Answer:
40
Step-by-step explanation:
11+29=40
Answer:
B)0 to 21 electoral votes
Step-by-step explanation:
edge 2023
How do i solve for the maximum and minimum of z?
Answer:
Step-by-step explanation:
[tex]We\ summarize\ (1) \ and\ (2),\ \ (2) \ and\ (3):\\\displaystyle\\\left \{ {{2x\geq -6\ |:2} \atop {-2x\geq -6\ |:(-2)}} \right. \ \ \ \ \ \left \{ {{x\geq -3} \atop {x\leq 3}} \right. \ \ \ \ \ \Rightarrow\ \ \ \ x\in[-3;3].\\[/tex]
[tex]2)\ We\ subtract\ equation\ (2) \ from \ equation (1),[/tex]
How long can it take for the body to process the alcohol in one standard drink (0. 6 ounces)? 2 hours 1. 5 hours 1 hour 30 minutes
Answer:
1 hour
Step-by-step explanation:
Which sequence is modeled by the graph below?
We can observe
9/3=33/3=1Its a geometric progression having first term 9(3)=27 and common ratio as 1/3
So
The firmula is
a_n=27(1/3)^{n-1}Option C
Answer:
[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]
Step-by-step explanation:
From inspection of the graph, the given points are:
(2, 9)(3, 3)(4, 1)If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
a is the first termr is the common ratio[tex]a_n[/tex] is the nth termRewrite the given points as terms of the sequence:
(2, 9) ⇒ a₂ = 9(3, 3) ⇒ a₃ = 3(4, 1) ⇒ a₄ = 1To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]
Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:
[tex]\implies a_2=9[/tex]
[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]
[tex]\implies \dfrac{1}{3}a=9[/tex]
[tex]\implies a=27[/tex]
Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:
[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]
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The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.8 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. What is the median recovery time? days c. What is the Z-score for a patient that took 4 days to recover? d. What is the probability of spending more than 3.8 days in recovery? e. What is the probability of spending between 3.2 and 4.2 days in recovery? f. The 90th percentile for recovery times is days.
Using the normal distribution, we have that the desired information is given as follows:
a) X ~ N(3,1.8).
b) 3 days.
c) Z = 0.5556.
d) 0.33 = 33%.
e) 0.2048 = 20.48%.
f) 5.3 days.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex]
Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.
The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:
Z = (4 - 3)/1.8 = 0.5556.
The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:
Z = (3.8 - 3)/1.8 = 0.44.
Z = 0.44 has a p-value of 0.67.
1 - 0.67 = 0.33.
The probability is of 0.33 = 33%.
The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:
X = 4.2:
Z = (4.2 - 3)/1.8
Z = 0.67.
Z = 0.67 has a p-value of 0.7486.
X = 3.2:
Z = (3.2 - 3)/1.8
Z = 0.11.
Z = 0.11 has a p-value of 0.5438.
0.7486 - 0.5438 = 0.2048 = 20.48%.
The 90th percentile is X when Z = 1.28, hence:
1.28 = (X - 3)/1.8
X - 3 = 1.8 x 1.28
X = 5.3 days.
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q=mc(T₂-T₁)
Solve for T₂
What is the simplest form of this expression? (x − 4)(x^2 + 3x − 5)
Answer:[tex]x^3-x^2-17x+20[/tex]
Step-by-step explanation:
At a furniture manufacturer, worker a can assemble a shelving unit in 5 hours. worker b can assemble the same shelving unit in 3 hours. which equation can be used to find t, the time in hours it takes for worker a and worker b to assemble a shelving unit together? rate (shelving units per hour) time (hours) fraction completed worker a one-fifth t worker b one-third t 5 t 3 t = 1 one-fifth t minus one-third t = 1 one-fifth t one-third t = 1 5 t minus 3 5 = 1
If they work together, they need 15/8 hours to assemble one shelving unit.
What does work mean in math?
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.According to tittle, we know worker A can assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.
If A & B work together , they will spend the same time t to assemble only one shelving .
