The answer is very simple
First you need to solve the algebraic operations of the line and take it to its minimum expression
The drawing below represents the frame for an isosceles triangle-shaped roof. The height of the roof is 4 feet. What is the distance from Point A to Point B in feet? B 41 3 feet 8v 6 feet 8V3 feet 8 feet
We can make a drawing to see better:
In the picture above, we can see the sides AC and BC are equals because triangle ABC is isosceles, and also the segments AD and DB are equals for the same reason.
We can calculate the lenght of segment AD as:
[tex]\begin{gathered} \tan (30)=\frac{CD}{AD} \\ AD=\frac{CD}{\tan (30)}=\frac{4}{\frac{1}{\sqrt[]{3}}} \\ AD=4\cdot\sqrt[]{3} \end{gathered}[/tex]With the lenght of segment AD we can calculate the lenght of AB as:
[tex]AB=2\cdot AD=8\cdot\sqrt[]{3}[/tex]The correct answer is in yellow.
The monthly rents for five apartments advertised in a newspaper were $650, $650, $750, $1650, and $850.the mean, median, and mode of the rents to answer the question. Which value best describes the monthlyrents?
SOLUTION
Given the question in the image, the following are the solution steps to get the correct answer
Step 1: Write the monthly rents
[tex]\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850[/tex]We need to calculate the mean, median and moce of these data to allow us choose the best answer
Step 2: Calculate the mean
a
[tex]\begin{gathered} \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}1650,\text{\$}850 \\ \operatorname{mean}=\frac{sum\text{ of monthly rents}}{number\text{ of monthly rents}} \\ \operatorname{mean}=\frac{\text{\$}650+\text{\$}650+\text{\$}750+\text{\$}1650+\text{\$}850}{5}=\frac{4550}{5}=\text{\$}910 \end{gathered}[/tex]Step 3: Calculate the median
The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number.
[tex]\begin{gathered} By\text{ rearrangement},\text{ we have} \\ \text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \operatorname{median}=\text{\$}750 \end{gathered}[/tex]Step 4: Calculate the mode
The mode is the number in a data set that occurs most frequently.
[tex]\begin{gathered} \text{data}=\text{\$}650,\text{\$}650,\text{\$}750,\text{\$}850,\text{\$}1650 \\ \mod e=\text{\$}650 \end{gathered}[/tex]Hence, the value that best describe the rents is mean because $910 is the average rent
Option A
Orang has worked as a nurse at Springfield general hospital for 5 years longer than her friend Bill. Two years ago she had been at the hospital for twice as long. How long has each been at the hospital?
Answer:
• Bill = 3 years
,• Hoang = 8 years.
Explanation:
Let the time Bill had worked in the hospital = b years.
Hoang has worked for 5 years longer than her friend Bill, therefore:
• The time ,Hoang, had worked in the hospital = (b+5) years.
Two years ago:
• Bill's Time = (b-2) years
,• Hoang's Time = (b+5-2) years
Two years ago she had been at the hospital for twice as long as Bill.
[tex]\implies b+5-2=2b[/tex]Solve the equation for b:
[tex]\begin{gathered} b+5-2=2b \\ b+3=2b \\ 2b-b=3 \\ b=3 \end{gathered}[/tex]Hoang has been at the hospital for 8 years and Bill has been there 3 years.
If x varies inversely as y and x=16 when y=5, find x when y=20.
Since x varies inversely as y, then it can be represented as the expression below:
[tex]y=\frac{1}{a}\cdot x[/tex]Where a is the proportionality constant. We need to find a to determine the value of x when y is 20. For that we will use the two values given as shown below:
[tex]\begin{gathered} 5=\frac{1}{a}\cdot16 \\ 5\cdot a=16 \\ a=\frac{16}{5}=3.2 \end{gathered}[/tex]The expression is:
[tex]y=\frac{1}{3.2}\cdot x[/tex]If y is 20, then x must be:
[tex]\begin{gathered} 20=\frac{1}{3.2}\cdot x \\ x=3.2\cdot20 \\ x=64 \end{gathered}[/tex]The value of x must be 64.
