Jane's school is due west of her house and due south of her friend Norma's house. The distance between the school and Norma's house is 8 kilometers and the straight-line distance between Jane's house and Norma's house is 9 kilometers. How far is Jane's house from school? If necessary, round to the nearest tenth.
Answers
Answer
Distance = 4.1 km
Explanation
Let the distance between Jane's house from school be x
The distance can be calculated using pythagora's theorem
[tex]\begin{gathered} \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = 9km, opposite = 8km and adjacent = x km} \\ 9^2=8^2+x^2 \\ \text{Isolate x}^2 \\ 81=64+x^2 \\ \text{Collect the like terms} \\ 81-64=x^2 \\ 17=x^2 \\ \text{Take the square roots of both sides} \\ \text{x = }\sqrt[]{17} \\ \text{x = 4.1 km} \end{gathered}[/tex]Therefore, the distance between Jane's house from school is 4.1 km
Related Questions
the location of the red star is (3, 4).if it was reflected across the y-axis what would the new coordinates be? thanks in advance :D
Answers
The rule for reflection along y-axis is:
[tex](x,y)\rightarrow(-x,y)[/tex]So the point (3,4) when reflected along y-axis becomes (-3,4).
So (-3,4) is the answer.
Identify the mean, median, and mode for the dot plot below.Dotplot of Random Values⠀0 1 2 3 4 5 6 7 8 9Random ValuesMean =Median =Mode =andType the lower number then the higher number
Answers
ANSWER :
mean = 4.84
median = 4.5
mode = 7 and 9
EXPLANATION :
From the problem, we have a dot plot. The dots represent the frequency of each item.
0 has a frequency of 3
1 has a frequency of 3
2 has a frequency of 7
3 has a frequency of 6
4 has a frequency of 6
5 has a frequency of 3
6 has a frequency of 4
7 has a frequency of 8
8 has a frequency of 2
and 9 has a frequency of 8
The total items or data is the sum of frequencies.
That will be :
[tex]3+3+7+6+6+3+4+8+2+8=50[/tex]Recall that the mean is the average of the data.
To get this, get the sum of the products between the data and their frequencies divided by the total data.
That will be :
[tex]\frac{0(3)+1(3)+2(7)+3(6)+4(6)+5(3)+6(4)+7(8)+8(2)+9(8)}{50}=4.84[/tex]The mean is 4.84
Median is the middle term when the data is arranged from least to greatest.
Since there are 50 items, the middle term is between 25th and 26th term.
Let's rewrite the data from lowest to greatest.
0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, "4", "5", 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9
The 25th term is 4 and the 26th term is 5.
Since the median is between these two terms, we need to get the average, that will be :
[tex]\frac{4+5}{2}=4.5[/tex]So the median is 4.5
Mode is the data with the most or highest frequency.
In this case, 7 and 9 have both 8 frequencies.
So the modes are 7 and 9
HELP HELP HELP PLEASE!!!!!
Answers
9x=72
x=8
answer : 8
1: Find the number of terms, n, of the arithmetic series given
Answers
Given,
The first term of the series is 21.
The last term of the series is 39.
The sum of the series is 210.
Required
The number of terms in the series.
The sum of the series is calculated as,
[tex]S=\frac{n}{2}(a+a_n)[/tex]Substituting the values then,
[tex]\begin{gathered} 210=\frac{n}{2}(21+39) \\ 420=n(60) \\ n=7 \end{gathered}[/tex]Hence, the number of terms in the series is 7.
The measurements of a rectangular room, in a scale drawing, are 2 1/2 inches by 3 1/2 inches. The scale is 1/2 inch = 3 feet. If carpet costs $1.75 per square foot, how much will it cost to put carpet in this room?
