Answer:
5 nickels
Step-by-step explanation:
You can setup and solve a system of equations, or you can solve by trial and error until you get the correct answer.
Here is the solution by trial and error.
If all 20 coins are quarters, the value is 20 * $0.25 = $5
That is too much value.
Let's try 16 quarters. 16 quarters are worth 16 * $0.25 = $4.
That is the correct value, but it is only with quarters, and only 16 of them.
We need fewer quarters than 16.
Try 12 quarters: 12 * $0.25 = $3.00
The number of nickels is: 20 - 12 = 8
8 nickels are worth 8 * $0.05 = $0.40
12 quarters and 8 nickels are worth $3.00 + $0.40 = $3.40
There are 20 coins, but the value is too low.
The number of quarters is between 12 and 16.
Try 14 quarters and 6 nickels:
14 * $0.25 + 6 * $0.05 = $3.50 + $0.30 = $3.80
We are closer to $4 but not there yet.
Try 15 quarters and 5 nickels.
15 * $0.25 + 5 * $0.05 = $3.75 + $0.25 = $4
The total value is $4 and there are 20 coins. This is the answer.
15 quarters and 5 nickels works.
Answer: 5 nickels
PLEASE HELP!!!
Point A, located at (-2, 4), is translated down 6 units. What are the coordinates of A'?
(-8, 4)
(-8, -2)
(-2, -2)
(-2, 4)
Point B, located at (-4, -7), is reflected over the y-axis. What are the coordinates of B'?
(-4, 7)
(4, -7)
(4, 7)
(-4, -7)
Answer for A. (-8,-2)
answer for B. (4,-7)
A walking path across a park is represented by the equation y=-2x+5. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-2,9). Identify the equation that represents the new path.
A. y= {x+10
B. y= -2x - 5
C. y= 2x+13
D. y -- 1x+8
Answer:
[tex]y = \frac{1}{2}x+10[/tex]
Step-by-step explanation:
The given path is:
y = -2x+5
Comparing with the standard form of equation:
y = mx+b
So,
m = -2
We know that product of slopes of two perpendicular lines is -1
Let m1 be the slope of the perpendicular line
m*m1=-1
-2*m1 = -1
m1 = -1/-2
m1 = 1/2
So the slope of perpendicular path is 1/2.
Since the new path passes through (-2,9)
[tex]9 = \frac{1}{2}(-2) +b\\9 = -1 +b\\b = 10[/tex]
Putting the values of m and b in standard form
[tex]y = \frac{1}{2}x+10[/tex]
Hence the equation of new path is:
[tex]y = \frac{1}{2}x+10[/tex] ..
an equation in slope-intersept form the lines that passes thought (-8,1) and is perpindicular to the y=2x-17.
Answer:
y = (-1/2)x -3
Step-by-step explanation:
We are given
y = 2x-17
which is in slope-intercept form: y = mx +b
Where m is the slope. so, m= 2
But this is perpendicular, When a line is perpendicular then the slope become -1/m so in our case the slope m will be = -1/2
Using the point(-8,1) we can find the b i.e the y intercept
We have x = -8, y =1 and m=-1/2
y = mx + b
1 = (-1/2)(-8) + b
1 = 4 + b
=> b = 1-4
b = -3
The equation of slope intercept form will be
y = mx + b
Putting value of m= -1/2 and b = -3
y = (-1/2)x -3
I ONLY NEED THE 2nd ONE !!
Answer:
The length of the missing side of the triangle is represented by the equation:
(6a + 2b - 5) - (2a - 3b) - (a - 3)
= 6a + 2b - 5 - 2a + 3b - a + 3
= 3a + 5b - 2
what the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answer: ≈ 1.414
Step-by-step explanation:
You can use the pythagorean theorem, a^2 + b^2 = c^2
a^2 and b^2 are the legs and c^2 is the hypotenuse.
1^2 + 1^2 = c^2
1 + 1 = c^2
2 = c^2
√ 2 = √ c^2
c = ≈ 1.414
what is the slope of the line graphed below? (-1,3) (-2,-1)
Answer:
m=4
Step-by-step explanation:
3-(-1)/-1-(-2)=3+1/-1+2=4/1
Answer:
4
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]
[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]
[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]
Therefore, the slope is 4.
4 is the correct answer.
