The expression of the mathematical statement is a ≤ 10
How to represent the mathematical statement as an expression?From the question, we have the following mathematical statement that can be used in our computation:
a is less than or equal to 10
The key statement less than or equal to in mathematics and algebra can be represented using the following symbol
less than or equal to ⇒ ≤
So, we have the following representation
a is less than or equal to 10 ⇒ a is ≤ 10
This implies that we rewrite the above expression as follows
So, we have
a is less than or equal to 10 ⇒ a ≤ 10
The above expression cannot be further simplified
So, we leave it like that
Hence, the mathematical statement when expressed as an expression is a ≤ 10
Read more about word problems at
https://brainly.com/question/29223808
#SPJ1
Rapheal is traveling in a straight line at a constant speed from point A to point B. His distance from point B in miles is -20t + 45, where t is the number of hours he has been traveling. What is his speed in miles per hour?
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
A and B are the two points of a straight line.Distance between two points is given as :d₀ = -20t + 45 miles
t = the number of hours of travelling.The starting time = 0
i.e. the initial position = 0
Then
we put t=0
At t=0
d₀ = -20(0) + 45
= 0 + 45
= 45 miles
the distance travel after starting first hour is :
T= d₁ & d₀
than we put t = 1
At t = 1;
d₁ = -20(1) + 45
= -20 + 45
= 25 miles
now
Difference between d₁ & d₀ is
d = d₁ - d₀
45 - 25 = 20 miles
Total distance covered = 20 miles
To find the speed we use formula:
Speed = distance/time
Speed=20/1
Speed = 20 miles/hour
Rapheal is traveling in a straight line. Its speed in miles per hour is 20 miles per hour.
To know more about speed
https://brainly.com/question/22537052
#SPJ1
Solve the inequality |3x+3| + 3 > 15Write the answer in interval notation
Solution:
Given the inequality:
[tex]|3x+3|+3>15[/tex]To solve the inequality,
step 1: Add -3 to both sides of the inequality.
Thus,
[tex]\begin{gathered} |3x+3|+3-3>-3+15 \\ \Rightarrow|3x+3|>12 \end{gathered}[/tex]Step 2: Apply the absolute rule.
According to the absolute rule:
[tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex]Thus, from step 1, we have
[tex]\begin{gathered} 3x+3<-12\text{ or 3x+3>12} \\ \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3<-12 \\ add\text{ -3 to both sides of the inequality} \\ 3x-3+3<-3-12 \\ \Rightarrow3x<-15 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}<-\frac{15}{3} \\ \Rightarrow x<-5 \end{gathered}[/tex][tex]\begin{gathered} when \\ 3x+3>12 \\ add\text{ -3 to both sides of the inequality} \\ 3x+3-3>12-3 \\ \Rightarrow3x>9 \\ divide\text{ both sides by the coefficient of x, which is 3} \\ \frac{3x}{3}>\frac{9}{3} \\ \Rightarrow x>3 \end{gathered}[/tex]This implies that
[tex]x<-5\quad \mathrm{or}\quad \:x>3[/tex]Hence, in interval notation, we have:
[tex]\left(-\infty\:,\:-5\right)\cup\left(3,\:\infty\:\right)[/tex]A cattle train left the station and traveled toward New York at an average speed of 41.4 mph. A passenger train left 5.6 hours later and traveled in the opposite direction with an average speed of 22.5 mph. How long does the passenger train need to travel before the trains are 513 mi. apart?
You have the following information:
- Average speed of cattle train to New York: 41.4 mph
- Average speed of passenger train: 22.5 mph
- The passenger train left in the opposite direction, 5.6 hour after cattle train started its travel.