Answers
$551.25
Explanation
Step 1
convert the mixed numbers in fractions
[tex]\begin{gathered} 2\frac{1}{2}=\frac{(2\cdot2)+1}{2}=\frac{5}{2}=2.5 \\ 2\frac{1}{2}=2.5 \\ 3\frac{1}{2}=\frac{(3\cdot2)+1}{2}=\frac{7}{2}=3.5 \\ \frac{1}{2}=0.5 \\ \\ \end{gathered}[/tex]Step 2
find the factor of scale
remind 1 feet =12 inches
[tex]\begin{gathered} 0.5\text{ inches in plane}\rightarrow3\text{ feet} \\ 0.5\text{ inches inplane}\rightarrow(3\cdot12) \\ 0.5\text{ inch plane}\rightarrow36\text{ inch in the reality} \\ \text{the ratio is} \\ 0.5\colon36 \\ 1\colon72 \end{gathered}[/tex]it means, if you measure a inch in the drawing it corresponds to 72 inches in the real the room
Step 3
find the real measures
[tex]\begin{gathered} \frac{2.5}{x}=\frac{1}{72} \\ 2.5\cdot72=x\cdot1 \\ x=180\text{ inches} \\ \text{divide by 12 to obtain feet} \\ 180\text{ inches}\rightarrow180\text{ inches}\frac{1}{12\text{ inches}}\rightarrow15\text{ feet} \\ so,\text{ a measure is 15 feet} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \frac{3.5}{y}=\frac{1}{72} \\ 3.5\cdot72=y\cdot1 \\ y=252\text{ inches} \\ \text{divide by 12 to obtain feet} \\ 252\text{ inches}\rightarrow252\text{ in}\frac{1\text{ feet}}{12\text{ inch}}\rightarrow21\text{ feet} \end{gathered}[/tex]Step 5
find the area of the room
[tex]\begin{gathered} \text{Area}=\text{ x}\cdot y \\ \text{Area}=\text{ 15 feet }\cdot\text{ 21 feet} \\ \text{Area = 315 ft}^2 \end{gathered}[/tex]Step 6
finally, to obtain the total cost of the carpet, multiply the number of square feet by the cost per square foot of the carpet
[tex]\begin{gathered} \text{total cost= 315 ft}^2\cdot1.75\frac{\text{usd }}{ft^2} \\ \text{total cost=551.25 } \end{gathered}[/tex]a boy is 8 years older than his brother. four years from now the boy will be twice as old as his brother. how old is each boy now
Answers
Answer:
boy would be 12 brother would be 6
Step-by-step explanation:
8+4 = 12
---- brother = 6
2
One on my homework Am I right show me how you did it
Answers
To determine the surface area of the pyramid we will use the following formula (another method: compute the area of each triangle and add it to the base area):
[tex]SA=a^2+2a\sqrt{\frac{a^2}{4}+h^2},[/tex]where a is the side length of the base of the pyramid, and h is its height.
Substituting
[tex]\begin{gathered} a=20m, \\ h=13m \end{gathered}[/tex]in the above formula, we get:
[tex]SA=(20m)^2+2(20m)\sqrt{\frac{(20m)^2}{4}+(13m)^2}.[/tex]Simplifying the above result, we get:
[tex]SA≈1056m^2.[/tex]Answer:
[tex]1056m^2.[/tex]Which graph shows f(x) = 1/2 x + 2 and its inverse?
Answers
We have a line given by the following function:
[tex]f(x)=\frac{1}{2}x+2.[/tex]The inverse function of f(x) is the function g(x), that satisfies:
[tex]g(f(x))=x.[/tex]To find the inverse function, we replace x by y in the equation of f(x), and then we equal to x and solve for y, we get:
[tex]\begin{gathered} x=f(y)=\frac{1}{2}y+2, \\ x-2=\frac{1}{2}y, \\ y=2*(x-2), \\ y=2x-4. \end{gathered}[/tex]So the inverse function is:
[tex]g(x)=2x-4.[/tex]Plotting f(x) and g(x), we get the following graph:
Comparing this graph with the options, we conclude that option A is the correct answer.
