1) Given this equality,
15x = 75 Divide both sides by 15
x=5
2) Then we can write that since x = 5 and 15x = 75 we have here is the Division Property of Equality.
Because in this case, we divided both sides by 15, which is different from zero to find equivalent equality.
3) So
In a factory, the production hours t and output y are having linear relationship. When the
factory operates for 5 hours per day, it may have the number of outputs of 2000 units and 3500
units for 8 hours of operation.
(a) Model an equation that gives the outputs, y, in terms of operation hours, t, per day.
(b) If the factory wants to have 4500 units of production per day, how long it should operate?
(c) Draw the graph in excel of the production against operation hours t up to first 20 hours.
Considering the linear relationship between the variables, we have that:
a) The function is: y = 500t - 500.
b) The factory should operate for 10 hours to have a production of 4500 units.
c) The graph for the first 20 hours of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the given linear relationship, we have two points, as follows:
(5,2000) and (8,3500).
The slope is given by change in y divided by change in x, hence:
m = 1500/3 = 500.
Then:
y = 500t + b.
When t = 5, y = 2000, hence we solve for the intercept as follows:
2000 = 500(5) + b
b = -500.
Then the function is:
y = 500t - 500.
For 4500 units, the time is found as follows:
4500 = 500t - 500
500t = 5000.
t = 5000/500
t = 10 hours.
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The table represents a quadratic function. Write an equation of the function in
standard form.
X- -3,-2,-1,0
An equation of the function in standard form for the given table of values is equal to -2x² - 7x - 6 = 0.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by;
y = f(x) = ax² + bx + c = 0
In order to write an equation of the quadratic function in standard form, we would formulate a system of equations from the data provided in the table above as follows:
-6 = a(-3)² + b(-3) + c ⇒ -6 = 9a - 3b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
-2 = a(-1)² + b(-1) + c ⇒ -2 = a - b + c .......equation 3.
From equation. 2, we derive:
c = -4a + 2b .....equation 4.
Substituting equation 4 into equation 1 and 3, we derive the following equations:
-2 = a - b - 4a + 2b ⇒ -2 = -3a + b
-6 = 9a - 3b - 4a + 2b ⇒ -6 = 5a - b
By using the elimination method, the value of a is given by:
[-2 + (-6) = (-3a + 5a) + (b + (-b)]
-2 - 6 = -3a + 5a + b - b
-8 = 2a
a = -4
Next, we would determine the value of b as follows:
-2 = -3a + b
b = -2 + 3a
b = -2 + 3(-4)
b = -2 - 12
b = -14
For the value of c, we have:
c = -4a + 2b
c = -4(-4) + 2(-14)
c = 16 - 28
c = -12.
Substituting the respective values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-4x² - 14x - 12 = 0
Dividing all through by 2, we have the following quadratic function:
-2x² - 7x - 6 = 0
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Complete Question:
The table represents a quadratic function. Write an equation of the function in standard form.
X -3, -2, -1, 0
f(x)-6, 0, -2, 0
PLS ANSWER THIS MATH PROBLEM!!
For the linear function y = 2/3x + 1, we have that:
a) The slope is of 2/3 and the intercept is of 1.
b) The y-intercept is marked at y = 1 on the y-axis.
c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.
d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.
What is the definition of a linear function in slope-intercept format?A linear function, in slope-intercept format, is modeled as follows:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the function is:
y = 2/3x + 1.
Then, form item a, we have that:
The slope is of m = 2/3.The intercept is of b = 1.For item b, the y-intercept of b = 1 means that the function crosses the y-axis at b = 1.
For item c, we have to consider that the slope is of 2/3, meaning that when y increases by 2, x increases by 3. Point (0,1) is on the graph of the function, hence point (3,3) will also be, as x increases by 3 from 0 to 3 and y increases by 2 from 1 to 3.
Considering the discussion above, the graph of the function is given at the end of the answer, with the intercept and point (3,3) labeled.
