The two numbers are 4 and 1.
What are the two numbers?To solve the problem, we will use algebraic equations.
We will call 2 numbers x and y. So, we know that:
------ x + y = 5 (equation 1)
------ xy = 20 (equation 2)
We will solve for y in terms of x:
y = 5 - x
We will substitute for y into equation 2 and simplify:
x(5 - x) = 20
5x - x^2 = 20
x^2 - 5x + 20 = 0
As a quadratic equation which will be solved using the quadratic formula, the solutions are x = 4 and x = 1. We can check that these solutions satisfy both equation 1 and equation 2.
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Can you solve this for me please
The possible values of a are:
(i) A unique solution: a such that a² ≠ 5
(ii) Infinitely many solutions: a such that a² = 5
(iii) No solution: for all other values of a.
How to determine linear system?To solve this system of linear equations, use Gaussian elimination to reduce the augmented matrix to row echelon form. Then, examine the resulting matrix to determine the number of solutions.
The augmented matrix for the system is:
[1 2 -3 | 4 ]
[3 -1 5 | 2 ]
[4 1 a²-14 | a+2]
Using row operations, transform the matrix as follows:
[1 2 -3 | 4 ]
[0 -7 14 | -10]
[0 -7 a²-2 | a-6]
The third row is a linear combination of the first two rows, so we can eliminate it. This gives us:
[1 2 -3 | 4 ]
[0 -7 14 | -10]
Further simplify this matrix by dividing the second row by -7:
[1 2 -3 | 4 ]
[0 1 -2 | 10/7]
Use back-substitution to solve for the variables, start with the second row:
y - 2z = 10/7
Rearranging this equation:
y = 2z + 10/7
Substituting this into the first row:
x + 2(2z+10/7) - 3z = 4
Simplifying this equation:
x + (4/7)z = 18/7
So, the solution to the system is:
x = (18/7) - (4/7)z
y = 2z + 10/7
z is free
Now, examine the possible values of a:
(i) A unique solution: If the system has a unique solution, then there can be no free variables. From our solution above, we see that z is a free variable. Therefore, the system can have a unique solution only if a is such that the third row in the original augmented matrix does not reduce to a multiple of the first two rows. This is equivalent to the condition -7 ≠ a² - 2, or a² ≠ 5.
(ii) Infinitely many solutions: If the system has infinitely many solutions, then there must be at least one free variable. From our solution above, we see that z is a free variable. Therefore, the system can have infinitely many solutions for all values of a such that a² = 5.
(iii) No solution: If the system has no solution, then there must be a row in the reduced row echelon form that has all zeros except in the last column. However, our reduced matrix does not have this form. Therefore, the system has no solution for any value of a.
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A deposit of $2,960 is placed into a scholarship fund at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually, and paid at the end of the six months. How much is in the account right after the last deposit?
The account will have $7240 after the last deposit.
Given that, $2960 is being deposited at the beginning of every six months for 13 years. The fund earns 7% annual interest, compounded biannually,
So,
When the amount is compounded biannually,
[tex]A = P(1+r/2)^{2t[/tex]
A = final amount, P = initial amount, r = rate and t = time,
[tex]A = 2960(1+0.07/2)^{2(13)[/tex]
[tex]A = 2960(1.035)^{26[/tex]
[tex]A = 7240[/tex]
Hence, the account will have $7240 after the last deposit.
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Which shape depicts the cross-section?
O A.
OB.
O C.
D.
The shape generated by the cross-section is a rectangle. So the correct option is D.
Which shape depicts the cross-section?Notice that the cross-section goes through two opposite sides of the cube.
Then the shape that we will get will also be a quadrilateral of parallel sides. Notice that if the plane was parallel to the square, the cross-section would be also a cube, but because it is slanted, one of the sides will be larger, then we will get a rectangle, thus, the correct option is the last one.
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Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are
(–1, 0). What are the coordinates of B?
Answer:
We know that point A(5, 1) maps to A'(6, -2) in the translation. To find the translation vector, we can subtract the coordinates of A from the coordinates of A':
Translation vector = A' - A = (6, -2) - (5, 1) = (1, -3)
This means that every point in the preimage moves 1 unit to the right and 3 units down to reach its corresponding point in the image.
We also know that point B'(−1, 0) is the image of a point B in the preimage. To find the coordinates of point B, we can apply the translation vector to B':
B = B' - Translation vector = (-1, 0) - (1, -3) = (-2, 3)
Therefore, the coordinates of point B in the preimage are (-2, 3).
Square root of 6 rounded to the nearest hundredth
The value of expression √6 would be,
⇒ √6 = 2.4
We have to given that;
To find the value of number √6.