In order to determine how long does the passenger need to travel before the trains are 513 mi apart, you take into account that you can express the previous situation in an algebraic way. If you consider x as the distance traveled by cattle train in a time t, the you have:
x = vt = (41.4)t = 41.4 t
Now, if you consider x' as the distance traveled by the passenger train in the opposite direction in a 5.3h after the left of cattle train, you have:
x' = v't = (22.5)(t + 5.3) = 22.5 t + 119.25
Next, if you are interested in the time on which passengers and cattle train will be separated by 513 mi, then you can write:
x - (-x') = 513 Here, you specify the distance between both trains are 513
x + x' = 513
The minussign of -x' is due to the fact the passengers trains goes in the opposite direction.
Then, by replaacing the expressions for x and x' you obtain:
(41.4t) + (22.5t + 119.25) = 513
Now, you can simplify the previous expression, and solve it for t:
41.4t + 22.5t + 119.25 = 513
63.9t = 513 - 119.25
63.9t = 393.75
t = 393.75/63.9
t = 6.16
Hence, both trains will be at a distance of 513 mi apart between them, after 6.16 hours
The surface area of the solid cone requiring paint rounded to the nearest whole number is how many square centimeters?
In order to calculate the surface area of the cone, first let's calculate its slant height.
If the diameter is 5 cm, the radius is 2.5 cm. Now, using the Pythagorean theorem, we can calculate the slant height s:
[tex]\begin{gathered} s^2=h^2+r^2 \\ s^2=11.4^2+2.5^2 \\ s^2=129.96+6.25 \\ s^2=136.21 \\ s=11.67\text{ cm} \end{gathered}[/tex]Now, we can calculate the surface area using the formula below:
[tex]\begin{gathered} S=\pi rs+\pi r^2^{} \\ S=\pi\cdot2.5\cdot11.67+\pi\cdot2.5^2 \\ S=29.175\pi+6.25\pi \\ S=35.425\pi \\ S=111.29\text{ cm}^2 \end{gathered}[/tex]Rounding to the nearest square centimeter, we have a surface area of 111 cm².
Find the cube roots of 4−6i4−6iShow all your work.Include an explanation and diagram showing how DeMoivre's Theorem helps to solve this problem.
Given the following complex number
[tex]z=4-6i[/tex]We will find the cube root of the complex number using the following formula:
[tex]^3\sqrt{z}=\sqrt[3]{|z|}*(cos\text{ }\frac{\theta+2\pi k}{3}+i*sin\text{ }\frac{\theta+2\pi k}{3})[/tex]The formula is called De Moivre's theorem of the nth root
We have substituted n = 3
So, first, we will convert the given number from the rectangular form to the polar form
[tex]\begin{gathered} |z|=\sqrt{4^2+6^2}\approx7.211 \\ \theta=tan^{-1}\frac{-6}{4}=303.7\degree \end{gathered}[/tex]Substitute the magnitude and the angle and k = 0, 1, 2
So, there are 3 cubic roots of the given number as follows:
[tex]\begin{gathered} k=0\rightarrow z_1=\sqrt[3]{7.211}(cos\frac{303.7}{3}+i*sin\frac{303.7}{3})=1.932(cos101.23+i*sin101.23) \\ \\ k=1\rightarrow z_2=\sqrt[3]{7.211}(cos\frac{303.7+2\pi}{3}+i*sin\frac{303.7+2\pi}{3})=1.932(cos221.23+i*sin221.23) \\ \\ k=2\rightarrow z_3=\sqrt[3]{7.211}(cos\frac{303.7+4\pi}{3}+i*sin\frac{303.7+4\pi}{3})=1.932(cos341.23+i*sin341.23) \end{gathered}[/tex]For f(x) = 2x+1 and g(x) = x² − 7, find (f+ g)(x).
Given the functions:
[tex]\begin{gathered} f(x)=2x+1 \\ \\ g(x)=x^2-7 \end{gathered}[/tex]By definition, (f+g)(x) is equivalent to:
[tex](f+g)(x)=f(x)+g(x)[/tex]Finally, using the expressions for f and g:
[tex]\begin{gathered} f(x)+g(x)=2x+1+x^2-7 \\ \\ \therefore(f+g)(x)=x^2+2x-6 \end{gathered}[/tex]a portion of the graph of f(x) = -x^2 - 2x +8 is shown. which of the following describes all solutions for f(x)?
