Answer:
Step-by-step explanation:
width = x
length= x + 5
a) x + 5
b) x * (x+5) = 300
x^2 + 5x = 300
x^2 + 5x - 300 = 0
Δ = 25 + 1200 = 1225
width = (-5 + 35)/2 = 15 cm
lenght = 15 + 5 = 20 cm
Answer:
a) length = x + 5
b) [tex]x^{2}[/tex] + 5x - 300 = 0
Step-by-step explanation:
x = width
x + 5 = length
(x)(x + 5) = 300
[tex]x^{2}[/tex] + 5x = 300
[tex]x^{2}[/tex] + 5x - 300 = 0
(x+20)(x-15)
x = -20 or x = 15 ( disregard the -20. measurements can't be negative)
width = 15
length = x+ 5 = 15+5 = 20
The angle θ between 5i-j+k & 2i-j+k is
Step-by-step explanation:
Let,
[tex] \sf \vec{a} = 5 \hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{a}| = \sqrt{ {5}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{25 + 1 + 1} \\ = \sqrt{27} \\ \\ \sf \vec{b} = 2\hat{i} - \hat{j} + \hat{k} \\ \therefore \: \sf \: | \vec{b}| = \sqrt{ {2}^{2} + {( - 1)}^{2} + {1}^{2} } \\ = \sqrt{4 + 1 + 1} \\ = \sqrt{6} \\ \\\sf \: \vec{a}. \vec{b} = (5 \hat{i} - \hat{j} + \hat{k}).(2\hat{i} - \hat{j} + \hat{k}) \\ = 5 \times 2 + ( - 1) \times ( - 1) + 1 \times 1 \\ = 10 + 1 + 1 \\ = 12 \\ \\ \sf \: angle \: between \: \vec{a} \: and \: \vec{b} \: = \theta \\ \\ \: so \\ \sf \vec{a}. \vec{b} = | \vec{a}| . | \vec{b}| cos\theta \\ = > \sf \: cos \theta \: = \frac{ \vec{a}. \vec{b}}{ | \vec{a}| . | \vec{b}| } \\ = > cos \theta = \frac{12}{ \sqrt{27} \times \sqrt{6} } = 0.94 \\ = > \theta = {cos}^{ - 1} (0.94) \\ = > \green{\theta = 19.47 ^{ \circ} }[/tex]
solve the following ineuality -1+6(-1-3x) >-39-2x
Step-by-step explanation:
(=) 5 (-1-3x) >-39-2x
(=) -5-15x > -39-2x
(=) -13x > -34
=> x < 34/13
Divide p(x)=x^3-4x^2+x+6 by (x-3). Find the remainder and the quotient.
Answer:
Quotient is x² - x - 2
Remainder is 0
find the derivative of e power ax divide by log bx
Answer:
Step-by-step explanation:
-1/5y+7=7
What is the value of y?
The sides of a triangle are in the ratio of 4:5:7 and its perimeter is 64. Find its sides
Answer:
16,20,28
Step-by-step explanation:
64 /(4+5+7)
64/16= 4
sides of triangle=4×4 :5×4: 7×4
=16:20:28
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
find the solution to the system of equations.
y= -7x + 3
y= -x - 3
Answer:
x = 1 y = -4
Step-by-step explanation:
-7x + 3 = -x - 3
-7x = -x - 6
-6x = -6
x = 1
y = - (1) - 3
y = -1 - 3
y = -4
On a recent trip to the convenience Store you picked up 4 gallons of milk 4 bottles of water and 5 snack size bags of chips your total was $28.35 if a bottle of water cost twice as much as a bag of chips and a gallon of milk cost $2.10 more than a bottle of water how much does each item cost
Answer:
The milk cost $2.10 each the snacks cost $1.535 each the water cost $3.07 each
Step-by-step explanation:
I think Im right
A local school board member randomly sampled private and public high school teachers in his district to compare the proportions of National Board Certified (NBC) teachers in the faculty. The results were:
Answer:
0.025 ;
(-0.7198 ; 0.7698)
Step-by-step explanation:
From the table :
_____________ private schls ___ public schls
Sample size, n _____ 80 __________ 520
P, NBC teachers ___ 0.175 ________ 0.150
P1 = P of private school teachers
P2 = P of public school teachers
Difference in proportion :
P1 - P12 = 0.175 - 0.150.= 0.025
The 90% confidence interval for 2 - sample proportion :
C.I = (p1-p2) ± [Zcritical * √(p1(1-p1)/n1 + (p2(1-p2)/n2)]
Zcritical at 90% = 1.645
C.I = 0.025 ± [1.645 * √((0.175*0.825)/80 + (0.150*0.850)/520)]
C.I = 0.025 ± [1.645 * √(0.0018046875 + 0.0002451)]
C.I = 0.025 ± 1.645 * 0.0452755
C.I = 0.025 ± 0.07448
C.I = (-0.7198 ; 0.7698)
If P is (-5, 4) and Q is (7, -5), what is 2/3 of that?
