To prove that point d is equidistant from the jungle gym and monkey bars, we need to show that the distances from d to both points are equal.
Let's call the distance from d to the jungle gym "x" and the distance from d to the monkey bars "y". We need to show that x = y.
Since angle acd is a right angle, we can use the Pythagorean theorem to relate the distances:
ad^2 + cd^2 = ac^2
We know that ad = bd (since the jungle gym and monkey bars are the same distance from d), so we can write:
bd^2 + cd^2 = ac^2
We also know that c lies on ab, so we can write:
ac = ab - bc
Substituting this into our equation, we get:
bd^2 + cd^2 = ab^2 - 2abbc + bc^2
Since d is on cd, we can write cd = y, and since c is on ab, we can write ab = x + y. Substituting these into our equation, we get:
bd^2 + y^2 = (x + y)^2 - 2xy + x^2
Simplifying, we get:
bd^2 - x^2 = 2xy - y^2
Now, if we can show that bd = x, then we will have proven that y = x and therefore that point d is equidistant from the jungle gym and monkey bars.
To do this, we can use the fact that triangle adb is isosceles (since ad = bd). This means that angle adb is equal to angle bad. We also know that angle acd is a right angle. Therefore, angle adb + angle acd = 90 degrees.
Since angle adb = angle bad, we can write:
2 angle adb + angle acd = 180 degrees
Substituting in the values of our angles, we get:
2 angle adb + 90 degrees = 180 degrees
Solving for angle adb, we get:
angle adb = 45 degrees
Now, we can use the fact that triangle adb is isosceles to write:
angle bad = (180 - 45)/2 = 67.5 degrees
Finally, we can use the law of sines to relate bd and x:
bd/sin(67.5) = x/sin(45)
Simplifying, we get:
bd = x
Therefore, we have shown that point d is equidistant from the jungle gym and monkey bars.
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which expression is equivalent to 2^3/2^7
Answer:
Below
Step-by-step explanation:
2^3 / 2^7 = 2^(3-7) = 2^(-4) = 1/ (2^4) = 1/16 = .0625
~~~~pick your poison
The required expression [tex]2^3/2^7[/tex], after simplification is equivalent to 1/16.
To simplify the expression [tex]2^3/2^7[/tex], we can apply the rule of exponentiation that states when dividing two numbers with the same base, we subtract the exponents.
In this case, the base is 2.
Using the rule, we subtract the exponent of the denominator from the exponent of the numerator:
[tex]2^3/2^7 = 2^{7} = 2^{-4}[/tex]
The expression [tex]2^{-4}[/tex] can be further simplified by using the rule that states any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent:
[tex]2^{-4} = 1/2^4[/tex]
= 1/16
Therefore, the expression [tex]2^3/2^7[/tex] is equivalent to 1/16.
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2-step Word problemas please help my
Answer:
1: 9 polar bears and 38 penguins
2: 47 snowglobes
3: 130 snowballs
4: 97 penguins
Step-by-step explanation:
i did the math
3. What is the volume of this complex figure?
3 m
4 m
6m
4 m
7m
Answer:
27,64,216,64,243
Step-by-step explanation:
Any number raise to power 3
What are the coordinates of R′ for the dilation D(0. 5, P)(PQRS)?
Answer:
the coordinate of the R' after the dilation is (-1,-0.5)
Step-by-step explanation:
A quantity with an initial value of 3600 decays continuously at a rate of 80% per year.
What is the value of the quantity after 0.2 decades, to the nearest hundredth?
Answer:
Step-by-step explanation:
The decay rate of 80% per year means that after each year, the value of the quantity decreases by 80/100 * 3600 = 2880.
To find the value of the quantity after 0.2 decades, we need to multiply the number of years by 10, since a decade is equal to 10 years. In this case, 0.2 decades is equal to 0.2 * 10 = 2 years.
The value of the quantity after 2 years can be found using the formula:
3600 * (1 - 0.8)^2
Plugging in the values, we get:
3600 * (1 - 0.8)^2 = 3600 * (0.2)^2 = 3600 * 0.04 = 144
So, the value of the quantity after 0.2 decades, to the nearest hundredth, is 144.
