Answer:
[tex]r=\frac{14}{3}[/tex]
Step-by-step explanation:
Set up an equation and solve for r using the formula for slope:
[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]
Find the domain and range of the function graphed below.
Domain:
Range:
The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
How to find the domain and range of a functionThe domain of a function is the input value for which the function exists while the range is the output value for which the function exists.
For the graph, the domain lie across the x-axis. The domain of the function is [-2, 2) while the range is [4, 2) (along the y -axis).
Note that point where the circles are shaded shows a closed interval
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"Last week you sold 30, 45, 50, 75, and 80 units each day of the week, in that order. On average, how many units did you sell per day?"
Answer:
56
Step-by-step explanation:
1) Add together all numbers. 30+45+50+75+80 = 280.
2) Divide result by amount of numbers. 280/5 = 56
3) You are welcome. :)
On an average, you sold 56 unit per, day.
What is average?A number that is calculated by adding quantities together and then dividing the total by the number of quantities.
Given that, Last week you sold 30, 45, 50, 75, and 80 units each day of the week.
To find the average, we will, first add together all numbers and then divide the result by the sum of numbers.
Therefore,
Adding together all numbers = 30+45+50+75+80 = 280.
Divide result by amount of numbers = 280/5 = 56
Hence, On an average, you sold 56 unit per, day.
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 Mrs. Lee earned a $3,000 bonus at work. She will use $1,737 of it to replace her water heater. If she wants to divide the rest of the bonus evenly between her 3 children, how much will each child receive?
Answer: 421
Step-by-step explanation:
Subtract 3,000 by 1,737 and the product of that divided by 3 which will give you 421
6 sushi rolls cost $8.99
Jason bought 3 shirts that each cost the same.He has a coupon for $10 off and he spent $65 altogether.Which equation can be used to find the cost of each shirt
Answer:
3x-10=65
Step-by-step explanation:
So, since he used the coupon, you can do 65+10=75.
The cost before the coupon is 75.
The cost of each shirt is 75/3, but that doesn't solve the question.
You can do (assume each shirt's cost is x)
3x-10=65
I could give more in depth but I can't see the options, sorry!
Answer:
(65+10) / 3= x
x would equal what each shirt costs
Step-by-step explanation:
1/3 + 1/3=
5/10-2/10=
=
4/5-2/5=
11+1=
=
Answer:
Step-by-step explanation:
1/3 + 1/3= 2/3
5/10-2/10=3/10
4/5-2/5=2/5
11+1=12
Find the measures of angles 1 through 6.
Answer:
<1 = 88° , <2 = 129°, <3 = 82°, <4 = 147°, <5 = 94°, <6 = 86°
Step-by-step explanation:
<1 + 92° = 180°
<1 = 88°
<2 + 51° = 180°
<2 = 129°
<3 + 98° = 180°
<3 = 82°
<4 + 33° = 180°
<4 = 147°
<1 + <2 + <3 + <4 + <5 = 540°
88° + 129° + 82° + 147 + <5 = 540°
<5 = 94°
<5 + <6 = 180°
94° + <6 =180°
<6 = 86°
Evaluate each expression if f = –4, g = 2, and h = 7.
h – f
Answer:
11
Step-by-step explanation:
h - f = 7 - (-4) = 7 + 4 = 11
A chef used one-half of a bag of potatoes for a meal. If the potatoes fed 2 people, what
fraction of the bag did each person get?
(Help plss as soon as you can)
Answer: 1/4
Step-by-step explanation: each person had half of the half of bag.
