Using the order of operation which states
[tex]\begin{gathered} B\Rightarrow Bracket \\ O\Rightarrow Orders \\ D\Rightarrow Division \\ M\Rightarrow Multilication \\ A\Rightarrow Addition \\ S\Rightarrow Subtraction \end{gathered}[/tex]Expressions in brackets/parentheses are evaluted first, followed by expressions involving orders, division, multiplication, addition and subtraction in that order.
Thus,
1)
[tex]\begin{gathered} 3+(7-5)2\times6\text{ = ?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 3+(2)2\times6 \\ \text{Evaluate expressions involving multiplication,} \\ 3+24 \\ \text{Add up the expressions,} \\ 3+24\text{ = 27} \end{gathered}[/tex]thus, 3+(7−5)2×6 = 27
2)
[tex]\begin{gathered} 25\mleft(4+4\mright)\times2=\text{?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 25(8)\times2 \\ \Rightarrow400 \end{gathered}[/tex]thus, 25(4+4)×2 = 400
3)
[tex]\begin{gathered} 8-6\div2+3\times5\text{ = ?} \\ \text{Evaluate expressions involving division. thus,} \\ 8-3+3\times5 \\ \text{Evaluate expressions involving multipliation. thus,} \\ 8-3+15 \\ \text{Evaluate expressions involving addition. thus,} \\ 8+12 \\ \text{Add up the terms,} \\ 8+12\text{ = 20} \end{gathered}[/tex]thus, 8−6÷2+3×5 = 20
4)
[tex]\begin{gathered} 7\times3-15\div5=\text{ ?} \\ \text{Evaluate expressions involving division. thus,} \\ 7\times3-3 \\ \text{Evaluate expressions involving multiplication. thus,} \\ 21-3 \\ \text{Subtract the terms,} \\ 21-3\text{ = }18 \end{gathered}[/tex]thus, 7×3−15÷5 = 18
5)
[tex]\begin{gathered} 8+2\mleft(1+12\div2\mright)2=\text{ ?} \\ \text{Evaluate the terms in parentheses. thus,} \\ 8+2\times\: 7\times\: 2 \\ \text{Evaluate the terms involving multiplication. thus,} \\ 8+28 \\ \text{Add up the terms,} \\ 8+28\text{ = }36 \end{gathered}[/tex]thus, 8+2(1+12÷2)2 = 36.
NO LINKS!! Use the method of substitution to solve the system. (If there's no solution, enter no solution). Part 6z
Answer:
(-1, 7, - 4)(1, -1, 4)=====================
Given systemx² + z² = 174x + y = 3y + z = 3Rearrange the last two equation4x = 3 - yz = 3 - yThis gives us:
z = 4xSubstitute the value of z into fist equationx² + (4x)² = 17x² + 16x² = 1717x² = 17x² = 1x = 1 and x = - 1Find values of z and yx = 1 ⇒ z = 4*1 = 4 ⇒ y = 3 - 4 = - 1 x = - 1 ⇒ z = 4*(-1) = - 4 ⇒ y = 3 - (-4) = 7Answer:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x^2+z^2=17\\\;4x+y=3\\\;\;\;y+z=3\end{cases}[/tex]
To solve by the method of substitution, first rearrange the third equation to make y the subject:
[tex]\implies y=3-z[/tex]
Substitute this into the second equation and solve for z:
[tex]\begin{aligned}\implies 4x+(3-z)&=3\\3-z&=3-4x\\-z&=-4x\\z&=4x\end{aligned}[/tex]
Substitute the found expression for z into the first equation and solve for x:
[tex]\begin{aligned}\implies x^2+(4x)^2&=17\\x^2+16x^2&=17\\17x^2&=17\\x^2&=1\\x&=\pm1\end{aligned}[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}\implies x=-1 \implies 4(-1)+y&=3\\-4+y&=3\\y&=7\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies 4(1)+y&=3\\4+y&=3\\y&=-1\end{aligned}[/tex]
Substitute the found values of x into the derived expression for z and solve for z:
[tex]\begin{aligned}\implies x=-1 \implies z&=4(-1)\\z&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies x=1 \implies z&=4(1)\\z&=4\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y,z)=\left(\; \boxed{-1,7,-4} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y,z)=\left(\; \boxed{1,-1,4} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Consider the scenario: A town’s population has been decreasing at a constant rate. In 2010 the population was 5800. By 2012 the population had dropped to 4,600. Assume the trend continues predict the population in 2016.