I hope this helps you, and have a wonderful day!
find the derivative in the form dy/dx
Answer:
dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
Step-by-step explanation:
* Lets revise some rules for the derivative
- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
- The derivative of u/v = (vu'-uv')/v²
- The derivative of the constant is 0
* Lets solve the problem
∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]
- Let u = 4x³ - 7 and v = 3x^5 + 1
∵ u = 4x³ - 7
∴ u' = 4(3)x^(3-1) - 0 = 12x²
∵ v = 3x^5 + 1
∴ v' = 3(5)x^(5-1) + 0 = 15x^4
∵ The derivative of u/v = (vu' - uv')/v²
∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]
∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]
- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the
same bracket in the 2nd fraction
∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
What is .5x5 equal???
Answer:
The answer is 25
Step-by-step explanation:
Which of the following is the equation of a line parallel to the line y = 3x + 2,
passing through the point (10.1)?
A. -3x - y = 29
B. 3x - y = 29
C -3x + y = 29
D. 3x + y = 29
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 is in this form with slope m = 3
• Parallel lines have equal slopes, hence
y = 3x + c ← is the partial equation of the parallel line
To find c substitute (10, 1) into the partial equation
1 = 30 + c ⇒ c = 1 - 30 = - 29
y = 3x - 29 ← in slope- intercept form
Subtract y from both sides
0 = 3x - y - 29 ( add 29 to both sides )
29 = 3x - y, thus
3x - y = 29 ← in standard form → B
Answer:
B
Step-by-step explanation:
Use the properties of exponents to rewrite the expression.
(-5uv)(-5uv)(-5uv)(-5uv)
The expression can be simplified to [tex]625 \times (uv)^4.[/tex]
To rewrite the expression (-5uv)(-5uv)(-5uv)(-5uv) using the properties of exponents, you can consolidate it using the exponent rule that states when you multiply numbers with the same base, you add the exponents. In this case, the base is -5uv, and you are multiplying it four times, so the exponent is 4:
[tex](-5uv)(-5uv)(-5uv)(-5uv) = (-5uv)^4[/tex]
Now, you can simplify further by applying the rule for raising a power to a power, which states that when you raise an exponentiated term to another exponent, you multiply the exponents:
[tex](-5uv)^4 = -5^4 \times (uv)^4[/tex]
-5^4 means -5 multiplied by itself four times:
[tex]-5^4 = -5 \times -5 \times -5 \times -5 = 625[/tex]
So, the expression can be simplified to:
[tex]625 \times (uv)^4[/tex]
This is the expression rewritten using the properties of exponents.
for such more question on expression
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Compute the distance between the two points. (–3, 4) and (21, 11)
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]
We replace:
[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]
Thus, the distance between the two points is 25 units.
Answer:
25
Answer:
The distance is 25 units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(21 - -3)² + (11 - 4)²]
= √[(21 +3)² + (11 - 4)²]
= √[24² + 7²]
= √(576 + 49)
= √625
=25
Therefore the distance is 25 units
Triangle QRS is dilated according to the rule DO,2 (x,y).
What is true about the image △Q'R'S'? Check all that apply.
DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
Step-by-step explanation:
Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule
[tex](x,y)\rightarrow (2x,2y)[/tex]
So,
[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
False options:
QR is longer than Q'R', because QR is twice shorter than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).
Answer:
1, 2, 5 on Ed
Step-by-step explanation:
Determine the end behavior for function f(x)=-x^4+5x^3-3
Answer:
Step-by-step explanation:
The dominant term of this function is x^4. The graph of x^4 starts in Quadrant II and continues in Quadrant I.
If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV. This is the end behavior for f(x)=-x^4+5x^3-3.
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
y+3 = -7/5(x+2)
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (4--3)/(-7--2)
= (4+3)/(-7+2)
=7/-5
= -7/5
The point slope form is y-y1 = m(x-x1)
y--3 = -7/5(x--2)
y+3 = -7/5(x+2)
We could use the second set of points
y-4 = -7/5(x--7)
y-4 =-7/5(x+7)
What is 7% of £14.50? Please show me the working outs in a simplest way possible. Thank you
[tex]\text{Hey there!}[/tex]
[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]
[tex]\text{Percentages (\%) usually run out of 100}[/tex]
[tex]\text{First, put the numbers set to multiply from each other.}[/tex]
[tex]\text{7\%}\times\text{14.50}[/tex]
[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]
[tex]\dfrac{7\%}{100}[/tex]
[tex]\dfrac{7\%}{100}=0.07[/tex]
[tex]\text{Next, solve for your answer.}[/tex]
[tex]\text{0.07}\times\text{14.50 = ?}[/tex]
[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]
[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
At which value of x does the graph of the function F(x) have a vertical asymptote?
