The speed of the current in a certain stream is 6 mph. If a boat travels 94 miles
downstream in the same time that it takes to travel 47 miles upstream, which best
describes the speed of the boat in still water?
The speed of the boat in still water is 18 mph.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know distance = speed×time.
Therefore, time = distance/speed.
Let, The speed of the boat at still water be 'x'.
Therefore, From the information,
94/(x + 6) = 47/(x - 6).
94(x - 6) = 47(x + 6).
94x - 564 = 47x 282.
47x = 846.
x = 18.
So, The speed of the boat is 18 mph in still water.
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on a number line point D is at -6 and point E is at 8 point F lies between points D and E if DF:FE is 3:1 where does point F lie on the number line
The point F lies on 4.5 in the number line.
Number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.
Here in the give problem that,
Point D lies on -6 in number line
Point E lies on 8 in number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence the point F lies on 4.5 in the number line.
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Answer: 4.5
Step-by-step explanation:
The graph represents the piecewise function
The piece-wise function is defined as follows:
[tex]f(x) = x^2, 0 \leq x < 3[/tex].[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex].[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex].What is a piece-wise function?A piece-wise function is a function that has multiple definitions, depending on the input.
In this graph, for x at least 0 and less than 3, the parabolic curve passes through (0,0), (1,1), (2,4) and has an open interval at (3,9), hence the definition is:
[tex]f(x) = x^2, 0 \leq x < 3[/tex]
For x greater than 3 and at most 6, it is a line going through (3,9) and (6,4), hence:
[tex]m = \frac{9 - 4}{3 - 6} = -\frac{5}{3}[/tex]
[tex]f(x) = -\frac{5}{3}x + b[/tex]
Goes through (3,9), hence:
[tex]9 = -\frac{5}{3}(3) + b[/tex]
b = 14.
So
[tex]f(x) = -\frac{5}{3}x + 14, 3 < x \leq 6[/tex]
For x between 6 and 10, it is a line going through (6,4) and (10,10), hence:
[tex]m = \frac{10 - 4}{10 - 6} = \frac{6}{4} = \frac{3}{2}[/tex]
Then:
[tex]f(x) = \frac{3}{2}x + b[/tex]
When x = 10, f(x) = 10, hence:
[tex]10 = \frac{3}{2}(10) + b[/tex]
10 = 15 + b
b = -5.
Hence:
[tex]f(x) = \frac{3}{2}x - 5, 6 \leq x \leq 10[/tex]
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value of in the equation a=2+3+10
[tex]\huge{\boxed{\mathfrak{ANSWER}}} [/tex]
[tex]a=2+3+10[/tex]
[tex]a = 15 [/tex]
[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]
Find the value of x, given that the two triangles are similar.
Answer:
10.5 is the correct answer.
Step-by-step explanation:
Due to the fact Triangle CAB has "6" as its length, and Triangle FDE has "2" as its length, you multiply 3.5 and 3.
3.5 x 3=10.5
2 x 3=6
3.5/2=10.5/6, so the answer is 10.5.
Answer:
x = 10.5 cmStep-by-step explanation:
Find the value of x, given that the two triangles are similar.
Given that the two triangles are similar we can solve with a proportion
6 : 2 = x : 3.5
x = 6 * 3.5 : 2
x = 21 : 2
x = 10.5
jackie brought 9 plants
Answer:
I think its the thrid one because it is the only one with the correct top equation(I can't see the rest)
Step-by-step explanation:
Need the answer to the question
Angelina's family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and
hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
A. The ordered pair (-3, 6) is viable.
B. The ordered pair (7, 2) is viable.
C. The ordered pair (15,-7) is viable.
D. The ordered pair (18,3) in non viable
The ordered pair (7,2) is viable and Option B is the correct answer.
What is Relationship ?Relationship between variables defines the way one variable is dependent upon the other variable.
