Answer:
I believe b is 5.
Step-by-step explanation:
When you place the points in the values, you get 5=3(0)+b. When you simplify it, you get 5=b. I really hope this is correct, I apologize if it isn't! I hope this helps! :)
I think it’s five too
In rhombus JKLM, if m<KLJ = 38°, find m<JIVIL.
Answer:
∠JML = 104°
Step-by-step explanation:
JL bisects angle KLM, so ...
∠KLM = 2·∠KLJ = 2·38° = 76°
Adjacent angles in any parallelogram are supplementary, so ...
∠JML = 180° -∠KLM = 180° -76°
∠JML = 104°
1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is the surface area of the parametric surface given by r2(u,v)=5r1(u,v) with −4≤u≤4,−4≤v≤4?
Surface area of [tex]\(r_2(u,v)\)[/tex] is [tex]\(25\)[/tex] times the area of parameter domain[tex]\(D\),[/tex] yielding [tex]\(1600\)[/tex] if [tex]\(D\)[/tex] is [tex]\(8 \times 8\).[/tex]
Let's break it down step by step:
step:-1. **Define the parametric surfaces**: We have two parametric surfaces: [tex]\( r_1(u,v) = f(u,v)i + g(u,v)j + h(u,v)k \)[/tex] and [tex]\( r_2(u,v) = 5r_1(u,v) \).[/tex]
step:-2. **Calculate the partial derivatives**: Compute the partial derivatives of [tex]\( r_1 \)[/tex] with respect to [tex]\( u \)[/tex] and [tex]\( v \)[/tex] denoted by [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \).[/tex]
step:-3. **Multiply by 5**: Since[tex]\( r_2(u,v) = 5r_1(u,v) \),[/tex] the partial derivatives of [tex]\( r_2 \)[/tex] with respect to [tex]\( u \)[/tex] and [tex]\( v \)[/tex] will be 5 times the corresponding partial derivatives of [tex]\( r_1 \)[/tex], denoted by [tex]\( r_{2u} \)[/tex] and [tex]\( r_{2v} \).[/tex]
step:-4. **Calculate the cross product**: Compute the cross product of [tex]\( r_{2u} \)[/tex] and[tex]\( r_{2v} \),[/tex] denoted by [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex]. This will be 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \),[/tex] as the cross product is linear with respect to the vectors involved.
step:-5. **Surface area integral**: Use the formula for the surface area integral: [tex]\( A = \iint_D \| r_u \times r_v \| \, dA \),[/tex] where [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] replaces [tex]\( \| r_{u} \times r_{v} \| \).[/tex]
step:-6. **Calculate the integral**: Integrate[tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] over the parameter domain [tex]\( D \)[/tex]. Since [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] is constant and equal to 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \)[/tex], the integral becomes [tex]\( 25 \times \text{Area of } D \).[/tex]
step:-7. **Determine the area of the parameter domain**: If the parameter domain [tex]\( D \)[/tex] is a rectangle with sides of length 8 in both directions, its area is [tex]\( 8 \times 8 = 64 \).[/tex]
step:-8. **Final calculation**: Multiply the area of [tex]\( D \)[/tex] by 25 to get the surface area of[tex]\( r_2(u,v) \)[/tex], which is[tex]\( 25 \times 64 = 1600 \).[/tex]
So, the surface area of the parametric surface given by [tex]\( r_2(u,v) = 5r_1(u,v) \)[/tex] is 1600.
The surface area of the parametric surface [tex]\( \mathf{r}_2(u, v) \)[/tex] is 25.
To find the surface area of the parametric surface given by [tex]\( \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \)[/tex] where [tex]\( -4 \leq u \leq 4 \)[/tex] and [tex]\( -4 \leq v \leq 4 \)[/tex], given that the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] over the same parameter range is 1, follow these steps:
Surface Area of [tex]\( \mathf{r}_1(u, v) \)[/tex]
The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is given to be 1.
