Answers
Two triangles than make the whole triangle are proportional then
[tex]15\longrightarrow30[/tex]and the upper side of the left triangle is x
we can calculate the lenght of upper triangle
[tex]36-15=21[/tex]then
[tex]21\longrightarrow x[/tex]we join the relations
[tex]\begin{gathered} 15\longrightarrow30 \\ 21\longrightarrow x \end{gathered}[/tex]we use cross-multiplication. The product of 21 by 30 dividing between 15 is equal to x
[tex]\begin{gathered} x=\frac{21\times30}{15} \\ \\ x=42 \end{gathered}[/tex]the value of x is 42 units
Related Questions
2y = 14xDirect variationk =Not direct variation
Answers
2y = 14x
divide both sides by 2
so,
y = 7x
direct variation and k = 7
Which mathematical property is demonstrated?5 • 7 • 4 = 5 • 4 • 7commutative property of additioncommutative property of multiplicationassociative property of additionassociative property of multiplication
Answers
What we can observe in equality is the commutative property of multiplication.
The answer would be Commutative Property of Multiplication
If the sample space, S = {1, 2, 3, 4, …, 15} and A = the set of odd numbers from the given sample space, find Ac.A.{1, 2, 3, 4, 5, 6, …, 15}B.{1, 3, 5, 7, 9, 11, 13, 15}C.{1, 2, 3, 4, 15}D.{2, 4, 6, 8, 10, 12, 14}
Answers
A^c is the complement of set A.
Given that A is a subset of S, then A^c contains the elements present in set S but not in set A.
The sets are:
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A = {1, 3, 5, 7, 9, 11, 13, 15} (odd numbers present in S)
Therefore, the elements present in set S but not in set A are:
[tex]A^c=\mleft\lbrace2,4,6,8,10,12,14\mright\rbrace[/tex]
When solving the system below algebraically using the substitution method, which of the following could be an equation you could create to solve for y?A. -4(2y - 20) + 3y = 30B. -4(-2y + 20) + 3y = 30C. -2y + 20 = -3y + 30D. 4(x + 2y = 20
Answers
The goal of the substitution method is to eliminate one of the variables using one of the equations of the systems. We are told that we want to solve for y, that is, we should use one equation to eliminate the variable x.
Since the coefficient of x in the first equation is 1, we will use the first equation to eliminate x in the second equation. So, we have the first equation
[tex]x+2y=20[/tex]So, by subtracting 2y on both sides, we get
[tex]x=20-2y[/tex]which is equivalent to
[tex]x=-2y+20[/tex]So, if we replace this value of x in the second equation,w e get
[tex]-4\cdot(-2y+20)+3y=30[/tex]which corresponds to option B
Can anyone help me pls this is my last grade for algebra and Ik failing the class right now I need this grade to be able to pass my class pls help
Answers
For every room added, the price increase is $50, therefore the slope is equal to 50.
Since the value for one room is $125 and we know that each room costs $50, then the y-intercept is the value for 1 room minus 50.
[tex]b=125-50=75[/tex]Now we can create the function for this situation:
[tex]f(x)=50\cdot x+75[/tex]Where f(x) is the price and x is the number of rooms to be cleaned. Since the function is linear, the unit rate is equal to the slope, so the unit rate is 50.
The amount charged to drive to the client's home is the fixed part of the price, so it is equal to the y-intercept. The price is $75.
To find the cost of 8 rooms we need to make x = 8 and calculate the value of the expression.
[tex]f(8)=50\cdot8+75=475[/tex]The value would be $475.
what digit is in the
Answers
So, let's turn the notation from mixed number to fraction:
[tex]1\frac{11}{100}\text{ = }\frac{100}{100}+\frac{11}{100}=\text{ }\frac{111}{100}[/tex]As you can see, the whole becomes 100/100 and then you just add the numerators.
Answer: 111/100
The table below represents the status of different animals.Mammal Bird Reptile Amphibian TotalEndangered 59 75 14TotalThreatened 12 15 32 9371 90 461215168219What is the approximate probability that a selected animal will be a reptile and endangered?