Given the function:
[tex]f(x)=-x^2-2x+8[/tex]Let's determine the expression which describes the solution for f(x).
From the graph, we can see the x-values go from -5 to 3.
The expression which describes the solution will be:
[tex](x,-x^2-2x+8),where-5\leq x\leq3[/tex]ANSWER:
[tex](x,-x^{2}-2x+8), where-5\leqslant x\leqslant3[/tex]Which angles are adjacent to each other? Select all that apply.
Answer:
I think it's all the options but I cant confirm.
Step-by-step explanation:
adjacent angles are angles that:
- have the same vertex
- share one side
E is the midpoint of DF, DE = 2x + 4 and EF = 3x - 1 how do I find the value of x, DE, EF and DF
We know that
E is midpoint of DF, that means DE is equal to EF, so we can form the following equation
[tex]DE=EF[/tex]Replacing the given equations, we have
[tex]\begin{gathered} 2x+4=3x-1 \\ 4+1=3x-2x \\ x=5 \end{gathered}[/tex]Now, we replace this value in each equation to find each part of the segment.
[tex]\begin{gathered} DE=2x+4=2(5)+4=10+4=14 \\ EF=3x-1=3(5)-1=15-1=14 \end{gathered}[/tex]Therefore, each part of the segment is 14 units, and DF is 28.What is the digit in the units place of the sum of 1^1+ 2^2+ 3^3+ 4^4 +.....+ 99^99 + 100^100?
Let us write down first few factors
1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256
5^5 = 3125
6^6 = 46656
.
.
.
100^100 = ... finish in zero
The last two digits in the sum would be 20
The digit in the unit would be 0
I thought this answer was the sixth root, cubed, value of 16. But I am not sure so I need help with the question
In order to find the correct options, we need to know the following property:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]So, rewriting the expression 243^(3/5), we have:
[tex]243^{\frac{3}{5}}=\sqrt[5]{243^3}[/tex]That is, 243^(3/5) is the 5th root of 243 cubed. Its value is:
[tex]\sqrt[5]{243^3}=\sqrt[5]{14348907}=27[/tex]If these two figures are similar, what is the measure of the missing angle?
If the two figures are similar, then the missing angle equals 70°.
Solve for y Simplify your answer as much as possible Find by linear equation.
Given the equation:
[tex]-7=\frac{3y+7}{4}-\frac{9y-5}{2}[/tex]We will solve the equation to find y
Multiply the equation by 4 to eliminate the denominators
[tex]\begin{gathered} 4(-7)=4\cdot\frac{3y+7}{4}-4\cdot\frac{9y-5}{2} \\ \\ -28=(3y+7)-2(9y-5) \\ -28=3y+7-18y+10 \end{gathered}[/tex]Combine the like terms
[tex]\begin{gathered} -28=(3y-18y)+(7+10) \\ -28=-15y+17 \\ \end{gathered}[/tex]Subtract (17) to both sides
[tex]\begin{gathered} -28-17=-15y+17-17 \\ -45=-15y \end{gathered}[/tex]Divide both sides by (-15)
[tex]\begin{gathered} \frac{-45}{-15}=\frac{-15y}{-15} \\ \\ y=3 \end{gathered}[/tex]So, the answer will be y = 3
farm stand has cherries on 2 shelves. Each shelf has 4 boxes. Each box has 8 ounces of cherries. How many ounces of cherries are displayed in all? Write an expression that represents the amount.
64 ounces of cherries are displayed in all in the farm stand.
According to the question,
We have the following information:
Farm stand has cherries on 2 shelves.
Number of boxes in each shelf = 4 boxes
So, the number of boxes in 2 shelves will be (2*4) or 8.
