Answer:
[tex]A\approx 37.95^{\circ}[/tex]
Step-by-step explanation:
We have been given that [tex]\text{tan}(A)=0.78[/tex]. We are asked to find measure of angle A in degrees.
We will inverse tangent to find measure of angle A as:
[tex]A=\text{tan}^{-1}(0.78)[/tex]
[tex]A=37.954230875133^{\circ}[/tex]
Upon rounding our answer to nearest hundredth, we will get:
[tex]A\approx 37.95^{\circ}[/tex]
Therefore, the measure of angle A is approximately 37.95 degrees.
What is the value of b in the equation below?
when dividing subtract the powers
so you would do 6-2 = 4
so b = 4
Answer:
The value of b is 4.
Step-by-step explanation:
The given equation is
[tex]\frac{5^6}{5^2}=a^b[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, the given equation can be written as
[tex]5^{6-2}=a^b[/tex]
[tex]5^{4}=a^b[/tex]
On comparing both the sides, we get
[tex]a=5,b=4[/tex]
Therefore the value of b is 4.
The area of a book cover is 63.8 in². The width of the book is the difference of the length and 3 inches. Let x represent the book's length. Which quadratic equation represents the area of the book cover?
x(x - 3) = 63.8
x(3 - x) = 63.8
2x - 3 = 63.8
x + x - 3 = 63.8
The correct quadratic equation representing the area of the book cover is [tex]\( x(x - 3) = 63.8 \)[/tex].
To understand why this is the correct equation, let's break down the information given in the question:
1. The area of the book cover is given as 63.8 square inches.
2. The width of the book is the difference between the length and 3 inches. If we let [tex]\( x \)[/tex] represent the length of the book, then the width can be represented as [tex]\( x - 3 \)[/tex].
3. The area of a rectangle (which is the shape of the book cover) is calculated by multiplying its length by its width.
Using the information above, we can set up the equation for the area of the book cover as follows:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
[tex]\[ 63.8 = x \times (x - 3) \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 63.8 = x^2 - 3x \][/tex]
This is a quadratic equation in standard form. The other options given do not correctly represent the relationship between the length, width, and area of the book cover:
[tex]- \( x(3 - x) = 63.8 \)[/tex] incorrectly represents the width as [tex]\( 3 - x \)[/tex] instead of [tex]\( x - 3 \)[/tex].
[tex]- \( 2x - 3 = 63.8 \)[/tex] is a linear equation, not a quadratic one, and does not represent the area calculation.
[tex]- \( x + x - 3 = 63.8 \)[/tex] simplifies to [tex]\( 2x - 3 = 63.8 \)[/tex], which is also a linear equation and does not represent the area calculation.
a line perpendicular to a plane, would intersect the plane at one what
A line perpendicular to a plane, would intersect the plane at one point.
Perpendicular linesWhen a line is perpendicular directly away from the plane, the line will tend to intersect the plane at one points or single points.
The reason why the line intersect the plane is because the line cannot point to other places except directly away from the plane.
Therefore a line perpendicular to a plane, would intersect the plane at one point.
Learn more about Perpendicular lines here:https://brainly.com/question/1202004
#SPJ9
Krystal left the hardware store and traveled toward the recycling plant at an average speed of 61 mph. Scott left at the same time and traveled in the opposite direction with an average speed of 65 mph. Find the number of hours Scott needs to travel before they are 252 mi. Apart
Since Krystal and Scott is heading on opposite directions, therefore the distance between the two would be the sum of their distances from where they left, so:
total distance (d) = distance covered by Krystal (dK) + distance covered by Scott (dS)
d = dK + dS
We know that the formula for distance is:
distance = velocity * time
So,
d = vK * t + vS * t
where
vK = velocity of Krystal = 61 mph
vS = velocity of Scott = 65 mph
d = 252 miles
Therefore:
252 = 61 t + 65 t
126 t = 252
t = 2 hours
Therefore Scott needs to travel for 2 hours.
One pound of feathers would be easier weighing than one pound of iron
What is the value of 64? 60 = 1 61 = 6 62 = 36 63 = 216
If GH is the angle bisector of FGI, which statement about the angle is true
The angle bisector of a given angle divides it into two equal parts. If GH is the angle bisector of FGI, angle FGH and angle HGI will be equal.
Explanation:If GH is the angle bisector of FGI, it means that it splits the angle FGI into two equal parts. Hence the angles FGH and HGI are equal.
For example, if angle FGI is 60 degrees, then the angle FGH and HGI (formed as a result of the bisector) would each be 30 degrees because the bisector divides the 60 degrees into two equal parts. This is the fundamental concept of an angle bisector in geometry.
Learn more about Angle Bisector here:https://brainly.com/question/37543581
#SPJ12
The linear function y = 1.2x represents Alberto’s speed, y, in meters per minute, when his stride rate is x steps per minute. Alberto’s average stride rate during a 10-kilometer race is 180 steps per minute.
What is Alberto’s average speed during the race?
Answer:
What is Alberto’s average speed during the race?
216 meters per minute
Based on the linear model, which is the best prediction of how long it will take Alberto to finish the 10-kilometer race?