What are the leading coefficient and degree of the polynomial?12 – 20u-u?Leading coefficient:Пx 5?Degree:
In a polynomial, the term with the highest power of the variable is the leading term. The coefficient of the leading term is the leading coefficient.
In the polynomial given;
[tex]12-20u-u^2[/tex]The leading term is
[tex]-u^2[/tex]The leading coefficient therefore is -1
The degree of the polynomial is the exponential power of the leading term. In the given polynomial, what we have is a second degree polynomial
ANSWER:
Leading coefficient = -1
Degree = 2
Lynn had an opening balance of $179.30 in her checking account.She made deposits of $432 and had bank charges of $5.35. If herclosing balance was $353.82, how much did she write in checks?a. $625.89b. $258.05c. $262.83d. $252.13
Given:
Opening balance $179.30 then she deposits $432 and had bank charges $5.35
Closing balance is $353.82
[tex]\text{Amount written in the check = 179.30+432-5.35-353.82}[/tex][tex]\text{Amount written in the check = \$}252.13[/tex]Therefore, Option d is the correct answer.
Melody has a monthly commission plan under which she receives 2% on the first $40,000 ofsales during the month and 3% on sales above $40,000. If Melody has sales of $73,000 during amonth, computer her commission for that month.
Melody sales is above $40, 000
For sales above $40, 000, she gets 3%
So Melody commission for that month is 3% of $73,000
= 3/100 x $73000
= 3 x $730
=$2190
two mechanics worked on a car. the first mechanic worked for 5 hours and the second mechanic worked for 15 hours together they charged a total of $1,225 what was the rate charge per hour by each mechanic if the sum of the two rates was $125 per hour
Given : two mechanics worked on a car
The first : worked for 5 hours
The second : worked for 15 hours
Total charge for both = $1,225
Let the charge rate per hour for the first is x and for the second is y
So,
[tex]5x+15y=1225[/tex]the sum of the two rates was $125 per hour so,
[tex]x+y=125[/tex]so, we have the following system of equations :
[tex]\begin{gathered} 5x+15y=1225 \\ x+y=125 \end{gathered}[/tex]Form the second equation : y = 125 - x
Substitute at the first equation with y to find the value of x
so,
[tex]\begin{gathered} 5x+15\cdot(125-x)=1225 \\ 5x+1875-15x=1225 \\ 5x-15x=1225-1875 \\ -10x=-650 \\ \\ x=\frac{-650}{-10}=65 \\ \\ y=125-x=125-65=60 \end{gathered}[/tex]so, the rate of the first one who worked 5 hours = $65 per hour
And the rate of the second will be = $60 per hour
Generate ordered pairs for y = x^2 - 9 using x = -4,-2,0,2 and 4. Identify the corresponding graph.
Given,
The equation is y=x^2-9.
The values of x are -4, -2, 0, 2, 4.
The odered pair are,
At x= - 4,
The value of y is,
[tex]y=(-4)^2-9=7[/tex]The ordered pair is (-4, 7).
At x= - 2,
The value of y is,
[tex]y=(-2)^2-9=-5[/tex]The ordered pair is (-2, -5).
At x= 0,
The value of y is,
[tex]y=(0)^2-9=-9[/tex]The ordered pair is (0, -9).
At x= 2,
The value of y is,
[tex]y=(2)^2-9=-5[/tex]The ordered pair is (2, -5).
At x= 4,
The value of y is,
[tex]y=(4)^2-9=7[/tex]The ordered pair is (4, 7).
The corresponding graph is,
Subtract 5y^2-6y-11 from 6y^2+2y+5?