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Find the slope and the y-intercept of the graph of the linear equation 3x−4y=−16.
Answer:
the slope is 3/4
the y-intercept is 4
Step-by-step explanation:
You want the slope and y-intercept of the line defined by the equation 3x -4y = -16.
Slope-intercept formThe values of interest can be found easily from the slope-intercept form of the equation of the line. Solving for y puts the equation in that form.
3x -4y = -16 . . . . . . given
-4y = -3x -16 . . . . . subtract 3x
y = 3/4x +4 . . . . . . divide by -4
Compare this to the slope-intercept form equation:
y = mx + b . . . . . . . line with slope m and y-intercept b
We see that ...
m = 3/4, b = 4
The slope is 3/4
The y-intercept is 4
A restaurant decides to include a 16% tip automatically in all customers’ bills. The restaurant will apply the 16% tip after applying a 5% sales tax. If the total cost of a meal is c dollars, write two different expressions that represent the total bill, including both tax and tip.
Two different expressions that represent the total bill, including both tax and tip for the meal sold by the restaurant, are:
c dollars + 5% of c dollars + 16% of c dollarsc dollars + 21% of c dollarsWhat expressions can we get for the total amount to be paid by the customer?To arrive at the amount to be paid by the customer, we first have to get the original amount that they should pay for the meal. Next, they are meant to apply the 16% tip for the total meal and this is gotten by calculating 16% of the total meal.
Next, we ought to get 5% of the sales tax which will also be applied to the total bill. When all of these are summed up, we will arrive at the total amount to be paid by the customer. Another way will be, to sum up, all of the percentages and apply them to the total bill.
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find sin(c). round to the nearest tenth if necessary a. .92b. .42c. .38d. 1.08
We have following:
The sine of the angle is given by the quotient of the opposite side and the hypotenuse
[tex]\sin C=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]replacing:
[tex]\begin{gathered} \sin C=\frac{5}{13} \\ \sin C=0.38 \end{gathered}[/tex]The answer is the option C. 0.38
Expand and simplify 3(2x + 1) + 2(x + 4) =
Answer:
3(2x+1)+2(x+4)
3x2x and 3x1
6x+3+2(x+4)
2xx and 2x4
6x+3+2x+8
and the like terms
6x+2x and 3+8
8x+11
Step-by-step explanation:
Answer:
8x +11
Step-by-step explanation:
3(2x+1)+2(x+4)
Use the distributive property to multiply 3 by 2x+1.
6x+3+2(x+4)
Use the distributive property to multiply 2 by x+4.
6x+3+2x+8
Combine 6x and 2x to get 8x.
8x+3+8
Add 3 and 8 to get 11.
8x+11
A straight road named Planet Drive will connect the diner and the community garden.What is the equation of the line that represents Planet Drive? Show your work
As the line intersected the y-axis at x = 4, the equation of the line which represents planet Drive to the community garden is x = 4.
How is line equation represented?The shortest distance that separates two points is represented by a line. A line can be horizontal, slanted, or straight. A equation of a line in slope-intecept form has been expressed as:
y = mx + b
where,
m is called the slope
b is the y-intercept
From the graph shown, you recognize that the planet drive line is a horizontal as well as the general equation of the a horizontal line is represented as x = a where;
'a' is indeed the x-intercept of a line, which is the point at which the line intersects the y-axis.
Because, the line intersected the y-axis at x = 4, the equation of the line which reflects planet Drive to community garden is x = 4.
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Help me please it’s due today please help me please help me please help me please help me please help me?
The results of the logical expressions are
¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.
