Answers
The inequality that is true for all values of x is:
√(4x²) ≤ 4x²
Which of the inequalities is true for all values of x?Let's try to find which inequality is true for all real values of x.
For example, let's look at option C, here we have the inequality:
4(x² - 3) ≤ 3(x² - 4)
Let's expand both sides to get:
4x² - 12 ≤ 3x² - 12
4x² ≤ 3x²
4 ≤3
We removed the x-variable, but 4 is not smaller or equal to 3, so this is false.
Now option D, we have:
√(4x²) ≤ 4x²
Notice that bout outcomes are always positive, but in the left side we have a square root.
We can simplify this to get:
2x ≤ 4x²
x ≤ 2x²
This is trivially true, the only region where we can have problems is the region between 0 and 1, but the factor corrects that.
So this one is the correct option.
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Related Questions
Which functions are linear? Responses A y = 8x2 − 2y = 8 x 2 − 2 B y = 12 x + 8y = 1 2 x + 8 C y = 2x − 4y = 2x − 4 D y = 3x + 2y = 3 x + 2 E y = x − 2y = x − 2
Answers
Answer:
B, C, D, E------------------------
Linear function has a form of:
y = mx + bFrom the given options we can choose linear functions:
B) y = 12x + 8;C) y = 2x − 4;D) y = 3x + 2;E) y = x − 2.What is the solution to x2 + 4x>12?
Answers
The sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2
In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)
What is Algebraic expressiοn ?An algebraic expressiοn is a mathematical phrase that can cοntain variables, cοnstants, and οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, and divisiοn) that are used tο represent quantities and their relatiοnships.
Tο sοlve this inequality, we need tο find the values οf x that satisfy the inequality [tex]x^2 + 4x > 12.[/tex]
First, we can mοve all the terms tο οne side οf the inequality tο get:
[tex]x^2 + 4x - 12 > 0[/tex]
Next, we can factοr the left-hand side οf the inequality tο get:
(x + 6)(x - 2) > 0
Nοw we need tο find the values οf x that make the inequality true. We can dο this by analyzing the signs οf the expressiοns οn each side οf the inequality fοr different ranges οf x.
When x < -6, bοth factοrs (x + 6) and (x - 2) are negative, sο their prοduct is pοsitive.
When -6 < x < 2, the factοr (x + 6) is pοsitive and the factοr (x - 2) is negative, sο their prοduct is negative.
When x > 2, bοth factοrs are pοsitive, sο their prοduct is pοsitive.
Therefοre, the sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2
In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)
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Brayden is 5 feet 9 inches tall and does trick roping with a lasso, which is a rope with a circular loop at one end. He jumps through the loop, which has a diameter that is 1.5 times his height. What is the circumference of the loop? Write your answer in feet, using 3.14 for П.
Answers
Answer: First, we need to convert Brayden's height to inches, since the diameter of the loop is given in inches.
5 feet 9 inches = (5 x 12) + 9 = 69 inches
Next, we can find the diameter of the loop:
Diameter = 1.5 x 69 inches = 103.5 inches
Finally, we can find the circumference of the loop using the formula:
Circumference = П x Diameter
Circumference = 3.14 x 103.5 inches
Circumference = 325.29 inches
To convert to feet, we divide by 12:
Circumference = 27.11 feet (rounded to two decimal places)
Therefore, the circumference of the loop is approximately 27.11 feet.
Step-by-step explanation:
Endpoints of a diameter (2,7) ( -18,1)
Answers
The endpoints of the diameter are (-10, -3) and (-18, 1).
What is the midpoint formula?
The midpoint formula is a mathematical formula used to find the midpoint between two given points in a coordinate plane. The midpoint is the exact middle point between the two given points, which is equidistant from each point. The formula for finding the midpoint is:
Midpoint = ( (x1 + x2) / 2, (y1 + y2) / 2 )
To find the endpoints of a diameter, we need to find the midpoint of the diameter first.
The midpoint formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Using the given points, we have:
Midpoint = ((2 + (-18))/2, (7 + 1)/2)
Midpoint = (-8, 4)
Now that we have the midpoint, we can find the endpoints of the diameter by reflecting one of the points across the midpoint.
Let's reflect the point (2, 7):
Endpoint 1 = (2, 7) → ( -8 - (2), 4 - 7)
Endpoint 1 = (-10, -3)
Therefore, the endpoints of the diameter are (-10, -3) and (-18, 1).