Answer: 10
Step-by-step explanation:
Sqrt (7- -5)^2+(-5-4)^2 =
Sqrt (12)^2+(-9)^2 =
Sqrt 225 = 15
2/3 * 15 = 30/3 = 10
The sum of four
consecutive odd number is 8o. Find the number
Answer:
The sum of 4 consecutive odd number is 80
Let X be the first of these numbers
Then the next odd number is X+2
The third is X+4The fourth is X+6
All of these add up to 80
(X) + (X+2) + (X+4) + (X+6) = 80
Using the commutative and associative laws, let's transform this equation into
(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80
Subtract 12 from both sides of the equation gives4X = 68
Divide both sides by 4 gives
X = 17
Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!
Power Function:
Analyze and model the power function: Exercise 1
(Correctly identify the function and later use it to answer the questions asked, including the development and the answer)
Answer:
The function is:
f(x) = axⁿAccording to data in the table we have:
f(1) = 3 ⇒ a(1)ⁿ = 3 ⇒ a*1 = 3 ⇒ a = 3f(2) = 12 ⇒ 3*2ⁿ = 12 ⇒ 2ⁿ = 4 ⇒ n = 2Since we found the values of a and n, the function becomes:
f(x) = 3x²The number of infected to the tenth day:
f(10) = 3*10² = 300The distance from the plane to the building __ meters
Answer:
1200 ×90÷8 is not correct ans
What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
If a person invested half of her money at 9% and half at 7% and received $160 interest, find the total amount of money invested.
Answer:
$2000
Step-by-step explanation:
let x be the money she invested
lets assume this was for 1 year
0.09(x/2) + 0.07(x/2) = 160
multiply each side by 2 to cancel the denominators:
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Answer: $2000
Let the amount of money she invested be x
Lets assume the time of investment as 1 year
ATQ
0.09(x/2) + 0.07(x/2) = 160
0.09x + 0.07x = 320
0.16x = 320
x = 2000
Must click thanks and mark brainliest
Is the relationship shown by the data linear? If so, model the data with an equation.
Answer:
4th option
Step-by-step explanation:
The relationship is linear,
putting the value of x in the right side of the equation of option 4, you'll get the value of the left side
putting, x=1
y+4=-1/2(x-1)
y=-1/2(1-1)-4
y=-4
putting, x=7
y+4=-1/2(7-1)
y=-1/2(6)-4
y=-6/2-4
y=-3-4
y=-7
Of the travelers arriving at a small airport, 60% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 50% are traveling for business reasons, whereas 70% of those arriving on private planes and 80% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.
What is the probability that the person
a. is traveling on business?
b. is traveling for business on a privately owned plane?
c. arrived on a privately owned plane, given that the person is traveling for business reasons?
d. is traveling on business, given that the person is flying on a commercially owned plane?
Answer:
a) 0.55 = 55% probability that the person is traveling on business
b) 0.14 = 14% probability that the person is traveling for business on a privately owned plane.
c) 0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
d) 0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
50% of 60%(major airlines)
70% of 20%(privately owned airplanes)
80% of 100 - (60+20) = 20%(comercially owned airplanes). So
[tex]p = 0.5*0.5 + 0.7*0.2 + 0.8*0.2 = 0.55[/tex]
0.55 = 55% probability that the person is traveling on business.
Question b:
70% of 20%, so:
[tex]p = 0.7*0.2 = 0.14[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
Question c:
Event A: Traveling for business reasons.
Event B: Privately owned plane.
0.55 = 55% probability that the person is traveling on business.
This means that [tex]P(A) = 0.55[/tex]
0.14 = 14% probability that the person is traveling for business on a privately owned plane.
This means that [tex]P(A \cap B) = 0.14[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.55} = 0.2545[/tex]
0.2545 = 25.45% probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons.
