Answer:
at 8%: $3760at 2%: $2460Step-by-step explanation:
You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.
__
lookThe given system of equations is ...
x = y +13000.08x +0.02y = 350We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.
planTo eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.
Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.
The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.
solutionWe choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results
(0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)
0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses
0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated
x = 3760 . . . . . . . . . divide by 0.10
y = x -1300 = 2460
__
The amount invested at 8% was $3760; the amount invested at 2% was $2460.
_____
Additional comment
We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.
Had we multiplied by -0.08 to eliminate x, we would have ...
-0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)
0.02y = -0.08y +246
We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.
0.10y = 246
y = 2460; x = 2460+1300 = 3760
Question 3 of 10
Mark all the statements that are true.
What is the solution to the inequality StartFraction d Over 7 EndFraction + 4 ≤ 0? (–∞, –28) (–∞, –28] (28, ∞) [28, ∞)
The solution to the inequality d / 7 + 4 ≤ 0 will be (–∞, –28]. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality equation is given below.
d / 7 + 4 ≤ 0
By simplifying the equation, we have
d / 7 ≤ – 4
d ≤ – 28
Then the value of d must be less than or equal to the negative 28.
Then the correct option is B.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
The square of the difference between a number and 7 is 81 . Find the number(s).
Answer:
16 or -2
Step-by-step explanation:
Let the number be x.
Difference between the number and 7
= x -7 or 7-x
The square of the difference between x and 7
= (x -7)²
(x -7)²= 81
Square root both sides:
[tex]x - 7= \pm \sqrt{81} [/tex]
[tex]x - 7 = \pm9[/tex]
Add 7 to both sides:
[tex]x = 7\pm9[/tex]
x= 16 or x= -2
Thus, the number could either be 16 or -2.
What is the common difference in the following arithmetic sequence?
2.8, 4.4, 6, 7.6, ...
–4.8
–1.6
1.6
4.8
Answer:
1.6
Step-by-step explanation:
4,4-2.8 = 1.6
6-4.4 = 1.6
7.6-6 = 1.6
Then common difference is 1.6
For each of the following research questions, determine whether an observational study, an
experiment, or neither should be used to answer the question. Note - each term on the right may be
used more than once or not at all.
The situations described can be classified as experiment, and observational study.
What is an experiment?An experiment is a tool to test a hypothesis about the occurrence of a particular phenomenon. According to the above, it can be stated that student-centered instruction can be classified as an experiment because this method of education is used and it is verified whether it is effective or not.
What is an observational study?An observational study is a methodology to identify the occurrence of an event in a particular situation. From the foregoing, it can be inferred that the participation of women in the 2016 election is the product of an observational study because only the number of voters should be counted and the number of women who participated should be identified.
Note: This question is incomplete because there is some information missing. Here is the information missing.
OPTIONS:
Does learner-centered instruction increase students' success rates in maths?
What proportion of registered women voters voted in the 2016 U.S. presidential election?
Learn more about experiments in: https://brainly.com/question/11256472
#SPJ1
Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
Sector Area
angle of sector
360
tor) πr²
8 cm
Sector Area = [?] cm²
Round to four decimal places.
129°
8 cm
Answer: 72.0472
Step-by-step explanation:
[tex]A=\left(\frac{129}{360} \right)(\pi)(8^{2}) \approx \boxed{72.0472}[/tex]
Please help me!!! I will give brainliest to the correct answer.
[tex]\mathsf {2(10 + 2) = 3(y + 3)}[/tex]
[tex]\mathsf {24 = 3y + 9}[/tex]
[tex]\mathsf {3y = 15}[/tex]
[tex]\textsf {y = 5}[/tex]
[tex]\textsf {The value of y will be 5. }[/tex]
Prove: m/EIF = m/GIH
Step
m/EIF+m/FIG = 180
m/FIG+m/GIH
= 180
m/EIF+mZFIG= m/FIG+mZGIH
m/EIF = m/GIH
Reason
Distributive Property Transitive Property of Equality Definition of Supplementary Angles
Subtraction Property of Equality Multiplication Property of Equality Simplify
Division Property of Equality Reflexive Property of Equality Addition Property of Equality
Substitution Property of Equality Definition of Complementary Angles
An
13
Se
Tea
16
Finis
The question is incomplete. Below you will find the missing content in the figure.
Prove: m/EIF = m/GIH
Step Reason
m∠EIF+m∠FIG = 180°
m∠FIG+m∠GIH= 180°
m∠EIF+m∠FIG= m∠FIG+m∠GIH
m∠EIF = m∠GIH
The figure is shown below.
