Answer:
[tex]\large\boxed{m=\dfrac{5}{2}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===================================\\\\\text{We have the equation of a line:}\ y=-\dfrac{2}{5}x+\dfrac{4}{5}\to m_1=-\dfrac{2}{5}.\\\\m_2=-\dfrac{1}{m_1}\to m_2=-\dfrac{1}{-\frac{2}{5}}=\dfrac{5}{2}[/tex]
Help me with this question thanks
Answer:
arrow going from 9 to -infinity (open circle)
Step-by-step explanation:
equalize equation by multiplying both sides by 3 to obtain the equation 9>t
then simply plug in numbers to see if they check out, ie: 3> 4/3 makes sense, but 3> 10/3 doesn't.
Draw the arrow to accommodate for the answers that DO fit.
open circle, because it doesn't work for t=9
Answer:
see below
Step-by-step explanation:
3 > t/3
Multiply each side by 3
3*3 > t/3 *3
9 > t
t < 9
There is an open circle at 9, since the symbol is less than
The line goes to the left.
A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of
each year, which summation represents the money in the account 10 years after the initial deposit?
Answer:
[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]
Step-by-step explanation:
The amount (A) in a deposit after 1 year is calculated as follows:
A = P*(1 + r)
where:
P is the present value
r is the annual rate (decimal)
After the first year:
A = 300*(1 + 0.055) = $316.5
After the second year, the account will have a new amount of $316.5 due to the new $300 and the interest gained with the previous $316.5:
A = 316.5 + 316.5*(1 + 0.055)
After the third year:
A = 316.5 + [316.5 + 316.5*(1 + 0.055)]*(1 + 0.55)
A = 316.5 + 316.5*(1 + 0.055) + 316.5*(1 + 0.055)^2
After 10 years:
[tex]\sum_{n=1}^{10} 316.5 (1.055)^{n-1} [/tex]
Find the rate of change for the line that passes through the point (-2, 6) and (-5, 9).
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{9}) \\\\\\ \stackrel{\textit{average rate of change}~\hfill }{slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}}\implies \cfrac{9-6}{-5-(-2)}\implies \cfrac{9-6}{-5+2}\implies \cfrac{3}{-3}\implies -1[/tex]
What’s the mode of data set 23,95,100,23,100,100
Answer:100
Step-by-step explanation:
That is the most common number
Hello There!
Mode: The number that occurs most often in a set of numbers
in this case, the number 100 occurs more than any other number in the set. This means that the mode for this set of data is 100.
Find the difference. Express your answer in
simplest form.
g+1/g+2 - (5g+4)/g+2
Click on the correct answer.
A.-4g + 5/2g+4
B. -4g+5/g+2. C. 6g – 3/g+2
D. 6g - 3/2g +4
Answer:
-4g-3
------------
g+2
Step-by-step explanation:
g+1 5g+4
------------- - ------------------
g+2 g+2
Since the denominators are the same, subtract the numerators
g+1 - (5g+4)
Distribute the negative sign
g+1 -5g-4
-4g-3
Put this back over the denominator
-4g-3
------------
g+2
Answer:
-4g-3, g+2
Step-by-step explanation:
Find x 4.0 58 degrees
Answer: 4.7
Step-by-step explanation:
Use Soh Cah Toa
[tex]sin \theta=\dfrac{opposite}{adjacent}\\\\\\sin(58^o)=\dfrac{4.0}{x}\\\\\\x=\dfrac{4.0}{sin(58^o)}\\\\\\x=4.7[/tex]
Answer:
The value of x = 4.7
Step-by-step explanation:
From the figure we can see aright triangle with height = 4.0 and one angle is 58°
Points to remember
Trigonometric ratios
Sin θ = Opposite side/Hypotenuse
To find the value of x
Sin 58 = Opposite side/Hypotenuse
= 4/x
x = 4/Sin (58)
= 4/0.848
= 4.71 ≈ 4.7
Therefore the value of x = 4.7
what is missing sequence number?