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using complete sentences, compare the range values of the data sets. what does this comparison tell you in terms of the situation the data represent?
Answers
The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison. Option D is correct.
In comparing the test scores of two groups, it is important to choose appropriate measures of center and variation to accurately represent the data. If both distributions are nearly symmetric, the mean and standard deviation are commonly used.
However, if the distributions are skewed, it is better to use the median and standard deviation as measures. In this particular case, the scores of Group B are skewed right, which means that the mean may not be a reliable measure of center. Instead, the median should be used. The range is not a good measure of variation for skewed data because it is sensitive to extreme values, so the standard deviation is more appropriate. Hence, option D is answer.
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--The complete question is, The table shows the test scores of students who studied for a test as a group (Group A) and students who studied individually (Group B).
Which would be the best measures of center and variation to use to compare the data?
The scores of Group B are skewed right, so the mean and range are the best measures for comparison.
Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.
Both distributions are nearly symmetric, so the median and the interquartile range are the best measures for comparison.
The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison.--
How many four letter code words can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel?
Answers
Required number of four letters are 120.
What are letters?
Letters are symbols that represent sounds or phonemes in a language. They are used to form words and written communication. The letters of the alphabet are the basic units of written language, and each language has its own set of letters that represent its sounds. In many languages, the letters are organized into an alphabet, which is a standardized order of the letters used for writing. The letters can be written in uppercase or lowercase form, and they may have different shapes or styles depending on the font used. In addition to the letters of the alphabet, there are also other types of symbols used in written communication, such as punctuation marks, numerals, and special characters.
The given word "MIRAGE" has six letters, and we need to form a four-letter code word using these letters such that the second-to-last letter is a vowel and no letter is repeated.
There are two vowels in "MIRAGE" - "I" and "A". We can choose one of these two vowels to be the second-to-last letter in the four-letter code word. Once we have chosen the vowel, we can choose any one of the remaining five letters for the last letter in the code word, since no letter can be repeated.
After choosing the second-to-last and last letters, we have two letters left to choose for the first two positions in the code word. Since no letter can be repeated, we have four choices for the first letter, and three choices for the second letter.
Thus, the total number of four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel is 2 (choices for the second-to-last letter) x 5 (choices for the last letter) x 4 (choices for the first letter) x 3 (choices for the second letter)
= 2 x 5 x 4 x 3
= 120
Therefore, there are 120 four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel.
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What is the volume
of a pyramid with
sides of 22 inches and
30 inches, and a
of height of 15 inches?
Answers
I need help........ !!!!!!!
Answers
Based on the information, cot x = - cot x. This is not true for any value of x, so there is no solution to the equation.
How to explain the equationTrigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved.
Using trigonometric identities, we can simplify the left-hand side of the equation as follows:
csc x cos x = (1/sin x) * cos x = cos x / sin x = cot x
Therefore, the given equation is equivalent to:
cot x = - cot x
This is not true for any value of x, so there is no solution to the equation.
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I NEED HELP ON THIS ASAP!!!
Answers
1. The perimeter is approximately 24.16 units.
2. Determining the height of this triangle was different from the previous activities because we had to first find the length of one side of the triangle and then find the corresponding height that intersects that side at a right angle. In previous activities, the height was either given or easily determined from the given information.
The surface area of this square pyramid is 741 ft². Can the value of x be 24? Explain.
(the pyramid's length and base are 13, and x is the height.)
Answers
Therefore , the solution of the given problem of surface area comes out to be x cannot equal 24.
What does an area actually mean?By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.
Here,
The calculation for a square pyramid's surface area is:
=> S = l² + 2lh
where S is the surface area, h is the height of the pyramid, and l is the length of one edge of the square base.
=> l² = 13² = 169
We also know that the pyramid's surface area is 741 square feet, so we can construct the following equation:
=> 741 = 169 + 2(13)(x)
When we condense the right half, we obtain:
=> 741 = 169 + 26x
169 from both parts are subtracted, giving us:
=> 572 = 26x
When we multiply both parts by 26, we get:
=> x = 22
As a result, rather than 24 feet, the pyramid's height is 22 feet.
Thus, x cannot equal 24.
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The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5
Answers
Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen
To determine which player was more consistent, we need to find the best measure of variability for the data. The two common measures of variability are range and interquartile range (IQR).
