Answer:
14.784
Step-by-step explanation:
A tutor work with 3 students. The oldest student is 6 years oldder then the middle student, and the youngest student is 3 years younger than the middle student. The sum of the ages of the students is 30. How many years old is the youngest student
Answer:
9 years old.
Step-by-step explanation:
Since the ages of all of these students are being represented in relation to the middle student's age then we can create formulas for each student and then apply them to the formula for the sum of their ages and solve for the middle child's age (M) like so... (oldest child's age is represented by variable O and youngest child's age is represented by variable Y)
O = M + 6
Y = M - 3
30 = (M+6) + M + (M-3) ... combine like terms
30 = 3M + 3 ... subtract 3 from both sides
27 = 3M ... divide both sides by 3
9 = M
Now we know that the middle child is 9 years old.
3. Formulate 900 lbs of a 35% CP ration using Soybean Meal (46% CP) and Oats (12% CP). How many pounds of soybean meal will be used? How many pounds of oats will be used?
Answer:
The amount of Soyabean = 608.82 pounds.
The amount of Oats = 900-608.82 = 291.18 pounds.
Step-by-step explanation:
Given that the Soybean Meal has 46% CP and Oats has 12% CP.
The total amount of ration is 900 lbs of 35% CP.
Let x pounds of Soyabean has been used, so,
the amount of Oats = 900-x lbs.
The CP amount in 900 lbs mixture will be equal to the sum of CP amounts in x lbs Soyabean and 900-x lbs Oats, i.e
35% of 900 = 46% of x + 12% of (900-x)
[tex]\Rightarrow \frac{35}{100}\times 900=\frac{46}{100}\times x+\frac{12}{100}\times (900-x)[/tex]
[tex]\Rightarrow 35\times 900 = 46x + 12\times 900 - 12 x[/tex]
[tex]\Rightarrow 34x= 900(35-12)[/tex]
[tex]\Rightarrow x = (900\times 23)/34[/tex]
[tex]\Rightarrow x = 608.82[/tex] lbs.
So, the amount of Soyabean = 608.82 pounds.
The amount of Oats = 900-608.82 = 291.18 pounds.
1.
Which of these expressions is equivalent to 3(x - 2)?
A.
3x – 6
B.
3x
2
C.
3x + 2
D.
3x + 6
Answer:
A. 3x - 6
General Formulas and Concepts:
Pre-Alg
Distributive PropertyStep-by-step explanation:
Step 1: Define expression
3(x - 2)
Step 2: Expand
Distribute 3 to both terms: 3x - 6Kenzie is putting the family vacation videos onto a flash drive. The flash drive can hold 200 minutes of video. Kenzie has used 45% of the memory space already. How many minutes of the flash drive has she already used?
Answer:
90 minutes
Step-by-step explanation:
In order to calculate a percentage of the minutes of video we simply need to divide the percentage by 100 and then multiply that value by the total number of minutes that the flash drive can hold. Since we are given this total number of minutes then we can simply plug it in and solve for x which represents the percentage of memory used in minutes.
x = 200 * (45 / 100)
x = 200 * 0.45
x = 90 minutes
Therefore, Kenzie has already used 90 minutes of video on the flash drive.
What is the relationship between angle b and angle d?
A) corresponding
B) vertical
C) supplementary
D) alternate interior
Answer:
corresponding I believe
Step-by-step explanation:
if I'm wrong someone tell me and I'll go in the corner
Answer:
D) Alternate interior
Step-by-step explanation:
Its a bit hard to explain for me, since I did this stuff in 5th grade and now I'm in 10th.
P.S: Please mark my answer as brainliest, I need it to rank up.
What is the midpoint of the line segment that has endpoints (3,8) and (1,−4) ?
Answer:
D
Step-by-step explanation:
Midpoint Formula:
[tex]\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}[/tex]
[tex]\frac{3+1}{2}[/tex] ⇒ [tex]\frac{4}{2}[/tex] ⇒ [tex]2[/tex]
[tex]\frac{8+-4}{2}[/tex] ⇒ [tex]\frac{8-4}{2}[/tex] ⇒ [tex]\frac{4}{2}[/tex] ⇒[tex]2[/tex]
[tex](2,2)[/tex]
Philip's rectangular deck is 5 yards wide. The ratio of the width to the length is 4 to 5. What is the approximate length of Philip's deck in feet? Hint: 1 yard = 3 feet.