5 6 9 - 25 40
Answer:
15
Step-by-step explanation:
term 1 is equal to 5.
term 2 is equal to 5 + (1) = 5 + 1 = 6
term 3 is equal to 6 + (1 + 2) = 6 + 3 = 9
term 4 is equal to 9 + (1 + 2 + 3) = 9 + 6 = 15
term 5 is equal to 15 + (1 + 2 + 3 + 4) = 15 + 10 = 25
term 6 is equal to 25 + (1 + 2 + 3 + 4 + 5) = 25 + 15 = 40
Juan just took a 40 question math test. He scored 75%. How many questions did he get correct
Answer:
30
Step-by-step explanation:
40
x 0.75
-----------
= 30
What is the solution to this system of equations?
4x + 5y = 7
3x – 2y = –12
Answer:
x = -2 and y = 3
Step-by-step explanation:
It is given that,
4x + 5y = 7 -----(1)
3x – 2y = –12 ----(2)
To find the value of x and y
eq(1) * 3 ⇒
12x + 15y = 21 ----(3)
eq(2) * 4 ⇒
12x - 8y = -48 ---(4)
eq(3) - eq(4) ⇒
12x + 15y = 21 ----(3)
12x - 8y = -48 ---(4)
0 + 23y = 69
y = 69/23 = 3
Substitute the value of y in eq(1)
4x + 5y = 7 ----(1)
4x + 5*3 = 7
4x = 7 - 15 = -8
x = -8/4 = -2
Therefore x = -2 and y = 3
Answer:
x = -2 and y = 3
Step-by-step explanation:
Which expression is equivalent to 16^3?
A. 2^7
B. 2^11
C. 2^12
D. 2^64
For this case we must find an expression equivalent to:
[tex]16 ^ 3[/tex]
We can rewrite 16 as [tex]2 * 2 * 2 * 2 = 2 ^ 4[/tex]
Rewriting the expression we have:
[tex](2 ^ 4) ^ 3 =[/tex]
By definition of power properties we have to:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So, we have:
[tex](2 ^ 4) ^ 3 = 2 ^ {12}[/tex]
Answer:
Option C
Answer:
C
Step-by-step explanation:
edg2021
If Allison wants to find 80% of 630 which table should she use?
Answer:
optain A or the first one
Step-by-step explanation:
hop this helps
Finding 80% of 630 doesn't require using a table and can be calculated by simply multiplying 0.80 by 630 which gives 504.
Explanation:To determine 80% of 630, Allison doesn't necessarily need a table. However, we can illustrate the solution using a simple self-created table. The calculation is rather straightforward. If Allison wants to find 80% of 630, she can simply multiply 0.80 (which is the decimal equivalent of 80%) by 630.
Step-by-step process:
Convert 80% to decimal form by dividing 80 by 100, which gives 0.80. Multiply 0.80 by 630 which gives 504.
Therefore, 80% of 630 is 504.
Learn more about Percentage Calculation here:https://brainly.com/question/329987
#SPJ11
The magnitude of m is 29.2 meters, and the magnitude of n is 35.2 meters. If m and n are perpendicular, what is the magnitude of their sum?
Answer:
45.73 m
Step-by-step explanation:
An object is launched upward
from 62.5 meters above ground level with an
initial velocity of 12 meters per second. The
gravitational pull of the earth is about 4.9
meters per second squared. How long will the
object take to hit the ground?
Check the picture below. The picture is using feet, but is pretty much the same trajectory for meters.
so the object hits the ground when y = 0, thus
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{12}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{62.5}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-4.9t^2+12t+62.5\implies \stackrel{\textit{hitting the ground}}{\stackrel{h(t)}{0}=-4.9t^2+12t+62.5}[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{using the quadratic formula} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+12}t\stackrel{\stackrel{c}{\downarrow }}{+62.5} \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t=\cfrac{-12\pm\sqrt{12^2-4(-4.9)(62.5)}}{2(-4.9)}\implies t=\cfrac{-12\pm\sqrt{144+1225}}{-9.8} \\\\\\ t=\cfrac{12\mp\sqrt{1369}}{9.8}\implies t=\cfrac{12\mp 37}{9.8}\implies t= \begin{cases} \stackrel{\approx}{-2.55}\\ 5 \end{cases}[/tex]
we can't use -2.55, since it's seconds and can't be negative, so t = 5 seconds later.
