Answer:
52
Step-by-step explanation:
Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.
SOMEONE PLEASE HELP ME WITH MATH! WILL GIVE BRAINLIEST TO FIRST PERSON WHO ANSWERS!!
Solve each system by substitution.
1. -5x-8y=9
y= -3.
2. y= -3x
-6x-2y=3
3. 6x+5y=10
y=-8x+2
4.6x+2y= -6
y= -3x -3
Thank you!
5 radians is the same as _____.
Answer:
286°28'44
Step-by-step explanation:
Walter bought a square plot of land. the perimeter is 544 feet. how wide is the property?
perimeter of a square = is side times 4
so divide 544 by 4
544/4 = 136
the property is 136 feet wide
Miss broom invested $10,000 into an account with an interest rate of 6% compounded annually which equation models the time it will take for his money to double?
A- logbase2 1.06= T
B- log2 =T
C-log1.06 =T
D= logbase1.06 2=t
Juanita’s boss told her that once she has worked with the company for 10 years, her salary will be increased to 3 times what she makes now plus $2,000. If s represents her original salary, which expression represents what her salary will be after 10 years at the company?
Answer:3s+2,000
Step-by-step explanation:
Find the exact solution to the equation. Show your work for credit. (1 point) four to the power of quantity twelve minus four x equals two hundred and fifty six.
The exact solution to the equation [tex]4^{(12 - 4x)[/tex] = 256 is x = 2. By recognizing that 256 is 4 raised to the fourth power, we equate the exponents and solve for x.
To solve this problem, we need to recognize that 256 is a power of 4. 4⁴ = 256. With this insight, the equation can be rewritten as:
[tex]4^{(12 - 4x)[/tex] = 4⁴
Since the bases are the same, we can equate the exponents:
12 - 4x = 4
Now, we'll isolate the variable x:
Subtract 12 from both sides: -4x = 4 - 12
-4x = -8
Divide both sides by -4: x = 2
Thus, the exact solution to the given equation is x = 2.
I want to make sure of my answer is right?
20 2/7 = 142/7 -20/35
find common denominator ( in this case it is 35)
35/7 =5 , multiply 142*5=710, 7*5 =35
142/7 = 710/35
710/35 - 20/35 = 710-20 = 690
690/35 now simplify that fraction
690/35 = 19.714
19*35 = 665
690-665=25
19 25/35
25/35 can reduce to 5/7
answer = 19 5/7
Which of the following is a factor of 6x2 + 2x − 21?
4x − 3
2x + 7
6x − 3
None of the above
if 6a-8b=0 and c=12b, the ratio of a to c is equivalent to the ratio of one to what number?
The measure of ∠B is (3x – 4 )° and the measure of ∠D is (2x – 6)°. What are the measures of angles B and D?
The measures of angles B and D are 110° and 70° respectively.
What is cyclic quadrilateral?The rule of cyclic quadrilateral states that, the sum of the opposite is supplementary i.e 180°
Therefore, applying this rule, Angle B and D are supplementary
Then, B+D=180°
Given that, B=3x-4 and D= 2x-6
Thus, (3x-4)+(2x-6)=180°
3x-4+2x-6=180°
3x+2x-4-6=180°
5x-10=180°
5x=180°+10
5x=190°
Then, x =190/5
x=38°
Then solving for B and D;
B=3x-4
B=3(38)-4
B=114-4
B=110°
Also, D=2x-6
D=2(38)-6
D=76-6
D=70°
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if f (x) =-14x-2, then f^-1 (x) =
Use the functions h(x) = 2x + 5 and t(x) = 7x − 6 to complete the function operations listed below.
Part A: Find (h + t)(x). Show your work. (3 points)
Part B: Find (h ⋅ t)(x). Show your work. (3 points)
Part C: Find h[t(x)]. Show your work. (4 points)
One number is 2 more than 3 times another. their sum is 22. find the numbers. 8, 14
how close are a meter and a yard? convert 1 meter into yards by using the fact
that there are 100 centimeters in a meter, 2.53 centimeters in a inch, 12 inches in a foot, and 3 feet in a yard.
Wich of the operations ,+,-,x➗are inverse o each other
33.
In quadrilateral PQRS, the coordinates are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry to show that the diagonals are perpendicular?
Apply the Distance Formula to show that opposite sides to show they are congruent.
Find the slopes of their product is 1.
