Answer:
3:2
Step-by-step explanation:
To answer questions like this I would makeup an age for Alan
Like say Alan is 10 years old
John is 3 times the age of 10 so he is 30
Ralph is twice the age of 10 so he is 20
so 30/20 can be simplified to 3/2
There are other ways to solve it but that is how I would solve it
I hope it helped you
Answer:
3:2 or 3/2
Step-by-step explanation:
Let Alan's age be x
So according to the assumed variable, John's age will be three times of Alan's age
John's Age = 3x
Similarly,
Twice of Alan's age = 2x
so, Ralph's age = 2x
Since we have to find the ratio of John's age to Ralph's age that will be equal to
3x : 2x
which can also be written as:
3:2 or 3/2 ..
Peter can paint a room in 5 hours, Paul can paint a room in 6 hours, Neil can paint a room in 7 1/2 hours and Mary can paint a room in 3 3/4 hours.
Which two painters above can team up to paint a whole room in 3 hours?
Write and solve a Rational Equation that shows you are correct. Please show your work.
paul and mary
peter and mary
peter and paul
Answer:
Peter and Neil
Step-by-step explanation:
Given rates of work:
Peter = 5 hours / room
Paul = 6 hours / room
Neil = 7.5 hours / room
Mary = 3.75 hours / room
Recall the formula for combined rate for two individuals A & B is given as
Combined rate = (A's rate x B's rate) / (A's rate + B's rate)
In our case , the combined rate is given to be 3 hours, so we must find a combination of rate A and rate B that will give us 3 hours.
If you try all the combinations in the above formula, we will find that if we substitute Peter's and Neil's rates into the formula, we will get exactly 3 hours.
Combined rate for Peter and Neil
= (Peter's rate x Neil's rate) / (Peter's rate + Neil's rate)
= (5 x 7.5) / (5+7.5) = 3 hours to complete 1 room
No other combination gives exactly 3 hours.
Rewrite the following linear equation to slope form :y+2=7(2x-4)
Answer:
y = 14x -30
Step-by-step explanation:
The slope intercept form is:
y = mx + b,
Slope intercept form is useful for finding the slope and y intercept of a line, hence why it is called "slope intercept" because it is easy to see the slope and the y intercept of a line in this form. Since the slope denoted by m, and y intercept denoted by b are clearly given.
y + 2 = 7(2x - 4)
Distribute 7 across the parentheses by multiplying x and 2x and 4 by 7.
y+2 = 14x - 28
subtract 2 from both sides. This cancels the 2 on the left and moves it to the right, while keeping the equation balanced.
y+2 -2 = 14x - 28 -2
y = 14x - 30
y = 14x -30
As you can see our y = 14x -30 now looks like the point slope equation we had above. m = 14, and b = -30. This means the line goes up 14 for every single unit you move to the right, and intersects the y axis at (0, -30).
Please mark me brainliest.
Which equations represent the line that is perpendicular to the line 5x – 2y = -6 and passes through the point (5,-4)?
Check all that apply.
y=-x-2
L2x + 5y = -10
U 2x - 5y = -10
y+4 = (x - 5)
y-4 = (x + 5)
Answer:
None of these apply
Step-by-step explanation:
Step 1: Bring the equation into the form of y=mx+c
5x-2y = -6
-2y = -6-5x
y = 6+5x
2
y = 5/2x + 3
Step 2: Identify the slope (m)
Slope is the number with x (5/2)
Step 3: Find slope of the perpendicular line.
Slope of line 2 (perpendicular line) = -1/slope of line 1
m2 = -1/m1
m2 = -1/5/2
m2 = -2/5
Step 4: Find the y-intercept of the perpendicular line,
slope = -2/5
x and y coordinates = (5, -4)
y = mx + c
-4 = -2/5 (5) +c
-4 + 2 = c
c = 2
Step 5: Form equation of perpendicular line
y = mx + c
y = -2/5x + 2
Step 6: Check all equations and match with y = -2/5x + 2
a) y = x - 2 (It does not apply because this equation does not have a slope and y-intercept is not the same).
b) 2x + 5y = -10
5y = -10 -2x
y = -2/5x - 2 (This does not apply because the y-intercept does not match-it should be +2))
c) 2x - 5y = -10
-5y = -10 - 2x
y = 2/5x + 2 (This does not apply because the slope does not match-it should be -2/5)
d) y + 4 = (x - 5)
y = x-5-4
y = x-9 (This does not apply as the slope and y - intercept do not match)
e) y - 4 = (x + 5)
y = x + 9 (This does not apply as the slope and y - intercept do not match)
!!