These results are generally classified as boolean values
How to solve the logical expressions?We start by solving the first expression
Logic expression (3)
¬ q v p
The above expression uses the or operator
The rule of the or operator is that:
It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to true
Logic expression (4)
¬ p ∧ ¬ q
The above expression uses the and operator
The rule of the and operator is that:
It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false
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Answer:The results of the logical expressions are¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.These results are generally classified as boolean valuesHow to solve the logical expressions?We start by solving the first expressionLogic expression (3)¬ q v pThe above expression uses the or operatorThe rule of the or operator is that:It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to trueLogic expression (4)¬ p ∧ ¬ qThe above expression uses the and operatorThe rule of the and operator is that:It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false
Step-by-step explanation:
Compare the sides and angles by filling in the blank with a < or > symbol.
Q: 23The side opposite to larger angles is always larger than angle oppostie to smaller side.
a sideangle the
Since side opposite to angle 68 is AB and side opposite to angle 65 is CD. The angle of measure 68 is more than angle 65. So,of measure
[tex]AB>CD[/tex]Show your work, due today
1. x = 8 -8 When the number that is the sum or answer, the number that is in the lines is usually the same but is the opposite, os if it is positive, then it is negative.
2. x = 7, -7
3. A = 6, -10 8 - 2 = 6 8 + 2 = 10 Switch it up, put the negative sign with the 10.
This is all that I can do right now I hope this helped I will try to answer more later.
See question and photo please: The
Answer: 50.24ft²
Step-by-step explanation:
Total area of square = 8 * 8 = 64 ft²
Diameter of circle = 8 ft
The formula of area of circle = π r²
(4 = r)
(r² = 16)
3.14 * 16
50.24ft²
what is the value of (-20.16)+( -3.9)?
A. 16.26
B. - 24.06
C. 24.06
D. -16.26
Answer:
24.06................
Answer:
B
Step-by-step explanation:
[tex]( - 20.16) + ( - 3.9) \\ [/tex]
=
[tex] - 20.16 - 3.9[/tex]
=
[tex] \frac{ - 1203}{50} or - 24.06[/tex]
I need to learn how to do equations with variable on both side
I will give an example on an equation with variables on both sides, then explain.
Example : 20-x = 5x - 4
→the first step in solving an equation with a variable on both sides is to get the variable on one side. This is done by reversing the addition or subtraction of one of the terms with the variable.
20-x =
Each of Sean’s comedy routines lasts for 35 minutes. He tells an average of 3 jokes every minute. It takes _ comedy routines to hear 360 jokes
It takes four (4) comedy routines to hear 360 jokes
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
1 minute = 3 jokes
X minutes = 360 jokes
Cross-multiplying, we have:
3X = 360
X = 360/3
X = 120 minutes
Now, we can determine the number of comedy routines required for 360 jokes as follows:
Number of comedy routines = 120/35
Number of comedy routines = 3.42 ≈ 4 comedy routines.
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Aisha drew a square that had a side length of 2 inches. What is the perimeter of 's Aisha square ?
Divide.
−10 ÷ −2
Drag and drop the correct number into the box to complete the sentence.
mu 3.) Add six to twelve, then divide the sum by four. Divide the quotient by negative nine and then
D multiply by twenty-four. What is the result?
com
eneral
eas to
pecific
onclusi
ns.
answer:
4.) Estimate the total cost of groceries if the prices are $6.47, $14.72, $7.99, $9.40, and $2.79.
Round each to the nearest dollar and add.
1) Using order of operations, the solution to the given expression is; 12
2) The estimated cost of groceries if the prices are estimated to the nearest dollar is; $42
How to use order of operations?In mathematics , the acronym for the right order of operations is PEMDAS which denotes;
P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction.