The range is the difference between the highest and lowest values in the data set. For Player A, the range is 6 - 1 = 5, and for Player B, the range is 11 - 1 = 10.
The interquartile range (IQR) is a measure of dispersion based on dividing the data into quartiles. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
To find the IQR for each player, we first need to find the quartiles.
For Player A:
Arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 6
Find Q1: (2 + 2) / 2 = 2
Find Q3: (3 + 3) / 2 = 3
Calculate IQR: Q3 - Q1 = 3 - 2 = 1
For Player B:
Arrange the data in order: 1, 1, 2, 4, 4, 5, 5, 5, 11
Find Q1: (2 + 4) / 2 = 3
Find Q3: (5 + 5) / 2 = 5
Calculate IQR: Q3 - Q1 = 5 - 3 = 2
Therefore, Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5. In contrast, Player A has an IQR of 1, indicating that 50% of their scores fell within the range of 2 to 3.
Therefore, we can conclude that Player B was more consistent than Player A.
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I need help answering this question
Answers
Answer: Add them. 6ft+4ft+4ft=10ft, 3in+6in+9in=18in. 10ft and 18in is also equal to 11ft and 6in. Therefore, the answer is 11 feet and 6 inches.
This
distance-time graph shows the journey of a hot-air balloon.
For how long during the journey was the balloon more than 600 m from the
ground?
Give your answer in minutes.
< Back to task
1200
Distance from ground (m)
1000
800-
600
400
200-
04
13:30 13:40 13:50 14:00 14:10 14:20 14:30 14:40 14:50
Time
Watch video
Answer >
Answers
Answer:
its 1000 because if you count the blue line thing up it will show you do you have a profile picher i need one you can be my freind pleas i have only two my name is Isabella
a researcher is conducting a test to determine if a test prep program increases the pass rate for a certification program. what assumptions must be met in order to use the large sample z-test for a difference in two proportions?
Answers
To use the large sample z-test for a difference in two proportions, assumptions that must be met include having independent samples, a large sample size, and success-failure conditions must be met.
In order to use the large sample z-test for a difference in two proportions, the following assumptions must be met:
The sample is random and each observation is independent. The sample size for each group is large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of success.
The two groups being compared are independent of each other. The data is binomially distributed, meaning each observation is either a success or a failure. The populations from which the samples are drawn have similar variances.
If these assumptions are met, the large sample z-test can be used to test the null hypothesis that there is no difference between the two proportions.
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Penny was paid 306 25 this week her pay rate is $8.75. How many hours did she work?
Answers
Answer:
35 hours
Step-by-step explanation:
We Know
Her pay rate is $8.75
Penny was paid 306.25 this week
How many hours did she work?
We Take
306.25 / 8.75 = 35 hours
So, she works 35 hours.
The leneght of four insects are 0.02 cm ,1/8cm,0.1cm and 2/3cm. Arrange the leneght in descending order
Answers
The descending order of the length of the four insects is as follows: 2/3 cm, 0.1 cm, 0.02 cm, 1/8 cm.
The length of four insects are 0.02 cm, 1/8 cm, 0.1 cm, and 2/3 cm.
Arrange the length in descending orderIn order to arrange the lengths of the four insects in descending order, we need to convert the fractions to decimals so that we can compare all the values.
1/8 cm = 0.125 cm
2/3 cm = 0.6667 cm
Now we have the values in decimal form, we can proceed to arrange them in descending order from the highest to the lowest value:
2/3 cm = 0.6667 cm
0.1 cm
0.02 cm
1/8 cm = 0.125 cm.
In conclusion, the lengths of four insects were arranged in descending order by first converting the fractions to decimals before comparing them.
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Help please! No silly answers. Need this as soon as possible thank you.
Answers
Step-by-step explanation:
Every ten minutes the car travels eleven miles
11 miles / 10 min = 1.1 mile / min <=====unit rate
after 18 minutes : 1.1 mile/min * 18 min = 19.8 miles
What is the area? I need answers asap
Answers
Answer:
88
Step-by-step explanation:
1.find the area of the triangle 1/2 x b xh
1/2 x 5 x6=15
rectangle=13 x 8 =104
3subtract area of rectangle - area of triangle =104-15
The Empire State Building weighs about 7.3×108pounds. The One World Trade Center building weighs 88,200,000 which building is heavier by how much ?
