multiply the second equation by -1, you get
y=5x-10
-y=3x-14
add both of the equations together
0=8x-24
then
24=8x
x=3
to find y replace x in one of the original equations
y=5x-10
y=5(3)-10
y=15-10
y=5
(x,y)
(3,5)
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
The investments are $ 4000 and $ 3000 in the respective accounts
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
In the given question,
x = amount invested at 10 %
( 7000 - x ) = amount invested at 11 %
The total interest was $730 :
.10 (x) + .11 (7000-x) = 730
0.1 x + 770 - 0.11 x = 730
0.01 x = 40
x = 4000
Therefore, the amount invested in an account that pays 10 % per year is $ 4000.
Hence , the amount invested in an account that pays 11 % per year is
= ( 7000 - x ) = 7000 - 4000 = $ 3000.
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Assuming that b is positive, solve the following equation for b.
b
S
- 1
b≈
(2x-6)dx=13 Round your final answer to 4 decimal places.
(Give the positive answer only.)
The value of b is given as follows:
b = 8.4.
How to obtain the value of b?The value of b is obtained solving the definite integral in this problem.
The integral of the function 2x - 6 is given as follows:
x² - 6x.
At x = b, the numeric value of the integral is given as follows:
b² - 6b.
At x = -1, the numeric value of the integral is given as follows:
(-1)² - 6(-1) = 1 + 6 = 7.
Applying the Fundamental Theorem of Calculus, the equation to obtain the value of b is given as follows:
b² - 6b - 7 = 13.
b² - 6b - 20 = 0.
Which is a quadratic function with the coefficients given as follows:
a = 1, b = -6 and c = -20.
The discriminant is given as follows:
D = b² - 4ac
D = (-6)² - 4(1)(-20)
D = 116.
Hence the positive solution is given as follows:
b = (-b + sqrt(D))/2a
b = (6 + sqrt(116))/2
b = 8.4.
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13. Solve the inequality.
12 ≤ 2x 4 <10
-
-10 ≤x < 4
-2
-4 ≤x≤ 3
-4 ≤x < 7
The solution of the inequality is -4≤x<7. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -12≤2x-4<10.
Here, -12≤2x-4
Add 4 on both the sides of an inequality, we get
-8≤2x
Divide 2 on both the sides of an inequality, we get
-4≤x
Now, 2x-4<10
Add 4 on both the sides of an inequality, we get
2x<14
Divide 2 on both the sides of an inequality, we get
x<7
So, the solution of the inequality is -4≤x<7
Therefore, option D is the correct answer.
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why is this graph not a function?
The graph is not a function because it fails the vertical line test
How to determine why it is a not functionFrom the question, we have the following parameters that can be used in our computation:
The graph (added as an attachment)
The given graph when represented as an equation, is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
This is so because they do not pass the vertical line test
Hence, the graph is not a function
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Find the center and radius! In standard form! ( Type an ordered pair)
Step-by-step explanation:
The center of the circle is (-2,-3)
The radius is 2 since the distance from the center to the point on the circle is 2
Therefore the standard equation is
[tex](x + 2) {}^{2} + (y + 3) {}^{2} = 4[/tex]
Please help I dont understand how to get the length of segment DF
the measure of the angle will be 70°.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.
The sum of all angle of triangle = 180
The given triangle two angles are given 44° and 68°
The other angle is 180° - (44+68) = 180 - 110 = 70°
Hence the measure of the angle will be 70°.
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A rectangular garden 12 feet by 16 feet has a stone path along the perimeter with the same width, w. The area of the garden and path is 420 square feet.
The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420
This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:
(12+2w)(16+2w) = 420
Expanding and simplifying, we get:
4w² + 56w - 204 = 0
Dividing by 4, we get:
w² + 14w - 51 = 0
Factoring, we get:
(w+17)(w-3) = 0
Since the width of the path cannot be negative, the only valid solution is w = 3.
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Complete question is in the image attached
n the blanks below.
Find the slope of the line passing through the points (8, -4) and (8, -7).
slope:
Find the slope of the line passing through the points (-3, -9) and (-3, 9).
slope:
The slope of the line passing through the points (8, -4) and (8, -7) is undefined.
The slope of the line passing through the points (-3, -9) and (-3, 9) is undefined.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (-7 - (-4))/(8 - 8)
Slope, m = (-7 + 4)/0
Slope, m = -3/0
Slope, m = undefined.
Since the change in the x-axis equals to zero, the slope of the two lines are undefined:
Slope, m = (9 - (-9))/(-3 - (-3))
Slope, m = 18/0
Slope, m = undefined.