Answer: 726.83
Step-by-step explanation:
Find the x- and y-components of the vector d⃗ = (3. 0 km , 30 ∘ left of +y-axis). Express your answer using two significant figures. Enter the x and y components of the vector separated by a comma
For the information provided the x- and y-components of the vector are 1.5 km and 2.6 km, respectively.
To find the x- and y-components of the vector, we can use trigonometry.
The x-component of vector is given by:
d_x = d × cos(θ)
where d is the magnitude of the vector and θ is the angle between the vector and the x-axis.
In this case, d = 3.0 km and θ = 60 degrees (since the vector is 30 degrees to the left of the y-axis).
So, d_x = 3.0 km × cos(60°) = 1.5 km.
The y-component of vector is given by:
d_y = d × sin(θ)
In this case, d_y = 3.0 km × sin(60°) = 2.6 km.
Expressing the answer using two significant figures gives:
d_x = 1.5 km, d_y = 2.6 km.
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Describe the long run behavior of f(p)=(p+1)^3(p+4)^3(p-1)
Answer:
Step-by-step explanation:
The long-run behavior of a function can be determined by examining its asymptotes and the behavior of the function near these asymptotes.
For the function f(p)=(p+1)^3(p+4)^3(p-1), there are three points to consider as possible asymptotes: p = -1, p = -4, and p = 1.
At p = -1, the factor (p-1) is equal to zero, so the function has a vertical asymptote there. This means that as p approaches -1 from either side, the function will approach infinity.
At p = -4, the factor (p+4)^3 is equal to zero, so the function also has a vertical asymptote there. Similarly, as p approaches -4 from either side, the function will approach infinity.
At p = 1, the factor (p+1)^3 is equal to zero, so the function has another vertical asymptote there. In this case, as p approaches 1 from either side, the function will approach negative infinity.
So, the long-run behavior of the function can be described as follows:
The function approaches infinity as p approaches -1 or -4 from either side.
The function approaches negative infinity as p approaches 1 from either side.
Therefore, the long-run behavior of f(p)=(p+1)^3(p+4)^3(p-1) is characterized by three vertical asymptotes at p = -1, p = -4, and p = 1.
Answer:
[tex]\text{As } p \to -\infty, f(p) \to -\infty\\\\\text{As } p \to \infty, f(p) \to \infty[/tex]
====================================================
Explanation:
Each factor is a cubic of degree 3.
The degree of the entire polynomial is 3+3+3 = 9.
Since the degree is odd and the leading coefficient is positive, this means the graph falls to the left and rises to the right.
"falls to the left" means [tex]\text{As } p \to -\infty, f(p) \to -\infty[/tex]
"rises to the right" means [tex]\text{As } p \to \infty, f(p) \to \infty[/tex]
This is verified using a graphing tool like Desmos as shown in the screenshot below. I'm using x in place of p.
Two numbers are in the ratio of 2:3. If 15 is added to both the numbers, then the ratio betwee two numbers becomes 11: 14. Find the greater number.
Answer:
Below
Step-by-step explanation:
(2x+15) / ( 3x+15) = 11/14 cross multiply to get
28x + 210 = 33x + 165
45 = 5x
x = 9 so the larger number is 3 X 9 = 27
(smaller number is 2 x 9 = 18)
Hugo is serving fruit sorbet at his party.He has 1 gallon of fruit sorbet to serve to 32 friends .If each person receives the same amount,how many cups of fruit sorbet will each person get?
Answer:
4 cups of fruit sorbet.
Step-by-step explanation:
There are 128 cups in 1 gallon. So, 1 gallon of fruit sorbet is equal to 128 cups.
Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.
The solution is, each person get 4 cups of fruit sorbet.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
Hugo is serving fruit sorbet at his party.
He has 1 gallon of fruit sorbet to serve to 32 friends .
now. we get,
There are 128 cups in 1 gallon.
So, 1 gallon of fruit sorbet is equal to 128 cups.
so, we have,
Therefore, each person will receive 128 cups / 32 people = 4 cups of fruit sorbet.