Answers
Step-by-step explanation:
7.3 x 10^8 <=====move decimal point EIGHT place to the right
730, 000, 000 pounds
88, 200 ,000 I think you can now see the larger one
and do the subtraction to see by how much !
Answer:
The Empire State Building is heavier by 6.418 x [tex]10^{8}[/tex]
Step-by-step explanation:
World Trade Center
8.82 x [tex]10^{7}[/tex]
(6.14 x [tex]10^{8}[/tex]) - (8.82 x [tex]10^{7}[/tex])
You need to have the same power of 10 to subtract
7.3 x [tex]10^{8}[/tex] - .882 x [tex]10^{8}[/tex]
6.418 x [tex]10^{8}[/tex]
Helping in the name of Jesus.
Solve for x, please :))))))
Answers
Answer:
5x - 10 = 2(2x + 2)
5x - 10 = 4x + 4
x = 14
Middle Segment of a Triangle:
Triangles are geometric figures with three sides and three internal angles. We can find different types of lines inside a triangle; one of them is the middle segment. The middle segment of a triangle is a line parallel to one of the sides and bisecting the other two sides. Let L be the line of the middle segment and AC the side parallel to the line L, then the formula of the middle segment is:
L = AC/2
We are given a diagram:
Our objective is to find the missing length of RQ.
We can see that the RQ line divides the ST and UT lines in equal parts. Moreover, the SU and RQ lines are parallel; therefore, we can conclude that the RQ line is the middle segment of the STU triangle. So:
RQ = SQ/2
→2x+2 = (5x-10)/2
→2(2x+2) = 5x-10
→4x+4 = 5x-10
→ 5x-4x = 10+4
x = 14
and RQ = 30
and SU = 60
Find the value of x for this problem l
Answers
Answer:
x = 15
Step-by-step explanation:
the measure of a tangent- tangent angle is half the difference of the measures of the intercepted arcs.
the sum of the arcs in a circle = 360° , then
minor arc FH = 360 - 17x
Then
[tex]\frac{1}{2}[/tex] (17x - (360 - 17x) ) = 75 ( multiply both sides by 2 to clear the fraction )
17x - (360 - 17x) = 150
17x - 360 + 17x = 150
34x - 360 = 150 ( add 360 to both sides )
34x = 510 ( divide both sides by 34 )
x = 15
The measure of angle x of the circle is x = 15
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the measure of the tangent-tangent angle be = 17x°
Now , the angle created by two tangents in a circle that intersect outside the circle is known as the tangent-tangent angle. This angle's dimension is half the difference between the dimensions of the two intercepted arcs.
So , ( 1/2 ) (17x - (360 - 17x) ) = 75
Multiply by 2 on both sides , we get
(17x - (360 - 17x) = 150
34x = 510
Divide by 34 on both sides , we get
x = 15
Hence , the measure of x of circle is 15
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art 2: 10 Points each. Show all work for full credit.
11. Ryan bought three bags of mixed tulip bulbs at a local garden store. The first bag contained 7 yellow
bulbs, 8 red bulbs, and 5 white bulbs. The second bag contained 3 yellow bulbs, 11 red bulbs, and 6
white bulbs. The third bag contained 13 yellow bulbs, 2 red bulbs, and 5 white bulbs. Ryan combined
the contents of these three bags into a single container. He randomly selected one bulb, planted it, and
then randomly selected another and planted that one. Determine if it is more likely that Ryan planted a
red bulb and then another red bulb, or planted a yellow bulb and then a white bulb. Justify your answer.
Answers
It is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.
How to solve probability?
To determine which scenario is more likely, we need to calculate the probability of each outcome. Let's start by calculating the probability of planting two red bulbs in a row.
The probability of selecting a red bulb from the first bag is 8/20, from the second bag is 11/20, and from the third bag is 2/20. Thus, the probability of selecting two red bulbs in a row is:
(8/20) * (11/20) + (8/20) * (2/20) + (11/20) * (2/20) = 0.345
Now, let's calculate the probability of planting a yellow bulb and then a white bulb.
