A rectangle has a height to width ratio of 3:4.5. Give two examples of dimensions for rectangles that could be scaled versions of this rectangle.
We have been given that a rectangle has a height to width ratio of 3:4.5.
Let h be height and w be width of rectangle.
We can set our given information in an equation as:
[tex]\frac{h}{w} =\frac{3}{4.5}[/tex]
[tex]h=\frac{3}{4.5} *w[/tex]
Now we will substitute h=1 in this equation.
[tex]1=\frac{3}{4.5} *w[/tex]
[tex]3w=4.5[/tex]
[tex]w=\frac{4.5}{3} =1.5[/tex]
We can see that width of rectangle is 1.5 times height of rectangle.
Our one set of dimensions of rectangle will be: height=1 and width=1.5.
We can get many set of dimensions for our rectangle by multiplying both height and width of rectangle by same number.
Multiplying by 5 we will get our dimensions as: height 5 and width 7.5.
Therefore, (1 and 1.5) and (5 and 7.5) dimensions for rectangle will be scaled version of our rectangle.
Two examples of dimesions for rectangles that could be scaled versions of this rectangle are (2,3) and (4,6).
Rectangle has a height and width.
[tex]\dfrac{height}{width}=\dfrac{3}{4.5}\\\\\dfrac{height}{width}=\dfrac{30}{45}\\\\\dfrac{height}{width}=\dfrac{2}{3}[/tex]
[tex]height = 2x\\width=3x[/tex]
Now let [tex]x=1[/tex]
So dimensions of height and width is [tex]2\times1 \; and\; 3\times1[/tex]
So it is [tex](2,3)[/tex]
Now let [tex]x=2[/tex]
So dimensions of height and width is [tex]2\times2 \; and\; 3\times2[/tex]
So it is [tex](4,6)[/tex]
Hence many dimesions of rectangles are possible.
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Which graph best represents the following equation?
y+7=lx+5l
Explain why.
Answer:
The graph at the bottom.
Step-by-step explanation:
We have been given equation of an absolute value function [tex]y+7=|x+5|[/tex]. We are asked to choose the graph of the given function.
We know that standard absolute function is in form [tex]y=|x-h|+k[/tex], where, (h,k) represents vertex of function.
Let us convert our given function in standard form.
[tex]y+7-7=|x+5|-7[/tex]
[tex]y=|x+5|-7[/tex]
[tex]y=|x-(-5)|-7[/tex]
Since the vertex of our given function would be at point [tex](-5,-7)[/tex], therefore, the graph at the bottom is the correct choice.
A contractor is excavating a ramp into a trench for a construction project. How much dirt will the crew have to remove? To answer, find the volume of the triangular prism in the figure shown.
A. 192 ft.3
B. 96 ft.3
C. 120 ft.3
D. 144 ft.3
Answer: Option B. 96 ft^3
Solution:
Volume of the prism: V=?
V= A * H
Height of the prism: H=4 ft
Area of the base (triangle) : A=b*h/2
Base of the triangle: b=6 ft
Height of the triangle: h=8 ft
A=(6 ft)*(8 ft)/2
A=48 ft^2/2
A=24 ft^2
V=A*H
V=(24 ft^2)*(4 ft)
V=96 ft^3
Rob found that the coefficient of determination between the length of essays submitted to a teacher x and the score the teacher gave the essay y was about 0.661. What can we conclude?
Answer:
The coefficient of determination is used to measure how well a model fits the real data, or how well it can replicate them. The closer to 1 the value of R ^ 2 the more accurate the model is.
In this case, that R ^ 2 = 0.661 means that the model fits moderately to the variable to be studied.
For a linear regression model, the coefficient of determination is the square of the correlation coefficient r of Pearson. So:
[tex]r =\sqrt{R^2}[/tex]
r = 0.813
This value of r close to 1 means that the length of the essays sent to a teacher (x) and the score that the teacher gave to the essay (and) are highly related.
There are twenty-four calories in a candy bar. Sally ate eight candy bars. How many calories are there in thirty -nine candy bars?
Answer:you dont even know how to write the sentence right so fail
Step-by-step explanation:
A snorkeler dives for a shell on a reef. After entering the water, the diver descends 11/3 feet in one second. Write an equation that models the diver's position with respect to time.
x^2 -12x +11
We have the x intercepts so we can create the equation (x-1)(x-11). Multiply it and you get your answer
Answer:
f(t)=t²-12t+11
Step-by-step explanation:
1) Having an attentive reading, we can see from the picture two coordinate points (1,0) and (11,0).
