Answer:
perimeter of a triangle is the total
Step-by-step explanation:
p=48cm
Length=3x
width=x
Now P= 2(L+W)
48 =2(3x+x)
48=2(4x)
48=8x
dividing both sides by 8
we have x=6
and so length=18 and width =6
is -0.25 a rational number
Answer:
Yes
Step-by-step explanation:
please help with this it is a final
austin wants to pour 71.26 grams of salt into a container so far he has poured 23.1 How much more salt should Austin pour?
Answer:
Your answer is 48.16 grams.
Austin needs to pour 48.16 grams of salt.
Here the total amount of salt is 71.26 grams.
But he pours 23.1 grams.
So when we minus 71.26-23.1, it is equal to 48.16 grams.
Therefore, Austin needs to pour 48.16 grams of salt.
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A group spends $277.50 to rent 15 tubes for a float down the Ichetucknee River. One person tubes cost $12.50 and two person tubes cost $20. How many of each type of tube does the group rent?
The number of One-person tubes and two-person tubes is 3 and 12 respectively.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
A group spends $277.50 to rent 15 tubes for a float down the Lchetucknee River. One-person tubes cost $12.50 and two-person tubes cost $20.
The equation can be written as,
12.5x + 20y = 277.5
Here, x is the number of One-person tubes and y is two-person tubes.
Also, x + y = 15
Solve the above equation by elimination method,
x = 3 and y = 15 - 3 = 12
Therefore, the number of One-person tubes and two-person tubes is 3 and 12 respectively.
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need help and show all work.
Step-by-step explanation:
that is a college question ?
oh my ...
to clarify :
perpendicular means intersecting or touching at a right angle (90°).
bisector means it is a line that cuts the other line in half.
1.
because of the bisector this means DF = FC = DC/2.
so, since FC = 17, so is DF (=y) = 17.
2.
for the same reason
2x - 3 = x + 8
x - 3 = 8
x = 11
the angle must be 90°.
so,
5y = 90
y = 18
3.
for the same reason
10 = 4a
a = 10/4 = 2.5
4.
for the given reasons of 1-3, this figure is a kite. that means the left side is a mirror image of the right side. so, all the lengths on one side are equation to the lengths of the other side.
x - 11 = 19
x = 30
5.
for the same reasons
3y + 5 = 26
3y = 21
y = 7
6.
the perimeter of EDP is then
EP + DP + ED = 19 + 19 + (9 + 9) = 56
because ED = EC + CD
and for the above reasons EC = CD = 9
so, ED = 9 + 9 = 18
7.
the perimeter of EDQ is then
EQ + DQ + ED = 26 + 26 + 18 = 70
8.
for the same reasons as above
x = 90°
9.
remember, the sum of all angles in a triangle is always 180°.
180 = 90 + 55 + y
y = 180 - 90 - 55 = 35°
10.
180 = y + M + z = 35 + (55+71) + z = 161 + z
z = 180 - 161 = 19°
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=√t, y=t^2−2t; t=4
The equation of the tangent to the given curve x = t⁴ + 3 , y = t³ + t at the corresponding point is y = x - 2 .
In the question ,
it is given that ,
the parametric equation is x = t⁴ + 3 , y = t³ + t ,
differentiating with respect to t ,
we get ,
dx/dt = 4t³ and dy/dt = 3t² + 1
On dividing dx/dt by dy/dt to get the slope ,
we get
dy/dx = (3t² + 1)/ (4t³)
Substituting in t=1
dy/dx = (3 + 1)/4 = 1
Slope (m) = 1 ;
Substituting t = 1 , in the parametric equation ,
we have , x = 4 and y = 2 .
So , (y - 2) = 1(x - 4)
y - 2 = x - 4
y = x - 2
Therefore , the equation of the tangent is y = x - 2 .
The given question is incomplete , the complete question is
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = t⁴ + 3 , y = t³ + 3 ; t = 4 ?