Subtract 5y^2 - 6y - 11 from 6y^2 + 2y + 5
They are both quadratic expression
6y^2 + 2y + 5 - (5y^2 - 6y - 11)
Firtstly, use the negative sign to open the parentheses
6y^2 + 2y + 5 - 5y^2 + 6y + 11
Secondly, collect the like terms
6y^2 - 5y^2 + 2y + 6y + 5 + 11
since y^2 is common, factorize it out
y^2(6 - 5) + y(2 + 6) + 26
y^2(1) + y(8) + 26
y^2 + 8y + 26
The answer is y^2 + 8y + 26
Please Help! I will give brainliest! Need the correct answer!
Answer:
HL
Step-by-step explanation:
The two triangles are rectangle and have a congruent hypotenuse and a congruent leg
Bonnie is searching online for airline tickets two weeks ago the cost to fly from Orlando to Denver was $200 .now the cost is $345. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with with the new ticket price?
Answer:457
Step-by-step explanation:
kiruiand kariuki formed a trading partnership .in the first month kirui contributed 1/12 of his salary towards the cost of the company kariukis contribution was 1/10 of his monthly salary giving a total of ksh 980 .their respective contributions the following month were 1/8 and 1/6 of their salaries .if a total contribution for the second month was cash 1550, what were their monthly salaries
kirui's monthly salary is 6000 and kaiuki's monthly salary is 4800.
Let
kirui's salary =x
kariuki's salary=y
Given,
In first month,
Total contribution=980
kirui's contribution=[tex]\frac{x}{12}[/tex]
kariuki's contribution=[tex]\frac{y}{10}[/tex]
In second month,
Total contribution=1550
kirui's contribution =[tex]\frac{x}{8}[/tex]
kariuki's contribution=[tex]\frac{y}{6}[/tex]
Equation for first month,
[tex]\frac{x}{12} +\frac{y}{10} =980\\\\5x+6y=58800....i[/tex]
Equation for second month,
[tex]\frac{x}{8} +\frac{y}{6} =1550\\\\3x+4y=37200....ii[/tex]
Solving eq.
[tex]5x+6y=58800= > 15x+18y=176400\\3x+4y=37200= > 15x+20y=186000\\\\Subtracting the equations,\\\\15x+18y=176400\\15x+20y=186000\\---------\\-2y=-9600\\\\y=4800[/tex]
Substituting y in eq.[tex]ii[/tex]
[tex]3x+4(4800)=37200\\\\3x=18000\\\\x=6000[/tex]
Thus, kirui's monthly salary is 6000 and kaiuki's monthly salary is 4800.
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Order each set of numbers from least to greatest. numbers are in the photo
Answer:
Explanation:
Given the below set of numbers;
[tex]\lbrace2.8,-2\frac{3}{4},3\frac{1}{8},-\bar{2.2}\rbrace[/tex]Let's go ahead and reduce the mixed fractions to improper fractions;
[tex]undefined[/tex]To find the angle of rotation θ between the previous x and y axes and the new x′ and y′ axes, we use the formula: cotangent of 2 theta equals A minus C all over B , where 2θ lies on the interval (0°, 180°).TrueFalse
The equation is the given one:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Which is the same as:
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]And the interval of the angle θ must be (0°,90°) so, 2θ must be (0°,180°).
So the statement is True.
what is 6 / 1/5 helppppp
We have the following:
[tex]6\div\frac{1}{5}[/tex]we carry out the operation, in a division, a cross multiplication is made, like this
[tex]\frac{6}{1}\div\frac{1}{5}=\frac{30}{1}=30[/tex]Therefore, the answer is 30
we have to write the equation of the line using y=mx+b passing through the points (6,2) and (2,4)
The general equation of line passes through point (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passes through point (6,2) and (2,4).
[tex]\begin{gathered} y-2=\frac{4-2}{2-6}(x-6) \\ y-2=\frac{2}{-4}(x-6) \\ y=-\frac{1}{2}x+3+2 \\ =-\frac{1}{2}x+5 \end{gathered}[/tex]So equation of line is y = -1/2x + 5.