Relationship Between [tex]\( \mathf{r}_1 \) and \( \mathf{r}_2 \)[/tex]
[tex]\[ \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \][/tex]
Effect of Scaling on Surface Area
When a surface is scaled by a factor k, the surface area is scaled by a factor of k². This is because surface area is a two-dimensional measure, and scaling each dimension by k multiplies the area by k².
Calculation for [tex]\( \mathf{r}_2(u, v) \)[/tex]
In this problem, the scaling factor k is 5. Therefore, the surface area of [tex]\( \mathf{r}_2(u, v) \)[/tex] will be [tex]\( 5^2 \)[/tex] times the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex].
[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times \text{Surface area of } \mathf{r}_1(u, v)\][/tex]
Substitute the Given Surface Area
The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is 1.
[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times 1 = 25\][/tex]
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality? x > 64 and x < 68 x > 64 or x < 68 x < 64 and x < 68 x < 64 or x < 68
Answer:
Option A is correct.
Step-by-step explanation:
64 < x < 68
This inequality represent that the height x should be greater than 64 and less than 68.i.e.
x>64 and x<68
So, Option A is correct.
Answer:
x>64 and x<68
Step-by-step explanation:
Mike correctly found the slope and y intercept of the line passing through the points(-5,-2)and (3,14)as follows.
Answer:
y= 2x+8
Step-by-step explanation:
The standard form of an equation of line in slope-intercept form is:
y= mx+b
Where m is the slope of the line and b is the y-intercept of the line.
To obtain the equation from the given information we need to put the values of m and b into the standard form of equation.
We are given
m = 2
and
b = 8
So putting the values of m and b
y = (2)x +8
y= 2x+8 ..
THE ANSWER IS :y=2x +8
just know its right.
For each x and n, find the multiplicative inverse mod n of x. Your answer should be an integer s in the range 0 through n - 1. Check your solution by verifying that sx mod n = 1.(a) x = 52, n = 77(b) x = 77, n = 52(c) x = 53, n = 71(d) x = 71, n = 53
To find the multiplicative inverse of x modulo n, we need to find an integer s such that (x * s) mod n = 1. We can calculate the multiplicative inverses for the given values: (a) x = 52, n = 77: s = 65. (b) x = 77, n = 52: s = 33. (c) x = 53, n = 71: s = 51. (d) x = 71, n = 53: s = 9.
Explanation:To find the multiplicative inverse modulo n of x, we need to find an integer s such that (x * s) mod n = 1. Let's calculate the multiplicative inverses for the given values:
a) For x = 52 and n = 77:
x * s ≡ 1 (mod n)
52 * s ≡ 1 (mod 77)
s ≡ 65 (mod 77)
So, the multiplicative inverse of 52 modulo 77 is 65.
b) For x = 77 and n = 52:
77 * s ≡ 1 (mod 52)
s ≡ 33 (mod 52)
The multiplicative inverse of 77 modulo 52 is 33.
c) For x = 53 and n = 71:
53 * s ≡ 1 (mod 71)
s ≡ 51 (mod 71)
The multiplicative inverse of 53 modulo 71 is 51.
d) For x = 71 and n = 53:
71 * s ≡ 1 (mod 53)
s ≡ 9 (mod 53)
The multiplicative inverse of 71 modulo 53 is 9.
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What is the value of the expression |a + b| + |c| when a = –3, b = –7, and c = –15?
Answer:
Step-by-step explanation:
Formula
abs(a + b) + abs(c)
Givens
a = - 3
b = - 7
c = - 15
Solution
abs(-3 - 7) + abs(-15)
abs(-10) + abs(-15)
10 + 15
25
Please help me simplified this
For this case we have that by definition, the perimeter of the quadrilateral shown is given by the sum of its sides:
Let "p" be the perimeter of the quadrilateral, then:
[tex]p = 7 + y + 7 + x\\p = 7 + 7 + x + y\\p = 14 + x + y[/tex]
So, the perimeter of the figure is: [tex]14 + x + y[/tex]
Answer:
[tex]p = 14 + x + y[/tex]
Answer:
perimeter = x + y + 14
Step-by-step explanation:
The perimeter is the sum of the side lengths:
perimeter = x + 7 + y + 7
The constants can be combined to give ...
perimeter = x + y + 14
___
An "equation" will have an equal sign somewhere. Since you want to find the perimeter, it makes sense for the equation to show you how to find the perimeter. (I have used "perimeter" to represent the perimeter. It is often represented using the letter P. Of course, you can choose any variable or other representation you like.)