3) From the given statement, we are to add 6 to 12, then divide the sum by 4. Thereafter, we divide the quotient by negative nine and then multiply by twenty-four. This is expressed as;
[(6 + 12)/4] = 18/4 = 9/2
Then divide by -9 to get;
(9/2) ÷ 9 = 1/2
Then we multiply by 24 to get;
1/2 * 24 = 12
4) Let us first estimate each cost to the nearest dollar to get;
$6.47 ≈ $6
$14.72 ≈ $15
$7.99 ≈ $8
$9.40 ≈ $9
$2.79 ≈ $3
Total estimated cost = 6 + 15 + 8 + 9 + 3 = $42
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I'm not sure what the correct answers is, heh..please help me
Given expression is
[tex]\sqrt[4]{2}=2^{\frac{1}{4}}[/tex]Among the given options the simplication that applies the power rule is
[tex](2^{\frac{1}{4}})^4=2^{\frac{1}{4}}.2^{\frac{1}{4}}.2^{\frac{1}{4}}.2^{\frac{1}{4}}[/tex]This can be simplified as
[tex]2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}=2^{\frac{4}{4}}=2[/tex]Hence the corresponding simplification is D.
−67b+6≤9b+43minus, 67, b, plus, 6, is less than or equal to, 9, b, plus, 43
The variable "b" is greater than or equal to −37/76.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.The inequality to be solved is given below :−67b+6 ≤ 9b+43Move the like terms to one side of the inequality.6−43 ≤ 9b+67bSimplify and merge the terms.−37 ≤ 76bSeparate the constant and the variable in the inequality.−37/76 ≤ bOur final result is obtained.The variable "b" is greater than or equal to −37/76.To learn more about inequalities, visit :
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Answer please number 15 only
Answer:
a) -2/9
Step-by-step explanation:
2/3 - 5/6, you would need to start by making the denominators the same, so 2/3 would become 4/6. 4/6-5/6 = -1/6.
-1/6 ÷ 3/4, use the keep change flip rule
-1/6 × 4/3 then multiply directly across:
-1×4=-4
6×3=18
-4/18 reduces to -2/9
please help this is due today
Carlos sells coupon booklets for $5.50 apiece. He makes $60.50. Monica sells the same books for $4.75 each and makes $57. Who sells more booklets? How many more?
Answer:
Monica sells one more book (12) than Carlos (11).
Step-by-step explanation:
Carlos: $60.50/$5.50 = 11
Monica: $57.00/$4.75 = 12
Monica sells one book more than Carlos.
I added a picture of my question need answer quickly please
The statements that are true regarding the temperature include:
1. At noon, the temperature is - 9 1/2°F.
2. The temperature at 5pm is - 15 3/4°F.
3. The change in temperature from noon to 5pm is - 6 1/4°F.
How to calculate the temperature?From the information, the temperature at 6A.M is -14°D and the temperature increases at an average of 3/4°F each hour until noon. Then it drops at 1 1/4°F until 5P.M.
The temperature at noon will be:
= -14 + (3/4 × 6)
= -14 + 4.5
= -9.5°F
The temperature at 5pm will be:
= -9.5 - (1 1/4 × 5)
= -9.5 - 6.25
= -15.75
The total change in temperature will be:
= Ending temperature - Starting temperature
= -15.75°F - (-14°F)
= 1.75°F
The temperature change from noon to 5 pm will be:
= -15.75 - (-9.5)
= -6.25 = 6 1/4°F
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Two cars start moving from the same point. One travels south at 16 mi/h and the other travels west at 12 mi/h. At what rate (in mi/h) is the distance between the cars increasing three hours later?
Answer:
20 mi/h
Step-by-step explanation:
You want the speed of separation after 3 hours between two cars that started from the same point. One is moving at 16 mi/h south, the other is moving at 12 mi/h west.
Velocity vectorsSince both cars started from the same point, the speed of separation is the magnitude of the difference between the respective velocity vectors. A graphical representation of the velocity vectors shows them to be the legs of a right triangle. Their difference is the length of the hypotenuse, which can be found using the Pythagorean theorem.
s = √(16² +12²) = √(256 +144) = √400
s = 20
The speed of separation is a constant 20 mi/h.
__
Additional comment
If the cars did not start at the same point, then the speed of separation would be changing with time. It could be found using the derivative of the distance between the cars, or by considering the car speeds in the direction each car is from the other at the time of interest.