It is given that x is the number of visitors and y is the number of winners,
It has to be seen and chosen that which ordered pair makes sense
The ordered pair is viable if the no. of visitor is positive and more than the number of winners.
Therefore ordered pair (7,2) is viable and Option B is the correct answer.
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Name
Two-Variable Statistics
Relationship between Two Categorical Variables - Marginal and Joint Relative Frequency -
Part 2
Warm Up
Complete the table and calculate the percent for each total.
The completed table is given below,
the percentage of girls in the class is 47.62%,
the percentage of boys in the class is (100-47.62)% = 52.38%,
the percentage of students that love Math is 36.5%,
the percentage of students that love Reading is 22%, and
the percentage of students that love Science is 41.27%
To make comparison and statistical analysis easier, numerical data is systematically and logically represented in tabulations as rows and columns. Grouping relevant data together makes comparison easier and aids in statistical analysis and interpretation.
To put it another way, tabulation is the process of organizing data and presenting it in a tabular format. Depending on the type of categorization, it might be double, complicated, or simple.
The below table yields that
The total number of students is 315
The fraction of girls in the class is 150/315 = 0.4762
So, the percentage of girls in the class is 47.62%
Hence the percentage of boys in the class is (100-47.62)% = 52.38%
The fraction of students that love Math is 115/315 = 0.365
So, the percentage of students that love Math is 36.5%
The fraction of students that love Reading is 70/315 = 0.22
So, the percentage of students that love Reading is 22%
The fraction of students that love Science is 130/315 = 0.4127
So, the percentage of students that love Science is 41.27%
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the equation that represents the canned goods order is 24x+64y=384
x= number of minutes fruit cans
y= number minutes of for vegetable cans
explain how to calculate the x- and y- intercepts
The x-intercept is (16, 0) and y- intercept is (0, 6).
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given: 24x+64y=384
For y- intercept, put x=0
Then,
24*0+64y=384
64y= 384
y= 6
Now, for x- intercept put y=0
Then,
24x+64*0=384
24x= 384
x= 15
Hence, the x-intercept is (16, 0) and y- intercept is (0, 6).
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Answer:
Sample Answer: Substitute 0 for the x-value in the equation and solve for y. The result is y = 6, so the y-intercept is at (0, 6). Next, substitute 0 for the y-value in the equation and solve for x. The result is x = 16, so the x-intercept is at (16, 0).
Step-by-step explanation:
Given the function f(x) = −5x2 − x + 20, find f(3).
HELP ASAP/NOW....NO LINKS OR JOKING
for which value of x is F(x)=0
A. 3
B. -5
C. -3
D. -6
Answer:
D) -6
Explanation:
f(x) = 0 suggests the x value which will make the function zero.
Find slope:
⇒ (y₂ - y₁)/(x₂-x₁)
⇒ (2 - 1)/(-2-(-4))
⇒ 1/2
Equation:
⇒ y - 2 = 1/2(x - (-2))
⇒ y = x/2 + 3
f(x) = x/2 + 3If f(x) = 0
x/2 + 3 = 0
x/2 = -3
x = -6
Keri did jumping jacks for ⅗ of a minute and sit-ups for ½ a minute. How many more seconds did Keri do jumping jacks than sit-ups?
PLS HELP AND HURRY
Answer:
so we need to subtract the situps from the jumping jack so
3/5-1/2
first we need to simplify to the same bottom number
6/10=3/5
5/10=1/2
6/10-5/10=1/10
so 1/10 of 60 is
1/10*60=6
Hope This Helps!!!
What is the solution to this equation?
8x-5(x-3) = 18
OA. x=5
OB. x = 1
OC. x = 11
OD. x=7
Answer:
x=1
Step-by-step explanation:
8x-5(x-3) = 18
The first step is to distribute
8x -5x+15 = 18
Combine like terms
3x+15 = 18
Subtract 15 from each side
3x+15-15=18-15
3x=3
Divide by 3
3x/3 =3/3
x=1
Find the equation of the line in slope-intercept form containing the points (6, -1) and (-3, 2).