That means, 1/5t + 1/3 t = 1 (equation)
1/5 t is worker A's workload during time t , 1/3 t is worker B workload.
So, 1/5 t + 1/3t = 1 is the answer
⇒ 5t + 3t = 15
⇒ t = 15/8 hours
If they work together, they need 15/8 hours to assemble one shelving unit.
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Answer:
Letter C is the correct answer or 1/5 t + 1/3t = 1
Lucy started the proof of the law of cosines using triangle WXY as shown.
W
Z
X
Given: XZ WY, AWXZand AYXZare right triangles
z; y cos (W) = WZ
Step 1: cos (W) =
Step 2: sin (W) =
Step 3: ZY = x - y cos (W)
Step 4: w²= (z-y cos (W))² + XZ²
Which step contains the first error in calculation?
z; XZ sin (W) = y
OA Step 1- the cosine ratio was applied incorrectly
OB. Step 2 - the sine ratio was applied incorrectly
OC. Step 3- the incorrect value was subtracted
OD. Step 4- the area formula should have been used instead.
4
The step which contains the first error in calculation is: B. Step 2 - the sine ratio was applied incorrectly.
What is the law of sines?The law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
Mathematically, the law of sines is given by this equation:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
For any right-angled triangle, the ratio of the length of its opposite sides to the length of its hypotenuse is generally referred to as sine ratio. Thus, sine ratio is given by this formula:
cos(θ) = Opp/Hyp
Where:
Opp is the opposite side of a right-angled triangle.Hyp is the hypotenuse of a right-angled triangle.θ is the angle.In this context, we can infer and logically deduce that the step which contains the first error in calculation is step 2:
sin(W) = y/XZ; XZsin(W) = y.
In conclusion, the correct step should have been written as follows:
sin(W) = XZ/y; ysin(W) = XZ.
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Answer:
step 2 is incorrect
Step-by-step explanation:
B. Step 2 - the sine ratio was applied incorrectly
Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?
The triangle is a right triangle because 52 + 122 = 132.
The triangle is a right triangle because 5 + 13 > 12.
The triangle is not a right triangle because 52 + 132 > 122.
The triangle is not a right triangle because 5 + 12 > 13.
9
Answer:
the triangle is a right angle triangle. I can't see the correct explanation here so I will explain
Step-by-step explanation:
to work out whether triangles are right angle you do :
square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled
i hope this helps . if you need any more help pls ask :)
Please help me with alg 2 question!
Answer:
J
Step-by-step explanation:
i need help please? thank you :)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 14z + 48 }{ {z}^{2} + 6x - 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z}^{2} - 8z - 6z+ 48 }{ {z}^{2} + 9z- 3z- 27} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {z(}^{} z- 8) - 6(z - 8) }{ {z}^{} (z+ 9)- 3(z + 9)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(}^{} z- 8) (z - 6) }{ {}^{} (z+ 9)(z - 3)} ÷ \cfrac{z -8}{z-3} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ (z - 6) }{ {}^{} (z+ 9)}[/tex]
Break into two parts and simplify
[tex]\\ \rm\dashrightarrow \dfrac{z^2-14z+48}{z^2+6z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z^2-8z-6z+48}{z^2+9z-3z-27}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)}{(z+9)(z-3)}[/tex]
Now divide by the denominator
[tex]\\ \rm\dashrightarrow \dfrac{(z-8)(z-6)(z-3)}{(z+9)(z-3)(z-8)}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{z-6}{z+9}[/tex]
list all the 3-digit numbers that can be created by rearranging these number tiles. 6 7 2
Answer:
627
267
276
762
726
and the no. itself, 672
6. If x is the largest of three consecutive integers, represent the sum of the three integers.
a) If x is the largest of three consecutive integers, how do we represent the three integers?
b) How do we convert this information into a solvable equation?
c) Find the sum
Answer:
See below
Step-by-step explanation:
x = largest
x-1 previous
x -2 smallest
sum = x + x-1 + x-2
sum = 3x -3
Prove the cofunction identity using the addition and subtraction formulas. sec 2 − u = csc(u) use a reciprocal identity, then apply a subtraction formula to simplify
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
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70 POINTS !! Charlotte has a map of the village. The scale on the map is such that 1cm represents 25m.
a) On the map, the church is 7cm from the village store. What is the real distance from the church to the village store?
b) Charlotte calculates her car is parked approximately half a kilometer from the church. On the map, how many cm would represent this distance?