Write the equation of the line that passes through the given points (2,3) (2,5)
Answer:
x = 2
Step-by-step explanation:
Note that the coordinates (2, 3) and (2, 5) both have the same x- coordinate.
This indicates that the points lie on a vertical line parallel to the y- axis.
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through.
In this case the x- coordinate is 2, hence the equation of the line is
x = 2
Write y + 1 = –2x – 3 in standard form.
Question 8 options:
a)
x + 12y = −2
b)
2x + y = -4
c)
-2x-y = 4
d)
y = -2x-4
Answer:
b) 2x + y = -4
Step-by-step explanation:
To go from the Point-Slope Formula [y - y₁ = m(x - x)₁] to the Slope-Intercept Formula [y = mx + b], move -1 to the RIGHT side of the equivalence symbol to get this: y = -2x - 4. Although this is a correct answer choice, this is NOT what the question is looking for because you have to go an extra step further, Standard Formula. To go from the Slope-Intercept Formula to the Standard Formula [Ax + By = C], move 2x to the LEFT side of the equivalence symbol, and you will end up with this: 2x + y = -4. So, your answer is b).
Answer:
b) [tex]2x+y=-4[/tex]
Step-by-step explanation:
We have been given an equation [tex]y+1=-2x-3[/tex]. We are asked to write our given equation in standard form.
We know that standard form of an equation is [tex]Ax+By=C[/tex].
Let us convert our given equation in standard form as:
[tex]y+1-1=-2x-3-1[/tex]
[tex]y=-2x-4[/tex]
[tex]y+2x=-2x+2x-4[/tex]
[tex]2x+y=-4[/tex]
Therefore, the standard form of our given equation would be [tex]2x+y=-4[/tex].
What is 9.18 × 103 in standard form?
Answer:
9.179999999999999e+103
Answer:
C) 7,900
Step-by-step explanation:
Quadrilateral PERK has vertices at P(4,4), E(12,4), R(10,−2), and K(2,−2). Find the vertices of the quadrilateral after a dilation with scale factor 32.
These are the options. 1,2,3, and 4.
1. P'(8/3, 8/3), E'(8, 8/3), R'(20/3, −4/3), and K'(4/3, −4/3)
2. P'(−6, −6), E'(−18, −6), R'(−15, 3), and K'(−3, 3)
3. P'(6, 6), E'(18, 6), R'(15, −3), and K'(3, −3)
4. P'(−8/3, −8/3), E'(−8, −8/3), R'(−20/3, 4/3), and K'(−4/3, 4/3)
Answer:
option 3
Step-by-step explanation:
Dilation by a scale factor of 3/2 multiplies each of the coordinate values by 3/2. For example, P' = (3/2)P = (3/2)(4, 4) = (6, 6).
The only choice with coordinates matching these is option 3.
An airplane takes off at an angle of 75° from its starting point. When the plane has traveled a total distance of 600 feet, its vertical height above the runway to the nearest foot is 580 feet.
true or false
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph with the function it represents
Graph Function
A f(x) = x
B f(x) = x^2
C f(x) = x^3
D f(x) = √(x - 1)
E f(x) = 1/x
To match each graph with the function it represents, we need to consider the shape of the graph and the equation of the function.
Graph A: This graph is a straight line that passes through the origin and has a slope of 1.
This indicates that the function is linear and has the following equation:
f(x) = x
Graph B: This graph is a parabola that opens upwards and has its vertex at the origin.
This indicates that the function is quadratic and has the following equation:
f(x) = x^2
Graph C: This graph is a cubic function that opens upwards and has a point of inflection at the origin.
