2 + m > 10
substituting with m = 7, we get:
2 + 7 > 10
9 > 10
which is false, because 9 is less than 10
The length of the longest slide is what inches the other two sides will each be what inches in length?
We know that the rod from which we made the triangle is 13 in long, this means that the perimeter of the triangle. from the diagram given we notice that the perimeter is:
[tex]x+(x-1)+(x-1)[/tex]equating this to 13 and solving for x we have:
[tex]\begin{gathered} x+(x-1)+(x-1)=13 \\ 3x-2=13 \\ 3x=13+2 \\ 3x=15 \\ x=\frac{15}{3} \\ x=5 \end{gathered}[/tex]Hence, the value of x=5 which means that the longest side measure 5 inches. To determine the length of the other sides we notice that they are given by x-1, which means that their length is 5-1=4 inches,
Therefore, the length of the longest side is 5 inches. The other two sides will each be 4 inches in length.
What is 7050.387 rounded to the nearest ten
Hello!
When we round something to the nearest tenth, it means that the number must have just one decimal place.
Let's analyze this number and round it:
7050.387
How can we write 387 as one number?
Well, it's very close to 400, and we can "hide" these zeros.
Let's try it:
[tex]7050.387\cong7050.400\cong7050.4\cancel{00}[/tex]Answer:7050.4.
Identify the algebraic expression for the given word phrase.
6 times the sum of r and 9
A. 6 + r + 9
B. 6 (r + 9)
C. r (6 + 9)
D. 6r + 9
b because 6 times the sum of r and 9 means 6(r+9)
(3,-8),(-2,5) write an equation for the line in point slope form .Then rewrite the equation in slope intercept form
The equation for the line in point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1, y1) is a point of the line. If we have two points (x1,y1) and (x2, y2), the slope is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, replacing (3, -8) and (-2, 5), we get that the slope and the equation of the line are:
[tex]m=\frac{5-(-8)}{-2-3}=\frac{5+8}{-5}=\frac{-13}{5}[/tex][tex]\begin{gathered} y-(-8)=\frac{-13}{5}(x-3) \\ y+8=-\frac{13}{5}(x-3) \end{gathered}[/tex]Therefore, the equation in slope-intercept form is calculated as:
[tex]\begin{gathered} y+8=-\frac{13}{5}x-\frac{13}{5}\cdot(-3) \\ y+8=-\frac{13}{5}x+\frac{39}{5} \\ y=-\frac{13}{5}x+\frac{39}{5}-8 \\ y=-\frac{13}{5}x-\frac{1}{5} \end{gathered}[/tex]Answer: Point-slope form:
[tex]y+8=-\frac{13}{5}(x-3)[/tex]slope-intercept form:
[tex]y=-\frac{13}{5}x-\frac{1}{5}[/tex]...
>
Question
A triangle with area 40 square inches has a height that is four less than six times the width. Find the width and height of the
triangle
Provide your answer below:
width:
inches, height:
inches
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SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the formula for the area of the triangle
[tex]Area=\frac{1}{2}\times base\times height[/tex]STEP 2: Represent the statements to get an equation
[tex]\begin{gathered} width=base \\ From\text{ the statement,} \\ six\text{ times of the width}=6w \\ four\text{ less than six times the width }=6w-4 \\ \therefore height=6w-4 \end{gathered}[/tex]STEP 3: Substitute into the formula in step 1
[tex]\begin{gathered} height=6w-4,width=base=w,Area=40in^2 \\ Area=\frac{1}{2}\times w\times(6w-4) \\ Area=\frac{w(6w-4)}{2}=\frac{6w^2-4w}{2}=40 \end{gathered}[/tex]STEP 4: Cross multiply
[tex]\begin{gathered} 6w^2-4w=40\times2 \\ 6w^2-4w=80 \\ Subtract\text{ 80 from both sides} \\ 6w^2-4w-80=80-80 \\ 6w^2-4w-80=0 \\ Divide\text{ through by 2, we have:} \\ 3w^2-2w-40=0 \\ By\text{ factorization;} \\ 3w^2-12w+10w-40=0 \\ 3w(w-4)+10(w-4)=0 \\ (w-4)(3w+10)=0 \end{gathered}[/tex]STEP 5: Find the values of w
[tex]\begin{gathered} w-4=0,w=0+4,w=4 \\ 3w+10=0,3w=0-10,3w=-10,w=\frac{-10}{3} \\ \\ Since\text{ the width cannot be negative, width=4 inches} \end{gathered}[/tex]STEP 6: Find the height
[tex]\begin{gathered} Recall\text{ from step 2:} \\ h=6w-4 \\ Substitute\text{ 4 for w} \\ h=6(4)-4=24-4=20in \end{gathered}[/tex]Hence,
width = 4 inches
height = 20 inches
why you can always solve a right triangle if you know the measures of one side and one acute angle.