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Describe a single transformation of △ABC that is a composition of the following pair of transformations:
T<−5,−3>(ABC) followed by T<−4,−2> (A'B'C).
A. T<−1,−5>(ABC)
B. T<−9,−5>(ABC)
C. T<−9,−1>(ABC)
D. T<−1,−1>(ABC)
The required overall translation is T<−9,−5>(ABC). The correct answer would be option B.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Starting with triangle ABC, we first apply the transformation T<−5,−3>, which means each vertex of the triangle is shifted 5 units to the left and 3 units down. So the triangle becomes A'B'C'.
Next, we apply the transformation T<−4,−2> to triangle A'B'C', meaning that each vertex is shifted 4 units to the left and 2 units down.
To find the overall effect of these two transformations, we can think of the second transformation as shifting the entire triangle produced by the first transformation.
In other words, we're combining the effects of the two transformations by adding the translations together.
So, the overall translation is T<−5 + −4, −3 + −2> = T<−9,−5>,
Thus, the correct answer would be option B: T<−9,−5>(ABC).
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Shermanos changes $15 for a supreme pizza how much will you pay for 2 supreme pizzas including 8.875% tax?
. One number is five more than the other. Their sum is 33. Find the numbers.
Answer:
14 and 19
Step-by-step explanation:
14+5=19
14+19=33
If f(r)=√, which equation describes the graphed function?
The equation that describes the graphed function is given as follows:
A. y = f(-x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]y = \sqrt{x}[/tex]
The function was reflected over the y-axis, hence it is given as follows:
[tex]y = \sqrt{-x}[/tex]
Then it was moved 3 units right, hence the definition is given as follows:
[tex]y = \sqrt{-(x - 3)}[/tex]
[tex]y = \sqrt{-x + 3}[/tex]
Hence:
y = f(-x + 3), as x was replaced by -x + 3.
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Hannah has to make 168 gallons of punch for a big party. The punch is made of soda and fruit drink. The cost of the soda is $1.57 per gallon and the cost of the fruit drink is $2.41 per gallon. Hannah's budget requires that the punch cost $1.66 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?
Gallons of soda =
Gallons of fruit punch =
The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.
How much fruit drink and soda does he need?The system of equations that represents the question is:
f + s = 168 equation 1
2.41f + 1.57s = (1.66 x 168)
2.41f + 1.57s = 278.88 equation 2
Where:
f = number of gallons of fruit drink s = number of gallons of sodaThe elimination method would be used to determine the required values
Multiply equation 1 by 2.41
2.41f + 2.41s = 404.88 equation 3
Subtract equation 2 from equation 3
126 = 0.84s
s = 126 / 0.84
s = 150
Substitute for s in equation 1
f + 150 = 168
f = 168 - 150
f - 118 gallons
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The triangles are similar. What is the missing length?
8
18
72
16
The answer is B. 18
When solving similar triangles, you must set up a proportion. We do not know what the other two lengths are for side AB, but we can still solve another way. For side AC, we can set up a proportion of 33/44. We're going to take AM and put that over the total. The total length of side AB is 24, and we're going to use x for AL.
33/44 = x/24
Once finished solving the proportion, you are left with 18
The missing length of triangle is 18.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.Equilateral Triangle - A triangle has three sides that are of the same length.A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.Triangle with a Right Angle - A triangle with one of its angles equal to 90°.Now,
As these triangles are similar that means
we can find the proportion of sides from given sides and
from that find x.
So, here AC/AM=AL/AB
44/33=24/x
AL=24*33/44
AL=18
Hence,
The missing length AL of triangle is 18.
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Which statements correctly describe how the graph of the geometric sequence below should appear?
640, 160, 40, 10, ...
Select two options.
Answer:
Step-by-step explanation:
The graph of the geometric sequence 640, 160, 40, 10, ... should have the following characteristics:
Decreasing: The values in the sequence decrease at a constant rate, so the graph should decrease as well.
Straight Line: Since the sequence is a geometric sequence, the graph will be a straight line when plotted on logarithmic axes.
Negative Slope: The slope of the line should be negative, since the values are decreasing.
Non-Linear: When plotted on linear axes, the graph will not be a straight line and will curve downward, since the difference between consecutive terms is decreasing.
Therefore, the graph of the geometric sequence should appear as a straight line with a negative slope when plotted on logarithmic axes, and as a non-linear curve with a downward slope when plotted on linear axes.
help please!!!!!!!!!!
Answer:
5x(8-1)=(5x10)-(5x4)
An angler catches a fish that weighs 20 kg. The fish’s bones make up approximately 10% of the fish’s total weight. What is the weight of the fish meat, not including the bones, in pounds? Round to the nearest tenth if necessary.
