Answer: s= -8
Step-by-step explanation:
The gradient of the ski slope can ge used as the slope (literally) of a line equation:
y = mx + b,
where m is the slope and b the y-intercept (the value of y when x = 0).
The first slope would be y = -(1/3)x + b.
The slope is (-1/3) since the ski run is headed downhill. The second ski slope is assumed to have the same gradient ("two parallel straight ski slopes").
y' = -(1/3)x' + b
We may assume that b is the same for both slopes - they start and end at the same point.
We can find b by using the given point (2,-3):
y' = -(1/3)x' + b
-3 = -(1/3)(2) + b
-3 = -(2/3) + b [Add -(2/3) to both sides: (-3 + 2/3 = -9/3 + 2/3 = -7/3]
-7/3 = b
b = -(7/3)
The second ski slope, y', thus has the equation
y' = (1/3)x' -(7/3)
We want the value of s in (s, -5).
y' = (1/3)x' -(7/3)
-5 = (1/3)s -(7/3)
(1/3)s = -5 +(7/3) [-15/3 + 7/3 = -8/3]
(1/3)s = -(8/3) [Multiply both dies by 3]
s = -(24/3)
s = -8
Express the given in terms of the logarithms of prime numbers:
[tex]log_{4} 405[/tex]
[tex]log_{7}(\frac{8}{81} )[/tex]
The required expression in terms of logarithm of prim numbers are;
[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]
[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]
Prime numbers are numbers that can only be divisible by 1 and itself.
From the given logarithmic expression, we will need to write 405, 8, and 81 as the product of prime numbers
405 = 3 * 3 * 3 * 3 * 5
405 = 3^4 * 5
8= 2* 2 * 2
8 = 2^3
81 = 3 * 3 * 3 * 3
81 = 3^4
The logarithm expression [tex]log_4405 \ and \ log_7(\frac{8}{81} )[/tex] can be expressed in terms of prime numbers as;
[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]
Similarly;
[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]
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Solve the system by substitution. x=-y-9 6x-5y=1
Answer:
x= -64, y= 55
Step-by-step explanation:
x=-y-9
6(y-9)-5y=1
6y-54-5y=1
y=55
x=-55-9
x=-64
Answer:
{x=-4
{x= -5
Step-by-step explanation:
Substitute into one of the equations:6(- y -9) - 5y=1
Apply Multiplicative Distribution Law:- 6y-54-5y=1
Rearrange unknown terms to the left side of the equation:-6y -5y = 1+54
Combine like terms:- 11y= 1+54
Calculate the sum or difference:-11y=55
Divide both sides of the equation by the coefficient of variable:y= 55÷(-11)
Remove the parentheses:y = -55÷11
Calculate the product or quotient:y=-5
Substitute into one of the equations:x=-(-5)-9
Remove the parentheses:x=5-9
Calculate the sum or difference:x=-4
The solution of the system is:{x=-4
{x=-5.
A baker baked some loaves of bread. 240 loaves were sold by the end of the day. The baker was left with 9/25 of the number of loaves that were baked. How many loaves of bread did the baker bake on that day?
Please do this in a easy way and explain no algebra
Answer:
The baker baked 375 loaves of bread that day.
Step-by-step explanation:
The baker baked a total of x loaves of bread.
240 loaves were sold by the end of the day.
The baker was then left with 9/25 of the number of loaves that were baked.
We get the equation:
x-240 = 9x/25
When you solve the equation, you will see that x=375.
Therefore, the baker baked 375 loaves of bread that day.
let r(t) be the rate in gallons per hour at which water enters a tank. what are the units of r'(t)?
The units of [tex]r'(t)[/tex] are gallons per square hour.
Dimensionally speaking, [tex]r(t)[/tex], expressed in gallons per hour, is length raised to third power divided by time. Capacity units are volume units.
As rate of change represents the instantaneous change of [tex]r(t)[/tex] in time, then we find that units are length raised to third power divided by time raised to second power.
Hence, the units of [tex]r'(t)[/tex] are gallons per square hour.
To learn more on dimensional analysis, we kindly invite to check this verified question: https://brainly.com/question/10874167
The function P(h) = 21h represents the total salary at a rate of $21 per
hour, P. as a function of the number of hours worked, h.
Find the total salary, when the number of hours worked is 34.
Replace h with 34:
p(h) = 21(34)
Multiply :
21x 34 = 714
Answer: $714
HELP - John uses 1/3 cup of orange juice for every 1/6 cup pineapple juice for fruit punch. Write the number of cups of orange juice John uses for 1 cup of pineapple juice.
Express the following equation in standard form y=5x-3
Answer:
5x - y = 3
Step-by-step explanation:
Standard form of a linear equation is expressed as Ax + By = C
In order to express the given equation in this form, we need to isolate the constant. We can achieve this by subtracting 5x from both sides:
y = 5x - 3
y - 5x = -3
If possible, we want A to be positive, so we can multiply both sides by -1:
-1(y - 5x) = -1(-3)
-y + 5x = 3 or 5x - y = 3
WHAT IS THE AREA OF THE FIGURE BELOW? 8 units. 9 units. 10 units. 12 units.