Answer:
A. 175 m
B. 20 cm
Step-by-step explanation:
[tex]\frac{1 cm}{25 m} =\frac{7 cm}{x m}[/tex]
x = 175 m
[tex]\frac{25 m}{1 cm} = \frac{500 m}{x cm}[/tex]
x = 20 cm
Answer:
No1. 175 m
no2. 20 cm
6. For what value of p, the binary number 110P/2 represents 25?
Step-by-step explanation:
25 as binary number is
11001
1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 1 = 25
25×2 = 50 = 11001 × 2 = 110010
multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.
and so, we see
110P = 110010
P = 010
FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.
so, the problem should have looked like
110P/10 = 11001
110P = 11001×10 = 110010
P = 010
Answer:
01
Step-by-step explanation:
From decimal to binary;
25/2==> 1 (remainder)
12/2===>0
6/2==>0
3/2===>1
1
=11001
Checking the answer;
11001
=1*2^4+1*2^3+0*2*2+0*1+1*2^0
=1*16+1*8+0+0+1*1
=16+8+0+0+2
=25
Please please please help
Answer:r=14°
Step-by-step explanation:
(5r-5)°+ (8r+3)°=180
(Sum of angles on a straight line =180°)
Collect like terms
5r+8r-5+3=180
13r-2=180
13r=180+2
13r=182
r=182/13
r=14°
the senior class was going on a field trip to disneyland. A total of 350 student went on the trip. they filled seven busses . how many student were on each bus
Answer:
50 ^^
Step-by-step explanation:
So first an easy way to solve this problem is by removing the zeros then you'll have 35 and
7x1=7
7x2=14
7x3=21
7x4=28
7x5=35
So 7x5 dont forget to add your zeros to 35 and 5 and boom your answer is 50
need more explaining tell me ^^
Help me please! I’ll make you a brainlest show you work!!
The solution to the following mathematical problems are;
5² -3⁴ / (2³-5)(6² ÷ 9) = - 14/320² ÷ {3(5-9)² + 2} = 884/12 + (5-7)² -72 ÷ 6×2 = -13EvaluationSolve using
BODMAS
B - bracketO - offD - division M - MultiplicationA - additionS - Subtraction5² -3⁴ / (2³-5)(6² ÷ 9)
= 25-81 / (8-5)(36÷9)
= -56 / (3)(4)
= -56/12
= - 14/3
20² ÷ {3(5-9)² + 2}
= 400 ÷ {3(-4)² + 2}
= 400 ÷ {3(16) + 2}
= 400 ÷ (48+3)
= 400 ÷ 50
= 8
84/12 + (5-7)² -72 ÷ 6×2
= 7 + (-2)² - 12 × 2
= 7 + (4) - 24
= 11 - 24
= -13
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After a gas-filled balloon is released, it rises 90 feet by the end of the first minute. by the end of the second minute, the balloon rises 120 feet, and by the end of the third minute, it rises 150 feet. how many feet would the balloon rise in 8 minutes? a. 300 c. 390 b. 330 d. 660 please select the best answer from the choices provided a b c d
Answer:
330
Step-by-step explanation:
the change in hirght = 120 - 90 = 30
so 90 + (30 x 8)
= 90+240
= 330//
Find the area of this parallelogram. D(-3,4) c(3,4) a(-6,-4) b(0,-4)
If the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
Given that the vertices of parallelogram ABCD is A(-6,-4),B(0,-4)
,C(3,4),D(-3,4).
We are required to find the area of parallelogram ABCD.