A spinner is divided into four equal sections that are numbered 2, 3, 4, and 9. The spinner is spun twice. How many outcomes have a product less than 20 and contain at least one even number?
Answer with Step-by-step explanation:
On spinning the spinner twice,we have 16 different outcomes:.
We write the outcomes with their product:
Product
2 2 4
2 3 6
2 4 8
2 9 18
3 2 6
3 3 9
3 4 12
3 9 27
4 2 8
4 3 12
4 4 16
4 9 36
9 2 18
9 3 27
9 4 36
9 9 81
outcomes have a product less than 20 and contain at least one even number are in bold letters.
Hence, outcomes have a product less than 20 and contain at least one even number are:
10
There are 8 outcomes of spinning the spinner twice that result in a product less than 20 and contain at least one even number.
To determine how many outcomes of spinning a spinner twice result in a product less than 20 and contain at least one even number, we start by listing all possible outcomes.
The spinner is divided into four equal sections: 2, 3, 4, and 9. When spun twice, there are 16 outcomes in total:
(2,2)(2,3)(2,4)(2,9)(3,2)(3,3)(3,4)(3,9)(4,2)(4,3)(4,4)(4,9)(9,2)(9,3)(9,4)(9,9)We now filter these outcomes to find those with a product less than 20 and at least one even number:
(2,2) - Product: 4(2,3) - Product: 6(2,4) - Product: 8(3,2) - Product: 6(3,4) - Product: 12(4,2) - Product: 8(4,3) - Product: 12(4,4) - Product: 16The total number of outcomes that meet the criteria is 8.
A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 220 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
Answer:
* The largest area can be enclosed is 6050 feet²
Step-by-step explanation:
* Lets explain the situation to solve the problem
- There is a rectangular parking
- The parking will surrounded by fencing from three sides only
- The length of fencing is 220 feet
- Lets consider the width of the rectangle is x and the length of it is y
- The side along the street will not fence
* Lets put all of these data in equation
∵ The width of the parking is x
∵ The length of the parking is y
- He will not fence the side along the street
∴ The perimeter of the parking = x + y + x
∴ The perimeter of the parking = 2x + y
- The length of the fencing = the perimeter of the park
∵ The length of the fencing = 220 feet
∵ The perimeter of the parking = 2x + y
∴ 2x + y = 220 ⇒ (1)
- Lets find the area of the parking
∵ The area of any rectangle is length × width
∵ The width of the rectangle is x
∵ The length of the rectangle is y
∴ The area of the parking (A) = x × y
∴ The area of the parking = xy ⇒ (2)
- Lets find the value of y from equation (1) and substitute this value
in equation (2)
∵ 2x + y = 220 ⇒ subtract 2x from both sides
∴ y = 220 - 2x
- Substitute this value in equation (2)
∵ A = xy
∴ A = x(220 - 2x) ⇒ open the bracket
∴ A = 220x - 2x²
- To find the largest area differentiate the area with respect to x
and equate the result by 0 to find x which gives the largest area
∵ A = 220x - 2x²
- Lets remember the differentiation rules
# If y = a x^n, where a is the coefficient of x then dy/dx = (an) x^(n-1)
# If y = ax, then dy/dx = a
# If y = a, where a is constant then dy/dx = 0
∴ dA/dx = 220 - 2(2) x^(2-1)
∴ dA/dx = 220 - 4x
- Put dA/dx = 0 ⇒ for largest area
∵ dA/dx = 0
∴ 220 - 4x = 0 ⇒ add 4x to both sides
∴ 220 = 4x ⇒ divide both sides by 4
∴ 55 = x
* The width of the parking is 55 feet
- Substitute this value of x in the equation of the area to find the
largest area
∵ A = 220x - 2x²
∵ x = 55
∴ A = 220(55) - 2(55)² = 12100 - 6050 = 6050 feet²
* The largest area can be enclosed is 6050 feet²
To find the largest area that can be enclosed by the given amount of fencing, we can use the concept of optimization and solve for a rectangular lot's dimensions that maximize the area. The largest area that can be enclosed is 6050 square feet.
