The length of the fishing pole is approximately 2.40 meters.
the equation is
x = 0.5 / cos (78)How to find the angle of elevationThe equation that relates the length of the fishing pole, the distance from the base of the pole to the wall, and the angle of elevation is:
cos (angle of elevation) = adjacent / hypotenuse
In this case, the hypotenuse side is the length of the fishing pole, x, and the adjacent side is the distance from the base of the pole to the wall, 0.5 meters. The angle of elevation is 78 degrees. Therefore:
cos (78) = 0.5 / x
x = 0.5 / cos (78)
x ≈ 2.40 meters
Therefore, the length of the fishing pole is approximately 2.40 meters.
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Which of the following inequalities does the graph represent?
Number line -5 to +5 in single-integer increments - assessment graphic
Responses
–3 < t < 4
–3 < t < 4
t < –3 or t > 4
t < –3 or t > 4
–3 ≤ t ≤ 4
–3 ≤ t ≤ 4
t ≤ –3 or t ≥ 4
The statement t < –3 or t > 4 is the inequality that the graph represents.
What is inequality?Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.
The graph represents the inequality t < –3 or t > 4. This can be seen by the number line, which has the integers -5 to 5 incrementally marked, with the bars extending beyond the -3 and 4 markers. This indicates that the value of t is less than -3 or greater than 4, but not equal to either of these values. Therefore, the statement t < –3 or t > 4 is the inequality that the graph represents.
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1. b^3/b^0
2. a•x^5/ a•x^4
3. a • b²•a²•b³
4. b-2•b²•a⁰
Use the properties of exponents to rewrite each
expression in the text box.
The following expressions solved with the properties of exponents;
b³
ax
a³ × b⁵
b
How to solve using properties of exponents?b³ / b⁰
= b^(3-0)
= b³
a•x⁵ / a•x⁴
= ax⁵ / ax⁴
= ax^(5-4)
= ax¹
= ax
a • b²• a²•b³
= a^(1+2) × b^(2+3)
= a³ × b⁵
b^-2•b²•a⁰
= b^(-2+2) × a⁰
= b¹ × 1
= b
Therefore, the properties of exponents states that when numbers of the same base are divided, the exponent will be subtracted and
when numbers of the same base are multiplied, the exponent will be added.
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Help me pls pls pls pls
Answer:
Step-by-step explanation:
The middle one
There are 15 total blocks that is your denominator.
There are 5 shaded that is your numerator.
5/15
Write the equations
for this line in
slope-intercept
form.
Answer:
y=2/3x+-1
Step-by-step explanation:
What is true of the triangle below?
Answer:
Step-by-step explanation:
where is the triangle
what is the axis of symmetry of this quadratic? -5x² + 70x + 3
Answer:
x=7
Step-by-step explanation:
You graph it and find the middle point that would create a line through it and see where it his the x-axis.
solve for v. 4v-18=6(v-6)
Answer:
v = 9
Step-by-step explanation:
4v - 18 = 6(v - 6)
1.) Distribute 6 into the parenthesis
4v-18 = 6v - 36
2.) Move 6v to the other side by subtracting from both sides
4v - 6v -18 = -36
3.) Move 18 to the other side by adding 18 on both sides
4v - 6v = 18 + -36
4.) Combine like terms
-2v = -18
5.) Divide -2 on both sides to get v by itself
v = 9
Answer:
the answer is 9
Step-by-step explanation:
4v-18=6(v-6)
4v-18=6v-36
4v-6v= -36+18
-2v= -18
divide both sides by -2
v=9
It's pretty easy... Please help me ASAP and show your work. If I get 2 questions I will mark one person BRAINLIEST. So PLEAASEEEEEEEEEEE
Help on #4, #7, and #8
The given problems are solved:
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Question 4:
To calculate angle A,
Consider tan function.
[tex]tan A=\frac{opposite side }{adjacent side}[/tex]
[tex]tan A=\frac{9.6}{7.2}[/tex]⇒ 1.34
A= 53.26°
Question 7:
In triangle PQR, ∠Q=80°, PQ=8 and QR= 6,
PR=?
Area of triangle = 1/2 *a*b*sinC
= 1/2*8*6*sin°80
=24*0.984
Area of triangle = 23.616 square units.
Question 8:
Consider the triangle JKL, here two sides and one angle is given,
we can use cosine law,
The equation set us is given by,
[tex]a^{2} = b^{2}+ c^{2} -2bcCos\alpha\\b ^{2} = a^{2}+c^{2} -2acCos\beta\\ c^{2} = b^{2} +a^{2} -2baCos\gamma[/tex]
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ting is making a circular garden with a radius of 6 feet.How far across is the garden at its widest point?What is the length of edging material to the nearest hundredth needed to enclose the garden?Use 3.14
The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.