Given:
In 2010 the population was 5800.
2012 the population had dropped to 4,600.
Let 't=0' be the year 2010.
P(t) represents the year population of the town t years after 2010.
Slope of a function P(t) is
[tex]\begin{gathered} m=\frac{4600-5800}{2012-2010} \\ m=-600 \end{gathered}[/tex]Population of town t years after 2010.
[tex]P(t)=-600(t)+5800[/tex]Population in the year 2016 that is t=6
[tex]\begin{gathered} P(6)=-600(6)+5800 \\ =2200 \end{gathered}[/tex]Population in the year 2016 is 2200
find the area, to the nearest thousandth, of the standard normal distribution between the given z-scores. z= 1 and z= 1.9
The area, to the nearest thousandth, of the standard normal distribution between the z-scores z= 1 and z= 1.9 is 0.130
find the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval. Leave your answer in terms of n, the number of subintervals.
Explanation
The area under a curve between two points can be found by doing a definite integral between the two points
Step 1
a) set the intergral
[tex]\begin{gathered} limits:\text{ 1 and 2} \\ function:\text{ f\lparen x\rparen=6-2x} \end{gathered}[/tex]hence
[tex]Area=\int_1^26-2x[/tex]Step 2
evaluate
let ; numbers of intervals
[tex]\begin{gathered} \begin{equation*} \int_1^26-2x \end{equation*} \\ \int_1^26-2x=\lbrack6x-x^2\rbrack=(12-4)-(6-1)=8-5=3 \end{gathered}[/tex]therefore, the area is
[tex]area=3\text{ units }^2[/tex]
I hope this helps you
The graph of f(x) = x² is translated to formg(x) = (x-2)2-3.--5-4-3-2-1-2+Which graph represents g(x)?#
Step 1
Plot the graph of f(x)
[tex]f(x)=x^2[/tex]Step 2
The function of g(x) suggests that f(x);
[tex]\begin{gathered} 1)\text{ it was moved 2 units towards the right} \\ 2)\text{ It was then moved 3 units down} \end{gathered}[/tex]Thus, the graph of g(x) will look like this;
Answer;
help me please!! (10 pts)
(2,3) (4,6) (6,9) (8,12) is the set of ordered pair lie on the function that is direct proportion.
Direct proportion is mathematical comparison between two variable
when one increase also increase the other or one decrease also decreases the other then , they are direct proportion.
In direct proportion , the ratio of these variable remains same no matter what.
The following are the set of ordered pair,
a. (2,6) (4,8) (6,10) (8,12)
calculating ratio,
[tex]\frac{2}{6} = \frac{1}{3} \neq \frac{4}{8} = \frac{1}{2}[/tex]
Ratio is changing so, ordered pair are not direct proportion
b. (2,2) (4,2) (6,2) (8,2)
ratios = [tex]\frac{2}{2} =1 \neq \frac {4}{2} = 2[/tex]
Ratio is different
c. (2,1) (4,3) (6,5) (8,7)
Ratio is different , the ordered set is not direct proportion
d. (2,3) (4,6) (6,9) (8,12)
ratios = [tex]\frac{2}{3}=\frac{4}{6}[/tex]
Ratios are same in entire ordered set
Hence , (2,3) (4,6) (6,9) (8,12) is a direct proportion.
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Is the expression 4sr2(2rs + 3s) completely factored? Complete the sentence with the correct explanation.
The expression 4sr²(2rs + 3s) is not completely factored.
How to factor an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
In other words, an expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
An expression is completely factored when no further factoring is possible.
Therefore, let's check if the expression is completely factored.
4sr²(2rs + 3s)
The expression still have a common factor which is s. This means its not completely factored.