Apply the Distance Formula to show that opposite sides to show sides are congruent.
Find the slopes and show that their product is -1.
Answer: The answer is (d) Find the slopes and show that their product is -1.
Step-by-step explanation: Given in the question and shown in the attached figure that the vertices of the quadrilateral PQRS are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). We are asked to use geometry to show that the diagonals PR and QS are perpendicular to each other.
We know that the two lines are perpendicular if the product of their slopes is --1.
So, first we will find the slopes of PR and QS, multiply them, and check the value.If the value is -1, then the diagonals are perpendicular to each other.
That is, if 'm' and 'p' are the slopes of the diagonals PR and QS, and if m × p = -1, then the two diagonals are perpendicular.
Thus, the correct answer is (d).
Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$. if $f(0) = 2$, then what is $f(2012)?$
Given:
f(0) = 2
So first of all, we let x = 2012, y = 0:
Then, F(2012) = 2012 + f(0)
Since f(0) = 2, then f(2012) = 2012 + 2 = 2014.
To add, the process that relates an input to an output is called a
function.
There are always three main parts of a
function, namely:
Input
The Relationship
The Output
The classic way of writing a function is "f(x) = ... ".
What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.
What a function does with the input can be usually seen as:
f(x) = x2 reveals to us that function "f" takes "x" and squares it.
Factor this expression. With work please!
Suppose there are 10,000 civilizations in the milky way galaxy. if the civilizations were randomly distributed throughout the disk of the galaxy, about how far (on average) would it be to the nearest civilization? (hint: start by finding the area of the milky way's disk, assuming that it is circular and 100,000 light-years in diameter. then find the average area per civilization, and use the distance across this area to estimate the distance between civilizations.)
Evaluate P(6,2).
A.) 12
B.) 30
C.) 360
The value of the [tex]\rm ^6p_2[/tex] is 30.
We have to determineThe value of P(6,2).
According to the question
The value of the [tex]\rm ^6p_2[/tex] is determined by using permutation.
The probability of selecting an ordered set of 'r' objects from a group of 'n' number of objects.
The order of objects matters in the case of permutation.
The formula to find [tex]\rm ^np_r[/tex] is given by:
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}[/tex]
Substitute n = 6 and r = 2 in the formula;
[tex]\rm ^np_r = \dfrac{n!}{(n-r)!}\\ \\ \rm ^6p_2 = \dfrac{6!}{(6-2)!}\\ \\ \rm ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4!}\\ \\ ^6p_2= \dfrac{6 \times 5\times 4 \times 3\times2 \times 1}{4\times 3 \times2 \times 1}\\ \\ ^6p_2= 6 \times 5}\\ \\ ^6p_2= 30[/tex]
Hence, The value of the [tex]\rm ^6p_2[/tex] is 30.
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write an equation for a line perpendicular to the x-axis that passes through the point (5,1)
The equation of a line perpendicular to the x-axis passing through the point (5,1) is x = 5. This is because a vertical line crossing the x-axis at a specific point will have the same x-coordinate for all its points.
Explanation:In mathematics, a line perpendicular to the x-axis is a vertical line that crosses the x-axis at a specific point. All points on this line will share the same x-coordinate. Therefore, a line that is perpendicular to the x-axis, and passes through the point (5,1) will have the equation x = 5. This equation represents a line that is vertical and intercepts the x-axis at the point where x equals 5. This is because in each point on the line, x remains constant, which is the characteristic of a vertical line in a Cartesian Coordinate System.
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800x200 I know the answer is 160000 but I want to see how quick you guys answer...
Find the surface area of the cone to the nearest tenth.
A. 203 cm2
B. 1341.5 cm2
C. 747.7 cm2
D. 213.5 cm2
The surface area of the given cone is 747.32.
What is area of a cone?"The total surface area of a cone is defined as the total area of the cone occupied in a three-dimensional area. It is equal to the sum of the curved surface and the base of the cone. "
Surface area of the cone is [tex]\pi*r(l+r )[/tex]
[tex](22/7)*7*(27+7)[/tex]
= 747.32
The surface area of the cone is 747.32
Hence, option C is correct.
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Angles θ and Φ are supplementary, and theta equals 3pi/7 find the measure of theta
From Plato: Φ =7π/7 or π.
