Answer:
x = 5 and y = -5
Step-by-step explanation:
You can use algebra or graphing to solve this. I will be using algebra, with substitution.
Step 1: Move the 5 over in the 1st equation
3x + 2y = 5
x = y + 10
Step 2: Substitute in x
3(y + 10) + 2y = 5
Step 3: Distribute
3y + 30 + 2y = 5
Step 4: Combine like terms
5y + 30 = 5
Step 5: Move the 30 over
5y = -25
Step 6: Divide both sides by 5
y = -5
Step 7: Plug it back in into an original equation to find x
x = -5 + 10
x = 5
Answer:Answer:
x = 5 and y = -5
Step-by-step explanation:
You can use algebra or graphing to solve this. I will be using algebra, with substitution.
Step 1: Move the 5 over in the 1st equation
3x + 2y = 5
x = y + 10
Step 2: Substitute in x
3(y + 10) + 2y = 5
Step 3: Distribute
3y + 30 + 2y = 5
Step 4: Combine like terms
5y + 30 = 5
Step 5: Move the 30 over
5y = -25
Step 6: Divide both sides by 5
y = -5
Step 7: Plug it back in into an original equation to find x
x = -5 + 10
x = 5
Step-by-step explanation:
2. The average age of 25 students is 10years
and the average age of another class
30 Students is 15 years. Find the average age
of students of the two classes
Answer:
12.7 years to the nearest tenth.
Step-by-step explanation:
The total of the ages for the 25 students = 10*25 = 250.
For the 30 students it is 15*30 = 450.
The average for the 2 classes = (250 + 450) / (25 + 30)
= 700 / 55
= 12.7 years to the nearest tenth.
If you can, please help answer this algebra question. Which terms are true about the given function?
Answer:
third option
Step-by-step explanation:
When x is less than 3, f(x) is negative so the first statement is false. The second statement is also false because the entire function is not positive. The third statement is true because when x is less than 3 f(x) is negative. The fourth statement is false because the entire function is not negative.
Using the graphing method, which of the following choices is the
solution of system: 3y = x-9
y = -x + 1
Answer:
y=x_1 is the solution of system
Translate into an algebraic expression: If I travel d miles in h hrs downstream on a river with a current of c mph, what would my speed in still water have been?
Answer:
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
Step-by-step explanation:
Dimentionally speaking, speed is distance divided by time. Since, the person is travelling downstream, absolute speed is equal to the sum of current speed and speed of the person regarding current. Both components are constant. That is:
[tex]c + v = \frac{d}{h}[/tex]
Where:
[tex]c[/tex] - Current speed, measured in miles per hour.
[tex]v[/tex] - Speed of the person regarding current, measured in miles per hour.
[tex]d[/tex] - Distance travelled downstream, measured in miles.
[tex]h[/tex] - Time spent on travelling, measured in hours.
Speed in still water occurs when current speed is zero. Then, such variable is obtained after subtracting current speed on both sides of the expression. Hence:
[tex]v = \frac{d}{h} - c[/tex]
The speed is still water is [tex]v = \frac{d}{h} - c[/tex].
Verify inverse functions
Answer:
Step-by-step explanation:
Hello
(fog)(x)=f(g(x))=10(x-6)/10+6=x-6+6=x
(gof)(x)=(10x-6+6)/10=10x/10=x
So YES the functions are inverse
hope this helps
In the diagram, m = 128° and m = 76°. What is m∠ABC? A. 104° B. 116° C. 128° D. 102° E. 96°
Answer:
B. 116
Step-by-step explanation:
Answer:
D) 102
Step-by-step explanation:
Angle ABC is an inscribed angle.
Inscribed angle = 1/2 * Intercepted Arc
The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204
m<ABC = 1/2(204)
m<ABC = 102 degrees
You answer is D) 102
A rectangle has a length of 12 mm and a width of 15 mm. A new rectangle was created by multiplying all of the dimensions by a scale factor of 1 3 . A rectangle with length 12 millimeters and width 15 millimeters. A smaller rectangle with length 4 millimeters and width 5 millimeters. Which statement best describes the change in the perimeter of the new rectangle? The new perimeter will be One-half times the perimeter of the original rectangle. The new perimeter will be One-third times the perimeter of the original rectangle. The new perimeter will be 2 times the perimeter of the original rectangle. The new perimeter will be 3 times the perimeter of the original rectangle.
Answer:
4 mm by 5 mm1/3 the perimeter of the originalStep-by-step explanation:
When each of the dimensions is multiplied by 1/3, the result is a rectangle that is ...
(12 mm)·(1/3) by (15 mm)·(1/3) = 4 mm by 5 mm
The result is ...
a smaller rectangle with length 4 millimeters and width 5 millimeters
__
The perimeter of the smaller rectangle has the same ratio to the original that the side lengths do.
The new perimeter will be 1/3 times the perimeter of the original rectangle.
The change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.
What is the perimeter of a rectangle?For a known length and width of a rectangle, the expression for calculating the perimeter of a rectangle is 2(L × w).
