Answer:
Speed of current = 5 mph
Step-by-step explanation:
Let u be the speed of boat and v be the speed of current.
A boat makes a 120-mile trip downstream in 3 hours.
120 = 3(u+v)
u + v = 40
It makes the return trip in 4 hours.
120 = 4(u-v)
u - v= 30
Adding both equations
u + v + u - v = 40+30
2u = 70
u = 35 mph
35 + v = 40
v = 5 mph
Speed of current = 5 mph
5x+4x2(2x+7)-6x2-9x+(x+3)(x-8)
Write this expression as a polynomial in standard form
Which statement describes similar figures?
two figures that are the same size
two figures that are the same size but a different shape
two figures that are the same shape but different sizes
none of the above
What would be an appropriate measure to describe the amount of water in a puddle?
milliliters
feet
tons
miles
Answer:
milliliters
Step-by-step explanation:
Suppose f(x) = x2 and g(x) = 4x2. Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) vertically compressed by a factor of 4.
B. The graph of g(x) is the graph of f(x) horizontally stretched by a factor of 4.
C. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 4.
D. The graph of g(x) is the graph of f(x) shifted 4 units left.
If y = 15 when X=12 find Y when X=32
By acknowledging the linear relationship between X and Y, we set up a proportion based on the given values and solve for Y when X = 32, finding Y approximately equals 40.
Explanation:This problem relates to the concept of
linear relationships
in mathematics. By understanding the relationship between two variables x and y, you can find the value of one by knowing the value of the other. Here, if y = 15 when X = 12, we can say that the ratio of y to x is constant. Therefore to find the value of Y when X = 32, we will maintain the same ratio. Now, set up a proportion 15/12 = Y/32 and solve for Y. Cross-multiplication gives us: Y = 15 * 32 / 12. After calculating this, Y equals approximately 40. Therefore, the value of Y when X is 32 will be around 40, keeping the relationship linear.
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the first side of a triangle is 3 m shorter than the second side. the third side is 4 times as long as the first side . the perimeter is 27 m. find the length of each side
Given: ∆ABC, AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
m∠ABC = 48°
Find: m∠PCD
Answer: The measure of angle PCD is 42 degree.
Explanation:
It is given that in ∆ABC,
AB = CB
BD − altitude to AC
P ∈ BD, PB = PC
∠ABC = 48°
Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.
According to the angle sum property the the sum of interior angles of a triangle is 180.
[tex]\angle ABC+\angle BAC+\angle BCA=180^{\circ}[/tex]
[tex]48^{\circ}+2\angle BAC=180^{\circ}[/tex]
[tex]\angle BAC=66^{\circ}[/tex]
The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.
[tex]\angle PBC=\frac{48}{2}=24^{\circ}[/tex]
Since PB=PC , so triangle BPC is an isosceles triangle.
[tex]\angle PBC=\angle PCB=24^{\circ}[/tex]
From the figure it is noticed that,
[tex]\angle PCD+\angle PCB=\angle BCA[/tex]
[tex]\angle PCD+24^{\circ}=66^{\circ}[/tex]
[tex]\angle PCD=66^{\circ}-24^{\circ}[/tex]
[tex]\angle PCD=42^{\circ}[/tex]
Therefore, the measure of angle PCD is 42 degree.
Use the Pythagorean Theorem to find the missing measure when a = 24 and b = 7.
If you travel 156 miles on 4 gallons of gasoline how far can you travel on 12 gallons how many miles on 6 gallons
You can travel a distance of 468 miles on 12 gallons of gasoline and a distance of 234 miles on 6 gallons of gasoline.
What is Proportion?Proportion is the setting of two or more ratios to be equal.
That is, if there is a ratio between a and b and another ratio between c and d, then we can say that,
a : b = c : d ⇒ a/b = c/d ⇒ a d = b c
We have,
Distance travelled is 156 miles on 4 gallons of gasoline.
We have to find the distance travelled on 12 gallons and 6 gallons of gasoline.
Let x be the distance travelled on 12 gallons of gasoline and y be the distance travelled on 6 gallons of gasoline.
We have a proportional relation here,
156 : 4 = x : 12 = y : 6
First taking the relation,
156 : 4 = x : 12
⇒ 156/4 = x/12
⇒ 39 = x/12
⇒ x = 39 × 12
⇒ x = 468
Taking the second relation,
156 : 4 = y : 6
⇒ 156/4 = y/6
⇒ 39 = y/6
⇒ y = 39 × 6
⇒ y = 234
Hence you can travel 468 miles on 12 gallons and 234 miles on 6 gallons.