If each person receives the same amount,
then, each person will receive 4 cups of fruit sorbet.
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If the number x² y is a negative integer, then -y is a positive number
Answer: Yes, this statement is true. If the number x² y is a negative integer, it means that x² is a positive integer and y is a negative integer. Therefore, -y would be a positive number.
Step-by-step explanation:
What are the scaled dimensions of a kitchen with dimensions 6.3m by 4.8, if the kitchen plan is drawn to a scale of 1:500?
The scaled dimensions of a kitchen with dimensions 6.3m by 4.8m, if the kitchen plan is drawn to a scale of 1:500, are given as follows:
1.26 cm and 0.96 cm.
How to obtain the scaled dimensions?The scaled dimensions are obtained applying the proportions in the context of the problem.
The scale is of 1:500, meaning that each dimension is divided by 500, as follows:
6.3 m: 6.3/500 = 0.0126 m = 1.26 cm.4.8 m: 4.8/500 = 0.0096 m = 0.96 cm.More can be learned about proportions at https://brainly.com/question/24372153
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Quick help with this problem, help!
Answer:
5/4
Step-by-step explanation:
You want the product abc when 5x^-2y^(3/2)/√(25xy^4) is written as ax^by^c.
Rules of exponentsThe applicable rules of exponents are ...
[tex]a^ba^c=a^{b+c}\\\\\dfrac{1}{\sqrt{a}}=a^{-\frac{1}{2}}\\\\(a^b)^c=a^{bc}[/tex]
ApplicationUsing these rules, the expression can be simplified to ...
[tex]\dfrac{5x^{-2}y^{\frac{3}{2}}}{\sqrt{25xy^4}}=(5x^{-2}y^{\frac{3}{2}})(5^2xy^4)^{-\frac{1}{2}}=(5x^{-2}y^{\frac{3}{2}})(5^{2(-\frac{1}{2})}x^{-\frac{1}{2}}y^{4(-\frac{1}{2})})\\\\=5^{1-1}x^{-2-\frac{1}{2}}y^{\frac{3}{2}-2}\\\\=1\cdot x^{-\frac{5}{2}}y^{-\frac{1}{2}}[/tex]
From this last expression, we determine ...
a = 1b = -5/2c = -1/2ProductThe product of the values of interest is ...
abc = (1)(-5/2)(-1/2)
abc = 5/4
Kayla and Kevin have the same-size notebooks.
Kayla covered 5/6 of hers with stickers. Kevin covered 5/8 of his with stickers. Who covered more
8
of the notebook? Explain your answer.
if the second number is lower than that's the answer. so in this case kayla
2-81
When graphing the function f(x)= x2-11x+18
window for determining the domain and range of the function?
O Xmin: -10, Xmax: 10
Ymin: –10, Ymax: 10
O Xmin: -5, Xmax: 5
Ymin: –5, Ymax: 5
Xmin: 0, Xmax: 10
Ymin: 0, Ymax: 10
O Xmin: -10, Xmax: 0
Ymin –10 Ymax: 0
on your graphing calculator, what is the most appropriate viewing
The most appropriate viewing range for the quadratic function is given as follows:
Xmin 0, Xmax 10.YMin - 15, Ymax, 15.How to obtain the viewing range?The quadratic function for this problem is defined as follows:
f(x) = x² - 11x + 18.
The function can be factored as follows:
f(x) = (x - 2)(x - 9).
Hence the roots are:
x - 2 = 0 -> x = 2.x - 9 = 0 -> x = 9.Meaning that the viewing range should include x = 2 and x = 9.
The coefficients of the function are:
a = 1, b = -11, c = 18.
Hence the x-coordinate of the vertex is of:
x = -b/2a
x = 11/2
x = 5.5.
Hence the minimum value of the function is the y-coordinate of the vertex, given as follows:
y = 5.5² - 11(5.5) + 18
y = -12.25.
Meaning that Ymin should be less than -12.25.
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Which equation is quadratic in form?
