4
Consider the inequalities -1/4a > 3 a and b – 12> -3. What values, if any, make
both inequalities true? Show your work.
Answers
To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0
To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9
Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:
-1/4(-1) > 3(-1)
1/4 > -3
This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:
b – 12 > -3
b > 9
Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.
Related Questions
nswer the following question by entering the numeric value with appropriate units. if the length of one side of a square is 12.0 m m , what is the perimeter of the square? express the perimeter with the appropriate units.
Answers
Kaia's window is in the shape of a trapezoid. Three of the angles are 80°, 100°, and 109°. What is the measure of the fourth angle?
Answers
Answer:
71°
Step-by-step explanation:
Kaia's window is in the shape of a trapezoid. Three of the angles are 80°, 100°, and 109°. What is the measure of the fourth angle?
The sum of angles in a trapezoid is equal to = 360°
We are given 3 angles in the trapezoid as: 80°, 100°, and 109°.
The measure of the fourth angle is calculated as:
360° = 80°+ 100° +109° + fourth angle
360° - (80°+ 100° +109°)
360° - 289°
= 71°
The measure of the fourth angle is 71°
How much will it cost to pour a circular slab 18 ft in diameter by 3 in. For a patio if the concrete costs $40.00 per cubic yard? (1 cubic yard = 27 cubic feet)
Answers
Answer:
$94.24
Step-by-step explanation:
Given :
Diameter of circular slab = 18feet
Thickness of slab = 3 inches ; inches to ft = 3 /12 = 0.25 feets
Volume of slab = πd²t/4 = (π*18²*0.25) / 4 = 63.6 ft³
1 cubic yard = 27 feet
Volume in yard = 63.6 / 27 = 2.356 yd³
Concrete = $40 per yd³
Cost = $40 * 2.356 = $94.24
Use a graphing utility to find or to approximate the x-intercepts of the graph of the function.
y = 5x²-24x + 16
Answers
Answer: (2.4, -12.8)
Step-by-step explanation:
if every individual in the population has an equal chance of being selected for a sample, the sample is said to be a/an _____________ sample.
Answers
If every individual in a population has an equal chance of being selected for a sample, the sample is said to be a "random sample" or a "simple random sample."
A random sample is a sampling technique used in statistics to gather data from a population. It is considered one of the most unbiased and reliable methods for selecting a sample. In a random sample, each individual in the population has an equal probability of being selected, regardless of their characteristics or attributes.
This equal chance of selection eliminates any systematic bias and ensures that the sample is representative of the population.
The process of obtaining a random sample involves assigning a unique identifier to each individual in the population and using a randomization method to select the desired number of individuals.
Random sampling can be conducted through various techniques, such as simple random sampling, where individuals are selected directly from the population using a random number generator or a randomization table.
The goal of a random sample is to reduce the potential for selection bias and increase the generalizability of the findings to the larger population. By giving every individual an equal opportunity to be included in the sample, researchers can make more accurate inferences and draw conclusions about the population as a whole.
This type of sampling method ensures that each member of the population has an equal opportunity to be included in the sample, making it a representative subset of the population.
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pls help me with this question
Answers
Answer:
32 cm
Step-by-step explanation:
The volume of the container is:
V= area of the base * the heigth
Since the container has a rectangular base the area of it is:
A = length * width
Let L be the missing length
A = L * 10
V = 10* 25 * L
The container can hold 8 Liters when it's completely full to its brim.
8 liters is 8000 cm^3 ( multiply by 1000)
8000 = 10*25*L
8000 = 250 *L
L = 8000/250
L = 32 cm
v=8litres which is 8 × 1000
l=?
b=10
h=25
since, v=lbh (volume of cuboid)
8000=l × 10 × 25
l=8000/250
l=32
therefore the length is 32cm
1) Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x^(1/4) and y=x/6, about the line x=−3
Answers
The mean of a set of numbers must be one of the numbers of the set. (7.SP.3.a)
Sometimes
Always
ONever
Answers
Answer:
The answer is Sometimes.
Alex has 10 different kinds of lunch meat and 9 different kinds of cheese. If he wants to make a sandwich with one kind of meat and two kinds of cheese, how many different sandwiches could he make
Answers
Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.
To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.
To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is \(9C2\)= 9! / (2!(9-2)!) = 36.
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Write the equation of the parabola that has its vertex at (-2,7) and passes through (-1,3).