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A sample of 200g of an isotope decays to another isotope according to the function A(t)=200 e⁰.⁰⁵⁴⁺
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
The amount of sample after 25 years and the half life are given as 51.8 g and 12.83 years respectively.
How to find the decay rate of an exponential function?An exponentially decaying function has a general form f(x) = (1 -r)ˣ, where r is called the decay rate. it can be found by having any two values of x for which f(x) is known.
The given function for the decay of an isotope is given as A(t) = 200[tex]e^-0.054t[/tex].
Now, the given problem can be solved as follows,
(a) The amount of sample after 25 years is given as,
A(25) = 200[tex]e^{-0.054 \times 25}[/tex]
= 200[tex]e^{-1.35}[/tex]
= 200 × 0.259
= 51.8
(b) The half life can be calculated as,
100 = 200[tex]e^{-0.054t}[/tex]
=> [tex]e^{-0.054t}[/tex] = 1/2
=> t = 12.83
Hence, the sample left after 25 years will be 51.8 g and it will take 12.83 years for the sample to decay to half of its amount.
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find the point at which the given lines intersect find a n equation of the plamn tjat cpontains these lines
The point at which the given lines intersect is (6,0,2) and an equation of the plane that contains these lines is x+y=6.
(a) In the given question we have to find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2]
r = [6,0,2] + s[-3,3,0]
The equations of the lines can be written as :
The points for first line is
L(1)⟹x=3+3t, y=3-3t, z=0+2t and
The points for second line is
L(2)⟹x=6-3s , y=0+3s , z=2+0s .
Set the z coordinates equal from the line one and two, and we get :
2t = 2
Divide by 2 we get
t=1 .
Substitute the value of t into the point of x of first line :
x=3+3(1)
x=3+3
x=6
Equating the value of x equal to the coordinate of x of line two
6=6-3s
Subtract 6 on both side, we get
-3s=0
s=0
Now substitute the value of t into the point of y of first line:
y=3-3(1)
y=3-3
y=0
Equating the value of y equal to the coordinate of y of line two
0=0+3s
s=0
Now substitute the value of t into the point of z of first line:
z=0+2(1)
z=2
Equating the value of z equal to the coordinate of z of line two
2=2+0(s=0)=2 .
We thus have the point of intersection is :
P=(x,y,z)
P=(6,0,2)
Hence, the point at which the given lines intersect is (6,0,2)
(b) The direction vector for the first line is
[tex]\vec{v_{1}}=3\hat{i}-3\hat{j}+2\hat{k}[/tex]
and the direction vector for the second line is
[tex]\vec{v_{2}}=-3\hat{i}+3\hat{j}+0\hat{k}[/tex]
We can find a normal vector to the line as :
[tex]\vec{N_{1}}=\vec{v_{1}}\times\vec{v_{2}}[/tex]
[tex]\vec{N_{1}}=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\-3 &3 &-2 \\ -3 &3 & 0 \end{vmatrix}[/tex]
[tex]\vec{N_{1}}=\hat{i}(0-(-6))-\hat{j}(0-6)+\hat{k}(-9-(-9))[/tex]
[tex]\vec{N_{1}}=6\hat{i}+6\hat{j}[/tex]
is a normal vector
But , we can also use
[tex]\vec{N}=\frac{\vec{N_{1}}}{6}[/tex]
[tex]\vec{N}=\hat i+\hat j[/tex]
as the normal vector to the plane .
We can thus use the point P=(6,0,2) and the normal vector [tex]\vec{N}=\hat i+\hat j[/tex] to write the equation of the plane :
1(x-6)+1(y-0)+0(z-2)=0
x-6+y+0=0
x+y=6
Hence, an equation of the plane that contains these lines is x+y=6.
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The right question is
(a) Find the point at which the given lines intersect.
r = [3,3,0] + t[3,-3,2] r = [6,0,2] + s[-3,3,0]
(x,y,z) = ( )
(b) Find an equation of the plane that contains these lines.