Ounces of cherries in each box = 8 ounces
Now, the ounces of cherries in 8 boxes can be easily found by multiplying the ounces of cherries in 1 box by the number of total boxes.
Ounces of cherries in 8 boxes = (8*8) ounces
Ounces of cherries in 8 boxes = 64 ounces
Now, the expression that represents the amount is (number of shelves*number of boxes*ounces of cherries in each box).
Hence, the ounces of cherries displayed in all is 64 ounces.
To know more about cherries here
https://brainly.com/question/17179286
#SPJ1
An electronics store sends an email survey to all customers who bought tablets. The previous month, 570 people bought tablets. Surveys were sent to 300 of these people, chosen at random, and 138 people responded to the survey. Identify the population and the sample. (4 points)The population is 570. The sample is 138.The population is 570. The sample is 300.The population is 300. The sample is 138.The population is 138. The sample is 570.The population is 138. The sample is 300.
Answer:
The population is 300. The sample is 138.
Explanation:
In statistics, population refers to the entire group of persons or things that a study is to be carried out on. Looking at the given question, we can see that, even though there were 570 people that bought tablets, the surveys were only sent to 300 people chosen at random. It shows that only 300 of the 570 people are to be surveyed, therefore, the population is 300.
A sample is the particular/specific group of persons or things that data is to be received from.
Looking at the given question, we can see that, out of the 300 people that the surveys were sent to, only 138 people responded to the survey. So the sample is 138.
Michael annual salary is 39,110 and has a budget of 26%of annual salary for housing what is the most that Michael may spend on monthly rent
Since each year has 12 months, divide the annual salary by 12 to find the monthly salary. Then, multiply it by 26/100 to find the amount of money that Michael may spend.
[tex]\frac{39,110}{12}\times\frac{26}{100}=847.38333\ldots[/tex]Therefore, the most that Michael ay spend on monthly rent, is approximately:
[tex]847.38[/tex]which part of the aldr braiding expresses 3 + 7 D is the c o e f f i n c i e n t
the coefficient is the number that accompanies the variable, so:
[tex]3+7D[/tex]The coefficient is 7
Audrey was attempting to draw a picture that would be the cover of the upcoming movie, Up 2. Thepicture would be of the house being carried by balloons again. She started her drawing with theballoons, which she wanted to make all the same size.She drew a circle for the balloon and found the radius, which was 9cm. How big around will all ofAudrey's balloon drawings be?——Please help me.
Audrey drew a circle for the balloon, this circle has a radius of 9 cm.
To know how big the baloon is you have to determine its circumference.
To calculate the circumference of a circle you have to multiply its diameter by number pi:
[tex]C=d\pi[/tex]The formula is C=dπ
The diameter is twice the circle so the diameter of the baloon is:
[tex]\begin{gathered} d=2r \\ d=2\cdot9 \\ d=18\operatorname{cm} \end{gathered}[/tex]The calculation for the diameter is:
d=2r
d=2*9
d=18cm
So the circumference of a circle with diameter 18cm is:
[tex]\begin{gathered} C=18\pi \\ C\cong56.548\operatorname{cm} \end{gathered}[/tex]For this balloon:
C=18π
C≅56.548xm
Consider the graph of the linear function shown.What is the approximate average rate of change of this function from = -2 to r = 2?lesleso3-Yes
The average rate of change of this function from x = -2 to x = 2 can be gotten by finding the slope of the line using both x coordintes;
From the graph, when x1 = -2, y1 = 2.5
Also when x2 = 2, y2 = 0.5
Using the formula for calculating slope expressed as;
m = y2-y1/x2-x1
Substitute the given values
m = 0.5-2.5/2-(-2)
m = -2.0/2+2
m = -2/4
m = -1/2
Hence average rate of change of this function from x = -2 to x = 2 is -1/2. Option C is correct.
