Answer:
$ 46 and it's not enough
Step-by-step explanation:
6 + 5x
x = weeks
so after 8 weeks, his money should be
6 + 5(8) = 6 + 40 = $ 46
Not enough for buying RC model airplane
The money for Louis have after 8 week will be $46.
And, It is not enough.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The plane cost $48. His grandfather gave him $6 and his mother gave him an allowance of $5 per week.
And, He would have 6+5x dollars after x weeks.
Now,
The money after 8 week = 6 + 5 × 8
= 6 + 40
= $46
Thus, The money for Louis have after 8 week will be $46.
Since, The plane cost $48.
Hence, It is not enough.
Therefore, The money for Louis have after 8 week will be $46.
And, It is not enough.
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Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure. answwers: A) (x, y) → (x + 4, y + 5) B) (x, y) → (x – 4, y – 5) C) (x, y) → (x – 4, y + 5) D) (x, y) → (x + 5, y – 4)
Answer:
C. (x, y) -> (x - 4, y + 5)
Step-by-step explanation:
A is at (2, -2)
A' is at (-2, 3)
To get from 2 to -2, you must subtract 4, so (x - 4)
To get from -2 to 3, you must add 5, so (y + 5)
(x - 4, y + 5)
I hope this helps :))
The algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure should be option C. (x, y) -> (x - 4, y + 5)
Algebraic description:Since
A is at (2, -2)
A' is at (-2, 3)
So,
To get from 2 to -2, you should deduct 4, so (x - 4)
And,
To get from -2 to 3, you should deduct 5, so (y + 5)
Therefore,
(x - 4, y + 5)
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Find the surface area of the rectangular prism.
7 km
5 km
3 km
Answer:
142 km^3
Step-by-step explanation:
A=2(wl+hl+hw)
A=2(7*5+3*5+3*7)
A=142
Answer:
[tex]142km^{2}[/tex]
Step-by-step explanation:
you need to find the area of every side and then add them all together so
you do the equation
[tex]2[(7*5)+(3*5) + (7*3)][/tex]
I multiply everything by 2 because there is 2 of every side
once you solve this you get the answer of [tex]142km^{2}[/tex]
Shelly sells cars, and she has to sell 50 cars per month t get a bonus. If Shelly sold 28% of the number of cars needed to get a bonus, then how many did she sell?
Answer: 14
Step-by-step explanation:
28% of 50
Answer:
She selled 14 cars
Step-by-step explanation:
28÷100=0.28...
0.28×50=14
So she selled 14 cars
write the equation of the line passing through the points (-1,2) and (3,4)
Answer:
[tex]{y=\frac{1}{2}x+\frac{5}{2}[/tex]
Step-by-step explanation:
We can write the equation in slope intercept form.
[tex]y=mx+b[/tex]
Finding Slope:Slope is (rise/run). [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,2) and (3,4).
[tex]\frac{4-2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]
The slope is 1/2.
Finding Y-intercept:We can use the equation [tex]y=\frac{1}{2}x+b[/tex] to solve for the y-intercept.
Replace 'y' and 'x' with a given point and solve for 'b'. I will use (3,4).
[tex]4=\frac{1}{2}(3)+b\\\\4=\frac{3}{2}+b\\\\\frac{3}{2}+b=4\\\\\frac{3}{2}-\frac{3}{2}+b= 4-\frac{3}{2}\\\\[/tex]
[tex]b=\frac{5}{2}[/tex]
The y-intercept is 5/2.
Final Equation:As stated above, slope intercept form is [tex]y=mx+b[/tex]. 'M' is the slope and 'b' is the y-intercept.
We are given the slope of 1/2 and the y-intercept of 5/2.
[tex]y=mx+b\rightarrow\huge\boxed{y=\frac{1}{2}x+\frac{5}{2}}[/tex]
Write 286,200 in scientific notation.
Answer:
2.862*10^5
Step-by-step explanation:
First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 286200 you will get 2.862.
next, since you moved the decimal place to the left 5 times, the xoonent would be a positive 5.