AnswerGraph A.
hi would you be able to help me ignore my work
Answers
Solution:
Given the system;
[tex]\begin{gathered} 4x+6y=32.............equation1 \\ \\ 3x-6y=3..............equation2 \end{gathered}[/tex]Add equation1 to equation2, we have;
[tex]\begin{gathered} 4x+3x+6y-6y=32+3 \\ \\ 7x=35 \\ \\ \frac{7x}{7}=\frac{35}{7} \\ \\ x=5 \end{gathered}[/tex]Substitute x = 5 in equation2;
[tex]\begin{gathered} 3x-6y=3 \\ \\ 3(5)-6y=3 \\ \\ 15-6y=3 \\ \\ 6y=15-3 \\ \\ 6y=12 \\ \\ y=2 \end{gathered}[/tex]ANSWER:
[tex]x=5,y=2[/tex]Solve the following exponential equation. Round your answer to three decimal places.10ˣ = 9 x =
Answers
To solve the equation 10ˣ = 9, we find the logarithm of both sides of the equation.
[tex]\begin{gathered} 10^x=9 \\ \text{ taking the log of both sides, we have} \\ \log 10^x=\log 9 \end{gathered}[/tex]Using logarithm rule, we have
[tex]\begin{gathered} x\log 10=\log 9 \\ \log 10=1 \\ \text{ Hence} \\ x=\log 9 \end{gathered}[/tex][tex]x=\log 9=0.954[/tex]/
x = 0.954
how many grams of sugar are there in a 200 ml glass of juice if there is 18.5 grams of sugar in 250ml of juice
Answers
There is 14.8 grams of sugar are there in a 200 ml glass of juice.
How do you define a unitary method?The term unitary corresponds to a specific or unique unit. As a result, the goal of this method is to determine the values in connection to a single unit. The unitary method is a technique that involves determining a value of a single unit and then calculating the value of the neccessary number of units based on that value.For the given question,
There are 18.5 gram of sugar in 250 ml of glass of juice.
This can be written as;
250 ml ------> 18.5 grams of sugar.
For 1 ml of the glass of juice, divide both sides by 250.
1 ml ------> 18.5/250 grams of sugar.
For 200 ml of the glass of juice, multiply both sides by 200.
200 ml ------> 18.5×200/250 grams of sugar.
200 ml ------> 14.8 grams of sugar.
Thus, 14.8 grams of sugar are there in a 200 ml glass of juice.
To know more about the unitary method, here
https://brainly.com/question/28540270
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The related graph of a quadratic equation is ___ shown below. Use the graph to determine the solutions of the equation.
Answers
Hello there. To solve this question, we have to determine the solutions to the quadratic equation shown in the graph.
For this, we simply have to find, by inspection, the points for which it is equal to zero, that is, when it crosses the x-axis:
It is easy to see that is passes through the points x = -3 and x = 2, since the coordinate plane was divided into a lot of squares with side length equal to 1.
Hence we say that the answer to this question is:
[tex]-3,2[/tex]This is the answer and it is contained in the third oval.
Determine if the situation is Linear, Quadratic, or Exponential.A ball is shot from a cannon into the air with an upwardvelocity of 40 ft/sec. The equation that gives the height (h) ofthe ball at any time (t) is: h(t)= - 16t2 + 40ft + 1.5.o Linearo Quadratico Exponential
Answers
Notice that the equation provided for the height in terms of the time has the same form as the following equation :
[tex]ax^2+bx+c[/tex]which is the general form of a quadratic equation.
Answer: Quadratic
I've forgotten how to turn a fraction into a decimal...could you help?
Answers
To convert a fraction into a decimal you have to divide the numerator by the denominator. For example, to convert 39/8, you need to divide 39 by 8, which is equal to 4.875.
Write an equation in slope-intercept form of a line passing through the given point andparallel to the given line.13. (4, 2); x+ y= 1
Answers
The equation of the line in slope-intercept form is,
[tex]y=mx_{}+b[/tex]where,
m = slope
The equation of the line given is,
[tex]x+y=1[/tex]Let us now rearrange the equation in the slope-intercept form in order to obtain the slope.
Therefore,
[tex]\begin{gathered} x+y=1 \\ y=-x+1 \\ \therefore\text{ The slope(m) is -1.} \end{gathered}[/tex]We were told the point is parallel to the equation of the line.
