EXPLANATION
As we already know, scale factor is the number by wich all the components of an object are multiplied in order to create a proportional enlargement or reduction.
First, we need to turn 6ft into inches units in order to have same magnitudes.
1 ft = 12 inches
So, the relationship is now 1in: 12 in
Scale factor = blueprint size / garden size
Isolating the blueprint size:
BluePrint size = Scale Factor * Garden Size
So, replacing terms:
----> The width will be 42* 1/12 = 3.5
----> The length will be 72 * 1/12 = 6
Answers:
A. The length of the blueprint is 6
B. The width of the blueprint is 3.5
The table shows x- and y-values for the equation y = 3x -1 Which number is missing in the table? 23 15 20 37
y = 3x-1
When x = 8
y = 3(8) -1
y = 24-1
y = 23
Micha starts riding his bike at 12:05pm Her rides for 35 minutes What time does he stop riding his bike?
If Micha rides for 35 minutes, she'll stop riding her bike at 12:40pm
How to graph inequalities y + 6 < 10 or 2y - 3 > 9
We need to graph on the number line the solution to the compounded inequality
[tex]\begin{gathered} y+6<10 \\ \text{or } \\ 2y-3>9 \end{gathered}[/tex]In order to do so, let's work with each inequality separately. The final solution will be the union of the two solutions since it can be one "or" the other.
Step 1
Subtract 6 from both sides of the first inequality:
[tex]\begin{gathered} y+6<10 \\ \\ y+6-6<10-6 \\ \\ y<4 \end{gathered}[/tex]So, the solution to the first inequality is all real numbers less than 4 (not included). Therefore, we graph this solution using an empty circle:
Step 2
Add 3 to both sides of the second inequality, and then divide both sides by 2:
[tex]\begin{gathered} 2y-3+3>9+3 \\ \\ 2y>12 \\ \\ \frac{2y}{2}>\frac{12}{2} \\ \\ y>6 \end{gathered}[/tex]Thus, the solution to this inequality is all the real numbers greater than 6 (not included: empty circle):
Answer
Therefore, the solution to the compounded inequalities is the union of both solutions:
twice a number decreased by 4 Is atleast 12
EXPLANATION
The appropiate relationship is:
2x - 4 = 12
Adding +4 to both sides:
2x = 12 + 4
Adding numbers:
2x = 16
Dividing both sides by 2:
x = 16/2
Simplifying:
x = 8
The solution is 8
Solve VABC if a = 34 feet, b = 20 feet, and c = 18 feet. .
Cosine theorem:
[tex]\begin{gathered} a^2=b^2+c^2-2bccosA \\ b^2=a^2+c^2-2ac\cos B \\ c^2=a^2+b^2-2ab\cos C \end{gathered}[/tex]a= 34ft
b = 20ft
c = 18ft
[tex]\begin{gathered} a^2-b^2-c^2=-2bc\cos A \\ \frac{a^2-b^2-c^2}{-2bc}=\cos A \\ \\ A=\cos ^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex][tex]B=\cos ^{-1}(\frac{b^2-a^2-c^2}{-2ac})[/tex][tex]C=\cos ^{-1}(\frac{c^2-a^2-b^2}{-2ab})[/tex][tex]\begin{gathered} A=\cos ^{-1}(\frac{34^2-20^2-18^2}{-2(20)(18)}) \\ \\ A=\cos ^{-1}(\frac{432}{-720})=126.86 \end{gathered}[/tex][tex]\begin{gathered} B=\cos ^{-1}(\frac{20^2-34^2-18^2}{-2(34)(18)}) \\ \\ B=\cos ^{-1}(\frac{-1080}{-1224})=28.07 \end{gathered}[/tex][tex]\begin{gathered} C=\cos ^{-1}(\frac{18^2-34^2-20^2}{-2(34)(20)}) \\ \\ C=\cos ^{-1}(\frac{-1235}{-1360})=24.75 \end{gathered}[/tex]VABC:
A=126.86º
B=27.07º
C=24.75º
a=34ft
b=20ft
c=18ft
Determine whether the relation is a function.13) {(-6, -5), (-3, -7), (4, 6), (4,8)}A) Not a functionB) Function
A) Not a function
ExplanationA function is a relation which describes that there should be only one output for each input
Step 1
let's check the given ordered pair
[tex]\begin{gathered} (x,y),\text{ x is the input, y is the output} \\ (-6,5)\text{ , -6}\Rightarrow5 \\ (-3,-7),\text{ -3}\Rightarrow-7 \\ (4,6),\text{ 4}\Rightarrow6 \\ (4,8).\text{ 4}\Rightarrow8 \end{gathered}[/tex]we can see that
the input 4 has 2 outputs 6 and 8, so
this is not a function, hence the answer is
A) Not a function
I hope this helps you
the base of the pyramid is a square. the volume is ___ cubic cm. measurements:l = 6 cmw = 10 h = 15(unable to send pictures of question without app crashing. my apologies.)