The complete factorisation is as follows;
4sr²(2rs + 3s) = 4s²r²(2r + 3)
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find x=, if x-3=13 please
Answer:
[tex]x - 3 = 13 \\ \\ x = 13 + 3 \\ \\ x = 16[/tex]
-3 goes to other side and changes into +3
in DEF, K is the centroid. If KH=12 find DH
the lines that cross the centroid are divided into 2 by this the short line corresponds to 1/3 of the complete line and the long line corresponds to 2/3 of the complete line
so KH is 1/3 of DH
if KH=12, then
[tex]\begin{gathered} DH=3KH \\ DH=3\times12 \\ DH=36 \end{gathered}[/tex]the value of DH is 36
Hi!A particle moves along a straight line, so its speed is () = ^2 − + 6, where t is the time measured in seconds and the speed is measured in meters timessecond.a) Calculate the distance traveled between the seconds t=1 and t=3
In this problem
the distance traveled between the seconds t=1 and t=3 is given by
[tex]\int_1^3(t^2-t+6)dt=\frac{50}{3}\text{ m}[/tex]The answer is
50/3 metersor 16.67 metersExplanation of integrals
In this problem we have
[tex]\int_1^3(t^2-t+6)dt=\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt[/tex][tex]\begin{gathered} \int_1^3t^2dt=\frac{t^3}{3} \\ Evaluate\text{ at 3 and 1} \\ \frac{(3)^3}{3}-\frac{1^3}{3}=\frac{27}{3}-\frac{1}{3}=\frac{26}{3} \end{gathered}[/tex][tex]\begin{gathered} -\int_1^3tdt=-\frac{t^2}{2} \\ evaluate\text{ at 3 and 1} \\ -\frac{3^2}{2}+\frac{1^2}{2}=-\frac{9}{2}+\frac{1}{2}=-4 \end{gathered}[/tex][tex]\begin{gathered} \int_1^36dt=6t \\ evaluate\text{ at 3 and 1} \\ 6(3)-6(1)=12 \end{gathered}[/tex]substitute
[tex]\int_1^3t^2dt-\int_1^3tdt+\int_1^36dt=\frac{26}{3}-4+12=\frac{50}{3}[/tex]Which Venn diagram correctly shows the relationships between the subsets of rational numbers?
By definition, consider that natural numbers are all numbers from 1 to infinity. Whole numbers are the same natutal numbers plus zero. Integers are all numbers from minus infinity to infinity and rational are all number with finite decimals, and periodic infinite decimals.
Then, based on the previous description, the diagram which correctly shows the subsets of rational numbers is:
diagram F.
I tested positive for covid yesterday so i have no motivation to do this problem. Please don’t be slow when answering, I am every tired.
The value of sector KL is 52
If JM and KN are two diamters of the circle,
then they intersect at the center
The sector JK and NM are equal
Thus,
The sector JN and KM are also equal
sector KM = sector KL + sector LM
Sector JN = Sector KM
sector JN = sector KL + sector LM
125 = 6x + 4 + 8x + 9
125 = 14x + 13
14x = 125 - 13
14x = 112
x = 8
sector KL = 6x + 4
= 6(8) + 4 = 48 + 4 = 52
Therefore, the sector KL is 52
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WILL GIVE BRAINLEST! I NEED HELP ASAPPP! The highest score on an Algebra test was 40 points more than the lowest. When added together, the lowest and highest score was 152. Write an equation to find the highest score, then solve.
A= x + x + 40 = 152; 56
B= x + x = 152; 76
C= x + x - 40 = 152; 96
D= x + x + 40 = 152; 96
Answer:
D is correct.
Step-by-step explanation:
Let x be the lowest score. Then x + 40 is the highest score.
[tex]x + x + 40 = 152[/tex]
[tex]2x + 40 = 152[/tex]
[tex]2x = 112[/tex]
[tex]x = 56[/tex]
[tex]x + 40 = 96[/tex]
Lowest score is 56, highest score is 96.
14. John rides his motorcycle for 0.2 hours with a constant speed of 68 km/h and then foranother 13 minutes with a constant speed of 102 km/h. What is his average speed for thetotal trip?
We must calculate the weighted average as follows:
[tex]\begin{gathered} \frac{68\cdot0.2+102\cdot\frac{13}{60}}{0.2+\frac{13}{60}} \\ \frac{13.6+22.1}{0.416}=85.68 \\ \end{gathered}[/tex]Therefore, the average speed is 85.68 km/h
the circumference of a circular garden is 109.9 feet. what is diameter of the garden? use 3.14 and do not round your answer.
The circumference of a circle is given by the formula:
[tex]C=\pi d[/tex]Where d is the diameter of the circle.
If the circumference is 109.9 ft, we have:
[tex]\begin{gathered} 109.9=3.14\cdot d \\ d=\frac{109.9}{3.14} \\ d=35\text{ ft} \end{gathered}[/tex]So the diameter of the garden is 35 feet.
