SOLUTION
We are told that the length of the rectangle is 17 inches less than 7 times its width.
Now, let the letter L represent the length and the letter w represent the width of the rectangle.
This statement can be represented algebraically as
[tex]L=7w-17[/tex]So, Area =
[tex]\text{Area = L x w}[/tex]We are also told the Area A of the rectangle = 2204. Now
[tex]\begin{gathered} 2204=L\times w \\ \\ 2204=(7w-17)\times w \end{gathered}[/tex]We have to find the width, then we find the length L
[tex]\begin{gathered} 2204=(7w-17)\times w \\ 2204=7w^2-17w \\ 7w^2-17w-2204=0 \\ \\ \text{Solving the quadratic equation } \\ \\ w=19\text{ or w = -16.57} \end{gathered}[/tex]Since the width cannot be negative, w = 19 inches
The length becomes
[tex]\begin{gathered} L=7w-17 \\ L=7\times19-17 \\ L=133-17 \\ L=116\text{ inches } \end{gathered}[/tex]is this data symmetric and mound shaped? explain25 25 26 26 27 27 28 28 29 29
First we have to visualize the points in a graph:
as we can see, the data is not symmetrical with respect the mean of the data, therefore, this data is not symmetric nor mound shaped
A four-digit number is to be made using the digits 1, 3, 5, and 8. How many numbers can be made if repeated digits are allowed?
We want to make a four digit number using numbers 1, 3, 5 and 8 and allowing repetition.
Therefore, there is four possibilities each for the units, tens houndreds and thousands.
Then, the total number of possibilities is:
[tex]4\cdot4\cdot4\cdot4=4^4=256[/tex]Over the course of 5 hours, the temperature dropped 10°C.
The temperature dropped the same number of degrees each hour.
What operation represents
the change in temperature
each hour?
Using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operations which represent this is 10/5 = 2°C.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, the operation that represents the change in temperature:
Time taken is 5 hours.
The temperature drop is 10°C.
The same amount of temperature in each hour.
Then, the operation will be:
10/5 = 2°C
Therefore, using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operation which represents this is 10/5 = 2°C.
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The total cost to develop camera pictures is proportional to the number of pictures being made. Maria paid 5.50 for 50 pics made. What number represents the constant in this proportional relationship.
Answer: 0.11
Step-by-step explanation:
Suppose y represents the cost, x represents the number of pictures, then y=kx {positive proportional function}
when x=50, y=5.5
5.5=50k
k=5.5/50
k=55/500
k=0.11
A line has a slope of 2 and passes through the point (-2,8). What is the equation of theline?
The general equation of line passes through the point (x_1,y_1) and has slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,8) and has slope of 2.
[tex]\begin{gathered} y-8=2(x-(-2)) \\ y=2\cdot x+2\cdot2+8 \\ y=2x+12 \end{gathered}[/tex]So answer is y = 2x + 12.
X =
(3x - 18)°
(7x-54)°
Answer:
[tex]x=\frac{289\pm \sqrt{1873}}{42}[/tex]
Optimization
Solve the following optimization problem.
Hassan is baking cookies for his school bake sale fundraiser. He decides on making oatmeal chocolate chip
(m) and peanut butter cookies (p). He is planning on selling the peanut butter cookies for 20 cents each,
and the oatmeal chocolate chip for 25 cents each. He is limited to 700 cookies total by his ingredients, and
he doesn't want to make more than 400 of either cookie. He must make at least half as many peanut butter
cookies as oatmeal chocolate chip cookies. How many of each kind of cookie should he make to get the
most money?
Answer:
between $10 and $20 for undecorated cookies; or between $12 and $25 for cookies
Step-by-step explanation:
Translate solve and check:
"Twice a number, increased by three times the difference of the number and 3 is 11"
Answer:
number is 4
Step-by-step explanation:
let n be the number then twice the number is 2n and the difference of the number and 3 is n - 3 , so
2n + 3(n - 3) = 11 ← distribute parenthesis and simplify left side
2n + 3n - 9 = 11
5n - 9 = 11 ( add 9 to both sides )
5n = 20 ( divide both sides by 5 )
n = 4
As a check
twice the number is 2 × 4 = 8
increased by 3 times the difference of n and 3 is
8 + 3(4 - 3) = 8 + 3(1) = 8 + 3 = 11 ← Correct
Factor completely, then place the factors in the proper location on the grid.
b2 - 7b + 12
Answer:
(b - 4)(b - 3)
Step-by-step explanation:
b² - 7b + 12
consider the factors of the constant term (+ 12) which sum to give the coefficient of the b- term (- 7)
the factors are - 4 and - 3 , since
- 4 × - 3 = + 12 and - 4 - 3 = - 7 , then
b² - 7b + 12 = (b - 4)(b - 3)
18. Maddie has no more than $40 to spend at the store on new paint and paintbrushes for her art project. Paintbrushes cost $3 each and paint colors are sold for $6 each. If Maddie buys 4 paintbrushes, how many new paint colors can she afford?
