a.
Answer:
240 cm^3
b.
Answer:
208cm^2
Graph the solution set of the inequality and write the solution using interval notation.
Solution:
Consider the following inequality:
\(-4<\frac{3x-2}{5}\leq6\)this is equivalent to:
\((-4)(5)<3x-2\leq(6)(5)\)this is equivalent to:
\(-20<3x-2\leq30\)solving for 3x, this is equivalent to:
\(-20+2<3x\leq30+2\)this is equivalent to:
\(-18<3x\leq32\)solving for x, we get:
\(-\frac{18}{3}this is equivalent to:\(-6in interval notation, this is equivalent to:
\((-6,\frac{32}{3}\rbrack\)the solution set on the real line is:
An report describes a survey of 251 adult Americans. Participants in the survey were asked how often they change the sheets on their bed and were asked to respond with one of the following categories: more than once a week, once a week, every other week, every three weeks, or less often than every three weeks. For this group, 11% responded more than once a week, 51% responded once a week, 26% responded every other week, 5% responded every three weeks, and 7% responded less often than every three weeks.
(a) Use the given information to make a relative frequency distribution for the responses to the question. How Often? Relative frequency
More than once a week Once a week Every other week Every three weeks Less often than
every three weeks
More than once a week: 0.11
Once a week: 0.51
Every other week: 0.26
Every three weeks: 0.05
Less often than every three weeks: 0.07
Relative Frequency Survey ResultsTo make a relative frequency distribution, follow these steps:
Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.
Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.
And that's it! These are the relative frequencies for each category in the data.
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A particular disease is tested for and the results determine that it occurs in about 1 of every 750 Hispanic females and about 1 of every 138,000 non-Hispanic females 26,000 Hispanic females were to be tested, about how many of them would you expect to have this particular disease?
Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.
Hispanic female;A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."
The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:
1 / 750 = 0.001333
This means that for every 750 Hispanic females, one is expected to have the disease.
To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:
0.001333 * 26,000 = 34.658
So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.
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(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
the three data sets show the number of text messages sent by jada, and diego, and lin over 6 days. one of the data sets has a mean of 4, one has a mean of 5, and one has a mean of 6.
1. which data set has which mean? what does this tell you about the text messages sent by the three students?
2. which data set has the greatest variabillity? Explain
1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.
2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.
How to calculate the mean for the set of data?In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:
Mean = [F(x)]/n
Question 1.
In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;
Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6
Mean number of text for Jada = 30/6
Mean number of text for Jada = 5.
Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6
Mean number of text for Diego = 36/6
Mean number of text for Diego = 6.
Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6
Mean number of text for Lin = 24/6
Mean number of text for Lin = 4.
Question 2.
In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;
Standard deviation = √(1/n × ∑(xi - u₁)²)
Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]
Standard deviation for Jada = √(6/6) = 1
Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]
Standard deviation for Diego = √(14/6) = 1.53
Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]
Standard deviation for Lin = √(76/6) = 3.6
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Kindly solve the following with the cirrect method .SOLVE ALL . I'll give brainliest + thanks + follow
The following percentages are listed below:
12.5 %40 %6.25 %6.667 %41.667 %75 %How to use percentages in real life situationsIn this question we have seven cases of real life situations in which percentages are used. Mathematically speaking, percentages are represented by the following expression:
x = r / r' × 100 (1)
Where:
r - Real quantityr - Maximum quantityNow we proceed to determine quantities related to percentages:
2.8 mm as a per cent of 2.24 cm
x = (2.8 mm / 22.4 mm) × 100 %
x = 12.5 %
What per cent of 1.5 m is 60 cm?
x = (60 cm / 150 cm) × 100 %
x = 40 %
What per cent of 2 kg is 125 g?
x = (125 g / 2000 g) × 100
x = 6.25 %
What per cent of R 6 to 40 p?
x = (40 / 600) × 100
x = 6.667 %
What per cent of a day is 10 h?
x = (10 h / 24 h) × 100
x = 41.667 %
What per cent of 7 1 / 3 m in 5 1 / 2 m ?
x = [(11 / 2) / (22 / 3)] × 100 %
x = 75 %
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A candy store has 6 boxes of chocolates. Each box has 500 pieces How many pieces are there altogether in the 6 boxes?
The following are the ages of 12 history teachers In a school district 29,30,32,32,39,41,46,49,50,51,52,53 minimum lower quartile median upper quartile maximum and interquartile range
The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
How does interquartile range work?Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.
According to the given information:To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.
Step 1: Find the median (Q2)
When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:
Median (Q2) = (41 + 46)/2 = 43.5
Step 2: Find the lower quartile (Q1)
The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:
Q1 = (32 + 32)/2 = 32
Step 3: Find the upper quartile (Q3)
The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:
Q3 = (50 + 51)/2 = 50.5
Now we have all the information we need to construct the five-number summary and interquartile range:
Minimum: 29
Lower quartile (Q1): 32
Median (Q2): 43.5
Upper quartile (Q3): 50.5
Maximum: 53
Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5
the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.