Mac is 5 feet tall and casts a 4 foot 6 inch shadow. At the same time, a nearby tree casts a 20
foot shadow
Which is the closest to the height of the tree?
I will convert feet to inches.
4 feet, 6 inches = 54 inches
20 feet = 240 inches
5/x = 54/240
Let x = closest height of tree
54x = 5(240)
54x = 1,200
x = 1200/54
x = 22.2222222222
The tree is about 22 feet tall.
Answer:
22 inches
Step-by-step explanation:
Height of Mac = 5 feet
Height of shadow of Mac = 4 foot 6 inches = [tex]4+\frac{6}{12}= 4.5[/tex] inches .
We are given that At the same time, a nearby tree casts a 20 foot shadow .
Let the height of the tree be x
ATQ
[tex]\frac{5}{4.5}=\frac{x}{20}[/tex]
[tex]\frac{5}{4.5} \times 20=x[/tex]
[tex]22.22=x[/tex]
Hence the height of the tree is approximately 22 inches .
What is the yintercept of the line given by the equation below?
y=-10x+ 14
Answer: 14
Step-by-step explanation:
Answer:
The y-intercept is: (0,14).
Sin(-x)= -cos x for all values of x. True or false
Answer:
That's incorrect. The simplest way to show this is by evaluating the functions at a given point. Let's say x=0, then:
Sin(-x) = Sin(0) = 0
-cos x = -cos (0) = -1
Therefore, Sin(-x)≠-cos x.
The given expression :
[tex]\sin (-x)=-\cos x[/tex] is a false expression i.e. it is not true for all the values of x.
Step-by-step explanation:We are asked to check whether the trignometric expression is true for all the values of x or not.
The expression is given by:
[tex]\sin (-x)=-\cos (x)[/tex]
We consider x=0
Then on taking left hand side of the expression we have:
[tex]\sin (-0)\\\\i.e.\\\\\sin (0)\\\\=0[/tex]
and the right hand side of the expression is:
[tex]-\cos x\\\\i.e.\\\\-\cos 0\\\\i.e.\\\\-1[/tex]
i.e. we have:
[tex]0=-1[/tex]
which is false.
Hence the statement is not true for all the values of x.
Which statement is true about a number and its additive inverse?
A. Their product is always one.
B. Their sum is always one.
C. They are always reciprocals of each other.
D. Their sum is always zero.
Answer:
Option D is correct.
Step-by-step explanation:
The additive inverse of a number is the same number with the negative sign
i.e. if we have a number 1 then it's additive inverse would be -1
So if we add both the number and its additive inverse the answer would be zero.
1+(-1) = 0
So, Option D their sum is always zero is correct.
Answer: Option D
Their sum is always zero
Step-by-step explanation:
Given any number x, the additive inverse of x is -x.
For example, the additive inverse of 3 is - 3, the additive inverse of 2.2 is -2.2.
In this way, note that adding a number with the additive inverse of this number will always result in the number zero.
[tex]x + (-x) = 0[/tex]
Therefore, the correct option is option D
A factory has to transport raw materials to a project site. The total weight of the raw material will not be less than 1,500 tons. The factory manager plans to use two different trucking firms. Big Red has heavy-duty trucks that can transport 200 tons at a cost of $50 per truckload. Common Joe is a more economical firm, costing only $20 per load, but its trucks can transport only 90 tons. The factory manager does not wish to spend more than $450 on transportation. The availability of trucks is the same for both firms.
Answer:
common Joe is cheaper
Step-by-step explanation:
1500/200 =7.5 truckloads
7.5×50=$375
1500/90=16.666 truckloads
16.666×20=$333.