Now, We get;
⇒ √6 = 2.44
⇒ √6 = 2.4
Thus, The value of expression √6 would be,
⇒ √6 = 2.4
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If your base pay is 10000 your commission rate is 40% you sell 15 cars and you earn 40000 how much does each car cost
Answer: $4,000
Step-by-step explanation:
If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.
Since the commission rate is 40%, we can set up the equation:
40% x Total Sales = Commission Earned
We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:
40% x Total Sales = Commission Earned
40% x (15 x Price per Car) = $30,000
6 x Price per Car = $30,000
Price per Car = $5,000
However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:
Commission per Car = 40% x Price per Car
Commission per Car = 40% x $5,000
Commission per Car = $2,000
Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:
Amount earned per Car = Total Earnings / Number of Cars Sold
Amount earned per Car = $40,000 / 15
Amount earned per Car = $4,000
please help with this semi circle !! Radius circumference
The radius of the circle is 6 inches and the circumference is 30.84 in
How to find the circumference?For a circle of radius R, the circumference is given by:
C = (pi*R + 2*R)
Where pi = 3.14
For the given semicircle, we can see that the diameter is 12 inches. Then the radius is half of that, we will get.
R = D/2 = 12in/2 = 6 inches.
Now we can replace that in the circumference formula to get.
C = (3.14*6in + 2*6in)
C = 30.84 in
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One quarter of a bread recipe calls for 2/3 cup of bread flour how much flour is needed per recipe
The number of cups of flour required to make 1 recipe is 8/3.
Given that, one quarter of a bread recipe calls for 2/3 cup of bread flour.
Amount of flour required per 1 recipe = Number of quarters × Number of cups of flour
= 4 × 2/3
= 8/3
Therefore, the number of cups of flour required to make 1 recipe is 8/3.
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A teacher has a box of 100 pencils and wants to divide it equally among 25 students what fraction of the box of pencils would each student get
Answer:1/25
Step-by-step explanation:100/25=4. So 1/25 of the box.
2. The showroom for a new apartment complex includes a scale model of the building.
The scale factor is 1/3.41 If the actual apartment building will be 39 m wide, how wide is the model?
a. 13.7 m
b. 9.1 m
c. 133 m
d. 11.4 m
The calculatd value of the model width is 11.4 m
How wide is the model?From the question, we have the following parameters that can be used in our computation:
Scale factor = 1/3
Actual apartment building will be 39 m wide
Using the above as a guide, we have the following:
Model width = Scale factor *Actual apartment building
Substitute the known values in the above equation, so, we have the following representation
Model width = 1/3.4 * 39
Evaluate
Model width = 11.4
Hence, the model width is 11.4 m
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What is the perimeter of square HIJK?
104
-10 -8
-6
-4
K
-2
8
units
6
4
2
0
-2
-4
-6
-8
A
H
lot
6
8
-10
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Perimeter =>
well, we know is a square, so that means all sides are equal, so if we just find one side and multiply it by 4, that's our perimeter, hmmmm let's use the points of K(-2 , 0) and J(3 , 5)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ K(\stackrel{x_1}{-2}~,~\stackrel{y_1}{0})\qquad J(\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ KJ=\sqrt{(~~3 - (-2)~~)^2 + (~~5 - 0~~)^2} \implies KJ=\sqrt{(3 +2)^2 + (5 -0)^2} \\\\\\ KJ=\sqrt{( 5 )^2 + ( 5 )^2} \implies KJ=\sqrt{ 25 + 25 } \implies KJ=\sqrt{ 50 } \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE perimeter} }{4\sqrt{50} ~~ \approx ~~ }\text{\LARGE 28.3}[/tex]
Which statement is true about the end behavior of the function repnesented by the graph
The statement which is true about the end behaviour of the given quadratic function is;
As x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f (x) approaches ∞.Which answer choice correctly describes the end behaviour of the graph?As evident from the task content; the answer choice which correctly describes the end behaviour of the given quadratic function is to be determined.
By observation, the given quadratic graph opens upwards and on this note, its end behaviour is such that; As x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f (x) approaches ∞.
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Which of the following is the graph of the inverse of the function shown below? (1 point)
The graph of the inverse of the function is shown below.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
From the information provided, we can logically deduce the following ordered pairs from the graph of the parent function:
x, f(x) = {(-2, 5), (-1, 1), (1, 2), (2, 3)}
In order to determine the inverse of this function f(x), we would interchange (swap) both the input value (x) and output value (y) as follows:
Inverse of f(x) = {(5, -2) (1, -1), (2, 1), (2, 3)}
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Last one that’s due 200 pts
The concentration (C) in ounces of sugar per ounce of milk will be C = 10/(10/t + 1) + 1
The domain is all real numbers except t = 0.