The rule for parallelism is,
[tex]\begin{gathered} m_1=m_2 \\ \therefore-1=-1 \end{gathered}[/tex]The formula to calculate for the equation of a line given one point is,
[tex]y-y_1=m(x-x_1)[/tex]Given
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ m=-1 \end{gathered}[/tex]Substitute and simplify
[tex]\begin{gathered} y-2=-1(x-4) \\ y-2=-1x+4 \\ y=-x+4+2 \\ \therefore y=-x+6 \end{gathered}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]y=-x+6[/tex]graph model for y=11/10x+76
Answers
what is the least common denominator of 3/4 and 5/12
Answers
3/4 5/12
Denominator are 4 and 12
4= 4,8,12
12 = 12
LCM = 12
Over the last three evenings, Kira received a total of 54 phone calls at the call center. The first evening, she received 10 fewer calls than the second evening. The third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answers
Let x, y, and z be the number of calls Kira received during the first, second, and third day, respectively. Therefore, the equations are
[tex]\begin{gathered} x+y+z=54 \\ x=y-10 \\ z=2y \end{gathered}[/tex]Solve the system of equations as shown below
[tex]\begin{gathered} \Rightarrow x+y+z=x+(x+10)+2(x+10)=4x+30 \\ \Rightarrow4x+30=54 \\ \Rightarrow4x=24 \\ \Rightarrow x=6 \end{gathered}[/tex]Use the value of x to find y and z,
[tex]\begin{gathered} x=6 \\ \Rightarrow6=y-10\Rightarrow y=16 \\ and \\ z=2y=2*16=32 \end{gathered}[/tex]Therefore, the answers are:First evening: 6 callsSecond evening: 16 callsThird evening: 32 callsI need to find the slope of 7,1 and 7,-5
Answers
The slope is given by the formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1,y1) and (x2,y2) are the coordinates of two points on the line.
We have (7,1) and (7,-5). Let's replace these values and find m:
[tex]m=\frac{-5-1}{7-7}=\frac{-6}{0}=\text{ undefined}[/tex]The slope is undefined, which means it is a vertical line at x=7.
Find the equation of the axis of symmetry of the following parabola using graphingtechnologyy = -2x^2 + 16
Answers
Given data:
The given equation is y=-2x^2+16.
Subtiute -x for x in the given equation.
y=-2(-x)^2+16
=-2x^2+16
Thus, the y-axis is the axis of symmetry.
50 POINTS!!
If C(g) represents the cost, in dollars, of filling up a gas tank with g gallons, what is the interpretation of C(18) = 54.54?
I need the steps as well.
Answers
Answer:
When reading C(18) = 54.54, notice the input quantity is 18, which is the number of gallons (g). The output value is 54.54, and the cost of filling up the gas tank is C. So, this tells us that the cost of 18 gallons of gas is $54.54.
1/5 1) Find the equation of the line passing through the points (-1,-5) and (2,-2). Write the equation in slope - intercept form. oy = x - 2 Oy = -2 y = -2 oy=r - 4 Next Submit Search o 99+
Answers
The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with the points (-1,-5) and (2,-2),
[tex]m=\frac{-2-(-5)}{2-(-1)}=\frac{3}{3}=1[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept of the line.
Replacing with point (-1, -5) and m = 1,
-5 = 1(-1) + b
-5 = -1 + b
-5 + 1 = b
-4 = b
The equation is:
y = x - 4
hello I seem to be having difficulty on this question can you please help me
Answers
The data set of the sample is
62 82 79 76 73 70 67 64 61 66 66 66 63 63 63 60 60 71 71
we have that
(84.5-59.5)/5=5
therefore
The classes are equal to
N 1) 59.5-64.5 ------> midpoint 62
N2) 64.5-69.5 -----> midpoint 67
N3) 69.5-74.5 -----> midpoint 72
N4) 74.5-79.5 -----> midpoint 77
N5) 79.5-84.5 -----> midpoint 82
Find out the frequency for each class
N 1) 59.5-64.5 ------> 8
N2) 64.5-69.5 ----->4
N3) 69.5-74.5 ----> 4
N4) 74.5-79.5 ------> 2
N5) 79.5-84.5 ----> 1
see the figure below to better understand the problem
For the power 5⁴ find the following Part A Identify the base. Part B Identify the exponent. Part C Expand as repeated multiplication.
Answers
Answer:
5 is the base
4 is the exponent.