Explanation:
To find the largest area that can be enclosed, we can use the concept of optimization. Let's assume the length of the rectangular lot is x feet. The remaining length, which is not fenced, will be 220 - 2x feet. The width of the lot will be y feet. So we have 2x + y = 220. To find the largest area, we need to express the area in terms of a single variable. A = xy, substitute y = 220 - 2x. So A = x(220 - 2x) = 220x - 2x^2. To find the maximum value of A, we can find the vertex of the parabola, which corresponds to the maximum. The x-coordinate of the vertex is -b/2a. In this case, a = -2, b = 220, so x = -220/(-2*2) = 55.Plug this value of x into the equation y = 220 - 2x. y = 220 - 2(55) = 110. So the dimensions of the lot that will enclose the largest area are 55 feet by 110 feet. Substituting these values into the area formula A = xy, we get A = 55 * 110 = 6050 square feet.
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Use substitution to solve each system of equations. y = 4x + 22 4x – 6y = –32
(–5, 2)
(2, –5)
(–8, 1)
(4, 7)
Answer:
(-5,2)
Step-by-step explanation:
The given system is
1st equation: y = 4x + 22
2nd equation: 4x – 6y = –32
We plug in the first equation into the second equation to obtain:
4x – 6(4x + 22) = –32
We expand the parenthesis to obtain:
4x – 24x -132= –32
Group similar terms;
4x – 24x = –32+132
Combine similar terms
-20x =100
Divide both sides by -20
x =-5
Put x=-5 into the 1st equation
y = 4(-5) + 22
y=-20+22
y=2
The solution is:
(-5,2)
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) What is your decision regarding H0? Reject Do not reject What is the p-value? (Round your answer to 4 decimal places.) rev: 10_28_2017_QC_CS-107404 Next Visit question mapQuestion 2 of 4 Total 2 of 4 Prev
Answer:
15 million
Step-by-step explanation:
This is a one-tailed test with a significance level of 0.025. The test statistic is -1.83, and we reject the null hypothesis. The p-value is approximately 0.0344.
Explanation:This is a one-tailed test because the alternative hypothesis (H1) is specifying a less than condition (<) for the population mean.
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis (H0) if the test statistic is less than the critical value.
The test statistic is calculated by subtracting the hypothesized population mean from the sample mean and dividing by the standard deviation divided by the square root of the sample size. In this case, the test statistic is [(215 - 220) / (15 / sqrt(64))] = -1.83 (rounded to 3 decimal places).
In order to make a decision regarding H0, we compare the test statistic with the critical value. If the test statistic is less than the critical value, we reject H0. Otherwise, if the test statistic is greater than or equal to the critical value, we fail to reject H0. In this case, -1.83 is less than the critical value, so we reject H0.
The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. To find the p-value, we look up the test statistic in the standard normal distribution table. In this case, the p-value is approximately 0.0344 (rounded to 4 decimal places).
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Can someone help me with this math question?
Answer:
see attachment
Step-by-step explanation:
It is convenient to use a spreadsheet for this purpose.
The first row of numbers is constant at $45, as there is no daily charge associated with that payment method.
The second row of numbers uses the formula ...
cost = $12 + $4×(number of days)
The third row of numbers uses the formula ...
cost = $6×(number of days)
___
Of course, you can use these formulas to fill in the numbers by hand. For example, for 15 days, the charges are ...
Early Pay: $45 (no calculation necessary)Deposit Plus: $12 + $4×15 = $12 +60 = $72Daily Pay: $6×15 = $90A number is increased by 54. The sumos then divided by 9. The result is 21. Write an equation to represent the discription, use n for the number
Answer:
(n+54)/9 = 21
Step-by-step explanation:
A number: n
Is increased by 54: n+54
The sum is divided by 9: (n +54)/9
and the result is 21:
(n +54)/9 = 21
If f = {(4, 2), (6, 1), (8, 4), (10, 2), (12, 5)}, what is the range
Answer:
Range = {2,1,4,5}
Step-by-step explanation:
When a function is given in the form if a relation. i.e. ordered pairs.