Answer:
x = -8 & x = 3
Step-by-step explanation:
Vertical asymptote occur when denominator is 0.
So to find the x-values, we need to middle term factor the denominator. Shown below:
[tex]x^2+5x-24\\=(x+8)(x-3)\\x=3, -8[/tex]
Thus, at x = 3 and at x = -8 -- there is vertical asymptote.
simplify the expression below. 4^5 x 4^3
Answer:
4^8
Step-by-step explanation:
Because both expressions have the same base, we can add the exponents to simplify the expression:
[tex]4^5*4^3 = 4^{5+3} = 4^8[/tex]
Answer: 4^8 or 65,536
Step-by-step explanation:
The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents.
Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)
Answer:
The scale factor is equal to 1/2
The dimensions of each channel when splits the screen is 46 in x 38 in
Step-by-step explanation:
we know that
The dimensions of the new television is 92 in x 76 in
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
A1 -----> the area of the new television
A2 ----> the area of each channel when splits the screen
z-----> the scale factor
[tex]z^{2} =\frac{A2}{A1}[/tex]
we have that
The area of the new television is 4 times the area of each channel
[tex]A1=4A2[/tex]
[tex](A2/A1)=1/4[/tex]
[tex]z^{2} =\frac{1}{4}[/tex]
[tex]z=\frac{1}{2}[/tex] -----> the scale factor
so
When splits the screen, the dimension of each channel is equal to
92/2 in x 76/2 in
so
46 in x 38 in
Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides
Verify the value of the scale factor
92/46=1/2
or
76/38=1/2
Find the perimeter of the region that is NOT shaded.
39 ft
29 ft
58 ft
See the attached picture:
Points that lie on the same line are sold to be
collinear
Horizontal
ordered
Answer: b,c,e or 2,3,5
Step-by-step explanation:
Which expressions are equivalent to the given expression? Check all that apply.
(–2.4a – 1.8b) – (–3.8a – 4.4b) + (2.0a + 3.0b)
A. 3.4b – 3.2a
B. 3.4a – 3.2b
C. 5.6b + 3.4a
D. 3.2b + 3.4a
E. 3.4a
Answer:
5.6b + 3.4a
Step-by-step explanation:
Simply evaluate be match each term with its corresponding variable, and watch out for where you have to distribute negatives, meaning that you have a couple of double negatives in there.
Double Negative = Positive
Answer:
it’s C and E
Step-by-step explanation:
What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
A.) f[g(7)] = 9
B.) f[g(7)] = 143
C.) f[g(7)] = 239
D.) f[g(7)] = 281
Answer:
C
Step-by-step explanation:
To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)
g(7) = (2 × 7) - 5 = 14 - 5 = 9, then
f(9) = 3(9)² - 4 = 243 - 4 = 239 → C
Option C is correct.
Composite function :Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]
We have to find [tex]f(g(7))[/tex].
[tex]g(7)=2*7-5=14-5=9[/tex]
So that, [tex]f(g(7))=f(9)[/tex]
[tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]
Learn more about the composite function here:
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PLZZZZ GEOMETRY HELP solve for HI
Answer:
2 units
Step-by-step explanation:
ok, so, the line below says HJ is (x+1) units long. therefore:
2x-16+8 = x+1
now, let's isolate the variable.
2x-x = 1+16-8
x = 9
since we now defined variable x, we can add it to the equation that determines the length of HI.
2x-16
2(9)-16
18-16
2
the length of line segment HI is 2 units
hope this helped!
HI + IJ = HJ
With this knowledge you can from an equation like so...
2x - 16 + 8 = x + 1
Now combine like terms and solve for x
2x + (- 8 + 8) = x + 1 + 8
2x = x + 9
2x - x = x - x + 9
x = 9
To find HI plug 9 in for x and simplify
2(9) - 16
18 - 16
2
The length of HI is 2!!!
Hope this helped!