These points, has coordinates for x and y. Since those y-coordinates are zero, we have x-intercepts. Or the zeros of a function, in a quadratic function. Those intercepts minus x values equals zero. These x-intercepts we'll rename it as t, for time.
2) Plugging it in and writing it as groups:
f(t) = returns in feet
t= for time
f(t) =(t-1)(t-11)
Distributing the factors multiplying (t-1) times (t-11), goes:
f(t) =t²-12t+11
How do you do this!?!
11x + y = 4, x + y = -2, x - 2y = 18
How can you determine which equations can be graphed more easily using x- and y-intercepts, rewriting in slope-intercept form, or using a table of values?
Which method works best for you personally? When does it not work as well?
11x + y = 4
x | y
0 | 4
[tex]\frac{4}{11}[/tex] | 0
plot the y-intercept (0, 4) and the x-intercept ([tex]\frac{4}{11}[/tex], 0)
or
11x + y = 4
-11x -11x
y = -11x + 4 ⇒ m = [tex]\frac{-11}{1}[/tex], b = 4
plot at point the y-intercept "b = 4" (0,4). plot the next point using the slope "m = [tex]\frac{-11}{1}[/tex]" from point (0,4), count down 11 and to the right 1 (1,-7).
Using intercepts would not provide an accurate graph because you have to estimte where ([tex]\frac{4}{11}[/tex], 0) is, so it is best to use slope-intercept form.
***********************************************************************************************************
x + y = -2
x | y
0 | -2
-2 | 0
plot the y-intercept (0, -2) and the x-intercept (-2, 0)
or
x + y = -2
-x -x
y = -x - 2 ⇒ m = [tex]\frac{-1}{1}[/tex], b = -2
plot at point the y-intercept "b = -2" (0,-2). plot the next point using the slope "m = [tex]\frac{-1}{1}[/tex]" from point (0,-2), count down 1 and to the right 1 (1,-3).
Both methods are easy to use so either can be used.
**********************************************************************************************************
x - 2y = 18
x | y
0 | -9
18 | 0
plot the y-intercept (0, -9) and the x-intercept (18, 0)
or
x - 2y = 18
-x -x
-2y = -x + 18
[tex]\frac{-2y}{-2} = \frac{-1}{-2}x + \frac{18}{-9}[/tex]
y = [tex]\frac{1}{2}x[/tex] - 9
plot at point the y-intercept "b = -9" (0,-9). plot the next point using the slope "m = [tex]\frac{1}{2}[/tex]" from point (0,-9), count up 1 and to the right 2 (2,-8).
Using intercepts will make a large graph since you have to plot (18,0) so it is best to use the slope-intercept form.
A recipe for cookies requires 2/3 cup of butter. Rama wants t make 3/4 of the recipe. How many cups of butter should rama use to make cookies?
answer is equal to 2X3/3X4 which is equal to1/2
[tex]\frac{3}{4}[/tex] of [tex]\frac{2}{3}[/tex]
[tex]\frac{3}{4} * \frac{2}{3} = \frac{3(2)}{4(3)} = \frac{1}{2}[/tex]
Answer: [tex]\frac{1}{2}[/tex] cup of butter
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: (3 × 2) × 6 = 36 A. 3 × (2 × 6) = 36 B. (3 + 2) × 6 = 30 C. 6 + (5 × 6) = 36 D. 3 × (2 + 6) = 24
Answer : A
A. 3 × (2 × 6) = 36
we have 3 times 2 times 6. All the numbers have multiplication in between . so it comes under Associative property of multiplication.
B. (3 + 2) × 6 = 30
we have 3+2 . there is a + sign in between. so it does not comes under Associative property of multiplication
C. 6 + (5 × 6) = 36
we have 6 + . there is a + sign in between. so it does not comes under Associative property of multiplication
D. 3 × (2 + 6) = 24
we have 2 + 6 . there is a + sign in between. so it does not comes under Associative property of multiplication
Tom always keeps his 4 gardens clean.He takes 20 minutes to clean a single garden.How much time will it take to clean all four gardens.
It will take Tom 80 minutes to clean all 4 gardens. Or, 1 hour and 20 minutes.
Multiply the polynomials. Simplify the answer. Show your work.
(5x^2+8x-6)(8x^2+3x+1)
5x^2 + 8x - 6(8x^2 + 3x + 1)
Distributive property.
40x^4 + 15x^3 + 5x^2 + 64x^3 + 24x^2 + 8x - 48x^2 - 18x - 6
Combine like terms.
40x^4 + 79x^3 - 19x^2 - 10x - 6
Use the distributive property and [tex]a^n\cdot a^m=a^{n+m}[/tex]
[tex](5x^2+8x-6)(8x^2+3x+1)\\\\=(5x^2)(8x^2)+(5x^2)(3x)+(5x^2)(1)+(8x)(8x^2)+(8x)(3x)+(8x)(1)+(-6)(8x^2)+(-6)(3x)+(-6)(1)\\\\=40x^4+15x^3+5x^2+64x^3+24x^2+8x-48x^2-18x-6\\\\=40x^4+(15x^3+64x^3)+(5x^2+24x^2-48x^2)+(8x-18x)-6\\\\=40x^4+79x^3-19x^2-10x-6[/tex]
Rewrite the fractions 3/4 and 5/16 as fractions with a least common denominator.
Answer:
12/16 and 5/16
Step-by-step explanation:
To rewrite 3/4 and 5/16 with a least common denominator, factorize the denominators to find the LCD, which is 16. Multiply 3/4 by 4/4 to get 12/16. The fraction 5/16 remains unchanged.
The denominator 4 is 22, and 16 is 24. The LCD is the higher power of 2 present in these denominators, which is 24 or 16. You then find what to multiply each fraction's denominator to get the LCD. In the case of 3/4, multiply numerator and denominator by 4 to get 12/16. There is no need to change 5/16 because it's already expressed with the LCD as denominator.
So, the fractions with the same denominator are:
3/4 becomes 12/16
5/16 remains 5/16
These fractions can now be easily added or subtracted as they have a common denominator.
Which expression is a possible leading term for the polynomial function graphed below?
A. -4x^8
B. -4x^5
C. 4x^5
D. 4x^8
Answer: Option A. -4x^8
Step-by-step explanation:
The polynomial function given in the graph has 4 real roots. And because the graph falls to the left and right, it will have even order and negative leading coefficient.
So we have only one option that matches the required conditions, and i.e. option A.
30 pointtttsssssssssssssss
Hey there!
When you multiply two exponents, you "add" the numbers on the exponents.
3+3=6
Therefore, m³·m³=[tex]m^{6}[/tex]
Therefore, your answer is A
I hope this helps! I hope your day is as grand as 10[tex]^{6}[/tex]!
The answer to your question is m^{6} or A
Its cost 9,328 points to build each apartment building in the computer game big city building. What is the cost to build 5 apartment buildings?
The cost would be:
46,640 Points.
Merlyn’s weight went down from 125 pounds to 110 pounds after dieting. What was her percent weight loss? a. 10% b. 12% c. 15% d. 18%
[tex]\frac{(new) - (original)}{original} = \frac{110 - 125}{125} = \frac{-15}{125} = -0.12[/tex] The negative means it is a decrease.
0.12 x 100 = 12%
Her weight decreased 12%
Answer: B
What is the proportion of the value of the missing number on 75/100 equals. ?/400
75 : 100 = x : 400
x = 75 * 400 : 100
x = 300
A neighborhood development that is 4 acres is to be divided into 2/3 acre lots.How many lots can be created
no of lots to be created=4/2/3=12/2=6
To find the answer of this question, you would take 4 acres and divide it by 2/3. This is because the development is 4 acres and is being divided into a certain number (that we are going to find) of 2/3 acre lots.
So by dividing the area of the neighborhood development lot (4 acres) by 2/3, you would find the total number of 2/3 acre lots that are going to be created.
4 acres / 2/3 acre lots
To divide fractions, you would multiply the fraction by its reciprocal. So your new expression, instead of 4 ÷ 2/3, would be 4 × 3/2.
Multiply straight across.
4 × 3/2 = 12/2 = 6
6 neighborhood development lots can be created by dividing the 4 acre lot into 2/3 acre lots.
Sharon's been $3.45 armor on sunflower seeds the price of sunflower seeds is $0.89 per pound how many pounds of sunflower seeds does sharon buy
3 pounds of sunflower seeds.
Is this answer right
Everything looks good until the final step. The answer is not c = 26. It should be more like c = 25.495 which is approximate. You would use your calculator to find this value. If you round to the nearest whole number, then c = 25; however, this is a bad idea because it implies that the hypotenuse is the same length as the longer leg, which is not the case here. Recall that the hypotenuse is always the longest side.
The final answer is 25.49 or 25.5
solve for x:
22x+11=4x-7
22x + 11 = 4x - 7
-4x -11 -4x -11
18x = -18
X=-1
Hello there!
Solve for x.
[tex]22x+11=4x-7[/tex]
Explanation
↓↓↓↓↓↓↓↓↓↓
First you had to subtract by 11 from both sides of the equations.
[tex]22x+11-11=4x-7-11[/tex]
Simplify
[tex]22x=4x-18[/tex]
Then you subtract by 4x from both sides of the equations.
[tex]22x-4x=4x-18-4x[/tex]
Simplify
[tex]18x=-18[/tex]
Divide by 18 from both sides of the equations.
[tex]\frac{18x}{18}=\frac{-18}{18}[/tex]
Simplify it should be the correct answer.
[tex]x=-1[/tex]
Answer⇒⇒⇒⇒⇒⇒x=-1
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
Linda makes $96 per work day. How much dose she make in 3/8 of a d
[tex]\frac{96 (dollars)}{1 (day)} * \frac{3}{8} day = \frac{96(3)}{8} dollars[/tex] = 12(3) dollars
= $36
A buffet offers ranch or caesar dressing.The ratio of ranch dressing used to caesar dressing used 8:3.If the buffet uses 72 cases of ranch dressing,how many cases of caesar do they use?
To find out how many cases of Caesar dressing are used, divide the ranch cases used by the ranch ratio (72/8=9) and then multiply by the Caesar ratio (9*3=27). Therefore, the buffet uses 27 cases of Caesar dressing.
The question involves finding out how many cases of Caesar dressing the buffet uses if they use 72 cases of ranch dressing and the ratio of ranch to Caesar dressing is 8:3.
First, we determine the unitary ratio by dividing the number of ranch cases used by the corresponding ratio number for ranch. In this case, 72 cases divided by 8 gives us 9 cases per unit ratio.
Since the ratio for Caesar dressing is 3, we then multiply the unit ratio by 3 to find the number of Caesar cases used.
72 cases of ranch ÷ 8 (ranch ratio) = 9 cases per unit
9 cases per unit × 3 (Caesar ratio) = 27 cases of Caesar dressing
Find the values of x and y.
(image below)
Opposite angles have the same measures. This allows you to set and solve the following equations:
[tex] \begin{cases} 26-6x = 20-8x \\ 5y = 9y-76 \end{cases} [/tex]
To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:
[tex] \begin{cases} -6x+8x = 20-26 \\ 5y-9y = -76 \end{cases} [/tex]
Sum like terms:
[tex] \begin{cases} 2x = -6 \\ -4y = -76 \end{cases} [/tex]
Divide the first equation by 2 and the second by -4:
[tex] \begin{cases} x = -3 \\ y = 19 \end{cases} [/tex]
If Damian needs to borrow money to pay for something, he needs to request which of the following?
which of the following???
Answer:
B. A loan
Step-by-step explanation:
hope this helps
help with math graph 35 points
Because the equation is in slope-intercept form, we know the first point will be -4, as that is the y-intercept.
We can input a value of x into the equation to find the y value that goes along with that value of x.
y = (-5/6)x - 4
We'll use x = 6 for this.
y = (-5/6)6 - 4
y = -5 - 4
y = -9
to draw the graph we only require 2 points
choose any value of x, substitute into the equation and solve for y
x = 0 : y = 0 - 4 = - 4 ⇒ (0, - 4 )
x = 6 : y = - 5 - 4 = - 9 ⇒ (- 6, - 9 )
Plot these 2 points and draw a straight line through them for graph
Find the area of a rectangle with a perimeter of 12 meters and a base of 4 meters
The data set shows the number of practice passes a quarterback successfully completed preparing for a competition and the number of passes the quarter throw during a timed competition. (photo 1)
Use technology to find the equation and coefficient of determination for each type of regression model. Use the number of practice passes for the input variable and the number of competition passes for the output variable. (photo 2)
Which model best fits the data set?
Answer:
The model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex].
Step-by-step explanation:
To find the different regression models, the Excel software was used.