How to calculate the valueThe concentration (C) in ounces of sugar per ounce of milk will be
C = S/M
C = (10 + 10t)/(10 + t)
C = 10/(10/t + 1) + 1
The concentration after five minutes, will be:
C = 10/(10/5 + 1) + 1
C = 10/3
C ≈ 3.33 ounces of sugar per ounce of milk
The time it takes to reach a concentration of 8 ounces of sugar per ounce of milk, will be:
8 = 10/(10/t + 1) + 1
7 = 10/(10/t)
70/t = 10
t = 7 minutes
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A diameter of a circle has endpoints A(-4,2) and B(3,2). Find the center of the circle, radius, and write an equation for the circle. * 0 points
an airplane is climbing 500 feet for every 700 feet it travels. estimat the airplane's climb angle while this is happeing.
The value of airplane's climb angle while this is happening is,
⇒ 35.53 degree
We have to given that;
An airplane is climbing 500 feet for every 700 feet it travels.
Hence, We can formulate;
The value of airplane's climb angle while this is happening is,
⇒ tan x = 500 / 700
⇒ tan x = 0.714
⇒ x = 35.53 degree
Thus, The value of airplane's climb angle while this is happening is,
⇒ 35.53 degree
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It asks me to write a fraction as a mixed number. If I have 20/10, what is the mixed number?
A car is purchased for $32,000. Each year it loses 25% of its value. After how many years will the car be worth $5800 or less
Answer: 6 years
Step-by-step explanation: 32,000 divided by 25% is 24,000. 24,000 divided by 25% is 18,000. 18,000 divided by 25% is 13,500. 13,500 divided by 25% is 10,125. 10,125 divided by 25% is 7,593.75. 7,593.75 divided by 25% is 5,695.3125. so 6
liz and fareed each start a new savings account. Liz starts her account with $75. Fareed starts with $100. They both save $50.
What are there amounts after 4 weeks?
Therefore, after 4 weeks, Liz will have $275 in her savings account and Fareed will have $300 in his savings account.
After 1 week
Liz will have saved $75 + $50 = $125, and
Fareed will have saved $100 + $50 = $150.
After 2 weeks,
Liz will have saved a total of $125 + $50 = $175, and
Fareed will have saved a total of $150 + $50 = $200.
After 3 weeks,
Liz will have saved a total of $175 + $50 = $225, and
Fareed will have saved a total of $200 + $50 = $250.
After 4 weeks,
Liz will have saved a total of $225 + $50 = $275, and
Fareed will have saved a total of $250 + $50 = $300.
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Mason is ordering a one-topping pizza. He can get either thin crust or hand tossed and can choose from 15 toppings. How many different pizzas can Mason order?
A. 15
B. 17
C. 7
D. 30
What is the component form of resultant of 4b - 2a?
ā= (6,-2)
b=(-5,2)
Enter your answer by filling in the boxes.
4b- 2a =(_,_)
Answer:
To find the resultant of 4b - 2a, we need to first calculate 4b and -2a separately, and then add them together.
4b = 4(-5, 2) = (-20, 8)
-2a = -2(6, -2) = (-12, 4)
Now, we can add (-20, 8) and (-12, 4) component-wise to find the component form of the resultant:
4b - 2a = (-20, 8) + (-12, 4) = (-20 - 12, 8 + 4) = (-32, 12)
Therefore, the component form of the resultant of 4b - 2a is (-32, 12).
Answer: (-32, 12)
Step-by-step explanation: I took the test.
Given:
a = (6, -2)
b = (-5, 2)
4b = 4( -5, 2) = ( -20, 8)
-2a = -2( 6, -2) = ( -12, 4)
(-20, 8)
( -12, 4)
+______
(-32, 12)
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
Vertical translation
The type of transformation shown is vertical translation. That is option D.
What is Transformation in geometry?Transformation of geometrical figures or points is the manipulation of a given figure to take the same shape but with different direction of its original angles.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Given a polygon ABDC.
It is transformed to another polygon with the same size A'B'D'C'.
Here the polygon ABDC is just moved downwards as it is and mark is as A'B'D'C'.
In rotation or reflection transformation, the points will change it's correspondent place.
Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.
Since the shifting is done vertically, it is vertical translation.
Hence the transformation is vertical translation.
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can someone help with those 2 questions please? I’ll reward you with brainsliet.
The polynomial (2m + 2n)6 = 12m + 12n.
For the long division, the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.
How to divide polynomials?To expand the expression (2m + 2n)6, using the distributive property of multiplication over addition:
(2m + 2n)6 = 2m(6) + 2n(6)
Simplifying further, evaluate the products:
= 12m + 12n
Therefore, (2m + 2n)6 = 12m + 12n.
