PLEASE HELP A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.
Answers
================================================
Work Shown:
A = area of larger rectangle
A = length*width = 9*15 = 135 square feet
B = area of smaller rectangle
B = length*width = 7*4 = 28 square feet
C = area of shaded region
C = difference in areas of A and B
C = A - B = 135 - 28 = 107 square feet
Related Questions
A number is no more than five. How would you graph this inequality?
Answers
Answer:
X<=5 and you would graph it with a closed dot on five and an arrow going left of it.
Step-by-step explanation:
Answer:
[tex]a<5\\\\a\in R[/tex]
Step-by-step explanation:
In several ways, for example, let:
[tex]a[/tex], an arbitrary constant, where:
[tex]a\in R[/tex]
Besides:
[tex]a< 5[/tex]
Because the number can be greater than five.
Therefore, the graph, would be all number over the interval:
[tex](-\infty, 5)[/tex]
As you can see, all numbers bellow the line [tex]y=5[/tex].
TIME REMAINING
52:37
Lines c and d are parallel lines cut by transversal p.
Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8.
Which must be true by the corresponding angles theorem?
∠1 ≅ ∠7
∠2 ≅ ∠6
∠3 ≅ ∠5
∠5 ≅ ∠7
Answers
Answer:
b
Step-by-step explanation:
PLEASE HELP!!!! What is 2(3j + 6 + 5j) as a verbal expression?
Answers
Answer:
"sixteen j plus twelve"Step-by-step explanation:
Given the expression[tex]2(3j + 6 + 5j)[/tex] let us begin by simplifying the expression first by performing operation with the terms inside the brackets
[tex]2(3j + 6 + 5j) = 2(8j + 6 )[/tex]
We can continue by opening the bracket to further simplify the expression
[tex]2(8j + 6 ) = 16j+2[/tex]
[tex]16j + 12[/tex] is our final answer, now to express this verbal, this is a complex number/expression, expressed as "sixteen j plus twelve"
Sketch the graphs of the equations: y = −3 −x
Answers
This is a linear equation in slope-intercept form. We can see that the slope is -1 and the y-intercept is -3 -- the line passes through (0, -3).
To graph this, we can simply plot the point (0, -3) and draw a line with slope negative 1 (this means that for every unit right, we have to move 1 unit down.
I have attached a picture of the graph.
How did the temperature change if: at first it decreased by 60 % and then increased by 80% ?
Answers
Answer:
28% decrease
Step-by-step explanation:
If we decrease by 60%, we are keeping 100-60 = 40%
Let x be the original amount
decrease by 60% = keep 40%
.40 x
If we increase by 80%, we are keeping 100+80 = 180%
(.40x) * 180%
.40x * 1.80
.72x
Take .72 times the original amount
100 - .72 = 28
It decreased 28 %
Answer:
28% decrease
Step-by-step explanation:
What is the remainder in the synthetic division problem below?
-2 1 2 -3 1
O A. 11
O B. 7
O C. 9
O D. 13
Answers
Answer:
B
Step-by-step explanation:
-2 / 1 2 -3 1
____-2 _ 0_ _6_____
1 0 -3 7
Write down the first number 1 as it is.
Step 2: Multiply 1 by -2 ( 1*-2 = -2) and write under the next number. Then add
2 +(-2) = 0
Step 3: Now Multiply 0 by -2 ( 0 * -2 =0) and write under the next number ie, -3.
-3 +0 = -3
Step 4: Multiply -3 by -2, ( -3*-2 = 6) and write under the number 1
1 + 6 = 7
7 is the remainder
The remainder in the synthetic division problem given is 7.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given a synthetic division problem.
Put the first number straight down.
So 1 is taken down.
Multiplying 1 by -2, we get -2.
2 + (- 2) = 0
Multiplying 0 by -2, we get 0.
-3 + 0 = -3
Multiplying -3 by -2, we get 6.
1 + 6 = 7, is the remainder.
Hence the remainder is 7.
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1. Find P(rolling 2 or 5) with one number cube.
