Answers:
2% bond: $11000
4% bond: $13000
========================================================
Explanation:
x = amount invested in the 4% bond
y = amount invested in the 2% bond
Amounts are in dollars
The two amounts add to $24,000 so
x+y = 24000
y = -x+24000 is one equation to set up
0.04x = interest earned from the 4% bond
0.02y = interest earned from the 2% bond
0.04x+0.02y = total interest earned = $700
0.04x+0.02y = 700 is another equation to set up
------------
The system of equations is
[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]
Apply substitution. Solve for x.
0.04x+0.02y = 700
0.04x+0.02(-x+24000) = 700
0.04x-0.02x+480 = 700
0.02x= 700-480
0.02x= 220
x= 220/(0.02)
x = 11000
Use this to find y
y = -x+24000
y = -11000+24000
y = 13000
The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance on the map, x, that represents 50 miles? StartFraction 5 over 200 EndFraction = StartFraction x over 50 EndFraction StartFraction 200 over 5 EndFraction = StartFraction x over 50 EndFraction StartFraction 50 over 200 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 50 EndFraction = StartFraction x over 200 EndFraction
The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The scale on a map shows that 200 miles is represented by 5 inches on a map.
Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be
x/50 = 5 / 200
Then the correct option is A.
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At the taco truck an order of 1 taco and 3 quesadillas cost $ 26.50. An order if 3 tacos and 1 quesadilla cost $19.50. for 5 tacos and 1 quesadilla. What is the cost of one taco and the cost of one quesadilla?
Answer:
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
Step-by-step explanation:
Let the cost of tacos be x and the cost of quesadillas be y.
Given condition:x + 3y = 26.50 ------------------(1)
3x + y = 19.50 -------------------(2)
Multiply Eq. (2) by 3
3(3x + y) = 19.50 * 3
9x + 3y = 58.5 -----------------(3)
Subtract Eq. (3) from (1)
x + 3y - 9x - 3y = 26.50 - 58.50
x - 9x = -32
-8x = -32
8x = 32
Divide 8 to both sides
x = $4
Put x = 4 in (1)
4 + 3y = 26.50
Subtract 4 to both sides
3y = 26.50 - 4
3y = 22.50
Divide 3 to both sides
y = $7.50
So,
The cost of 1 taco = $4
The cost of 1 quesadilla = $7.50
[tex]\rule[225]{225}{2}[/tex]
PLEASEEEEEE HELPPPPPPP!!! 50 POINTSSSSSS
12 = 6^2 + 7^2 - 2 (6) (7) (cosA)
solve for the cosA
Step-by-step explanation:
please mark me as brainlest
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there are 20nstudents in a math class who have brown hair this represent 80 percent of the students in the class with equation can be used to find the total os student in the math
Answer:
Equation is 20 = 0.8 time x
x=25
Step-by-step explanation:
80% = 0.8
So to find x we 20/8
and we get 25 as the final answer
Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²
Answer: [tex]\frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]
The radius of a circle is 4 millimeters. What is the circle's area? Use 3.14 for pi.
(The answer MUST BE ONE OF THE ANSWERS BELOW)
Answer:
50.24 mm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = 3.14 ( 4)^2
= 50.24 mm^2
Answer:
c. 50.24 square millimeters
Step-by-step explanation:
Radius of circle = 4 milimeters.
Area of a circle = πr²
Area = 3.14 × 4² (π = 3.14)
= 50.24 square millimeters
Please help my question is in the attachment!
Answer:
a = -9
b = -3
c = 11
d = 19
Step-by-step explanation:
a. x = -2
y= x² + 3x + 1
y= -2²+ 3(-2)+1
y= -4-6+1
y = -9
b. x= -1
y= x² + 3x+ 1
y= -1² + 3(-1) +1
y= -1 -3 + 1
y = -3
c. x =2
y = x² + 3x +1
y= 2²+ 3(2) +1
y= 4 +6 +1
y = 11
d. x= 3
y = x² +3x +1
y = 3² +3(3) +1
y= 9 +9 +1
y = 19
what is the answer please??
