Answer: 42.5ft
Step-by-step explanation: The wording in your question is a little unclear. I assume that you are looking for how far the anchor line is from the base of the tower.
If so, you can use the Pythagorean Theorem.
a^2 + b^ = c^2
96^ + b^2 = 105^2
Solve for b, gives you about 42.53ft round up and it is 42.5 ft :)
Happy to help
In two or more complete sentences, compare the number of -intercepts in the graph of f(x) =x^2 to the number of x-
intercepts in the graph of g(x) = x^2 +2. Be sure to include the transformations that occurred between the parent function
f(x) and its image g(x).
The number of y-intercepts for g(x) is larger than that for f. (x). The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).
what is coordinates ?When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a two-dimensional plane requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the distance from top to bottom. In (12.5), for example, there are 12 units below and 5 above.
given
The graph of f(x) is moved two units to the right and three units downward to get the graph of g. (x).
The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).
Given that a>0, f(x) and g(x) are ascending parabola.
Since the origin is f(x vertex, )'s f(x) has just one y-intercept, or (0,0).
Given that g(x) is an upward parabola with a vertex at (2,-3), g(x) has two y-intercepts.
Because of this, the number of y-intercepts for g(x) is larger than that for f. (x).
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Linear equations
I need help with these
Instructions: choose two linear equations in each box. Write them below. For #3-#8, find the slope and y-intercept of each equation.
Then graph each line on a coordinate plane on the next page. Label each line neatly with its corresponding equation.
The graph of the equations are added as attachment
How to determine the graphs of the equationsChoose two linear equations
In this case, we make use of the following linear equations
y = 2x + 4 and y = -3x + 5
The slope and y-intercept of each equation
A linear equation is represented as
y = mx + c
Where
Slope = m and y-intercept = c
This means that the slope and y-intercept of each equation are
y = 2x + 4
Slope = 2
y-intercept = 4
y = -3x + 5
Slope = -3
y-intercept = 5
See attachment for the graph of the functions
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Aiden run at a contant peed of 3. 5 meter per econd for 1/2 hour. Then, he walk at a rate of 1. 6 meter per econd for 1/2 hour. How far did Aiden run and walk in 60 minute?
Aiden run and walk in 60 minute, then the distance = 9180 meters
Given that,
Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.
Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.
(1) 3. 5 meter per second for 1/2 hour.
We can,
1 hour = 3600 seconds
Then,
[tex]\frac{1}{2}[/tex] hour = 1800 seconds
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
So,
We can write,
Distance = speed * time
3.5 * 1800 = 6300 meters (Equation-1)
(2) 1. 6 meter per second for 1/2 hour.
We can,
1 hour = 3600 seconds
Then,
[tex]\frac{1}{2}[/tex] hour = 1800 seconds
So,
We can write,
Distance = speed * time
1.6 * 1800 = 2880 meters (Equation-2)
Then,
We can add the equation - 1 and 2,
= 6300 meters + 2880 meters
= 9180 meters
Therefore,
Aiden run and walk in 60 minute, then the distance = 9180 meters
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What is a pixel Mcq?
The fundamental color-programming unit on a computer screen or in a digital image is the pixel, a word that was created from the phrase "picture element." Consider it more as a conceptual than a physical unit. In a digital display, pixels are the smallest unit.
What is pixel made of?The smallest component of a visual display or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.
For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects image quality; more pixels per inch produce better images.
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Find the value of x.
Answer:
x=15
Step-by-step explanation:
[tex]\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15[/tex]
Answer:
x = 15.
Step-by-step explanation:
By the External angle of a triangle theorem:-
The external angle = the sum of the 2 opposite internal angles.
So:
10x - 23 = 7x - 26 + 5x - 27
10x - 7x - 5x = -27 - 26 + 23
-2x = -30
x = 15.
(4x - 8) - (3x + 10)
[tex](4x - 8) - (3x + 10)[/tex]
Distribute negative sign:
[tex]4x-8+-1(3x)+(-1)(10)[/tex]
[tex]4x-8-3x-10[/tex]
Combine Like Terms:
[tex](4x-3x)+(-8-10)[/tex]
[tex]=\fbox{x - 18}[/tex]
Answer:
[tex]x - 18[/tex]
[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]
Adam earn 13.72 each hour that he works.He works 9 hours each week.How much does Adam earn each week.
Answer:
He makes $123.48 a week
Please Help!
Reduce The following -
4:8
3:9
10:2
3:18
Answer:
4:8=1:2
3:9=1:3
10:2=5
3:18 is the same thing as 3:18
The table gives the annual global plastic production over time, in years, since 1960.