5. How long will it take Debbie to save $4,000 for the down payment if she continues to add $75 every month?
Explain how you arrived at your answer.
Answer: 4.5 years or 54 months
Step-by-step explanation: Divide $4,000 by $75 a month to get 53.33 then round to 54. 54 months = 4.5 years.
At a benefit concert, nine bands have volunteered to perform but there is only enough time for five of the bands to
play. How many lineups are possible?
Answer:
126 lineups
Step-by-step explanation:
This is a problem in combinatorics which asks in how many ways can a subset of 5 be formed from a larger set of 9
In general, if you were to see how many ways a subset of [tex]r[/tex] can be formed from a larger subset [tex]n[/tex] denoted by [tex]nC_r[/tex] we use the formula
[tex]nC_r = \dfrac{n!}{ r! (n - r)! }[/tex]
There are calculators that can compute this and I used a scientific calculator to do so.
[tex]9C_5 = 126[/tex]
e(x) = 10(4-x)
Find e(-3).
Answer:
70
Step-by-step explanation:
Substitute the value -3 into the expression and simplify:
10(4 - -3)
10(4 + 3)
10(7)
70
What is the perimeter of quadrilateral BCDE? Round to the nearest tenth.
The perimeter of the quadrilateral is √2+√8+√5+√13
What is the perimeter of quadrilateral BCDE?We can use the distance formula to find the length of the segments that make up the quadrilateral.
We must find the length of the segments between the points (0,2),(1,3)(1,3),(3,1)(3,1),(2,−1)(2,−1),(0,2)
Recall the distance formula d=√(x2−x1)2+(y2−y1)2Applying this formula to the four pairs of points gives the following.
d=√(1−0)2+(3−2)2=√1+1=√2d=√(3−1)2+(1−3)2=√4+4=√8d=√(2−3)2+(−1−1)2=√1+4=√5d=√(0−2)2+(2+1)2=√4+9=√13
So the perimeter of the quadrilateral is √2+√8+√5+√13
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How do I find the inverse of the relation
Answer:
5, -11. -3, 8. 10, 17. -15, 13.
Step-by-step explanation:
All you have to do is switch x and y
Question
Find the value(s) of a where the tangent line to the graph of the function f(x) = -11x + is parallel to the line
y = -19x - 18.
The value(s) of a where the tangent line to the graph of the function f(x) = -11x + is parallel to the line y = -19x - 18 is x=1,-1.
What is Slope of function?
Finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable). The slope itself identifies the line's slope and direction. Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily observe the slope.
[tex]f(x)=-11 x+\frac{8}{x}$$[/tex]
Slope of function [tex]$\rightarrow f^{\prime}(x)=\frac{-21-8}{x^2}$[/tex]
Given line: y=-19 x-18
Slope [tex]$\rightarrow y^{\prime} \rightarrow-19$[/tex]
Since function and line both are parallel, hence slope of both will be equal.
[tex]$$\begin{aligned}-19 & =-11-\frac{8}{x^2} \\-8 & =\frac{-8}{x^2} \\x & =1,-1\end{aligned}$$[/tex]
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solve the inequality n minus four sevenths is greater than or equal to negative two thirds for n.
n is greater than or equal to negative 2 over twenty one
n is less than or equal to two over twenty one
n is greater than or equal to negative twenty six over twenty one
n is less than or equal to twenty six over twenty one
The solution to the inequality n - 4/7 ≥ -2/3 is (a) n ≥ -2/21
How to solve the inequality expression?From the question, we have the following parameters that can be used in our computation:
n minus four sevenths is greater than or equal to negative two thirds
By definition, inequalities are used to relate unequal values
Express the inequality properly
So, we have
n - 4/7 ≥ -2/3
Add 4/7 to both sides
So, we have
n ≥ -2/3 + 4/7
Evaluate the sum of the fractions
This gives
n ≥ -2/21
Hence, the solution is (a) n ≥ -2/21
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a number squared divided by 15
Answer:
Step-by-step explanation:
If a number is squared and then divided by 15, the resulting expression can be written as (x^2)/15, where x is the number. For example, if the number is 5, then the expression can be written as (5^2)/15 = 25/15. In general, the value of the expression (x^2)/15 will be the square of the number x divided by 15.