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Solve the following equation. 14 = w2
If a ball is thrown in the air with an initial
height of 4 feet, and if the ball remains in
the air for 3.8 seconds, then accurate to
the nearest foot, how high did it go?
Remember, the acceleration due to
gravity on Earth is -32 ft/sec².
[?] feet
The requried ball reached a maximum height of approximately 62 feet
Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:
\(h(t) = -16t^2 + vt + h_0\)
here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.
At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:
h₀ = h(t) + 16t²
= 4 + 16(1.9)²
≈ 4 + 57.76
≈ 61.76
Therefore, the ball reached a maximum height of approximately 62 feet
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(h - 3)2 for h = 5. help plz
Answer:
4
Step-by-step explanation:
(h-3)2
(5-3)2 (substitution)
(2)2 (subtraction)
4 (multiplication)
Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
Given the triangles EFG and HIJ, you can identify that:
\(EG=19\text{ }\)\(EF=18\)\(\begin{gathered} FG=16\text{ } \\ \\ \text{ }HI=90 \\ \\ IJ=80 \end{gathered}\)\(\begin{gathered} m\angle F=67\text{ \degree} \\ \\ m\angle I=67\text{ \degree} \end{gathered}\)By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find in they are in proportion. Set up that:
\(\frac{EF}{HI}=\frac{FG}{IJ}\)Substituting values and simplifying, you get:
\(\begin{gathered} \frac{18}{90}=\frac{16}{80} \\ \\ \frac{1}{5}=\frac{1}{5} \end{gathered}\)Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measure.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is: Third option.
Which is more, 6 liters or 6,001 milliliters?
Answer: 6,001 milliliters
Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.
Answer:
I believe 6 liters is more.
Find the value of f(-4)
Step-by-step explanation:
PLEASE TYPE FULL QUESSTION
What is another name for EA?
CF
BD
CG
EC
Answer:
Step-by-step explanation:
Cf +1/2=EA
A farmer has 1776 feet of fencing available to enclose a rectangular area bordering a river. If no fencing is required along the river, find the dimensions of the fenced area that will maximize the area. What is the maximum area?
As per the given perimeter of the rectangular area, the maximum area without fencing is 788544 square feet.
Perimeter of rectangle
Perimeter of the rectangle is defined as the total length or distance around the boundary of a rectangle.
And the formula that is used to measure the perimeter of the rectangle is
P = L x B
Where
L refers the length
B refers the breadth
Given,
A farmer has 1776 feet of fencing available to enclose a rectangular area bordering a river.
Here we need to find if no fencing is required along the river, then what will be the dimensions of the fenced area that will maximize the area.
Let us consider L and W be the length and width of the rectangular respectively.
And also, let the river run along L.
So, the perimeter to be covered by fence is written as,
=> P = L + 2W.
Therefore, when we apply the value of perimeter in it, then we get,
=> 1776 =L + 2W
Here we need the value of L, so, the equation is rewritten as,
=> L = 1776 - 2W
Now, we have to apply these value on the area formula, then we get,
A = (1776-2W) x W
When we simplify it, then we get,
=> A = 2700W-2W²
This is in the form of quadratic equation.
So, let us assume that the vertex of the rectangular at maximum area will give maximum width.
Then it can be obtained as, (W,A),
where the value of
W = -b/2a
Here the value of b = 1776 and a = -2
By applying these values on the formula, then we get the value of W as,
=> W = -1776/2*(-2)
=> W = -1776/-4
=> W = 444ft.
Therefore, the length is
=> L = 1776 - 2(444)
=> L = 1776 - 888
=> L = 888
Maximum area, A=888*888 = 788544 square feet.
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Which of the following is true of protecting classified data?
True statement for Protecting classified data is classified material must be appropriately marked.
Classified information being transmitted from one commission office to another shall be protected with a classified document cover sheet and hand delivered by an appropriately cleared person to another appropriately cleared person.
Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties.
Data classification is broadly defined as the process of organizing data by relevant categories so that it may be used and protected more efficiently. Data classification involves tagging data to make it easily searchable and trackable.
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Use the parallelogram to find m
m
Using the parallelogram law to find m, the value of m is 50°.
What is the parallelogram law?The parallelogram law states that the sum of the squares for a parallelogram's four sides is equal to the sum of the squares for its two diagonals.
The parallelogram must have equal opposed sides in Euclidean geometry.
If ABCD is a parallelogram, then AB = DC and AD = BC, the parallelogram law is stated as:
2(AB)² + 2 (BC)² = (AC)² + (BD)²
If the parallelogram is a rectangle, the parallelogram law is stated as:
2(AB)² + 2 (BC)² = 2(AC)²
The value of the unknown angles in the parallelogram are as follows:
CED = 180 - (60 + 33 + 37)
CED = 50°
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Find an equation for the line below.
Answer:
y=2/4x+4.5
Step-by-step explanation:
Use rise over run to get 2/4 and the line splits 4 and 5 to get 4.5
Hope this Helps :)
Answer:
Step-by-step explanation:
Unsure
Find AE. Round the answer to the nearest tenth.