geometry special parallelogramsSide GH =Side JG =Side FH =
we have that
In a rhombus the length sides are congruent
the diagonals bisect each other and are perpendicular
so
If mmIn the right triangle IFJ
mtan(30)=FJ/IJ
Remember that
[tex]\tan (30^o)=\frac{\sqrt[]{3}}{3}[/tex]FJ=4
substitute the given values
[tex]\begin{gathered} \frac{\sqrt[]{3}}{3}=\frac{4}{IJ} \\ \\ IJ=\frac{12}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=4\sqrt[]{3} \end{gathered}[/tex]Find the length side IF
Applying Pythagorean Theorem
IF^2=4^2+IJ^2
IJ^2=48
IF^2=16+48
IF^2=64
IF=8 units
that means
side GH=8 units
side JG=side IJ=4√3 units
side FH=2*side FJ=2*4=8 units
The illustration below shows the graph of y as afunction of xComplete the following sentences based on thegraph of the function.(Enter the x-intercepts from least to greatest.)* This is the graph of a (nonlinear, linear orconstant) function.* The y-intercept of the graph is the function value y = ___.The x-intercepts of the graph (in order from leastto greatest) are located at x = ___ and x = ___.* The greatest value of y is y = ___ and it occurswhen x = ___.* For x between x = 2 and x = 6, the function value y (<, 2, or =) 0.
* This is the graph of a (nonlinear, linear or constant) function.
Answer:
This is the graph of a nonlinear function (In this case it is a quadratic function).
--------------------------------------------------------------------------------------
The y-intercept of the graph is the function value y =
Answer:
From the graph we can conclude that, the y-intercept is:
[tex]y=-6[/tex]----------------------------------------------------------------------------
The x-intercepts of the graph (in order from least to greatest) are located at x = ___ and x = ___.
Answer:
From the graph, we can conclude that the x-intercepts are located at:
[tex]\begin{gathered} x=2 \\ and \\ x=6 \end{gathered}[/tex]----------------------------------------------------------------------
The greatest value of y is y = ___ and it occurs
Answer:
From the graph, we can see that the vertex of the function is:
[tex]\begin{gathered} y=2 \\ when \\ x=4 \end{gathered}[/tex]----------------------------------------------------------------
For x between x = 2 and x = 6, the function value y is.
Answer:
For those values, y is always greater than or equal to 0, so:
[tex]2\le x\le6\to y\ge0[/tex]Find the distance between the points (4,1) and (2,4) using distance formula
Given:-
[tex](4,1)(2,4)[/tex]To find the distance.
So the distance formula is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting we get,
[tex]\begin{gathered} d=\sqrt{(2-4)^2+(4-1)^2} \\ d=\sqrt{-2^2+3^2} \\ d=\sqrt{4+9} \\ d=\sqrt{13} \end{gathered}[/tex]So the required distance is root 13.
At a party 15 handshakes took place. Each person shook hands exactly once with each of the other present. How many people were at the party?
2 people => 1 handshake (AB)
3 people => 3 handshakes (AB, BC, AC)
4 people => 6 handshakes (AB, AC, AD, BC, BD, CD)
Do you see a pattern here?
We can write a general formula for this
[tex]handshakes=\frac{n\cdot(n-1)}{2}[/tex]Since we are given that there were 15 handshakes
[tex]15=\frac{n\cdot(n-1)}{2}[/tex][tex]\begin{gathered} 2\cdot15=n\cdot(n-1) \\ 30=n\cdot(n-1) \\ 30=6\cdot(6-1) \\ 30=6\cdot(5) \\ 30=30 \end{gathered}[/tex]This means that n = 6 people were present at the party.
You can substitute n = 6 into the above formula and you will notice that it will give 15 handshakes
[tex]handshakes=\frac{n\cdot(n-1)}{2}=\frac{6\cdot(6-1)}{2}=\frac{6\cdot5}{2}=\frac{30}{2}=15[/tex]A bookshelf holds 5 novels, 4 reference books, 3 magazines, and 2 instruction manuals.