Answers
Solution
Animals that are reptiles and endangered = 14
Total animals = 219
[tex]\begin{gathered} Probability\text{ of a selected animal will be reptile and endagered } \\ =\frac{14}{219} \\ =0.0639 \\ =0.06\text{ \lparen 2 decimal places\rparen} \end{gathered}[/tex]You spin the spinner twice.5243What is the probability of landing on a number less than 3 and then landing on a 5?Simplify your answer and write it as a fraction or whole number.Submit
Answers
To get the probability of an event, we need two things:
1. The total number of possibilities
2. The total number of possibilities considered favorable
For the first event A which is landing on a number less than 3, we only have one favorable possible which is landing on 2.
For the second event B which is landing on a 5, we also only have one favorable possible which is landing a 5 itself.
Now, for both events, the total number of possibilities is 4.
So, the probability of landing on a number less than 3 is 1/4 while the probability of landing on a 5 is also 1/4.
So, the probability of landing on a number lesser than 3 AND landing on a 5 is:
[tex]P(A\text{ }and\text{ }B)=P(A)\times P(B)[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{4}\times\frac{1}{4}[/tex][tex]P(A\text{ }and\text{ }B)=\frac{1}{16}[/tex]Answer:
The probability of landing on a number lesser than 3 AND landing on a 5 on the next spin is 1/16.
Find limit as x approaches three from the right of f of x. .
Answers
EXPLANATION
The expression means that we need to compute the limit as the function f(x) approaches 3 from the right.
We need to use the lines that comes from the right of 3 and gets as close as we want to x=3.
That is the line that has the open circle around y=3
Therefore, the limit is equal to 3
what is the area of a sector bounded by a 114 arc
Answers
Step1: Write out the given parameter
Θ=114°,r= 6ft
Step2; Write out the formula
The area of a sector is given as
[tex]\frac{\theta}{360}\times\pi r^2[/tex]Step3: substitute the parameters into the formula
[tex]\frac{114}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \frac{114}{10}\pi \\ \frac{57}{5}\pi \end{gathered}[/tex]Hence the area of the sector is (57/5)π interms o
I need to know the answer to this question please
Answers
Answer:
Explanation:
Given:
[tex]3)\text{ }(32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4)[/tex]To find:
the property demonstrated in the equation
Associative property is in the form:
(a + b) + c = a + (b + c)
The left side = right side
[tex]\begin{gathered} (32\div16)\div4\text{ = 32 }\div\text{ \lparen16}\div4) \\ Associative\text{ property was applied but the left side is not equal to the right side} \end{gathered}[/tex]That is why associative priperty is used for addition and multiplication
Find the inverse of the function. Is the inverse a function? Simplify your answer.F(x)=2x-1f^-1(x)=
Answers
The definition of the inverse function is
[tex]\begin{gathered} f(f^{-1}(x))=x \\ \text{and} \\ f^{-1}(f(y))=y \end{gathered}[/tex]In our case,
[tex]f(x)=2x-1[/tex]Then,
[tex]\begin{gathered} f^{-1}(f(x))=x \\ \Rightarrow f^{-1}(2x-1)=x \\ \Rightarrow f^{-1}(x)=\frac{x+1}{2} \end{gathered}[/tex]We need to verify this result using the other equality as shown below
[tex]\begin{gathered} f^{-1}(x)=\frac{x+1}{2} \\ \Rightarrow f(f^{-1}(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})-1=x+1-1=x \\ \Rightarrow f(f^{-1}(x))=x \end{gathered}[/tex]Therefore,
[tex]\Rightarrow f^{-1}(x)=\frac{x+1}{2}[/tex]The inverse function is f^-1(x)=(x+1)/2.
We say that a relation is a function if, for x in the domain of f, there is only one value of f(x).
In our case, notice that for any value of x, there is only one value of (x+1)/2=x/2+1/2.
The function is indeed a function, it is a straight line on the plane that is not parallel to the y-axis.
The inverse f^-1(x) is indeed a function
Jalen measured a bookcase to be 8.4 ft the actual measurement is 5.6 ft what is Gary percent error
Answers
We start by calculating the difference between the expected measured value and the value measured by Gary:
8.4 ft - 5.6 ft = 2.8 ft
Now we estimate what 2.8 ft is of the actual measurement 8.4 ft. That is:
2.8 / 8.4 = 0.33333... this is written in percent form as: 33.33%
This is the percent error.