Answer:
18.75 feet
Step-by-step explanation:
Step 1
we find the length of Philip's rectangular deck in yards
The ratio of the width to the length is 4 to 5.
Philip's rectangular deck is 5 yards wide.
Hence,
Hence:
4/5 = 5/x
Cross Multiply
4x = 5 × 5
4x = 25
x = 25/4
x = 6.25 yards
The length of Philip's field = 6.25 yards
Hint: 1 yard = 3 feet.
Converting the yard to feet
1 yard = 3 feet
6.25 yards = x
Cross Multiply
x = 6.25 × 3 feet
x = 18.75 feet
Therefore, the length of Philip's field in feet = 18.75 feet
x·6−14=46
Answer asap!!!! thank you!!
Answer:
x=10
Step-by-step explanation:
[tex]6x-14=46\\6x=60\\x=10[/tex]
Considere la siguiente ecuación: 16a – ( 3a – (6 – 9a) ) = 30a + ( – (3a + 2) – (a + 3) ) III) Al romper paréntesis, agrupar términos semejantes y simplificar. La ecuación queda:
Answer:
La ecuación simplificada es [tex]a = \frac{11}{19}[/tex].
Step-by-step explanation:
Tenemos la siguiente ecuación simultánea: [tex]16\cdot a - [3\cdot a - (6-9\cdot a)] = 30\cdot a +[-(3\cdot a+2)-(a+3)][/tex]. El procedimiento consiste en destruir los paréntesis desde dentro hacia fuera, agrupar los términos semejantes y simplificar. Presentamos el proceso paso por paso:
1) [tex]16\cdot a - [3\cdot a - (6-9\cdot a)] = 30\cdot a +[-(3\cdot a+2)-(a+3)][/tex] Dado
2) [tex]16\cdot a -\{3\cdot a + (-1)\cdot [6+(-1)\cdot 9\cdot a]\} = 30\cdot a +\{(-1)\cdot (3\cdot a +2)+(-1)\cdot (a+3)\}[/tex] [tex]-b = (-1)\cdot b[/tex]
3) [tex]16\cdot a -\{[(-1)\cdot (6)+(-1)\cdot (-1)\cdot 9\cdot a]\}= 30\cdot a +\{\left[(-1)\cdot (3\cdot a) + (-1)\cdot (2)\right] +[(-1)\cdot a +(-1)\cdot (3)] \}[/tex] Propiedad distributiva
4) [tex]16\cdot a -(-6+9\cdot a) = 30\cdot a +(-3\cdot a -2-a-3)[/tex] [tex]-b = (-1)\cdot b[/tex]/ [tex](-b)\cdot (-c) = b\cdot c[/tex]
5) [tex]16\cdot a +(-1)\cdot (-6+9\cdot a) = 30\cdot a -4\cdot a-5[/tex] Propiedad distributiva/Definiciones de adición y sustracción/[tex]-b = (-1)\cdot b[/tex]
6) [tex]16\cdot a +[(-1)\cdot (-6)+(-1)\cdot (9\cdot a)] = 26\cdot a -5[/tex] Propiedad distributiva/Definiciones de adición y sustracción/Propiedad modulativa.
7) [tex]16\cdot a +6-9\cdot a = 26\cdot a - 5[/tex] [tex]-b = (-1)\cdot b[/tex]/ [tex](-b)\cdot (-c) = b\cdot c[/tex]
8) [tex]7\cdot a +6 = 26\cdot a - 5[/tex] Propiedad distributiva/Definiciones de adición y sustracción.
9) [tex]6+5 = 26\cdot a -7\cdot a[/tex] Compatibilidad con la adición/Definición de sustracción.
10) [tex]11 = 19\cdot a[/tex] Propiedad distributiva/Definiciones de adición y sustracción.
11) [tex]19\cdot a = 11[/tex] Simetría de la igualdad.
12) [tex]a = \frac{11}{19}[/tex] Compatibilidad con la multiplicación/Existencia del inverso multiplicativo/Propiedad modulativa/Definición de división/Resultado.
La ecuación simplificada es [tex]a = \frac{11}{19}[/tex].