When the function is given in the form of ordered pairs then the set of first elements i.e. x-coordinates of all ordered pairs forms domain while the set of second elements i.e. y-coordinate of all ordered pair is called range.
So in the given function:
Range = {2,1,4,5}
The repeating values are only written once..
Write the equation 9y = 12x + 0.2 in standard form. Identify A, B, and C.
Question 19 options:
45x – 60y = 1 where A = 45, B = –60, and C = –1
45x – 1y = 1 where A = 45, B = –60, and C = 1
60x + 45y = –1 where A = 60, B = 45, and C = 1
60x – 45y = –1 where A = 60, B = –45, and C = –1
Answer: D) 60x-45y = - 1 where A = 60 , B = -45 , and c = - 1
Step-by-step explanation: Clear it : 45y=60x+1
Step 2: Isolate the constant on one side: ( -1 = -45y +60x)
step 3: A= 60 , B= - 45 , C= - 1
Answer:
60x-45y = - 1 where A = 60 , B = -45 , and c = - 1
Step-by-step explanation:
In a class of 30 students 15 know Italian, 10 know French, and 3 know both languages. The rest of the students learn Spanish. How many students learn Spanish?
8 students know Spanish since 12 students know French and 7 students know Italian
Answer:
8 students learn Spanish.
Step-by-step explanation:
In a class total number of students are 30.
Students who know Italian = 15
Students who know French = 10
Students who know both = 3
Rest all students know Spanish.
By Venn diagram attached number of students who know Spanish
= [ 30 - (12 + 3 + 7 )]
= 30 - (22)
= 8 students.
8 students learn Spanish.
Emerson is making a box without a top from a rectangular piece of cardboard, with dimensions 12in by 16in, by cutting out square corners with side length x in.
A) Write an equation for the volume V of the box in terms of x.
B) Use technology to estimate the value of x that gives the greatest volume. Round the value to the nearest tenth.
C) Assume Emerson used the value of d you found in Part (b) to make his box. What were the dimensions of Emerson’s box?
Answer:
Step-by-step explanation:
The volume of a rectangular box is width times length times height:
V = wlh
After the cardboard is folded, the width is 12 - 2x, the length is 16 - 2x, and the height is x.
So the volume is:
V = (12 - 2x) (16 - 2x) x
If we graph this, we get a wave: desmos.com/calculator/rsjosgzuxz
The wave is the highest at around x = 2.3 in.
If we set x = 2.3:
w = 12 - 2x = 7.4
l = 16 - 2x = 11.4
h = x = 2.3
Mike wants to redesign a box. Currently, it’s length is 20 cm, it’s width is 30 cm and it’s height is 40cm. he wants to keep the volume and the length unchanged and increase the height by 25 percent. What will be the new width of the box?
Answer:
24 cm
Step-by-step explanation:
The product of height and width will remain the same, so the new width (w) will be given by ...
w·(new height) = (old width)·(old height)
w·(1.25·40 cm) = (30 cm)(40 cm)
w = (30 cm)/1.25 = 24 cm . . . . . . . divide by 1.25·40 cm and simplify
_____
This derives from the fact that volume and length are unchanged. The formula for the volume in terms of length, width, and height is ...
V = LWH
Then the product of W and H is the constant ...
V/L = WH . . . . . divide by L
For our purpose, we only need to know that V and L are unchanged, so the product WH is unchanged. We don't need to know their values.
Of course, increasing the height by 25% is equivalent to multiplying it by 1.25:
H + 25/100·H = H·(1 + 0.25) = 1.25H
A function in which each y value has more than one corresponding x value is called a
A: nonlinear function
B: many to one function
C one to one function
D linear function
For each Y value to have more than one x value would be a linear function.
It would make a straight line.