Question d:
Event A: Commercially owned plane.
Event B: Business
80% of those arriving on other commercially owned planes are traveling for business reasons.
This means that:
[tex]P(B|A) = 0.2[/tex]
0.2 = 20% probability that the person is traveling on business, given that the person is flying on a commercially owned plane.
What is the distance between the following points?
y
+
+++ 3
1 2 3 4 5 6 7 8 9
.
-27
-3+
-4
-5+
-6
-7
-8
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
Answer:
8.49 or 6√2
Step-by-step explanation:
Use the distance formula to calculate the distance between the two points. The distance formula is √(x1-x2)^2+(y1-y2)^2 plug in (2,-3) and (8,-9) to get the solution of √72 or 8.49
Square root 1.000441
Answer: 1.00022048
Step-by-step explanation:
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
3a + 2b = 9
and
8x + y = 60
(i) What is the value of 9a + 6b?
(ii) What is the value of 4x + 3y?
Answer:
i dont kbow lol gggggggggg
HELP PLEASE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please?
Answer:
46%
Step-by-step explanation:
Divde the smaller # by the bigger # to get the precentage
An average San Francisco customer uses what percent of electricity used by an average Houston customer?
In other words, San Francisco is what part of Houston?
---Just like, 7 is what part of 49? These are the same questions and would be solved in the same way
San Francisco / Houston
6753 / 14542
0.4644 = 46.44%
ANSWER: 46%
Hope this helps!
Solve d – 0.31 ≥ 1.87 Question 1 options: A) d ≤ 2.18 B) d = 2.18 C) d ≥ 1.56 D) d ≥ 2.18
Answer:
D) d ≥ 2.18
Step-by-step explanation:
d – 0.31 ≥ 1.87
d >_ 1.87 + 0.31
d >_ 2.18
A line is perpendicular to the line y = 4x - 3 and has x-intercept (2,0). Which of the following is an equation of the line?
Answer:
y = -1/4x+1/2
Step-by-step explanation:
y = 4x - 3
This is in slope intercept form, y = mx+b where the slope is m
The slope is 4
Perpendicular lines have slopes that are negative reciprocals
-1/4 is the slope of the perpendicular line
y = -1/4x+b
Using the point (2,0)
0 = -1/4(2)+b
0 = -1/2+b
b = 1/2
y = -1/4x+1/2
Please help! Thank you.
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
What fraction is equivalent to 0.46464646...
A)
46∕999
B)
46∕99
C)
23∕50
D)
46∕100
Answer:
Hello,
answer is B
Step-by-step explanation:
[tex]0.\overline{46}=\dfrac{46}{99}[/tex]
The answer is a fraction with numerator is the period (46) and the denominator is a number made with 9 as longer that there are digits in the periode (here 2 digits ==> 99)
Which equation can she use as statement 5? 60:x = 48:(48 + 36) 60 + x = 48 + 36 60 − x = 48 − 36 60:(60 + x) = 48:(48 + 36)
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
Which of the following pairs of functions are inverses of each other?
A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x -9 and g(x)=x+9/2
C. f(x) = 3-6 and g(x)=x+6/2
D. f(x)= x/3+4 and g(x) = 3x - 4
The pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
To determine if two functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.
Let's analyze the given options:
A. f(x) = 5 + x and g(x) = 5 - x
To check if they are inverses, we compute f(g(x)) = f(5 - x) = 5 + (5 - x) = 10 - x, which is not equal to x. Similarly, g(f(x)) = g(5 + x) = 5 - (5 + x) = -x, which is also not equal to x. Therefore, these functions are not inverses.
B. f(x) = 2x - 9 and g(x) = x + 9/2
By calculating f(g(x)) and g(f(x)), we find that f(g(x)) = x and g(f(x)) = x, which means these functions are inverses of each other.
C. f(x) = 3 - 6 and g(x) = x + 6/2
Similar to option A, we compute f(g(x)) and g(f(x)), and find that they are not equal to x. Hence, these functions are not inverses.
D. f(x) = x/3 + 4 and g(x) = 3x - 4
After evaluating f(g(x)) and g(f(x)), we see that f(g(x)) = x and g(f(x)) = x. Therefore, these functions are inverses of each other.
In summary, the pair of functions that are inverses of each other is B. f(x) = 2x - 9 and g(x) = x + 9/2.
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