The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.
Slope of the line:
A slope of a line is the change in y coordinate with respect to the change in x coordinate.
Given,
The point (9,10) that cuts off the least area from the first quadrant
Here we need to find the slope and y intercept of the line.
A line is passing through a point (9,10) cuts off least area in first quadrant.
The equation of the line passing through point (9,10) and has slope m can be expressed as,
=> y - 10 = m (x - 9)
=> y = m(x - 9) + 10
=> y - mx = - 9m + 10
Divide the terms by - 9m + 10, then we get,
=> (y/- 9m+10) - (mx/ - 9m+10) = 1
=> (mx/9m+10) - (y/9m+10) = 1
It can be rewritten as,
[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]
We know that,
The equation of straight line in intercept form is
=> x/a + y/b = 1
So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:
a = 9m-10/m
b = 10 - 9m
The area of the triangle made by the line in first quadrant can be expressed as,
=> A = 1/2 x (9m-10/m) x (10 - 9m)
=> A = -1/2 (9m-10)²/m-----------------------(1)
Differentiate the equation (1) with respect to m.
[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]
[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]
[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]
when we simplify it,
=> dA/dm = -(9m-10)/2m² [9m-10]
Let dA/dm = 0, then
=> 0 = -1/2m² (9m-10)(9m-10)
=> 0 = 1/m² (10-9m)(9m-10)
=> 0 = (10 - 9m) (9m -10)
Therefore, the value of m is,
=> 10 - 9m = 0
=> -9m = -10
=> m = 10/9
And
=> 9m - 10 =0
=> 9m = 10
=> m = 10/9
The line will be in first quadrant and forms a triangle with axes if the slope is negative.
Substitute m = -10/9
Then, b = 10-9m
Then,
=> y = 10 - 6(-10/9)
=> y = 10 + 20/3
=> y = 50/3
So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.
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In the diagram, roads a and b are parallel.
Solve for x and find the measure of VTU.
Answer:
102
Step-by-step explanation:
<QRT and <VTU are alternate exterior angles, so they are congruent.
m<QRT = m<VTU
x + 40 = 2x -22
62 = x
m<QRT = x + 40 = 62 + 40 = 102
m<VTU = 2x - 22 = 62*2 - 22 = 124 - 22 = 102
jeremy has 25 marbles, he gives 5 to his teacher, then he give five to his best friends. once he gets home he gives 5 to his sister right the terms in order to determine how many marbles he has
Answer: 25 - 15 = 10
Step-by-step explanation:
You order three sandwiches. The tax was 8% off and you tip 5 dollars, You pay a total of $20.66. How much does one sandwich cost?
The cost of one sandwich is $5.7
How to determine the cost of one sandwich?The given parameters are:
Order = 3
Tax = 8% off
Total cost = $20.66
Tip = $5
The cost of one sandwich is calculated as:
Total cost = Order * Cost of One (x) * (1 - tax) + Tip
This gives
20.66 = 3 * x * (1 - 8%) + 5
Subtract 5 from both sides
15.66 = 3 * x * (1 - 8%)
Make x the subject
x = 15.66/[3 * (1 - 8%)]
Evaluate
x = 5.7
Hence, the cost of one sandwich is $5.7
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An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. using for distance in kilometers and for number of hours, an equation that represents this situation d=50t is .
Speed is the constant of proportionality for the relationship between distance and time.
Relationship between these two values is distance is directly proportional to time .
As given,
Distance =400 kilometers
Time=8 hours
Let s, d, and t represents speed, distance and time.
Speed = d / t
= 400/8
= 50 km/ hour
= constant
Hence ,
d = 50t
⇒ d ∝ t
Therefore, speed is the constant of proportionality for the relationship between distance and time.
Relationship between these two values is distance is directly proportional to time .
The complete question is:
An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. using for distance in kilometers and for number of hours, an equation that represents this situation d=50t.
What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?
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A county has 225 acres of vacant land.