Answer:
See below
Step-by-step explanation:
Area of a circle = pi * r^2
for this circle : Area = 3.142 * 10 * 10 = 314.2 cm^2
The formula for area of a circle is [tex]\pi r^{2}[/tex]
So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.
Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.
If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.
Brainliest if helpful.
Factorise and evaluate
50 × 11 + 50 × 9
Answer:
1000
Step-by-step explanation:
50 × 11 + 50 × 9 ← factor out 50 from each term
= 50(11 + 9)
= 50(20)
= 1000
ƒ(x) = x² - x - 1
What is the average rate of change of f over
the interval -1 ≤ x ≤ 1?
Answer: -1
Step-by-step explanation:
[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]
An expression is shown below:
4ck2 + 10k2 − 16ck − 40k
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Part A:
The greatest common factor is 2k
2k(2ck + 5k - 8c - 20)
Part B:
factor by grouping
2k (k(2c + 5) - 4(2c + 5))2k(k - 4)(2c + 5)2k(k - 4)(2c + 5) is the final factored form
help pls i jusiot jiojfgnio43nfginfmowenfviowngognior3
Answer:
i dont know
Step-by-step explanation:
sorry please be a bit more clear on what help you would like
^
Which is the graph of the linear inequality 2x - 3y < 12?
The graph of the linear inequality 2x – 3y < 12 is given below. Then the correct option is A.
The missing options are given below.
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 is given below.
2x – 3y < 12
Then the correct graph will be given below.
Then the correct option is A.
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What is the weighted average cost of capital (WACC) for ABC Limited which has the following capital structure? $5m of equity with a cost of equity of 15%; $2m of mezzanine finance with a cost of 9.5%; $1m of senior debt with a cost of debt of 7%.
Answer:
the answer is 13.73 %
a supermarket display consists of boxes of cereal. the bottom row has 23 boxes. each row has three fewer boxes than the row below it. the display has six rows.
Answer:
93 boxes
Step-by-step explanation:
sixth row has 23 boxes
fifth row has 20 boxes
fourth row has 17 boxes
third row has 14 boxes
second row has 11 boxes
first row has 8 boxes
the total is thus 23+20+17+14+11+8=93
PLEASE HELP!!
Discussion Topic
Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This
approach follows the teachings of Euclid, in which he describes the relationships between
points, lines, and planes without any numerical measurement. You saw evidence of Euclidean
geometry inside several proofs and geometric constructions.
In contrast, the focus of this unit is understanding geometry using positions of points in a
Cartesian coordinate system. The study of the relationship between algebra and geometry was
pioneered by the French mathematician and philosopher René Descartes. In fact, the
Cartesian coordinate system is named after him. The study of geometry that uses coordinates
in this manner is called analytical geometry.
It's clear that this course teaches a combination of analytical and Euclidean geometry. Based
on your experiences so far, which approach to geometry do you prefer? Why? Which
approach is easier to extend beyond two dimensions? What are some situations in which one
approach to geometry would prove more beneficial Han the other? Describe the situation
and why you think analytical or Euclidean geometry is more applicable.
Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.
Which approach is easier to extend beyond two dimensions?The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.
Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle to a square pyramid.
What are some situations in which one approach to geometry would prove more beneficial than the other?Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).
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A line intersects the points (8, 2) and (12, -10). What is the slope of the line in simplest form? m = [?]
Work Shown:
[tex](x_1,y_1) = (8,2) \text{ and } (x_2,y_2) = (12,-10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-10 - 2}{12 - 8}\\\\m = \frac{-12}{4}\\\\m = -3\\\\[/tex]
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Goes through (8, 2) and (12, -10)}[/tex]
Find: [tex]\textsf{The slope of the line}[/tex]
Solution: In order to determine the slope of the line we need to use the slope formula where we just plug in the values and simplify.
Plug in the values
[tex]\textsf{y = }\frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]\textsf{y = }\frac{-10 - 2}{12 - 8}[/tex]Simplify the expression
[tex]\textsf{y = }\frac{-12}{12 - 8}[/tex][tex]\textsf{y = }\frac{-12}{4}[/tex][tex]\textsf{y = -3}[/tex]Therefore, the slope of the line that fits the description that was provided in the problem statement is -3.