The correct answer is B: many-to-one function. This is the type of function where one y value is associated with multiple x values, differing from linear, nonlinear, and one-to-one functions.
A function in which each y value has more than one corresponding x value is known as a many-to-one function. This type of function allows for multiple x values to be paired with a single y value. This should not be confused with nonlinear functions or one-to-one functions. Moreover, while linear function is often associated with straight lines, in algebra, a linear function may actually include more than one term, each having a single multiplicative parameter. For example, y = ax + bx² is linear in this algebraic sense because terms x and x² each have one parameter (a and b). However, a function like y = [tex]x^b[/tex], where b is an exponent rather than a multiplicative parameter, is an example of a nonlinear function as it cannot be accurately described using linear regression.
The expression is the result of applying the change of base formula to a logarithmic expression.
Which could be the original expression?
x= 8 is the correct answer
Answer:
x = 8
Step-by-step explanation:
Given equation is,
[tex]log_5(10x-1)=log_5(9x+7)[/tex]
We know that,
[tex]log_a(b)=log_a(c)\implies b = c[/tex]
[tex]\implies 10x -1 = 9x + 7[/tex]
Subtracting 9x on both sides,
[tex]x - 1 = 7[/tex]
Adding 1 on both sides,
[tex]x = 8[/tex]
Hence, the solution would be x = 8
f(x)=4x2+8x-9 find and simplify f(2+x)
a. 23+x
b. 4x^2+8x-11
c. 4x^2+2x+23
d. 4x^2+24x+23
Answer:
d. 4x^2 +24x +23
Step-by-step explanation:
Evaluating polynomials is sometimes easier when they are written in Horner form:
f(x) = (4x +8)x -9
Substituting (x+2) for x, we have ...
f(x+2) = (4(x+2)+8)(x+2) -9
= (4x +16)(x +2) -9
= 4x^2 +24x +32 -9
= 4x^2 +24x +23 . . . . . matches choice D
_____
Alternative method
You can observe that the answer choices differ in the coefficient of the x-term. So, to make the correct selection, you only need to find the coefficient of the x-term. That will be the sum of coefficients of the x-terms in 4(x+2)^2 and 8(x+2). Those x-terms are 4·4x and 8x, so have a sum of (16+8)x = 24x. This matches choice D.
What is the average rate of change of the function over the interval x = 0 to x = 5?
f(x) = 2x^2 - 1
Enter your answer, as a fraction, in the box.
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2x^2-1\qquad \begin{cases} x_1=0\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(0)}{5-0} \\\\\\ \cfrac{[2(5)^2-1]~~-~~[2(0)^2-1]}{5}\implies \cfrac{50-(-1)}{5}\implies \cfrac{50+1}{5}\implies \cfrac{51}{5}\implies 10\frac{1}{5}[/tex]
Willie has 4 baseball caps. Two of the caps are blue. One of the caps is red and one is green. What fraction of the caps is blue?
Answer:
2/4
when simplified = 1/2
Your answer is 1/2
Step-by-step explanation:
Amt. of Baseball caps = 4
Blue caps = 2
which can be written as 2/4
when simplified 2/4 ÷ 2/2 = 1/2
Willie has 4 baseball caps, of which 2 are blue. To find the fraction of caps that are blue, divide the number of blue caps (2) by the total number of caps (4), resulting in a fraction of 1/2.
Explanation:Willie has 4 baseball caps in total, and 2 of those caps are blue. To determine what fraction of the caps is blue, you divide the number of blue caps by the total number of caps.
So, the calculation would be:
Number of blue caps = 2Total number of caps = 4Fraction of caps that are blue = Number of blue caps ÷ Total number of caps = 2 ÷ 4 = 1/2Therefore, the fraction of Willie's caps that are blue is 1/2, which means half of the caps are blue.
Solve for x. Geometry plz help
- The solution/answer is 10.