Answer:
300 cubic meters.
Explanation:
The volume of any pyramid is obtained using the formula below:
[tex]V=\frac{1}{3}\times\text{Base Area}\times Height[/tex]Substitute the given values:
[tex]\begin{gathered} V=\frac{1}{3}\times(6\times10)\times15 \\ =\frac{1}{3}\times60\times15 \\ =300\operatorname{cm}^3 \end{gathered}[/tex]The volume of the pyramid is 300 cubic meters.
5 points10) Some sixth-, seventh-, and eighth-grade students spend time at theelementary school tutoring students. Of the students who tutor, 12 aresixth-graders, 18 are seventh-graders, and 6 are eighth-graders. Whatpercent of tutors are seventh-graders? *18%36%50%75%
50%
1) Gathering the data
12 are 6th graders
18 7th graders
6 8th graders
2) Let's add them up at first to get the whole number of students who tutor:
12 +18 +6 = 24 +12 = 36
So we can say that
36 -------------- 100%
The 7th graders: 18 students
So we can write a proportion for that
36-------100%
18 ------- x
36x = 1800 Divide both sides by 36
x =50
3) So the answer is 50% of them are 7th graders.
find the measures of the angles labeled in the figure below. measure of angle EFD=measure of angle EHF=measure of angle HFG=measure of angle G=
EXPLANATION:
We must bear in mind that the internal angles of a triangle must add up to 180 degrees.
We will first find values of unknown angles and finally add to find the corresponding measures.
[tex]\begin{gathered} To\text{ find F:} \\ corresponds\text{ }to\text{ the same angle }measure\text{ }54(F) \\ To\text{ find G:} \\ We\text{ add }the\text{ two internal }angles\text{ 54 }and\text{ s}ubtract\text{ }180\colon \\ 54+54=180 \\ 180-54-54 \\ 180-108 \\ 72\text{ ( }angle\text{ G)} \\ To\text{ find E;} \\ We\text{ must }the\text{ measures }H\text{ and G} \\ H=54\text{ ; G= 72 E=X} \\ 54+72=180 \\ 180-54-72 \\ 54(\text{Angle E)} \\ To\text{ find D} \\ We\text{ must the measures: 33 +54 and }substract\text{ 180} \\ 33+54=180 \\ 180-33-54 \\ 93\text{ (angle D)} \end{gathered}[/tex]Now to find the measurements given in the exercise; We must take the values found according to what each exercise asks for and add them.
[tex]\begin{gathered} \text{Measure of angle EFD:} \\ E(54)+\text{ F(54})+D(93)=201 \\ \text{Measure of angle EHF:} \\ E(54)+H(54)+F(54)=162 \\ \text{Measure of angle HFG:} \\ H(54)+F(54)+G(72)=180 \\ \text{Measure of angle G:} \\ G=\text{ 72 degr}ees \end{gathered}[/tex]Samson buys a newcomputer for class. Thecomputer costs $550, aswell as an additional tax of10.2%.How much does he pay forthe computer?
The cost of the computer is: $550
The additional tax is: 10.2%
To find the final cost of the computer, first, we need to find how much is the tax of 10.2%.
Step 1. Calculate how much is 10.2% of $550.