What is the value of n in the equation 2n² + 4n = 0? What is the value of n in the equation 2n² + 4n = 0 ?
N = 0
2(0)² + 4(0) = 0
0 + 0 = 0
Over which interval is the graph of the parent absolute value function decreasing?
(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)
The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
What is the parent absolute value function?An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.
The absolute value function is f(x) = |x| is defined as,
f(x )
x = x < x = 0 < x = -x
Observe that the graph is V-shaped.
The vertex of the graph is (0,0).
The domain is the set of all real numbers.
The x-intercept and the y-intercept are both 0.
Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
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please help! I need this quickly
write an equation in standard form of the line passing through the points (12,6) and (-3,11)
Answer:
x + 3y = 30
Step-by-step explanation:
We are given that a line contains the points (12,6) and (-3,11).
We want to write the equation of this line in standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0, and a cannot be negative.
Regardless, before we write an equation in slope-intercept form, we must first write the equation in a different form, such as slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.
So first, let's find the slope of the line.
The slope (m) can be found using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.
Even though we already have 2 points, let's label their values to avoid any confusion and mistakes when calculating.
[tex]x_1=12\\y_1=6\\x_2=-3\\y_2=11[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{11-6}{-3-12}[/tex]
Subtract
m=[tex]\frac{5}{-15}[/tex]
Simplify
m=[tex]-\frac{1}{3}[/tex]
The slope is -1/3
Here is the equation of the line so far in slope-intercept form:
[tex]y=-\frac{1}{3} x + b[/tex]
We need to solve for b.
As the equation passes through (12,6) and (-3,11), we can use either one to help solve for b.
Taking (12, 6) for example:
[tex]6=-\frac{1}{3}(12) + b[/tex]
Multiply
[tex]6=-\frac{12}{3} + b[/tex]
Divide
6 = -4 + b
Add 4 to both sides.
10 = b
Substitute 10 as b in the equation.
[tex]y = -\frac{1}{3} x + 10[/tex]
Here is the equation in slope-intercept form, but remember, we want it in standard form.
In standard form, the values of both x and y are on the same side, so let's add -1/3x to both sides.
[tex]\frac{1}{3} x + y = 10[/tex]
Remember that a (the coefficient in front of x) has to be an integer, 1/3 is not an integer.
So, let's multiply both sides by 3 to clear the fraction.
[tex]3(\frac{1}{3} x + y) = 3(10)[/tex]
Multiply.
x + 3y = 30
Topic: finding the equation of the line (standard form)
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Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros
of -3, -3, 4, and 2.
y(x) =
The factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
How to determine the factored form?The given parameters are:
Leading coefficient, a = 1Zeros = -3, -3, 4, and 2.Rewrite the zeros as:
x = -3, x = -3, x = 4 and x = 2
Set the zeros to 0
x + 3 = 0, x + 3 = 0, x - 4 = 0 and x - 2 = 0
Multiply the zeros
(x + 3) * (x + 3) * (x - 4) *(x - 2) = 0
Express as a function
y(x) = a(x + 3) * (x + 3) * (x - 4) *(x - 2)
Substitute 1 for a
y(x) = (x + 3)²(x - 4)(x - 2)
Hence, the factored form of the polynomial function is y(x) = (x + 3)²(x - 4)(x - 2)
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It has been estimated that 72.7% of alcoholics need professional help to stop drinking. What is the probability that a random alcoholic can kick the habit without professional help? It has been estimated that 72.7 % of alcoholics need professional help to stop drinking . What is the probability that a random alcoholic can kick the habit without professional help ?
The probability that a random alcoholic can kick the habit without professional help is 0.273 .
What is Probability ?Probability is the study of likeliness of an event to happen.
It has a range of 0 to 1 , where 0 indicates uncertainty and 1 indicates certainty.