Using long division to divide the polynomial x³ - 6x² + 11x - 6 by the polynomial x² - 4x + 3. The steps are as follows:
x - 2
------------------
x² - 4x + 3 | x³ - 6x² + 11x - 6
- (x³ - 4x² + 3x)
- 2x² + 8x
- 2x² + 8x - 6
+ 6
Therefore, x³ - 6x² + 11x - 6 = (x - 2)(x² - 4x + 3) + 6.
So the quotient is x - 2, the remainder is 6, and the dividend can be written as (x - 2)(x² - 4x + 3) + 6.
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Mei Mei bought 15 chicken wings for $28.50. If Mei Mei spent $34.20, how many chicken wings did she buy?
Answer:18 wings
Step-by-step explanation: 28.50 divided by 15 is 1.9 so if you do 1.9 x 18 you get 34.2
Answer:
18 wings
Step-by-step explanation:
Use a proportion.
15/$28.5 = x/$34.2
28.5x = 15 × 34.2
28.5x = 513
x = 18
Answer: 18 wings
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. Write the rule that best represents the dilation that was applied to triangle ABC to create triangle A'B'C'. -10-9-S A B C
The rule of dilation is a dilation by a scale factor of 2
Determining the rule of dilationFrom the question, we have the following parameters that can be used in our computation:
ABC with vertices at A(1, 1)A'B'C' with vertices at A'(2, 2)The scale factor is calculated as
Scale factor = A'/A
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (2, 2)/(1, 1)
Evaluate
Scale factor = 2
Hence, the rule of dilation is (2x, 2y)
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What is the surface area of the triangular prism?
10 cm
5 cm
5 cm
5 cm
4 cm
The surface area of the triangular prism is 120 sq cm
What is the surface area of the triangular prism?From the question, we have the following parameters that can be used in our computation:
Dimensions = 10 cm 5 cm 5 cm 5 cm and 4 cm
Using the formula of the surface area of the triangular prism, we have
Surface area = bh + (l1 + l2 + l3) * h
Substitute the known values in the above equation, so, we have the following representation
Surface area = 10 * 5 + (5 + 5 + 4) * 5
Evaluate
Surface area = 120
Hence, the surface area is 120 sq cm
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1. Write the following number in scientific notation: 0.000089
O 89 x 106
8.9 x 105
89 x 10-6
8.9 x 10-5
Answer:
To write the number 0.000089 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point, and count the number of places we moved the decimal point. In this case, we need to move the decimal point 5 places to the right:
0.000089 = 8.9 × 10^(-5)
Therefore, the number 0.000089 in scientific notation is 8.9 × 10^(-5).
Brenda is a metalsmith who makes custom signs out of different types of metals. She sold 10
signs this week in the following metals:
copper, silver, brass, silver, aluminum, copper, brass, copper, silver, copper
Based on the data, estimate how many of the next 40 signs Brenda sells will be made of
brass.
If necessary, round your answer to the nearest whole number.
Answer:
8
Step-by-step explanation:
Brenda sold 2 brass signs of the 10 signs she sold this week. You want an estimate of the number of brass signs she will sell out of the next 40.
ProportionWe expect the proportion of brass signs to remain the same, so the number (x) of brass signs in the next 40 signs is expected to be ...
x/40 = 2/10
x = 40(2/10) = 8
We estimate Brenda will sell 8 brass signs out of the next 40 signs she sells.
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A small sleepy town in California has been losing population since 1993. In 1993 the population was 10500 but it has been decreasing by about 5.2% per year.
If this trend continues, predict the population in 2018. Round your answer to the nearest integer.
The population of the town in 2018 will be 5,040.
To predict the population in 2018, we need to use the following formula:
Population in 2018 = Population in 1993 × (1 - rate of decrease)[tex].^n[/tex]
Here, the population in 1993 is 10,500, the rate of decrease is 5.2% or 0.052 (in decimal form), and the number of years from 1993 to 2018 is 25.
Substituting these values, we get:
Population in 2018 = 10,500 × (1 - 0.052)^25
= 10,500 × 0.480
= 5,040
Rounding this answer to the nearest integer, we get a predicted population of 5,040 in 2018.
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1. A limit imposed by the government on the quantity of a good or product that can be brought into the
country is called a
a. tariff
b. quota
c. foreign bill of exchange
I
d. value added tax
2. Which of the following would not be an effective argument for the U.S. to enact trade restrictions?
Oa
a. they shield U. S. workers from competition by cheap foreign labor
b. they may benefit the security and defense of the nation
c. they help the U.S. maintain diverse industries
Od. they make foreign products cheaper to U.S. shoppers
3. What does it mean if a country is on the gold standard?
O
a. it sets the value of its currency in relation to a specific amount of gold
b. it creates specific standards by which gold is made into jewelry
c. it uses gold instead of paper currency
d. none of these
LICAL
jorgo lovel of income is less