Given:
A wire 45 meters long is cut into two pieces
One piece is 5 meters longer than the other.
To find:
The length of the two pieces.
Solution:
Let length of one piece be x.
One piece is 5 meters longer than the other. So,
Length of another piece = x+5
Total length of wire is 45. So,
[tex]x+(x+5)=45[/tex]
[tex]2x+5=45[/tex]
Subtract 5 from both sides.
[tex]2x=45-5[/tex]
[tex]2x=40[/tex]
Divide both sides by 2.
[tex]x=\dfrac{40}{2}[/tex]
[tex]x=20[/tex]
Now,
Length of one piece = 20 meters
Length of another piece = 20 + 5
= 25 meters
Therefore, the length of two pieces are 20 and 25 meters.
Writing an Equation Given Two Point
A line has an x-intercept of 3 and a y-intercept of -6.
The slope-intercept form of its equation is
I WILL MARK YOU BRAINLIEST PLEASE HELP. It needs to be correct
9514 1404 393
Answer:
a) the originb) 2Step-by-step explanation:
Lines AA', BB', and CC' all converge at the origin. The origin is the center of dilation.
__
Each image point is twice as far from the origin as its corresponding pre-image point. The scale factor is 2.
Michael consumes a 16 ounce bag of potato chips and 12 ounce bag of pretzels every day after school. How many more ounces of potato chips than pretzels will Michael have eaten at the end of a 5 day school week?
A.
20 ounces
B.
80 ounces
C.
60 ounces
D.
28 ounces
Answer:
b
Step-by-step explanation:
Consider a right triangle with leg b = 7.1 and opposite angle B = 39.3. Using a calculator, determine the other angle and the remaining sides of the triangle. Express your answers using at least one decimal place.
Answer:
i. a = 8.7, b = 7.1 and c = 11.2
ii. A = [tex]50.7^{o}[/tex], B = [tex]39.3^{o}[/tex] and C = [tex]90^{o}[/tex]
Step-by-step explanation:
Given a right triangle with, b = 7.1 and B = [tex]39.3^{o}[/tex].
I. Applying the trigonometric function to determine leg a, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]39.3^{o}[/tex] = [tex]\frac{7.1}{a}[/tex]
a = [tex]\frac{7.1}{Tan 39.3^{o} }[/tex]
= 8.675
The length of leg a is 8.7.
ii. To determine leg c,
Sin [tex]39.3^{o}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{7.1}{c}[/tex]
⇒c = [tex]\frac{7.1}{Sin39.3^{o} }[/tex]
= 11.21
The length of leg c is 11.2.
iii. Given that: B = [tex]39.3^{o}[/tex] and C = [tex]90^{o}[/tex]
Then,
A + B + C = [tex]180^{o}[/tex] (sum of angles at a point)
A + [tex]39.3^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]
A + [tex]129.3^{o}[/tex] = [tex]180^{o}[/tex]
A = [tex]180^{o}[/tex] - [tex]129.3^{o}[/tex]
= [tex]50.7^{o}[/tex]
Mike had 180 blue and red pencils. He had 45 blue. What percentage of his pencils are red.
The percentage of red pencils Mike had is 75%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Mike had 180 blue and red pencils and 45 were blue.
So, The number of red pencils is,
= (180 - 45).
= 135.
Therefore, The percentage of red pencils is,
= (135/180)×100%.
= 75%.
Some other concept related to percentage is percentage change,
The net amount change will now be divided by the original sum and multiplied by 100%, giving us the percentage change, which is,
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Which expression is equal to (x+2)(x-4)/(x-4)(x+4)
A) x-2/x+4
B) x+4/x+2
C) x-2/x-4
D) x+2/x+4
Answer:
The expression equal to [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex] is [tex]\frac{(x+2)}{(x+4)}[/tex]
Option D is correct.
Step-by-step explanation:
We need to solve the expression [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex]
Since it is a fraction, and all terms are multiplying with each other we can cancel out common terms.
Since x-4 is both in numerator and denominator so, it will be cancelled out and we will get:
[tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}\\=\frac{(x+2)}{(x+4)}[/tex]
So, the expression equal to [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex] is [tex]\frac{(x+2)}{(x+4)}[/tex]
Option D is correct.
Answer:
D.) x+2/x+4
I took the quiz :)
Step-by-step explanation:
In the activity, Heavy Flying, we looked at constraints for transporting packages from Careful Calculators and Charlie's
Chicken Feed
• Charlie's Chicken Feed containers weigh 40 pounds and are 2 cubic feet in volume.