Answers
Answer:
1/3
Step-by-step explanation:
There are 6 possible outcomes when rolling 1 die
1,2,3,4,5,6
There are 2 outcomes that fit the category of 2 or a 5
P ( rolling 2 or a 5) = number of 2's or 5's / total number of outcomes
= 2/6
=1/3
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
A fair dice has 6 outcomes, 1, 2, 3, 4, 5, 6.
The outcomes 2 and 5 are 2 outcomes out of total 6 outcomes.
[tex]\frac{2}{6}=\frac{1}{3}[/tex]
Mark scored an 89 on his first
test, an 85 on his second test, a
95 on his third test, and an 83 on
his fourth test. What is Mark's
average test score for all 4 tests?
Answers
Answer:
88
Step-by-step explanation:
89+85+95+83= 352,
352/4 = 88
Simplify each expression using the proper order of operations. please help thank you so much :)
[tex]\frac{41-3^2}{\sqrt{36}*3-26 }[/tex]= ?
12 +[tex]\sqrt[3]{8}[/tex] *(9-2)= ?
[tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]= ?
[tex]\frac{28}{4}[/tex] -[tex]\sqrt[3]{8}[/tex]*2^3= ?
7^2 - 5* 8+1= ?
(2*[tex]\sqrt{16}[/tex]) -([tex]\sqrt[3]{27}[/tex]*[tex]\sqrt{81}[/tex] ) + 7= ?
Answers
Answer:
a) [tex]\boxed{-4}[/tex]
b) [tex]\boxed{26}[/tex]
c) [tex]\boxed{-12}[/tex]
d) [tex]\boxed{-9}[/tex]
e) [tex]\boxed{10}[/tex]
f) [tex]\boxed{-12}[/tex]
Step-by-step explanation:
1) [tex]\frac{41 - 3^2}{\sqrt{36}* 3-26 }[/tex]
=> [tex]\frac{41-9}{6*3-26}[/tex]
=> [tex]\frac{32}{18-26}[/tex]
=> [tex]\frac{32}{-8}[/tex]
=> -4
2) [tex]12+\sqrt[3]{8} * (9-2)[/tex] ∴ [tex]\sqrt[3]{8} = 2[/tex]
=> [tex]12+2*(7)[/tex]
=> 12 + 14
=> 26
3) [tex]\frac{28-(7^2+3)}{-13+3*5}[/tex]
=> [tex]\frac{28-(49+3)}{-13+15}[/tex]
=> [tex]\frac{28-52}{2}[/tex]
=> [tex]\frac{-24}{2}[/tex]
=> -12
4) [tex]\frac{28}{4} - \sqrt[3]{8} * 2^3[/tex]
=> 7 - 2 * 8
=> 7 - 16
=> -9
5) [tex]7^2-5*8+1[/tex]
=> 49 - 40 + 1
=> 9 + 1
=> 10
6) [tex](2 * \sqrt{16} ) - (\sqrt[3]{27} * \sqrt{81} ) + 7[/tex]
∴ [tex]\sqrt{16} = 4, \sqrt[3]{27} = 3 , \sqrt{81} = 9[/tex]
=> (2 * 4) - (3 * 9) + 7
=> 8 - 27 + 7
=> -19 + 7
=> -12
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply order of operations to solve each expression.
[tex]\frac{41-9}{6 \times 3-26}[/tex]
[tex]\frac{41-9}{18-26}[/tex]
[tex]\frac{32}{-8}=-4[/tex]
[tex]12+2\times 7[/tex]
[tex]12+14=26[/tex]
[tex]\frac{28-(49+3)}{-13+15}[/tex]
[tex]\frac{28-52}{2}[/tex]
[tex]\frac{-24}{2} =-12[/tex]
[tex]7-2 \times 8[/tex]
[tex]7-16=-9[/tex]
[tex]49-40+1[/tex]
[tex]=10[/tex]
[tex](2 \times 4)-(3 \times 9) +7[/tex]
[tex]8-27+7[/tex]
[tex]=-12[/tex]
A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.