Therefore, the answer is 2.862*10^5
The number of pets 40 students own is recorded
Number of pets: 2 , 4, 6, 8, 10
Number of students: x, 2, y, 6, 14
a) (i) show that x+y=18
(ii) If the mean of the distribution is 6.4, show that x +3y =30
(iii) Hence, find the value of x and of y
b) Using your answers in (a) (iii), find
(i) the median,
(ii) the mode,
Of the distribution
Answer:
a.
i) & ii) -> See Explanation Below
a.
iii) [tex]y = 6[/tex] and [tex]x = 12[/tex]
b.
i) [tex]Median = 7[/tex]
ii) [tex]Mode = 10[/tex]
Step-by-step explanation:
Given
Number of pets: 2 , 4, 6, 8, 10
Number of students: x, 2, y, 6, 14
Total students = 40
Required
a) (i) show that x+y=18
Given that total number of students is 40;
This implies that
[tex]x + 2 + y + 6 + 14 = 40[/tex]
Collect like terms
[tex]x + y = 40 - 14 - 6 - 2[/tex]
[tex]x + y = 18[/tex]
a) (ii) If the mean of the distribution is 6.4, show that x +3y =30
The mean of a distribution is calculated as thus
[tex]Mean = \frac{\sum fx}{\sum x}[/tex]
[tex]\sum fx}[/tex] is gotten by multiplying number of pets by corresponding number of students
[tex]\sum fx} = 2 * x + 4 * 2 + 6 * y + 8 * 6 + 10 * 14[/tex]
[tex]\sum fx} = 2 x + 8 + 6y + 48 + 140[/tex]
[tex]\sum fx} = 2 x + 6y + 48 + 140+ 8[/tex]
[tex]\sum fx} = 2 x + 6y + 196[/tex]
[tex]\sum x}[/tex] is the total number of students
[tex]\sum x} = 40[/tex]
So;
[tex]Mean = \frac{\sum fx}{\sum x}[/tex] becomes
[tex]Mean = \frac{2 x + 6y + 196}{40}[/tex]
Substitute 6.4 for Mean
[tex]6.4 = \frac{2 x + 6y + 196}{40}[/tex]
Multiply both sides by 40
[tex]256 = 2 x + 6y + 196[/tex]
Subtract 196 from both sides
[tex]256 -196= 2 x + 6y + 196-196[/tex]
[tex]60= 2 x + 6y[/tex]
Divide both sides by 2
[tex]\frac{60}{2}= \frac{2 x}{2} + \frac{6y}{2}[/tex]
[tex]30 = \frac{2 x}{2} + \frac{6y}{2}[/tex]
[tex]30 = x + 3y[/tex]
Reorder
[tex]x + 3y = 30[/tex]
a) (iii) Hence, find the value of x and of y
Using
[tex]x + y = 18[/tex] and
[tex]x + 3y = 30[/tex]
Subtract both equations
[tex](x + y = 18) - (x + 3y = 30)[/tex]
[tex]x - x + y - 3y = 18 - 30[/tex]
[tex]y - 3y = 18 - 30[/tex]
[tex]-2y = -12[/tex]
Divide both sides by -2
[tex]\frac{-2y}{-2} = \frac{-12}{-2}[/tex]
[tex]y = \frac{-12}{-2}[/tex]
[tex]y = 6[/tex]
Substitute 6 for y in [tex]x + y = 18[/tex]
[tex]x + y = 18[/tex] becomes
[tex]x + 6 = 18[/tex]
Subtract 6 from both sides
[tex]x + 6 - 6 = 18 - 6[/tex]
[tex]x = 12[/tex]
b.
i) Calculate the Median
First, we need to tabulate the given data properly
Number of Pets ------ Number of students ------- Cumulative Frequency
2 ------------------------------12 -----------------------------------12
4 ------------------------------2 -----------------------------------14
6 ------------------------------6 -----------------------------------20
8 ------------------------------6 -----------------------------------26
10 ------------------------------14 -----------------------------------40
Since the number of pets is already arranged in ascending order,
the next step is to calculate the median element
Number of students = 40
[tex]Median = \frac{40}{2}[/tex]
Median = 20
Given that number of students (40) is an even number,
The median is the average of the 20th and 21st element
From the table above; the median can be gotten from
6 ------------------------------6 -----------------------------------20
8 ------------------------------6 -----------------------------------26
The 20th element = 6
The 21st element = 8
[tex]Median = \frac{6 + 8}{2}[/tex]
[tex]Median = \frac{14}{2}[/tex]
[tex]Median = 7[/tex]
ii) Mode
The mode is the corresponding data with the highest frequency
The highest frequency is 14;
The number of pets with frequency of 14 is 10
Hence,
[tex]Mode = 10[/tex]
Which compound inequality is equivalent to |ax-b| > c for all real numbers a,
-Cc
ООО
-C>ax-b>c
ax-b>-c or ax->
ax-b<-c or ax-b>c
The equivalent compoud inequality is (D) ax - b > c or ax - b < -c
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The absolute value expression is
| ax -b | > c
Given that c > 0, then it means that:
| ax -b | > 0
So, we have the following inequalities equivalent to | ax -b | > c
ax - b > c
ax - b < -c
Hence, the equivalent compound inequality is (D) ax - b > c or ax - b < -c.