~Just a girl in love with Shawn Mendes
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A. Q(1, 11)
B. R(2, 4)
C. S(4,-4)
D. T(9,-2)
Answer:
The correct answer is R(2, 4)
Step-by-step explanation:
Which are possible first steps in solving the equation 4x + 3 = 18?
Answer:
C D and E
Step-by-step explanation:
The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work
Log(4^(x + 3)) = Log(18)
(x + 3) Log(4) = log (18)
(x + 3) * 0.6021 = 1.2553
x + 3 = 1.2553/0.6021
x + 3 = 2.08496
Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.
You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy. It does say possible first steps.
Answer:
C.Take the base-4 logarithm of each side.
D.Take the natural logarithm of each side.
E. Take the common logarithm of each side.
Step-by-step explanation:
Please Help I Will Offer 30!!!!
Answer:
Step-by-step explanation:
Compare y = (1/2)x - 3 and y = (-1/2)x - 3.
They have different slopes but the same y-intercept (0, -3). Eliminate the first answer choice.
They have different slopes. Eliminate the second answer choice.
Their graphs intersect, so they have a solution. Eliminate the third choice.
They have different slopes but the same intercept, so they have one solution. The fourth answer choice is the correct one.
Answer:
the fourth one is the corect one
Step-by-step explanation:
the fourth one is the corect one because i did the mathand i checked it twice and its right and also i asked my friend and he said it the fourth one
hope that helps you
A teacher wanted to buy a chair, a bookshelf, two tables and a desk. She spent $900 for all five items and the chair and the desk combined 70% of her total. If the bookshelf cost $50, how much did each of the tables cost?
Find the cost of the chair and desk by multiplying the total amount pent by the 70%
Chair and desk = 900 x 0.70 = $60
Subtract that cost from the total spent:
900 - 630 = $270 was spent on the other three items.
Subtract the cost of the bookshelf:
270 - 50 = 220
The two tables cost 220.
For the price of one table divide that cost by 2:
220/2 = 110
One table cost $110.
The cost of each table is $110.
Given that
There are five items i.e. chair, bookshelf, 2 tables, and a desk.
The total amount incurred for these 5 items should be $900.
And, the chair + desk = 70% of total.
The cost of the bookshelf is $50.
Since 70% of total = chair + desk
That means
Chair + desk = 0.70 of $900 = $630
So the other items cost should be
= $900 - $630
= $270
And, the cost of bookshelf is $50
So, the two tables cost should be
= $270 - $50
= $220
So for one it should be
= $220 ÷ 2
= $110
Therefore we can conclude that the cost of each table is $110.
Learn more about the cost here: brainly.com/question/5282141
X+3y=28 find the value of y when x equals 28
Answer:
y = 0Step-by-step explanation:
x + 3y = 28
Put x = 28 and solve for y:
28 + 3y = 28 subtract 28 from both sides
28 - 28 + 3y = 28 - 28
3y = 0 divide both sides by 3
3y : 3 = 0 : 3
y = 0
Which angles form a linear pair?
Answer:
Step-by-step explanation:
The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Answer:
Adjacent angles formed by two intersecting lines form a linear pair.
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. A linear pair of angles must add up to 180 degrees.
If two angles are adjacent angles that are formed by two intersecting lines, then they are called linear.
to solve the system of equations below, grace isolated the variable y in the first equation and then substituted into the second equation. what was the resulting equation? 3y=12x x^2/4+y^2/9=1
Answer:
The resulting equation is
x^2/4+16x^2/9=1
Step-by-step explanation:
The given equations are:
3y=12x eq(1)
x^2/4+y^2/9=1 eq(2)
We need to isolate variable y in equation 1
Divide both sides of the equation with 3
3y/3 = 12x/3
y = 4x
Now, substitute the value of y=4x in second equation
x^2/4+y^2/9=1
x^2/4 + (4x)^2/9 = 1
The resulting equation is
x^2/4+16x^2/9=1
Answer:
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Step-by-step explanation:
Given system of equations,
[tex]3y=12x-----(1)[/tex]
[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]
As per statement,
Isolating the variable y in the first equation,
[tex]y=\frac{12}{3}x=4[/tex]
Now, substituting into the second equation,
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Which is the resulting equation,
Simplifying the equation,
[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]
[tex]\frac{9x^2+64x^2}{36}=1[/tex]
[tex]73x^2=36[/tex]