Answer (assuming it is allowed to be in point-slope format):
[tex]y-4 = \frac{2}{3}(x-1)[/tex]
Step-by-step explanation:
1) First, determine the slope. We know it has to be perpendicular to the given equation, [tex]y = -\frac{3}{2} x-4[/tex]. That equation is already in slope-intercept form, or y = mx + b format, in which m represents the slope. Since [tex]-\frac{3}{2}[/tex] is in place of the m in the equation, that must be the slope of the given line.
Slopes that are perpendicular are opposite reciprocals of each other (they have different signs, and the denominators and numerators switch places). Thus, the slope of the new line must be [tex]\frac{2}{3}[/tex].
2) Now, use the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex] to write the new equation with the given information. Substitute [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] for real values.
The [tex]m[/tex] represents the slope, so substitute [tex]\frac{2}{3}[/tex] in its place. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects. Since the point crosses (1,4), substitute 1 for [tex]x_1[/tex] and 4 for [tex]y_1[/tex]. This gives the following equation and answer:
[tex]y-4 = \frac{2}{3}(x-1)[/tex]
Solve for f
-5f +5 < 15
Question 1 options:
f < 8
f > -2
f = 3
f < 2
I NEED HELP ASAP
Step-by-step explanation:
step 1. -5f + 5 < 15
step 2. -5f < 10 (subtract 5 from each side)
step 3. f > -2 (divide both sides by -5 - dont forget to flip arrow when dividing by a negative number).
One number added to twice another number is 30. The sum of the numbers is 19.
Write and solve a system of equations to represent this situation.
What is the value of the smaller number?
What is the value of the larger number?
I don't understand :(
Answer:
The smaller number is 8
The bigger number is 11
Step-by-step explanation:
let the first number be A
let the second number be B
A + 2B = 30..... equation 1
A + B = 19...... equation 2
Subtract equation 2 from 1.
A + 2B = 30
- A + B = 19
-------------------
0 + B = 11
B = 11
Substitute B = 11 into equation 2
A + B = 19
A + 11 = 19
collect like terms
A = 19-11
A = 8.
A= 8 and B = 11
find the slope of the line passing through the points (-3,2) and (-3,-7)
Slope = change in Y / change in x
Slope = (-7 - 2) / (-3 - -3)
Slope = -9/0
Because the change in x = 0, the slope is undefined.
The answer is the slope is undefined.
hideki is draining a 45 gallon aquarium at a rate of 15 gallons per minute what is the initial value of the linear function that represents the situation ?
Answer:
45.
Step-by-step explanation:
Since Hideki is draining a 45 gallon aquarium at a rate of 15 gallons per minute, to determine what is the initial value of the linear function that represents the situation, the following calculation must be performed:
45 (starting number) - 15(number of gallons per minute) X(minutes) = Y
Therefore, the equation would be 45 - 15X = Y, with which the initial value of the linear function that represents the situation is 45.
what is the speed, if distance is 900 miles and time 300 minutes
Answer:
3 mi/min
Step-by-step explanation:
speed =distance/time
900/300=3
4. A regular hexagon is shown below. Find the value of x. (11x + 21)
Answer:
We need the picture
Step-by-step explanation:
a line can divide the figure into two identical four sided polygons each polygon has two bases and one one base is twice the length of the other base identify the polygon and give it's perimeter
Answer:
Step-by-step explanation:
I know know it that that girl is wrong
The polygon being described is a trapezoid, where one base is twice the length of the other base.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
The polygon being described is a trapezoid, where one base is twice the length of the other base.
Let the shorter base be b and the longer base be 2b.
To divide the figure into two identical trapezoids, the line must pass through the midpoint of the longer base, creating two trapezoids that are mirror images of each other.
The perimeter of each trapezoid can be found as follows:
Perimeter = sum of lengths of all sides
Hence, the polygon being described is a trapezoid, where one base is twice the length of the other base.