B. 46 minutes
In a test of a gender-selection technique, results consisted of 248 baby girls and 13 baby boys. based on this result, what is the probability of a girl born to a couple using this technique? does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
Solve 4a+3=11 plz step by step
The value of solution of expression is, a = 2
We have to give that,
An expression to simplify,
4a + 3 = 11
Now, Simplify the expression by combining like terms as,
4a + 3 = 11
Subtract 3 on both sides,
4a + 3 - 3 = 11 - 3
4a = 8
Divide 4 into both sides,
a = 8/4
a = 2
Therefore, the solution is, a = 2
To learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ6
A store sells two sizes of fresh wreaths. an? 18-inch wreath costs ?$1515?, and a? 22-inch wreath costs ?$3535. in one? day, the number of? 22-inch wreaths sold was fourfour more than twicetwice the number of? 18-inch wreaths, for a total of ?$820820. how many of each were? sold
The number of 18 inches of wreaths sold was 9 while 22 inches were 51.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say a number of 18 inches of wreaths is x while 12 inches is y.
Given that,
In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths.
So,
y = 5x + 6
And
Total amount
15x + 35y = 1920
⇒ 3x + 7y = 384
By substitution,
3x + 7(5x + 6) = 384
38x = 342
x = 9
So y = 5(9) + 6 = 51
Hence "The number of 18 inches of wreaths sold was 9 while 22 inches were 51".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
The given question is incorrect, the correct question is ;
A store sells two sizes of fresh wreaths. An 18-inch wreath costs $15, and a 22-inch wreath costs $35. In one day, the number of 22-inch wreaths sold was six more than five times the number of 18-inch wreaths, for a total of $1920. How many of each were sold? .... The number of 18-inch wreaths sold was and the number of 22-inch wreaths sold was
The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.6 trillion?
can someone help with factoring the trinomial below
Solution of this equation
What is the value of the 30th percentile for the data set 6283, 5700, 6381, 6274, 5700, 5896, 5972, 6075, 5993, 5581?
The 30th percentile for the given data set is 5758.8, calculated by arranging the data in ascending order and interpolating between the 3rd and 4th values.
To find the 30th percentile for the given data set, first arrange the data in ascending order and then calculate the rank of the 30th percentile. The formula to find the kth percentile for a data set with n observations is:
Rank = (k/100) * (n + 1)
For the given data set of 10 values, the 30th percentile rank would be:
Rank = (30/100) * (10 + 1) = 3.3
Since the rank is not a whole number, the 30th percentile lies between the 3rd and 4th values in the ordered set. After arranging the data:
5581
5700
5700
5896
5972
5993
6075
6274
6283
6381
The 3rd and 4th values are 5700 and 5896. We must interpolate to find the exact 30th percentile:
30th Percentile = 5700 + 0.3 * (5896 - 5700) = 5700 + 0.3 * 196 = 5700 + 58.8 = 5758.8
The 30th percentile is 5758.8.
Solve the inequality. Graph the solution set. 26 + 6b 2(3b + 4)
we have
[tex]26 + 6b\geq2(3b + 4)[/tex]
Applying the distributive property on the right side
[tex]26 + 6b\geq6b+8[/tex]
subtract [tex]6b[/tex] from both sides
[tex]26\geq 8[/tex] -------> is true
for all real numbers the inequality is true
therefore
the graph is a shaded area everywhere.
the answer is
the solution is all real numbers
The solution is all real numbers.
It is required to find the solution.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Applying the distributive property on the right side
26+6b≥6b+8
Then subtract 6b from both sides we get,
26≥8
For all real numbers the inequality is true.
Therefore, the solution is all real numbers.
Learn more details about inequality here:
https://brainly.com/question/20383699
#SPJ2
Samantha wants to use her savings of $1150 to buy shirts and watches for her family. the total price of the shirts she bought was $84. the watches cost $99 each. what is the maximum number of watches that samantha can buy with her savings? (1 point)
Answer:
Maximum number of watches Samantha can buy equals:
10
Step-by-step explanation:
Samantha wants to use her savings of $1150 to buy shirts and watches for her family.
The total price of the shirts she bought was $84.
The watches cost $99 each.
Let she bought x watches
then, 84+99x≤1150
subtracting by 84 on both sides, we get
99x≤1066
dividing both sides by 99, we get
x≤ 10.7676
Hence, maximum number of watches Samantha can buy equals:
10
Help with math!!!!!!
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equation of this cubic polynomial function. Recall that the zeros are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
The equation of the function is [tex]y = \frac 16(x -2)(x -3)(x -5)[/tex], and the y-intercept of the function is -5
A cubic function is represented as:
[tex]y = a(x -x_1)(x -x_2)(x -x_3)[/tex]
The zeros are (2, 0), (3, 0), and (5, 0).
This means that:
(x1, y) = (2, 0)
(x2, y) = (3, 0)
(x3,y) = (5, 0)
So, we have:
[tex]y = a(x -2)(x -3)(x -5)[/tex]
The graph passes through the point (0,-5).