In general, to calculate a percentage we divide the quantity by 100 and then multiply by the percentage we need. In this case:
[tex]\frac{550}{100}\times10.2[/tex]Solving the operations:
[tex]5.5\times10.2[/tex][tex]=56.1[/tex]The tax is $56.1
Step 2. Add the cost of the computer and the tax to find how much he paid for the computer:
[tex]550+56.1=606.1[/tex]Answer: $606.1
Arthur has 20/8 cups of dishwashing detergent. He uses 1/4 cup of detergent for each load of dishes. what is the greatest number of loads of dishes Arthur was with this amount of detergent
Total = 20/8 cups of dishwashing detergent.
he has 20/8 = 5/2 = 2 1/2 cups of dishwashing detergent, per load he uses 1/4
per load
2 1/2 - 1/4
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The general formula
x= number of loads
20/8 - x* 1/4= 0
20/ 8 = x 1/4
x 1/4 = 20/ 8
x= 4* (20/8 )
x= 10
The greatest number of loads of dishes Arthur was with this amount of detergent is 10
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metro atlanta home prices are rising rapidly, and much of its a soaring demand from deep-pocketed investors,as reported in the AJC March 21st of this year. In March2022, the median sale price of a home in the Metro area was $401,500. Before the the pandemic hit, in january2020, the median sale price was $279,000 Find the rate increase of the average cost of a home in Atlanta from january2020 before the pandemic hit Atlanta to the present
We are asked to determine the rate of increase in the value of a home,
We need to have into account that at the beginning of the considered period the cost was 279000 and after two years the cost is 401500, therefore, we can use the following formula:
[tex]r=\frac{\Delta C}{\Delta t}[/tex]Where:
[tex]\begin{gathered} \Delta C=\text{ difference in cost} \\ \Delta t=\text{ difference in time} \end{gathered}[/tex]Now, we substitute the values:
[tex]r=\frac{401500-279000}{2}[/tex]Solving the operations:
[tex]r=61250[/tex]Therefore, the rate is an increase of $61250 per year.
The number of compounding periods is equal to what: what is the formuls
Answer
When compound interest is discussed, the time rate for the compound interest is usually mentioned. For example, they would say that
- a certain amount of money has its interest compounded at 5% annually,
- a certain amount of money has its interest compounded at 7% every 3 months,
- a certain amount of money has its interest compounded at 2% every 6 months,
In each of the examples given above, the compounding period is 1 year, 3 months and 6 months respectively.
If one is now asked to calculate the compound interst on a particular amount of money after time, T, we usually express this time T in terms of the number of time periods, t, that exist inside the given time T.
Hence, the time T is expressed in terms of time period t, as
T = nt
Such that the number of compounding periods in T is given as
n = (T/t)
[tex]undefined[/tex]solve the system. given your answer as (x, y, z)-4x -y - 3z = -5-6x + y - 3z = -172x + 2y - z = - 10
Answer:
(1, -5 ,2)
Explanation:
Given the system of equations:
[tex]\begin{gathered} -4x-y-3z=-5\ldots(1) \\ -6x+y-3z=-17\ldots(2) \\ 2x+2y-z=-10\ldots(3) \end{gathered}[/tex]Make z the subject in the third equation:
[tex]z=2x+2y+10[/tex]Substitute z=2x+2y+10 into the first and second equations:
First Equation
[tex]\begin{gathered} -4x-y-3z=-5 \\ -4x-y-3(2x+2y+10)=-5 \\ -4x-y-6x-6y-30=-5 \\ -4x-6x-y-6y=-5+30 \\ -10x-7y=25\ldots(4) \end{gathered}[/tex]Second Equation
[tex]\begin{gathered} -6x+y-3z=-17 \\ -6x+y-3(2x+2y+10)=-17 \\ -6x+y-6x-6y-30=-17 \\ -6x-6x+y-6y=-17+30 \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Next, solve equations 4 and 5 simultaneously:
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -12x-5y=13\ldots(5) \end{gathered}[/tex]Multiply equation (4) by 5 and equation (5) by 7.