To learn more on Quadrilateral click:
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A runner ran of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.
How long did it take to run the entire race?
Answer:
4.2
Step-by-step explanation:
the kilometro is 5 and race is 21. 5÷21=4.2
expand the following expression by using the distributive method 7(10-3x))
Answer:
Step-by-step explanation:
7(10)-7(3x)
80-21x
Answer:
70+21x
Step-by-step explanation:
multiply the number that outside on the ( ) for the numbers that are in side
find ratio of 120 :80
120 : 80
= 12 : 8
= 6 : 4
= 3 : 2
This is the answer
Answer:
120/10=12
80/10=8
12/4=3
8/4=2
Nothing can further decide, then we have
3:2
shape?
6. What is the volume of the following
A 144 cm
B. 72 cm3
C. 432 cm3
D. 216 cm
Answer:
A
Step-by-step explanation:
v=1/3Ab*h= 1/3(72)*6
72*2= 144 cm3 so
A
if my answer helps please mark as brainliest.
Question 11 (1 point)
Evaluate the function.
Given f(x) = x2 - 5x + 5, find f(3).
Answer:
f(3) =-1
Step-by-step explanation:
f(x) = x^2 - 5x + 5
Let x=3
f(3) = 3^2 -5(3) +5
= 9 -15+5
= -6+5
=-1
Divide using long division.
(x3 + 3x2 + x - 4) + (x - 1)
Answer:
2x+3x2 +x3 −5
Step-by-step explanation:
Hope this helps
Answer:
x^2 - 2x + 2
step-step explanation:
Find angle. Picture below!
Answer:
m<QRP=42degrees
m<Q=79degrees
m<P=59degrees
Step-by-step explanation:
17. **4• 2 = (3 x 100 000) + (2 x 10 000)+
(8 x 1 000) + (4 x 100) + (2x1)
Yukandaki eşitliğe göre (* + %) - ( + ) işle-
minin sonucu kaçtır?
A. 9
B.8
C. 7.
D. 6
Cevap:9 umarım doğrusunu seçersin
For the rational function f(x)=(-13x-27)/(x^(2)-4x-12), F(x)=2
A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinic follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members of the health plan):
2.31, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97, 2.02.
a. Find a 95% two-sided CI on the mean number of CAT scans performed each month at this clinic.
b. Historically, the mean number of scans performed by all clinics in the system has been 1.95. If there any evidence that this particular clinic performs more CAT scans on average than the overall system average?
Answer: a. 1.981 < μ < 2.18
b. Yes.
Step-by-step explanation:
A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.
First, we calculate mean of the sample:
[tex]\overline{x}=\frac{\Sigma x}{n}[/tex]
[tex]\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}[/tex]
[tex]\overline{x}=[/tex] 2.08
Now, we estimate standard deviation:
[tex]s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }[/tex]
[tex]s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }[/tex]
s = 0.1564
For t-score, we need to determine degree of freedom and [tex]\frac{\alpha}{2}[/tex]:
df = 12 - 1
df = 11
[tex]\alpha[/tex] = 1 - 0.95
α = 0.05
[tex]\frac{\alpha}{2}=[/tex] 0.025
Then, t-score is
[tex]t_{11,0.025}[/tex] = 2.201
The interval will be
[tex]\overline{x}[/tex] ± [tex]t.\frac{s}{\sqrt{n} }[/tex]
2.08 ± [tex]2.201\frac{0.1564}{\sqrt{12} }[/tex]
2.08 ± 0.099
The 95% two-sided CI on the mean is 1.981 < μ < 2.18.
B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.
Can someone help me? I'd appreciate it
7
Jackson is creating a rectangular board game that includes a diagonal line from two of the corners of the game. How long is the diagonal if the board game is 10 inches
long by 8 inches wide? Explain your reasoning. Round your answer to the nearest tenth of an inch.
Helppp
Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.