This indicates that the function has the following equation:
f(x) = x^3
Graph D: This graph is a square root function. It has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1.
This indicates that the function has the following equation:
f(x) = √(x - 1)
Graph E: This graph is a reciprocal function. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
This indicates that the function has the following equation:
f(x) = 1/x
Vhich solid figure has two parallel bases that are congruent polygons and
rectangular faces joining the bases?
A. Pyramid
B. Cone
c. Cylinder
D. Prism
Answer:
D
Step-by-step explanation:
Prism is the solid figure that has two parallel bases that are congruent polygons and rectangular faces joining the bases, i.e. option D.
What is prism?A prism is a 3D figure with two parallel bases and two congruent bases. The bases, which also have two of the faces, can be any polygon and are congruent. The other faces are rectangles and joins bases. A prism is named according to the shape of its bases. i.e. Triangular prism, Rectangular prism, etc.
We have,
A solid figure with two parallel and congruent bases.
Now,
From the above mentioned definition,
i.e.
A prism is a 3D figure with two parallel bases and two congruent bases. The bases, which also have two of the faces, can be any polygon and are congruent. The other faces are rectangles and joins bases.
So,
It is clear that the given solid figure is of prism.
Hence, we can say that the Prism is the solid figure that has two parallel bases that are congruent polygons and rectangular faces joining the bases, i.e. option D.
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What’s the volume??
Answer:
5/96.
Step by Step explanation:
The volume = width * length * height
= 1/3 * 5/8 * 1/4
= 1*5*1 / 3*8*4
= 5 / 96.
=
Find how many two digit numbers are divisible by 3
I'll use arithmetic series to find it.
First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.
So,
[tex]a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30[/tex]
There are 30 such numbers.
What is the range of the given function?
O {x|x = -5, 1, 4, 6}
O {yl y=-7,-1, 0, 9}
O {x|x = -7, -5, -1,0, 1, 4, 6, 9}
O yly=-7, -5, -1, 0, 1, 4, 6, 9}
|__x__|__y__|
|_-5__|__9__|
|_1___|__0__|
|_4___|__-7_|
|_6___|__-1_|
(table above^)
Answer:
Step-by-step explanation:
we know that
The Domain of the function are all the values of x that can take the function
in this problem the domain is
The Range of the function are all the values of y that can take the function
in this problem the range is
therefore
{y | y = –7, –1, 0, 9} baaaam
know my brain hurts i hope this helped because i really tried haha sorry if it doesnt
Determine the linear equation from the graph below.
1 Height of a balloon
3
+
.
.
.
.
.
Height (1000 ft)
10 20 30 40 50 60
Time (sec)
Answer: [tex]y=\frac{1}{30}x+1[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The slope of the line can be calculated with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Pick to points of the given line. You can choose the point (60,3) and the point (30,2).
Then, substituting into the formula, you get:
[tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]
You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:
[tex]b=1[/tex]
Substituting the slope and the y-intercept found into [tex]y=mx+b[/tex], you get the equation of this line:
[tex]y=\frac{1}{30}x+1[/tex]
Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.
Answer:
The equation of the given line is :y = 0.04x + 0.6.
Step-by-step explanation:
From the given data , we can select two coordinates to determine the equation of the given line:
Let the point be [tex](10,1),(60,3)[/tex]
The equation of the line will be determined by the help of point slope form:
Slope of the line = [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex](y-y_1)=m(x-x_1)[/tex]
The equation of the line is :
[tex]m=\frac{3-1}{60-10}=\frac{2}{50}=0.04[/tex]
[tex](y-1)=0.04(x-10)[/tex]
[tex]y-1=0.04x-0.4[/tex]
[tex]y=0.04x+0.6[/tex]
The equation of the given line is :y = 0.04x + 0.6.
A sequence is defined by the following:
A1 = 6 and an = -1.2n-1
What is the 4th term?
-12.4416
-10.368
10.368
12.4416
Answer:
Step-by-step explanation:
a1 = 6
a2 = -1.2*a_(n-1)
a2 = -1.2*a_1
a2 = -1.2 * 6
a2 = -7.2
a3 = -1.2*a_(n-1)
a3 = -1.2*a_2
a3 = -1.2 * - 7.2
a3 = 8.64
a4 = -1.2 * a_3
a4 = -1.2 * 8.64
a4 = -10.368
Answer: The correct option is (B) -10.368.