In a right triangle, one angle is always 90.
If you know one acute angle, you automatically know the other (3rd) angle.
3 angles are solved.
Now, comes the sides.
If you already know 1 side, you can easily know another side by using the basic trig identities SIN, COS, or TAN.
When you know 2 sides, the 3rd side can always be find using:
• pythagorean theorem, or
,• again, trigonometric ratios (sin, cos, tan).
What makes a function a function?
In a relationship between two variables x and y, the data set is a function, if every element of the domain corresponds to exactly one element of the range
that means
one element of x corresponds to exactly one element of y
In any function, there is an input value (independent variable or x variable) and there is an output value (dependent variable or y variable)
What makes a function a function? ------> one element of the input (variable x) corresponds to exactly one element of the output (variable y)
The mass of a typical comet is about 1 x 10¹3 kg, while the mass of a typical asteroid is about 3 x 10¹⁹ kg.
Approximately how many times the mass of a typical comet is the mass of a typical asteroid?
100,000 times
300,000 times
1,000,000 times
O 3,000,000 times
The mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
It is given in the question that:-
Mass of a typical comet = [tex]1*10^{13}kg[/tex]
Mass of a typical asteroid = [tex]3*10^{19}kg[/tex]
We have to find the how many times the mass of a typical comet is the mass of a typical asteroid.
Mass of a typical asteroid/ Mass of a typical comet is given by:-
[tex]\frac{3*10^{19}}{1*10^{13}}=3*10^6[/tex]
We can write [tex]3*10^6[/tex] as 3,000,000.
Hence, the mass of the typical comet is 3,000,000 times the mass of a typical asteroid which is the fourth option among the given options.
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Graph the equation. y = 2x 20 N 18 16 14 12 10 8 6 4 N. 0 1 2 3 4 ул 6 10 2. y = 2x
Make a table, and give values to x.
Solve the equation and obtain y values.
Graph the points and join them:
x = 0
y= 2x = 2 (0) = 0
x= 2
y= 2(2) = 4
x= 4
y= 2(4) = 8
Graph:
Brainliest and 20 points please solve
Answer:
part a: x = 5
part b: no
Step-by-step explanation:
part a : 8x + 3 = 9x - 2, subtract 8x from both sides which leaves you with 1x or just x. add 2 to both sides which gives you 5. 5 is equal to 1x.
part b: a complementary angle is 2 angles whos sum equals 90 degrees. m<ABC = 43 & m<DBE = 43 & they both equal 86 not 90.
Answer/Step-by-step explanation:
A C
\ (8x + 3) /
\ /
\ /
\ /
B
/ \
/ \
/ \
/ (9x - 2) \
D E
A. Solve for x.
m∠ABC = m∠DBE
(8x + 3) = (9x - 2)
8x + 3 = 9x - 2
-9x -9x
------------------------
-x + 3 = -2
-3 -3
--------------------
-x = -5
÷-1 ÷-1
----------------
x = 5
B. Are vertical angles also complementary angles?
No, vertical angles are angles that are congruent to each other or in other words, equal. In the equation above (8x + 3) = (9x - 2). If I were to plug 5 into the equation I would get
(8(5) + 3) = (9(5) - 2)
(40 + 3) = (45 - 2)
43 = 43
Complementary angles equal to 90°. It wouldn't make sense to add these numbers together because I would end up with a fraction if I set the equation equal to 90°
I hope this helps!