5⁴ = 625
Explanation:
Given the general expression in indices;
[tex]a^n[/tex]a is known as the base of the expression
n is the exponent
Comparing with the given expression 5⁴, you will see that a = 5 and b = 4. Hence;
5 is the base
4 is the exponent.
5⁴ = 5 * 5 * 5 * 5
5⁴ = 25 * 25
5⁴ = 625
Hence the value of 5⁴ is 625
Answer:
5^4 = 625
a) 5
b) 4
c) 5 x 5 x 5 x 5
Step-by-step explanation:
The base is the number you multiply, the larger one.
The exponent is the amount of times you multiply that number by itself, or the smaller one.
When priced at $30, a toy has monthly sale of 4000 units. For each $1 increase in price, sells will decrease by 100 units. Find the maximimum total revenue possible levenue - Price Questiny [hinti price = (30 + 1x) and quanlity = (400-10x)
Answers
In order to determine the maximum revenue, consider that the revenue is equal to the product of the price and the quantity of products sold.
Based on the information of the question, you have:
Revenue = price * quantity
R(x) = (30 + x)(4000 - 100x)
where R is the function for the revenue.
Use distribution property to expand the previous factor:
(30 + x)(4000 - 100x) = 30(4000) + 30(-100x) + x(4000) + x(-100x)
= 120000 - 3000x + 4000x - 100x²
= 120000 + 1000x - 100x²
to determine the maximum, calculate the derivative of the previous expression, equal to zero and solve for x, as follow:
R'(x) = 1000 - 200x = 0
-200x = -1000
x = 1000/200
x = 5
next, replace the previous value of x into the formula for R(x):
R(5) = (30 + 5)(4000 - 100(5))
R(5) = (35)(3500)
R(5) = 122500
Hence, the maximum total revenue possible is $122,500
Writing an equation for a function after a vertical and horizontal translation. (See picture)
Answers
Given:
Given that a graph of the function
[tex]f(x)=x^2[/tex]Required:
To find the function h(x) in the graph.
Explanation:
The graph of h(x) is horizontal translate left 2 units.
Therefore,
[tex]\begin{gathered} h(x)=(x-(-2))^2 \\ \\ =(x+2)^2 \end{gathered}[/tex]And vertical translate upward 4 units.
So,
[tex]h(x)=(x+2)^2+4[/tex]Final Answer:
[tex]h(x)=(x+2)^2+4[/tex]Since you want to compare the salaries of the two leagues, use the data in the spreadsheet to create two dot plots on the number lines below-one showing the American League team payrolls and the other showing the National League team payrolls. Each interval on the number lines isequal to $10 million. Type an "o" at the approximate position each team's payroll on the number line.
Answers
Team payrolls
Line interval = $10 millions
Write the equation of the translated parent function f(x) = ex where is it translated 1 unit right and 2 units down
Answers
Given the parent function:
[tex]f(x)=e^x[/tex]first, to translate it 1 unit right, we have to find f(x-1):
[tex]f(x-1)=e^{x-1}[/tex]next, to translate it 2 units down, we have to find the following expression:
[tex]\begin{gathered} f(x)+c,c<0 \\ \Rightarrow f(x)+c=e^x-2 \end{gathered}[/tex]combining both transformations, we get:
[tex]g(x)=e^{x-1}-2[/tex]therefore, g(x) = e^(x-1) - 2 is the translation of the parent function 1 unit right and 2 units down
90+27 apply the distributive property to factor out the greatest common factor
Answers
Given:
90 + 27
Let's apply the distributive property to factor out the greatest common factor.
First find greatest common factor of 90 and 27
Greatest common Factor of 90 and 27 = 9
Thus, we have:
[tex]\begin{gathered} 9(\frac{90}{9}+\frac{27}{9})\text{ } \\ \\ =\text{ 9(10 + 3)} \end{gathered}[/tex]Applying distribuive property, we could rewrite as: 9(10 + 3)
ANSWER:
9(10 + 3)
63 divided by the sum of 3 and 4
Answers
You can find the math expression dividing the statement in parts:
63 divided by: 63/
the sum of 3 and 4: 3+4=7
then, you get:
[tex]\frac{63}{7}=9[/tex]