Right to sleep as a fraction by the Y intercept as well
Given:
The points (0,3) and (2,0) lie on the line.
Required:
We need to find the slope and y-intercept of the given line.
Explanation:
The y-intercept is the point where the line crosses the y-axis.
The given line crosses the y-axis at 3.
y-intercept=(0,3).
Consider the slope formula,
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitu\text{te }y_2=0,y_1=3,x_2=2\text{ , and }x_1=0\text{ in the formula.}[/tex][tex]slope=\frac{0-3}{2-0}[/tex][tex]slope=\frac{-3}{2}[/tex]Final answer:
[tex]slope=\frac{-3}{2}[/tex]y-intercept=(0,3).
Help find the indicated functional value for the floor function
We need to find the greates integer less than f(-0.75):
In this case the integer nearest to -0.75 is -1.
Juan has already run 6 miles this month. He plans to run an additional 2 miles per day. At this rate, how long will it take Juan to run 40 miles?Hint: Write and solve a 2-step equation
ANSWER
[tex]17\text{ days}[/tex]EXPLANATION
We want to find how long it will take Juan to run 40 miles.
To do this, we have to set up an equation that describes the situation.
We have that Juan has already run 6 miles and he wants to run an additional 2 miles per day.
This implies that after d days, he would have run:
[tex]6+2d[/tex]For Juan to run 40 miles, it implies that:
[tex]6+2d=40[/tex]Solve that for d:
[tex]\begin{gathered} 2d=40-6=34 \\ d=\frac{34}{2} \\ d=17\text{ days} \end{gathered}[/tex]That is how long it will take Juan to run 40 miles.
What number must be added to the expression below to complete the
square?
x²-x
O A. -1/1
4
O B. /
O C. - 12/2
O D.
-12
Answer:
1/4
Step-by-step explanation:
Completing the square
x^2 -x
Take the coefficient of the x term
-1
Divide by 2
-1/2
Square it
(-1/2) ^2 = 1/4
Add this to each side
12 in.4 inShoe Box2 inWhat is the volume of the shoebox shown above in cubic inches?18 cubic inches48 cubic inches*96 cubic inches114 cubic inches
We have a shoebox with 3 dimensions, we are asked to find the volume of this shoebox
To do this we use the following volume formulation
[tex]V=l\cdot w\cdot h[/tex]Where the length is l=12, the width is w=2 and the height is h=4, now we replace a solve this
[tex]V=12\cdot2\cdot4V=96[/tex]In conclusion, the shoebox is 96 cubic inches
it wants me to solve for the other leg and for the hypotenuse of the 45-45-90 triangle
Given:
In the given 45-45-90 triangle,
Use the tan ratio,
[tex]\begin{gathered} \tan 45^{\circ}=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan 45^{\circ}=\frac{v}{7} \\ 1=\frac{v}{7} \\ v=7 \end{gathered}[/tex]Use the cosine ratio,
[tex]\begin{gathered} \cos 45^{\circ}=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos 45^{\circ}=\frac{7}{u} \\ \frac{1}{\sqrt[]{2}}=\frac{7}{u} \\ u=\frac{7}{\sqrt[]{2}} \\ u=7\sqrt[]{2} \end{gathered}[/tex]Answer: option a)
[tex]u=7\sqrt[]{2},v=7[/tex]q (3.2r – 7)Write an equivalent expression by combining like terms
From the problem, we have the expression :
[tex]q(3.2r-7)[/tex]By distributive property, multiply q to the parenthesis.
[tex]3.2qr-7q[/tex]Since the terms are NOT like terms, we cannot combine them.
Therefore, the answer is :
3.2qr - 7q
What is the difference between discrete and continuous data set?
Let's explain the difference between discrete and continuous data set.
• Discrete data set can be said to be a set of data with distinct and seperate values.
Discrete data contains finite values that are countable.
Discrete data set has clear sapces between values.
