Answer:
This will be a 30°-60°-90° triangle because the hypotenuse is 2 cm, which is twice the length of the shorter leg.
Solve each equation. 5-4 t=12
The solution of the given equation 5-4t = 12 is at t = -7/4.
According to the given question.
We have a linear equation in one variable.
5 - 4t = 12
As we know that, linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, th esolution for the given equation 5 - 4t = 12 is given by
5 - 4t = 12
⇒ -4t = 12 - 5 (subtracting 5 from both the sides)
⇒ -4t = 7
⇒ -t = 7/4 (dividing both the sides by 4)
⇒ t = -7/4
Hence, the solution of the given equation 5-4t = 12 is at t = -7/4.
Find out more information about equation here:
https://brainly.com/question/25348678
#SPJ4
9+6.6x=7x-8.7
Help me solve it please
Answer:
x = 44.25
Step-by-step explanation:
9 + 6.6x = 7x - 8.7
-7x -7x
---------------------------
9 - 0.4x = -8.7
-9 -9
-0.4x = -17.7
÷-0.4 ÷-0.4
-------------------
x = 44.25
Simplify each rational expression. State any restrictions on the variable. c²-8 c+12 / c²-11 c+30
Simplify each rational expression. State any restrictions on the variable.
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\frac{(c-2)}{(c-5)}[/tex]
How the rational expression is simplified?
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }\\\\= > \frac{(c-2)(c-6)}{(c-5)(c-6)} \\= > \frac{(c-2)}{(c-5)}[/tex]
What are the restrictions on the variable ?
If c= 5 , the denominator becomes,
[tex]c^{2} -11c+30[/tex] =25-55+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
If c= 6 ,the denominator becomes,
[tex]c^{2} -11c+30[/tex] = 36- 66+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
So, the restrictions on the variable are: c≠ 5,6
To learn more about variable restrictions, refer:
https://brainly.com/question/10957518
#SPJ4
Your teacher asks you to find a recipe that includes two ingredients with a ratio of 1/2 over one 1/8 cup . Give an example of two ingredients in a recipe that would meet this requirement
The recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
The example is with flour and sugar
Let
x = the number of cups of flour
y = the number of cups of sugar
We know that:
Ratio means the comparison between the two values.
Ratio = x / y
Now, we can let
x = 1 / 2 cups of flour
y = 1 / 8 cups of sugar
Ratio will be
= 1 / 2 : 1 / 8
= 8 : 2
= 4 : 1
Therefore, the recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
Learn more about ratio here:
https://brainly.com/question/2328454
#SPJ9
Suppose you toss a coin four times. What is the probability of getting four tails?
Answer:
1/16
Step-by-step explanation:
Coin toss
probability 1/2×1/2×1/2×1/2 = 1/16
Find the value of x and y.
Answer:
9. x = 10310. x = 50Step-by-step explanation:
9)
x + x - 26 = 180
2x = 180 + 26
2x = 206
x = 206 : 2
x = 103
check
103 + 103 - 26 = 180
180 = 180
the answer is good
10.
2x - 40 = x + 10
x = 40 + 10
x = 50
check
2 * 50 - 40 = 50 + 10
60 = 60
the answer is good
PART 2!!
Topic: Addition and Subtraction of polynomials
Directions: Simplify each rational expressions
Step-by-step explanation:
4.
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] \: [/tex]
5.
[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]
[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]
[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]
[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]
[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]
[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve these problems ~
Problem 1 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
Problem 2 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]
[ taking 2 common out ]
[tex]{ \qquad \sf \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]
Which product is NOT equal to 13 ?
a. (4+√3 )(4-√3 )
b. (5-2 √3 )(5+2 √3 )
c. (6+√23 )(6-√23 )
d. (7-√6 )(7+√6 )
Answer:
the answer is D
Step-by-step explanation:
because it gives us 43 as the answer
Can yall help me with this
From the values that we have the magnitude of the value of the stock A would be given as 4.15. Option A is correct.
What is the magnitude of a stock?This is the term that is sued to refer to how far the run of a particular stock is in terms of its price. In order to get the magnitude, we would have to find the absolute value of the stock A as we have it here.
Remember the absolute value would have to change the value to be positive if it was negative.
Hence we would have
I-4.15I = 4.15
Hence the solution is 4.15
Read more on magnitude here:
https://brainly.com/question/24468862
#SPJ1
c. What do you notice about these three angles?
Answer:
Added all up, they will form 180 degrees aka a straight line.
Step-by-step explanation:
To find S, just add 45 + 80. We get 125. Then, subtract 125 from 180!
S = 55 :)
please help me again!! i’m probably not focusing because i’m tired.
Answer: x=14
Step-by-step explanation:
First let's find all the inner angles of the triangle.
124+DCB=180 ==> Angles DCB and 124 lie on a straight line. Straight lines measure 180 degrees and are called straight angles.