Explanation:
Let 'x' be the number of paint colors Maddie can buy.
She buys 4 paintbrushes that cost $3 each. This means that she already spent 4x3=$12 in paintbrushes. This amount plus the amount of money she'll spend in the paint colors must be at most $40:
[tex]12+6x\le40[/tex]Solving for x:
[tex]\begin{gathered} 12-12+6x\le40-12 \\ 6x\le28 \\ x\le\frac{28}{6} \\ x\le4.\bar{6} \end{gathered}[/tex]Since x must be a whole number (is the amount of paint colors) and it has to be less than 4.666... then Maddie can afford 4 paint colors
Answer:
Maddie can afford 4 paint colors
Solve for x. x+15.09=−2.57x =
To solve the presented question for X, every change we make in one of the sides of the equality, we must do the same to the other. This way, the equality remains. In the present case, we will subtract 15.09 in both sides, as it follows:
[tex]\begin{gathered} x+15.09=-2.57 \\ x+15.09-15.09=-2.57-15.09 \\ x=-17.66 \end{gathered}[/tex]how long will it take to get to 280 kilo. at a rate of 70 kilo./per hour
Shane bought 36 gallons of gas this week this amount is 6 gallons more than twice the amount of gas he bought last week how many gallons of gas in Shane by last week
so, she bought 15 gallons of gas last week
Explanation
Step 1
Let
36 gallons this week
x= number of gallons of gas Shane bought las week
this amount is 6 gallons more than twice the amount of gas he bought last week , then
[tex]36=2x+6[/tex]Step 2
solve for x
[tex]\begin{gathered} 36=2x+6 \\ \text{subtract 6 in both sides} \\ 36-6=2x+6-6 \\ 30=2x \\ \text{divide each side by 2} \\ \frac{30}{2}=\frac{2x}{2} \\ x=15 \end{gathered}[/tex]so, she bought 15 gallons of gas last week
A local hamburger shop sold a combined total of 814 hamburgers and cheeseburgers on Wednesday. There were 64 more cheeseburgers sold than hamburgers.
How many hamburgers were sold on Wednesday?
Answer:
814 + 64 = 878
Step-by-step explanation:
just take the # from the previous day and add the 64.
When it says more, add when it says less, subtract.
Maya is asked to solve the equation 2(3x + 6) - 3(x - 10). The table shows her steps.Step 1: 6x + 12 = 3(x - 10)Step 2: 6x + 12 = 3x + 30Step 3: 3x + 12 = 30Step 4:3x = 18Step 5: x= 6Where did Maya make a mistake in solving the equation, and why?A. Maya made a mistake between the Given and Step 1 because she did not correctly distribute 2 to (3x + 6).B. Maya made a mistake between Step 1 and Step 2 because she did not correctly distribute 3 to (x10).C. Maya made a mistake between Step 2 and Step 3 because she did not correctly subtract 3x from 6x.D. Maya made a mistake between Step 3 and Step 4 because she did not correctly subtract 12 from 30.
Let's solve the following equation to see where Maya made a mistake:
2 (3x + 6) = 3 (x - 10)
Step 1: Solving parenthesis
6x + 12 = 3x - 30
Step 2: Like terms
6x - 3x = -30 - 12
Step 3: Complete the subtractions at both sides
3x = -42
Step 4: Dividing by 3 at both sides
3x/3 = -42/3
x = -14
Maya didn't multiply correctly 3 * - 10
Yes, Javionery, option B is the correct one.