• Careful Calculators containers weigh 50 pounds and are 3 cubic feet in volume.
On Monday, the pilot transferred containers that totaled 30,000 pounds and 1,600 cubic feet in volume.
1. Write a system of equations to model this situation.
2. Write a matrix equation to model this situation.
3. Solve. How many of each container was transported?
Show your work by uploading a picture or typing in the text box.
Answer: 500 chicken feed and 200 careful calculators
Step-by-step explanation:
2x+3y=1,600
40x+50y=30,000
those are your first two equations
your first matrix equation for A is 2, 3,40,50 and B is 1,600 and 30,000 when you enter those in your calculator and 500 and 200 should be your result.
a) The system of equations are 2x + 3y = 1600 and 40x + 50y = 30000
b) The matrix equations are solved
c) The solution to the system of equations is
The number of chicken feed = 500
The number of careful calculators = 200
What is multiplication of matrices?The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix
Given data ,
Let the number of chicken feed be represented as x
Let the number of careful calculators be y
Now , the equation will be
Charlie's Chicken Feed containers weigh 40 pounds and are 2 cubic feet in volume
And , Careful Calculators containers weigh 50 pounds and are 3 cubic feet in volume
Substituting the values in the matrices , we get
[tex]\left[\begin{array}{ccc}2 &3 \\ 40 &50 \\\end{array}\right] * \left[\begin{array}{ccc}x\\y\\\end{array}\right]= \left[\begin{array}{ccc}1600\\30000\\\end{array}\right][/tex]
On simplifying the matrix equation , we get
2x + 3y = 1600 be equation (1)
40x + 50y = 30000 be equation (2)
Now , multiply equation (1) by 20 , we get
40x + 60y = 32000 be equation (3)
Subtracting equation (2) from equation (3) , we get
10y = 2000
Divide by 10 on both sides of the equation , we get
y = 200 careful calculators
Substituting the value of y in equation (1) , we get
2x + 3 ( 200 ) = 1600
2x + 600 = 1600
Subtracting 600 on both sides of the equation , we get
2x = 1000
Divide by 2 on both sides of the equation , we get
x = 500 chicken feeds
Therefore , the value of x and y are 500 and 200 respectively
Hence , the system of matrix equations are solved
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GH¯¯¯¯¯¯¯ has endpoints G(−3, 2) and H(3, −2).
Find the coordinates of the midpoint of GH¯¯¯¯¯¯¯ .
A. (−3, 0)
B. (0, 2)
C. (0, 0)
D. (0, −2)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]( \frac{ - 3 + 3}{2} \: , \: \frac{ - 2 + 2}{2} ) = ( \frac{0}{2} \: , \: \frac{0}{2} ) = \\ [/tex]
[tex](0 \: , \: 0)[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is (( C )) .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Please help! this assignment is due under 10 minutes! please with explatiation Thank you!
can't see the question its blurry
Answer:
The 1st graph is The answer
Need help with this
(I think it’s 49 but I’m not sure)
Answer:
Its 49
Step-by-step explanation:
Can i get brainliest
What is the slope of the line that intersects this two points (12,2), (-7,5)
(12,2) (-7,5)
x1 y1. x2 y2
use this formula to solve:
y2-y1/x2-x1
=
(5)-(2)
(-7)-(12)
slope: -3/19
8. If k = log2 3 then log2 48 =
Answer:
16k
Step-by-step explanation:
k=3log2
k=(48\16) log2
16k= 48log2
16k=log2 48
Numbers can be expressed in logarithms.
The value of [tex]\mathbf{log_248}[/tex] is [tex]\mathbf{k + 4}[/tex]
The expressions are given as:
[tex]\mathbf{k = log_23}[/tex]
[tex]\mathbf{log_248}[/tex]
Express 48 as 3 * 16
[tex]\mathbf{log_248 = log_2(3 \times 16)}[/tex]
Split
[tex]\mathbf{log_248 = log_2(3) + log_2(16)}[/tex]
Express 16 as 2^4
[tex]\mathbf{log_248 = log_2(3) + log_2(2^4)}[/tex]
Rewrite as:
[tex]\mathbf{log_248 = log_2(3) + 4log_22}[/tex]
In logarithms:
[tex]\mathbf{log_aa = 1}[/tex]
So, we have:
[tex]\mathbf{log_248 = log_2(3) + 4(1)}[/tex]
[tex]\mathbf{log_248 = log_2(3) + 4}[/tex]
Substitute [tex]\mathbf{k = log_23}[/tex]
[tex]\mathbf{log_248 = k + 4}[/tex]
Hence, the value of [tex]\mathbf{log_248}[/tex] is [tex]\mathbf{k + 4}[/tex]
Read more about logarithms at:
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Cheyenne is deciding between the ways she has to buy music. Albums on CD cost
$13 but downloads of an album only cost $10. If she can spend up to $150 on
music purchases, which of these expresses her purchasing restrictions when she
buys c CDs and downloads d albums?