Answers
The quadratic equation for the given vertex and point is:
y = -4(x + 2)² + 7
How to write the equation for the parabola?A parabola whose vertex is (h, k) and that has a leading coefficient a, can be written in the vertex form as:
y = a*(x - h)² + k
Here we know that the vertex is (-2, 7), then we can write the equation as:
y = a*(x + 2)² + 7
We also know that the parabola passes through (-1, 3), then we can replace these two values in the equation to get:
3 = a*(-1 + 2)² + 7
3 = a + 7
3 - 7 =a
-4 = a
Then the equation for the parabola is:
y = -4(x + 2)² + 7
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Which graph represents the function
f(x)=√x+3-4
Answers
Answer:
I believe it is the last option but I'm not completely sure because the pic is blurry. But if the beginning of the graph is at (-3, -4) then the last option is definitely correct.
Step-by-step explanation:
Remember h controls horizontal movement k controls vertical movements.
always remember to take the opposite of h.
;)
The ratio of a to b is 4/7. If a is 16, find the value of b.
Answers
Answer:
B=28
Step-by-step explanation:
1, 1, 2, 3, 5, 8 are the first six numbers of the fibonacci sequence. what is the eighth number?
Answers
Answer:
21
Step-by-step explanation:
1, 1, 2, 3, 5, 8, 13, 21
The required eighth number in the Fibonacci sequence is 21.
Given that,
1, 1, 2, 3, 5, and 8 are the first six numbers of the Fibonacci sequence. what is the eighth number is to be determined
The sequence is defined as the specific pattern of numbers in which they are arranged.
Here,
given Fibonacci sequence is 1, 1, 2, 3, 5, 8
The Fibonacci numbers, sometimes known as Fn, are a set of numbers in mathematics where each number is the sum of the two numbers before it.
According to the above definition,
7 th number = 5th number + 6th number =
7 th number = 5 + 8 = 13
8th number = 8 + 13 = 21
Thus, the required eighth number in the Fibonacci sequence is 21.
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Find the circumference and area
Answers
Pi=3.14
r=5.5
So C=2(3.14)(5.5)=34.56
So the circumference is 34.56 mi
And the area is A=pi(r)²
So you have
A=3.14(5.5)²
So A=95.03 mi²
So the area is 95.03 mi² and the circumference is 34.56 mi
Hope this helps!
A box is 10in. high, 20in. long, and 12in. wide. What is the longest poster you could fit in the box? Use pencil and paper. Explain why you can only fit one maximum-length poster in the box but you can fit multiple 22-in. posters in the same box.
Answers
The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).
To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.
Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.
As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.
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Functions - Inverse Sine, Cosine and Tangent Find the inverse tangent functions to discover why Mr. Piatt, the math teacher, was a good dancer. Match the solution at the top with the problem number below. = A Ž=1 6 =D EL * = E +=M * = G -O =H ER ET 1. cost 2. tan 1 3. sind 4. tan! 5 5. sin() 6. tan (-1) 7 sin 1 8. cos 9. sin 10. cos" 0 11 tan (13) 12 sin (1) 13. cos 14. COS
Answers
The result of inverse trigonometric function are: cos, tan^-1, sin, tan^-1(5), sin^-1, tan^-1(-1), sin^-1(1), cos, sin, cos^-1(0), tan(13), sin^-1(1), cos, cos^-1.
Inverse trigonometric functions are used to determine the angle measures of a right triangle given the length of two sides. In this problem, we are matching the inverse tangent solutions to the corresponding trigonometric problems. The inverse tangent function, tan^-1(x), gives the angle whose tangent is x.
Therefore, matching tan^-1(1/6) with problem number 2 means finding the angle whose tangent is 1/6. Similarly, matching cos^-1(0.5) with problem number 10 means finding the angle whose cosine is 0.5. The other inverse trigonometric functions, such as sin^-1(x) and cos^-1(x), give the angles whose sine and cosine are x, respectively.
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If 4 rectangles were put together to form a shape with a perimeter of 88.then what is the breadth of each recangle
Answers
The breadth of each rectangle is 11 units.
Let's consider that each rectangle has a length of l and breadth of b. We have been given that the perimeter of the shape that is formed by putting together the 4 rectangles is 88 units. We know that, the perimeter of a rectangle is given by the formula 2(l + b).
Therefore, the perimeter of the shape is given by the formula: P = 2(l + b) + 2(l + b) = 4(l + b)
From the given information, we know that the perimeter of the shape is 88.