Rectangle WXYZ has vertices located at W(−6, 4), X(−6,−1), Y(2,−1), and Z(2, 4) on a coordinate plane. It is translated 4 units right and 2 units down to produce rectangle W'X'Y'Z'. What is the location of the vertices of the transformed rectangle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Rectangle WXYZ
W(−6, 4)
X(−6,−1)
Y(2,−1)
Z(2, 4)
Step 02:
Translated
4 units right ===> x + 4
2 units down ===> y - 2
W' (−6+4, 4 -2) = W' (-2, 2)
X' (−6+4,−1 - 2) = X' (-2,-3)
Y' (2+4,−1-2) = Y' (6,-3)
Z' (2+4, 4-2) = Z' (6, 2)
The answer is:
W' (-2, 2)
X' (-2,-3)
Y' (6,-3)
Z' (6, 2)
9(11 - x) = 3(3x -9) what is x
x = 7
Explanation:9(11 - x) = 3(3x -9)
Expanding the expression:
9(11) - (9x) = 3(3x) -3(9)
99 - 9x = 9x - 27
collect like terms:
99 + 27 = 9x + 9x
126 = 18x
Divide both sides by 18:
126/18 = 18x/18
x = 7
You have two spinners each with three sections of equal size labeled with numbers 1,2,3. You spin both and observe the numbers. Let x be the sum of the two numbers. Find the probability distribution for X.
From the given problem with two spinners with three sections of equal size labeled as 1, 2, and 3.
Spinner 1 : 1 2 3
Spinner 2 : 1 2 3
The sum is as follows :
1+1 = 2
1+2 = 3
1+3 = 4
2+1 = 3
2+2 = 4
2+3 = 5
3+1 = 4
3+2 = 5
3+3 = 6
There are 9 total outcomes
There are (1) 2,
(2) 3's
(3) 4's
(2) 5's
and
(1) 6
and their corresponding probability can be calculated by :
[tex]\text{probability}=\frac{\text{ quantity}}{\text{ total quantity}}[/tex]Probability of 2 = 1/9
Probability of 3 = 2/9
Probability of 4 = 3/9 or 1/3
Probability of 5 = 2/9
Probability of 6 = 1/9
Construct the probability distribution :
To check if your probability distribution is correct.
The sum of P(X) must be equal to 1
1/9 + 2/9 + 1/3 + 2/9 + 1/9 = 1
Therefore the distribution is correct.
Students were divided into 10 teams with 12 on each team. later, the same day students were divided into teams with 3 on each team. how many teams were there then?
At first, the students were divided into 10 teams with 12 on each of them; we can write this as:
team 1 = 12 students
team 2 = 12 students
team 3 = 12 students
team 4 = 12 students
team 5 = 12 students
team 6 = 12 students
team 7 = 12 students
team 8 = 12 students
team 9 = 12 students
team 10 = 12 students
Sum up the number all the students and this adds up to: 120 students.
Then, the question says these 120 students were divided into teams with 3 students on each team.
This time the number of teams created will be more.
team 1 = 3 students
team 2 = 3 students
teams 3 = 3 students
...
And so on.
In order to get the number of teams, we simply divide the number of students by the number of students in a team.
[tex]\frac{120}{3}=40\text{ teams}[/tex]Therefore, the number of 3 person teams are 40 teams
hi I'm 9 years old my name is Emma can
Given:
Perimeter = 40 feet,
The measure of the four sides is 11 feet, g, 11 feet, and g.
We know that the perimeter = the sum of the four sides.
[tex]\text{perimeter =11+g+11+g}[/tex]Replace perimeter =40, we get
[tex]\text{40=11+g+11+g}[/tex]Adding 11 and 11, we get
[tex]\text{40=11+11+g+g}[/tex][tex]\text{40=22+g+g}[/tex]if RS=2x+6 ST=x+4 and RT= 40 Find RS
RS + ST = RT
Substituting with data,
2x + 6 + x + 4 = 40
(2x + x) + (6 + 4) = 40
Consider the following equation find the X- and y- Intercepts, if possible
Answer:
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
Explanation:
The x-intercept is the point where the graph crosses the x-axis, so to find the x-intercept, we need to replace y = 0 on the given equation and solve for x
y - 2x = 1
0 - 2x = 1
-2x = 1
-2x/(-2) = 1/(-2)
x = -1/2
Then, the x-intercept is (-1/2, 0)
The y-intercept can be calculated replacing x = 0 and solving for y, so
y - 2x = 1
y - 2(0) = 1
y - 0 = 1
y = 1
Then, the y-intercept is (0, 1)
Therefore, the answers are
x-intercept: (-1/2, 0)
y-intercept: (0, 1)
if the author sells x Books per day his profit will be : J(X)= (-0.001x^2)+3x-1800Find the max profit per dayFind the amount of books the author must sell for the most profit
The given function in a quadratic function in standard form where
a = -0.001, b = 3, and c = -1800
It is a parabola that is facing downwards, therefore, the vertex of this parabola, (x,y) is the maximum of the function where
x is the amount of books that the author must sell for the most profit, and
y is the max profit per day.