George was painting a picture frame. The frame was 5inches wide & 3inches tall. What is the perimeter of the picture frame?
Answers
The perimeter can be calculated by adding the legnths off all 4 sides.
Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:
[tex]P=5+5+3+3=16[/tex]16 inches.
12x+18 rewrite using distributive property
Answers
we have
12x+18
REmember that
12=(2^2)*(3)
18=(2)*(3^2)
substitute
(2^2)*(3)x+(2)*(3^2)
Factor (2)*(3)=6
6(2x+3)
therefore
the answer is
6(2x+3)Evaluate the expression for the given variable values. (p+g) P-29 if p = 4 and q = 8-13-122024
Answers
We have the expression:
[tex]\frac{(p+q)^2}{p-2q}[/tex]We have to evaluate it for p = 4 and q = 8.
To do that, we replace the variables p and q with the given values and calculate:
[tex]\begin{gathered} f(p,q)=_{}\frac{(p+q)^2}{p-2q} \\ f(4,8)=\frac{(4+8)^2}{4-2\cdot8} \\ f(4,8)=\frac{12^2}{4-16} \\ f(4,8)=\frac{144}{-12} \\ f(4,8)=-12 \end{gathered}[/tex]Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]
Jenny makes money by mowing lawns. She can mow 8 lawns in 5 hours. At this rate, how long does it take her to mow 12 lawns?
Answers
Answer is 20 hours.
Given:
Jenny can make 8 lawns in 5 hours.
The objective is to calculate the time required for her to mow 12 lawns.
Consider the required time as t.
The rate of equation can be represented as,
[tex]\begin{gathered} r=\frac{12}{8} \\ r=4 \end{gathered}[/tex]Now, the time required can be calculated as,
[tex]\begin{gathered} r=\frac{t}{5} \\ 4=\frac{t}{5} \\ t=20\text{ hours} \end{gathered}[/tex]Hence, the time required for her to mow 12 lawns is 20 hours.
(MP Reason An internet company spends half their yearly profits on advertising for the next year. Of the remaining half, they spend 1/5 on new computers. What fraction of the total profits does the company spend on new computers? Use the number line to show how you can to make his bowl? Write an equati Harcourt Pub 4 find the fraction. 1 o Module 8. Lesson 3
Answers
Let the total profit be represented by 1
The internet company spends half their yearly profits on advertising for the next year. The amount of the profit spent on advertising is 1/2 = 0.5
The amount left is 1 - 0.5 = 0.5
Of the remaining half, they spend 1/5 on new computers. It means that the amount spent on new computers is
1/5 * 0.5 = 0.1 = 1/10
Therefore, the fraction of the total profits does the company spend on new computers is
0.1/1 = 0.1 = 1/10
The number line is shown below
graph f(x) = 2sin x
Answers
Explanation
We are given the function:
[tex]f(x)=2\sin x[/tex]We are required to graph the function above.
- Using a graphing calculator, we have:
For the function, f(x) = 38 • 0.24%, what is the decay factor? A) 38 B) 0.24 C) 0.14 D) 0.76
Answers
The decay factor is equal to 24%. In decimal form its equal to 0.24. Hence, the answer is B) 0.24
Nine hundred people who attended a movie were asked whether they enjoyed it. The table shows the results.Did Not EnjoyTotalChildrenAdultsTotalEnjoyed461277738114162900How many more children were surveyed than adults? Enter a numerical answer only
Answers
Given:
Total number of people that attended = 900
The total number of adults that attended = 277 + 114 = 391
Total number of children that attended = Total number of people - number of adults
= 900 - 391 = 509
To find how many more children were surveyed than adults, subtract the number of adults from the number of children.
Thus, we have:
Number of children surveyed than adults = 509 - 391 = 118
Therefore, 118 more children were surveyed more than adults.
Let's complete the table below:
ENJOYED DID NOT ENJOY TOTAL
CHILDREN 461
Status
Recovery
!!