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Find volume of triangular prism
Answer:
125 inches^3
Step-by-step explanation:
First find the area of the triangle using the formula:
[tex] \frac{bh}{2} [/tex]
This results in 12.5 inches^2.
Then because it's volume, we need to multiply by the length, due to that being how big it is; resulting in 125 inches^3.
solve for x, x+3y=-3
Answer:
x=-3y-3
Step-by-step explanation:
x+3y=-3
x=-3y-3
Answer:
x= -3y-3
Step-by-step explanation:
x+3y= -3
Subtract 3y from both sides
x= -3y-3
please help quickly!!!!!!!!!!!1
Answer:
1 3/5
Step-by-step explanation:
1 5/7 ÷ 1 1/14
Change from mixed numbers
(7*1+5)/7 ÷ (1*14+1)/14
12/7 ÷15/14
Copy dot flip
12/7 * 14/15
12/15 * 14/7
4/5 *2/1
8/5
Change to a mixed number
1 3/5
Answer:
24/15
Step-by-step explanation:
first we change the mixed fraction to improper fraction
12/7÷15/14
12/7×14/15
24/15
Select the graph that would represent the best presentation of the solution set for Ixl <5.
Answer:
< = region below graph
> = region above graph
< = region below graph
> = region above graph
Step-by-step explanation:
To find the distance an object has traveled, you use the formula D=RT; where D=distance, R=rate and T=time. What was the rate a person drove if they traveled 313.5 miles in 4 hours? A. 78.374 miles per hour B. 78.375 miles per hour C. 1,254 miles per hour D. 12,540 miles per hour
Answer:
78.375 miles per hour = R
Step-by-step explanation:
D= RT
The miles are 313.5 which is D and the time is 4 hours
313.5 = R * 4
Divide each side by 4
313.5/4 = R
78.375 miles per hour = R
Pete, Chris, and Dina realized that the number of A’s they each received on their report cards were in a ratio of 4:2:5. If Pete got 14 more A’s than Chris, how many A’s did Dina get?
Answer:
A's received by Dina is 35.
Step-by-step explanation:
Given
number of A’s received by Pete, Chris, and Dina on their report cards were in a ratio of 4:2:5.
Let the
A's received by Pete = 4x
A's received by Chris = 2x
A's received by Dina = 5x
This, is done so that ratio of 4:2:5 remains intact.
Now, given Pete got 14 more A’s than Chris got
Thus, writing it mathematically
A's got by Pete = A's got be Chris + 14
we will be using A's got Pete and Chris in term of x as defined above
4x = 2x+ 14
=> 4x - 2x = 14
=> 2x = 14
=> x = 14/2 = 7
A's received by Dina = 5x = 5*7 = 35( Answer).
Which is the graph of 2x - 4y > 6?
4
TY
417
41Y
N
2.
N
N
a
2
4
2
4 -2
-2
-4 -2
-2
2
-4-2
2
AN
-2
X
Answer:
Step-1: the x-intercept and the y-intercept
2x - 4y = 6
For y = 0, we get the x-intercept.
2x - 4(0) = 6
2x = 6, and then divide by two on both sides.
Hence, the x-intercept is
For x = 0, we get the y-intercept.
2(0) - 4y = 6
-4y = 6, and then divide by -4 on both sides.
Hence, the y-intercept is y = -3/2 = ( 0, -3/2)
The graph of the inequality 2x - 4y > 6 is the same as y < 0.5x - 1.5
How to determine the graph?The inequality is given as:
2x - 4y > 6
Divide through by 2
x - 2y > 3
Subtract x from both sides
- 2y > -x + 3
Divide both sides by -2
y < 0.5x - 1.5
See attachment for the graph of the inequality 2x - 4y > 6
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Which symbol correctly compared these two fractions
Answer:
The answer is C.