[tex]\begin{gathered} -50x-35y=125 \\ -84x-35y=91 \\ \text{Subtract same sign} \\ 34x=34 \\ x=\frac{34}{34} \\ x=1 \end{gathered}[/tex]Substitute x=1 into equation (4):
[tex]\begin{gathered} -10x-7y=25\ldots(4) \\ -10(1)-7y=25 \\ -7y=25+10 \\ -7y=35 \\ y=\frac{35}{-7} \\ y=-5 \end{gathered}[/tex]Recall: z=2x+2y+10
[tex]\begin{gathered} z=2x+2y+10 \\ =2(1)+2(-5)+10 \\ =2-10+10 \\ z=2 \end{gathered}[/tex]The solution of the system is:
[tex](1,-5,2)[/tex]question is in image
The function f(x) is given by,
[tex]f(x)=x^2[/tex]The function g(x) is given by,
[tex]g(x)=\frac{-2}{3}x^2[/tex]If f(x) becomes -kf(x), where 0Comparing the above functions, we get
[tex]g(x)=-\frac{2}{3}f(x)[/tex]So, k=2/3. Hence, 0 < 2/3 < 1.
Therefore, the graph of g(x) is the graph of f(x) compressed vertically and reflected across the x axis.
Hence, option D is correct.
an office administrator has an office supply budget $150. The office administrator will purchase folders, which are $2.15 each and notebooks, which are $4.60 each. which inequality represent the constrain on the number of folders f and notebook n the office administrator can purchase
If the price of each folder is $2.15, and the amount of folders is f, the total price paid for folders is the product of the unitary price by the amount bought.
[tex]\text{price}1=2.15f[/tex]Similarly, the price paid for notebooks is the unitary price of one notebook ($4.60) multiplied by the amount of notebooks (n).
[tex]\text{price}2=4.6n[/tex]Finally, the total cost of both products together is the sum of these products.
[tex]\text{cost}=\text{price}1+\text{price}2=2.15f+4.6n[/tex]The supply budget is $150, so the total cost needs to be lesser than or equal this value.
Therefore, we have that:
[tex]\begin{gathered} \text{cost}\le150 \\ 2.15f+4.6n\le150 \end{gathered}[/tex]So the correct option is B.
Make the following conversion in the metric system by multiplying by the appropriate conversion factor. Write your answer as a whole number or decimal.20 m to millimeters ?mm
Each meter has 100 centimeters, each centimeters has 10 milimeters, so 20 meters has 20.000 milimeters.
Over the weekend, Devon baked 12 muffins. She divided them evenly among 3 plates to giveto neighbors.The letter m stands for the number of muffins on each plate. Which equation can you use tofind m?12 x 3 = m12 : 3 = m
The information given is listed below:
number of muffins (m) = 12, number of plates = 3
number of muffin on each plate = number of muffins /
taliyah 1. If Mrs. Wozniak runs 8 miles a day. How many miles will she run in 4 weeks? Your answer 2. Fach fourth trade class at a local elementan answered 1 209 multiplication fact problems last
Use the given rate to find how many miles will Mrs. Wozniak run in 4 weeks. Remember that 1 week is equal to 7 days, then 4 weeks is 28 days.
[tex]28days\cdot\frac{8miles}{1day}=224miles[/tex]She will run 224 miles in 4 weeks.
use the function f(x)=-3(x+1)2+18what is the y intercept ?does it have a max or min
hello,
First of all, we must remember that a first degree function must be in the formula f (x) = ax + b, so, lets use this form:
[tex]undefined[/tex]1 11a.) A sign in a bakery gives the following options. Find each unit price to the nearest cent, and show your reasoning. You can get 3 mini-cakes for $32. What is the cost of ONE mini-cake? * O $10.66 O $10.65 O $10.67 O $10.59
Since we can get 3 mini-cakes for $32, we can find the price of each mini-cake by taking the ratio of price to number of mini-cakes, like this:
unit price = 32/3 = 10.67
Then, the cost of ONE mini-cake is $10.67
Hello. I need help with this practice problem. I will include a picture. Thank you soo much
Firstly, we need to compare the information ew have from both sides of the equation, the denominators.
The different between the denominator is that the right side has the factor (w + 6), while the lest side does not.