Express the distance,d, from a point on the graph x+y=2 to the point (6,8) as a function of x
Answer:
[tex]d=\sqrt[]{2(x^2+36^{})}[/tex]Explanation:
Given the equation of the line as;
[tex]x+y=2[/tex]We can express y in terms of x by subtracting x from both sides of the equation;
[tex]y=-x+2[/tex]Let the point on the line be P(x, y)
We'll use the below distance formula to determine the distance between point P(x, y) to the given point (6, 8) as seen below;
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(6-x)^2+(8-y)^2} \\ d=\sqrt[]{(36-12x+x^2)+\lbrack8-(-x+2)\rbrack^2} \\ d=\sqrt[]{(36-12x+x^2)+(6+x)^2} \end{gathered}[/tex][tex]\begin{gathered} d=\sqrt[]{(36-12x+x^2)+(36+12x+x^2)} \\ d=\sqrt[]{72+2x^2} \\ d=\sqrt[]{2(x^2+36^{})} \end{gathered}[/tex]What is an equation of the line that passes through the point (4,2)(4,2) and is perpendicular to the line 4x+3y=214x+3y=21?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]4x+3y=21\implies 3y=-4x+21\implies y=\cfrac{-4x+21}{3} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{4}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-4}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{-4}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-4}\implies \cfrac{3}{4}}}[/tex]
so we're really looking for the equation of a line whose slope is 3/4 and it passes through (4 , 2)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{3}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-2=\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=\cfrac{3}{4}x-1 \end{array}}[/tex]
18. Without doing any calculations, do you think Cylinder 1 and Cylinder 2 will have the same volume? Explain your reasoning. Cylinder 1 4 cm om Cylinder 2 on Fill in each box to complete the following statements. 4 cm To the nearest tenth, the volume of Cylinder 1 is To the nearest tenth, the volume of Cylinder 2 is
Without doing any calculations, do you think Cylinder 1 and Cylinder 2 will have the same volume?
No, because the radius are different. In the first cylinder the radius is 4cm and 7cm in the second one.
The volume V of a cylinder is given by
[tex]V=\pi r^2h[/tex]where Pi is 3.1416, r is the radius and h is the height.
Then, the volume of cylinder 1 is
[tex]V_1=(3.1416)(4^2)(7)cm^3[/tex]which gives
[tex]V_1=351.9cm^3[/tex]Now, the volume of cylinder 2 is
[tex]V_2=(3.1416)(7^2)(4)[/tex]which gives
[tex]V_1=615.8cm^3[/tex]Therefore, the answer are
[tex]\begin{gathered} \text{cylinder 1, }V_1=351.9cm^3 \\ \text{cylinder 2, }V_2=615.8cm^3 \end{gathered}[/tex]What is the vertex of the graph of p(x) = x2 +6 ?
The graph p(x) = x² + 6 is a parabola. The equation can also be written as y = x² + 6.
A parabola follows the standard equation y = a (x - h)² + k where the vertex is (h,k).
From our equation y = x² + 6, we can convert this into a standard form which is y = 1 (x - 0)² + 6. Please take note that this standard form is just equal to the given equation.
From this converted standard form y = 1 (x - 0)² + 6, we can see that our h = 0, and our k = 6, therefore, our vertex is found at point (0,6).
What is the solution to the system of equations graphed below?
Answer:
(0,-4)
Step-by-step explanation:
write the coordinates of the point where the two lines intercept themselves
Answer:
A. (0,-4)
x is 0 and y is -4
is the expression 15y a coefficient or a constant
ASAP
Answer: The expression is not a coefficient, so it is a constant.
Step-by-step explanation:
Answer:
Constants are the terms in an expression that includes only numbers, the value of which does not change. Coefficient of a variable is the number written along with the variable in the term. So the expression 15y is a coefficient.
You are now on your way to college and need to make some money decisions. Your parents are going to help pay for some of your necessities but they want to know what you need. You are budgeting your money for textbooks and trying to decide how many hardback and paperback textbooks you can afford. Hardback books cost $45 and paperback books cost $20. You have $440 dollars to spend on textbooks. You know you need to buy 12 textbooks for the school year. Your task is to find out how many hardback and paperback textbooks you can buy.
You can buy 8 hardbacks and 4 paperback textbooks.
What is a Simultaneous Equation?This refers to two or more algebraic equations that have common variables and are resolved at the same time.
From the question:
Hardback books cost, H =$45
paperback books cost, P = $20.
The total amount to spend on textbooks = $440.
The total amount of textbooks needed for the school year is Hardback books+ paperback books= 12.
Solving Simultaneously we have:
H + P = 12 ..............(i)
45H + 20P = 440...........(ii)
Equation (i) * -20
-20H - 20P = -240............(iii)
Add Equation (iii) and Equation (ii)
45H + 20P = 440...........(ii)
+ -20H - 20P = -240............(iii)
We have:
25H = 200
H =200/25
H = 8
Substitute H = 8 into Equation (ii)
45(8) + 20P = 440...........(ii)
360 + 20P = 440
collecting like terms:
20P =440 - 360
20P = 80
Divide both sides by the coefficient of P
20P/20 =80/20
P= 4
Hence, You can buy 8 hardbacks and 4 paperback textbooks.