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Triangle ABC is similar to triangle PQR, as shown below:
Which ratio is equal to r:c?
A. c:p
B. p:a
C. r:a
D. q:c
rotate the triangles so r and c line up
when you do that Q=B, a=p, C=R, b=q, A=P
so answer would be B. p:a
we know that
If triangle ABC is similar to triangle PQR
then
the corresponding sides are proportional
so
[tex]\frac{RQ}{CB} =\frac{RP}{AC}= \frac{PQ}{AB}[/tex]
substitute the values
[tex]\frac{p}{a} =\frac{q}{b}= \frac{r}{c}[/tex]
therefore
[tex]\frac{r}{c}[/tex]
is equal to
[tex]\frac{q}{b}[/tex] and [tex]\frac{p}{a}[/tex]
the answer is the option B
[tex]\frac{p}{a}[/tex]
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answer:Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.
Step-by-step explanation:
Introduction to addition or subtraction of fractions with different denominator 3/4-1/8
Tori computers the value of 8 • 95 in her head by thinking 8(100 - 5)= 8•100 - 8•5 which number property is she using ?
Which of the following would eliminate the variable on the left side of the given equation?
36 - 19w = -6w + 41
A.) add -19w
B.) add 6w
C.) add 19w
D.) add -36
n is the set of real number that are factors of 36
The volumes of the two solids are equal, and the cross sections shown are taken at the same height above the bases. Find the missing length of the cross section of the rectangular pyramid. Round your answer to the nearest hundredth.
A. 1.59m
B. 1.62m
C. 1.67m
D. 1.76m
HELP!
Solve for x.
−1/3x≤−6
Enter the solution to the inequality in the box.
Answer:
x [tex]\geq[/tex] 18
Step-by-step explanation:
A clothing store owner tracks the amount of money the last 10 customers spend in her store. The owner concludes that the typical amount spent by any customer is $28.80. The owner's conclusion
A) is valid. The last 10 customers only bought sale items.
B) is correct. This is the average amount spent by any customer.
C) is invalid. This is not a good representation of all customers.
D) is unfair. The last ten people in the store may have been tired.
An equilateral triangle has a perimeter of 3x+9. what is the length of each side of the triangle
Which number is not in scientific notation?
a. 1.1 x 10^213
b. 7.8 x 10^8
c. 3.02 x 10^-10
d. 35 x 10^4
Maria was given a 5% raise on her weekly salary of $375.
Select from the drop-down menu to correctly complete the sentence.
A. 0.005(400)
B. 0.05(400)
C. 0.5(400)
D. 5(400)
Please explain your answer so I can understand it Thanks!
In a company, it takes 4 employees 4 days to complete a task. It would take 2 employees 8 days to complete the same task. Which function can be used to represent e, the number of employees working on the task, and d, the number of days it takes them to complete that task?
The function representing the relationship between the number of employees and the number of days it takes to complete the task is[tex]\[ e \times d = 16 \][/tex].
To represent the relationship between the number of employees (e) and the number of days (d) it takes to complete a task, we can use the formula:
[tex]\[ e \times d = k \][/tex]
where k is a constant representing the amount of work to be done.
Given the information that 4 employees complete the task in 4 days, and 2 employees complete it in 8 days, we can set up two equations using the formula:
[tex]\[ 4 \times 4 = k \][/tex]
[tex]\[ 2 \times 8 = k \][/tex]
Now, solve each equation for ( k):
[tex]\[ 4 \times 4 = 16 \][/tex]
[tex]\[ 2 \times 8 = 16 \][/tex]
Since both equations give us the same constant ( k ), we can conclude that:
[tex]\[ e \times d = 16 \][/tex]
Therefore, the function representing the relationship between the number of employees and the number of days it takes to complete the task is:
[tex]\[ e \times d = 16 \][/tex]
Factor this polynomial expression. x2 – 18x + 81
Factorizing the polynomial expression x² - 18x + 81 = (x - 9)²
What is factorization?Factorization is the simplification of an expression into a smaller expression using its factors.
To factor this polynomial expression. x² - 18x + 81, we proceed as follows
Since we have the polynomial expression x² - 18x + 81, we multiply x² by 81 to get x² × 81 = 81x².