We can find the vertex using
[tex]x=\frac{-b}{2a}[/tex]Substitute the following values, and we get
[tex]\begin{gathered} x=\frac{-b}{2a} \\ x=\frac{-3}{2(-0.001)} \\ x=\frac{-3}{-0.002} \\ x=1500 \end{gathered}[/tex]Now that we have x, plug it in the original function to solve for y
[tex]\begin{gathered} J(x)=\mleft(-0.001x^2\mright)+3x-1800 \\ J(1500)=-0.001(1500)^2_{}+3(1500)-1800 \\ J(1500)=-2250+4500-1800 \\ J(1500)=450 \end{gathered}[/tex]We have determine that the vertex of the function is at (1500,450). We can now conclude that
The max profit per day is $450.
The amount of of books the author must sell for the most profit is 1500 books.
What is the slope of a line parallel to the line whose equation is 5x-3y=18
Slope and slant both refer to an incline away from a reference surface or line that is generally straight.The definition of slope is "a vertical inclination in an oblique direction"Here, the land abruptly slopes either upward or downhill.
How to Determine a Line's Slope?
slope,The inclination of a line with respect to the horizontal is measured numerically.The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). To determine how much the y coordinates have changed, find the difference.To determine how much the x coordinates have changed, find the difference.Find the slope by dividing y by x.
Y=mx+b, where m is the slope and b is the y-intercept, is the slope-intercept form.
y=mx+b
Change the formula to 3y+18=5x.
−3y+18=5x
From both sides of the equation, deduct 18.
−3y=5x−18
Simplify by multiplying each term in 3y=5x18 by 3.
Subtract 3 from each term in 3y=5x18.
−3y/−3=5x/−3+−18/−3
Make the left side simpler.
Tap to take additional steps:Y= -5X/3+-18/-3
Make the right side simpler.
Tap to take additional steps: y=5x/3+6
Write in the form y=mx+b.
Tap to take additional steps: y=5/3x+6
The slope is- 5/3 using the slope-intercept form.
.
m=−5/3
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What is the diameter of a circle with radius 15
Given Data:
The radius of the circle is r=15.
The diameter of the circle can be determined as,
[tex]\begin{gathered} d=2r \\ =2\times15 \\ =30 \end{gathered}[/tex]Thus, the required diameter of a circle is 30.
find a b c d e f from the picture
Given data:
The value of a is (3+4+2)=9
The value of b is (5+1+2)=8
The value of c is (1+8+1)=10
The value of d is (
DEF is a right triangle. If FE= 12 and DE= 5, find DF.
Answer:
DF = 13
Explanation:
The Pythagoras theorem says that
[tex]FE^2+ED^2=DF^2[/tex]Now in our case,
FE = 12
ED =
Hello, a little confused on this section. Thanks for your help!
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
notation for domain and range:
we must analyze the graph to find the solution.
graph:
The domain is reflected on the x-axis and the range is reflected on the y-axis.
Inequality / Agebraic:
D:
R:
Interval:
D:
R:
Set-Builder:
D:
R:
help meeeeeeeeee pleaseee !!!!!
If the average daily sales price of the toy is $6.50, then 2750 toys will have been sold overall.
Variables and functionsIn the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
While the dependent values are the codomain, the independent values are known as the domain.
Given that y = 6000 - 500x is the function that depicts the price-sales relationship for the quantity of toys
The total number of toys sold if the toy sells for $6.50 per day is: y = 6000 - 500 (6.50) y = 6000 - 3250 y = 2750 toys
The total quantity of toys sold is provided above.
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Josh wants to use Rockaway Hall, the Groove Guru Band, and PJ's Party Supplies. Josh has a total of
650 dollars and wants to invite 25 people. His friend told him he would be able to afford the band for 4 hours. Is that true?
1) Assume that x is the number of hours and that y is the total cost. To model, write an equation. 2) Tutoring his friend in geometry is the second way he can get money.
One of the first areas of mathematics is geometry, along with arithmetic.