From the given information:
A rectangle's length = 12 mm, and width = 15 mm
Using a Scale factor of 1 : 3A new smaller rectangle's length = 4 mm, and width = 5 mmTherefore, we can deduce that the change in perimeter of the new rectangle will be 3 times the perimeter of the original rectangle.
This is because by using the scale factor:
[tex]\mathbf{\dfrac{1}{3}(12) \times \dfrac{1}{3}(15)}[/tex]
We can get the value for the length and width of the new smaller rectangle as 4 mm and 5 mm respectively.
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On average,ea rectangular garden ha an area of 144 meter square. During a redesign of the garden center, the dimension of the rectangular garden are altered but the area is unchanged .The width is doubed and length is decreased by 12m.
Answer:
New dimensions are; Width = 12m and Length = 12m
Step-by-step explanation:
Let length of rectangle be L
Let width be W
Area of rectangle has a formula;
Area = Length x Width = LW
We are given the area = 144 m²
So,
LW = 144 - - - (eq1)
Now, we are told that width is doubled and length is decreased by 12m but area remains the same.
Thus, we have;
Width as 2W and Length as L - 12.
Area = 2W(L - 12)
So,
2W(L - 12) = 144 - - - (eq2)
Equating eq 1 and 2,we have;
LW = 2W(L - 12)
W will cancel out to give;
L = 2(L - 12)
L = 2L - 24
2L - L = 24
L = 24m
From equation 1, LW = 144
Thus; W = 144/L = 144/24
W = 6m
So new design of rectangle now has a dimension of;
Width = 2W = 2 × 6 = 12m
Length = L - 12 = 24 - 12 = 12m
So, new dimensions are; Width = 12m and Length = 12m
What is the vertex of the quadratic function?
f(x) = (x – 8)(x – 4)
A. (4,8)
B. (-6,4)
C. (6,-4)
D. (-4,8)
Answer:
C(6,-4)
Step-by-step explanation:
-8+-4=-12
-12÷2=-6
I hope this helps
Answer:
C
Step-by-step explanation:
(6,-4)
Which is the correct formula to calculate the volume of a sphere?
a.
Four-thirds pi r squared
c.
One-third pi r cubed
b.
Four-thirds pi r cubed
d.
4 pi r cubed
Please select the best answer from the choices provided
A
B
C
D
Not a
Answer:
B
Step-by-step explanation:
Volume of Sphere = 4/3 x 3.14 (pi) x r^2
A line contains the point (-4,6) and has a slope of -2/3 write the equation of the line using point-slope form
Answer:
(y-6)=-2/3(x+4)
Step-by-step explanation:
Solve log x = 4. x = 4 x = 40 x = 1,000 x = 10,000
Answer:
x = 10000
Step-by-step explanation:
log x = 4
Raise each side to the base of 10
10^log x = 10 ^4
x = 10 ^4
x = 10000
Answer:
x = 10,000
Step-by-step explanation:
I got it right on the test.
What is a reasonable estimate of the rate of change for the interval 300 <= x <= 400?
Answer:
The correct option is;
B. -2
Step-by-step explanation:
From the graph, we have;
At x₁ = 300, y₁ = 800
At x₂ = 400, y₂ = 600
The formula for the slope, m, of a graph is given as follows;
[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{600 - 800}{400 - 300}= \dfrac{-200}{100} = -2[/tex]
Therefore, a reasonable estimate of the rate of change for the interval 300 ≤ x ≤ 400 is -2 which is a negative slope as expected as the y-coordinate values, which is the value of the function, decreases while the x-coordinate values which is the independent variable increases as we go from 300 ≤ x ≤ 400.
10 people have pink cups. then 5 of those 10 people got red cups and threw the pink cups away. how many people have pink cups?⇒⇒
Answer:
5 people have pink cups
Step-by-step explanation:
10-5=5
:D
Answer:
5
Step-by-step explanation:
10-5=5
^--^
Which is the scale factor of the dilation?
Answer:
needs more information!
Step-by-step explanation:
need more information
The following scatter plot demonstrates the relationship between to two variables x and y. The scatter plot shows what. correlation between the variables
Answer:
Positive correlation
Step-by-step explanation:
From the scatter plot shown in the graph above, we can observe that the data points that are clustered in a band run upwards from left of the graph to the right.
In simple terms, both variables move along the same direction, which means, as variable on one axis increases, the variable on the other axis increases as well.
This shows that the variables depicted on the scatter plot are positively correlated. It shows a positive correlation between the variables.
The relationship between the variables on the scatter plot it a positive correlation
From the graph, we have the following highlights
As the x-values increase, the y-values also increase The points appear to be on a straight lineWhen the x and the y values increase or decrease in the same direction, then the correlation of the graph is positive.
Hence, the relationship between the variables on the scatter plot it a positive correlation
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Hi, can I get some help with this question? DON'T WORRY ITS JUST A ASSIGNMENT. NOT A TEST. Thank you
Answer:
d.
Step-by-step explanation:
i looked at the graph!
The height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet. Find the length of the base and the height of the triangle
Answer:
Step-by-step explanation:
The length of the base is 3 feet and the height of the triangle is 6 feet.
What is the area of a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.
Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.