The height of the baseball in feet after t seconds is given by the equation
h = – 1672 + 52t + 4. A fan catches the ball 16 feet off the ground when it is coming
down. When does the fan catch the ball?
The fan catches the ball
seconds after it is hit.
(Note: the ball is 16 feet high at one point when it is going up and again when it is
coming down.)
The solution is
Answers
Answer: The fan catch the ball after 3 seconds.
Step-by-step explanation:
Given, A baseball 4 feet off the ground is hit with an upward velocity of 52 feet per second.
The height of the baseball in feet after t seconds is given by the equation
[tex]h = - 16t2 + 52t + 4[/tex]
If a fan catches the ball 16 feet off the ground when it is coming down.
then, at that time h= 16 feet
At h= 16
[tex]16=-16t^2+52t+4\\\\\Rightarrow\ 16t^2-52t+12=0\\\\\Rightarrow\ 4t^2-13t+3=0[/tex]
[tex]\Rightarrow\ 4t^2-t-12t+3=0\Rightarrow\ t(4t-1)-3(4t-1)=0\\\\\Rightarrow\ (4t-1)(t-3)=0\\\\\Rightarrow\ t=\dfrac{1}{4},\ t=3[/tex]
From the graph , it can be observe that when ball comes back , for height 16 feet the corresponding time t= 3 sec
So, the fan catch the ball after 3 seconds.
Glven: F(x) = 2x - 1; G(X) = 3x + 2; H(x) = x2
Find F/G/H(2)
121
27
71
Answers
Answer:
3/32
Step-by-step explanation:
One approach to doing this probelm is to evaluate all three functions F, G and H at x = 2:
F(2) = 2(2) - 1 = 3
G(2) = 3(2) + 2 = 8
H(2) = (2)^2 = 4
3/8
Then (F/G)(2) = (3/8), and (F/G/H) = -------- = 3/32
4
PLEASE HELP!!! I AM DESPERATE BECAUSE MY CLASS IS IN A FEW MINUTES. Solve using statement reason.
Answers
Answer:
Statement 1. P
Reason 1. Theorem: The measure of an external angle of a triangle is equal to the sum of the measures of the remote interior angles.
Statement 2. 132 = 3x + 54
Statement 3. x = 26
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number and the equation.
HELP ME PLS!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
23
el número es 32 y si sumamos los dos dígitos suman 5
y si restamos 9 a 32 nos queda 23.
Help please and show work too
Answers
Answer:
Below
Step-by-step explanation:
51)
Let n be the first even number.
So the four consecutive even numbers are:
● n
● n+2
● n+4
●n+6
The smallest minus twice the larger is 4
● n-2(n+6)= 4
●n-2n-12 =4
● -n -12 =4
● -12 = 4+n
● -12-4 = n
● -16 = n
so the first even number is -16 and the largest one is -10
● -16+6= -10
■■■■■■■■■■■■■■■■■■■■■■■■■
Let m be the first integer
So the five consecutive integers are:
● m
● m+1
● m+2
● m+3
● m+4
The sum of this terms is 5.5 times the middle(m+2)
● m+m+1+m+2+m+3+m+4 = 5.5(m+2)
● 5m + 10 = 5.5 m +11
● -0.5 m = 1
●-m = 2
● m= -2
So the integers are;
● -2
● -1 (-2+1)
● 0
● 1
● 2
please help me with vivid explanation
Answers
Answer:
864 m²
Step-by-step explanation:
First calculate the total area of the rectangular field
The area of a rectangle is given by the product of the length and the width
let A be the total area
A = 100*120
A = 12000 m²
Calculate the area of the small rectangles
Let A' be the total area of the four small rectangles and A" the area of one small rectangle A' = 4 A" A' = 4 [([tex]\frac{120-4}{2}[/tex])*([tex]\frac{100-4}{2}[/tex])] A' = 4*58*48A' = 11136 m² Substract the A' from A to get the area of the roadLet A"' be the area of the road
A"' =A-A'
A"' = 12000-11136
A"' = 864 m²
HELP ME PLZ NEED ANSWER Which relation is a function? A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin. A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair. A coordinate grid containing a U shaped graph with arrows on its ends. The U shape opens upwards and the bottom of the U shape is located at the origin. Coordinate grid with graph of a vertical line at x equals 3.
