The solution of the system of equations is (2, 4, 5)
The given equations are :
3x+10y-12z = 40 equation(1)
x-5y = 0 equation (2)
x-4z = 0 equation(3)
From 2nd equation, x -5y = 0, 5y = x, y = x/5
From 3rd equation, x -4z = 0, 4z = x, z = x/4
Putting the values of y and z in equation (1), we get :
[tex]3x +10y -12z = 40\\\\3x +10*\frac{x}{5} -12*\frac{x}{4} = 40\\\\3x +2x -3x =40\\\\2x = 40\\\\x = \frac{40}{2} = 20[/tex]
Now, putting the value of x = 20 to evaluate y and z, we have,
y = 20/5 = 4
and z = 20/4 = 5
Hence, the solution of the system of equations is (2, 4, 5)
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solve the equation-2/3d-1/4d=-22 for d
Answer:
d = 24
Step-by-step explanation:
[tex] \rm \implies - \dfrac{2}{3} d - \dfrac{1}{4} d = - 22 \\ \\ \rm \implies - \frac{2}{3} d \times \frac{4}{4} - \frac{1}{4} d \times \frac{3}{3} = - 22 \\ \\ \rm \implies - \frac{8}{12} d - \frac{3}{12} d = - 22 \\ \\ \rm \implies \frac{ - 8d - 3d}{12} = - 22 \\ \\ \rm \implies \cancel{- } \frac{11}{12} d = \cancel{-} 22 \\ \\ \rm \implies d = 22 \times \frac{12}{11} \\ \\ \rm \implies d= 2 \times 12 \\ \\ \rm \implies d= 24[/tex]
Each child in the family has at least one brother, two sisters and two parents.
What is the fewest number of children their parents might have?
Ooo this is like a riddle. Let me attempt to answer:
Let's start with one of the brothers. That's 1 child. There has to be 1 more brother for each brother to have one other brothers. Then for that brother to have two sisters, they have to have two girls. This is 4 children.
Now from a girl's perspective. You are a girl so you are already 1 child. To have one brothers, there has to be 1 boy. Then to have two sisters, there has to be two additional girls. That's 3 girls and one boy - which are still 4 children in all.
Of course two parents are two parents for all.
The fewest number of children the parents have is 4
I hope this helps!
State all integer values of xx in the interval -4 ≤ x ≤ 3 that satisfy the following inequality: -5x -3 > 8
The integer which satisfies both inequalities -4 ≤ x ≤ 3 and -5x -3 > 8 are -3 and -4.
What is inequality?A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given first inequality,
-4 ≤ x ≤ 3
The integer associated with the above inequality is -4,-3,-2,-1,0,1,2,3.
As per the given second inequality,
-5x -3 > 8
-5x > 8 + 3
-5x > 11
x < -11/5
x < -2.2
The integer associated with the above inequality is -3,-4....
The integer satisfies both inequalities are -3 and -4.
Hence "The integer which satisfies both inequalities -4 ≤ x ≤ 3 and -5x -3 > 8 are -3 and -4".
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Help please!!!!!!!!!!!!!!!!!!!!
Answer:
f(-2)= -2
f(-0.75)= -1
f(1)= 1
KHAN ACADEMY LESSON HELP ME : Two-step inequality word problems
Answer: d> 5 1/2
Step-by-step explanation:
34 + (12 × d) > 100
34 + 12d > 100
12d > 100 - 34
12d > 66
d > 66 / 12
d > 5 1/2 days
Therefore, the number of days, (d), it will take Katie to collect over 100 seashells is 5 1/2 days.
Complete the number line as needed to plot the given points. Then, plot the following integers on the number line.
-22.-28.-21.-25. Write the numbers in order from least to greatest using inequalities.