Examples of discrete data are:
• 10 kids
,• 7 laptops
,• 24 balls
• Continuous data set is said to be the set of data with random variables which may or may not be whole number.
Continuous data changes over time and can also have different values at different time intervals.
Continuous data can be any measured value.
Continuous data set falls on a continuos sequence.
Examples of continuous data are:
• 4.84 miles
,• 84.3 meters
,• 8 kg
A Place from this table is chosen at random. Let event A= The place is a city. what is P(Ac)?
Okay, here we have this:
How The probability of an event is a ratio that compares the number of calculating favorable outcomes with the number of possible outcomes. We obtain:
[tex]P(A^C)=\frac{numberof\text{cities}}{numberofplaces}=\frac{4}{7}[/tex]Finally we obtain that the correct answer is the option B.
4x - 4y = 20y = -5Solve the system of linear equations by graphing
The given system of equation:
4x - 4y = 20
y = -5
Plot the equation in the graph
the point at which both the lines meet is the solution of the system of equation:
the graph is :
The lines intersect at (0,-5) i.e x = 0, y = -5
So, the solution of the system of equation is x = 0 & y = -5
Answer:
x = 0
y = -5
find the average rates of change of each function for each 1-hour interval from t=0 to t=6
Step 1
Given;
[tex]Organization\text{ A, B and C}[/tex]Required; To determine the type of function representing each company
Step 2
Determine the type of function for company A
[tex]Since\text{ the number of donations quadruples each hour company A has an exponential}[/tex]An exponential function represents the number of donations collected by organization A
Determine the type of function for company B
[tex]Rate\text{ of change=}\frac{8-4}{2-1}=\frac{12-8}{3-2}=\frac{4}{1}=4[/tex]Since the rise and the run measured at points on the table are the same a linear function represents the number of donations collected by organization B.
Determine the type of function for company C
A quadratic function represents the number of donations collected by organization C
Step 3
Fill the chart.
Average rate of change for company A
[tex]undefined[/tex]Solve the equation 4x2 + 8x + 1 = 0 by completing the square.
Let's compare the given equation with the notable product below:
[tex](a+b)^2=a^2+2ab+b^2[/tex]Since the first term is 4x², we have a = 2x.
Then, the second term is 8x, so since a = 2x, we have b = 2, this way 2ab = 8x
Now, since b = 2, we have b² = 4.
The constant term is just 1, so we need to add 3 units:
[tex]\begin{gathered} 4x^2+8x+1+3-3=0 \\ 4x^2_{}+8x+4-3=0 \\ (2x+2)^2=3 \\ 2x+2=\pm\sqrt[]{3} \\ 2x=-2\pm\sqrt[]{3} \\ x=\frac{-2\pm\sqrt[]{3}}{2} \end{gathered}[/tex]Therefore the correct option is the third one.
Select the correct answer. A pyramid is placed inside a rectangular prism with height h. Area of the base of the pyramid and the prism is B. A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h, of the prism. Which expression gives the volume of the pyramid? A. V = 2 3 B h B. V = 1 4 B h C. V = 2 B h D.
An expression which gives the volume of this pyramid is D. V = 1/6 Bh.
How to calculate the volume of a pyramid?Mathematically, the volume of a pyramid can be calculated by using this formula:
V = 1/3 × B × h
Where:
V represents the volume of a pyramid.h represents the height of a pyramid.B represents the base area of a pyramid.Since the pyramid has the same base area (B) as the prism but half (1/2) the height (h) of the prism, the new volume of this pyramid can be derived as follows:
New height, h = h/2
Substituting the parameters into the formula, we have:
Volume, V = 1/3 × B × (h/2)
Volume, V = 1/6 Bh
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Complete Question:
A pyramid is placed inside a prism as shown. The pyramid has the same base area, B, as the prism but half the height, h, of the prism. Which expression gives the volume of the pyramid?
A. V = 2/3 Bh
B. V = 1/4 Bh
C. V = 2 Bh
D. V = 1/6 Bh