Describe Circumference of circle?The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.
Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.
To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting, r = 6 into the formula, we get:
C = 2π(6)
C = 12π
To approximate this value using 3.14, we can substitute π = 3.14 and get:
C ≈ 12(3.14)
C ≈ 37.68
Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.
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Range and domain ??
{(-3,0), (3,-7), (-1,-6), (-1,-5), (-5, -1)}
help me on this and tell me if i got them right
The volume of a rectangular prism is 320 m³.
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.
1) Given that, base area is 40 m² and height is 8 m.
So, the volume = 40×8
= 320 m³
2) 2) In the basketball game, Scott attempted 14 free throws.
He made half of them = 14/2
= 7
So, he made 7 throws
3) Today's high is 47 degrees Fahrenheit.
The weatherman says it will hit freezing tonight.
So, the temperature is represented as -47 degrees.
4) The given numbers are 5489 and 6752
Now, the sum is 5489 +6752
= 12241
Estimated to the nearest thousand as 12000.
5) Jace had 38 paper airplanes at home.
Christopher gave him 14 more paper airplanes to play with at home. Then Ameera gave him 29 paper airplanes.
So, total airplanes= 38+14+29
= 81
So, Jace had total 81 paper airplanes.
Therefore, the volume of a rectangular prism is 320 m³.
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Convert 0.807 to a fraction in simplest form and a percent.
1. Write in function notation a rule that moves a pre-image 4 units right and 7 units down.
A. f(x) (x + 4, y + 7)
B. f(x) (x + 4, y - 7)
C. f(x)(x-4, y + 7)
D. f(x) (x - 4, y - 7)
The function notation that moves a pre-image 4 units right and 7 units down is f(x) ⇒ (x + 4, y - 7)
What is translation?Translation is the movement of a point on the coordinate plane either left, right, up or down. Translation is a rigid transformation because it preserves the shape and size. Reflection and rotation are also rigid transformations.
If a point A(x, y) is translated a units right and b units down, then the new point is A'(x + a, y + b)
The function notation that moves a pre-image 4 units right and 7 units down is (x, y) ⇒ (x + 4, y - 7)
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on a linear graph, this is called the
In ΔNOP, p = 490 inches, m∠N=57° and m∠O=55°. Find the length of n, to the nearest inch.
The value of n is 443 inches when using the triangle rule and law of sine.
What is meant by Sine Rule?An oblique triangle's sides and angles are related according to the rule of sines (non-right triangle). The laws of sines and cosines are crucial trigonometrical formulas for "solving a triangle." The sine rule states that there is an equal relationship between a triangle's side lengths and the sine of each of its opposite angles.Triangles' side length to opposite angle ratios are governed by the law of sines. For all three sides and perpendicular angles, this ratio remains constant. So long as the necessary information is known, we may use the sine rule to determine the missing side or angle of any triangle.The formula is given as
a / sin A = b / sin B = c / sin C
In this triangle NOP, we can find the value of angle P
∠N + ∠O + ∠P = 180
57 + 55 + ∠P = 180 : Sum of angles in a triangle is equal 180 degrees
∠P = 180 - 112
∠P = 68
Using law of sine
p/sin P = n/sin N
490/sin68 = n / sin57
n = [(490 × sin 57) / sin 68]
n = 443 inches
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Pls help me thanks :)))
Answer:
y = - 1 , y = 17
Step-by-step explanation:
y² - 16y + 64 = 81 ← y² - 16y + 64 is a perfect square
)y - 8)² = 81 ( take the square root of both sides )
y - 8 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 8 to both sides )
y = 8 ± 9
then
y = 8 - 9 = - 1
x = 8 + 9 = 17
A grocery store sells a bag of 3 oranges for $0.90. How much does one orange cost?
Answer:
$0.30
Step-by-step explanation:
They tell you that a bag of 3 is $0.90. 3 can go into 90 a total of 30 times. 0.90/3 is 0.30
Answer:
first take a total price and then divided by the total bags to get price of each
Step-by-step explanation:
0.90÷3=0.30How do you visualizationa Kruskal algorithm?
Visualizing Kruskal's algorithm involves representing the graph, its edges, and the minimum spanning tree in a visual format.