The numbers has been plotted on the number line and the order of the numbers from least to greatest is -28 < -25 < -22 < -21
The given numbers are
-22, -28, -21 and -25
The inequality is the mathematical statement that shows the relationship between one expression and another expression with inequality sign. The inequalities maybe less than, less than or equal, greater than, greater than or equal . The equal sign will not be a part of inequality
The numbers are
-22, -28, -21 and -25
Plot the numbers in the number line
The order of the numbers from least to greatest is -28 < -25 < -22 < -21
Hence, the numbers has been plotted on the number line and the order of the numbers from least to greatest is -28 < -25 < -22 < -21
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What is the probability that the song that was picked was one she liked or one she has not heard but did not enjoy?
The probability that the song that was picked was one she liked or one she has not heard but did not enjoy is 17/22.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
Total number of songs = 22
Probability of liked song = 10/22
The probability of she has not heard but did not enjoy = 7/22
The probability that the song that was picked was one she liked or one she has not heard but did not enjoy:
= 10/22 + 7/22
= 17/22
Thus, the probability that the song that was picked was one she liked or one she has not heard but did not enjoy is 17/22.
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An ice cream store sells 4 drinks, in 4 sizes, and 7 flavors. In how many ways can a customer order a drink?
Using mathematical operations, we know that the store can sell its drinks in a total of 112 ways.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, all the possible ways in which a customer can order a drink:
We know that:
This store sells 4 drinks.
The store has 4 different sizes of drinks.
The store sells 7 flavors.
Then, the total ways will be:
4 × 4 × 7
112
Therefore, using mathematical operations, we know that the store can sell its drinks in a total of 112 ways.
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I need help with this please help me
Answer:
3, 4, 5
Step-by-step explanation:
You have parallel lines crossed by a transversal, and one obtuse angle marked as 99°. You want the angle designators of the congruent angles.
Congruent anglesWhere a transversal crosses parallel lines, corresponding angles are congruent. In this figure, angle 3 corresponds to the one marked 99°, so it is congruent.
Anywhere that lines cross, vertical angles are congruent. Angles 3 and 4 are vertical angles, as are angle 5 and the one marked 99°.
Hence angles 3, 4, 5 are all congruent to the one marked 99°.
__
Additional comment
You may have observed that the listed congruent angles are all of the obtuse angles in the figure. Similarly, all acute angles in the figure are congruent. Since the acute and obtuse angles are supplementary (form linear pairs), angles 1, 2, 6, 7 are all 81°.
Find the value of the linear correlation coefficient r. Round your answer to 3 decimal places if necessary.
(1 , 6) , (3 , 4) , (5 , 2)
The correlation coefficient, r, of the data (1 , 6) , (3 , 4) , (5 , 2) is calculated as: r = -1
What is Correlation Coefficient?The correlation coefficient can be described as a numerical value that ranges from -1 through 0, to 1. It is a test of the strength of the relationship between two different variables. It is denoted as "r".
The formula for finding the correlation coefficient (r) between two variables x and y is given as:
r = Σ(xi - mean of x)(yi - ȳ) / √(Σ[xi - mean of x)²Σ(yi - ȳ)²]
Given the following data:
(1 , 6) , (3 , 4) , (5 , 2)
Therefore, the table in the attached diagram shows how to derive each of the variables in the formula used for calculating the correlation coefficient, r, between X and Y.
Thus, applying the formula, we have:
Correlation coefficient (r) = -8/√(8*8)
Correlation coefficient (r) = -1
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Graph the logarithmic function g(x) = log₂ (x+2) −3.
The graph of the given logarithmic function is (see in attachments).
Graph:
In mathematics, a graph is an orderly visual representation of any data. The graph shows how the variable quantities are related to one another. A graph is used in graph theory to represent the collection of objects that are interconnected in some way. The edges between the nodes reflect the connections between the nodes, while the vertices or nodes of the objects are essentially mathematical concepts.
Numerous types of graphs are used to visually display data in mathematics and statistics. Graph theory is the study of points and lines. It is a field of mathematics that focuses on graph analysis.
This image provides a visual representation of the mathematical truth. Graph theory is a method for studying relationships.