Sorry, I can't upload the picture so If you know the answer you can tell me.
Answer:
8
Step-by-step explanation: 6 (half the perimeter). By truial and error, 2 units by 4 units.
74.88 is what percent of 72?
Answer:
104%
Step-by-step explanation:
I really need help with these geometry questions.
Hey there!
I'm going to go in order from images.
1. The angle measure 60 is linear to angle 6, this would make them supplementary.
Angle 6: 180 - 60 = 120
Angle 6 is vertical to angle 2, this makes them congruent. If angle 6 equals 120 measure 2 also equals 120.
2. Measure 6 is vertical from measure 2. We established in the last problem measure 2 equals 120.
If angle 2 equals 120 measure 6 also equals 120.
3. The 2 equations are alternate exterior angles.
2x+5=8x-7
+7 +7
2x+12=8x
-2x -2x
12=6x
12/6= 2
x=2
4. I cannot explain this one without showing it visually lol.
Measure 5 equals 30 degrees.
5. Measure 1 is verticle to the measure that reads 60. Vertical angles are congruent.
If measure 1 is congruent to the measure that reads 60. Measure 1 equals 60.
I hope this helps!!!
b. 6 times the sum of 12 and 8
Answer:
120
Step-by-step explanation:
12+8 = 20
20*6 = 120
Those are the right answer
Answer:
100 yes there are trust me
the reciprocal of 4 is
the answer of ur question is 0.25
pLS HELP ME 15 points in total
Answer:
Its 53 because 1=1 and 2=2
Step-by-step explanation:
Painted Pots lets customers choose and paint their own pottery. The store has teapots in
multiple sizes. Rebecca chose to paint the largest teapot offered, which cost $18. She also
painted 4 small teacups to go with her teapot. Rebecca spent a total of $42 on pottery.
3
Which equation can you use to find c, the cost of each teacup?
Time
elapse
00
09
18(C + 4) = 42
40 + 18 = 42
SmartSco
Out of 100
18C + 4 = 42
4(0 + 18) = 42
What was the cost of each teacup?
Using a linear equation, we find c using:
[tex]42 = 18 + 4c[/tex]
A linear function has the following format:
[tex]A(n) = A(0) + cn[/tex]
In which:
c is the slope, which is the price per unit.A(0) is the y-intercept, which is the fixed price.In this problem, fixed price of $18, hence [tex]A(0) = 18[/tex]
She bough 4 units, and it cost $42, hence: [tex]n = 4, A(n) = 42[/tex]
Then
[tex]A(n) = A(0) + cn[/tex]
[tex]42 = 18 + 4c[/tex]
Hence, the equation to find c is:
[tex]42 = 18 + 4c[/tex]
A similar problem is given at https://brainly.com/question/16302622
easy one for you folks.
Length = 4m
Width = ½ of length = ?
Then width will be,
→ 4 × 1/2
→ 4 ÷ 2 × 1
→ 2 × 1 = 2
Thus, 2 is the width.
Which transformation maps the strip pattern onto itself?
pdpdpdpdpd
A. half-turn
B. vertical reflection
C. glide reflection
D. vertical translation
The mapping of the strip pattern onto itself is a Glide reflection.
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Glide reflection is a combination of reflection over a line and then translation along that line.
As we can see, the mapping of the strip pattern onto itself is a Glide reflection.
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Answer:
A: Half-turn
Step-by-step explanation:
i took the test and got it wrong due to the wrong answer above.
What is the Slope of the line containing the points (3,4) and (5,6)? Please help
Answer:
1
Step-by-step explanation:
Y2-Y1/X2-X1 would become 4-6/3-5 which would become-2/-2 and that equals 1 because its a whole number and when you divide or add two negative numbers, it becomes a positive
Simplify the expression.
(6/7c)^2
A.) 12/14c^2
B.) 42c^2
C.) 36/7c D.) 36/49c^2
we have (6/7c)^2 = (6^2)/(7c)^2 = 36/49c^2
so the answer is D
ok done. Thank to me :>
Please help due today
Answer:
Step-by-step explanation:
Each boundary line equation is of the form ...
y = mx + b
the value of m is the coefficient of x. The value of b is the constant. You find their values by matching the given relation to the form above, and identifying the matching parts.
y ≤ 1/2x +2 ⇒ m = 1/2, b = 2
y < -2x -3 ⇒ m = -2, b = -3
_____
The slope (m) in each case tells you how many units up (m>0) or down (m<0) the line will go for each unit to the right. The y-intercept (b) in each case gives you a starting point on the y-axis, making it easier to draw the line.
The < part of each inequality symbol tells you the graph will be shaded below the boundary line. (Y-values in the solution set are less than those on the line.) The "or equal to" part of the first inequality symbol tells you the boundary line will be solid. (Y-values on that line are part of the solution set.) The lack of that in the second inequality tells you the boundary line will be dashed.
The graph is shown in the attachment.
EXAMINE THE PARAGRAPH PROOF. WHCIH THEOREM DOES IT OFFER PROOF FOR?