124+DCB=180
124-124+DCB=180-124
DCB=180-124
DCB=56 degrees
6x+CBD=180 ==> straight angle
2x+CBD+56=180 ==> total degrees of a triangle is 180 degrees
6x+CBD=2x+CBD+56 ==> they both equal 180
6x+CBD-CBD=2x+CBD-CBD+56
6x=2x+56
6x-2x=2x-2x+56
4x=56
4x/4=56/4
x=14
5 Granola bars cost $4.00
b. Fill in the table that shows the
costs for 10, 15, and
20 granola bars. Find the cost for a
single granola bar in each case.
Answer:
1 granola bar =
Step-by-step explanation:
10 granola bars= $4.00 x 2 = $8.00
15 granola bars=$4.00 x 3 = $12.00
20 granola bars=$4.00 x 4 = $16.00
1 granola bar = $0.80p
what can 6 divided by using a -1/2?
2(-4)² + (-4)³ +24 - 18(-12)2
Answer:
-440
Step-by-step explanation:
Simplify
2(-4)^2+(-4)^3+24-18(-12)2
2(16)+(-64)+24-432
32-64+24-432
-440
Write an explicit formula for each geometric sequence. 25,5,1, 1/5, . . .
The explicit formula is [tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
For the Geometric sequence, the explicit formula for the nth term is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where,
a = first number of the series
r = common ratio
n = number of series
[tex]a_{1}[/tex] = a
[tex]a_{2}[/tex] = ar
[tex]a_{3}[/tex] = a [tex]r^{2}[/tex]
.....
Therefore the series is a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],,,,.....
Here we have the series 25, 5, 1, 1/5
Here common ratio = 1/5
and if we want to find the 5th term the formula is
[tex]a_{5}[/tex] = 25 ×[tex](\frac{1}{5} )^{4}[/tex]
= [tex]\frac{1}{25}[/tex]
To know more about the explicit formula of the geometric sequence refer to the link given below:
https://brainly.com/question/24198356
#SPJ4
The graph shows the cube root parent function. Which statement is true? A. (0, 1) is the x and y-intercept of the function. B. The function has no intercepts. C. (1, 1) is the x and y-intercept of the function. D. (0,0) is the x and y-intercept of the function.
Answer:
D
Step-by-step explanation:
X and y come together at (0,0) right?
if the car continues at the same accerleration meaning the slope of the line does not change how fast would it be going in 15 seconds
The car's velocity after 15 seconds is 60.3 m/s.
What is velocity?Velocity is the directional speed of a moving object as an indication of its rate of change in position as observed from a specific frame of reference and measured by a specific time standard.The linear regression equation obtained by fitting the data using technology is:
y = 3.64x + 5.7x = times(seconds) ; y = velocity(m/s)The approximate velocity at time = 0 and x = 0 is as follows:
y = 3.64(0) + 5.7y = 0 + 5.7y = 5.7 m/sAfter 15 seconds, the velocity is:
At time, x = 15 secondsy = 3.64(15) + 5.7y = 60.3 m/sTherefore, the car's velocity after 15 seconds is 60.3 m/s.
Know more about velocity here:
https://brainly.com/question/25749514
#SPJ9
A company rents out 14 food booths and 21 game booths at the county fair. The fee for a food booth is $175 plus $9 per day. The fee for a game booth is $50 plus $8 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
A simplified expression for the amount, in dollars, that the company is paid is $3,500+273d.
Given that, a company rents out 14 food booths and 21 game booths at the county fair. The fee for a food booth is $175 plus $9 per day. The fee for a game booth is $50 plus $8 per day.
What is an expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given, the fair lasts for d days, and all the booths are rented for the entire time.
So, Food Booth Fee can be calculated as follows:
14(175+9d)
=2,450+126d
Game Booth Fee can be calculated as follows:
=21(50+8d)
=1050+168d
So, the total Food and Game Booth Fees:
=2,450+126d+1050+168d
=3,500+273d
Therefore, a simplified expression for the amount, in dollars, that the company is paid is $3,500+273d.
To learn more about an expression visit:
https://brainly.com/question/13947055.
#SPJ1
In the first half football season, Marco ran 4 plays for a gain of 60 yards. During the second half of the season, Marco was responsible for 6 penalties resulting in a loss of 80 yards. What was his total yardage for his football season?
The drying time of one particular paint is approximately normally distributed with a mean of 45
minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to
dry completely. Find the standard deviation of this distribution.
The standard deviation of this distribution is 9.65 minutes.
Due to its description in terms of the second central moment, the standard deviation naturally arises in mathematical statistics.
Any distribution with finite first two moments can have its standard deviation defined, although the most common assumption is that the underlying distribution is normal.
In the above given question it is stated that:
mean(μ) of the distribution is 45 and let us consider the standard deviation to be σ
We convert this to standard normal as
[tex]P(X < x) = P(Z < \frac{( x - \mu)} {\sigma})[/tex]
We have , P(X > 55) = 0.15 (15%)
This can be simplified as:
P(X < 55) = 1 - 0.15
P(X < 55) = 0.85
[tex]P(Z < \frac{( x - \mu)} {\sigma}) = 0.85[/tex]
From Z table, z-score for the probability of 0.85 is found out to be 1.0364 ,
therefore :
[tex]\frac{( 55 - 45)}{ \sigma }= 1.0364\\\\ \sigma = ( 55 - 45) / 1.0364 \\\\\sigma = 9.65[/tex]
Hence the standard deviation is 9.65 minutes.