What is the Bernoulli inequality?A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used. It contains a few helpful variations, including those for any integer r 0 and real number x > 1. If x 0 and r 2, the inequality is strictly true.A statement about raising a number to a natural power is made by the binomial inequality: and. It can be easily demonstrated by induction and is essentially a condensed version of the binomial theorem.A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used.To learn more about Bernoulli inequality refer to:
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Solve the following system of linear equations by graphing.{5x - 2y = 10 {x - y = -1 Graph the equations on the same set of axes.Note: Use different points on each line when plotting the graphs.The solution point is: (_, _)
Kindly Check below
1) The first thing we need to do in this question, is to pick the method we are going to use to solve this system. Let's use the Elimination Method.
2) So, let's solve this system analytically (algebraically):
[tex]\begin{gathered} 5x-2y=10 \\ x-y=-1\:\:(\times-2) \\ \\ 5x-2y=10 \\ -2x+2y=2 \\ ------- \\ 3x=12 \\ \\ \frac{3x}{3}=\frac{12}{3} \\ \\ x=4 \end{gathered}[/tex]Now, let's plug into the 2nd original equation x=4 and solve it for y:
[tex]\begin{gathered} x-y=-1 \\ \\ 4-y=-1 \\ \\ -y=-1-4 \\ \\ y=5 \end{gathered}[/tex]So we know the solution is (4,5).
3) Now, let's graph these equations by setting two t-tables. Let's rewrite those equations from the Standard form to the Slope-intercept form.
5x-2y=10 -2y=10-5x, y=-5+5/2x
x-y=-1,-y=-1-x, y=x+1
4) Now, let's plot those points and trace the lines through them
(-2,-10), (-1,-7.5), (0,-5), (1,-2.5), (2,0)
(-2,-1), (-1,0), (0,1), (1,2), (2,3)
you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight how much should it weigh by then round to the nearest whole number
The weight of the pigs is 220.8 pounds.
How to calculate the value?From the information, when you raise pigs when you purchase the pig it weigh 46 pounds with in 5-6 months you pig will gain 380% in weight.
Therefore, the weight by then will be:
= Normal weight + ( Percentage × Previous weight)
= 46 + (380% × 46)
= 46 + 174.8
= 220.8
The weight is 220.8 pounds.
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There are 6000 students at Mountain High School, and 1/4 of these students are seniors. If 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students (not seniors) are also in favor of forming a debate team how many students do not favor this idea?
hello
tp solve this question, let's get the data out
we have a total of 6000 students. 1/4 of the students are seniors, let's find the numbers of seniors in the school
the number of senior students are
[tex]\frac{1}{4}\times6000=1500[/tex]we have 1500 seniors in the school.
we can find the seniors in support of a debate team by multiplying 2/3 by 1500
[tex]\frac{2}{3}\times1500=1000[/tex]now we know that 1000 students are in support of the debate team. let's subtract the numbers of students in support of debate team from numbers of seniors in the schoolto giveus the numbers of seniors that are not in support of debate team.
[tex]1500-1000=500[/tex]500 seniors from the school are not in support of a debate team.
Also note that 1/5 of the remaining students are not in support of the debate team.
which would be
[tex]\begin{gathered} 6000-1500=4500 \\ \frac{1}{5}\times4500=900 \end{gathered}[/tex]now, we can add the numbers of seniors that are not in support of a debate team plus number of remaining students not in support of a debate team
[tex]500+900=1400[/tex]from the calculationabove, a total of 1400 students are not in support of the idea
In college, we study large volumes of information- information that, unfortunately, we go not often retain for very long. The function f(x) = 80e +20 describes the percentage of information, fx), that a particular person remembers x weeks after learning the information. a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for x and find the percentage of information remembered after 1 week C. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after 1 year.
a)
[tex]f(0)=80\cdot e^{-0.5\cdot0}+20=100[/tex]b)
[tex]f(1)=80\cdot e^{-0.5}+20=68.52[/tex]c)
[tex]f(4)=80\cdot e^{-0.5\cdot4}+20=30.82[/tex]d)
[tex]f(48)=80\cdot e^{-0.5\cdot48}+20=20[/tex]Identify the value for C in the following equation that would make theconic section a hyperbola: 2x2 + y2 + 3x + 5y + 1 = 0
ANSWER:
C = -1
STEP-BY-STEP EXPLANATION:
We know that the general formula of hyperbola is the following
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Which means that the sign must have y must be negative for it to be a hyperbola.
Therefore y must be equal to -1.
[tex]2x^2-1y^2+3x+5y+1=0[/tex]