Therefore,4(l + b) = 88
Dividing both sides of the equation by 4, we get: l + b = 22
We have found the relationship between the length and breadth of each rectangle.
Now, we need to find the value of the breadth of each rectangle.
We know that there are 4 rectangles placed side by side to form the shape.
Therefore, the total breadth of all 4 rectangles put together is equal to the breadth of the shape.
Hence, we can find the breadth of each rectangle by dividing the total breadth by the number of rectangles.
Let's denote the breadth of each rectangle as b'.
Therefore, b' = Total breadth / Number of rectangles
b' = (l + b + l + b) / 4b' = (2l + 2b) / 4b' = (l + b) / 2
We have found that the sum of the length and breadth of each rectangle is equal to 22 units.
Therefore, the breadth of each rectangle is half the sum of the length and breadth of each rectangle.
Substituting this value in the above equation, we get:b' = (l + b) / 2b' = 22 / 2b' = 11
Therefore, the breadth of each rectangle is 11 units.
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Can any quadratic function in vertex form be written in standard form?
Answers
Yes, any quadratic function can be transformed from vertex form to standard form by multiplying out the squared binomial (x-h)^2, distributing the leading coefficient of a, and then combining like terms.
The following triangles are similar. True or False.
Answers
Answer:
False.
Step-by-step explanation:
Their angles are not corresponding, they are not congruent.
Answer:
False
Step-by-step explanation:
They aren't congruent
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (negative 5, 8), has a vertex at (negative 3, 4), and goes through (negative 1, 8).
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x + 3)2 + 4?
left 3, up 4
right 3, down 4
left 3, down 4
right 3, up 4
Answers
Answer:
A
Step-by-step explanation:
Edge 2021
Answer:
A. left 3, up 4
Step-by-step explanation:
Doing it on EDG right now!
Good luck to yalls :)
scatterplot is the best visualization for showing which of the following (choose one or more)? group of answer choices indirect or negative relationship between two ratio variables the relationship between two interval/ratio variables correlation frequency of two nominal variables
Answers
Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualisation for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
Scatterplots are best for showing:
⇒the relationship between two interval/ratio variables
⇒indirect or negative relationship between two ratio variables
Scatterplots display points on a coordinate plane, with one variable plotted on the x-axis and the other variable plotted on the y-axis. This allows us to see the pattern of relationship between the two variables. If there is a positive or negative relationship, we can see if the points tend to increase or decrease as we move from left to right or from bottom to top. If the relationship is indirect, we can see if the points tend to curve in one direction or another.
Scatterplots are not the best visualization for showing: correlation
frequency of two nominal variables
For showing correlation, a line of best fit (regression line) can be added to a scatterplot, but other visualizations such as a correlation matrix or a heat map are more commonly used.
For showing frequency of two nominal variables, a two-way table or a mosaic plot are better suited, as they can display the count or proportion of cases for each combination of the two nominal variables.
Therefore, Scatterplots are best for showing the relationship between two interval/ratio variables and indirect or negative relationship between two ratio variables.
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Evaluate the integral.xdx / (7x^2+3)^5
Answers
To evaluate the integral of xdx / (7x^2+3)^5, we first need to make a substitution. Let u = 7x^2+3, then du/dx = 14x.
Solving for x, we get x = sqrt((u-3)/7), which means dx = (1/(2sqrt(7(u-3))))du.
Substituting these values into the evaluation of integral, we get:
∫(x dx) / (7x^2+3)^5 = ∫[(sqrt((u-3)/7))/(2u^2)] du
Next, we need to simplify the integrand by factoring out a constant:
∫[(sqrt((u-3)/7))/(2u^2)] du = (1/2√7) ∫[(u-3)^(-1/2) / u^2] du
Using the power rule of integration, we can integrate the second term:
∫[(u-3)^(-1/2) / u^2] du = ∫u^(-5/2) (u-3)^(-1/2) du
Now, we can use the substitution method again, letting v = u-3, then dv/du = 1. Solving for u, we get u = v+3, which means du = dv.