Type here to search
Convert the following equation
into slope intercept form.
x-13y = 26
y = x -
Copyright ©ano-ana International Academy of Science. All Rights Reserved
10
Enter
Answers
Answer:
y=x+2
Step-by-step explanation:
x-13y=26
Bring the x to the other side
-13y=x+26
To get y by itself divide both sides by -13
-13y = x-26
----------- -----------
-13 -13
y=x+2
Logarithm 9) solve for P ( in terms of Q)Log (P - Q) = lop P - log Q
Answers
we have the expression
[tex]\text{log (P}-Q)=\log P-\log Q[/tex]Applying properties of log right side
[tex]\text{log (P}-Q)=\log (\frac{P}{Q})[/tex]Equate the numbers inside the parenthesis
[tex]P-Q=\frac{P}{Q}_{}[/tex]Solve for P
[tex]P-\frac{P}{Q}=Q[/tex][tex]P\lbrack1-\frac{1}{Q}\rbrack=Q[/tex][tex]P=\frac{Q}{\lbrack1-\frac{1}{Q}\rbrack}[/tex]Simplify
[tex]P=\frac{Q^2}{Q-1}[/tex]Use the given cost table for the same product from two different companies to create alinear system. Then solve the system to determine when the cost of the product will be thesame and what the price will be.Two online spice retailers sell paprika by the pound using the following pricing chart.Paprika (lb)iSpicei(x)SpiceMagics(x)1$19.75$65.252$34.50$49.25$76.50$87.7534$64.00$99.00i(x) =x + 5Sim)s(x) = 11.25x +forBoth iSpice and Spice Magic charge $pounds of paprika.
Answers
g(n) = 2n+6
c(n) = 2.25n+4
Both Chef Mate and Grocery Gourmet charge $22 for 8 ounces of vanilla extract.
From the question, we have
g(n) = 2n+6
c(n) = 2.25n+4
g(n) = c(n)
2n+6 = 2.25n+4
0.25n = 2
n = 8
g(n) = 2n+6
=2*8+6
=22
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
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The markings on the number line are evently spaced. Label the other markings on the number line. + + А B C -30 0 F 45 A= B = C = D = E = F=can someone please tell me the answers
Answers
The points are evenly spaced at a distance of 15 units between each other, then when we go to the right side of the graph from 0 we increase 15 units until we reach the point E, 15 units further we get to the point F, then we have the following labels:
E = 15
F = 15 + 15 = 30
As we got the left side from 0, we subtract 15 units for each marking, then we get:
D = 0 -15 = -15
C = -30 -15 = -45
B = -45 - 15 = -60
A = -60 - 15
Hello, I'm finding this a tad bit difficult.A little help please. Question 1a. Calculate the total are including the frame.Question 1b: Calculate the external perimeter of this picture frame.
Answers
Part a.
In the first part of the problem we need to calculate the total area including the frame, for this, we use the formula for the area of a parallelogram:
In this case, the values of a, b and c are:
[tex]\begin{gathered} a=42\operatorname{cm} \\ b=65\operatorname{cm} \\ c=0.39m=39\operatorname{cm} \end{gathered}[/tex]Thus, the area is:
[tex]\begin{gathered} A=65\operatorname{cm}\times39\operatorname{cm} \\ A=2,535\operatorname{cm}^2 \end{gathered}[/tex]2,535 centimeters squared.
Part b.
In this part, we are asked to find the external perimeter of the picture frame.
For this, we use the formula to find the perimeter of a parallelogram:
Substituting the values of a and b from part a into the perimeter formula:
[tex]\begin{gathered} P=2(a+b) \\ P=2(42\operatorname{cm}+65\operatorname{cm}) \\ P=2(107\operatorname{cm}) \\ P=214\operatorname{cm} \end{gathered}[/tex]The perimeter of the frame is 214 centimeters.