These ordered pairs represent a function:(0,2), (1,-1), (2,-4), (3,-7). Write a function rule (equation) to represent this function.
Answer choices
a.y=-3x+2
b.y=x+2
c.y=3x-7
d.y=3x+2
Answer:
A
Step-by-step explanation:
I included the steps in the picture I attached. lmk if you need me to explain more
a pickup truck travels 45 Mi on 2 and 1/3 gallons of gas how far did it travel on 1 gallon of gas
The pickup truck travels 19[tex]\frac{2}{7}[/tex] Miles in gallon.
What is Unit rate?A unit rate means a rate for one of something.
Given that a pickup truck travels 45 miles on 2[tex]\frac{1}{3}[/tex] gallons of gas,
Since there are 45 miles in 7/3 gallons
So, 45*3/7 in one gallon = 19[tex]\frac{2}{7}[/tex] Miles in one gallon
Hence, The pickup truck travels 19[tex]\frac{2}{7}[/tex] Miles in gallon.
For more references on unit rate, click;
https://brainly.com/question/11258929
#SPJ2
A new one-year membership at RecPlex costs $160. A registration fee of $28 is paid up front, and the rest is paid monthly. How much do new members pay each month? Write an equation for this..
Answer:
The first month new members have to pay 188 dollars for the membership.
The equation is 160x+28=y
x stands for the number of months and y stands for the total cost.
For the first month (membership starts) the total cost is 188$. For the second month the total money paid would be 348$. For the third month the total money paid would be 508$. And so on you can use the equation to solve for more months. Just substitute x for the number of months you are solving for.
can you writ the answe in a sheet on paper
Step-by-step explanation:
Make t the subject of the formula (5÷ t) -2 = s
__________________________________________________________
all the questions is on my page there is more 4
PLZZ HELP!!!!
1. Find the value of x and y.
2. In an A-figure house, the two congruent sides extend from the ground to form a 34° angle at the peek. What angle does each side form with the ground?
Problem 4
Note the markings at the top indicate that angle y represents half the angle BAC. In other words, we need 2 copies of angle y to make up angle BAC.
So we know that angle BAC = 2y
Due to the fact that triangle ABC is isosceles, we know that base angles B and C are congruent to 47.
Focusing on triangle ABC we have
A = 2yB = 47C = 47So,
A+B+C = 180 .... for any triangle, the angles always add to 180
2y+47+47 = 180
2y+94 = 180
2y = 180-94
2y = 86
y = 86/2
y = 43
Turn your attention to triangle ABD.
Here we have
angle A = y = 43angle B = 47angle D = xWe'll use the same idea as above, that all angles add to 180, to get...
A+B+D = 180
y+47+x = 180
43+47+x = 180
x+90 = 180
x = 180-90
x = 90
Answer: D) x = 90, y = 43===================================================
Problem 5
Let x be the angle formed by the diagonal sides and the horizontal ground. This is considered the base angle because this triangle is isosceles.
We have two base angles x and the third angle up top is 34
x+x+34 = 180
2x+34 = 180
2x = 180-34
2x = 146
x = 146/2
x = 73
Answer: C) 73The choir at wise middle school was preparing for their Hispanic concert. While rehearsing their opening song they noticed it took 48.7 seconds to sing it.They felt it was too long and sang it again taking off 2.9 seconds from the original time. The third time they sang it they were able to take an additional 0.47 seconds off their time. How long did it take the choir to sing the song the third time?
Answer:
45.88 seconds
Step-by-step explanation:
[tex]t_1[/tex] = Time taken to sing the fist time = [tex]48.7\ \text{s}[/tex]
Time taken to sing the second time was [tex]2.9\ \text{s}[/tex] less than the first time so
[tex]t_2=t_1-2.9\\\Rightarrow t_2=48.7-2.9\\\Rightarrow t_2=45.8\ \text{s}[/tex]
Time taken to sing the third time was [tex]0.47\ \text{s}[/tex] less than the the second time
[tex]t_3=t_2-0.47\\\Rightarrow t_3=45.8-0.47\\\Rightarrow t_3=45.88\ \text{s}[/tex]
So the time it took the choir to sing the third time was 45.88 seconds.