Answers
Answer:
A function is a relation in which each input has only one output.
Step-by-step explanation: In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.
A function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin which is the correct answer would be an option (A).
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
A function is a coordinate grid with a U-shaped pattern, arrows on both ends that open to the right, and the origin at the bottom of the U.
Because there is only one output of the relation, y, for any input x (1, 2, 3, or 0), is a function of x. Because the input y = 3 contains multiple outputs, including x = 1 and x = 2, x is not a function of y.
Therefore, the function is a coordinate grid containing a U-shape with arrows on both ends that open to the right, and in which the bottom portion of the U passes through the origin.
Hence, the correct answer would be option (A).
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A little shop sells Christmas toys. The wholesale price for each toy in a consignment of 50 toys was $5.5. Half of this quantity was sold before Christmas for the sales price of $15 per piece. two-fifth of the remaining toys have been sold in the next six days for half of the sales price. Finally, the rest of toys have been sold after the New Year for one-third of the sales price. What was the profit the shop made on selling these toys?
Answers
Answer:
[tex]Profit = \$250[/tex]
Step-by-step explanation:
Given
Number of Toys = 50
Unit Cost Price = $5.5
Unit Selling price = $15
Required
Determine the profit after sales
First, we need to determine the total cost price;
[tex]Cost\ Price = Number\ of\ toy *\ Unit\ cost\ price[/tex]
[tex]Cost\ Price = 50 * \$5.5[/tex]
[tex]Cost\ Price = \$275[/tex]
First, we need to determine the total sales;
____________________________________________________
Half of the toy was sold at $15;
[tex]Half\ of\ the\ toy = \frac{1}{2} * 50[/tex]
[tex]Half\ of\ the\ toy = 25[/tex]
[tex]Sales = \$15 * 25[/tex]
[tex]Sales = \$375[/tex]
____________________________________________________
Two-fifth of the remaining was sold at half of the sales price
From the above calculation;
[tex]Remaining\ Toy = 50 - 25[/tex]
[tex]Remaining\ Toy = 25[/tex]
Calculating Two-fifth of the remaining:
[tex]\frac{2}{5} * 25[/tex]
[tex]= \frac{50}{5}[/tex]
[tex]= 10[/tex]
Calculating half of the sales price:
[tex]\frac{1}{2} * \$15[/tex]
[tex]\$7.5[/tex]
This means that 10 toys were sold for $7.5
[tex]Sales = 10 * \$7.5[/tex]
[tex]Sales = \$75[/tex]
____________________________________________________
The remaining was sold at one-third of the sales price
From the above calculations (1 & 2);
[tex]Remaining\ Toy = 50 - 25 - 10[/tex]
[tex]Remaining\ Toy = 15[/tex]
Calculating one-third of the sales price:
[tex]\frac{1}{3} * \$15[/tex]
[tex]\$5[/tex]
This means that 15 toys were sold for $5
[tex]Sales = 15 * \$5[/tex]
[tex]Sales = \$75[/tex]
____________________________________________________
Now the total sales can be calculated;
[tex]Total\ Sales = \$375 + \$75 + \$75[/tex]
[tex]Total\ Sales = \$525[/tex]
[tex]Profit = Total\ Sales -\ Cost\ Price[/tex]
[tex]Profit = \$525 -\$275[/tex]
[tex]Profit = \$250[/tex]
10 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answers
Answer:
120
Step-by-step explanation:
The total number of triangles that can be made are 120.
We have a circle and 10 points are placed on it.
We have to find how many possible triangles can be made such that their vertices will be the given points.
What is a Combination?A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -
[tex]\frac{n!}{(n-r)!r!}[/tex]
In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -
[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]
10 x 3 x 4 = 120
Hence, the total number of triangles that can be made are 120.