I really didn't know for sure what u we're looking for
Answer:Common Joe
Step-by-step explanation:
Given
Total weight of Raw material is 1500 tons
Big Red can transport 200 tons at a cost of $50 per truckload
so Big Red need to do 8 rounds to completely transport the raw material
In first 7 round round it carries 200 tons and in last round it carry 100 tons
i.e. [tex]200\times 7+100[/tex]
so cost for Red bus=[tex]50\times 8=$400[/tex]
For Common Joe truck requires 17 round of loading to completely transport 1500 tons
In first 16 round it carries 90 tons and in last round it carries 60 tons
So cost for Common Joe is [tex]17\times 20=$340[/tex]
So Factory should choose Common Joe while considering Economy.
if a sum is 100 and the different is six what is the answer
Answer:
53+47
Step-by-step explanation:
100-53 is 47. 53-47 gives you 6
Answer:
The numbers are 53 and 47.
Step-by-step explanation:
You didn't write out the problem completely, but this may be the problem:
The sum of two numbers is 100. The difference of the two numbers is 6. What are the numbers?
Let the numbers be x and y.
The sum of two numbers is 100.
x + y = 100
The difference of the two numbers is 6.
x - y = 6
We have a system of two equations in two variables.
x + y = 100
x - y = 6
Add the equations.
2x = 106
x = 53
Now substitute 53 for x in the first equation and solve for y.
53 + y = 100
Subtract 53 from both sides.
y = 47
The numbers are 53 and 47.
vertical angles must check all that apply
Vertical Angles have to be congruent and have the same vertex.
The correct options are:
B. Have the same vertex.
C. be congruent.
Step-by-step explanation:Vertical Angles--
These are formed by the intersection of two lines.When two lines intersect then four angles are formed such that each pair of the opposite angles are called vertical angles.The vertical angles have a common vertex.Since, one vertex is obtained when the lines intersect.They could never be adjacent angles.Also, they may be obtuse, acute or right angles.The measure of each of the vertical angles are always equal i.e. the angles are congruent.what is the slope of the line containg (-2,5) and (4,-4)
Answer:
-3/2
Step-by-step explanation:
(Y2-Y1)/(X2-X1)
(-4 - 5) / (4 - (-2))
-9 / 6
Simplified: -3/2
Answer:
-3/2
Step-by-step explanation:
Which equation is a linear equation?
Question 4 options:
a)
23xy − 34y = 0
b)
3a + 5b = 3
c)
x2+y2 = 0
d)
4m2 = 6
Answer:
b) 3a + 5b = 3
Step-by-step explanation:
It is an exact replica of the Standard Formula [Ax + By = C]. The Standard Formula is an example of a linear equation.
Answer:
3a + 5b = 1 is a linear equation
Step-by-step explanation:
Required?
To state which equation is linear...
An equation is said to be linear if it obeys the following.
1. For Single variables: y = b
An example is y = 4
2. For 2 Variables; it can take any of the following form: Ax + By = C.
An example 3x + 5y = 4
.from option A through D, only option B fits the description.
Note that the arithmetic sign could take the negative form and the position of x and y or any other constraints can take an interchanged forms.
The key thing to watch out when naming a linear equation is that the highest power is 1.
Hence, the 3a + 5b = 1 is a linear equation
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of
hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)"
f(x) = 1500(115)
f(x) = 1500(2.15)
f(x) = 1500(215)
Answer:
Step-by-step explanation:
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
The answer to this problem is a f(x) = 1500(2.15)x
Answer:
[tex]f(x) = 1500(2.15)^x[/tex]
Step-by-step explanation:
Let the function that represents the population of bacteria after x hours is,
[tex]f(x)=ab^x[/tex]
For x = 0, f(x) = 1500,
[tex]1500=a(1+r)^0[/tex]
[tex]1500=a[/tex]
Now, the population increases at a rate of 115% each hour,
So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,
That is, for x = 1, f(x) = 3225,
[tex]3225 =ab[/tex]
[tex]3225=1500(b)[/tex]
[tex]\implies b =2.15[/tex]
Hence, the function that represents the given scenario is,
[tex]f(x)=1500(2.15)^x[/tex]
Given that the triangles shown below are similar, what is the value of x?
Answer:
c. 5
Step-by-step explanation:
Because 15 divided by 3 equals 5
So 25 divided by 5 equals 5 (dont know if it is correct)
From concept of similar triangles, the value of x is Option (C) 5 .
What are similar triangles ?Similar triangles are triangles that have the same shape but their sizes, dimensions may vary. All equilateral triangle, squares of any shape are example of similar objects. If two triangles are similar triangles then their corresponding angles are congruent and the corresponding sides are in equal proportion.