3x5 + 8x3 + 6 = 0
6x4 + 7x2 – 3 = 0
5x6 + x4 + 12 = 0
x9 + x3 – 10 = 0
The equation which is in the quadratic form is 6x⁴ + 7x² - 3 = 0. So Option B is correct.
What is a quadratic equation ?An equation is quadratic in form if it can be written in the form of ax + bx + c = 0, where a, b, and c are constants and x is the variable.
Among the given equations, we can see that the first, third, and fourth equations are not quadratic in form, since they contain x raised to powers other than 2.
The second equation, 6x⁴ + 7x² - 3 = 0, can be written in quadratic form by making a substitution.
If we let y = x², then we can write the equation as 6y² + 7y - 3 = 0,
which is a quadratic equation in y. Substituting back x² for y,
we get:
6x⁴ + 7x² - 3 = 0
So the second equation is quadratic in form.
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Answer:
Step-by-step explanation:
answer b, trust
Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?a. A rise in the unemployment rate accompanies a fall in real GDP.b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.c. Negative real GDP growth is associated with a fall in the unemployment rate.
a. A rise in the unemployment rate accompanies a fall in real GDP. - Consistent
b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed. - Not consistent
c. Negative real GDP growth is associated with a fall in the unemployment rate. - Not consistent
This is consistent with the observed relationship between real GDP growth and changes in the unemployment rate. An increase in real GDP is associated with a decrease in the unemployment rate, and vice versa.
This is because when GDP increases, businesses are able to hire more workers, leading to a decrease in the unemployment rate. Conversely, when GDP decreases, businesses may have to lay off employees or reduce their hours, leading to an increase in the unemployment rate.
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The complete question is:
Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?
a. A rise in the unemployment rate accompanies a fall in real GDP.
b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.
c. Negative real GDP growth is associated with a fall in the unemployment rate.
what is the equation of a line that is parallel to the line that is given by the equation x=-4?
The equation of the line which is parallel to the line x = -4 will be x = -3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is x = -4. The y-intercept is zero for the line.
The equation of the line parallel to the equation will be,
x = -3
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What is the x-coordinate of the image when M(4, −1) is reflected in y=3.
The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.
What is another way to say reflecting?When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.
What other word for reflecting is there?Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.
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WILL GIVE BRAINLIEST WHO EVER ANSWERS CORRECTLY, PLS HELP.
Answer:
Below
Step-by-step explanation:
From the image below you can see that
90 F + 60 L = 160 miles
and given F + L = 2 hours re arrange to F = 2 - L
and substitute this "F" into the first equation
90 (2-L ) + 60 L = 160 Solve for L
180 - 90 L + 60 L = 160
180 - 30 L = 160
- 30 L = -20
L = 2/3 hr then F = 1 1/3 hr ( because they add to '2' )
Help pls Thank you mwa
Step-by-step explanation:
Same as the triangles. Find the area of the large rectangle and the small rectangle, then subtract.
A = L x W
For the large rectangle
A = 30 x 25 = 750
For the small rectangle
A = 26 x 21 = 546
Now to subtract these two
750 - 546 = 240
Solve the system using the substitution method. For the system that does not have one unique solution, also state the number of solutions and
whether the system is inconsistent or the equations are dependent. Express numbers as integers or simplified fractions.
y=2x+7
4x+3y=-19
Answer:
(-4, -1)
Step-by-step explanation:
The system has one solution
Box plot pls help outliers
The boxplot without the outliers is (c)
What are outliersOutliers are data points that are significantly different from the other data points in a dataset.
An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
How to determine the boxplotUsing the definition in (a) as a guide, we have the boxplot to be (c)
This is so because it has a minimum of 15 and a maximum of 95 (just as the original boxplot)
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Find the measure of the missing angles.
Answer:
F = 29
E= 151
D = 90
Step-by-step explanation:
For F:
The angle F is on a 180 degree angle with a degree next to it that is 151. To get the value F subtract 180-151 and you get 29.
For E: If F is 29 then the angle opposite of F is also 29. So again to find the measure of angle E, subtract 180 minus 29 and you get 151.
