−4x−6=−5y+2 Write a formula for g(x) in terms of x
Answer:
4/5x + 8/5 = g(x)
Step-by-step explanation:
−4x−6=−5y+2
Solve for y
Subtract 2 from each side
−4x−6-2=−5y+2-2
-4x -8 = -5y
Divide each side by -5
-4x/-5 -8/-5 = -5y/-5
4/5x + 8/5 = y
Replace y with g(x)
4/5x + 8/5 = g(x)
2) The wind blew away 16 of your muffins. That was 4/7 of all of them! How many are left?
A) 28
B) 31
C) 12
D) 9.14286
Answer: Option C, 12 muffins are left
28 is the value of all the muffins, since 1/7 of the muffins would be 4. subtract 16 from 28, and you get 12.
Algebra determine whether the given coordinate are the vertices of a triganle explain.
To determine whether the given coordinates are the vertices of a triangle, we need to check if they form a triangle when connected. Let's consider the three given points as A(x1, y1), B(x2, y2), and C(x3, y3). Here's a step-by-step explanation:
1. Calculate the distances between each pair of points:
- Distance AB = √((x2 - x1)^2 + (y2 - y1)^2)
- Distance BC = √((x3 - x2)^2 + (y3 - y2)^2)
- Distance AC = √((x3 - x1)^2 + (y3 - y1)^2)
2. Check if the sum of the distances between two points is greater than the distance between the remaining pair of points. This is known as the Triangle Inequality Theorem:
- AB + BC > AC
- BC + AC > AB
- AC + AB > BC
3. If all three conditions are satisfied, the given coordinates are the vertices of a triangle.
In order to solve further, specific coordinates are needed.
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) The value of shares, t years after their floatation on the stock market, is modelled by V=10e 0.09t
Find the initial value of these shares and values after 5 years, 10 years and 12 years, respectively. Round your answer to two decimal places. [9 marks] During a recession, a firm's revenue declined continuously so that the total revenue (TR) in t years' time is modelled as TR=10e −0.19t
(in million dollars) Calculate the current revenue and revenue in 5 years' time. After how many years the revenue of this firm is going to drop to $1 million? Round your answer to two decimal places.
After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.
The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t
The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,
we get
V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.
The values after 5 years, 10 years and 12 years, respectively are:
For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars
The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)
The current revenue is the total revenue when t = 0.
So, putting t = 0 in TR = 10e−0.19t, we get
TR = 10e−0.19 × 0= 10e0= 10 million dollars
Revenue in 5 years' time is TR when t = 5.
So, putting t = 5 in TR = 10e−0.19t, we get
TR = 10e−0.19 × 5≈ 4.35 million dollars
To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.
Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1
Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303
Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.
So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.
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5. Rhombus DEFG with vertices D(1, 4), E(5, 5), F(4, 1),
and G(0, 0); 270° clockwise rotation about R(6,8)
Step-by-step explanation:
First things first, we are rotating about a point so the first we do is the move the clockwise rotation to the origin.
Since a rotation is a rigid transformation, we must move all the other points as well.
So move every point using the rotation vector
R(-6,-8), move every point to
D(1-6,4-8)=D'(-5,-4)
E(5-6,5-8)=E'(-3,-5)
F(4-6,1-8)=F'(-2,-7)
G(0-6,0-8)=G'(-6,-8)
So know since the center of rotation is middle at (0,0) , we can apply the rotation rules
For a 270 clockwise rotation, we apply this rule
(-y,x)
So for the points we know get
D''(5,-4)
E''(3,-5)
F''(2,-7)
G"(6,-8)
Know since we done our rotation, we undo what we did in step 1, we add 6 to the x coordinates and 8nto the y coordinate
D"'(11,8)
E"'(9, 3)
F"(8,1)
G"'(12,0)
So those are our new coordinates.
What's the surface area of the pyramid?
The Answer is C 226.8 ft
I remember doing this not to long ago
What evidence is needed to prove two triangles are similar by the SSS similarity theorem?
Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.
So, ∠P = ∠E and ∠Q = ∠F.
Hence, we can write: DP/DE = DQ/DF= PQ/EF.
The above expression is written as
DP/DE = DQ/DF=BC/EF.
It means that PQ = BC.
Hence, the triangle ABC is congruent to the triangle DPQ.
(i.e) ∆ ABC ≅ ∆ DPQ.
Thus, by using the AAA criterion for similarity of the triangle, we can say that
∠A = ∠D, ∠B = ∠E and ∠C = ∠F.
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Please answer this question asap.
Answer:
54
Step-by-step explanation:
the first one is the only one I know from the top off my head I'll try and send it to you. but the first one is 53
In a class of students, the following data table summarizes how many students play
an instrument or a sport. What is the probability that a student chosen randomly
from the class plays a sport?