44.0
40.0
39.6
4.4
4.0
Answer: approximately 40lbs.
Step-by-step explanation:
First, you multiply 20kg to 10%, or 0.10.
20(0.10)=2kg
Then you minus the 2kg from the initial weight
20kg
-2kg
18kg
1 kg is approximately 2.20462262 lbs., so you need to convert your kg to lbs
18kg * 2.20462262 lb/kg = 39.68320716 which is rounded up to approximately 40lbs
Hope that helps!
A cupcake shop makes 25 dozen
cupcakes every 2 days. At this rate, how
many cupcakes does the shop make in
five days?
A. 600
B. 650
C. 750
D. 900
I got a bit confused with this pls help.
Answer:
The correct answer is c. 750
Step-by-step explanation:
if the shops makes 25 dozen in two days that makes it 300 cupcakes In two days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know he/she is going to make half of the 25 dozen on the 5th day so you will take half of 300 which is 150 and add it all together, so will get 300+300+150= 750 as your answer.
e 1.5 Checkpoint: Rational and irrational numbers SNE
Select all the numbers that are irrational.
√55
36
39
√40
L
√√49
√55 and √40 are the irrational numbers.
What is Number system?A number system is defined as a system of writing to express numbers.
A rational number is the one which can be represented in the form of P/Q where P and Q are integers and Q ≠ 0.
But an irrational number cannot be written in the form of simple fractions.
√55 is an irrational number
√40 is an irrational number
√49 value is 7 which is a natural number
Hence, √55 and √40 are the irrational numbers.
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Please I could really use some help
Answer:
-1/2
Step-by-step explanation:
cos(-360+60)=-1/2
[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]
Current assets are assets that are expected to be converted to cash, sold or consumed in the next
12 months. They include cash, accounts receivable, notes receivable, inventory and prepaid
expenses. Step 8 explains each one in detail.
1. You are the owner of an appliance store. Choose four categories from above and explain how
that asset may fit into your business. For example, if I owned a company that installed furnaces,
my inventory would include different types of furnaces and air conditioners as well as controls
to operate them. Accounts receivable would include the installations we did but have not been
paid for yet.
How these current asset may fit into your business, like mine, is explained as follows:
Cash: Cash is a crucial asset for any business, as it is needed to pay for expenses such as salaries, rent, and other operating costs.Accounts Receivable: It represents the amount of money owed to the business by its customers and is a key part of the business's revenue stream. Inventory: Inventory represents the value of the goods that are available for sale and can include raw materials, work-in-progress, and finished products.Prepaid Expenses: Prepaid expenses can be a helpful asset for businesses that make regular payments for services or goods, such as insurance or rent. Explanation on items of the Current assets:Cash: Cash refers to physical currency or money that is readily available to a business or individual. It includes cash on hand, in bank accounts, or other forms of liquid assets that can be easily converted to cash.Accounts Receivable: Accounts receivable refers to the amount of money owed to a business by its customers or clients for goods or services that have been sold but not yet paid for. It represents the short-term credit that a business has extended to its customers.Notes Receivable: Notes receivable are similar to accounts receivable but involve more formal written agreements. They are written promises by a borrower to pay a specific sum of money at a future date to a creditor, with interest.Inventory: Inventory refers to the goods that a business holds for sale to customers or for use in its operations. It includes raw materials, work-in-progress, and finished goods that have not yet been sold.Prepaid Expenses: Prepaid expenses refer to payments made by a business for goods or services that have not yet been used or consumed. They are considered assets because they represent future economic benefits that will be realized by the business. Examples include prepaid rent, insurance premiums, and other prepayments.Read more about Current assets
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Which of the following angles is in the solution set of (see picture)
Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.
What best define about angle?The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to
The equation below can be set up to calculate this.
Tan(angle) = 80 ft / (200 ft – 4 ft)
Solving for the angle, we get:
angle = tan-1(80 ft / 196 ft (ca. 60 m))
angle = tan-1(0.408163265)
Angle = 36.87 degrees (to the nearest hundredth of a degree).
Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.
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Hi I need help.
An education reform lobby is compiling data on the state of education in the United States. In their research they looked at the percent of people who graduate high school in 10 different states. The data are provided below. Use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and the sample variance.
Round your answers to one decimal place.
High School Graduation Rate (%)
77.1
82.9
90
91.3
81.9
83.3
84.9
82.5
84.6
The sample variance and standard deviation are given as follows:
Variance = 87.22 %.
Standard deviation = 9.34%.
To obtain the variance and the standard deviation first, we must obtain the mean, which is given by the sum of all observations divided by the number of observations, hence:
Mean = (77.1 + 82.9 + 90 + 91.3 + 81.9 + 83.3 + 84.9 + 82.5 + 84.6)/10
Mean = 75.85.