So, sstarting from the expression on the left side, we can introduce the factor (w + 6) into the denominator by multiplying both the numerator and the denominator by this factor:
[tex]\frac{2}{w+7}=\frac{2}{w+7}\cdot\frac{w+6}{w+6}=\frac{2(w+6)}{(w+7)(w+6)}[/tex]The order of the factor dont change the result, so we can switch the factors on the denominator to get:
[tex]\frac{2}{w+7}=\frac{2(w+6)}{(w+6)(w+7)}[/tex]Now, by comparison, we can see that the blank part is the following:
[tex]2(w+6)[/tex]Let f(x)=3x - 4. Write a function gwhose graph is a reflection of the graphoff.
hello
the function given is
How do I find the sum of this equation and express it in simplest form [tex]( {n}^{3} - 5n - 2) + (4 {n}^{3} + n - 4)[/tex]
In ABC, A = 68°, a = 14 and c = 17. Which of these statements best describes the triangle?
Given for the triangle ABC:
[tex]\begin{gathered} \angle A=68\degree \\ a=14,c=17 \end{gathered}[/tex]Using the sine rule, we will solve the triangle by finding the missing angles
So,
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]substitute with the given data:
[tex]\begin{gathered} \frac{14}{\sin68}=\frac{17}{\sin C} \\ \\ \sin C=\frac{17}{14}\cdot\sin 68=1.125866 \end{gathered}[/tex]The value of (sin C) must be 1 or less than 1
So, the triangle ABC cannot be constructed
The answer will be the last option
May you help me with this
Given the function
[tex]h(x)=2x^2-3x+5[/tex]Set x=-3 and solve for h(-3) as shown below
[tex]\begin{gathered} x=-3 \\ \Rightarrow h(-3)=2(-3)^2-3(-3)+5=18+9+5=32 \\ \Rightarrow h(-3)=32 \end{gathered}[/tex]Therefore, the answer is 32
Connie is studying two number patterns. Pattern 1 starts at 0 and has the rule "add 4.Pattern 2 starts at 0 and has the rule "add 2."Drag a number into each box to complete Connie's patternsDrag a phrase into the last box to complete the comparison of the corresponding terms in each pattinPattern 1:0,
Let's start with Pattern 1.
SInce the rule is to add 4, we shall add 4 on the first number that is zero.
The pattern 1 shall be:
[tex]0,4,8,12[/tex]On the other hand, for Pattern 2, the rule is to add 2. So, let's add 2 on the first number that is 0. Pattern 2 shall be:
[tex]0,2,4,6[/tex]Based on these two patterns, we can see that the terms in Pattern 1 are two times the corresponding terms in Pattern 2.
Keisha has four favorite shirts one blue, one green, one red, one yellow and two favorite pairs of pants one black and one brown she decides to randomly choose a pair of pants and a shirt to wear for the day. What is the probability that Keisha chooses and outfit that is yellow and black or red and brown round your answer to the nearest whole percent?
Answer:
25%
Explanation:
First, let's calculated the total number of outfits that Keisha can choose. So, we will use the rule of multiplication as:
4 * 2 = 8
Shirts Pants
Because she has 4 options for shirts and 2 options for pants. So, there 8 possible outfits.
Then, from those outfits, there is 1 that is yellow and black, and 1 that is red and brown. So, the probability that Keisha chooses an outfit that is yellow and black or red and brown is:
[tex]P=\frac{1+1}{8}=\frac{2}{8}=0.25=25\text{ \%}[/tex]Therefore, the answer is 25%
My teacher gave the answer on the right but I want know how he did it
the given number is 6^4
here is the calculation.
[tex]6^4=6\times6\times6\times6[/tex]multiply the number 6 by the times of 4
now by multiplication, the answer is
[tex]6^4=1296[/tex]so, the answer is 1296.
I have a practice problem that I need explained an answered, thank you
From the question, we are given the matrices
We are to find which operation is defined and whic one is not
For the operation
[tex]M-N[/tex]For subtraction operation to be definded
The order of the matrices must be the same
Since the order of M is 4 x 2
And the order of N is 4 x 2
Therefore, the operation M - N is defined
For the operation
[tex]L-N[/tex]Similarly, for the operation to be definded
The order of the matrices must be the same
The oder of matrix L is 2 x 2 while the order of matrix N is 4 x 2
Since the oder of the matrices are not the same then
The operation L - N is not defined
For the operation
[tex]M+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix M is 4 x 2 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined
For the operation
[tex]Q+P[/tex]For addition operation to be defined, the Order of the matrices must be the same
The order of matrix Q is 2 x 1 while the order of matrix P is 2 x 2
Since the order of the matrices are not the same then the operation is not defined