What are the explicit equation and domain for an arithmetic sequence with a first term of 5 and a second term of 2?
an = 5 − 2(n − 1); all integers where n ≥ 1
an = 5 − 2(n − 1); all integers where n ≥ 0
an = 5 − 3(n − 1); all integers where n ≥ 1
an = 5 − 3(n − 1); all integers where n ≥ 0
The easiest way to answer this is to try all choices, plug in values for the 1st term and 2nd term then check if the answer matches with 5 and 2. (n = 1 and n = 2)
We know that n starts with 1 because that is our 1st term, we do not have 0th term, therefore that leaves us with 2 choices.
Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 2 (1 – 1) = 5 – 2 (0)
a1 = 5
n = 2
a2 = 5 – 2 (2 – 1) = 5 – 2 (1)
a2 = 3 (FALSE!)
Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 3 (1 – 1) = 5 – 3 (0)
a1 = 5
n = 2
a2 = 5 – 3 (2 – 1) = 5 – 3 (1)
a2 = 2 (TRUE)
Therefore the correct answer is:
an = 5 − 3(n − 1); all integers where n ≥ 1
Answer:
A is INCORRECT
Step-by-step explanation:
Just finished the FLVS test
A right triangle has legs that are 10.1in and 12.2 in long. What is the approximate length of the hypotenuse?
How can you eliminate the fraction from each side of the equation to make finding the
solution easier?
The equation is 1/2(x - 4) = 1/3x + 2
How can the average rate of change be found using a discrete graph?
The average rate of change can be found using a discrete graph by calculating the slope between two points on the graph. This provides insight into how the dependent variable changes as the independent variable varies.
Explanation:The average rate of change can be found using a discrete graph by calculating the difference in the y-values of two points and dividing it by the difference in the x-values of those same points. This will give you the slope of the line connecting the two points, which represents the average rate of change between those two points. For example, if you have two points (x1, y1) and (x2, y2), the average rate of change can be calculated as:
(y2 - y1) / (x2 - x1)
By finding the average rate of change at different intervals on the graph, you can analyze how the dependent variable changes in relation to the independent variable.
Which system is the only inconsistent system?
Select one:
a.
y
y
=
=
x+4
2x+4
y=x+4y=2x+4
b.
y
y
=
=
x
−x
y=xy=−x
c.
y
y
=4
=
x−3
4x+3
y=4x−3y=4x+3
d.
y
2y
=2
=
x−3
4x−6
y=2x−32y=4x−6
Option (c) represents an inconsistent system of equations, as the constant terms are not proportional, while the coefficients of x are. This system (y=4x-3, y=4x+3) has no solutions.
Explanation:In mathematics, specifically in algebra, an inconsistent system is a system of equations that has no solutions. To check which system is inconsistent from the options you've given, we need to compare the coefficients of each equation within a system. An inconsistent system will have proportional coefficients of x and y between the two equations, but the constant terms will not be proportional.
Looking at each option:
Option (a): y=x+4 and y=2x+4
Option (b): y=x and y=−x
Option (c): y=4x−3 and y=4x+3
Option (d): y=2x−3 and 2y=4x−6
From here, we can see that option (c): y=4x-3, y=4x+3 is inconsistent. In this system, the coefficients of x are proportional (4), but the constant terms (-3 and +3) are not proportional.
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The coordinates of the midpoint of GH¯¯¯¯¯¯¯¯are M(−2, 5) and the coordinates of one endpoint are H(−3, 7) .
The coordinates of the other endpoint are ( __ , __ )
The coordinate point of the other endpoint, G is (-1, 3)
The given parameters;
the midpoint = M(-2, 5)
one end point = H(-3,7)
To find:
the coordinate point of the other endpoint, GLet the coordinate point of the other endpoint = G(x, y)
The coordinate point of the other endpoint, G will be calculated using midpoint formula.
[tex]M(-2, 5) =( \frac{x + (-3)}{2} , \frac{y + 7}{2} )\\\\-2 = \frac{x - 3}{2} \ \ \ and \ \ 5 = \frac{y+ 7}{2} \\\\x-3 = 2(-2)\\\\x - 3 = -4\\\\x = -4 + 3\\\\x = -1\\\\y+ 7 = 2(5)\\\\y + 7 = 10\\\\y = 10 -7\\\\y = 3\\\\G= (-1, 3)[/tex]
Thus, the coordinate point of the other endpoint, G is (-1, 3)
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