Answer:
13c+10d>150
Step-by-step explanation:
3. Given A(3,5), B(7, 10), C(0, 2), and D(1, a),
determine the value of a for which:
a) Line AB is parallel to line CD.
b) Line AB is perpendicular to line CD.
please help!! i’m failing grade 10 precal and i need this❤️ will give 15 points
Answer:
1) if Line AB is parallel to line CD then value of a is: a=3
2) if Line AB is perpendicular to line CD then value of a is: a=1
Step-by-step explanation:
We are given A(3,5), B(7, 10), C(0, 2), and D(1, a) we need to find value of a for which:
We can use slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] to find value of a according to conditions given.
We are given:
[tex]x_1=3, y_1=5, x_2=7, y_2=10 \ for \ line \ AB \ and \\\x_1=0, y_1=2, x_2=1, y_2=a \ for \ line \ CD \[/tex]
a) Line AB is parallel to line CD.
When 2 lines are parallel there slope is same so, using this we can find value of a
[tex]Slope \ of \ line \ AB = Slope \ of \ line \ CD[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1}= \frac{y_2-y_1}{x_2-x_1}\\\frac{10-5}{7-3}=\frac{a-2}{1-0} \\\frac{5}{5}=\frac{a-2}{1}\\1=a-2\\a=1+2\\a=3[/tex]
So, if Line AB is parallel to line CD then value of a is: a=3
b) Line AB is perpendicular to line CD.
When 2 lines are perpendicular there slopes are opposite of each other so, using this we can find value of a
[tex]Slope \ of \ line \ AB =-\frac{1}{Slope \ of \ line \ CD}[/tex]
[tex]\frac{y_2-y_1}{x_2-x_1}=-\frac{1}{ \frac{y_2-y_1}{x_2-x_1}} \\\frac{y_2-y_1}{x_2-x_1}=-\frac{x_2-x_1}{y_2-y_1}\\\frac{10-5}{7-3}=-\frac{1-0}{a-2} \\\frac{5}{5}=-\frac{1}{a-2}\\1=-\frac{1}{a-2}\\a-2=-1\\a=-1+2\\a=1[/tex]
So, if Line AB is perpendicular to line CD then value of a is: a=1
In a newspaper, it was reported that the number of yearly robberies in Springfield in 2012 was 90, and then went down by 50% in 2013. How many robberies were there in Springfield in 2013?
Answer: 45
Step-by-step explanation:
A car rental agency advertised renting a car for $23.95 per day and $0.24 per mile. If Shawn rents this car for 3 days, how many whole miles can he drive on a $150 budget?
Answer:
23.95(3)+ 0.24=150 multipy 3 and 23.95
71.85+0.24m=150 subtract 71.85 from 150
0.24m=78.15 divide 78.15 by 0.24
m=325 miles
There were 20 cups of pudding left in the cafeteria after lunch. The lunch aide poured the extra pudding into quart sized containers how many quart sized containers will she need?
Answer:
5
Step-by-step explanation:
1 galon =16 tazas
1/4 de galon=4 tazas
1+.25= 1.25 ó 1+1/4=1, 1/4 y eso lo multiplico por 4
1.25 ×4= 5
Can someone help me? Giving 23 Points.
Answer:
Option 2 you welcome
explanation: I had this question a while back and I'm 100% sure that this is the right answer!
Choose all the expressions that are equal to 34 × 8,010.
A. 8,010 × 34
B. 34 × (801 × 102)
C. 30 × 4 × 8,010
D. 34 × (8,000 + 10)
E. (30 + 4) × 8,010
Answer: A. 8,010 × 34
D. 34 × (8,000 + 10)
E. (30 + 4) × 8,010
Step-by-step explanation:
First we need to calculate 34 × 8010 = 272340
A. 8,010 × 34 = 272340
This is equal to 34 × 8010.