Suppose that 17 inches of wire costs 68 cents.
At the same rate, how many inches of wire can be bought for 44 cents?
Answer:
188 cents or $1.88
Step-by-step explanation:
We first want to find how many cents per one inch, and we do this by dividing 17 from 68 (68/17). This gets us 4 cents per inch. Now we need to multiply 4 by 47 (4 x 47). Now we get 188 cents. The equation for this would be y = 4x
The same digits are used for the expressions 7² and 2⁷ . Explain how to compare the value of each expression.
Choose the correct answer below.
A. Write each power as repeated multiplication. These compare the bases of the exponents.
B. Write each power as repeated multiplication. Then compare the number of factors.
C. Write each power as repeated multiplication. Then evaluate and compare their values.
Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
What is the relation between power and base?
In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.Compare 7² and 2⁷.
7 ≠ 2
So, write the power as repeated multiplication of the given expression:
7² = 7 * 7
2⁷ = 2*2*2*2*2*2*2
Evaluate:
7² = 49
2⁷ = 128
Compare the values:
128 > 49
2⁷ > 7²
Hence, Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.
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A right angle has two equal sides. starting with the largest write the size of each angle in this triangle
The size of each angle of triangle, starting with the largest 90°, 45° and 45°.
What is a Triangle?Polygon which has three sides and three vertices is called as triangle.
Sum of all the angles of the triangle is 180°.
Given that a right angled triangle has two equal sides.
And the largest triangle of right angled triangle is 90°.
Right angled triangle which has two equal sides can be called right angled isosceles triangle.
And if one angle of isosceles triangle have angle is 90°. Then the rest of the two angle will be 45°.
Therefore, The rest of these two angles of the right angled triangle are 45⁰.
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I need alot of help with this question???
Answer:
no clue bro just help yourself
Step-by-step explanation:
add them
or multiply or divide or subtract and you'll get it
6z+2y=10 solve for y
Answer:
[tex]y = 5 - 3z[/tex]
Step-by-step explanation:
[tex]6z+2y=10[/tex]
divide by 2
[tex]3z + y = 5[/tex]
move the terms
[tex]y = 5 - 3z[/tex]
i need someone to solve this absolute value inequaility -3{x + 2} _< -9
Answer:
x > 1
Step-by-step explanation:
I am solving this equation, not including the "_" in the equation.
-3(x+2)<-9
Multiply both sides by -1 to reverse the inequality.
3(x+2)>9
Divide by 3
x+2>3
Subtract
x>1
Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
What are Equivalent expressions:A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.
In general, if anything is considered equal then the two of them are said to be equivalent. Similarly to this, if any two or more algebraic equations have identical solutions or roots then the equations are Equivalent expressions even they look different.
Here we have
Expressions
3a +b +13a
20b +11a -3b
20b -5b +2b
To simplify given expressions add or subtract like terms as given below
3a +b +13a => (3a+13a) +b = 16a + b
Therefore,
The equivalent expression of 3a +b +13a is 16a + b
20b +11a -3b => (20b-3b) + 11a = 17b + 11a
Therefore
The equivalent expression of 20b +11a -3b is 17b + 11a
20b-5b+2b => 20b+2b - 5b = 22b -5b = 17b
Therefore,
The equivalent expression of 20b-5b+2b is 17b
Therefore,
The equivalent expressions are 16a + b, 17b + 11a, and 17b.
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Evan added -2 1/2+4 and got 6 1/2 draw arrows on the number line to represent the problem and explains Evans error
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2. On adding he would be getting 1 1/2
What is number line?A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.