Plays a sport
Does not play a sport
Plays an instrument Does not play an instrument
3
8
10
9
Answer:
3 OR 8 hope this helps!
Step-by-step explanation:
Examine the table, which represents a linear function.
Input (x) Output (y)
−3 14
0 7
3 0
6 −7
What is the initial value of the function?
A: 3
B: -3
C: 0
D: 7
Answer: 7
Step-by-step explanation:
The initial value of the function is the value of \(y\) when \(x=0\).
what is the equation of the line that passes through the point (-5,2) and has a slope of 4/5
Answer:
y = \(\frac{4}{5}\) x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = \(\frac{4}{5}\) , then
y = \(\frac{4}{5}\) x + c ← is the partial equation
To find c substitute (- 5, 2 ) into the partial equation
2 = - 4 + c ⇒ c = 2 + 4 = 6
y = \(\frac{4}{5}\) x + 6 ← equation of line
Answer:
Below.
Step-by-step explanation:
Use the point-slope form of a straight line.
y - y1 = m(x - x1)
Here m = 4/5, x1 = -5 and y1 = 2, so
y - 2 = 4/5(x - -5))
y - 2 = 4/5 x + 4
y = 4/5x + 6 is the answer in slope-intercept form.
Standard form:
Multiply through by 5:
5y = 4x + 30
4x - 5y = -30 is the answer in standard form.
PLS HELP ME AND MY BROTHER WITH THIS!!!!!!
Answer:
A
Step-by-step explanation:
I think the answer is A because 39÷6= 6.5, so than I took that 6.5 and multiplied it by 12 to get 78 teaspoons of blue paint.
Hope this helps!!! Have a lovely day
A matter for presentation is written in 24 pages. Each page has 20 lines. If the number of lines per page is increased to 24, then in how many pages will presentation will end?
EXPLAIN TOO
Answer:
check answer plz
Step-by-step explanation:
is it correct,plz check
Can i have help please
Answer:
All new reflected coordinates
T (-3, 6)
S (-2, 4)
U (-4, 4)
R (-3, 2)
Step-by-step explanation:
This is because the are reflected sideways on x = 1. This works like a mirror or opening a page of a book if that helps visualise it.
Simplify \(\frac{sec(a)-csc(a)}{sec(a)+csc(a)}\)
The simplified version of (sec a - cosec a) / (sec a + cosec a) is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
Given:
(sec a - cosec a) / (sec a + cosec a)
Multiply the numerator and denominator by (sec a - cosec a)
(sec a - cosec a) / (sec a + cosec a) × (sec a - cosec a)
(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)
As we know,
\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)
sec² a cosec² a - 2sec a cosec a / (sec²a - cosec²a)
sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)
cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)
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Which expression is equivalent to 83 ⋅ 8−7? (1 point)
a
fraction: 1 over 8 to the power 10
b
1 over 8 to the power 4
c
810
d
84
\(8^{3} \cdot 8^{-7} =8^{-4}=\boxed{\frac{1}{8^4}}\)
The ponderal indexis a measure of the "leanness" of a person. A person who is h inches tall and weighs w pounds has a ponderal index I given by I = a. Compule the ponderal index for a person who is 76 inches tall and weighs 192 pounds: Round to the nearest hundredth. b. What is a man's weight if he is 77 inches tall and has a ponderal index of 11.56 ? Round to the nearest whole number. a. The ponderal index for a person who is 76 inches tall and weighs 192 pounds is (Round to the nearest hundredth as needed.)
The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.
To compute the ponderal index, we need the formula and the value of the constant "a."
a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.
b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.
To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.
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What is the equation of the line? Identify the values of A, B, and C in the
standard form of the equation.
The equation of line is
____
Answer: B
Step-by-step explanation:
Brainiest please '
What is the slope of the line shown?
Answer:
The slope of the line show is always writen in the form of rise/ run or y/x. Bassically the answer should look like a fraction. In this case, the slope of the line is 1/2. Graphing points on the line always make this process eaiser. From one point to another measure the rise/run or y/x and that will be your slope. Here the line rises one point and runs 2. The slope of the line is positive because it slants right in quadrant one of the graph.