I need help!! I will give 5.0 star
So, here we need to differentiate tan³[tex](\theta)[/tex], wr.t.[tex]\theta[/tex], but let's recall some identities which will be very useful in this question :
[tex]{\boxed{\bf{\dfrac{d}{dx}\{\tan (x)\}=\sec^{2}(x)}}}[/tex][tex]{\boxed{\bf{\dfrac{d}{dx}(x^n)=nx^{n-1}}}}[/tex][tex]{\boxed{\bf{\sec^{2}(\theta)=\tan^{2}(\theta)+1}}}[/tex]Coming back on the question, consider :
[tex]{:\implies \quad \sf \dfrac{d}{d\theta}\{\tan^{3}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{3-1}(\theta)\dfrac{d}{d\theta}\{\tan (\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\sec^{2}(\theta)}[/tex]
Using the identity ;
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)\{1+\tan^{2}(\theta)\}}[/tex]
[tex]{:\implies \quad \sf 3\tan^{2}(\theta)+3tan^{4}(\theta)}[/tex]
[tex]{:\implies \quad \sf 3\tan^{4}(\theta)+3\{\sec^{2}(\theta)-1\}}[/tex]
[tex]{:\implies \quad \boxed{\bf 3\tan^{4}(\theta)+3\sec^{2}(\theta)-3}}[/tex]
Hence, Proved
sophia is designig a logo with three lines,y, m, and n. Line m passes through point (-2, -1) and is perpendicular to the graoh of y=-2/3 x +6. line n is parallel to line m and passes through the point (4, -3). what is the equation in slope-intercept form of linen?
Answer:
y = 3/2x - 9
Step-by-step explanation:
Finding equation of line m
⊥ to the line y = -2/3x + 6new slope = -(-3/2) = 3/2Passes through the point (-2, -1)y + 1 = 3/2(x + 2)y + 1 = 3/2x + 3y = 3/2x + 2Equation of line n
Parallel ⇒ slope is same = 3/2Passes through the point (4, -3)y + 3 = 3/2(x - 4)y + 3 = 3/2x - 6y = 3/2x - 9Answer:
[tex]\textsf{Equation of line n}:\quad y=\dfrac32x-9[/tex]
Step-by-step explanation:
Equation of line m
If two lines are perpendicular to each other, the product of their slopes will be -1.
The slope of the line [tex]y=-\dfrac23x+6[/tex] is [tex]-\dfrac23[/tex]
Therefore, the slope of the line m is:
[tex]\implies m \times -\dfrac23=-1[/tex]
[tex]\implies m=\dfrac32[/tex]
If line m passes through point (-2, -1), then the equation of line m is:
[tex]\implies y-(-1)=\dfrac32(x-(-2))[/tex]
[tex]\implies y+1=\dfrac32(x+2)[/tex]
[tex]\implies y=\dfrac32x+2[/tex]
Equation of line n
If line n is parallel to line m, then they will have the same slope.
Therefore, slope of line n is [tex]\frac32[/tex]
If line n passes through point (4, -3), then the equation of line n is:
[tex]\implies y-(-3)=\dfrac32(x-4)[/tex]
[tex]\implies y+3=\dfrac32x-6[/tex]
[tex]\implies y=\dfrac32x-9[/tex]
What is the measure of m?
6
24
m
m= 6y[?]
Give your answer in simplest form.
Similar triangles are those triangles whose corresponding sides are in the same ratio. The measure of m is 6√4.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
In the given triangles ΔABC and ΔBCD,
∠ACB = ∠DCB {Common Angles}
∠BDC = ∠ABC =90°
Therefore, the two triangles are so, for triangles.
(6+24)/BC = m/n = BC/24
BC² = 30×24
BC = √720
Now, using the Pythagorean theorem,
AC² = AB² + BC²
30² = m² + (√720)²
900 = m² + 720
180 = m²
m = 6√4
Hence, the measure of m is 6√4.
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the 3 sides of triangle are n, 4n + 1 , 5n- 8. if the perimeter of the triangle is 93 cm, what is the length of each side?
Answer:
10, 41, 42
Step-by-step explanation:
(n)+(4n+1)+(5n-8)=93 because triangle perimeter
10n-7=93
10n=100
n=10
Answer: 10 cm, 41 cm, and 42 cm
Step-by-step explanation:
We can set up an equation knowing the perimeter to solve for the lengths of each side. Then, we will plug the value of n into the different expressions that represent each side.