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How many three-letter "words" can be made from 4 letters "FGHI" if
a. repetition of letters is allowed
b. repetition of letters is not allowed
The number of three letter words that can be formed from the 4 letters "FGHI" is
(a) when repetition allowed is 64
(b) when repetition not allowed is 24 .
In the question ,
the four letters are given as "FGHI" ,
we need to find the how many 3 letter words can be formed ,
(a) when repetition is allowed
= (selecting a letter from 4 given letters)×(selecting a letter from 4 given letters)×(selecting a letter from 4 given letters) .
= ⁴C₁ × ⁴C₁ × ⁴C₁
= 4 × 4 × 4 .... because ⁴C₁ = 4
= 64
(b) when repetition not allowed
= (selecting a letter from 4 given letters)×(selecting a letter from the remaining 3 letters)×(selecting a letter from the remaining 2 letters)
= ⁴C₁ × ³C₁ × ²C₁
= 4 × 3 × 2
= 24
Therefore , The number of three letter words that can be formed from the 4 letters "FGHI" is (a) when repetition allowed is 64 , (b) when repetition not allowed is 24 .
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Complete the number sentence.
2 + (-10) =
Answer:
2 + (-10) = 2 - 10 = -8
A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
A graph for p of x is a downward open parabola with its vertex at (5, 725) and passes through the points (negative 10, 0), and (20, 0).
Use the graph to complete each statement about this situation.
The maximum profit the florist will earn from selling celebration bouquets is $
.
The florist will break-even after
one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (
,
).
Answer:
We use the attached graph
a. The maximum profit is the y value that is the value of P(x) that reaches maximum. From the graph the maximum value of P(x) is 675
So the maximum profit the florist will earn from selling bouquets = $675
b. Break even is the point where the profit p(x) becomes 0
From the graph we can see that P(x) =0 at x= -10 and x=20
x=-10 is invalid
So, break even after 20 one- dollar decreases
c. The interval of number of one dollar decreases is where the profit P(x) is greater than 0.
From the graph its very clear that the profit P(x) is greater than 0 in the interval 0 to 20.
So, The interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)
a rectangular classroom is 3 meters longer than it is wide. Its area is 180 square meters. How many meters long is it
The length of the rectangle-shaped classroom is 15 meters.
We have a classroom. The shape of the classroom is rectangular. The length of the classroom is 3 meters more as compared to its width. The area of the rectangular classroom is 180 square meters. We need to find the length of the classroom.
Let the width of the rectangle be represented by the variable "x". The length of the rectangle is "x + 3". We will use the formula for the area of a rectangle. The area of a rectangle is the product of its length and width.
A = x*(x + 3)
180 = x² + 3x
x² + 3x - 180 = 0
We will use the quadratic formula to solve for the values of "x".
x = [-3 ± √(3² - 4(1)(-180))]/2(1)
x = [-3 ± √(9 + 720)]/2
x = [-3 ± √729]/2
x = [-3 ± 27]/2
The values of the variable "x" are -15 and 12. The negative value is rejected because the measure of a dimension cannot be negative. Hence, the value of "x" is 12. The length of the rectangular classroom is x + 3 = 12 + 3 = 15 meters.
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Mrs. Gutierrez is obsessed with yoga outfits. She has $120 budget to purchase outfits,
and she wants to buy one pair of pants and three tops. If the price of one pair of yoga
pants is $43, what is the highest possible price of a yoga top that Mrs. Gutierrez can
purchase, if each top is the same price?
Answer:
$25.67
Step-by-step explanation:
120 - 43 = 77
77/3 = 25.67
What type of correlation is suggested by the scatter plot?
Positive Correlation
Negative Correlation
Equal Correlation
No Correlation
Answer:
Positive
Step-by-step explanation:
Appears to be a POSITIVE correleation
as height increases so does weight
Anyone have the answers for this
1) The interest that will accumulate for Marlie during the 4.5-year non-payment period is $3,629.34.
2a) The new principal when Marlie begins making loan payments will be $22,429.34.