Fit an exponential model to this data.
The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____
correlation between the model and the data, this prediction (4) _____.
Answer options:
1-
increased by 4.9 metric tons
decreased by 4.9 metric tons
increased by 4.9%
decreased by 4.9%
2-
40
60
70
3-
moderate
strong
weak
4-
is unreliable
can be accepted with confidence
The exponential model indicates that plastic production has increased by 4.9% per year.
Fit an exponential model to this data
The exponential model indicates that plastic production has increased by 4.9% per year.The model predicts that plastic production 15 years after 1960 was closest to 70 million metric tons.Because the correlation coefficient indicates strong correlation between the model and the data,this prediction can be accepted with confidence.The exponential model is a powerful tool for predicting future trends in plastic production, and it indicates that plastic production has been increasing at an annual rate of 4.9%.This is an important insight, as it can help us to anticipate the future of the industry.With this information, we can estimate that plastic production 15 years after 1960 was likely to be around 70 million metric tons.The strength of this prediction is supported by the correlation coefficient, which suggests a strong correlation between the model and the data.This suggests that the model is a good predictor of future plastic production, and that the prediction of 70 million metric tons is reliable.To learn more about the annual global plastic production over time refer to:
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find the values of x and y
Answer:
[tex]x=35^o\\y=85^o[/tex]
Step-by-step explanation:
[tex](2x + 25)^o = (3x - 10)^o\\2x + 25 = 3x - 10 \\2x - 3x = -10 - 25\\-x = -35\\x = 35[/tex]
[tex](2x+25)^o+y^o=180^o\\ 2(35) + 25 + y = 180\\70 + 25 + y = 180\\95 + y = 180\\y = 180 - 95\\y = 85[/tex]
What is the basis for the principle of substitution?
The basis for the principle of substitution is the fact that algebraic equations and expressions remain unchanged when the same quantity is substituted into them. This principle allows us to solve equations and simplify expressions by substituting one expression for another.
The principle of substitutionThe principle of substitution is a powerful tool used in algebra and calculus to solve equations and simplify expressions. This principle works by allowing us to substitute one expression for another, and the resulting equation or expression remains unchanged.
For example, when solving equations, we can substitute one value for the unknown variable to obtain a simpler equation which can then be solved. Similarly, when simplifying an expression, we can substitute one expression for another to reduce the complexity of the expression.
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In DABC AB=17cm, AD=15cm, BC=13cm and BD is perpendicular to AC. Calculate the length of BD
The length of BD is approximately 22.67cm.
What is the Pythagorean theorem?
The Pythagorean theorem is a fundamental result in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). It is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that it is knowledge that was already known to the ancient Babylonians and Indians.
The theorem can be written mathematically as:
c^2 = a^2 + b^2
This is a classic problem in trigonometry known as the Pythagorean theorem in a right triangle. Since BD is perpendicular to AC, we can use the Pythagorean theorem to find the length of BD, which states that in a right triangle, the square of the length of the hypotenuse (BD in this case) is equal to the sum of the squares of the other two sides (AB and AD).
So, BD^2 = AB^2 + AD^2
We are given that AB = 17cm and AD = 15cm, so we can substitute those values into the equation and solve for BD:
BD^2 = (17cm)^2 + (15cm)^2 = 289 + 225 = 514
To find the length of BD, we take the square root of both sides:
BD = √514cm
BD ≈ 22.67cm
Hence, the length of BD is approximately 22.67cm.
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7. Find FH
F
37-
H 13
G
FH = _
Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.
Describe the triangle.Given its three sides and three vertices, a triangles is a polygon. A fundamental geometric shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric shapes. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.
Here,
The given number indicates that FG is 8 & GH is 14.
FG + GH = FH thanks to the segment addition postulate.
In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.
This results in FH = 8 + 14 => FH = 22.
Therefore, is 22 miles away.
Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.
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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"
If a triangle ha a 22° angle and a 46° angle, what can be etablihed about the third angle meaure and the type of triangle?
The third angle measure is 112°, and the triangle is an obtuse triangle.
A triangle has 3 angles, and the sum of all angles inside a triangle is 180°.
So, 22 + 46 + x = 180
x = 112°
Since the triangle contains an angle measure greater than 90° (the 46° angle), it is an obtuse triangle.
An obtuse triangle is a triangle with one angle measure greater than 90°. In this triangle, the angle measure of 46° is the obtuse angle, and the other two (22° and 112°) are acute angles. Obtuse triangles are often used in construction and engineering applications because of their stability. The third angle measure is 112°, and the triangle is an obtuse triangle.