It is given that
The alcoholics that need professional help to stop drinking is 72.7 %
Therefore the probability of this is 72.7 /100 = 0.727
The probability that they will not need professional help is given by
q = 1 - p
q = 1 -0.727
q = 0.273
Therefore the probability that a random alcoholic can kick the habit without professional help is 0.273 .
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please answer this! (from khan academy 6th grade math)
Answer:
(-5, -7) and the x-axis
Step-by-step explanation:
when looking for a point that is 7 points away, we are looking for a difference of 7 in either the x-value or the y-value.
[remember: a point is written as (x, y) ]
We know that the x-value is -7, meaning that it is 7 units under the x-axis (meaning that it is 7 units away)
We know that our point, (2 , -7) has the same y-value as (-5, -7), so we are looking for a change in x. The difference (which is the change) between:
-5 and 2 is 7
(2 - (-5) = 2 + 5 = 7)
so, both the x-axis and the point (-5, -7) are 7 units away from (2, -7)
(the other point (-7, 7) is not near (2 , -7) at all--they have a larger difference on both the y-values, the x-values, and the length of if you made a diagonal line)
(I've attached an image to help you visualize what we're doing)
hope this helps!!
1. Henry is working in a pack room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs. Which of the following weights are allowable? Circle all allowable weights.
a. 34
b. 36
C. 29
d. 40
The allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Henry is working in a packed room. He is filling a bag with dry seasoning. The net weight of the bag is stated as 35
lbs. His tolerance is +/-5 lbs.
Weight of the bag = 35 lbs
Tolerance = ± 5 lbs
Allowable weights = 35 ± 5
= 35 + 5 = 40 lbs
= 35 - 5 = 30 lbs
Thus, the allowable weights are 30 lbs and 40 lbs if the weight of the bag is 35 lbs option (d) is correct.
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Given:
PLEASE HELP ASAP!
Part I: Use the given information to determine . Show all of your work.
Part II: Use complete sentences to explain the steps necessary in solving for . Justify your explanation by including all theorems, postulates, or definitions used.
The value of angle ∠DEC = 60 degree.
The complete question is
In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.
Part I: Find the m∠DEC.
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.
What is a Triangle ?A triangle is a polygon with three sides and three vertices and three angles.
As it is given that
AB || CD
Let BC be the transversal , then
∠CBA = ∠DCB (alternate opposite angles)
∠DCB = 56 degree
As the sum of opposite interior angle sis equal to exterior angle therefore ∠ ECB = 120 degree
∠DCE = 120-56 = 64 degree
BC || DE
∠EDC = ∠DCB = 56 degree (alternate opposite angles)
Sum of all the interior angles of a triangle is equal to 180 degree
56 +64+∠DEC = 180
∠DEC = 60 degree.
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for f(x)-4x+1 and g(x)-x^2-5, find (g/f) (x)
Answer:
A.
Step-by-step explanation:
let me know if you want an explanation :))
Answer:
A
Step-by-step explanation:
7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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To which subsets of the Real Numbers does square root of 36 belong.
Answer:
The square root of 36 is a rational number. A rational number is a number that can be written as a fraction, a/b, where a and b are integers.
Answer:
Step-by-step explanation:
Hi, let me help you out.
The square root of 36 is 6.
6 belongs to the following subsets.
Natural Numbers (All numbers greater than 1, except fractions or decimalsWhole Numbers (All Natural Numbers + 0; fractions are still NOT included)Integers (All Whole Numbers + negative numbers; this set includes neither fractions nor decimals, like the two number sets aboveRational Numbers (All integers plus - wait for it - fractions & decimals!)Overall, 6 belongs to 4 sub-sets.
__________________
Hope I helped! Best wishes.
___________________
The graph shown below expresses a radical function that can be written in the form F(x) = a(x+ k)^1/n+ C. What does the graph tell you about the value of a in this function?
For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.
Given the value of function F(x)=[tex]a(x+k)^{1/n}+C[/tex].
We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :
a[tex](x+k)^{1/n}[/tex]+C=0
a[tex](x+k)^{1/n}[/tex]=-C
a=-C/[tex](x+k)^{1/n}[/tex]
Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.
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