Let the point of intersection of height of parallelogram from point A is point E.
When we see the graph on which the parallelogram then we will be able to know that point E has coordinates of (-3,-4).
Area of parallelogram=Base*Height
=AB*DE
DE=[tex]\sqrt{(-4-4)^{2} +(-3+3)^{2} }[/tex]
=[tex]\sqrt{64}[/tex]
=8 units
AB=[tex]\sqrt{(-4+4)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36}[/tex]
=6 units
Area=6*8
=48 square units.
Hence if the vertices of parallelogram ABCD is A(-6,-4),B(0,-4),C(3,4),D(-3,4) ,then the area of parallelogram ABCD will be 48 square units.
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(06.02) which of these is the algebraic expression for "seven more than the product of three and some number?" 7 3 x 3 10 ÷ x 3x 7 3 7x
Answer:
Step-by-step Explanation:
The correct option is C.
The algebraic expression for "seven more than the product of three and some number = 3x + 7 = 0
What is Algebraic Expression?An algebraic expression is one that is composed of variables, integer constants, and algebraic operations. An algebraic expression is, for instance, 3x² 2xy + c.
According to the given Information:we can search for the product of 3 and "some number",
Let the number be x.
So, the product of x is 3 times = 3x
And now
7 more then the Product .
we add the 7 to the product .
3x + 7 = 0
So the equation will be 3x + 7 = 0
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I understand that question you are looking for is:
Which of these is the algebraic expression for "seven more than the product of three and some number?"
A. 7 + 3 + x
B. 3 + 10 ÷ x
C. 3x + 7
D. 3 + 7x
PLEASE ASAP - Drag each tile to the correct box. Arrange the figures from least to greatest according to their volumes. Assume the variable h has the same value for each figure.
Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:
Cone with radius of 3 units Cylinder with radius of 3 units Cone with radius of 6 units Cylinder with radius of 6 unitsWhat are the volumes of these shapes?The value of h is the same for all the shape so assume the value of h is 2 units.
The volume of a cylinder is:
= πr²h
First cylinder area:
= 22/7 x 3 x 2
= 56.54867 units
The second cylinder area:
= 22/7 x 6 x 2
= 226.19467 units
The volume of a cone is:
= πr²h/3
First cone volume:
= 22/7 x 3 x 2/3
= 18.84956 units
Second cone volume:
= 22/7 x 6 x 2/3
= 75.39822 units
The order is therefore:
Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units
In conclusion, the shapes with the larger radius of 6 units will have more volume.
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solve the equation
14x+7y=28
The local gym is offering this new promotion: An enrollment fee of $40 and a monthly fee of $30. Which of the following expressions represents the cost of the gym membership for m months?
40+30m=c40 plus 30 m is equal to c
30+40m=c30 plus 40 m is equal to c
40+30m40 plus 30 m
30+40m
The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The local gym is offering this new promotion:
An enrollment fee of $40 and a monthly fee of $30.
Let m be the total number of months
Total monthly fee = 30m
Total cost(including the enrollment fee of $40) = 40 + 30m
Let the total cost is c:
c = 40 + 30m
If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.
Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
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A local baseball team is struggling this season, and many fans of the team believe it may be time to replace the head coach. to estimate support for firing the current head coach, a television news station provides a link on its website where fans of the team can respond to the question: "do you feel the current head coach should be fired?" after 2,367 votes on the website, 79% of those who responded felt the coach should be fired. which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall support for firing the coach?
This is voluntary response bias. The result overestimates true support for firing the coach.
What is voluntary response bias? When sample participants are self-selected volunteers, as in voluntary samples, voluntary response bias emerges.An illustration would be call-in radio programs that invite listeners to participate in polls on contentious issues (abortion, affirmative action, gun control, etc.).The sample that results tends to overrepresent people with strong opinions. In a random sampling technique, every component of the population has a known, non-zero probability of being chosen, and the selection of the sample unit is dependent only on chance.By removing voluntary response bias and protecting against undercoverage bias, random sampling aids in the production of representative samples.Random sampling underpins all probability sampling techniques.To know more about voluntary response bias with the given link
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Find the domain and range of all parts.