We note that the problem here makes use of a 3-4-5 right triangle, with a multiplier of 4 mph.
In a bag there are 2 red buttons, 3 green buttons, and 4 purple buttons. A student writes the ratio for the number of purple buttons to green buttons as 3:4. Is this student correct? Explain why or why not.
Answer:
No
Step-by-step explanation:
No because it says purple to green buttons and the student put green to purple so the answer would be 4:3 not 3:4
Write an equation of a line that passes through (-1,3)and (1,4)
SOLUTION
We want to write an equation of a line that passes through (-1,3) and (1,4)
First, let us find the slope m of the line for the points (-1,3) and (1,4)
We have
[tex]\begin{gathered} m=\frac{4-3}{1-(-1)} \\ m=\frac{1}{1+1} \\ m=\frac{1}{2} \end{gathered}[/tex]Now, equation of a line in point slope form becomes
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(-1,3) \end{gathered}[/tex]plugging in the values, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=\frac{1}{2}(x-(-1) \\ y-3=\frac{1}{2}(x+1) \\ y-3=\frac{1}{2}x+\frac{1}{2} \\ y=\frac{1}{2}x+\frac{1}{2}+3 \\ y=\frac{1}{2}x+\frac{7}{2} \end{gathered}[/tex]Hence the answer becomes
[tex]y=\frac{1}{2}x+\frac{7}{2}[/tex]Combine like terms, if possible. Write the result with descending powers.
6x³ + 5x³+4x5
Select the correct choice below and, fill in the answer box to complete your choice.
OA. The polynomial cannot be simplified. The polynomial written in descending powers is__
OB. The polynomial can be simplified. 6x³ + 5x³+4x5=__
B. The polynomial can be simplified. 6[tex]x[/tex]³ + 5[tex]x[/tex]³ + 4[tex]x[/tex] + 5 = 11[tex]x^3[/tex] + 4[tex]x[/tex] + 5
Can someone please help me with this? Geometry by the way
Answer:
Step 1: DAB
Step 2: rotated triangle 180° using AC as center of rotation
Step 3: EAC
Step 4: now all 3 angles…
Step 5: a + b + c = 180°
Step-by-step explanation:
pls help i will give brainliest etc
Answer:
Quotient = 58.5
Step-by-step explanation:
Long division is a method used to divide large numbers by breaking the division down into multiple steps.
Parts of long division:
The dividend is the number that is divided by the divisor.The divisor is the number that divides the dividend. The quotient is the result obtained by the division.The remainder is the number left over.The divisor is placed to the left of the parenthesis.
The dividend is placed to the right of the parenthesis.
The quotient is placed above the dividend and separated from it by a bar.
To finish the given long division, subtract 64 from 68:
⇒ 68 - 64 = 4
Now divide the result by the divisor:
⇒ 4 ÷ 8 = 0.5
Finally, add 0.5 to 58 to give the final quotient:
⇒ 58 + 0.5 = 58.5
[tex]\large \begin{array}{r}58.5\\8{\overline{\smash{\big)}\,468\phantom{))}}}\\{-~\phantom{(}\underline{40\phantom{))..}}\\68\phantom{))}\\-~\phantom{()}\underline{\phantom{)}64\phantom{))}}\\4\phantom{))}\\-~\phantom{()}\underline{\phantom{)}\phantom{)}4\phantom{))}}\\0 \phantom{))}\\\end{array}[/tex]
Therefore, from inspection of the given long division:
The dividend is 468.The divisor is 8.The quotient is 58.5.What is the value of y? (20 points)
{question in image}
Answer:
Step-by-step explanation:
I will use cross multiplication to answer this question.
[tex]4(2y)=3y+10\\8y=3y+10\\8y-3y=10\\5y=10\\\frac{5y}{5} =\frac{10}{5} \\y=2[/tex]
I hope this helps!!!!!!!