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Drag the coordinates of the figure DEFG after the figure is reflected over the y-axis
R y= x(x, y) —> (y, x) The rule for a reflection over the y -axis is (x,y)→(−x,y) After reflection we get DGFE.
How can coordinates be determined after reflection?When a point is reflected across the line y = x, the x and y coordinates move.Similarly, when a point is mirrored across the line y = -x, the x and y coordinates are negated. As a result, the reflection of the point (x, y) across the line y = x is (y, x)Students investigate reflections over the x- and y-axes in this exercise, with a focus on the relationship between the coordinates of the pre-image and the image. As an extension, students can try to reflect a pre-image across the line y = x.A translation would be a transformation that moves all of the points in a figure by the same amount in the same direction. For example, this transformation shifts the parallelogram 5 units to the right and 3 units up. It is written as ( x , y ) → ( x + 5 , y + 3 )To graph is to create a diagram that depicts a relationship between two or more things. A graph can be made by drawing a series of bars on graph paper. To represent or put in the form of a graph.To learn more about translation, refer to:
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Simplify this expression:
4(1 − 2b) + 76 – 10.
Type the correct answer in the box.
Answer:
-8b + 70
Step-by-step explanation:
4(1 − 2b) + 76 – 10.
4 - 8b + 76 - 10
-8b + 70
I hope this helps!
Choose all the sets containing the number pi
natural numbers
whole numbers
integers
rational numbers
irrational numbers
real numbers
Answer:
π is an irrational number, so it is also a real number.
Translation of a PointWhat is the image point of (5,-5) after a translation right 2 units and up 3 units?Submit Answer
ANSWER
(7, -2)
EXPLANATION
We want to know the image point after a translation.
A translation is basically a shift in the position of the object.
The object point is (5, -5) and it translates 2 units right and 3 units up.
That means there is a shift +2 units on the x axis and +3 units on the y axis.
Therefore, the image point is:
(5 + 2, -5 + 3)
= (7, -2)
That is the image point.
what is the value of x?
Answer:
x=12
Step-by-step explanation:
5x-22=4x-10
5x-4x=-10+22
x=12
Giing that f(x)=3x^2-x-5, g(x)=-1 what is (f+g)(x)
SOLUTIONS
Giving that f(x)=3x^2-x-5, g(x)=-1 what is (f+g)(x)
[tex]\begin{gathered} f(x)=3x^2-x-5 \\ g(x)=-1 \end{gathered}[/tex][tex](f+g)(x)=f(x)+g(x)[/tex]Adding up the two function:
[tex]\begin{gathered} (3x^2-x-5)+-1 \\ simplify\text{ the bracket} \\ 3x^2-x-5-1 \\ 3x^2-x-6 \end{gathered}[/tex]Therefore the correct answer is:
[tex](f+g)(x)=3x^2-x-6[/tex]The scale on the map shows that 4 cm = 52 miles. How many miles apart are two towns if the measurement is 22 cm?
The distane between two towns can be determined as,
[tex]\begin{gathered} 4\text{ cm=52 miles} \\ 1\text{ cm=}\frac{52\text{ miles}}{4} \\ =13\text{ miles} \\ 22\text{ cm=22}\times13\text{ miles} \\ =286\text{ miles} \end{gathered}[/tex]Thus, the required distance is 286 miles.
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 0 ≤ x ≤ 1?
A) 1 B) 2 C) 4 D) 8
The average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1.
The average rate of change of the given quadratic function on the interval 0 ≤ x ≤1 is the slope of the secant line connecting the points (0,f(0)) and (1,f(1)).
That is the average rate of change is:
[tex]\frac{f(1)-f(0)}{1-0}[/tex]
From the graph, f(0) is 0 and f(1) is -1
We plug in these values to obtain
= [tex]\frac{(-1)-0}{1-0}[/tex]
This simplifies to;
= [tex]\frac{-1}{1}[/tex]
= -1
Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1.
What is quadratic function?A quadratic function is a polynomial function that has one or more variables and the largest exponent of the variable is two. Since the term of the highest degree of a quadratic function is the term of the second degree, it is also called a polynomial of degree 2. A quadratic function has at least one term that is a square term. This is an algebraic function.
The upper function of the square is of the form f(x) = x2 and connects points whose coordinates are of the form (number, number2). Transformations can be applied to this function, where it usually shows the form f(x) = a (x - h)2 k and can further be transformed to f(x) = ax2 bx c. We will explore each of them in detail in the following sections.
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