So, we have:
[tex]-5 = a(0 -2)(0 -3)(0 -5)[/tex]
Evaluate the products
[tex]-5 = -30a[/tex]
Solve for a
[tex]a = \frac{5}{30}[/tex]
[tex]a = \frac{1}{6}[/tex]
Substitute 1/6 for a in [tex]y = a(x -2)(x -3)(x -5)[/tex]
[tex]y = \frac 16(x -2)(x -3)(x -5)[/tex]
The y-intercept of the function is when x = 0.
Hence, the y-intercept of the function is -5
Read more about cubic functions at:
https://brainly.com/question/20896994
Which of the following statements is true regarding the relationship between circles and triangles? A. There are many circles that can be circumscribed about a triangle. B. There are many triangles that can be inscribed in a given circle. C. There is only one unique triangle that can be inscribed in a given circle. D. There are many triangles that can be circumscribed about a given circle.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
A circle can be characterized by its center's location and its radius's length.
How to make an inscribed circle in a triangle?There can be many different ways, one can include arc way, one can include angle bisector and perpendicular, and we can even try to discover some.
But usually, (for the angle bisector and perpendiculars), we do the following:
Divide one of the angles in half. Divide another angle in half.
The incenter, or point where they cross, is the inscribed circle's centre.
Construct a perpendicular from the triangle's centre point to one of its sides.
Draw an inscribed circle by placing the compass on the centre point and adjusting the length to where the perpendicular crosses the triangle.
The true statement regarding the relationship between circles and triangles is option B. There are many triangles that can be inscribed in a given circle.
Learn more about inscribing circle here:
https://brainly.com/question/17043518
#SPJ2
What is the equation of the graph below?
A graph shows a parabola that opens up and does not cross the x axis. The axis of symmetry is x equal negative 2. The parabola crosses through the points negative 1, 4 and negative 3, 4.
y = − (x − 2)2 + 3
y = (x + 2)2 + 3
y = − (x + 3)2 + 2
y = (x − 3)2 + 2
Find the ratio of 12:7
A man can run a mile in 4 minutes. calculate his average speed in kilometers per hour. show your work. (1 mile = 1.61 km)
1 mile =1.61km
60 minutes per hour
60/4 = 15 ( he can run 15 miles in one hour)
15 x 1.61 = 24.15 km per hour
round your answer if needed
The man's average speed in kilometers per hour is calculated by first converting the distance the man runs to kilometers, based on the 1 mile equals 1.61 kilometers conversion factor, and then converting time to hours, based on the 60 minutes in 1 hour conversion factor. The calculated speed is approximately 24.04 kilometers per hour.
Explanation:The man runs a mile in 4 minutes. Given that 1 mile equals 1.61 kilometers, we can first change the distance the man runs into kilometers: 1 mile * 1.61 km/mile = 1.61 km. Thus, the man's speed is 1.61 km per 4 minutes.
To convert this speed into kilometers per hour, we need to convert the time from minutes to hours. We know that 1 hour is equivalent to 60 minutes, so 4 minutes is equivalent to 4/60 = 0.067 hours. Therefore, the man's average speed in kilometers per hour is 1.61 km divided by 0.067 hours, which equals about 24.04 km/hr.
Learn more about Average Speed Calculation here:https://brainly.com/question/680492
#SPJ3
The product of twice a number and three three is the same as the difference of five five times the number and three fourths 3 4. find the number.
Factor the expression.
what is the reciprocal of 0.25
Use the following graph of the function f(x) = 2x^3 + x^2 - 3x + 1
What is the average rate of change from x = -1 to x = 1
A) -1
B) 1
C) 2
D) 4
The function f(x) = 5x is an exponential function true or false
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1? 1, –0.25, –1.5, –2.75, –4, . . . 1, 2.25, 3.5, 4.75, 6, . . . 4, 2.75, 1.5, 0.25, –1, . . . 4, 5.25, 6.5, 7.75, 8, . . .
Answer:
[tex]4,2.75,1.5,0.25......[/tex]
Step-by-step explanation:
f (1) = 4, [tex]f (n + 1) = f (n) - 1.25[/tex]
To get the sequence we start with n=1
Plug in n=1 in the formula
[tex]f (n + 1) = f (n) - 1.25[/tex]
[tex]f (1 + 1) = f (1) - 1.25[/tex]
[tex]f (2) = f (1) - 1.25[/tex], replace f(1)=4
[tex]f (2) = 4 - 1.25=2.75[/tex]
n=2
[tex]f (2 + 1) = f (2) - 1.25[/tex]
[tex]f (3) = f (2) - 1.25[/tex], replace f(2)=2.75
[tex]f (3) = 2.75 - 1.25=1.5[/tex]
n=3
[tex]f (3 + 1) = f (3) - 1.25[/tex]
[tex]f (4) = f (3) - 1.25[/tex], replace f(3)=1.5
[tex]f (4) = 1.5 - 1.25=0.25[/tex]
Sequence is [tex]4,2.75,1.5,0.25......[/tex]
Answer:
C.
4, 2.75, 1.5, 0.25, –1
Step-by-step explanation:
Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3+3b^2-b + 12)