Perimeter of a triangle:
P = side a + side b + side c
Plug in our known values:
93 cm = (n) + (4n + 1) + (5n - 8)
Simplify and combine like terms:
93 cm = n + 4n + 1 + 5n - 8
93 cm = n + 4n + 5n + 1 - 8
93 cm = 10n -7
Add 7 to both sides of the equation:
100 cm = 10n
Divide both sides of the equation by 10:
10 cm = n
n = 10 cm
-
Solve for the lengths of each side:
n = 10 cm
4n + 1 = 4(10) + 1 = 40 + 1 = 41 cm
5n - 8 = 5(10) - 8 = 50 - 8 = 42 cm
Which answer is $734,596 rounded to the nearest thousand??
1) 734,500
2)734,600
3)735,000
4)734,000
Thank you so much
Answer:
2
Step-by-step explanation:
which best represents the relationship between x and y
y=2x
y=x+2
y=4x
y=x+4
Answer:
In y = 2x the value of y is twice the value of x, and in y = x + 2 the value of y is two more than the value of x.
Same for the y=4x and y=x+4, just plug the numbers into the sentence.
Step-by-step explanation:
PLEASE
Write an equation in slope-intercept form of the line shown.
An equation is
Answer:
y = -x - 4
Step-by-step explanation:
m = (-5-0)/(1+4) = -5/5 = -1
b = (0, -4)
y = mx + b
y = -x - 4
Answer:
y = -x - 4
Step-by-step explanation:
Slope-intercept form is:
y = mx + b
The b is the y-intercept. That is where the line crosses the y-axis. This line crosses the y-axis at -4.
You could calculate the slope, but with a graph, you can SEE the slope without doing any calculation. Find a point on the line, any point. To get to the next point, you go DOWN1 and OVER1, (down1, over1, down1, over1)
This is -1/1. The slope is -1. Fill that in for m.
Leave the x and y as-is in
y = mx + b
fill in -1 for m and -4 for b.
y = -x - 4
If your teacher/prof is expecting to see a calc for slope. Find two points on the line. Subtract y-y and put that on top. Subtract x-x and put that on the bottom. Simplify.
Given points:
(1,-5) and (-4,0)
-5 - 0 is -5, put on top.
1 - -4 is 5, put underneath. You get -5/5, which is -1. Slope is -1.
Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)
Answer:
A. student A is correct; student B was confused by the division
B. 3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)
Step-by-step explanation:
Each student correctly made use of the trig identities ...
csc(θ) = 1/sin(θ)
1 -sin²(θ) = cos²(θ)
__
A.Student A's work is correct.
Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.
__
B.The transition from Step 2 can look like ...
[tex]\textsf{Step 3: }\ \dfrac{\left(\dfrac{1-\sin^2\theta}{\sin\theta}\right)}{\csc\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}\cdot\dfrac{1}{\csc\theta}=\dfrac{\cos^2\theta}{(\sin\theta)(\csc\theta)}\\\\\textsf{Step 4: }\ \cos^2\theta[/tex]
Stuck on this math question can anyone help me please?!?
Answer:
1) f(-6) = 8
2) f(3) = -2
3) f(x) = -5 when x = 4
Mr. Red's first year salary is $30,000 and it increases by $500 each year. What is the explicit rule for this sequence in simplified form?
What is the recursive rule?
The required recursive function will be expressed as an = 3000 + 500n
How to write recursive functionsGiven the following parameters
First year salary = $30,000
If it increases by $500 each year, let the number of years be "n", then the increment after "n" years is 500n
The required recursive function will be expressed as an = 3000 + 500n
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PLEASE HELP PLEASE HELP PLEASE
blue stars. let’s talk a bit about temperature. The color of a star is a function of its temperature. If a star looks red, that means its surface temperature is approximately 2,500 Kelvin. Just for comparison, our Sun, which actually looks white from space, measures about 6,000 Kelvin. The hotter the star, the further up the spectrum you go. The hottest stars are the blue stars. A star appears blue once its surface temperature gets above 10,000 Kelvin, or so, a star will appear blue to our eyes.