Teacher example 1: In how many ways can you choose one reference book or one instructional manual?
# of reference books + # of instructional manual - # of options that are both 4 + 2 Ways to choose a reference book OR an instruction manual?
You try: In how many ways can you choose a magazine or a reference book? # of magazine + # of reference book - # of options that are both mag and reference book
Ways to choose a magazine or a reference book?
This is so confusing to me. any help would be amazing, 100 points!! help as soon as possible
We can choose one reference book or one instructional manual from the bookshelf in 48 different ways.
Given,
Number of novels = 5
Number of reference books = 4
Number of magazines = 3
Number of instruction manuals = 2
Total number of books = 5 + 4 + 3 + 2 = 14 books
We have to find the number of ways of choosing one reference book or one instructional manual.
Number of ways = 4! x 2!
Number of ways = 24 x 2
Number of ways = 48
That is,
We can choose one reference book or one instructional manual from the bookshelf in 48 different ways.
Learn more about number of ways here;
https://brainly.com/question/20357322
#SPJ1
Which number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
Pls help me :( thx ur the best
Answer:
here you go, but when you go to Kumon you should do the work that they give you, it helps in the long run I promise
----from a former Kumon student, now I grade papers for Kumon
Please mark Brainiest
Answers to page 1 -2
1) 1 1/2
2) 1 1/8
3) 32/63
4) 1 3/40
5) 31/60
6) 11/35
7) 11/35
8) 17/20
9) 1 1/24
10) 27/28
11) 5/6
12) 1/4
Answers to page 3-4
1) 13/24
2) 1 2/45
3) 11/20
4) 2/3
5) 4/5
6) 5/21
7) 1 1/35
8) 67/72
9) 52/165
10) 23/36
11) 9/10
12) 5/6
Those are all the answers. btw the slashes are the line between the fractions if u get what I mean. :)
how many shirts can Jeanette sew at most of and still have 1. spool of thread left
Answer:
The number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Explanation:
Given a graph that relates the number of spools of thread left to the number of shirts sewn.
We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.
To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.
Tracing the line down we can observe that it is at shirt sewn equals 5.
So, the number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]4. Martin was asked to solve the following system of equations. Hegraphed the two equations below, and decided that the answer was"infinitely many solutions". Do you agree with Martin? Why or why not? Ifyou disagree, what should the answer be?*y=-x-3y=-***+3
Types of solutions in a system of equations:
Based on this image, we can see that when they are parallel lines (same slope), there is no solution because the lines never touch.
The type of solution Martin was describing is when the lines are the same (letter b in the image) and it looks like one line when graphed.
Answer: We disagree with Martin because the lines never touch, meaning that the system has no solutions.
An equation is incorrectly solved below.Equation: 2x+3=-4step 1: 2x+3-3=-4-3step 2: 2x=-1step 3: 2x/2=-1/2step 4: x=-1/2What is the first step that shows an error in the solution of the Equation? A. Step 1B. Step 2C. Step 3D. Step 4
To find the step where the error was made, we are going to correctly solve the equation:
[tex]2x+3=-4[/tex]We need to solve for x, first we subtract 3 from each side:
[tex]\begin{gathered} 2x+3-3=-4-3 \\ 2x=-7 \end{gathered}[/tex]We divide by 2 each side:
[tex]\begin{gathered} \frac{2x}{2}=\frac{-7}{2} \\ x=-\frac{7}{2} \end{gathered}[/tex]The first step that shows an error in the solution of the equation is the Step 2, because when we have two negative numbers, we add them, we do not subtract them.
Answer: B. Step 2
In New York, the tax on a property assessed at $520,000 is $10,400. If tax rates are proportional in this city, how much would the tax be on a property assessed at $370,000? Answer: $
Given that the tax on a property assessed at $520,000 is $10,400 and the tax