2b) Marlie will pay an additional $9,622.19 in interest for 10 years, including the 4.5-year period interest of $3,629.34 to make a total of $13,251.53.
3. If Marlie paid interest during the 4.5-year period, the total interest she will pay, thereafter, is $8,065.20.
4. Marlie's only interest payment due on January 1 is $67.21.
5a) With a private loan at 7.8% APR, Marlie's monthly payment is $226.11.
5b) The total amount Marlie will pay back with a private loan at 7.8% APR is $27,133.67.
5c) Based on a private loan, Marlie's total interest is $8,333.67.
How is interest on student loans computed?The interest on federal student loans is based on simple interest, unlike the interest on private loans, which is compounded.
We can compute simple interest using the simple interest formula (PRT/100) and compounded interest using an online finance calculator.
Student loan amount = $18,800
Interest rate = 4.29%
Non-payment period = 4.5 years
Loan repayment period = 10 years
Interest for the 4.5-year non-payment period = $3,629.34 ($18,800 x 4.29% x 4.5 years)
New Principal after 4.5 years = $22,429.34 ($18,800 + $3,629.34)
Additional interest on the loan after 4.5 years = $9,622.19 ($22,429.34 x 4.29% x 10 years).
Total interest = $13,251.53 ($9,622.19 + $3,629.34)
Interest for 10 years on principal = $8,065.20 ($18,800 x 4.29% x 10 years).
Only Interest monthly payment = $67.21 ($18,800 x 4.29% x 1/12)
N (# of periods) = 120 months (10 years x 12)
I/Y (Interest per year) = 7.8%
PV (Present Value) = $18,800
FV (Future Value) = $0
Results:
Monthly payments (PMT) = $226.11
Sum of all periodic payments = $27,133.67
Total Interest = $8,333.67
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Find the solution of the systems of equations
10x-2y=44
-2x-9y=10
Answer:
y = 0.54, x = 4.51
2. Esther trabaja como mesera en el restaurante de su familia. Ella trabaja 2 horas cada mañana durante el turno del
desayuno y regresa a trabajar cada noche para el turno de la cena. En los últimos cuatro días ella trabajó 28 horas.
Si Esther trabaja la misma cantidad de horas todas las noches, ¿cuántas horas trabajó durante cada turno de la
noche?
Respuesta:
5
Explicación paso a paso:
28- (2*4)= 20
20/4=5
28 es el total de horas
2 horas por la mañana durante cuatro días
20 es el total de horas por la noche
4 días trabajados
5 es horas cada día durante la noche
Answer:
Durante cada turno de la noche Esther trabajo 5 horas
Step-by-step explanation:
Primero hallemos cuantas horas trabaja Esther en un día
[tex]2 + x = horas\ en \ un\ dia[/tex]
2 es el número de horas que trabaja en cada turno de la mañana y [tex]x[/tex] el número de horas que trabaja en su turno de la noche (en este momento desconocemos el valor de [tex]x[/tex] y es el que queremos hallar). Ahora se tiene que en 4 días ester trabaja 28 horas en total, por lo tanto, multiplicamos 4 a ambos lados de la ecuación para conservar la igualdad
[tex]4\times (2 + x) = horas\ en \ cuatro \ dias[/tex]
[tex]8+4x= 28[/tex]
Ahora se despeja [tex]x[/tex] de la ecuación anterior
[tex]4x=28-8=20\\x=\frac{20}{4} =5[/tex]
De tal manera que Esther en cada turno nocturno trabaja 5 horas
Whats the answer...?
The required solution is 0.02 to the given numerical expression [1/(9-2)]².
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings.
For example 4/2 = 2
The numerical expression is given in the question as:
⇒ [1/(9-2)]²
We have to determine the solution to the given expression
As per the question,
⇒[1/(9-2)]²
⇒[1/7]²
⇒1/49
Apply the division operation to get the solution
⇒0.02040
Rounded to the nearest hundredth
⇒0.02
Thus, the required solution is 0.02 to the given numerical expression.