Perform the indicated operation 9 15/22 -3 2/11
Answer:
6 1/2
Step-by-step explanation:
Answer:6 1/2
Step-by-step explanation: do the math search it up
Joe had a balance of $34 on his credit card. He bought a sandwich and charged $40 on his credit card. 1a.) Write an equation that represents this scenario.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Credit card balance = $34
Amount of sandwich purchased = $40
The cost of sandwich purchased us added to the Initial credit card balance as the balance in a credit card is amount owed.
Hence it could be interpreted as though Joe has made purchases which amounts to $34 with his card before purchasing sandwich that costs $40
Hence; new card balance :
(Intial card balance + cost of sandwich)
$34 + $40 = $74
A construction uses beams that are 2,3, or 4 meters long. The measure of each beam must be converted to centimeters. Write a function to describe the situation. Find a reasonable domain and range for the function. (Hint 1 m = 100 cm)
Answer:
The function rule be 100 × x
The independent variables i.e. (2, 3, and 4) are considered to be the domain
The dependent variable (200,300,400) are considered to be the range
Step-by-step explanation:
The computation is shown below:
As we know that
1 m = 100 cm
So
2 m = 200 cm
3 m = 300 cm
4 m = 400 cm
The function rule be 100 × x
The independent variables i.e. (2, 3, and 4) are considered to be the domain
The dependent variable (200,300,400) are considered to be the range
Help please, thanks :)
Answer:
60°
Step-by-step explanation:
Angle 1 is a vertical angle to 60° by the definition of a vertical angle.
Answer:
∠1 = 60°
Step-by-step explanation:
If f(x) = 3x - 1 and 2f(b) = 28, what is the value of f(2b)?
=================================
Work Shown:
Solve the second equation for f(b)
2f(b) = 28
f(b) = 28/2
f(b) = 14
----------
Plug in x = b and solve for b
f(x) = 3x-1
f(b) = 3b-1 ... replace every x with b
14 = 3b-1 ..... plug in f(b) = 14
3b-1 = 14
3b = 14+1
3b = 15
b = 15/3
b = 5
-----------
f(x) = 3x-1
f(2b) = 3(2b)-1 .... replace every x with 2b
f(2b) = 3(2*5)-1 .... plug in b = 5
f(2b) = 3*10-1
f(2b) = 30-1
f(2b) = 29
The side of an equilateral triangle is 14 meters. What is the height of the triangle?.
Answer:
14... since all of it is equal
Step-by-step explanation:
WILL MARK BRAINLEST, PLEASE HELP !!!
Answer:
rate of change = first derivative= g'(x)=-2x+6
plug -3 to 5 into that g'(x) equation, it will be your answer
Step-by-step explanation:
9514 1404 393
Answer:
4
Step-by-step explanation:
The average rate of change of f(x) on the interval [a, b] is computed from ...
m = (f(b) -f(a))/(b -a)
On the interval [-3, 5] the average rate of change is ...
m = (f(5) -f(3))/(5 -(-3)) = ((-5^2 +6·5 +12) -(-(-3)^2 +6(-3) +12))/8
= (-25 +30 +12 +9 +18 -12)/8 = 32/8
m = 4
The average rate of change on the interval is 4.
__
Alternate solution
The first derivative of the function is ...
f'(x) = -2x +6
The average rate of change of a parabolic function on an interval is the rated of change at the midpoint of the interval. Here, the midpoint is x=(5+(-3))/2 = 1, so the average rate of change is ...
f'(1) = -2(1) +6 = 4
Find the rate of change
(Pls help!)
Answer: 11.5
Step-by-step explanation:
It’s delta y over delta x so you would take any two combination of coordinates and subtract and divide. I used 57.50-23 over 5-2... this gets you 34.5 over 3. This is also equal to 11.5 :)
What is the answer for X (geometry)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
In the lower triangle, one of the angles of which is 45 degrees, we know:
In the triangle, the side facing the angle 45° is √2 / 2 times the hypothenuse.