Then we must obtain the sum of the differences squared between each observation and the mean, as follows:
(77.1 - 75.85)² + (82.9 - 75.85)² + (90 - 75.85)² + (91.3 - 75.85)² + (81.9 - 75.85)² + (83.3 - 75.85)² + (84.9 - 75.85)² + (82.5 - 75.85)² + (84.6 - 75.85)² = 784.9825
The sample variance is given by the above sum divided by one less than the sample size, hence:
Variance = 784.9825/9
Variance = 87.22 %.
The standard deviation is the square root of the variance, hence:
Standard deviation = sqrt(87.22)
Standard deviation = 9.34%.
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This question I can not figure out Someone please help.
Answer:
x y
0 -2
4 -1
graph: should look like the picture attached
explanation:
A bag contains 8 green marbles and 32 blue marbles. If a representative sample con
Because the ratio of green marbles to blue males is 1:4 in the population, the e
be 8 blue marbles.
Answer:
The expected number of blue marbles in a sample of 8 marbles would be 4 times the number of green marbles, so 4 * 8 = 32. Thus, the expected number of blue marbles in a sample of 8 marbles is 32.
Step-by-step explanation:
If a graph of y=-9x + 11 were changed to a graph of y=-9x+14, how would the y-intercept change? OA. The y-intercept of the new graph would shift up 3 units. B. More information is needed to determine the change. C. The y-intercept would remain the same. D. The y-intercept of the new graph would shift down 3 units.
Answer:
Step-by-step explanation:
The y-intercept of a linear equation in slope-intercept form, y = mx + b, represents the point at which the line crosses the y-axis. In this form, "m" represents the slope of the line and "b" represents the y-intercept.
If we have a graph of y = -9x + 11, the y-intercept can be found by setting x equal to 0 and solving for y:
y = -9x + 11
y = -9 * 0 + 11
y = 11
So, the y-intercept of the original graph is (0, 11).
Now, if we have a graph of y = -9x + 14, the y-intercept can be found in the same way:
y = -9x + 14
y = -9 * 0 + 14
y = 14
So, the y-intercept of the new graph is (0, 14).
Comparing the y-intercepts of the two graphs, we can see that the y-intercept of the new graph has shifted up by 3 units, from (0, 11) to (0, 14).
Therefore, the correct answer is A: The y-intercept of the new graph would shift up 3 units.
You randomly draw once from this deck of cards.
4 6
1 6 9 4
8
1
1
2 6 7
What is the probability of not drawing an even number? Write your
answer as a fraction.
9
5
Answer:why not
Step-by-step explanation:that sa prrety nice ask
Answer: 5/8
Step-by-step explanation:
The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.
Sami is 5 feet 8 inches tall and his younger sister is 4 feet 11 inches tall. How many inches taller is sami than his sister?.
The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.
Height of Sami in feet and inches is equal to 5 feet 8 inches
Height of Sami's younger sister is equal to 4 feet 11 inches
Convert all height into inches we get,
1 feet = 12inches
5 feet = 5 × 12 inches
= 60 inches
4 feet = 4 × 12 inches
= 48 inches
Number of inches Sami's is taller than his younger sister is equal to
= ( 5 feet 8 inches ) - ( 4 feet 11 inches )
= ( 60 + 8 ) inches - ( 48 + 11 ) inches
= 68 inches - 59 inches
= 9 inches
Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.
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If joes shoes cost 44 dollars and 20 cents and joe has 10
dollars and 68 cents. How much money does joe need?
Answer: 44.20-10.68=33.52
He need 33.52$
Step-by-step explanation:
or problems 2-7, find the slope of the line.
1.
1.
-10
-10
2 PRACTICE
y
y
10
10
3.
y
10
H
5.
-10-
y
10
2
+
10
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The slope of the line in graph 2 is equal to 1.
The slope of the line in graph 3 is equal to 1/2.
The slope of the line in graph 4 is equal to 3/4.
The slope of the line in graph 5 is equal to 3.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (7 - 2)/(7 - 2)
Slope, m = 5/5
Slope, m = 1.
For the line in graph 3 with the given data points, we have:
Slope, m = (3 + 2)/(6 + 4)
Slope, m = 5/10
Slope, m = 1/2.
For the line in graph 4 with the given data points, we have:
Slope, m = (6 - 0)/(8 - 0)
Slope, m = 6/8
Slope, m = 3/4.
For the line in graph 5 with the given data points, we have:
Slope, m = (6 - 0)/(2 - 0)
Slope, m = 6/2
Slope, m = 3.
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