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y= - \cfrac{x}{ 3} + 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Equation of line (two point form) :
[tex]\qquad \tt \rightarrow \: (y - y_1) = \cfrac{y _1- y_2}{ x_1 - x_2} (x - x_1)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = \cfrac{2 - ( - 1)}{ - 3 - 6} (x - ( - 3))[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = \cfrac{2 + 1}{ - 9} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = - \cfrac{3}{ 9} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: (y - 2) = - \cfrac{1}{ 3} (x + 3)[/tex]
[tex]\qquad \tt \rightarrow \: y - 2= - \cfrac{x}{ 3} - \cfrac{3}{3} [/tex]
[tex]\qquad \tt \rightarrow \: y = - \cfrac{x}{ 3} - 1 \cfrac{}{} + 2[/tex]
[tex]\qquad \tt \rightarrow \: y = - \cfrac{x}{ 3} + 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
wich calculation can be used to find the value of p in the equation p^3=8
Answer:
The answer is 2
p³ = 8
p = ³√8
p = 2.
For the graph below, what should the domain be so that the function is at least 300? (1 point) graph of y equals minus 2 times the square of x plus 50 times x plus 300 a x ≥ 0 b −5 ≤ x ≤ 30 c 0 ≤ x ≤ 25 d all real numbers
The function is a quadratic function, then the domain will be all real numbers. Then the correct option is D.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The function is given below.
y = -2x² + 50x + 300
Then the function is a quadratic function, then the domain will be all real numbers.
Then the correct option is D.
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if x = 5 and y = 2 , work out the value of a) 3x+y b) 2x squared c) ( x-y) 2 squared out of the brackets
Answer:
a) 17
b) 50
c) 6
Step-by-step explanation:
a) 3x+y
3(5)+2
15+2
17
b) 2x²= 2×5²
2×25
50
c) (x-y)2= (5-2)2
(3)2
3×2
6
Solve the system of equations: 3x + 6y=6 and 2y - 3x = 6.
Answer:
x = -1, y = 1.5
Step-by-step explanation:
3x + 6y = 6 -----> x + 2y = 2
-3x + 2y = 6 -----> -3x + 2y = 6
------------------
4x = -4
x = -1, y = 1.5
PLEASE HELP ME WITH THIS ASAP
What is the value of 8+ h² when h = 3?
Answer:
17
Step-by-step explanation:
8 + h^2
Let h = 3
8 + 3^2
We find the value of 3^2 first using PEMDAS
8 + 9
Then add
17
The result is 17
Solution: 17
Detailed explanation:
[tex]\circ[/tex] Stick in the value of h, which we're provided with (3)
[tex]--\mapsto\boldsymbol{8+(3)^2}[/tex] *
*Be careful here! Here it's very easy to make a mistake, if you aren't familiar with the Order of Operations. The Order of Operations is shown below [tex]\swarrow[/tex]
P=Parentheses
This operation tells us to perform the operations in the parentheses first.
E=Exponents
This one tells us to evaluate all exponents, if any are present.
M=Multiplication | D=Division
These two are completely interchangeable; you can perform Multiplication first and then division, or the other way around.
A=Addition | S=Subtraction
Like the two operations above, A and S are also completely interchangeable.
________________________________________________________
________________________________________________________
Using the information above, let's evaluate (find the value of) the expression [tex]8+h^2[/tex].
We stick in the value of h, 3
[tex]\pmb{8+3^2}[/tex] is what we obtain
Here we see that exponents are present (3^2) so we'll evaluate that first, as P.E.M.D.A.S. tells us to do.
[tex]\pmb{8+9}[/tex] (3^2=3*3)
And Now we just need to add the numbers
[tex]\boldsymbol{17}[/tex]
Voila! There's our answer!
Cheers!! ^-^_____________________
Hope I helped. Best wishes.
Reach far. Aim high. Dream big.