Residents voted to turn some of the vacant land
into parks. Now, there are 36% less acres of
vacant land. How many acres of vacant land
does the county have now?
The acres of vacant land that the county have now will be 144 acres.
How to calculate the value?Since 36% has been used, the remaining percentage will be:
= 1 - 36%
= 64%
Therefore, the acres of vacant land that the county has now will be:
= 64% × 225
= 64/100 × 225
= 0.64 × 225
= 144
Therefore, the acres of vacant land that the county have now will be 144 acres.
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9. Marlee is making jewelry for a class craft
show. She began with 115 inches of wire.
She used 25.75 inches for rings. Then her
teacher gave her 30 1/4 inches of wire to
make more jewelry. She then used 38 1/2
inches for the bracelets and 60.2 inches for
necklaces. How much wire does Marlee
have left?
The wire that Marlee had left is 20.8 inches.
How to calculate the fraction?From the information given, it was stated that Marlee is making jewelry for a class craft show and that she began with 115 inches of wire.
Amount used for rings = 25.75 inches..
Amount given to her by the teacher = 30 1/4 inches.
Amount used for bracelets = 38 1/2
inches.
Amount used for necklace = 60.2 inches
It should be noted to know the wire left, we have to subtract the values that were used and then add the value that her teacher gave her from the original value. This will be calculated thus:
This will be:
= 115 - 25.75 + 30.25 - 38.5 - 60.2
= 20.8 inches
Therefore, in conclusion, the wire that Marlee had will be 20.8 inches left.
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What transformation would take triangle ABD to A’B’D ( translation, reflection , or rotation ) ?
Answer: Rotation
Step-by-step explanation:
find the length of a diagonal of a rectangular room of length 5 m, width 3 m and height 2.5 m
Answer:
What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem. 52+32−−−−−−√=6. Now this diagonal is a leg of the bigger right triangle whose hypotenuse is the required solid diagonal. You can see this from amd's picture. So apply Pythagorean theorem again. 62+(2.5)2−−−−−−−−−√=37.25−−−−√. You can work that out with a calculator.
In general for a cuboid with dimensions a, b and c(order doesn't matter), the solid diagonal is: a2+b2+c2−−−−−−−−−−√
Step-by-step explanation:
Answer:
√62+(2.5)2=√37.25.
Step-by-step explanation:
What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem.  52+32=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;"> 52+32−−−−−−√=6 52+32=6. Now
PLEASE HELP ! A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper? One ream of paper is 500 sheets.
Answer: the thickness of each sheet of paper is 2in thick.
Step-by-step explanation:
There is none.
If box contains 5 reams of paper, the estimated thickness of 2 sheets of paper is T/1250.
To estimate the thickness of 2 sheets of paper, we can use the given information about the number of reams in the box and the number of sheets in one ream of paper.
First, we know that one ream of paper contains 500 sheets. Since the box contains 5 reams, the total number of sheets in the box is 5 reams × 500 sheets/ream = 2500 sheets.
Next, we can calculate the thickness of one sheet by dividing the total thickness of the reams by the number of sheets. Let's assume the thickness of the 5 reams combined is T.
Thickness of one sheet = T/2500
Now, to estimate the thickness of 2 sheets, we multiply the thickness of one sheet by 2:
Estimated thickness of 2 sheets = (T/2500) × 2 = 2T/2500 = T/1250
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Solve and represent X< -2 or X<5 in all ways
Answer:
x<−2 or x<5
Step-by-step explanation:
x<−2 or x<5
We know either x<−2 or x<5
x<−2(Possibility 1)
x<5(Possibility 2)
Help please!! I need it quick
Applying the triangle proportionality theorem, the length of line EC is: 7.2 units.
How to Apply the Triangle Proportionality Theorem?Since lines AC and DE are parallel to each other in the triangle, and DE intersects sides AB and AC, then we would have the following proportion based on the triangle proportionality theorem:
BD/DA = CE/EA
BD = 18 units
DA = 15 units
CE = ?