Step-by-step explanation:
When you simplify the left fraction, you will get the right fraction.
[tex] \frac{3}{9}[/tex]
[tex] = \frac{3 \div 3}{9 \div 3} [/tex]
[tex] = \frac{1}{3} [/tex]
Therefore, the symbol is = ;
[tex] \frac{1}{3} = \frac{1}{3} [/tex]
Please help meeee
Tell me Tell me Tell me
Answer:
the answer would be c
Step-by-step explanation
hope it helps!
Find the y value for the point that divides the line segment CD into a ratio of 4:1.
Segment CD is shown. C is at 9, 6 and D is at 5, 1.
2
6.2
3
2.8
Answer:
Y = 2
Step-by-step explanation:
For point (x1,y1) and (x2,y2) on coordinate plane if is divided in ratio of m:n.
Then point of division is given by
(n*x1+m*x2)/ m+n, (n*y1+m*y2)/ m+n
________________________________
Given point
c = (9,6)
d = (5,1)
ratio = 4:1
using the above formula , point of division is
x= (1*9+4*5)/ 4+1 y= (1*6+4*1)/ 4+1
x= (9+20)/ 5 y= (6+4)/ 5
x= 29/ 5 y= 10/ 5 =2
Thus, answer is y = 2
Answer:
2 is correct
Step-by-step explanation: I got it right on test
HELP will give brainliest
Answer:
60 mph
Step-by-step explanation:
I guessed and checked random numbers that would be 20% speed reduction to 48 mph.
Answer: 38.4
Please mark my answer as Brainliest
Which set of numbers is arranged in increasing order?
Answer:
B
Step-by-step explanation:
To solve this, we can make all of the numbers decimals.
π=3.14159265 and so on
Root 10 is about 3.16227766
22/7 is about 3.14285714
3.14 is already a decimal.
Now, our numbers are far easier to compare.
Let's put the numbers in increasing order.
3.14, 3.14159265, 3.14285714, 3.16227766
Substitute the original numbers in.
3.14, π, 22/7, Root 10
Therefore, option B is correct.
PLEASE HELP is 48, 41, 50, 46 a solution??
heeeeeeeeeelpppppppppppp
Answer:
4
Step-by-step explanation:
The x value is the solution to x - 4 = 0, which is x = 4.
Answer: (4, -2)
Step-by-step explanation:
-3(x-4)
-3x + 12
-3x = -12
x = 4
please meee pleasee!
Answer:
D
Step-by-step explanation:
Tenth vs Hundreth.... ten times larger
Answer:
D. 0.73
Step-by-step explanation:
In the number 0.975, 7 stands for 7 hundredths i.e. 0.07
=> Multiplying 0.07 by 10 will make it 0.7 ( 7 tenths)
=> The number with 7 tenths or 0.7 is 0.73
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (-5, -7) and parallel to the line whose equation is y = - 4x + 4
Write an equation for the line in point-slope form.
Write an equation for the line in slope-intercept form.
There are 32 students in a class. They are taking either biology or chemistry or both. The
number of students taking biology is three times as many as the number of students
taking chemistry. If 4 students are taking both biology and chemistry, how many
students are in biology?
Answer:
27
Step-by-step explanation:
Let's call the number of students taking chemistry x which makes the biology students 3x. Since the overlap is 4 the amount of students who take chemistry only or biology only is x - 4 and 3x - 4 respectively therefore we can write:
x - 4 + 3x - 4 + 4 = 32
4x - 4 = 32
4x = 36
x = 9
Since x = 9, the amount of biology students is 3x which is 3 * 9 = 27.
Answer:
27
Step-by-step explanation:
An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle
horizontal to her line of sight and located directly above a tower (1). The observer also notices a
bird (B) circling directly above her. If the distance from the plane(P) to the tower () is 7,000 feet,
how far is the bird (B) from the plane (P)? Round to the nearest whole number.