To visualize a Kruskal algorithm, you need to follow the steps below:
1. Sort all the edges in ascending order of weight.
2. Create a new graph G' with the same vertices as the original graph G, but no edges.
3. Start with the smallest edge and add it to G' if it doesn't create a cycle. Repeat this step until you have added all the edges or you have a minimum spanning tree.
4. If you have a minimum spanning tree, you can visualize it by drawing the graph with the edges included in G'.
Here is an example:
Original graph G:
A---2---B---3---C
| |
4 1
| |
D---5---E
Step 1: Sort the edges in ascending order of weight: 1, 2, 3, 4, 5
Step 2: Create a new graph G' with the same vertices as G, but no edges.
Step 3: Start with the smallest edge (1) and add it to G'. This doesn't create a cycle, so we can add it.
G':
A B---1---C
| |
4 1
| |
D E
Next, add the second smallest edge (2) to G'. This also doesn't create a cycle, so we can add it.
G':
A---2---B---1---C
| |
4 1
| |
D E
Continue this process until you have added all the edges or you have a minimum spanning tree.
Step 4: Visualize the minimum spanning tree by drawing the graph with the edges included in G'.
Minimum spanning tree:
A---2---B---1---C
| |
4 1
| |
D E
I hope this helps! Let me know if you have any further questions.
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Solve the following problems on numbers. Show your solution.
1. The sum of the two numbers is 91. The smaller number is 17 less than the larger number. What are the numbers? (2 points)
2. Twice the sum of a number and 8 is 24. Find the number. (1 point)
3. Find three consecutive integers such that the sum of the first and the third is 8 more than the second number. (3 points)
Answer:
Q1. The larger number is 54 and the smaller number is 37.
Q2. The number is 4.
Q3. The three numbers are 7, 8 and 9.
Step-by-step explanation:
Q1.
Let the larger number be x and the smaller number be y.
x+y= 91 (1)
x-y= 17 (2)
From (2) :
x= y+17 (3)
sub (3) into (1) :
y+17+y= 91
2y= 74
y= 37 (4)
sub (4) into (3) :
x= 37+17
= 54
Q2.
Let the unknown number be x.
2x+16= 24
2x= 8
x= 4
Q3.
Let the smallest number be x.
2nd no. : x+1
3rd no. : x+2
x+(x+2)= (x+1)+8
2x+2= x+9
x= 7
x+1= 8
x+2= 9
Find the median and mean of
the data. Which reflects the
best measure of the center?
X
X
8
X
X
X
X
X
9
XX
10
X
40
the mean and the median of the given data set are 16.75 and 9.5 respectively.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, A data set 8, 9, 10, 40
From the general formula of mean:
mean = (sum of observations) ÷ (total number of observations).
mean = (8 + 9 + 10+ 40)/4
mean = 67/4
mean = 16.75
Since the median is:
The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.
Thus,
the median of the given data set = (9 +10)/2
the median of the given data set = 9.5
Therefore, the mean and the median of the given data set are 16.75 and 9.5 respectively.
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ROUND PLEASE AND THANK YOU!!!!!!
The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.
The length of the first secant in the image is x + 18, and the second is 24 + 16.
x + 18 times 18 = 40 times 16
18x + 324 = 640
18x = 316
x= approximately 17.6
I need help with this one and can u explain it
Answer:
x = 8
Step-by-step explanation:
Vertically opposite angles are congruent.
5x + 9 = 57 - x
Add x to both sides,
5x +x + 9 = 57
6x + 9 = 57
Subtract 9 from both sides,
6x = 57 - 9
6x = 48
Divide both sides by 6,
x = 48 ÷ 6
x = 8
Investigate the Trigonometric Ratios for 30 Degrees (3 points)
Hyp= 2.63
30 degrees
Adj = 2.278
Opp = 1.315
I have set this to make a 30 degree triangle.
Record the lengths of the three sides in the table below.
Adjust the red dot to change the size of your triangle.
Record the next set of measurements for that triangle.
Repeat until you have done 3 triangles, each for a 30
degree reference angle.
Triangle
1
2
3
Hypotenuse Opposite
Adjacent
The next set of measurements for the triangle are as follows:
Triangle 1 Triangle 2 Triangle 3
Hypotenuse: 5.26 7.89 10.52
Opposite: 2.63 3.945 5.26
Adjacent: 4.556 6.834 6.834
How to find the triangle measures while maintaining angle 30 degreesThis is done using the concept of similar triangles,
Similar triangles are two triangles that have the same shape but may be scaled to different sizes. In other words, similar triangles have the same angles, but their sides may be proportional.