Answer:
A. Area
[tex]2,535\operatorname{cm}^2[/tex]B. Perimeter
[tex]214\operatorname{cm}[/tex]To find the equation of a regression line, ŷ = ax + b, you need these formulas:Sya=rstb=ỹ alA data set has an r-value of 0.553. If the standard deviation of the x-coordinates is 3.996, and the standard deviation of the y-coordinates is 6.203,what is the slope of the line to three decimal places?A. 0.858B. 1.165C. 2.807D. 0.356
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} r=0.553 \\ S_x=3.996 \\ S_y=6.203 \\ \\ \text{ We have been given that:} \\ a=r\frac{S_y}{S_x} \\ \\ \text{ Since }a\text{ is the slope, we have that:} \\ a=0.553\times\frac{6.203}{3.996} \\ \\ a=0.8584231...\approx0.858 \end{gathered}[/tex]Final Answer
The slope is 0.858
Answer:
.0858
Step-by-step explanation:
what is the equation of a line that passes through point (-1,5) and has the slope of m=4
Answers
The general equation of a line is given as;
[tex]y=mx+b[/tex]In this question, the slope (which is m) is given as 4. Also we have the points x and y, given as (-1, 5). That is;
[tex]x=-1,y=5[/tex]Therefore the next step is to find the y-intercept (that is b in the equation).
We substitute for the known values as follows;
[tex]\begin{gathered} y=mx+b \\ 5=4(-1)+b \\ 5=-4+b \\ \text{Add 4 to both sides} \\ 5+4=-4+4+b \\ 9=b \end{gathered}[/tex]Now we know the value of b and m, we can substitute them as follows;
[tex]\begin{gathered} y=mx+b \\ m=4,b=9 \\ y=4x+9 \end{gathered}[/tex]Dave wants to borrow $22,000 from first finance bank. the bank will give him a 15 year loan at an interest rate od 4.85 % how mich will he pay the bank in interest over the life of the loan? Round to the nearest hundred dollar ?
Answers
Problem 7:
We determine the time as follows:
*We can proceed using the following expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum she can afford to pay each month, p is the base loan value, r is the interest rate, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{500}{20000})-\ln(\frac{500}{20000}-\frac{0.071}{12})}{12\ln(1+\frac{0.071}{12})}\Rightarrow t\approx3.8[/tex]So, she will take approximately 3.8 years to pay up the loan.
Problem 8:
We determine the time he has as follows:
We use the expression:
[tex]t=\frac{\ln (\frac{m}{p})-\ln (\frac{m}{p}-\frac{r}{n})}{n\ln (1+\frac{r}{n})}[/tex]Here, t is the time it will take to pay, m is the maximum he can afford to pay each month, p is the base loan value, r is APR, n is the number of periods. Now we replace:
[tex]t=\frac{\ln(\frac{400}{14000})-\ln(\frac{400}{14000}-\frac{0.068}{12})}{12\ln(1+\frac{0.068}{12})}\Rightarrow t\approx3.3[/tex]So, he will take approximately 3.3 years to pay the loan.
Problem 10:
We determine the amount he will have to pay as follows:
*We use the following expression:
[tex]V=P(1+n)^t[/tex]Here V is the value to obtain, P is the original amount, n is the interest rate and t is the number of periods, now we replace:
[tex]V=(22000)(1-0.0485)^{15}\Rightarrow V\approx44766.09[/tex]So, after 15 years he will have to pay approximately $44766.09.
solve quadratic by completing the squarex^2 + 12x + 23 = 0which form do i use and solve(x+___)^2(x - ___) ^2solutionx = ___
Answers
Quadratics are in the general form:
[tex]ax^2+bx+c[/tex]For completing the square, we use:
[tex](x+\frac{b}{2})^2=c+(\frac{b}{2})^2[/tex]Now, we have:
[tex]\begin{gathered} (x+\frac{12}{2})^2=-23+(\frac{12}{2})^2 \\ (x+6)^2=-23+(6)^2 \\ (x+6)^2=13 \end{gathered}[/tex]From here, we can easily solve for x with a little algebra. Shown below:
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\pm\sqrt[]{13} \\ x+6=\pm\sqrt[]{13} \\ x=-6\pm\sqrt[]{13} \end{gathered}[/tex]The answer(s) are:
[tex]\begin{gathered} x=-6+\sqrt[]{13} \\ x=-6-\sqrt[]{13} \end{gathered}[/tex]For further clarification
Form:
[tex](x+\frac{12}{2})^2=13[/tex]