The two angles are Supplementary angles and need to eaual 1980 degrees.
x-2 + 5x +2 = 180
Simplify:
6x = 180
Divide both sides by 6:
x = 180 /6
x = 30
Last answer choice is 4,2
Help
Use the midpoint formula:
(-7,-4) (-1,8)
(-7 + -1) /2 , (-4 +8) /2
-8/2 , 4/2
Midpoint = (-4,2)
Eric deposited $9,033.00 into a new savings account that earns interest compounded monthly. After 11 months, the balance in the account was $10,230.00. What was the interest rate on the account?
Round your answer to the nearest tenth of a percent.
Dang that’s tuff I feel bad
etermine if the following statement is true or false. If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%. A. The statement is true because some women will have sitting knee heights that are outliers. B. The statement is false because the 95th percentile for men is greater than the 5th percentile for women. C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women. D. The statement is false because some women will have sitting knee heights that are outliers.
Answer:
C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women.
Step-by-step explanation:
We suspect relevant data is missing, including exactly what clearance the the statement is referring to. It would be nice to know where the various men's and women's percentiles lie.
We give the above answer on the basis of the assumption that the largest of men are always larger than the smallest of women.
Solve for x. x2 - 2x - 24 = 0 A. -4, -6 B. -4, 6 C. 2, -6 D. 4, 6 Reset Next
Answer:
B. -4, 6
Step-by-step explanation:
Given the quadratic equation;
x^2 - 2x - 24 = 0
we can determine the solution by first factoring the expression on the left hand side. We determine two numbers whose product is -24 and sum -2. By trial and error the two numbers are found to be;
-6 and 4
We replace the middle term, -2x, with these two values;
x^2 + 4x -6x -24 = 0
x(x+4) -6(x+4) = 0
(x-6)(x+4) = 0
x-6 = 0 or
x + 4 = 0
x = 6 or x = -4
Answer: the answer is B
Step-by-step explanation: -4 & 6 are both zeros of the function .
Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 30 feet long. The function y = 15 tan θ models the height of the triangular garden. What is the height of the triangle when θ = 30 ° ? What is the height of the triangle when θ = 40 ° ? Vance is considering using either θ = 30 ° or θ = 40 ° for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.
Answer:
Part 1) The height of the triangle when θ = 30° is equal to [tex]8.66\ ft[/tex]
Part 2) The height of the triangle when θ = 40° is equal to [tex]12.59\ ft[/tex]
Part 3) The area of triangle with θ = 30° is less than the area of triangle with θ = 40°
Step-by-step explanation:
Part 1) What is the height of the triangle when θ = 30 ° ?
we have
[tex]y=15tan(\theta)[/tex]
substitute the value of theta in the equation and find the height
[tex]y=15tan(30\°)=8.66\ ft[/tex]
Part 2) What is the height of the triangle when θ = 40 ° ?
we have
[tex]y=15tan(\theta)[/tex]
substitute the value of theta in the equation and find the height
[tex]y=15tan(40\°)=12.59\ ft[/tex]
Part 2) Vance is considering using either θ = 30 ° or θ = 40 ° for his garden
Compare the areas of the two possible gardens
step 1
Find the area when θ = 30 °
The height is [tex]8.66\ ft[/tex]
Remember that the area of a triangle is equal to the base multiplied by the height and divided by two
so
[tex]A=(1/2)(30)(8.66)=129.9\ ft^{2}[/tex]
step 2
Find the area when θ = 40°
The height is [tex]12.59\ ft[/tex]
Remember that the area of a triangle is equal to the base multiplied by the height and divided by two
so
[tex]A=(1/2)(30)(12.59)=188.85\ ft^{2}[/tex]
Compare the areas of the two possible gardens
The area of triangle with θ = 30° is less than the area of triangle with θ = 40°
Anyone who could help with this it would be amazingly appreciated.
The sum of angles in ΔABD is ...
2a + b + d = 180
The sum of angles in ΔAHG is ...
a + h + 90 = 180
Solving this second equation for a, we have ...
a = 180 -90 -h = 90 -h
Substituting this into the first equation, we have ...
2(90 -h) +b +d = 180
180 -2h +b +d = 180 . . . . . eliminate parentheses
b + d = 2h . . . . . . . . . . . . . add 2h-180
h = (1/2)(b+d) . . . . . . . . . . divide by 2