Step-by-step explanation: Given that a sequence is defined b the following :
[tex]a_1=6,~~~a_n=-1.2a_{n-1}.[/tex]
We are to find the 4-th term.
To find the fourth term, we need to start from finding the first term.
If n = 2, then the second term is given by
[tex]a_2=-1.2\times a_1=-1.2\times 6=-7.2.[/tex]
If n = 3, then the third term is given by
[tex]a_3=-1.2\times a_2=-1.2\times (-7.2)=8.64.[/tex]
If n = 4, then the fourth term is given by
[tex]a_4=-1.2\times a_3=-1.2\times 8.64=-10.368.[/tex]
Thus, the fourth term of the given sequence is -10.368.
Option (B) is CORRECT.
LOOK AT PICTURE ↓↓↓↓↓↓↓↓↓↓↓
Answer:
2/5x - 2y≥ 2
Step-by-step explanation:
see attachment
f(x)x^2-2x and g(x)=6x+4 for which value of x does (f+g)(x)=0
Answer:
(f+g)(x)
Step-by-step explanation:
(f+g)(x)=
[tex] {x}^{2} - 2x + 6x + 4 = {x}^{2} + 4x + 4[/tex]
[tex](x + 2)(x + 2) = 0[/tex]
[tex](x + 2) = 0 \\ x = - 2[/tex]
what is one root of this equation 2x^2-4x+9=0?
A. -2+sqrt14/2i
B. -1+sqtr14/2i
C. 1+sqrt14/3i
D. 1+sqrt14/2i
E. 2+sqrt14/2i
For this case we have the following quadratic equation:
[tex]2x ^ 2-4x + 9 = 0[/tex]
The solutions are given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]
We have to:
[tex]a = 2\\b = -4\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (9)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-72}} {4}\\x = \frac {4 \pm \sqrt {-56}} {4}\\x = \frac {4 \pm \sqrt {-1 * 56}} {4}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 14}} {4}\\x = \frac {4 \pm2i \sqrt {14}} {4}\\x = \frac {2 \pm i\sqrt {14}} {2}[/tex]
Answer:
[tex]x_ {1} = \frac {2 + i \sqrt {14}} {2}\\x_ {2} = \frac {2-i \sqrt {14}} {2}[/tex]
Answer:
OPTION E: [tex]\frac{2+\sqrt{14}i}{2}[/tex]
Step-by-step explanation:
Given the Quadratic equation [tex]2x^2-4x+9=0[/tex], you can find the roots by applying the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac} }{2a}[/tex]
In this case you can identify that:
[tex]a=2\\b=-4\\c=9[/tex]
Then you can substitute values into the Quadratic formula:
[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(2)(9)} }{2(2)}[/tex]
[tex]x=\frac{4\±\sqrt{(56} }{4}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex], then:
[tex]x=\frac{4\±2\sqrt{14}i}{4}[/tex]
Simplifying, you get:
[tex]x=\frac{2(2\±i\sqrt{14}i)}{4}\\\\x=\frac{2\±\sqrt{14}i}{2}\\\\\\x_1=\frac{2+\sqrt{14}i}{2}\\\\x_2=\frac{2-\sqrt{14}i}{2}[/tex]
The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is its greatest possible value for width?
Answer:
width = 14 , length = 42
Step-by-step explanation:
Here we have to find the width of the rectangle using the fact that length is 3 times the width and perimeter is given
Let the length of the rectangle = x
Hence the width of the rectangle = 3 x
The formula for the perimeter is
P=2(l+b)
Given P = 112
Hence
112=2(l+b)
l+b=56
substituting values of l and b in this
x+3x= 56
4x=56
x=14
Hence width = 14 cms
length = 3*14 = 42 cms
Is the square root of 882252554089 a whole number or not?
Answer: It is a whole number.
Step-by-step explanation: As the square root of 882252554089 is equal to 939283, which has no decimal or fraction included, it is a whole number.