Using the pattern rule, find the missing
value in the table.
y = x + 8
input X 1
output y 9
2 3 4
10 | 11 | [?]
Enter the number that belongs in the green box.
Enter
Answer:
y=12
Step-by-step explanation:
y=x+8
9=1+8
10=2+8
and so in...
y=?
4+8=12
- Peter's bike bill is automatically
deducting $78 from his bank
account every month. If his bank
account balance is at $234, how
many months will it take for Pete to
run out of money?
PLEASE
The weekly production cost C of manufacturing x watches is given by the formula C = 6000 + 3x, where the variable C is in dollars.
" (a) What is the cost of producing 1000 watches?
Answer:
therefore, to produce 1000 watches , it would cost 9000 dollars.
Price : 9 dollars a watch
Step-by-step explanation:
C=6000 + 3x
what is the cost of producing 1000 watches?
first do this
C= (1000)= 6000 + 3(1000)
C= (1000)= 6000 +3000
C= 9000
Rick wants to buy a tool set with an original price of $165. Next week, the tool set will be on sale for $40 off. What is the sale
price of the tool set?
Answer:
$125 is the sale price.
Step-by-step explanation:
Answer:
24.24% off
Price of tool set: $125
Step-by-step explanation:
$40 is the price change
You can divide 40 by the original price which is 165 and then multiply by 100 to get your percentage change.
40 / 165 = 0.2424
0.2424 * 100 = 24.24
So there is 24.24% discount.
PLSS HELP ME TYSMMMMM
Answer:
Picture or question???????
Please help ASAP. Thanks so much.
Answer:
D. 1/9
Step-by-step explanation:
The x-coordinate is -1/3
A number is 4 times the sum of its digits. The units digit is two more than the tens digit. Find the number.
Answer:
24
Step-by-step explanation:
Let x = the 10's digit
Let y = the units
then
10x+y = "a number"
:
A number is 4 times the sum of its digits.
10x + y = 4(x + y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
Simply, divide by 3
2x = y
;
The units digit is two more than the tens digit.
y = x + 2
Replace y with 2x
2x = x + 2
2x - x = 2
x = 2
then
y = 4
:
24 is the number
The two digit number is equivalent to 24.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a number is 4 times the sum of its digits. The units digit is two more than the tens digit.
Let the number be {A}. Then, we can write -
A = 10x + y ......... (1)
also
A = 4(x + y) ........... (2)
The units digit is two more than the tens digit, so we can write -
y = x + 2 .............. (3)
So, we can write -
10x + y = 4(x + y)
10x + (x + 2) = 4(x + x + 2)
11x + 2 = 8x + 8
3x = 6
x = 2
So, we can write {y} as -
y = 4
Number will be -
10 x 2 + 4
n = 24
Therefore, the number will be equivalent to 24.
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Bryson has soccer practice for 2 1/4 hours 2 times a week. How much time does Bryson spend at soccer practice in 1 week?
Answer:
15.75
Step-by-step explanation:
The dollar value v (t) of a certain car model that is t years old is given by the following exponential function.
v (t) = 19,900(0.86)^t
Find the initial value of the car and the value after 11 years.
Round your answers to the nearest dollar as necessary.
Answer:
v(0) = 19,900, v(11) = 3,787.36
Step-by-step explanation:
v(0) = 19,900 (0.86)^0 = 19,900 * 1 = 19,000
v(11) = 19,900 (0.86)^11 = 19,900 * 0.190319 = 3,787.36
A computer game originally sold for $40 but is now on sale for 30% off. What is the sale price of the computer game?
Answer:
28
Step-by-step explanation:
Answer:
28
Step-by-step explanation:
30% of 40 is 12, 40-12=28, the answer is 28.
an examination class of 55% of pupil scored 70% , if 54 scored above 70%. how many scored above 70%.
Answer:
You just said the answers. 54
Step-by-step explanation:
5