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A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches.
The best estimate for the perimeter of the triangle will be 23.7 inches.
In Δ ABC ∠B =90° , ∠C = 30° , ∠A = 60° and hypotenuse AC = 10 inches
It has been described in the attachment.
Now, we shall calculate side AB and BC by using Trigonometric Ratios.
Sin 30° = AB / AC
or, AB = 10 × Sin 30° = 10 × 0.5 = 5 inches
And, Cos 30° = CB / AC
or,CB = 10 × Cos 30° = 10 × 0.866 = 8.66 inches
Now, we calculate the perimeter of the given triangle
The perimeter of the triangle is = AB + BC + CA
= (5.0 + 8.66 + 10.0 ) inches
= 23.66 inches ≈ 23.7 inches
Hence, the best estimate for the perimeter of the triangle will be 23.7 inches.
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The complete question is:
A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.
Use transformations to solve the inequality. Write down all the steps
Answer:
u ≤ 15
Step-by-step explanation:
=> u/3 ≤ 5
Multiplying both sides by 3
=> 3×u/3 ≤ 5 ×3
=> u ≤ 15
Pentagon SHAPE is located on the coordinate plane, where point H is located at coordinates (a, b).
The pentagon is reflected across the y-axis and then translated 2 units to the down to create pentagon S'H'A'P'E'
Create an expression for the y-coordinate of H
So, on solving the question we can say all sum of angles of a pentagon are 540 ; x = 340
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
coordinates (a,b)
all sum of angles of a pentagon are 540
90 + 30 + 120 +x = 540
x = 340
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The original price of a goldfish is $6.75. There is 5% sales tax on all purchases. What is the selling price of the goldfish including sales tax?
Answer:
$7.09
Step-by-step explanation:
5% times 6.75 and add that is 7.09 dollars including tax
Please explain how to work out angle BAC
The angle measure BAC is the sum of angles BAD and CAD.
What are Angles?Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.
Given a triangle ABC.
A line is drawn inside the triangle from vertex A to the opposite side BC.
Given that AD = BD = CD.
That is the line AD bisects the line BC.
So here we have two smaller triangles ABD and ACD.
Two corresponding sides of both the triangles are equal.
Then the third side is also equal.
AB = AC
And we get angle A is bisected.
By the angle bisector theorem,
Measure of angle BAC = Measure of angle BAD + Measure of angle CAD
Hence, Measure of angle BAC = Measure of angle BAD + Measure of angle CAD
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PLS HELP i rlly need to get this done
Answer:
1. yes
2. no
3. no
4. yes
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
The answer is 0
Step-by-step explanation:
The rules of signs:
+ * - = -
- * - = +
- * + = -
+ * + = +
So, using the rules of signs, your question is basically asking, what is 5-5, for which the answer is 0.
Evaluate each expression if a=2.5 and b=-8
-|b=2a|
3|b+6|-|a|
Answer: First=Undefined (if you had a typo, please respond and I will edit)
Second=3.5
Step-by-step explanation:
-|b=2a|
-|-8=2(2.5)|
-8=5
Undefined
3|b+6|-|a|
3|-8+6|-|2.5|
3|-2|-2.5
3*2-2.5
6-2.5
3.5
What is the length of ? Two perpendicular lines R S and P Q within a circle intersect at the point P. The lengths of the line segments are labeled as follows. R T equals x, T S equals x, P T equals 4, and T Q equals 16. Figure not drawn to scale A. 8 B. 10 C. 16 D. 20
Answer:
16
Step-by-step explanation:
option c 16 is the answer
What is the slope when y 10?
After solving, the slope when y = -10 is 0.
In the given question, we have to find the slope when y = -10.
The formula known as the slope relates to the method for calculating a line's steepness and inclination. The x and y coordinates of the locations along the line can be used to determine the slope of the lines. It is the ratio of the change in the y-axis to the change in the x-axis, to put it another way.
By utilizing the line equation, the slope of any line may be expressed as
y = mx + b, where m = slope.
When we compare the given equation y = -10 by the standard equation, we get m = 0.
So the slope when y = -10 is 0.
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The graph shows a linear function. Which equation is best represented by this graph?
Answer:
C
Step-by-step explanation:
The graph passes through [tex](-2,-5)[/tex] but not [tex](2,5)[/tex].
Eliminate B and D.The line is steep, and has a slope of more than 1.