Substituting these values into the integral, we get:
∫u^(-5/2) (u-3)^(-1/2) du = ∫(v+3)^(-5/2) v^(-1/2) dv
Using the product rule of integration, we get:
∫(v+3)^(-5/2) v^(-1/2) dv = (-2/3) (v+3)^(-3/2) (v^(1/2))
Now, we can substitute back in for u and simplify:
(-2/3) (u-3+3)^(-3/2) [(u-3)^(1/2)] = (-2/3) (7x^2)^(-3/2) [(7x^2+3)^(1/2)]
Finally, we can simplify further by factoring out constants:
(-2/3√7) (7x^2)^(-3/2) [(7x^2+3)^(1/2)] = (-2/3√7) (49x^3) / (7x^2+3)^(3/2)
Therefore, the solution to the integral of xdx / (7x^2+3)^5 is:
(-2/3√7) (49x^3) / (7x^2+3)^(3/2)
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32% of what weight is 60 oz
Answers
Answer:
200 oz
Step-by-step explanation:
Just use the equation
0.32x=200
The number of 32% which result in 60 oz would be 18.75
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.
We need to find the number that is state 32% of number weight is 60 oz
Let the unknown number is represneted by b.
It can be written by;
32% x b = 60
32/100 x b = 60
0.32 x b = 60
b = 60/0.32
b = 18.75
Therefore, the number would be 18.75
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Simplify
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Answers
Answer:
55.5\(x^{4}\)+24.21x³+73.79x²+33.81x+28.49
Step-by-step explanation:
To simplify this equation, follow these steps:
(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)
Multiply 7.5x² by all the terms in the right parenthesis.
7.5x² (7.4x² -2.1x +7.7)=55.5\(x^{4}\) - 15.75x³+ 57.75x²
Then multiply 5.4x by all the terms in the right parenthesis.
5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x
Now multiply 3.7 by all the terms in the right parenthesis.
3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49
Add all of those answers together.
55.5\(x^{4}\) - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=
=55.5\(x^{4}\)+24.21x³+73.79x²+33.81x+28.49
The answer is 55.5\(x^{4}\)+24.21x³+73.79x²+33.81x+28.49
Hope this helps!
If not, I am sorry.
If a teenage elephant weighs about one ton, how much would three teenage elephants weigh?
Answers
3 tons or 6000 pounds
what 24+90 please help ty
Answers
Answer:
114
Step-by-step explanation:
first lets add the ones places = 4+0 which is 4
ones place = 4
Then lets add tens places = 2+9 = 11
tens place = 11
so answer will be 114
Answer:
24+90=114 hope that helps
what is 3.944 rounded to the nearest hundreth?
Answers
the answer is 4
Step-by-step explanation:
Please answer this question asap
Answers
B= 3
C= -21
I hope this helped!
Hi, can you help me to solve this exercise, please!
Answers
Trigonometric Identities.
To solve this problem, we need to keep in mind the following:
* The tangent function is negative in the quadrant II
* The cosine (and therefore the secant) function is negative in the quadrant II
* The tangent and the secant of any angle are related by the equation:
\(\sec ^2\theta=\tan ^2\theta+1\)We are given:
\(\text{tan}\theta=-\frac{\sqrt[]{14}}{4}\)And θ lies in the quadrant Ii.
Substituting in the identity:
\(\begin{gathered} \sec ^2\theta=(-\frac{\sqrt[]{14}}{4})^2+1 \\ \text{Operating:} \\ \sec ^2\theta=\frac{14}{16}+1 \\ \sec ^2\theta=\frac{14+16}{16} \\ \sec ^2\theta=\frac{30}{16} \end{gathered}\)Taking the square root and writing the negative sign for the secant:
\(\begin{gathered} \sec ^{}\theta=\sqrt{\frac{30}{16}} \\ \sec ^{}\theta=-\frac{\sqrt[]{30}}{4} \end{gathered}\)There are 64 squares on a chess board. If 16 of them are covered by chess pieces, the ratio of white empty squares to black empty squares is 3: 5. How many empty squares are black?
Answers
Answer: 30 black empty squares
Step-by-step explanation: Let’s solve this problem step by step:
There are 64 squares on a chessboard and 16 of them are covered by chess pieces, so there are 64 - 16 = 48 empty squares.
The ratio of white empty squares to black empty squares is 3:5. This means that for every 3 white empty squares, there are 5 black empty squares.
The total ratio of white to black empty squares is 3 + 5 = 8.
To find out how many of the 48 empty squares are black, we can divide the total number of empty squares by the total ratio and then multiply by the ratio for black empty squares: (48 / 8) * 5 = 30.
So, there are 30 black empty squares on the chessboard.