The dimensions of the triangle will be calculated as,
A = (1/2) x b x h
A = (1/2) x b x ( b + 3 )
54 = ( 1 / 2 ) x ( b² + 3b )
108 = ( b² + 3b )
( b² + 3b - 108) = 0
( b² + 12b -3b -108 ) = 0
(b - 3 ) ( b+ 12 ) = 0
b = 3 and b = -12 ignore negative value.
The height will be calculated as,
h = b + 3
h = 3 + 3
h = 6 feet
Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.
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Complete the sentences below the radius of a circle is _____ the length of its diameter. the diameter of a circle is ______ the length of its radius
Answer:
Half; twice
Step-by-step explanation:
In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".
Thus,
2r = d
r = d/2
For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.
Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius
Lim x-> n/2 (2e^x cos x)
Answer:
A
Step-by-Step Explanation:
We want to find the limit:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}[/tex]
Use direct substitution.
Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})[/tex]
Recall the unit circle. cos(π/2) is simply 0. Hence:
[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0[/tex]
Therefore:
[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0[/tex]
So, our answer is A.
pleaseeeeeees help mee
Answer:
True
Step-by-step explanation:
order of letter matter. R and T first and last letters of triangle. H and F also first and last. so can say those sides are proportional.
please help me with this
Answer:
The answers are below
Step-by-step explanation:
a)67.592
b)21.748
c)241.402
Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B.
Answer:
[tex]m=-\frac{1}{6} \approx -0.1667[/tex]
[tex]M=(1,\frac{17}{2} )=(1,8.5)[/tex]
[tex]d=\sqrt{37} \approx 6.083[/tex]
Step-by-step explanation:
(i) For two different points on a line, the slope m is defined as the difference on the y-axis divided by the difference on the x-axis:
[tex]m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}[/tex]
Where:
[tex](x_1,y_1)=(-2,9)\\\\(x_2 , y_2)=(4,8)[/tex]
So:
[tex]m=\frac{8-9}{4-(-2)} =\frac{-1}{6} \approx -0.1667[/tex]
(ii)
To find the coordinates of the midpoint, you can use the following formula:
[tex]M=(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
Therefore:
[tex]M=(\frac{-2+4}{2} , \frac{9+8}{2} )=(\frac{2}{2} , \frac{17}{2} ) =(1,8.5 )[/tex]
(iii) The distance between two points is given by the following formula:
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]
Hence:
[tex]d=\sqrt{(4-(-2))^{2}+(8-9)^{2} } =\sqrt{(6)^{2}+(-1)^{2} } =\sqrt{36+1} =\sqrt{37} \\\\d\approx 6.083[/tex]
On a coordinate plane, point A is 2 units to the left and 3 units up. Point B is 2 units to the right and 3 units up.
How many units away are each of the points from the y-axis?
2
3
4
5
Answer:
2 for both
Step-by-step explanation:
The distance between the points and the y-axis will be the value of the x coordinate, as x is the horizontal distance from 0 and the y-axis.
Answer:
Answer 4
Step-by-step explanation:
Twice a certain number minus 7 is equal to 5. What is the number.
Answer:
6
Step-by-step explanation:
Let the number be x.
2x - 7 = 5
Add 7 to both sides.
2x = 5 + 7
2x = 12
Divide 2 into both sides.
x = 12/2
x = 6
The number is 6.
Answer:
6
Step-by-step explanation:
2x-7=5
2x=12
x=6
x=the varible that represents the number
4. /(x) = 4x – 5, translation 3 units up
45/30 in its simplest form
Answer:
3/2
Step-by-step explanation:
45/30 can be simplified.
The highest common factor of 45 and 30 is 15.
45÷15/30÷15
Divide.
3/2
What is the mean of this set: {2, 6, 7, 9, 9, 9)?
6
7
Ο Ο Ο Ο
8
9
Answer:
6.8 nearly 7
Step-by-step explanation:
beacuse mean is sum of all terms in a data/number of terms in the data
Answer: 7
Step-by-step explanation:
To find the mean of a set, you take the sum of the set and divide it by the number of numbers in the set.
[tex]\frac{2+6+7+9+9+9}{6} =\frac{42}{6} =7[/tex]
Starting from rest the motor boat travels around the circular path (radius of curvature= 40 m),at a speed (v= 0.8 t m/s),where (t) is in seconds. The magnitude of the boat's velocity when it has traveled 20 m is
Answer:
The magnitude of the boat's velocity is 5.66 m/s
Step-by-step explanation:
Given;
Radius of curvature of the circular path, r = 40 m
speed of the boat, v = 0.8 t m/s
The magnitude of the boat's velocity when it has traveled 20 m is ?
a = dv / dt,
v = 0.8 t (differentiate with respect to t)
dv / dt = 0.8 = a
thus, a = 0.8 m/s²
If the boat starts from rest, initial velocity, u = 0
Apply kinematic equation, to solve for the boat velocity at 20 m
v² = u² + 2as
v² = 0 + 2 x 0.8 x 20
v² = 0 + 32
v² = 32
v = √32
v = 5.66 m/s
Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s
Which is the area of the rectangle?
69
115
100
Answer:
A
Step-by-step explanation: