Answer:
[tex]L =21.945[/tex] --- Length
[tex]W = 7.9725[/tex] --- Width
Step-by-step explanation:
Given
Let
[tex]L \to Length[/tex]
[tex]W \to Width[/tex]
So:
[tex]Area = 175[/tex]
[tex]L = 6 + 2W[/tex]
Required
The dimension of the rectangle
The area is calculated as:
[tex]Area =L*W[/tex]
This gives:
[tex]175 =L*W[/tex]
Substitute: [tex]L = 6 + 2W[/tex]
[tex]175 =(6 + 2W)*W[/tex]
Open bracket
[tex]175 =6W + 2W^2[/tex]
Rewrite as:
[tex]2W^2+ 6W -175 = 0[/tex]
Using quadratic formula:
[tex]W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
This gives:
[tex]W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}[/tex]
[tex]W = \frac{-6 \± \sqrt{1436}}{2*2}[/tex]
[tex]W = \frac{-6 \± 37.89}{4}[/tex]
Split
[tex]W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}[/tex]
[tex]W = \frac{31.89}{4}, W = \frac{-43.89}{4}[/tex]
The width cannot be negative;
So:
[tex]W = \frac{31.89}{4}[/tex]
[tex]W = 7.9725[/tex]
Recall that:
[tex]L = 6 + 2W[/tex]
[tex]L =6 + 2 * 7.9725[/tex]
[tex]L =21.945[/tex]
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.:
Car
Compact Intermediate Full Size
Analyzer Computerized 50 55 63
Electronic 42 44 46
The following regression model can be used to analyze the data for a randomized block design involving two treatments and three blocks.
E(y) = 0 + 1x1 + 2x^2 + 3x^3
Show the values of the variables below.
Analyzer x1
Computerized __________
Electronic 1
Answer:
the value of the variable is 10
Solve the inequality -6c< -12
Answer: c<2
Step-by-step explanation:
-6c<-12
c<-12/-6
c<2
Madge has cut out two triangular shapes from a block of wood, as shown below. Are the two shapes similar? Show your calculations.
For the function f(x)=−7x^3−8x+2x^2, Step 1 of 2 : Find the slope of the tangent line at x=1.
Answer:
The slope of the tangent line at x = 1 is -25.
Step-by-step explanation:
We are given the function:
[tex]f(x)=-7x^3-8x+2x^2[/tex]
And we want to find the slope of the tangent line at x = 1.
The slope of the tangent line at a point for a function is given by its derivative. Find the derivative of the function:
[tex]f'(x)=-21x^2+4x-8[/tex]
Then the slope of the tangent line at x = 1 is:
[tex]f'(1)=-21(1)^2+4(1)-8=-25[/tex]
What is the y-intercept of the quadratic function below?
There is no y-intercept
(0, -1)
(-4, 0)
(-2, 3)
What are the four answers?
Answer:
CLAE
Step-by-step explanation:
1=43
2=28
3=24
4=83
Which graph shows the line y = 2x + 3?
C
НА
A
D
B
A. Graph A
Ο Ο
B. Graph D
C. Graph B
D. Graph C
the answer is letter B.graph D
What are elliptic and hyperbolic geometries? Why were they developed?
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
The key fact that makes elliptic and hyperbolic geometries different from Euclidean geometry is the consideration of curvature in spaces.
In this case, Euclidean geometry considers only spaces with no curvatures, whereas elliptic geometry considers spaces with a constant negative curvature and hyperbolic geometry makes with spaces with a constant positive curvature.
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
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Please help ,cant figure it out.
Answer:
B. √2^5
Step-by-step explanation:
(2^½. 2^¾)²
= 2¹ . 2^(1½)
= 2^(2½)
= 2^(5/2)
=√2^5
If angles of measures (x - 2) and (2x + 5) are a pair of supplementary angles, find the measures of those angles
Answer:
Solution: Since (x - 2)° and (2x + 5)° represent a pair of supplementary angles, then their sum must be equal to 180°. Therefore, the two supplementary angles are 57° and 123
Area of a trapezoid
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
6 cm
0
10 cm
8 cm
12 cm
Answer:
h
Step-by-step explanation:
h
1 +3 = ????????????????
One and three are both numbers. We can add the, together and get another number. The fact that these two numbers should be added is shown by the symbol between them. Adding 1 to 3 equals to 4.
Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.
1. 4
2. 1/4
3. -1/4
4. −4
Please help!!
Answer:
1. 4
Step-by-step explanation:
the slope of:
f(x) = 10/2=5
g(x) = 10/½=20
so, g(x) = f(4.x)
=> k = 4
The perimeter of a triangle is 57 inches. Twice the length of the longest side minus the length of the shortest side is 22 inches. The sum of the length of the longest side and twice the sum of both the other side lengths is 94 inches. Find the side lengths
[tex]\begin{cases} a = shortest\\ b = medium\\ c = longest \end{cases} \begin{array}{llll} \stackrel{\textit{perimeter is 57}~\hfill }{a + b + c = 57}~\\\\\stackrel{\textit{twice longest minus shortest}}{2c-a=22~\hfill }\\\\ \stackrel{\textit{longest plus twice others}}{c + 2(a+b) = 94~\hfill } \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2c-a=22\implies 2c=a+22\implies \boxed{2c-22=a} \\\\\\ \stackrel{\textit{we know that}}{c+2(a+b)=94}\implies c+2a+2b=94\implies c+2(2c-22)+b=94[/tex]
[tex]c+4c-44+2b=94\implies 5c-44+2b=94\implies 5c+2b=138 \\\\\\ 2b=138-5c\implies \boxed{b = \cfrac{138-5c}{2}} \\\\\\ \stackrel{\textit{we know the perimeter is}}{57=a + b + c}\implies 57 = \stackrel{a}{(2c-22)}+\stackrel{b}{\cfrac{138-5c}{2}}+c \\\\\\ 57=2c-22+\cfrac{138}{2}-\cfrac{5c}{2}+c\implies 57=3c-22+69-\cfrac{5c}{2} \\\\\\ 57=3c-47+\cfrac{5c}{2}\implies 10=3c-\cfrac{5c}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{20=6c-5c}[/tex]
[tex]\blacktriangleright 20=c \blacktriangleleft \\\\\\ \boxed{2c-22=a}\implies 40-22=a\implies \blacktriangleright 18=a \blacktriangleleft \\\\\\ \boxed{b = \cfrac{138-5c}{2}}\implies b=\cfrac{138-5(20)}{2}\implies b=\cfrac{38}{2}\implies \blacktriangleright 19 \blacktriangleleft[/tex]
Y=x^3/2(x^2+1) I need the steps.
Answer:
0
Step-by-step explanation:
If you are looking for the x- intercept image is below
if you are looking for the y- intercept its the same as the x. Image is below
What is the value of log Subscript 5 Baseline 125?
Answer:
[tex]log_5 \ 125 = 3[/tex]
Step-by-step explanation:
[tex]log_5 \ 125 = log_2 \ 5^3 = 3 \times log_5 \ 5 = 3 \times 1 = 3[/tex]
The value of [tex]$\log _{5} 125$[/tex] can be estimated utilizing the logarithm rule. The value of [tex]$\log _{5} 125$[/tex] exists 3.
What is a logarithm?The logarithm stands for the inverse function of exponentiation. In logarithm base must be raised to yield a given number for an exponent.
Given:
[tex]$\log _{5} 125$[/tex]
Estimate the value of the given logarithm, we get
[tex]$\log _{5} 125=\log _{5}(5)^{3}$[/tex]
[tex]$\log _{5} 125=3 \log _{5} 5$[/tex]
From logarithm rule [tex]$\log m^{n}=n \log m$[/tex], we get
[tex]$\log _{5} 125=3 \times 1$[/tex]
[tex]$\log _{5} 125=3$[/tex]
Therefore, the value of [tex]$\log _{5} 125$[/tex] is 3.
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If you apply these changes to the linear parent function, f(x) = x, what is the
equation of the new function?
• Vertically compress by a factor of 7.
• Shift up 9 units.
O A. DY) = 7x+9
O B. g(x) = = x+9
O C. () = 7(x-9)
O D. g(x) = + (x+9)
Answer:
The equation of the new function is [tex]g(x) = 7x + 9[/tex]
Step-by-step explanation:
Vertically compress by a factor of 7.
Vertically compressing a function by a units is the same as:
[tex]g(x) = f(ax)[/tex]
In this question:
[tex]f(x) = x, a = 7[/tex]. So
[tex]g(x) = f(7x) = 7x[/tex]
Shift up 9 units.
Shifting a function up a units is the same thing as adding a to the function. In this case, [tex]a = 9[/tex], and then:
[tex]g(x) = 7x + 9[/tex]
The equation of the new function is [tex]g(x) = 7x + 9[/tex]
A person invests $3,500 in an account that earns 7.5% interest compounded continuously. What is the value of the investment after 4 years?
I think it's: 4,674.14$
Answer:
A = $4724.36
Step-by-step explanation:
P = $3500
r = 7.5% = 0.075
t = 4years
n = 365
[tex]A = P(1 + \frac{r}{n})^{nt}\\\\[/tex]
[tex]=3500(1 + \frac{0.075}{365})^{365 \times 4}\\\\=3500(1.00020547945)^{365\times4}\\\\= 3500 \times 1.34981720868\\\\= 4724.36023037\\\\= \$ 4724.36[/tex]
what would it look like?
x^2 + y^2 = 12.25
The above equation is the equation for a circle. The formula for the equation of a circle is (x - h)^2 + (y - k)^2 = r^2.
Looking at the given equation, x and y, otherwise known as the center, are not shifted at all. This mean that the center of our circle is at (0,0).
To find the radius, we take the square root of 12.25, which is 3.5. Therefore, go 3.5 units up, down, left, and right (to make a + sort of shape) from the center and then connect the points to make the circle.
Hope this helps!! :)
Answer:
Step-by-step explanation:
The graph of x^2 + y^2 = 12.25 will be a circle with centre at (0, 0) and radius will be √12.25 = 3.5.
2x + y = 1 is a straight line
y = -2x + 1 so it will pass through the y axis at y = 1 and also through the point
(-1/2, 0).
Where the line passes through the circle will be the solutions to the system.
As part of a board game, players choose 5 unique symbols from 9 different symbols to create their secret password. How many different ways can the players create a specific 5 symbol password?
Give your answer in simplest form.
Answer:
[tex]15,120[/tex]
Step-by-step explanation:
For the first symbol, there are 9 options to choose from. Then 8, then 7, and so on. Since each player chooses 5 symbols, they will have a total of [tex]9\cdot 8 \cdot 7 \cdot 6\cdot 5=\boxed{15,120}[/tex] permutations possible. Since the order of which they choose them matters (as a different order would be a completely different password), it's unnecessary to divide by the number of ways you can rearrange 5 distinct symbols. Therefore, the desired answer is 15,120.
Answer:15,120
Step-by-step explanation:
7x_=8x7 Nonsense report
Answer:
hope it help ful ✓ ......Write a system of equations to describe the situation below, solve using substitution, and fill in the
blanks.
Peter is going to send some flowers to his wife. Cedarburg Florist charges $3 per rose, plus $21 for
the vase. Sally's Flowers, in contrast, charges $2 per rose and $26 for the vase. If Peter orders the
bouquet with a certain number of roses, the cost will be the same with either flower shop. How
many roses would there be? What would the total cost be?
If the bouquet contains
roses, it will cost $
My
Answer:
R=5
Step-by-step explanation:
3r+21
2r+26
3r+21=2r+26
r=5
Alex drives at an average speed that is
1
5
of the average speed that Roy's train travels.
Alex takes 15 minutes to travel 12 km in her car.
Roy travels for 1 hour and 20 minutes on his train.
How far does Roy travel to 2 dp?
plz i need asap
Answer:
ayy sensya na po Yan din po hanap Kong answer
I need to find the equal expression to -m(2m+2n)+3mn+2m². Help please?
[tex]m(2m+2n)+3mn+2m^2\implies \stackrel{\textit{distributing}}{2m^2+2mn}+3mn+2m^2 \\\\\\ 2m^2+2m^2+2mn+3mn\implies \stackrel{\textit{adding like-terms}}{4m^2+5mn}[/tex]
Find the height of this triangle.
Answer:
[tex]\sqrt{3}[/tex]
Step-by-step explanation:
x^2 + 1 = 4
x^2 = 3
[tex]\sqrt{3}[/tex]
Y=4x pls help pls help
Answer:
(1,4) , (3,12) , (5,20)
Step-by-step explanation:
You should put the first number in X and find the second number from equation.
the single discount of two successive discounts 10% and 5% is
Answer:
14.5%
Step-by-step explanation:
Use the number 100 as an example to find the single discount.
Take a 10% discount off of this:
100(0.9)
= 90
Take a 5% discount:
90(0.95)
= 85.5
So, after the successive discounts, $14.5 was discounted.
This means that the single discount is 14.5%.
So, the answer is 14.5%
6. There were 900 sweets in 3 boxes, A, B and C. 18 sweets were transferred from A to B and 5
sweets were transferred from B to c. of the sweets in C were then transferred to A. There were
then an equal number of sweets in all 3 boxes. How many sweets were there in each box at first?
28
Answer: a=168, b=287, c=445
Step-by-step explanation:
What is 7 and 1/3 times 2 and 2/11 equal?
Answer:
16
Step-by-step explanation:
First, convert both into improper fractions. 7 1/3=22/3. 2 2/11=24/11.
Lastly, multiply 22/3*24/11=528/33=16
Hope this helps!
The value of given expression is 28/33.
What is the product of two fractions?The product of two fractions is the product of the numerators and the product of the denominators.
Product of two fractions = Product of their numerators / Product of their denominators
Given that, 7 and 1/3 times 2 and 2/11.
Now, 7× [tex](\frac{1}{3} \times2)[/tex]× 2/11
= 7× 2/3× 2/11
= (7×2×2)/(3×11)
= 28/33
Therefore, the value of given expression is 28/33.
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Pls help its due at 11:10
Answer:
firstly
we all know that the angles of a triangle they all add up to 180° meaning when you add them all they must give you 180°
88°+33°+L = 180° ( sum of angle in a ∆)
121° + L = 180°
L = 180° - 121°
L = 59°
Step-by-step explanation:
first you you must add all your angles and all equal to 180°
that you add the like terms
than you transpose 121° to the right hand side