B. 34 × (801 × 102)
= 34 × 81702
= 2777868
This is not equal to 34 × 8010.
C. 30 × 4 × 8,010
= 961200
This is not equal to 34 × 8010.
D. 34 × (8,000 + 10)
= 34 × 8010 = 272340
This is equal to 34 × 8010.
E. (30 + 4) × 8,010
= 34 × 8010 = 272340
This is equal to 34 × 8010.
Therefore, the correct options are:
A, D, E.
hhHheLLlpP Help help help help help plzz
The school hiking club had a car wash on Saturday and Sunday. The students washed 30% of the
cars on Saturday. If they washed 24 cars on Saturday, how many cars did they wash on both days?
O A) 24
O B) 30
OC) 72
OD 80
Answer:
D) 80
Step-by-step explanation:
30 x 80 = 24
100
30/100 = 24/80
30% = 24
24 is 30% of 80
Hopefully this helped! Sorry if wrong. You are loved and you are beautiful/handsome!
-Bee
PLEASEEEEEE HELPPPPP ASAPPPP
If f(x) = 2x2
+3 and g(x) = x2 - 7, find (f + g)(x).
A. x² - 4
B. X2 + 10
C. 3x2 - 4
D. 3x2 - 10
Answer:
Im stupid so dont trust me but imma guess and say c
Answer:
YEH its B X to the second power Plus 10
Step-by-step explanation:
Please help on a maths question, Brainiest for the best answer!!!
perimeter = sum of all sides
= 4.3 + 7 + 4.3 + 7 + 4.3 + 7 + 2.7
= 36.6 cm
Answer:
36.6 cm
Step-by-step explanation:
Each side, starting with the one all the way to the left and going anticlockwise.
7 + 4.3 + 7 + 4.3 + 7 + (7 - 4.3 = 2.7) + 4.3 = 36.6
PLEASE I NEED HELP URGENT I WILL MARK, SOLVE AND EXPLAIN THE ANSWER
Which of these graphs is the solution set for the equation y = -4?
Answer:A
Step-by-step explanation:
You are trying to find the Y-Intercept. So because there is no slope it is the Y-int.Also hope this is correct, sorry if it is wrong.
Solve for
50
15
None of the above
Other
Solve -5 = 3x - 14.
X=__
Answer:
x=3
Step-by-step explanation:
-5 = 3x - 14
+14 + 14
3/9 = 3/3x
3 = x
An architect is planning a triangular pool with a perimeter of 99 ft.Two of the sides measure 20 and 42, respectively, what is the length of the missing side(x)?Solve for x
Given:
Perimeter of the triangle = 99 ft
Length of two sides are 20 ft and 42 ft.
To find:
The length of missing side.
Solution:
Let the missing side be x.
Perimeter of a triangle is the sum of all sides of that triangle.
[tex]x+20+42=99[/tex]
[tex]x+62=99[/tex]
Subtract 62 from both sides.
[tex]x=99-62[/tex]
[tex]x=37[/tex]
Therefore, the missing side of the triangle is 37 ft.
Jesse plays basketball for his high school team. In his last 12 twelve games he scored the following points: 18, 22, 19, 15, 24, 22, 18, 15, 10, 14, 18, 10. Barbara plays basketball for her high school team. In her last 10 games she scored the following points: 15, 12, 12, 16, 18, 22, 16, 20, 20, 14. Determine which player had the largest range of points scored? What is the difference is the range of points between the two players?
In the form of a paragraph, explain in complete sentences the steps necessary to compute the range of the points, which team player had the largest range of points and include the final answer in your explanation. Complete your work in the space provided.
Answer:
Jesse has the largest range between the two players. The difference between their ranges is 2.
Step-by-step explanation:
Jesse's range: 14
Barbara's range: 10
Range is determined by using the largest number and the smallest number in a set of integers and subtracting them. Jesse's highest number was 24, and his lowest would be 10. 24-10=14.
Barbara's highest score was 22, while her lowest was 12. 22-12=10.
subtracting Jesse's range from Barbara's range would equal 2.
(please don't cook me if this is incorrect but i'm 97% sure i'm right)
Find the slope of the line that passes through (24,-5) and (87, 64).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
Distance
80.7527089328897
Midpoint
(81.5,24)
Slope
7.27272727272727
x intercept
78.20
y intercept
−568.73
Step-by-step explanation:
Answer:
[tex]1 \frac{2}{21} [/tex]
Step-by-step explanation:
Please see the attached picture for the full solution.