It is given that Evan added -2 1/2 and 4 but got 6 1/2
The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because
4 - (-2 1/2)
= 4 + 2 1/2
= 6 1/2
This is wrong as he was asked to add -2 1/2 and 4 not to subtract.
Therefore, on adding -2 1/2 and 4, we get,
= 4 - 2 1/2
= 1 1/2
Evan's error was that he subtracted -2 1/2 from 4, and thus he got 6 1/2 . On Evan's error was that he subtracted from 4, and thus he got . On adding he would be getting 1 1/2
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I need understanding this
Answer:
x > 65/7
Step-by-step explanation:
First, we make the equation positive.
-7/5x < -13
We have to switch the sign when multiplying or dividing a negative number.
7/5x > 13
Now, we multiply by 5 and divide by 7.
7x > 65
x> 65/7
help meeeeeeeeeee pleaseee
The time taken for the population to reach 26.6 million is 2 years while the population in year 2000 is 18.5 million.
What is the population growth?We can be able to define population growth as the process by which the population of an area is increasing. We know that the increase or the decrease of population would have to be an exponential function.
Given that we have the function A =18.5e^0.1708t where A is the population after a given time from year 2000 and t is the number of years after year 2000. It then follows that 18.5 million refers to the population of the united states as at year 2000.
We now have;
26.6 =18.5e^0.1708t
26.6/18.5 = e^0.1708t
1.44 = e^0.1708t
ln(1.44) = 0.1708t
t = ln(1.44)/ 0.1708
t = 2 years
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A plane travels 900,000 meters in 700 seconds. What was its speed?
Answer:1285.7 meters per second.
Step-by-step explanation: divide 900,000 meters by 700 seconds
Answer:
A plane travels 360,000 meters in 900 seconds
Step-by-step explanation:
{y: y is an integer and y ≥ 2}
Answer:
Step-by-step explanation:
i believe the total would be 4
Answer: The set of integers greater than or equal to 2 is {2, 3, 4, 5, ...}. This set can be represented using set notation as:
{y: y is an integer and y ≥ 2}
This set includes all the integers that are greater than or equal to 2, including 2 itself. It does not include negative integers or fractions.
For example, the following are all elements of this set:
2, 3, 4, 5, 6, 7, 8, ...
The following are not elements of this set:
-1, 0, 1, 1.5, -3.14, ...
This set is infinite, because there are an infinite number of integers greater than or equal to 2.
As Jupiter and Earth travel along their respective orbits, what happens to the one-way communication time of radio waves carrying information between the two planets?
The one-way communication time between the Jupiter and Earth increases.
What are radio waves?Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 Ghz and below.
Given is that Jupiter and Earth travel along their respective orbits.
As the Jupiter and Earth travel along their respective orbits, they start to get apart from each other. This leads to an increase in one-way communication time.
Therefore, the one-way communication time increases as the Jupiter and Earth travel along their respective orbits.
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Analysis of variance is the most common inferential statistical procedure used to analyze experiments because O there are several different versions of it, and so it can be used to compare the effect of many different groups and variables there is one version of it and it is better for comparing two group more accurately than the two-sample tests. O it is the only statistical procedure that can test either between-subjects factors or within- subjects factors. O most researchers are more interested in differences between the population and one sample
Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.
Given that,
The most typical inferential statistical method used to evaluate trials is analysis of variance because
We have to find which of the options are suitable for the given statements.
Option-A is It comes in a variety of forms, making it possible to compare the effects of numerous groups and variables satisfy the statement.
Option-B is It comes in one form, and compared to two-sample tests, it is more accurate for comparing two groups does not satisfy the statement.
Option-C is It is the only statistical method that can test both within- and between-subjects factors does not satisfy the statement.
Option-D is The majority of academics are more focused on differences between one sample and the population as a whole does not satisfy the statement.
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