B
х
P
7000
1
1
1
33°
A
Answer: 10,779 feets
Step-by-step explanation:
From the sketch attached ;
∠POT is the Angle of elevation = 33°
Height of tower = 7000 Feets
Taking the triangle POT
WHERE PT = 7000 Feets (Opposite)
Distance (d) between the bird and plane is the ADJACENT,
NOTE: (BP = OT = d)
Taking the tangent of the angle of elevation;
Tan Θ = opposite / Adjacent
Tan 33° = 7000 / d
Cross multiply
d × 0.6494075 = 7000
d = 7000 / 0.6494075
d = 10779.054 = 10,779 feets
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0 0 2 1 cannot be determined
Answer:
0 solution
Step-by-step explanation:
Given
[tex]x^2 + 5x+ 7 = 0[/tex]
Required
Find number of solutions;
The number of solutions can be determined via the value of determinants, D;
Such that
[tex]D = {b^2} - {4ac}[/tex]
By comparing the general form of equation;
[tex]ax^2 +bc x + c = 0[/tex]
with [tex]x^2 + 5x+ 7 = 0[/tex]
This gives
[tex]a = 1\\b = 5\\c = 7[/tex]
So;
[tex]D = {b^2} - {4ac}[/tex] becomes
[tex]D = {5^2} - {4*1*7}[/tex]
[tex]D = {25} - {28}[/tex]
[tex]D = -3[/tex]
The calculated value of D is less than 0;
This implies that [tex]x^2 + 5x+ 7 = 0[/tex] has no real solution
In how many different ways can 2/15 be represented as 1/a+1/b, if a and b are positive integers with a greater than or equal to b?
Answer:
There are three possible combinations of positive integers such that a > b:
(1) a = 15 and b = 15
(2) a = 20 and b = 12
(3) a = 45 and b = 9
Step-by-step explanation:
Notice that the possible factors (different from "1") of the denominator "15" are: 3, 5, and 15.
The answer for the case a = 15 and b = 15 is obvious since :
[tex]\frac{1}{15} + \frac{1}{15} = \frac{2}{15}[/tex]
Then the possibility of a multiple of 5 for one of the denominators (let's say 5*n) and a multiple of 3 (let's say 3*m)for the other one gives the general equation:
[tex]\frac{1}{5n} +\frac{1}{3m} =\frac{2}{15}[/tex]
which should verify the following as we try to solve for one of the unknowns multiplicative factors which by the way have to be positive for the requirement given in the problem:
[tex]\frac{5n+3m}{15mn} =\frac{2}{15}\\\frac{5n+3m}{mn} =\frac{2}{1}\\5n+3m=2mn\\\frac{5n+3m}{mn} =2\\\frac{5}{m} +\frac{3}{n} =2\\\frac{5}{m}=2-\frac{3}{n}[/tex]
This last equation is very simple to analyze using integer values for "n" which would render a positive value on the right hand side, and then check from that set the ones that give an integer for the value "m".
Those found were:
For n=3, and m=5, a=15, and b=15 (the obvious solution discussed above)
[tex]\frac{1}{15} +\frac{1}{15}=\frac{2}{15}[/tex]
For n = 4 and m = 4, a = 20, and b = 12
[tex]\frac{1}{20} +\frac{1}{12}=\frac{32}{240}=\frac{2}{15}[/tex]
and for n=9 and m=3, a=45 and b = 9
[tex]\frac{1}{45} +\frac{1}{9}=\frac{54}{405}=\frac{2}{15}[/tex]
Solve the system of linear equations below.
6x + 3y = 33
4x + y = 15
A. x = 2, y = 7
B. x = -13, y = 7
C. x = y = 12
D. x = 5, y = 1
Answer:
A. x = 2, y = 7
Step-by-step explanation:
I graphed the equations on the graph below to find the solution to the system of linear equations.
Answer:
A. x = 2, y = 7...
Step-by-step explanation:
Classify the following triangle as acute, obtuse, or right.
80°
A. Obtuse
B. Acute
C. Right
D. None of these
Answer: I'm guessing it's acute
Step-by-step explanation:
Since all the angles are less that 90 degrees, it can't be right or obtuse. I'm gonna say acute
Write an equation that represents the table: x y 2 9 3 27 4 81
Answer:
the desired equation is y = 3^x
Step-by-step explanation:
if x = 2, then y = 9, and 9 is 3². If x = 4, y = 81 = 3^4.
Therefore we can conclude that the desired equation is y = 3^x