For D: D is also lying on a 180 degree angle. The angle next to it is 90. To get 180 add 90. 90 is the measure of angle d.
Answer:
d = 90°,e = 151°,f = 29°.-----------------------------------
Angle d is linear pair with a right angle, therefore:
d = 180° - 90°d = 90°Angle e is vertically opposite with 151° and therefore they are congruent:
e = 151°Angle f is adjacent with 151° and forming a linear pair, therefore:
f = 180° - 151°f = 29°what is the slope of this line?
Answer: -1/2
Step-by-step explanation: Down 1 over 2
Find the surface area of the prism.
S.A.
?
cm²
5cm
4cm
7cm
Please hurryyyy
The Total Surface Area for given prism will be 166 [tex]cm^2[/tex].
How to calculate the total surface area of Rectangular Prism?The entire surface area of a rectangular prism may be computed by adding the areas of its six sides. A rectangular prism's surface area may be determined using the following formula:
[tex]Surface Area = 2(l*w) + 2(l*h) + 2(w*h)[/tex]
where:
l = length of the rectangular prism
w = width of the rectangular prism
h = height of the rectangular prism
Using this formula for given problem,
Given,
l=5cm
w=4cm
h=7cm
[tex]\text{Total Surface area}=2.(5.7)+2.(4.5)+2.(4.7)\\\\=70+40+56\\\\=166\;cm^2[/tex]
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The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
What is Variability of data?Data variation can be caused by a variety of sources. Variability is also known as data spread. The standard deviation is a measure of variability since it measures the spread of data.
The range is the best measure of variability for the data shown, and its value is 45.
The range is defined as the difference between the largest and smallest values in a set of data.
In this case, the largest score is 88 and the smallest score is 20, so the range is 88 - 20 = 68.
The IQR (interquartile range) is another measure of variability, but it is not the best measure for this data set because the data set has only a few values and does not form a normal distribution. The IQR is a more appropriate measure for larger data sets that form a normal distribution.
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Geometry due soon please help!!!!!
Which of the following is not an example of a quadratic equation in real life?
A.The curve of hanging electrical wires
B.The path of a boat
C.The yellow arches of a big M
D.The path of a tennis ball
E.The path of a human cannonball
The yellow arches of a big M is not an example of a quadratic equation in real life.
What is quadratic equation ?
Quadratic equation can be defined as equation in which it is in the form of ax^2+bx+c = 0
where c is constant.
A quadratic equation is an equation in which the highest power of the variable is 2. In real life, many phenomena can be modeled by quadratic equations, such as the curve of hanging electrical wires, the path of a boat, the path of a tennis ball, and the path of a human cannonball.
However, the yellow arches of a big M is not a mathematical equation or a physical phenomenon that can be described by a quadratic equation. The arches are simply a design element of the McDonald's logo.
Therefore, The yellow arches of a big M is not an example of a quadratic equation in real life.
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Find the value of C so that the graph of
x² + y²
12x + 14y - C = 0
passes through the point (10, 1).
Answer:
C = 235
Step-by-step explanation:
given the graph passes through (10, 1 ) then the coordinates of the point make the equation true.
substitute x = 10, y = 1 into the equation and solve for C
10² + 1² + 12(10) + 14(1) - C = 0
100 + 1 + 120 + 14 - C = 0
235 - C = 0 ( subtract 235 from both sides )
- C = - 235 ( multiply both sides by - 1 )
C = 235
Evaluate the following expressions. a) 10^15/10^12.
b) 10^1/10^0
c) 10^5+10^-3
d) 10^5-10^3
(^ means to the power of)
On solving the provided question we can say that the expressions are
a) 1000
b 10
c) 100000.001
d) 99000
What is expression?In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operatοr Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.)
Expressiοns and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expressiοn. For instance, the expressiοn 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.
The expressiοns are
a)10¹⁵/10¹² = 10³ = 1000
b)10¹/10⁰ = 10/1 = 10
c)10⁵ + 10⁻³ = [tex]\dfrac{10^8 +1}{100}[/tex]= 100000.001
d)10⁵ - 10³ = 100000 - 1000 = 99000
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