For the given functions, the domains are:
1) All real numbers.
2) D: x≥ -3
3) D: set of all real numbers such that x ≠ 0
4) D: 7 ≥ x ≥-7
5) All real numbers.
How to get the domain of the given functions?
For any function, we assume that the domain is the set of all real numbers, and then we remove all the values of x that generate problems (like a denominator equal to zero or something like that).
1) f(x) = x^2 - 4
This is just a quadratic equation, the domain is the set of all real numbers.
2) f(x) = √(x + 3)
Remember that the argument of a square root must be equal to or larger than zero, so here the domain is defined by:
x + 3 ≥ 0
x≥ -3
The domain is:
D: x ≥ -3
3) f(x) = 1/x
We can assume that the domain is the set of all real numbers, but, we can see that when x = 0 the denominator becomes zero, then we need to remove that value from the domain.
Thus, we conclude that the domain is:
D: set of all real numbers such that x ≠ 0
4) f(x) = √(49 - x^2)
Here we must have:
49 - x^2 ≥ 0
49 ≥ x^2
√49 ≥ x ≥-√49
7 ≥ x ≥-7
The domain of this function is:
D: 7 ≥ x ≥-7
5) f(x) = √(x^2 + 1)
Notice that x^2 is always a positive number, then the argument of the above square root is always positive, then the domain of that function is the set of all real numbers.
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Pls help quickly!!!!! hector built a tent shaped like a rectangular pyramid. the volume of the tent is 56 cubic ft. the area of the base of the tent is 24 square ft. what is the hieght of hectors tent in feet?
The rectangular pyramid rises 7 feet in height.
What is a rectangle-shaped pyramid?Pyramids are three-dimensional objects with triangle-shaped faces and an all-encompassing polygonal base. It is referred to as a rectangular pyramid if the base of the structure is rectangular. Although all pyramids have a rectangular foundation, they all have triangular edges.
How is the height of the rectangular pyramid determined?
First, we understand that a rectangular pyramid's volume is determined by:
[tex]V=B * H / 3[/tex]
The height H is determined by the base B.
When we know the volume is 56 [tex]ft^{3}[/tex] and the base is 24 [tex]ft^{2}[/tex], we can then swap out those two numbers in the volume calculation to get:
[tex]56 f t^{3}=24 f t^{2} * H / 3[/tex]
When we solve it for H, we get:
[tex]H=3 *\left(56 f t^{\circ} / 24 f t^{2}\right)=7 f t[/tex]
The rectangular pyramid rises 7 feet in height.
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When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A. A linear inequalities graph of dotted boundary line intersects X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) B. A linear graph of solid line intercepts X-axis at the unit (2, 0) and Y-axis at the unit (0, minus 4) C. A linear inequalities graph of dotted boundary line intercepts at the X-axis (0.5, 0) and Y-axis (0, 2) D. A linear graph of a solid boundary line intersects X-axis at the unit (0.5, 0) and Y-axis at the unit (0, 2)
The correct graph is in the attached image.
Answer:
B. A linear graph of solid line intercepts X-axis at the point (2, 0) and Y-axis at the point (0, -4)
Step-by-step explanation:
The boundary line of an inequality is graphed as though the expression were an equality. The nature of the line used will depend on the nature of the inequality.
Form of the lineWhen the inequality includes the "or equal to" case (≤ or ≥), the boundary line is part of the solution set. It is drawn as a solid line.
When the inequality excludes the "or equal to" case (< or >), the boundary line is not part of the solution set. It is drawn as a dotted or dashed line.
The given inequality
y ≤ 2x -4
includes the "or equal to" case, so the boundary line is solid.
Y-interceptThe equation of the boundary line is written in slope-intercept form:
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 2x -4 . . . . . . . boundary line with slope 2 and y-intercept -4.
This tells you that the boundary line intercepts the y-axis at the point (0, -4).
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