[tex]\cal ReFlEcTioN[/tex]
_____________________
A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car
can travel on 7 gallons of gas?
Answer:
147 miles
Step-by-step explanation:
The first step is to find the number of miles traveled per gallon of gas
63 miles / 3 gallons = 21 miles per gallon
Take the rate and multiply by the number of gallons used to get the distance traveled
d = r * g
d = 21 * 7
d =147
The distance traveled is 147 miles
If TU = 8, UV = 3x, and TV = x + 10, what is TV?
The value of TV is 11.
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given:
TU= 8, UV = 3x and TV = x+10
TV= TU + UV
x +10= 8+ 3x
-2x = -2
x= 1
Hence, TV = 1+10= 11.
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translate the following to and expression 5 times the difference of a number and 12
Answer:
5(a-12)
Step-by-step explanation:
5(a-12)
A building 190 feet tall casts a 90 foot long shadow. if a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building
Answer:
About 64.65 degrees
Step-by-step explanation:
[tex] \tan(x) = \frac{190}{90} [/tex]
[tex]x = { \tan}^{ - 1} \frac{190}{90} = 64.65[/tex]
Make sure your calculator is in degree mode.
A teacher has a 2-gallon (32-cup) container of juice. She gives each student One-half cup of juice. Which equation represents the amount of juice that remains, y, after x students are served? a y = 32 x minus one-half b y = one-half x minus 32 c y = negative one-half x + 32 d y = negative 32 x + one-half
The equation represents the amount of juice that remains, y, after x students are served is y = negative one-half x + 32; option C
Equation of the unknownQuantity of juice = 2 gallon = 32 cupsQuantity given to each student = 1/2 cupNumber of juice remaining = yNumber of students served = xy = 32 - 1/2x
This can also be written as;
y = -1/2x + 32
Therefore, the correct answer is option C; y = -1/2x + 32
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Select the correct answer.
What is the value of this expression?
(10-4i) (4-5i) + (-15 + 20i)
Answer:
5-46i
Step-by-step explanation:
first multiply your (10-4i)(4-5i) so that would be 20-66i when simplified. then add that to -15+20i so it would look like 20-66i+(-15+20i). then simplify and you should get 5-46i.
Does this graph show a function? Explain how you know.
Answer:
No, the graph fails the vertical line test
Step-by-step explanation:
To determine if the graph is a function, we can use the vertical line test.
Use a vertical line, if the vertical passes through two or more points, the graph is not a function
Looking at the y axis ( which is a vertical line), it passes through two points
This means the graph is not a function
No, the graph fails the vertical line test
Which of the following have exactly 1 solution?
Choose all answers that apply.
A. -5x + 12 = -12x - 12
B.-5x+12=-5x-12
C. −5x+12=5x+12
D. −5x+12=5x−5
The equations;
-5x + 12 = -12x - 125x+12=-5x-12−5x+12=5x+12−5x+12=5x−5 all have exactly 1 solution.What is a linear solution?A linear equation is one in which there is only one solution. In a linear solution, the highest power of x is 1.
If we look at the equations listed, we will discover that they are all linear equations, as such;
-5x + 12 = -12x - 125x+12=-5x-12−5x+12=5x+12−5x+12=5x−5Will all have exactly 1 solution.
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What is the sum of the polynomials?
(6x+7+x²) + (2x²-3)
-x²+6x+4
3x²+6x+4
9x + 4
9x² +4
Answer:
3x^2 + 6x + 4
Step-by-step explanation:
6x + 7 + x^2 + 2x^2 - 3 = 3x^2 + 6x + 4
Answer:
3x²+6x+4
Step-by-step explanation:
Given:
(6x+7+x²) + (2x²-3)
Aim:
To add the polynomials
Solution:
Removing brackets first:
6x+7+x²+2x² - 3Collecting like terms to each other,
6x+7-3+2x²+x²Simplifying,
6x+4+3x²Rewriting it as,
3x²+6x+4Second choice is accurate.