In the problem, the proportion of the sides are equal and this will maintain the size of the angle
let the size of the angle be x
Sin x = opposite / hypotenuse
Sin x = 2.63 / 5.26 = 3.945 / 7.89 = 5.26 / 10.52 = 0.5
x = arc sin (0.5)
x = 30
To maintain same proportion the triangles where all a scaled version of the given triangle
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0.003/19.43 what is the answer
Answer:
0.000154
Step-by-step explanation:
how to find the missing dimension of. a cone when the when the highest s 4.2 and the volume is 3.6 cubed
To find the missing dimension of a cone when the height is 4.2 and the volume is 3.6 cubed is to equate the general formula with the given information.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
To obtain the missing dimension of a cone we must equate the general formula for the volume of a cone to the given information.
Therefore, (1/3)πr²×4.2 = 3.6
(1/3)πr² = 0.86.
r² = 0.86/1.05.
r² = 0.82.
r = 0.9
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6y^2+25y+4 factor the expression
Answer: (6y + 1) (y + 4)
Step-by-step explanation: (6y + 1) (y + 4) (6y)(y) + (6y)(4) + (1)(y) + (1)(4) 6y^2 + 24y + 1y + 4 6y^2 + 25y + 4
Answer:
multiply 6×2 an you get 12
step:1 =4×12y⁴ ¹+25y¹ ¹
step:2=48y⁴ ¹ +25y¹ ¹
step:3=48y³+25y⁰
step:4=48y³+25×1
step:5=48y³+25
answer=48y³+25
Can someone please help?? Thank you soo much
Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.
What is cost?Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The expression for the cost to buy x pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.
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25 POINTS AND BRAINLIEST Multiply and simplify. Circle your final answer (or highlight final answer in yellow if typing). (2 pts)
2p^3q^4r^2(2p^4q^2t^3)(3r)
Answer: To multiply the expression, we first distribute the constant factors:
2p^3q^4r^2 * 2p^4q^2t^3 * 3r = 6p^3q^4r^3 * 2p^4q^2t^3
Next, we multiply the variables by combining like terms:
6p^3q^4r^3 * 2p^4q^2t^3 = 6p^7q^6r^3t^3
This is the final simplified expression, and we can circle or highlight it as the answer.
Step-by-step explanation:
PLEASE HELP ASAP‼️‼️Are the sides proportional?
Set up each ratio of sides and determine if they are equal
ratios. Show all of your work.
3.61 cm
R
44°
S
11.97 cm
9.71 cm
15
N
T
17.955 cm
14.565 cm
121°
M
L
5.415 cn
The side lengths form a proportional relationship, and the ratios are as follows:
17.955/11.97 = 14.565/9.71 = 5.415/3.61.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
They must have Congruent angle measures.
They have Proportional side lengths.
Here, the triangles are similar, as they have the same angle measures.
17.955/11.97 = 14.565/9.71 = 5.415/3.61.
Thus, the side lengths form a proportional relationship, as the equivalent side have a ratio of 1.5.
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treena won a 7 day scholarship with $1000 to the pro shet basketball camp. rand trip travel exanse to the camp are $335 bh air or $125 by train. at the camp she much choose beteeen a week of individual instruction at $60 per dah or a week of group instruction at $40 per day. treenas food if she does not plan to spef money ofter then the scholarship ehat atr all choices of travel and induction plans that she could afford to make?
Answer:
To solve this problem, we need to calculate the cost of each travel and instruction option and then determine which options Treena can afford with her $1000 scholarship.
Option 1: Air travel and individual instruction
Travel cost: $335
Instruction cost: 7 x $60 = $420
Total cost: $335 + $420 = $755
Option 2: Air travel and group instruction
Travel cost: $335
Instruction cost: 7 x $40 = $280
Total cost: $335 + $280 = $615
Option 3: Train travel and individual instruction
Travel cost: $125
Instruction cost: 7 x $60 = $420
Total cost: $125 + $420 = $545
Option 4: Train travel and group instruction
Travel cost: $125
Instruction cost: 7 x $40 = $280
Total cost: $125 + $280 = $405
Now we need to determine which options Treena can afford with her $1000 scholarship. We'll start with the most expensive option and work our way down.
Option 1: $755
This option is too expensive for Treena's $1000 scholarship.
Option 2: $615
This option is also too expensive for Treena's $1000 scholarship.
Option 3: $545
This option is within Treena's budget, but she won't have any money left for food.
Option 4: $405
This option is also within Treena's budget, and she'll have $595 left for food.
Therefore, Treena's choices of travel and instruction plans that she could afford to make are:
- Train travel and group instruction with $595 left for food
- Train travel and individual instruction with no money left for food