Answer:
The answer is C.
Step-by-step explanation:
The theory of vertical angles, often known as the theorem of vertically opposite angles. According to the theorem, two opposed vertical angles created when two lines cross one other are always equal (congruent) to each other no matter what the circumstances are.
which statement correctly compares the function shown on this graph with the function y = 3x - 6?
Answer:
Perpendicular
Step-by-step explanation:
The equation of the graph is y = 1/3x + 4
The slope 1/3 and 3 are opposite reciprocals, which indicates that the two lines are perpendicular.
-Chetan K
1.
Prove that AMNO is congruent to AXYZ using triangle congruency theorems.
M
Given: ZMLX
2N =zY
YO NZ
Prove: AMNO = AXYZ
Z
I
Answer:
yes they are
Step-by-step explanation:
they are both congruent because they are the same shape and size, they are just on opposite sides
(congruent means that 2 objects are the same shape and size)
Answer:
yes they are
Step-by-step explanation:
Rewrite the equation by completing the square.
x? - 8x + 7 = 0
(x + __)^2 = 0
Answer:
(x - 4)² - 9 = 0
Step-by-step explanation:
x² - 8x + 7 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 8x
x² + 2(- 4)x + 16 - 16 + 7 = 0
(x - 4)² - 9 = 0
The monthly rent of Marilyn's house went from $500 to $440, If p is the
percent decrease in the rent, which proportion can be used to calculate p?
A)
р
100
OB)
$440-$500
$440
р
100
$440-$500
$500
$500-$440
$440
$500-$440
P
100
OD)
р
100
$500
Answer:
p=v-u/t440-500=-60 this is decreasing in the rent so it decreased
[ READ ATTACHMENTS ] !!! [ HELP ME ASAP PLEASE!! ]
A.) $4,000
B.) $5,100
C.) $4,100
D.) $3,900
Total up the Consumption,Investment, Government Spending and Exports then minus the Total Imports. So the correct answer is C. $4,100
Please answer this question
Answer:
Step-by-step explanation:
2)f(x) = 2x² +4x - 3
a = 2 ; b = 4 ; c = -3
1) Put x = -1 in the equation
f(x) = 2*(-1)² + 4*(-1) -3 = 2 - 4 -3 = -5
Vertex = (-1,-5)
2) Upward
3) Minimum
4) axis of symmetry = -b/2a = -4/2*2=-4/4= -1
x = -1
5) domain: all real numbers (-∞ ,∞)
Range : y ≥ -5 ; [-5 , ∞)
3) f(x) = 3x² - 6x + 4
Vertex : (1,1)
Opening : upward
Minimum
Axis of symmetry: x = 1
Domain: all real numbers
Range: y ≥ 1 ; [1, ∞)
4)f(x) = -x² - 2x - 3
a) Vertex: f(x) = -(-1)² - 2*(-1) - 3 = -1 + 2 - 3 = -2
Vertex( -1,-2)
b) downward
c) Maximum
d) Axis of symmetry: x = 2/-2 = -1
x = -1
e) Domain: all real numbers
Range: y ≤ -2 ; (-∞ , -2]
5)f(x) = 2(x -2)²
a) Vertex: (2, 0)
b) Opening: upward
c) Minimum
d) x = 2
e)Domain: all real numbers
Range: y ≥ 0 ; [0,∞)
What is the equation of the line that passes through the point (8,-8) and has a slope of -2
Answer:
y=-2x+8
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (8, -8) and has a slope of -2
We can write this equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
Since we already know the slope of the line, we can immediately plug it into the equation as m:
y=-2x+b
Now we need to find b
As the equation of the line passes through the point (8, -8), we can use it to help solve for b, since (8, -8) is a solution to the equation, meaning that it will yield a true statement when plugged into the equation
So substitute 8 as x and -8 as y:
-8=-2(8)+b
Multiply
-8=-16+b
Add 16 to both sides
8=b
Now substitute 8 as b into the equation:
y=-2x+8
Hope this helps!
.Equation of line in point slope form
[tex]\\ \sf\longmapsto y-y_1=m(x-x_1)[/tex]
[tex]\\ \sf\longmapsto y+8=-2(x-8)[/tex]
[tex]\\ \sf\longmapsto y+8=-2x+16[/tex]
[tex]\\ \sf\longmapsto 2x+y+8-16=0[/tex]
[tex]\\ \sf\longmapsto 2x+y-8=0[/tex]
Which of the following is another way to express the difference between -5 and 8?
O-5+8
O-5-(-8)
O-5+(-8)
08-5
to solve the equation, x+5=12, what property do you use?
Answer: inverse operation, subtraction
Step-by-step explanation: The key insight here is that we want to solve for x , and in doing so, we need to undo any operation being applied to it. Right now, only 5 is being added to it, so to solve for it, we need to do the inverse operation, subtraction
If you mean this: How to solve multiplication property of equality?
Multiplication Property of Equality
For all real numbers a, b, and c: If a = b, then a • c = b • c (or ab = ac).
I hope this is right :)