How to find the corresponding side using concept of proportion ?We know from concept of similar triangles, the corresponding sides are in equal proportion.
Both the triangle given in the diagram are similar.
The unknown side given is x .
Using proportion concept,
⇒ [tex]\frac{15}{3} = \frac{25}{x}[/tex]
⇒ [tex]x = \frac{25}{5}[/tex]
∴ [tex]x = 5[/tex]
Thus, From concept of similar triangles, the value of x is Option (C) 5.
To learn more about concepts of similar triangles, refer -
https://brainly.com/question/8474273
#SPJ2
A rectangle on a coordinate plane has vertices Q(-1, 1),R(6, 1), S(6,-8), and T(-1,-8)What are the dimensions of the rectangle? The base is 6 and the height is 9. The base is 9 and the height is 6. The base is 7 and the height is 9. The base is 9 and the height is 7.
ANSWER
The base is 7 and the height is 9.
EXPLANATION
If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
[tex]Base = |6 - - 1| = |7| = 7[/tex]
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
[tex]Height= |1 - - 8| = |9| = 9[/tex]
Therefore, the base is 7 and the height is 9.
Answer:
Base is 7, and Height is 9.
Step-by-step - If we consider any two pairs of points and the y-coordinates of these two points are constant (are the same), then that side forms one of the bases of the rectangle.
Consider, Q(-1, 1) and R(6, 1)
The y-values are the same.
The base of the rectangle is the absolute value of difference in the x-values.
We could have also used S(6,-8), and T(-1,-8) to obtain the same result.
For R(6, 1) and S(6,-8), the x-coordinates are the same. The height is the absolute values of difference in the y-values.
Therefore, the base is 7 and the height is 9.
Help Please..............................................
Answer:
0 and 1 have the same y values for the x values.
Which expression is equivalent to (125^2 / 125^4/3)
algebra II engenuity
Answer: Last option.
Step-by-step explanation:
To find which expression in equivalent to the expression [tex]\frac{125^2}{125^\frac{4}{3} }[/tex], you need to remember :
The Power of a power property:
[tex](a^m)^n=a^{(mn)}[/tex]
The Quotient of powers property:
[tex]\frac{a^m}{a^n} =a^{(m-n)}[/tex]
And the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Knowing that:
[tex]125=5*5*5=5^3[/tex]
Then, you get:
[tex]\frac{125^2}{125^\frac{4}{3} }=\frac{(5^3)^2}{(5^3)^\frac{4}{3} }=\frac{5^6}{5^4}=5^{(6-4)}=5^2=25[/tex]
In the diagram, a building cast a 35-ft shadow and a flagpole casts an 8-ft shadow. If the the flagpole is 18 ft tall, how tall is the building? Round the the nearest tenth.
Answer: 78.8 ft
Step-by-step explanation:
Similar triangles have proportional sides.
[tex]\dfrac{\text{building shadow}}{\text{building height}}=\dfrac{\text{flagpole shadow}}{\text{flagpole height}}\\\\\\\dfrac{35}{\text{building height}}=\dfrac{8}{18}\\\\\\\dfrac{35\times 18}{8}=\text{building height}\\\\\\\dfrac{35\times 9}{4}=\text{building height}\\\\\\\dfrac{315}{4}=\text{building height}\\\\\\\boxed{78.75=\text{building height}}[/tex]
How to rationalize the denominator of sqrt(a)/sqrt(a)-2
Answer:
√a(√a + 2) a - 2√a
----------------- = -----------------
a - 4 a - 4
Step-by-step explanation:
I am assuming that by "sqrt(a)/sqrt(a)-2" you meant:
√a
----------
√a - 2
To rationalize the denom., multiply numerator and denom. of this fraction by the conjugate of √a - 2, which is √a + 2:
√a(√a + 2)
-----------------
a - 4
In the diagram m ll n. identify all the angles that are congruent to angle 2
Answer:
A; 4,6,8
Step-by-step explanation:
Answer:
angles 4,6,8
Step-by-step explanation: Did it on i-ready and got it right.