In the figure below, the segments IJ and IK are tangent to the circle centered at O. Given that OJ=8.4 and OI=15.9, find IK.
Answer:
IK = 13.5
Step-by-step explanation:
A^2 + B^2 = C^2
(8.4)^2 + B^2 = (15.9)^2
70.56 + B^2 = 252.81
B^2 = 182.25
B =13.49925... ≈ 13.5 = IK
Please answer the question in the picture for brainliest
Answer:
26
Step-by-step explanation:
simply count the number of times the team scored more than 50 points by looking at the graph.
the team scored 51-60 points 11 times, 61-70 points 12 times and 71-80 points 3 times.
so the team scored more than 5 points a total of 11 + 12 + 3 = 26 times
Answer:
26
Step-by-step explanation:
Game scores above 50 points can be represented by the last three boxes to the left. To find the total number of times this happened, add up the values measured by the y-axis:
51-60 = 11 games
61-70 = 12 games
71-80 = 3 games
11 + 12 + 3 = 26
I hope this helps!
88.60 plus what equals 153.25
Answer:
64.65
Step-by-step explanation:
153.25 - 88.60 = 64.65
88.60 + 64.65 = 153.25
Answer:
64.65
Step-by-step explanation:
153.25 - 88.60 = 64.65
64.65 + 88.60 = 153.25
PLEASE ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️!
Answer:
the answer is B.(3,6)
because y>2
so,the answer is 3&6.
Drag each expression to show whether it is equivalent to 54x + 18 or
(6 · 9x) + (6 · 1).
Answer:
The first one should belong in the 54x+18 due to multiplication
The second answer choice has distributive property which has to belong in the 54x+18 category
The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.
The last one should be in the 54x+18 category because of the distributive property
Step-by-step explanation:
The Objectives: 54x+18 and (6(9x) + 6
The first one should belong in the 54x+18 due to multiplication
The second answer choice has distributive property which has to belong in the 54x+18 category
The third answer choice fits into the 6 times 9x + 6 times one category due to multiplication like the first answer choice.
The last one should be in the 54x+18 category because of the distributive property
What is true about the domain and range of the function?
The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers.
The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4.
The domain is all real numbers greater than or equal to
–4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Answer:
The domain is all real numbers greater than or equal to 4, and the range is all real numbers
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
Parallelogram RSTU is shown. The perimeter of parallelogram RSTU is 50
centimeters. What is the value of x? *
R.
(2x + 15) cm
S
(3x + 20) cm
U
T
-5
-2.
3
O 12
Answer: x = -2
Step-by-step explanation:
Given:
Perimeter = 50 cm
=> 2 (2x+15)+ 2(3x+20) =50
=> 4x+30+6x+40=50
=> 10x= -20
=> x= -20/10
=> x = -2
Please assist me with these question. I am having a hard time
Step-by-step explanation:
[tex] \frac{1}{3x} + \frac{7}{ {x}^{2} } + \frac{x + 2}{x} [/tex]
[tex] \frac{x}{ {3x}^{2} } + \frac{21}{3 {x}^{2} } + \frac{3 {x}^{2} + 6x}{3 {x}^{2} } [/tex]
[tex] \frac{ {3x}^{2} + 7x + 21 }{ {3x}^{2} } [/tex]
Choice D
Please help me I will mark BRAINLY
Answer:
see explanation
Step-by-step explanation:
(a)
5% of N 80000
= [tex]\frac{5}{100}[/tex] × 80000
= 0.05 × 80000
= N4000 ← VAT
(b)
total cost = 80000 + 4000 = N84000