The correct answer is m∠EIF = m∠GIH
Here lines FH and GE intersect each other at the point I.
we have to prove the angle
m∠EIF = m∠GIH
so,
m∠EIF+m∠FIG = 180° as angels ∠EIF and ∠FIG forming a linear pair summing up to 180°. angels ∠EIF and ∠FIG form straight angels on a line EG.
m∠FIG+m∠GIH= 180° as angels ∠FIG and ∠GIH forming a linear pair summing up to 180°. angels ∠FIG and ∠GIH form straight angels on a line FH.
m∠EIF+m∠FIG= m∠FIG+m∠GIH because of the substitution property of equality. we replace 180° by m∠FIG+m∠GIH.
m∠EIF = m∠GIH because of the subtraction property of equality. We can subtract the same elements from both sides by the subtraction property of equality.
Therefore m∠EIF = m∠GIH.
Learn more about property of equality
here: https://brainly.com/question/1601404
#SPJ10
HURRY Given f(x) = - 3/4x + 2, find ƒ(16). The solution is
Answer: Read attachment.
Step-by-step explanation: Attached is my work. Hope it helps!
If my answer was helpful, please mark as brainliest. Or not, it's fine.
Answer:
[tex]\fbox {f(16) = -10}[/tex]
Step-by-step explanation:
Given :
f(x) = -3/4x + 2
Substitute x = 16 :
f(16) = -3/4(16) + 2
f(16) = -12 + 2
f(16) = -10
Find the measure of line segment DE
[tex]DE=\sqrt{13^{2}+12^{2}-2(13)(12)(\cos 59^{\circ})} \approx \boxed{12.3}[/tex]
Select the correct answer.
What is the solution to this equation?
log(2x - 100) = 3
A = 1,000
B = 450
C = 550
D = 100
Compute the length of sides AB, AC.
1. The perimeter of the square is f(x) = 4x, where x is the side of the square. Find the domain of the function.
A. Set of rational numbers
B. Set of whole numbers
C. Set of integers
D. All of the choices
2. Find the domain of the function y = 3x + 8(3 - x).
A. Set of real numbers
B. Set of integers
C. Set of whole numbers
D. Set of natural numbers
Question 1
B. Set of whole numbers
Eliminate A and C because negative integers are in those sets.Question 2
A. Set of real numbers
The equation represents a line, which has a domain of all real numbers.If the perimeter of the square is 4x then the domain of the function will be set of rational numbers and the domain of the function y=3x+8(3-x) is set of real numbers.
Given The perimeter of the square is f(x)=4x and the function is y=3x+8(3-x)
We will first solve the first part in which we have been given that the perimeter of the square is 4x and we have to find the domain of the function.
First option is set of rational numbers which is right for the function.
Second option is set of whole numbers which is not right as whole number involves 0 also and the side of the square is not equal to 0.
Third option is set of integers which is not right as integers involve negative number also and side of square cannot be negative.
Hence the domain is set of rational numbers.
Now we will solve the second part of the question
f(x)=3x+8(3-x)
we have not told about the range of the function so we can put any value in the function and most appropriate option will be set of real numbers as real number involve positive , negative and decimal values also.
Learn more about perimeter here https://brainly.com/question/19819849
#SPJ10
someone help solve asap for points
Answer:
[tex]\textsf {p(-4) = -134}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}\\[/tex]
[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]
[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]
[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]
[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]
[tex]\textsf {p(-4) = 6 - 140}[/tex]
[tex]\textsf {p(-4) = -134}[/tex]
4+0.4+0.0024 in Standard Form
Answer:
In standard form thats 4.4024
In standard form, 4+0.4+0.0024 can be written as 4.4024
Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;
If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.
Given: 4+0.4+0.0024
In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024
For more information on the standard form, visit https://brainly.com/question/19169731
#SPJ10
need help with this question please
∠ A = 132°
Step-by-step explanation:
∠ A + ∠C = 180° (Angle sum of cyclic quadrilateral)
∠ A = 180° - ∠ C = 180° - 48°
∠ A = 132°
Ethan is following a healthy diet plan and is allowed 3000 calories and 30 grams
of fat a day.
He is trying to decide what to have for his lunch.
Chicken
Sandwich
Nutrition Facts
Energy
Protein
Carbohydrate
Sugar
Fat
Fibre
Sodium
per pack
265 kcal
36 g
15 g
2g
6g
1.2 g
476 mg
Jacket potato
with tuna
Nutrition Facts
Energy
Protein
Carbohydrate
Fat
Saturated Fat
Fibre
Sodium
per 1 serving
450 kcal
30 g
75 g
79
19
9.1 g
432 mg
a) If he chooses a chicken sandwich what percentage of his daily allowance of fat
will that be?
06
Which of the following describes the behavior of the graph shown over the interval (-2,2)?
Hello!
We are trying to describe the behavior of the graph given in the question.
To help us understand how to solve this question, we would need to understand concavity.
There are two types of concavity:
Concave upConcave downWhen a graph is concave up, the slope of the line would look like a "U".
When a graph is concave down, the slope of the line would look like a "U" that is flipped upside down.
In this case, we can see that the graph is concave down.