Suppose a binomial trial has a probability of success of 0.3 and 450 trials are performed. What is the standard deviation of the possible outcomes?6.3614.8511.629.72
The standard deviation of a binomial distribution with n trials and a probability of success of p is given by the formula:
[tex]\sigma=\sqrt[]{n\cdot p\cdot(1-p)}[/tex]From the problem, we identify:
[tex]\begin{gathered} n=450 \\ p=0.3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} \sigma=\sqrt[]{450\cdot0.3\cdot(1-0.3)}=\sqrt[]{450\cdot0.3\cdot0.7} \\ \sigma\approx9.72 \end{gathered}[/tex]How do I get to the answer of this question?
Okay, here we have this:
Considering the provided information, and that we must identify which of the provided options allow us to determine that the two triangles are similar, we obtain the following:
As the angle-angle similarity says that if two angles of one triangle are congruent with two angles of another triangle, then the triangles are similar.
Finally, we see that the only option that satisfies this statement is option D, since it indicates that two angles of the triangles are congruent. Therefore the correct option is D.
Given Point A, what is the coordinate for A' after the following transformation has occurred?LaTeX: \left(x,y\right)\rightarrow\left(x-5,\:-y+2\right)A (5, 7)Al.
Given:
The point A(5, 7).
To given transformation is (x-5, -y+2).
So,
The new point is,
[tex]A^{\prime}(5-5,-7+2)=A^{\prime}(0,-5)[/tex]Therefore, the coordinate for A' after the given transformation has occured is A'(0,-5).
what is the surface area, in square centimeters, of the pyramid ?
Find the values of x and y in the equation below.a³b4a²b= a*b²X=
To divide, subtract exponents to same base variables.
[tex](ab^3)^6[/tex]Multiply exponents of exponents
[tex]a^6b^{18}[/tex]x= 6
y= 18
Hello I need help with this I’m in a rush thanks
Recall that:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)},[/tex]and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.
If f(x)=5x+3 and g(x)=4x-5 we get that:
[tex]\frac{f}{g}(x)=\frac{5x+3}{4x-5}\text{.}[/tex]The domain of the above rational function is:
[tex]\begin{gathered} \mleft\lbrace x|g(x)\ne0\mright\rbrace=\lbrace x|4x-5\ne0\rbrace \\ =\lbrace x|4x\ne5\rbrace=\lbrace x|x\ne\frac{5}{4}\rbrace\text{.} \end{gathered}[/tex]Answer: Last option.
The graph of a quadratic function with vertex (-1,4) is shown in the figure below. Write the domain and range in interval notation.
Background:
• Domain,: a set of all possible values of the independent variable (,x,, in this case).
,• Range,: a set of all possible values of the dependent variable (,y,, in this case), after substituting the domain.
Based on the arrows of the function, we can conclude that those extend to infinity (negative and positive).
Also, based on the coordinates of the vertex given we can see that the first value of y is 4.
Answer:
• Domain
[tex](-\infty,\infty)[/tex]• Range
[tex](4,\infty)[/tex]A toy factory makes 5.7 x 10³ toys each day.At this rate, how many toys will be made in 9 days?Express the answer in scientific notation.
First We will put the number of toys per day in simple form:
[tex]5.7\times10^3=5.7\times1000=5700[/tex]Then, to know how many toys will be made in 9 days, let's multiply the number of toys per day by the given number of days:
[tex]5700\times9=51300[/tex]Now We will put the number in scientific notation:
[tex]5.13\times10^4[/tex]The sum of two numbers is 200 and their difference is 28.What are the two numbers?
Let us assume the numbers are x and y.
The first part of the question can be written as
[tex]x+y=200\text{ ---------------(1)}[/tex]and the second part can be written as
[tex]x-y=28\text{ --------------(2)}[/tex]From equation 1, we can get a value for y as
[tex]y=200-x\text{ -------------(3)}[/tex]Substitute for y in equation 3 into equation 2:
[tex]x-(200-x)=28[/tex]Expanding and solving, we get
[tex]\begin{gathered} x-200+x=28 \\ 2x=200+28 \\ 2x=228 \\ \therefore \\ x=\frac{228}{2} \\ x=114 \end{gathered}[/tex]Next, we substitute for the value of x into equation 3:
[tex]\begin{gathered} y=200-114 \\ y=86 \end{gathered}[/tex]Therefore, the two numbers are 114 and 86
At t seconds after launch is given by the function… how long will it take the rocket to reach its maximum height? What is the maximum height?
Given:
The height equation is,
[tex]h(t)=-16t^2+144t+6[/tex]Explanation:
For maximum/minimum of a function, the first derivative of function is 0.