A 9.7
B. 13.5
C. 16.1
D. 17.3
AE= 17.4 to nearest tenth
Step-by-step explanation:
Opposite + hypotenuse = SOH / sin
Sin 31 = 6/h
xh, then ÷ sin31
H= 6/sin31
H= 11.649....(a or b & 6 being a or b)
a^2 + b^2 = c^2
c = 13.1
Actually it's not a right-angle triangle
180 - 13+31 (or 44) = 136 degrees
Cosine rule: a^2=b^2+c^2 - 2bc cosA
AE = root 11.649...^2 + 7^2 - 2x11.649...x7xcos136
= 17.3791......
AE= 17.4 to nearest tenth
Hope this helps!
Two cyclists, 90 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the
other. If they meet 3 hours later, what' is the speed (in mi/h) of the faster cyclist?
The speed of the faster cyclist is 30 mph.
Two cyclists, distance = 90 miles.
let the speed of one cyclist is = x and
let the speed of the other cyclist = 2x
time after which both the cyclists will meet = 3 hours.
Since they are travelling towards each other the effective speed = 2x ₊ x
= 3x
we know that time = distance/speed
3 = 90/3x
3x = 30
x = 10 mph speed of one cyclist.
speed of the other cyclist will be 3x = 3 × 10 = 30 mph
The speed of the fastest cyclist is 30 mph.
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18) What is the slope of the line that contains points (–6, –6) and (–3, 1)?
The slope of the line is 7/9
How to determine the slope of the lineIt is important to note that the equation of a line is represented as;
y = mx + c
Where;
y is a point on the linem is the slope of the linex is a point on the x - axisc is the intercept of the y-axisThe formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/x₂ - x₁
Now, let's substitute the values into the formula from the points given we have;
Slope, m =1 -(-6)/ -3 - (-6)
expand the bracket
Slope, m = 1 + 6/ 3 + 6
add the values
Slope, m = 7/9
Hence, the value is 7/9
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Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5 B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15 C w = 5 \times 15w=5×15
The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.
Which equation correctly matches the given situation?It follows from the task content that the equation which correctly represents the Given situation is to be determined.
Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;
Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.
Consequently, answer choice C; w = 5 × 15 is correct.
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is (5, 20) a solution of the equation y = 4x explain.
A. Yes, 5 = 5. B. No, 5 ≠ 4.
C. Yes, 20 = 20 D. No, 5 ≠ 80.
Answer:
C. yes, 20 = 20
Step-by-step explanation:
the equation is y=4x and from the coordinates (5,20) we can see that x =5 and y = 20
substituting in the original equation we must check if
20 = 4(5)
20 = 20
left = right
yes it is a solution
Write the slope of tangent and normal to the curve y=f(X) at (x1,y1).
The slope of the tangent line is:
a = (df(x1)/dx)
The slope of the normal one is:
a' = -1/(df(x1)/dx)
How to find the slope of the tangent line?For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.
So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:
df(x1)/dx
And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:
a*(df(x1)/dx) = -1
a = -1/(df(x1)/dx)
Where df/dx reffers to the derivative of f(x).
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Can you solve this for me I’m stuck?
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
\((\stackrel{x_1}{65}~,~\stackrel{y_1}{149})\qquad (\stackrel{x_2}{105}~,~\stackrel{y_2}{221}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{221}-\stackrel{y1}{149}}}{\underset{\textit{\large run}} {\underset{x_2}{105}-\underset{x_1}{65}}} \implies \cfrac{ 72 }{ 40 } \implies \cfrac{ 9 }{ 5 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{149}=\stackrel{m}{ \cfrac{ 9 }{ 5 }}(x-\stackrel{x_1}{65})\implies y-149=\cfrac{ 9 }{ 5 }x-117 \\\\\\ y=\cfrac{ 9 }{ 5 }x-117+149\implies \boxed{y=\cfrac{ 9 }{ 5 }x+32} \\\\\\ \stackrel{\textit{Celsius is 70, so x = 70}}{y=\cfrac{ 9 }{ 5 }(70)+32}\implies \boxed{y = 158}\)
what is the distances between 2,2 and 2,6
Answer:
0,4
Step-by-step explanation:
Subtract the points
Type the correct answer in the box.A local school installed a new flagpole that has two lights on both sides of the flagpole that are 40 feet from each other. The distance between one of the lights and the flag is 30 feet.What is the value of x?The value of x is feet.
Given:
A local school installed a new flagpole that has two lights on both sides of the flagpole that are 40 feet from each other.
As shown in the figure the flagpole is in the middle between the lights
And the distance between the lights = 40
So, the distance (x) which represents the distance between the flagpole and the light = half of the distance between the lights
So,
\(x=\frac{1}{2}\cdot40=20\)So, the answer will be the value of x = 20 feet
find the measure of m
Answer:
47*
Step-by-step explanation:
Each corner of the square is 90*
angle CBE + angle ABE = 90*
fill in the blanks
43 + x = 90
subtract 43 from both sides
x = 47*
Find all zeroes of the function. Enter the real zeroes separated by commas.
Answer:
f(x)
=(x-4)[6(x^2)+23x+20]
=(x-4)(2x+5)(3x+4)
x=4,-2/5,-3/4