EA = 6 units
Plug in the values
18/15 = CE/6
(18)(6) = (CE)(15)
108 = CE(15)
Divide both sides by 15
108/15 = CE(15)/15
7.2 = CE
EC = 7.2 units
Therefore, applying the triangle proportionality theorem, the length of line EC is: 7.2 units.
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The cost of bananas varies directly with the number of pounds bought. If 6 pounds
cost $5.22, find the cost of 3 pounds.
Answer:
$2.61
Step-by-step explanation:
So, We have $5.22 for 6 pounds of Bananas.
If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3
In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100
5.22*100=522
Now we divide
522/2 = 261
Now we divide 261 by 100, since we multiplied by 100 earlier.
261/100 =2.61
So our answer is $2.61 for 3 pounds of bananas .
Hope this helps! ^^
Answer:$2.61 for 3 pounds
Thank for the brainliest
Step-by-step explanation:first you divided $5.22/6 because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61
Find an equation of the sphere determined by the given information. passes through the point (8, 3, -3), center (5, 6, 5)
The equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
The standard form of the equation of the sphere is :
[tex](x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}[/tex]
Where A (a, b , c) is the center and r is the radius.
From the question we should first find the radius
r = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}[/tex]
Point = (x , y , z) = (8 , 3 , -3)
Center = (a, b , c)= (5 , 6 ,5)
Substituting it in the formula
r = [tex]\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }[/tex]
By further calculation
r = [tex]\sqrt{9+9+64}[/tex]
So, we get
r =[tex]\sqrt{82}[/tex]
Substituting it in the standard form
[tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}[/tex]
[tex](x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
Therefore, the equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
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shae used the product of rule to prove that 7 to 0 power is equal to 1
Answer:
yes a product of any number to 0 is equal to 1
Five girls entered the pass, kick,
and punt competition. Below is how
far they threw the football
Kim 23.8 yds.
Julia
40 yds,
Trisha 38.94 yds.
Dianne 28.2 yds,
What is the combined total length for the 4 girls
Answer:
130.94
Step-by-step explanation:
'Combine' I assume is to add so here's the answer!
23.8+40+38.94+28.2= 130.94
Round 19.8 to 1 significant figure
Answer:
20
Step-by-step explanation:
the 0 is not significant since it is not sandwiched between 2 sigfigs and is not the last digit after a decimal
(1-tan4 A) cos4 A = 1-2 sin² A
Step-by-step explanation:
You want to demonstrate the identity ...
(1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)
Working with the left side, we have ...
[tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]
__
Additional comment
The referenced identities are ...
tan = sin/cos
cos² = 1 -sin²
and the factorization of the difference of squares:
a² -b² = (a +b)(a -b).
Satisfactory internal control ______ the probability of errors or frauds in the accounts.
Satisfactory internal control reduces the probability of errors or frauds in the accounts.
What functions may a strong internal control system perform?
To ensure that goals and objectives are met, effective internal controls are necessary. For management choices, they offer trustworthy financial reports. To reduce the possibility of public scandals, they make sure that applicable laws and regulations are followed.Why are internal controls necessary?
Internal controls are primarily used to protect organizations and advance their goals. Internal controls serve to reduce risks, safeguard assets, maintain record accuracy, enhance operational effectiveness, and promote conformity to laws, rules, and regulations.Learn more about system of internal controls
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17k to 19.04k increase. What is the percent increase?
Need Answered ASAP
Answer:
4 %
Step-by-step explanation:
x^3=-115 pleasess i need the answer now
Answer:
x = -∛115
Step-by-step explanation:
x^3 - (-115) = 0
= x^3 + 115
Factoring
(a+b) • (a^2-ab+b^2) =
a^3-a^2b+ab^2+ba^2-b^2a+b^3 =
a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=
a^3+0+0+b^3=
a^3+b^3
(115 isn't a cube.)