Differentiate the function with respect to x.
[tex]\begin{gathered} \frac{d}{dt}h(t)=\frac{d}{dt}(-16t^2+144t+6) \\ =-32t+144 \end{gathered}[/tex]For maximum and minimum,
[tex]\begin{gathered} -32t+144=0 \\ t=\frac{144}{32} \\ =4.5 \end{gathered}[/tex]So rocket reach it maximum height after 4.5 seconds of launch.
Substitute 4.5 for t in the equation to determine the maximum reached by rocket.
[tex]\begin{gathered} h(4.5)=-16(4.5)^2+144\cdot4.5+6 \\ =-324+648+6 \\ =330 \end{gathered}[/tex]So maximum height of rocket is 330 feet.
Josslyn has nickels and dimes in her pocket. The number of nickels is three more than seven times the number of dimes let d represent the number of dimes. Write the expression for the number of nickels
to solve this we need to translate into math terms, so
Step 1
a) let d represents the number of dimes
let n represents the number of nickles
so
re write the expressions
[tex]\begin{gathered} number\text{ of dimes=d} \\ seven\text{ times the number of dimes = 7d} \\ \end{gathered}[/tex]The number of nickels is three more than seven times the number of dimes in other words you have to add 7 to seven times the number of dimes to obtain the number of nickles
hence
[tex]n=7d+3[/tex]therefore , the expression for the number of nickles is
[tex]7d+3[/tex]I hope this helps you
I need help with this problem if anyone want to help me please do thanks
Solve e from the equation by substraction 96 to both sides of the equal sign:
[tex]undefined[/tex]Solve the radical equation.9-6=27-29What is the extraneous solution to the radical equation?O 1O 9Both 1 and 9 are extraneous solutions to the equation.O There are no extraneous solutions to the equation.
Given the radical equation:
[tex]q-6=\sqrt[]{27-2q}[/tex]Squaring both sides to eliminate the root.
[tex]\begin{gathered} (q-6)^2=27-2q \\ q^2-12q+36=27-2q \\ q^2-12q+2q+36-27=0 \\ q^2-10q+9=0 \end{gathered}[/tex]Factor the equation to find the roots:
[tex]\begin{gathered} (q-1)(q-9)=0 \\ q-1=0\rightarrow q=1 \\ q-9=0\rightarrow q=9 \end{gathered}[/tex]we will check ( q = 1 and q = 9 ) by substitution into the given equation:
When q = 1
[tex]\begin{gathered} q-6=1-6=-5 \\ \sqrt[]{27-2q}=\sqrt[]{27-2}=\sqrt[]{25}=5 \end{gathered}[/tex]So, ( q = 1 ) is an extraneous solution.
When q = 9
[tex]\begin{gathered} q-6=9-6=3 \\ \sqrt[]{27-2q}=\sqrt[]{27-18}=\sqrt[]{9}=3 \end{gathered}[/tex]So, ( q = 9 ) is the solution of the given equation.
So, the answer will be:
The extraneous solution to the radical equation is 1
Using the slope formula, find the slope of the line through the points (0, 0) and (5, 20).
The slope formula for 2 points is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(5,20) \end{gathered}[/tex]By substituting these values into the slope formula, we get
[tex]\begin{gathered} m=\frac{20-0}{5-0} \\ m=\frac{20}{5} \\ m=4 \end{gathered}[/tex]therefore, the slope is 4.
1. Find the surface area and volume of box where: L = 31.59ft, W = 24.98ft and H = 43.23ft.
ANSWER
[tex]\begin{gathered} A=6469.28ft^2 \\ V=34113.58ft^3 \end{gathered}[/tex]EXPLANATION
The surface area of the box (rectangular prism) is:
[tex]A=2(LW+WH+LH)[/tex]where L = length; W = width; H= height
Therefore, we have that the surface area of the box is:
[tex]\begin{gathered} A=2\lbrack(31.59\cdot24.98)+(24.98\cdot43.23)+(31.59\cdot43.23)\rbrack \\ A=2\lbrack(789.1182)+(1079.8854)+(1365.6357)\rbrack \\ A=2(3234.6393) \\ A\approx6469.28ft^2 \end{gathered}[/tex]The volume of the box is:
[tex]V=L\cdot W\cdot H[/tex]Therefore, the volume of the box is:
[tex]\begin{gathered} V=31.59\cdot24.98\cdot43.23 \\ V\approx34113.58ft^3 \end{gathered}[/tex]