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What is a Stem-and-Leaf plot?
4-5 sentences.
Answers
Answer:
A stem and leaf plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.
Step-by-step explanation:
Example: Long Jump
Sam got his friends to do a long jump and got these results:
long jump
2.3, 2.5, 2.5, 2.7, 2.8 3.2, 3.6, 3.6, 4.5, 5.0
And here is the stem-and-leaf plot:
Stem Leaf
2 3 5 5 7 8
3 2 6 6
4 5
5 0
Stem "2" Leaf "3" means 2.3
Note:
Say what the stem and leaf mean (Stem "2" Leaf "3" means 2.3)
In this case each leaf is a decimal
It is OK to repeat a leaf value
5.0 has a leaf of "0"
can you help me ? with this problem ty
Answers
b) 9cm
c) x=3(Aly’s solution)
b)9cm
c)x=3
That’s how I got it hope this helps :)
Plz help meeeeee 9q=81
Answers
Answer:
q=9
Step-by-step explanation:
9q=81
Divide each side by 9
9q/9=81/9
q = 9
Answer:
Q=9
Step-by-step explanation:
SO BASICALLY TO REMOVE THE 9 FROM ONE SIDE WE DIVIDE BOTH SIDES OF THE EQAUTION BY 9
9Q/9=81/9
WHICH SIMPLIFIES TO
Q=9
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
13. Marco took out an unsubsidized student loan for $20,000, which he will start paying in 4
years, after he graduates. If the interest rate is 4.2%, what is the amount he will owe once he
graduates?
Answers
Answer:
Marco will owe $ 23,360 once he graduates.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Principal of the loan = 20,000
Time in years = 4
Interest rate = 4.2%
2. What is the amount he will owe once he graduates?
Let's use the formula of the interest simple, this way:
A = P * (1 + r * t)
where P is the principal of the loan, r the interest rate and t, the time in years.
Substituting with the values we know, we have:
A = 20,000 * (1 + 4 * 0.042)
A = 20,000 * 1.168
A = 23,360
Marco will owe $ 23,360 once he graduates.
if 2x+1/4 = 12/20 what is the value of x
Answers
Answer:
7/40 or 0.175
Step-by-step explanation:
simplify to get 2x+1/4=3/5
subtract 1/4 from both sides to get 2x=7/20
divide by 2 to get 7/40
this answer i decimal form is 0.175
Answer:
x = 7/40
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2x + 1 /4 = 3 /5
Step 2: Subtract 1/4 from both sides.
2x + 1 /4 − 1 /4 = 3 /5 − 1 /4
2x = 7 /20
Step 3: Divide both sides by 2.
2x /2 = 7 /20 /2
x = 7 /40
Answer:
x = 7 /40
Hope this helps!!
help asap! <3 The golf scores for the 32 members of the Belmont Country Club were 108, 89, 74, 115, 92, 86, 103, 107, 94, 89, 111, 78, 116, 82, 99, 107, 74, 78, 101, 93, 85, 98, 109, 82, 83, 105, 91, 106, 97, 84, 92, 96. Which histogram correctly shows the frequency distribution of the scores using ten-point intervals?
Answers
Answer:
histogram D
Step-by-step explanation:
From left to right, your frequencies (aka height of columns) should be 4, 8, 9, 8, and 3
plssssss help number 18 and 20
Answers
Answer:
18).Total mass of materials = 4.8kg
For gravel
55% of the materials are gravel
So we have
55/100 × 4.8 kg
= 2.64kg
For sand
30% of the materials are sand
We have
30/100 × 4.8
= 1.44kg
For cement
The remaining materials were cement so we add the masses of both the sand and gravel and subtract it from the total mass
That's
4.8 - (2.64 + 1.44)
4.8 - 4.08
= 0.72 kg
20).She earns £ 800 per week
She receives a raise of 7.5% which is
100 + 7.5 = 107.5%
So we have
107.5 / 100 × £ 800
= £ 860
She now earns £ 860 per week
Hope this helps you
Step-by-step explanation:
1)of 4.8kg concrete 55% is gravel,30% is sand and 15% is cement.