A jar holds no more than 500 buttons. If 5 people bring 330 buttons each, how many jars are necessary to hold all of the buttons?
Answer:
We know
1 jar = 500 buttons
5 people bring 330 buttons EACH
We can find/solve by...
people x buttons = total buttons
total buttons / 500 = number of jars needed
So..
5 x 330 = 1650
1650 / 500 = 3.3
Your answer:
4 jars
Explanation
It's impossible to have 3.3 jars, so you must round up.
Step-by-step explanation:
The number of jar necessary to hold all buttons is 4 jars.
What is a unitary in math?Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.
Given that
1 jar holds = 500 buttons
5 people = 330 buttons each
So,
Total buttons 5 people bring
=330*5
=1650 buttons
Now,
number of jars needed= total buttons/500
number of jars needed= 1650/500
number of jars needed= 3.3 jar
Hence, the number of jars needed is 4 jars
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Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce. The table shows the costs of the ingredients.
What is the value of y in the table?
THE ANSWER IS 6
Answer:
y = $6
Step-by-step explanation:
In the image below, the table of your question is attached
Based on the information presented in the table.
1 ounce of oregano costs $4
Because there are 4 ounces, this means that
x = 4*($4) = $16
1 ounce of garlic powder $3
Because there are 2 ounces, this means that
y = 2*($3) = $6
Total cost of the ingredients = x+y = 22 $
29, 20, 36, 44, 30, 32, and 40.
Answer:
can't understand the question.
What do you need? The mean? Mode? Median?
what is the value of x? please hurry.
Answer:
8
Step-by-step explanation:
Use the pythagorean theorem. The hypotenuse (c) is 10, and one of the sides, let's say (b), is 6. Therefore, we need to solve for a and plug and chug. Let's do that:
[tex]c^2 = a^2+b^2[/tex]
[tex]a = \sqrt{c^2-b^2}[/tex]
Now let's plug in what we know:
[tex]a = \sqrt{10^2-6^2} = \sqrt{64} = 8[/tex]
Therefore, a = x = 8
factor -24a^3b^3c^3 - 84a^4b^2c
The answer to your question is b.
30 points.Please answer with explanation
Answer:
m∠1 = 142
Step-by-step explanation:
38 + m∠1 = 180
m∠1 = 142
On a number line 2.49 would be located where?
Answer:
In the middle of 2 and 3.
Step-by-step explanation:
2 < 2.49 < 3.
Therefore, 2.49 would be located in the middle of 2 and 3, assuming that the scale is 1.
Hope this helps!
It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.
What is the number line?
In math, a number line can be described as a straight line with numbers positioned at equivalent intervals or parts along its length. A number line can be expanded infinitely in any direction and exists usually expressed horizontally.
It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.
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I need help with this one too
Answer:
B
Step-by-step explanation:
I'm pretty sure that the shaded space represents all possible solutions, meaning that the X has to be greater than or equal to 2.
For which value of O is sin O= -1
Answer:
O = 2 π n - π/2 for n element Z
Step-by-step explanation:
Solve for O:
sin(O) = -1
Hint: | Eliminate the sine from the left hand side.
Take the inverse sine of both sides:
Answer: O = 2 π n - π/2 for n element Z
assuming you meant sin(θ) = -1, Check the picture below.
Virginia drew the figure at the right on the board. The steps below are used to solve for the unknown angle, x, in the figure but are not arranged in the correct order.
1·) x= 15
2.) 75 + 15= 90
3,) 75+x= 90
4,) 75-75 + x = 90-75
Which sequence shows the correct order of the steps Virginia should follow to find the measure of the unknown
A 1234
B 3412
C 4213
D 2314
Answer:
Option B 3412
Step-by-step explanation:
we know that
step 1
75°+x=90° -----> by complementary angles
step 2
Solve for x
Subtract 75 both sides
75°-75°+x=90°-75°
step 3
x=15°
step 4
Verify
Substitute the value of x in the equation of the step 1
75°+15°=90°
90°=90° ----> is correct
therefore
The correct order is
3-4-1-2