Now, we look for the factors of 81x² such that the sum of those factors equal - 18x
So, we have that 81x² = -9x × (-9x)
So, -18x = -9x - 9x
So, replacing this with -18x, we have that
x² - 18x + 81 = x² - 9x - 9x + 81
Now, factorizing, we have that
x² - 9x - 9x + 81 = x(x - 9) - 9(x - 9)
= (x - 9)(x - 9)
= (x - 9)²
So, factorizing x² - 18x + 81 = (x - 9)².
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Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
(−6, 0)
(−1, −2)
(−5, −1)
(−16, 2)
(0, −3)
Answer:
(−6, 0) , (−1, −2) and (−5, −1)
Step-by-step explanation:
The given inequality is x+3y ≥ −8
Substitute all the given points in this inequality and check which points satisfy.
For (−6, 0)
-6+3(0) ≥ −8
- 6 + 0 ≥ −8
- 6 ≥ −8 => True.
Hence, (−6, 0) is a solution.
For (−1, −2)
-1 + 3(-2) ≥ −8
-1 - 6 ≥ −8
- 7 ≥ −8 => True.
Hence, (−1, −2) is a solution.
For (−5, −1)
-5 + 3 (-1) ≥ −8
- 5 -3 ≥ −8
-8 ≥ −8=> True.
Hence, (−5, −1) is a solution.
For (−16, 2)
-16 +3 (2) ≥ −8
-16 + 6 ≥ −8
-10≥ −8 => False.
Hence,(−16, 2) is not a solution.
For (0, -3)
0 + 3(-3) ≥ −8
-9 ≥ −8=> False.
Hence, (0, -3) is not a solution.
Therefore, below ordered pairs are solutions of the given inequality
(−6, 0) , (−1, −2) and (−5, −1)
At the annual dogs show chantel noticed that there were three more Scottie’s than schnauzers. She also realized that the number of wire haired terriers was five less than twice the number of schnauzers if there were 78 dogs in all how many schnauzers were their?
Factor 9y 2 - 12y + 4.
Answer:
Factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
Step-by-step explanation:
As the expression is given in the question be .
= 9y² - 12y + 4
Simplify the above
= 9y² -6y -6y + 4
= 3y (3y -2) -2 (3y - 2)
= (3y-2)(3y-2)
Therefore factors of the expression given in the question i.e 9y² - 12y + 4 is (3y -2)(3y -2) .
What percent of 67.5 is 7.02 ? Answer in proportions
The percent of 67.5 is equal to 7.02 is for the number 10.4.
To find what percent of 67.5 is 7.02, we can use proportions.
Let's represent the unknown percentage as 'x'. The proportion can be set up as follows:
(7.02 / 67.5) = (x / 100)
Now, solve for 'x':
7.02 × 100 = 67.5 × x
702 = 67.5x
x = 702 / 67.5
x ≈ 10.4
Therefore, 7.02 is approximately 10.4 percent of 67.5.
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Hannah bought a jacket on sale for 20% off. The jacket originally costs $48. How much money did Hannah save by buying the jacket on sale?
$9.60
$2.00
$4.40
$10.30
Denis and Dasha solve this problem in two different ways. The perimeter of a rectangle is 54 centimeters. Its length is 6 centimeters. What is its width? Use the drop-down menus to complete the sentences below.
Final answer:
To find the width of a rectangle with a perimeter of 54 cm and a length of 6 cm, use the formula P = 2l + 2w. After plugging in the given values and simplifying, the width is calculated to be 21 cm.
Explanation:
Finding the Width of a Rectangle
To solve this problem, we remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given the perimeter is 54 centimeters and the length is 6 centimeters, we can set up the equation as follows: 54 = 2(6) + 2w. Simplifying this, we get 54 = 12 + 2w, and then subtracting 12 from both sides gives us 42 = 2w. Dividing both sides by 2, we find the width w to be 21 centimeters.
Step-by-Step Calculation
Start with the formula for the perimeter of a rectangle: P = 2l + 2w.Substitute the given values into the formula: 54 = 2(6) + 2w.Simplify the equation: 54 = 12 + 2w.Isolate the width term: 42 = 2w.Divide both sides by 2 to solve for the width: w = 21.Therefore, the width of the rectangle is 21 centimeters.
For a right triangle with an altitude of 12 and a base of 16, find the length of the hypotenuse.