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after 2 minutes a submarine had descended -390 feet. after 9 minutes the submarine had descended to -600 feet. assuming a linear function write an equation in the form d(t)=mt+b that shows the depth d(t) after t minutes.
The expression of time taken for the submarine to descend in
d(t)= mt + b is
d(t) = -30t - 330How to write the expressiondata gotten from the question
after 2 minutes a submarine had descended -390 feet
-390 = 2m + b
after 9 minutes the submarine had descended to -600 feet
-600 = 9m + b
The data from the question gives two linear equations with two unknown
-600 = 9m + b
-390 = 2m + b
solving the equations gives
m = -30
b = -330
the equation is then written as
d(t) = -30t - 330
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BASSICALY FRE POINTS!!!
Given the equation k over 12.6 equals 7.4, determine the value of k.
93.24
20.0
5.2
1.70
The value of k in the equation k over 12.6 equals 7.4 is A. 93.24
What is temperature?Temperature simply means the degree of hotness and coldness in a body.
Based on the information given, the equation is expressed as k over 12.6 equals 7.4. This will be:
k / 12.6 = 7.4
Cross multiply
k = 12.6 × 7.4
k = 93.24
Therefore, the correct option is A.
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Determine which set of side measurements could be used to form a triangle.
O 13, 19, 7
O 25, 12, 13
18, 2, 24
03, 1,5
Answer:
three
Step-by-step explanation:
o 13, 19, 7
Need help fast thank you
Answer: 1. 12.5 miles per hour 2. 0.36 hours
Step-by-step explanation:
Please refer to this explanation:
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= ax^2+bx+c and how they can be identified from the equation. How can this
form be used to find the other features of the graph?
Please help pretty please?
The main features that can be easily seen then a quadratic function is given are parabola, axis of symmetry, a maximum OR minimum value, and an y-intercept of the graph.
A quadratic function is in the form ax²+bx+c=y where a, b and c are real integers.
How to find the features of a quadratic equation?
Every quadratic equation has the following features:
parabola: a parabola is a curve that is mirror-symmetrical and is approximately U-shaped of which every quadratic function has it.axis of symmetry: this is a straight line that makes the shape of the object symmetrical.y-intercept: The y-intercept formula is used to find the y-intercept of the quadratic function.When the quadratic function is graphed, it will enable us to find the other features of the function when these are identified.
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1. Arrange the scores in order from least to greatest
2. Arrange the absolute values of the scores in order from least to greatest
Answer:
From least to greatest
= -7, -3, 2, 5
Absolute values from least to greatest
= 2, 3, 5, 7
(Absolute value is the distance of a number from 0 in the number line regardless of the direction, so I think this is the answer)
Solve the system of equations by graphing.
x-y=5
x+y=11
Answer: (8,3)
Step-by-step explanation:
See the picture attached
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The options given in the question are wrong. The correct answer should be 25
The value of x is 25
(x-7)2 = 36
x-7 = 36/2
x-7 = 18
x = 18+7
x = 25
We can solve the linear equation in one variable by moving the variables to one side of the equation, and the numeric part on the other side of the equation. For example, x - 1 = 5 - 2x can be solved by moving the numeric parts on the right-hand side of the equation which is summed up to be 6, while keeping the variables on the left side which sums up to be 3x. Hence, we get x + 2x = 5 + 1. Thus, 3x = 6. This gives x = 2.
Similarly, we got the value of x which is 25.
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6.04 x 10 to the power of negative 3 as an standard form
Answer:
The correct answer is 0.00604
Step-by-step explanation:
Tip: Think of how a number line is displayed: negative numbers are on the left side of the mid-point, zero in most cases, and positives numbers are to the right of the mid-point.
Since the exponent is a negative number, you know that you need to move the decimal point to the left the same number of places as the exponent. In this problem, the exponent is –3, meaning that you need to move the decimal point 3 places to the left.
*Remember to fill in any gaps with a zero after moving the decimal point.* Your answer should look like this: 6.04 in standard form is 0.00604
Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)