percent=Rate*Base
Pgravel=55%*4.8kg
Pgravel=2.64kg
Psand=30%*4.8kg
Psand=1.44kg
Pcement=15%*4.8kg
Pcement=0.72kg
2)percent=Rate*Base
percent=7.5%*£800
percent=60£
total earn=60£ + £800
total earn=£860
HELP NOWWWWW Jeanne wrote the numbers 1-100 and placed them in a bag. If she selects a number without looking, what is the probability that the number is odd? Input your answer as a decimal or fraction.
Answers
Answer:
P(odd) = 0.5
Step-by-step explanation:
There are 50 odd numbers for whole numbers 1-100, namely
{1,3,5,....97,99}
Therefore the probability that a single chosen number is odd is
P(odd) = 50/100 = 1/2
1/2 is the probability that the number is odd.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of outcomes and the total number of outcomes.
Total number of possibilities = 100
We want to find Probability of selecting odd:
There are 50 odd numbers for whole numbers 1-100, namely
Favourable possibilities are:
{1,3,5,....97,99} (Total 5 possibilities).
Therefore Probability = 50/100 = 1/2 or 50%
P(odd) = 50/100 = 1/2
Hence, 1/2 is the probability that the number is odd.
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Write each of the following expressions without using absolute value. |7m–56|, if m<8
Answers
Answer:
[tex]|7\cdot m -56| = -7\cdot m + 56[/tex] if [tex]m< 8[/tex]
Step-by-step explanation:
According to the definition of absolute value:
[tex]f(x)[/tex] if [tex]f(x) \geq 0[/tex]
[tex]-f(x)[/tex] if [tex]f(x) <0[/tex]
If [tex]m < 8[/tex], then:
[tex]y_{max} = 7\cdot (8) - 56[/tex]
[tex]y_{max} = 0[/tex]
[tex]y[/tex] becomes negative as [tex]m[/tex] diverges to [tex]-\infty[/tex].
Then, the absolute value can be rewritten as follows:
[tex]|7\cdot m - 56| = -(7\cdot m -56)[/tex] if [tex]m <8[/tex]
[tex]|7\cdot m -56| = -7\cdot m + 56[/tex] if [tex]m< 8[/tex]
Debby pays rent twice a year, buys groceries once every quarter, and buys a transit pass
every month. How should her yearly expenses be represented?
1. O2 + 4y + 122
2. O 2x + 4y + 12z
3. OI +y + 122
4. O 2x + 3y + 12z
Answers
Work Shown:
x = amount of rent paid per half year
2x = amount of rent paid annually
y = amount spent on groceries per quarter
4y = amount spent on groceries annually
z = amount spent on a transit pass monthly
12z = amount spent on transit pass annually
2x+4y+12z = total amount of money spent annually
Answer:
2x+4y+12z
Step-by-step explanation:
I just did the test and got it right
Can someone please help me solve this?
Answers
Answer:
(a)
Step-by-step explanation:
The tangent and the normal at point P are perpendicular.
Given
[tex]m_{tangent}[/tex] = 3, then
Given the gradient m of the tangent then the gradient of a line perpendicular to it is
[tex]m_{normal}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex] → (a)
Please solve this: Also show work.... Please help me.. Will give brainly
Answers
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]\frac{6x+1}{3}+1=\frac{x-3}{6}[/tex]
To make things simple, multiply everything by the LCM of the denominator. In this case, the LCM of 3 and 6 is 6.
[tex]6(\frac{6x+1}{3}+1) =6(\frac{x-3}{6}) \\6(\frac{6x+1}{3})+6(1)=(x-3) \\ 2(6x+1)+6=x-3[/tex]
Now, simplify and solve for x:
[tex]12x+2+6=x-3\\12x+8=x-3\\11x+8=-3\\11x=-11\\x=-1[/tex]