Thus ;
[tex]10 = hypothenuse \times \frac{ \sqrt{2} }{2} \\ [/tex]
[tex]hypothenuse \times \frac{ \sqrt{2} }{2} = 10 \\ [/tex]
Multiply sides by 2
[tex]hypothenuse \times \sqrt{2} = 2 \times 10[/tex]
Divide sides by √2
[tex]hypothenuse = \frac{2 \times 10}{ \sqrt{2} } \\ [/tex]
[tex]hypothenuse = \frac{ \sqrt{2} \times \sqrt{2} \times 10 }{ \sqrt{2} } \\ [/tex]
[tex]hypothenuse = 10 \sqrt{2} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The common side of the triangles is hypothenuse for both.
[tex]hypothenuse \times \cos(60) = x[/tex]
[tex]10 \sqrt{2} \times \frac{1}{2} = x \\ [/tex]
[tex]x = \frac{2 \times 5 \sqrt{2} }{2} \\ [/tex]
[tex]x = 5 \sqrt{2} [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is the Third Option .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Mr. Johnson has a piece of pipe 5 1/3 feet long. He decides to cut it into 3 equal pieces to use in making a railing for his porch. How long should he cut each piece?
HURRY!!! WILL GIVE ALOT OF POINT AND BRAINLIEST
Answer:
1.78
Step-by-step explanation:
7 is repeating but i rounded to the tenths its this. also, i just divided it by three because he cuts into three parts.
(ANSWER FAST PLSS)In AABC, what is the measure of angle B?
B
(2x)
(x+2).
140
A
046
0480
0700
092
HELP! help is needed ASAP! help is very much appreciated.
Answer:
Length of side e is 4.12
Length of side f is 4.24
The length of side f is larger than length of side e
Step-by-step explanation:
We are given two line segments e and f. We need to find lengths of both e and f and determine which is larger.
We can use distance formula to calculate lengths of line segments.
The Distance Formula is: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Finding length of side e:
We are given points (-2,3) and (-1,-1)
here we have [tex]x_1=-2, y_1=3, x_2=-1 , y_2=-1[/tex]
Putting values in distance formula and finding length
[tex]Length \ of \ side \ e= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ e= \sqrt{((-1)-(-2))^2+(-1-(3))^2}\\Length \ of \ side \ e= \sqrt{(-1+2)^2+(-1-3)^2}\\Length \ of \ side \ e= \sqrt{(1)^2+(-4)^2}\\Length \ of \ side \ e= \sqrt{1+16}\\Length \ of \ side \ e= \sqrt{17}\\Length \ of \ side \ e= 4.12[/tex]
So, Length of side e is 4.12
Finding length of side f:
We are given points (2,2) and (-1,-1)
here we have [tex]x_1=2, y_1=2, x_2=-1 , y_2=-1[/tex]
Putting values in distance formula and finding length
[tex]Length \ of \ side \ f= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ f= \sqrt{((-1)-(2))^2+(-1-(2))^2}\\Length \ of \ side \ f= \sqrt{(-1-2)^2+(-1-2)^2}\\Length \ of \ side \ f= \sqrt{(-3)^2+(-3)^2}\\Length \ of \ side \ f= \sqrt{9+9}\\Length \ of \ side \ f= \sqrt{18}\\Length \ of \ side \ f= 4.24[/tex]
So, Length of side f is 4.24
The length of side f is larger than length of side e
Graham has enough fencing to enclose a rectangular garden with a perimeter of 140 feet. If the width of his garden is 20 feet less than the length, what is the width of the garden?
Answer:
Width = 25 feet
Step-by-step explanation:
Perimeter of a rectangle = 2L + 2W
W = L - 20
P = 140
Hence,
140 = 2L + 2(L - 20)
140 = 2L + 2L - 40
Collect like terms
140 + 40 = 4L
180 = 4L
L = 180/40
L = 45 feet
Length = 45 feet
Width = L - 20 feet
=( 45 - 20) feet
= 25 feet
If 4(r + 2) – 13 = 11, what is the value of r?
What is the absolute value of -250?
Answer:
250
Step-by-step explanation:
Pretty much every time it asks for the abasloute value it just asks how much to get the zero on the number line. It will ALWAYS be positive. For example -5 will be 5 to get to zero on the numberline. Same thing with a positive 5.
Please answer these questions for 8th Grade Algebra! First-person to answer will be marked as brainiest! Worth lots of points!
1. x<=20
2. k<0
3. d<-3
4. m<=11
5. a>=3
6. 6<-5
This should help