The probability of selecting a yellow bulb from the first bag is 7/20, from the second bag is 3/20, and from the third bag is 13/20. The probability of selecting a white bulb from the first bag is 5/20, from the second bag is 6/20, and from the third bag is 5/20. Thus, the probability of selecting a yellow bulb and then a white bulb is:
(7/20) * (5/20) + (7/20) * (6/20) + (3/20) * (5/20) + (3/20) * (6/20) + (13/20) * (5/20) + (13/20) * (6/20) = 0.3905
Therefore, it is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.
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If using the method of completing the square to solve the quadratic equation x^2+8x-35=0x
2
+8x−35=0, which number would have to be added to "complete the square"?
Answers
To complete the square for the quadratic equation x²+8x-35=0, we need to add a constant to both sides of the equation that will result in a perfect square trinomial on the left-hand side.
To do this, we need to take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x in this equation is 8, so we take half of 8, which is 4, square it, which is 16, and add it to both sides of the equation:
x² + 8x - 35 + 16 = 16
x² + 8x + 16 = 51
On the left-hand side, we have a perfect square trinomial that can be factored as (x+4)². So, we have:
(x+4)² = 51
To solve for x, we take the square root of both sides:
x+4 = ±√51
Finally, we isolate x by subtracting 4 from both sides:
x = -4 ± √51
Therefore, the number that had to be added to "complete the square" is 16.
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Helppppppppppppppppppppppp
Answers
Answer is attached
Hope it helps ⬆️
3
Find the perimeter of a square that is 3 Inches on a side.
30 inches
0 12
3
4
inches
15 inches
07/1/20 inches
Answers
The perimeter of a square that is 3 inches on a side include the following: B. 12 inches.
How to calculate the perimeter of a square?In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;
P = 4x
Where:
P is the perimeter of a square.x is the side length of a square.By substituting the given side lengths into the formula for the perimeter of a square, we have the following;
Perimeter of a square, P = 4x
Perimeter of a square, P = 4(3)
Perimeter of a square, P = 12 inches.
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The perimeter of a square with 3 inches on a side is B. 12 inches.
What is the perimeter?The perimeter refers to the distance that encompasses or surrounds an object or drawing.
The formula for computing the perimeter is 2L + 2W. But for a square, the perimeter formula is 4L.
The length of each square side = 3 inches
The perimeter = 12 inches (4 x 3)
Thus, the perimeter of the square can be concluded to be 12 inches.
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How to solve it?
I suddenly forgot how to do simple equations
10p = 2
Answers
If 10p equals 2, then p would equal 0.2
Answer:
Step-by-step explanation:
Start by isolating the variable (in this case, "p") on one side of the equation. To do this, divide both sides of the equation by 10:
10p/10 = 2/10
Simplify both sides of the equation:
p = 0.2
So the solution is p = 0.2.
( please answer fast I rlly need it will get 20 points) Use the order of operations to evaluate the expression 8 + 18 ÷ 3 – 7.
5
7
9
10
Answers
Answer:
7
Step-by-step explanation:
Evaluate the expression:
[tex]8+18\div 3 - 7[/tex]
Divide 18 and 3.
[tex]8+6-7[/tex]
Add 8 and 6
[tex]14-7[/tex]
Subtract 14 and 7
[tex]7[/tex]
Last year, Isabel opened an investment account with $5600. At the end of the year, the amount in the account had decreased by 29.5%. How much is this decrease in dollars? How much money was in her account at the end of last year?
Answers
$1,652.
How much money was in her account at the end of last year?$3,948.
(I apologize for the incorrect initial response. I had entered my answer into the wrong tab by accident.)
Giving brainliest, please help!
Answers
Answer:
[tex]54in^{3}[/tex]
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
A= lwh
So we just plug in those values.
A= 3*3*6
A= 9*6
A= 54in^3
Find an angle in each quadrant with a common reference angle with 332°
Answers
Answer:
Step-by-step explanation:
In first quadrent, reference angle is equal to 332
in secodn quadrent, 332-180
angle - 180 so 332-180
fouth Quadrent, 360-332
Answer is equal to 28
Answer:
Quadrant 1: 152°
Quadrant 2: 28°
Quadrant 3 (Given): 332°
Quadrant 4: 208°
Step-by-step explanation:
A 332° angle in standard position has its terminal side in quadrant 3 since 332° is between 180° and 360°.
332° - 180° = 152°
The reference angle for 332° is 152°
Quadrant 1: 152°
Quadrant 2: 180° - 152° = 28°
Quadrant 3 (Given): 332°
Quadrant 4: 360° - 152° = 208°