Polynomial roots
P: -1, -5, -23, -115, 1, 5, 23, 115
Q: 1
P/Q: -1, -5, -23, -115, 1, 5, 23, 115
Divisor(s): None
In these sets of data, there are no rational roots shown.
Step-by-step explanation(part 2):
x^3 + 115 = 0
x^3 = -115
x = ∛-115
Negative numbers will always have real cube roots.
∛ -115 = ∛ -1 × 115 = ∛ -1 × ∛ 115 = (-1) × ∛ 115
Therefore,
x = -∛115
A local hamburger shop sold a combined total of 380 hamburgers and cheeseburgers on Saturday. There were 70 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Saturday?
Answer:
310 hamburgers were sold on Saturday
Step-by-step explanation:
1x + 70 =380
-70 -70 Reverse
1x = 310
/1 /1 Divide
x =310
Mr.Myers picked 13 1/8 bushels of red delicious apples and 27 2/8 bushels of golden delicious apples. How many bushels of apples did he pick ?
Answer:
40 3/8 bushels of apples
Step-by-step explanation:
13 1/8 bushels and 27 2/8 bushels
13 1/8 + 27 2/8 =
(13 + 27) = 40
(1/8 + 2/8) = 3/8
40 3/8
PLEASE HURRY!!
State the domain and range for the function f(x) = 2x² - 7.
Domain
[tex]-\infty \: < x < \infty[/tex]
Range
[tex]f\left(x\right)\ge \:-7\:[/tex]
Work out the area of the shaded shape.
3cm
4cm
h(x) = 18 - 9x + x4, evaluate h(2)
The value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
According to the given question.
We have a function h(x) = 18 - 9x + x^4
Here, we have to find the value of h(2). For this we will substiute x = 2 in the function h(x) = 18 - 9x + x^4.
Therefore, the value of h(2) for the function h(x) = 18 - 9x + x^4 is given by
h(x) = 18 - 9x + x^4
h(2) = 18 - 9(2) + 2^4
h(2) = 18 - 18 + 16
h(2) = 16
Hence, the value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.
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Solve the equation
3(4z-7)=-21+12z
Answer:
Step-by-step explanation:
Let's open the brackets,
12z - 21 = -21 + 12z (distributive property)
12z - 12z = -21 + 21
0z = 0
z = 0
Select the graph of the solution. Click until the correct graph appears.
|x| = 1
Answer:
It's the graph with two dots and no area marked, first image (for me).
Step-by-step explanation:
|x| = 1 means "the distance from x to the 0 point on the axis is exactly 1". There's only 2 numbers x that satisfy that condition: -1 and 1
The second and third image both show an area marked, so it cannot be the right answer, while the first image shows precisely two numbers: -1 and 1
Saeed plans to run 10 km. On the first day, he runs 2 km. What percent of the total distance does he run the first day?
Answer:
He runs 20% or 1/5 of the total distance the first day
Step-by-step explanation:
We know this due to the fact that 2km / 10km is equal to 1/5 and we then know that 1/5 equates to the percentage equivalence value of 20%
Melissa bought a new dishwasher for$1,200. The manufacturer is offering a 15% rebate. How much will the dishwasher cost after the rebate?
Answer:
$1020.00
Step-by-step explanation:
15% means 15/100 divide by 100 and you get .15
.15 x 1200 gives us the rebate. The rebate is 180. We subtract that from 1200. 1200 -180 = 1020
Another way to think about this, is that we are taking 15% off we are leaving on 85%
.85 x 1200 = 1020
Which relation is represented by the arrow diagram?
{(-0.5, -1), (1,7), (0.5, -0.2), (3.2, 1)}
{(3.2, 1), (0.5, -0.2), (1,1), (-0.5, 7)}
{(-1, -0.5), (7, 1), (-0.2, 0.5), (1, 3.2)}
{(-0.5, -1), (1, 7), (0.5, 1), (3.2, -0.2)}
Answer:
first order
Step-by-step explanation:
they're basically a linear function. to make it easier you could just put the coordinates on the side of the table.