We can tell that the slope is negative due to the fact that the slope is going down, which results in the graph having a negative slope.
We can also tell that the graph is decreasing due to the fact that the line is doing downward.
Answer:
C). negative and decreasing
The table shows ordered pairs of the function y=8-2x. What is the value of y when x = 8?
X
-3
-1
1
4
8
10
y
14
10
6
0
?
-12
Answer: -8
Step-by-step explanation:
[tex]y=8-2(8)=\boxed{-8}[/tex]
Sandra owns a rectangular pice of farmland that is 2/3 miles wide and has an area 5/9 square mile what is the leght of sandras farmalnd
Answer:
5/6 mile
Step-by-step explanation:
The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.
__
Here is the equation for the area of a rectangle.
A = LW . . . . . area is the product of length and width
When we fill in the area and width, we have ...
5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland
Solving this equation gives ...
L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L
L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division
The length of Sandra's farmland is 5/6 mile.
ABCD is a parallelogram. Find the measure of angle C.
A
B
C (3x+6)
D (2x+9)
Find out the measure for angle C
Answer:
C = 105°
Step-by-step explanation:
added in the picture
f(x) = -3 +3
Which graph represents the inverse of function ?
-3
N
-1
4
3-
2-
1-
-2+
-3-
-4+
-5+
W.
Y
54
-1-
4-
3-
2
-4
-2
N
-3
-5+
X.
Y
4-
3-
2-
-1-
3
X
e
Answer: Y
Step-by-step explanation:
Since f(x) passes through (0,3), its inverse should pass through (3,0).
This eliminates X and Z.Also, since f(x) has a negative slope, so its inverse should also have a negative slope.
This eliminates W.The graph of the inverse of function is shown in figure.
We have to given that,
Function is defined as,
f (x) = - 3x + 3
Hence, The inverse of function f (x) is,
f (x) = - 3x + 3
y = - 3x + 3
Solve for x,
3x = y + 3
Divide by 3;
x = (y + 3) / 3
Hence,
f⁻¹ (x) = (x + 3) / 3
f⁻¹ (x) = x/3 + 1
Therefore, The graph of the inverse of function is shown in figure.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
Write the equation of the line with a slope of 3/4 and a y'-intercept of -7 in Slope-Intercept and Poin Slope Form.
A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.
Answer:
4 kg
Step-by-step explanation:
so 1.6 * 4 is 6.4 so you just double check if you want
4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)
4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)
there is another way by setting up an equation. let me know in comments if you want to see it that way
If tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A tank weighs 5.6kg when it 1/4 filled with water
Tank weighs 10.4kg when it is full
We need to find the weight when it is empty.
Let weight of the tank “x” and the weight of the water in the full tank “y”.
From the problem statements, we deduce the following equations:
x + y/4 = 5.6kg => x = 5.6kg - y/4
x + y = 10.4kg => y = 10.5kg - x
y = 10.5kg - (5.6kg - y/4)
3y/4 = 4.9
Thus y = 6.53kg; x = 0.93kg
Hence, weight of the tank when it is empty is 0.93kg.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
A rectangular floor of area 21.6 m2 is going to be tiled. Each tile is rectangular, and has an area of 288 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?
Answer:
Area of Floor = 21.6.m²
Area of tile = 288 cm² = 0.0288 m²
No. of tiles = Area of floor/ area of tile
= 21.6/0.0288
= 750
750 tiles can be put into the spaceWhy can’t 1.07 pounds of sugar be compared to 1.23 cups of sugar.
Question 1 Fill in the missing (yellow) interior angle with (4x)° to solve for x. Diagram may not be to scale.
Please help!
Answer:
x=100/7
Step-by-step explanation:
The interior angles will sum to 360 so 72+89+99+7x=360
260+7x=360
7x=100
x=100/7
The factors of 25x4 − 49y2 are
Answer:
1
Step-by-step explanation:
49 is divisible by 7, 1, 49. 25 is divisible by 5, 1, 25. they are exclusively prime so the highest factor is 1 and the only
Answer:
Step-by-step explanation:
[tex]25x^4-49y^2=(5x^2)^2-(7y)^2\\=(5x^2+7y)(5x^2-7y)\\=(5x^2+7y)[(\sqrt{5} x)^2-(\sqrt{7y} )^2]\\=(5x^2+7y)(\sqrt{5} x+\sqrt{7y} )(\sqrt{5} x-\sqrt{7y} )[/tex]
Calculate the number of two-person committees that can be formed from a group of 10 people
Bikash borrowed Rs150,000 from Anish at the rare 21% per year at the end of 9 month. How compound interest should he pay compound half yearly.
What is the distance in units between the points (-1, 5) and (-1,
-3)?
Answer:
8 [units].
Step-by-step explanation:
if to see the given coordinates, then it is clear the x-coordinates are equal. It means, the required distance can be calculated:
d=5+3=8 [units].