For the linear regression model, the following equation was obtained:
[tex]y = 2.0809x + 1.291 [/tex]
with a coefficient of determination [tex]R ^ 2 = 0.8911 [/tex]
For the quadratic regression model, the following equation was obtained:
[tex]y = 0.1663x ^ 2-0.0498x + 4.8229[/tex]
with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]
Finally, for the exponential regression model, the following equation was obtained:
[tex]y = 4.4281e ^ {0.1513x}[/tex]
with a coefficient of determination [tex]R ^ 2 = 0.9635 [/tex]
The coefficient of determination [tex]R ^ 2[/tex] measures how well a predictive mathematical model fits reality. The value of [tex]R ^ 2[/tex] is always between 0 and 1. The closer you get to 1, the more accurate is the built model.
Therefore, the model that best fits the data is the one with the highest value of [tex]R ^ 2[/tex]. In this case it is the quadratic, with a coefficient of determination [tex]R ^ 2 = 0.9675[/tex]
The results obtained are summarized in the attached table.
To find the best fitting regression model and coefficient of determination, we conduct a regression analysis using the number of practice passes as the input variable and competition passes as the output. Different models fit the data differently, and by comparing the R2 values, we can determine which model is the best fit. This requires either software or a graphing calculator.
Explanation:The student's question pertains to regression modeling in mathematics, specifically finding the best fit model and coefficient of determination (R2) which quantifies how well the regression model fits the observed data. To determine which model most represents the data between the number of practice passes and competitive passes in question, we must first perform a regression analysis, using the practice passes as the input (x) and the competition passes as output (y).
There are various types of regression models, including linear, exponential, logarithmic, and quadratic, each fitting the data differently. Linear involves a straight line representing the data, while exponential and logarithmic models exhibit curves, and quadratic involves a parabola. Identification of the most suitable model is through comparing R2 values for each model where higher values indicate better fits.
It is important to note that this process generally requires software or a graphing calculator such as Excel, SPSS, R, or a TI calculator. Specific steps may vary depending on the tool used.
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1. what is the mode of the data set?
(13, 19, 13, 19, 14, 15, 18, 11, 19, 14)
A. 8
B. 15.5
C. 19
D. 14.5
2. these data show the number of grams of fat found in 9 different health bars.
12 14 16 16.5 11 18 18 14 20
what is the IQR (interquartile range) for these data?
A. 5
B. 18
C. 16
D. 9
The mode of the first data set is 19, and the IQR of the second data set is 4, but 4 is not a provided option in your question.
Explanation:The mode of a data set is the number that appears most frequently. In the data set you provided: (13, 19, 13, 19, 14, 15, 18, 11, 19, 14), the number 19 appears three times, which is more frequent than any other number. So, the correct answer is C. 19.The IQR (Interquartile Range) of a data set is computed as the difference between the first quartile (Q1) and the third quartile (Q3). For the data on grams of fat in health bars: (12, 14, 16, 16.5, 11, 18, 18, 14, 20), firstly we need to arrange the data in ascending order: 11, 12, 14, 14, 16, 16.5, 18, 18, 20. Then take the middle number of the first half (which is Q1=14) and the middle number of the second half (which is Q3=18). Hence, the IQR = Q3 - Q1 = 18 - 14 = 4. Unfortunately, 4 is not a provided option, so there may be a mistake in your question.Learn more about Statistics here:
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The following number belongs to which set of numbers 1.6 (the is a repeating decimal by the way)
A.Irrational number
B.Rational number, integers, and whole numbers
C. Rational numbers, and integers, but not whole numbers
D. Rational numbers, but not integers or whole numbers.
The repeating decimal 1.6 falls under the categorization of Rational numbers. It can be expressed as a fraction, specifically 5/3, but it does not qualify as an integer or a whole number as those contain no fractions or decimals.
Explanation:The number 1.6 (1.666...) is a repeating decimal and belongs to the set of numbers known as Rational numbers, but not integers or whole numbers.
By definition, Rational numbers are any numbers that can be expressed as the fraction of two integers. In other words, a number is rational if it can be written in the form a/b where a and b are integers and b is not zero. Here, 1.6 repeating can be written as 5/3 (a/b form), indicating it's a rational number.
Integers and Whole numbers are always without fractions or decimals. Hence, the number doesn't fall in these categories.
Therefore, the correct answer is D: 1.6 (1.666...) is a rational number, but it is not an integer or a whole number.
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