To learn more about standard deviation visit:
https://brainly.com/question/14856823
#SPJ1
Which graph represents a function with amplitude 4 and period π?
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
The correct option is On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
What is amplitude?The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Given:
function with amplitude 4 and period π.
also, The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.
so, the amplitude 4 means function has a maximum of 4 and minimum of negative 4.
Hence, On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
Learn more about amplitude here:
https://brainly.com/question/8662436
#SPJ1
Answer:
D
Step-by-step explanation:
just took it
50 PTS - Functional Notation. Please explain how to do this!
Determine the distance between the points (c,d) and (0,0). Answer of terms of c and d
Answer:
Step-by-step explanation:
(y2-y1)/(x2-x1)
(0-d)/(0-c)
-d/-c
d/c
How do you solve this equation I struggle with it
6623 divided by 17? please show work
Answer:
Decimal Form:
389.58823529
Mixed Number Form:
389 [tex]\frac{10}{17}[/tex]
Step-by-step explanation:
[tex]\frac{6623}{17}[/tex]
Decimal Form:
389.58823529
Mixed Number Form:
389 [tex]\frac{10}{17}[/tex]
i can't figure this out
2/3(x-3)+6x
Step-by-step explanation:
Have you understand? please notify when you don't understand
Find each difference.
-16-(-25)
The difference is 9.
How to find the difference?A difference is a result of subtracting two numbers.
It speaks of the difference in quantity between two numbers.
Given,
-16-(-25)
Solution:
Since (-) + (-) = +
-16-(-25) = -16 + 25
= 9
To learn more about differences, refer
brainly.com/question/946189
#SPJ4
-7x+4=-128+4x
with work pls :D
Answer:
Step-by-step explanation:
Rearrange terms -7x+4=4x-128 subtract 4 from both sides. Simplify . subtract 4x from both sides. simplify. divide both sides by the same factor. simplify. Solution x=12
A group is going to a state fair. If childrens tickets are $7.50 per child and adult tickets are $12 per adult, how many of each can go to the fair for $200? Write a linear equality, graph it, and show several solutions on graph. !! Help
Let c = children tickets
Let c = children tickets Let a = adult tickets
Let c = children tickets Let a = adult tickets Let c to be in place of x
Let c = children tickets Let a = adult tickets Let c to be in place of xLet a to be in place of y
Answer:
7.50c+12a<or=200 (you would have a inequality since that is the maximum number you could pay and no other information is given)
the graph is above and the inequality in slop intercept format is y= -5/8x+ 16 2/3
Solutions for c: 0 <or= c <or= 26* *(since that is the maximum whole number you can have for $200)
Solutions for a: 0 <or= a <or= 16* *(since that is the maximum whole number you can have for $200)
Note: In order for find other solutions your cordatnate has to be a whole number (that is positive or zero) within the red area shaded. However there are many examples given for answer purposes.
Step-by-step explanation:
$7.50 is the price of each children tickets and $12 is the price of each adult tickets and when combined equal to $200 so you can multiply the variables to get 7.5c+12a <or= 200.
To graph the inequality there's two ways;
Way 1: Change from standerd form to slope intercept form
Place 7.50c on the right side by subtracting 7.50c on each side of the inequality (the point is to islolate a); 7.50c - 7.50c + 12y < or = 200 - 7.50c. The 7.50c on the left side cancel each other out so we'll get 12a < or =200 - 7.50c Isolate a by dividing both sides by 12; 12a/12= (200 - 7.50c)/12 that equals to a < or = -5/8c + 16 2/3 Find an appropriate scale and graph you can use the a-interpect and c-intercpt to make a line since this is less than or equal to you shade the region below the lineWay 2: Isolate your variables to get your x and y intercept
To find the a-interpect you make c equal to 0 so it would be 12a = 200Divide 12 on both sides; 12a/12 =200/12. The a-interpect is 16 2/3 To find the c-intercpt you make a equal to 0 so it would be 7.50c = 200. Graph the point on your graph Divide 7.50c on both sides; 7.50c/7.50 =200/7.50. The a-interpect is 26 2/3. Graph the point on your graph Draw a continuous line from your two points
Write an equation of each line in point-slope form.
(-4,-3) and (2,7
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , -3) and (2 , 7), is y + 3 = 5/3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , -3) and (2 , 7).
m = (y2 - y1)/(x2 - x1)
m = (7 - -3)/(2 - -4)
m = 10/6
m = 5/3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/3 and (x1 , y1) = (-4 , -3)
(y - -3) = 5/3(x - -4)
y + 3 = 5/3(x + 4)
To learn more about equation of line in point slope form: brainly.com/question/24907633
#SPJ4