Eliminate A.I need help, answer quick and pls explain
The LCM of the numbers 1 - x² and (x - 1)³ is (1 - x²)(x - 1)
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The least common multiple (LCM) of a set of numbers is the smallest number that can be divisible by the set of numbers
Given the numbers:
1 - x² and (x - 1)³
(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)
(x - 1)³ = (x - 1)(x - 1)(x - 1)
The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)
The LCM is (1 - x²)(x - 1)
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Pls help me with this
The percent of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
f(x) = 500 (0.67)ˣ
Part A :
x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500
x = 1 ⇒ f(x) = 500 (0.67)¹ = 335
x = 2 ⇒ f(x) = 500 (0.67)² = 224.45
x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815
Part B :
Here 0.67 is the decay rate.
That is the rate of decay of the bug is 0.67.
67% of the bugs are decaying with each day.
Part C :
Percent of bugs remaining each day = 100% - 67% = 33%
Part D:
f(x) < 40
500 (0.67)ˣ < 40
(0.67)ˣ < 40 / 500
(0.67)ˣ < 0.08
Taking logarithms on both sides,
㏒ (0.67)ˣ < ㏒ 0.08
x ㏒ (0.67) < ㏒ 0.08
x (-0.1739) < (-1.0969)
Dividing doth sides by (-0.1739), the sign of inequality changes because of dividing by a negative number.
x > 6.3
Hence the percentage of the bugs eaten and remained are calculated.
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i need help with this please hurry!!!
So on solving the provided question, we can say that fraction we have are [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex] = 14/6
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here the fraction we have are
[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]
12/3 + 12/4 + 15/2
14/6
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Linear equation with colors lines black orange green and blue
The graph of Linear equation with colors lines black, orange, green and blue is shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that;
Linear equation with colors lines black orange green and blue.
Now, We know that;
The graph of linear equation is always a straight line.
Hence, The graph of Linear equation with colors lines black orange green and blue is shown in figure with straight line.
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d) Consider your answer in part (e). What is the probability that P-P is greater
than the value found in part (a)? Show your work.
The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.
What is probability?Simply put, probability measures how likely something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is mainly the study of events subject to probability.
In Population D:
Population Proportion :Turtles have shell length greater than 2 feet = 0.3
Random Sample = 40
Turtles have shell length greater than 2 feet in random sample = 15
In Population E:
Population Proportion :Turtles have shell length greater than 2 feet = 0.2
Random Sample = 60
Turtles have shell length greater than 2 feet in random sample = 11
Let [tex]\hat{p}_D[/tex] represents sample proportion for D
Let [tex]\hat{p}_E[/tex] represents sample proportion for E
[tex]$ \text{SampleProportion} =\frac{\text { Count of Success }}{\text { Size of the population }}$[/tex]
[tex]$$\begin{aligned}\hat{p}_D & =\frac{\text { Turtles have a shell length greater than } 2 \text { feet in random sample }}{\text { Random Sample }} \\& =\frac{15}{40} \\& =0.375\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\hat{p}_E & =\frac{\text { Turtles have a shell length greater than 2 feet in random sample }}{\text { Random Sample }} \\& =\frac{11}{60} \\& =0.183\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\text { Difference in sample proportion } & =\hat{p}_D-\hat{p}_E \\& =0.375-0.183 \\& =0.1917\end{aligned}$$[/tex]
[tex]$$\begin{aligned}\hat{\boldsymbol{p}} & =\frac{X_1+X_2}{N_1+N_2} \\& =\frac{15+11}{40+60} \\& =0.26\end{aligned}$$[/tex]
[tex]$$\begin{aligned}Z & =\frac{\left(\hat{p}_D-\hat{p}_E\right)-\left(p_D-p_E\right)}{\sqrt{\hat{p}(1-\hat{p}) \times\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} \\& =\frac{(0.375-0.183)-(0.3-0.2)}{\sqrt{0.26 \times 0.74 \times\left(\frac{1}{40}+\frac{1}{40}\right)}} \\& =\frac{0.0917}{\sqrt{0.1924 \times 0.04166}} \\& =0.0087\end{aligned}$$$$[/tex]
[tex]\begin{aligned}P\left(\hat{p}_D-\hat{p}_E\right. & > 0.1917) \\& =P(Z > 0.0087) \\& =1-P(Z \leq 0.0087) \\& =0.4681\end{aligned}$$[/tex]
Therefore, The probability that [tex]\hat{p}_D-\hat{p}_E[/tex] is greater than 0.1917 is 0.4681.
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