Step-by-step explanation:
find the rate of change (Slope) of each graph below (simplify answers)
Answer:
-2
Step-by-step explanation:
find two points where they line up on the cross sections of the graph
-2, 3
-1, 1
-1 x -2 y
it goes right 1 and down 2
-2/1 or -2
Type the missing number in this sequence,3, 9,_,24,33,43,54
Answer: 18
Step-by-step explanation:
1. If Carter invests $5300 at 7.2% /a and earned $1200 in interest. If this was a simple interest investment, how long did Carter invest her money? 2. Winnie needs a new washer and dryer and he finds one for $2112. He puts $500 up front but needs to take out a loan for the remaining amount. After a year and a half, he has paid off the loan that totaled to $1879. What was the annual interest rate that Winnie was being charged if it was compound semi-annually? Compounding Interest Equation Compound Interest Amount A = P(1 + i)" A= Amount (at the end) ($) P Principal ($) (starting amount) = effective interest rate (as a decimal) n = number of compound periods = # of years x cp cp = compounding factor Interest I=A-P /= Interest earned ($) thlut Day 22 Present Value in Compound Interest (Solving for the Principal) A PV = (1+i)n PV = Present Value ($) (starting amount) A = Amount ($) (at the end, future value) i = effective interest rate (as a decimal) n = number of compound periods = years x cp cp = compounding factor 7/8
1. Carter invested her money for approximately 4.78 years.2. the annual interest rate charged to Winnie with compound interest compounded semi-annually is approximately 92.4%.
Answer to the questions1. To find the duration of Carter's investment, we can use the simple interest formula:
Interest = Principal * Rate * Time
Given:
Principal (P) = $5300
Rate (R) = 7.2% = 0.072 (as a decimal)
Interest (I) = $1200
Substituting the values into the formula, we have:
$1200 = $5300 * 0.072 * Time
Simplifying the equation:
Time = $1200 / ($5300 * 0.072)
Time ≈ 4.78 years
Therefore, Carter invested her money for approximately 4.78 years.
2. To find the annual interest rate charged to Winnie with compound interest compounded semi-annually, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Given:
Principal (P) = $2112
Amount (A) = $1879
Number of compounding periods per year (n) = 2 (semi-annually)
Time (t) = 1.5 years
Substituting the values into the formula, we have:
$1879 = $2112(1 + r/2)^(2 * 1.5)
Simplifying the equation and isolating the variable:
(1 + r/2)^(3) ≈ 0.8888
Taking the cube root of both sides:
1 + r/2 ≈ 0.962
Subtracting 1 and multiplying by 2:
r ≈ 0.924
Therefore, the annual interest rate charged to Winnie with compound interest compounded semi-annually is approximately 92.4%.
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You sell tacos that cost $2 to produce. You sell them for $4. Your markup on cost, expressed as a percentage, is:
A. 100%
B. $2
C. 50%
D. $4
E. None of these
The markup percentage for your tacos is 100%. (option a)
To calculate the markup percentage, we need to compare the profit you make on each taco to the cost of producing that taco. In this case, the cost to produce one taco is $2, and you sell it for $4. The markup can be calculated using the following formula:
Markup Percentage = ((Selling Price - Cost Price) / Cost Price) * 100
Let's plug in the numbers and calculate the markup percentage:
Markup Percentage = (($4 - $2) / $2) * 100
Markup Percentage = ($2 / $2) * 100
Markup Percentage = 1 * 100
Markup Percentage = 100%
Hence the correct option is (a).
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Which expression is equivalent to 25x â€" 45y?
A. 25(5x â€" 20y)
B. 5(5x - 9y)
C. 70(x â€" y)
D. 10(15x â€" 35y)
Answer:
D
Step-by-step explanation:
Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica
what are two requirements that must be satisfied to perform a chi-square test (such as the test of homogeneity, the goodness-of-fit test, and the test of independence of proportions)?
The two requirements that must be satisfied to perform a chi-square test are All Ei>=1 and no more than 20% of the Ei are less than 5.
What is chi-square?
In order to establish if the expected and actual findings are well-fitting, the statistical test known as chi-square compares the differences between categorical variables from a random sample.
For the given equation,
To perform a chi-square test,
All Ei>=1 and no more than 20% of the Ei are less than 5
Hence, these two are the important requirements to carry out the chi-square goodness of fit test.
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Is 4 a factor of 64? How do you know?
Answer: yes
Step-by-step explanation: 64 is a factor of 4 because you can multiply it by 16 to get 64. Remember if you divide and get a whole number it is a factor .
What figure is created from the coordinate points (3, 2), (3, 6), and (5, 2)? square rectangle triangle parallelogram
Answer:
it's a triangle
Step-by-step explanation:
what's the total area of each smaller space is 5 feet on each side
Answer:
100
Step-by-step explanation:
100
The total area of the four squares is the sum of each individual area of each square. Hence, the total area of the square is 100 ft²
Given that :
Side length of each square, s = 5 feets Area of a square = s²The area of each square can be calculated thus :
Area = 5² = 25 ft²The area of the entire square :
(5² + 5² + 5² + 5²)
(25 + 25 + 25 + 25) = 100 ft²
The total area of the square is 100 ft²
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standard form: all exponets are ___________numbers & it is written in __________ order -5x^7+4x^2+3x-2
Plz help me with this!