
Answer:
The greatest number of identical dental care bags is 28.
In every bag will be 2 tubes of toothpaste, 4 packets of floss and 3 toothbrushes. One toothbrush will be leftover.
56 = 2 x 2 x 2 x 7
112 = 2 x 2 x 2 x 2 x 7
85 = 5 x 17
L.C.M. (56, 112, 85) = 2 x 2 x 2 x 2 x 5 x 7 x 17
= 560 x 17
= 9520
Therefore, 9520 is the correct answer.
to dilute a concentrated liquid fabric softener, the directions state to mix 3 cups of water with 1 cup of concentrated liquid. how many gallons of water will you need to make 6 gallons of diluted fabric softener?
Answers
6 gallons = 96 cups
Notice the ratio between water to concentrated liquid= 3:1
x:96
x=288 cups of water required
288/16=18 gallons
Hope I helped :)
Cheryl Assembled 128 chairs in 16 hours. How many chairs per hour?
Answers
(See attachment please)
What postulate can be used to prove that △ADC≅△CBA ?
Answers
hope this helps
How is angle a related to angle d?
A) vertical angles
B) alternate interior angles
C) alternate exterior angles
D) corresponding angles
Answers
Answer: Option 'A' is correct.
Step-by-step explanation:
since we have given a line AB and CD such that AB║CD,
And a transversal say 'l' cut the two parallel lines
And we know that when a transversal cuts two parallel lines we get linear pair and corresponding angles
But relation between angle 'a' and angle 'd' is vertically opposite angles.
So, Option 'A' is correct.
Louise used this figure to model the expression 20/4
What error did Louise make in her model?
The small arrows are pointed in the wrong direction.
The small arrows should all end in the same place as the large one.
The arrows should start at zero.
There should be one large arrow and 20 small arrows.
Answers
Answer:
The arrow should start at zero
Step-by-step explanation:
Because if it star any where else it would be incomplete
Please help thanks very much!
Answers
2nd one is BX for the median i think
if the inequality has the same number on both sides for the answer is that ok?
Answers
Template:
if |x| < k, then -k < x < k
----------------------------------------------------------------------------------
However, the inequality sign is not a "less than" sign. Instead its a "greater than" sign.
So instead you should use this template
if |x| > k then x > k or x < -k
So if
|6y+6| > 0
then
6y+6 > 0 or 6y+6 < 0
Solve each inequality for y
6y+6 > 0
6y+6-6 > 0-6 ... subtract 6 from both sides
6y > -6
6y/6 > -6/6 ... divide both sides by 6
y > -1
Do the same for the other inequality
6y+6 < 0
6y+6-6 < -6
6y < -6
6y/6 < -6/6
y < -1
---------------------------------------------------------------------------------
So overall, the two solutions are y > -1 or y < -1
The keyword "or" is important. You can only choose one inequality or the other, but not both.