A 100 m2hay shed is to be extended to give 475 m2of oor space in total, as shown. All angles are right angles. Find the value of x.
Answer:
[tex]x = 15.[/tex]
Step-by-step explanation:
Given
See attachment for floor space
Required
Find x
The floor can be partitioned into three space.
The dimension and the area of each space is:
Dimension: 10 by 10
[tex]A_1 = 10* 10 = 100[/tex]
Dimension: 10 by x
[tex]A_2 = 10* x = 10x[/tex]
Dimension: x by x
[tex]A_3 = x* x=x^2[/tex]
So, the total area is:
[tex]Area =100 +10x + x^2[/tex]
Given that:
[tex]Area = 475[/tex]
So, we have:
[tex]100+10x+x^2 =475[/tex]
Rewrite as:
[tex]x^2 +10x+100-475=0[/tex]
[tex]x^2 +10x-375=0[/tex]
Expand
[tex]x^2 + 25x -15x -375 = 0[/tex]
Factorize
[tex]x(x + 25) -15(x +25) = 0[/tex]
Factor out x + 25
[tex](x+25)(x-15)=0[/tex]
Solve:
[tex]x = -25\ or\ x = 15[/tex]
x cannot be negative; So:
[tex]x = 15.[/tex]
20 POINTS!!!!
Recall that the multiplicative inverse of a number a is the number b such that ab = 1. For example, the multiplicative inverse of 3 is . Also recall that division is multiplication by a number’s multiplicative inverse. For example, to divide by 3, just multiply by . With these definitions, use complete sentences to explain why we can’t divide by zero.
If two points on a line are given by (-7, -1) and (-7, 12), we would say the line equation is?
[tex] \large{ \tt{❃ \: SOLUTION}} : [/tex]
Remember : To find the equation of straight line passing through given points ( x₁ , y₁ ) and ( x₂ , y₂ ) , Use [tex] \tt{y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}(x - x_{1}}) [/tex]Let the given points ( -7 , -1 ) be ( x₁ , y₁ ) & ( -7 , 12 ) be ( x₂ , y₂ ).[tex] \underline{ \large{\tt{❁ \: USING \: TWO - POINT \: FORM \: OF \: EQUATION \: OF \: LINE : }}}[/tex]
[tex] \boxed{ \large{ \tt{❈ \: y - y_{1} = \frac{y_{2} - y _{1}}{x_{2} - x_{1}} (x - x_{1})}}}[/tex]
[tex] \large{ \tt{↦y - ( - 1) = \frac{12 - ( - 1)}{ - 7 - ( - 7)} \{x - ( - 7) \}}} [/tex]
[tex] \large{ \tt{↦y + 1 = \frac{12 + 1}{ - 7 + 7}(x + 7)} }[/tex]
[tex] \large \tt \:↦ \: y + 1 = \frac{12}{0} (x + 7)[/tex]
[tex] \large{ \tt{↦ \: y + 1 = 12(x + 7)}}[/tex]
[tex] \large{ \tt{↦y + 1 = 12x + 96}}[/tex]
[tex] \large{ \tt{↦ \: 12x + 96 = y + 1}}[/tex]
[tex] \large{ \tt{↦ \: 12x - y + 96 - 1 = 0}}[/tex]
[tex] \large{ \boxed{ \tt↦12x - y + 95 = 0}}[/tex]
Hence , 12x - y + 95 = 0 is the required equation of the line.✺ STUDY HARD ! No matter if it seems impossible , no matter if it takes time , no matter if you have to wake up all night , Just remember that the feeling of success is the best thing in the entire world. ♪
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What equals 394 in addition
Answer:
There are many answers
Step-by-step explanation:
393 + 1 = 394
392 + 2 = 394
391 + 3 = 394
And so forth...
Hope this helps :)
You can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation?
Answer:
Total income= $100
Step-by-step explanation:
Giving the following information:
Hourly rate=$10
To calculate the total income, we need to use the following formula:
Total income= hourly income*number of hours
For example, for 10 hours shoveling in a week:
Total income= 10*10
Total income= $100
Can someone please help me
Answer:
Her monthly rate per month is $12
Step-by-step explanation:
On the 0 month is what she already had in her bank account.
Also the months are going by 2's so it's going by $24 dollars every 2 months, so 24 divided by 2 is 12.
An airplane flies due north from ikeja airport for 500km.It then flies on a bearing of 060 from a further distance of 300km before over flying a road junction. Calculate A. Distance of airplane from ikeja airport when it was directly above the road junction B. The bearing of the airplane from ikeja airport at this instant
Answer:
482 km
63.94 degrees
Step-by-step explanation:
to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.
Cosine rule states that
C = [tex]\sqrt{A^{2} + B^{2} -2AB cos(c) }[/tex]
where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060
solving now, we have
C = [tex]\sqrt{500^{2} + 300^{2} -2 * 500 * 300 cos(60) }[/tex]
C = [tex]\sqrt{250000 + 90000 - [215000 cos(60) }][/tex]
C = [tex]\sqrt{340000 - [215000 * 0.5 }][/tex]
C = [tex]\sqrt{340000 - [107500 }][/tex]
C =[tex]\sqrt{232500}[/tex]
C = 482 km
The bearing can be gotten by using the Sine Rule.
[tex]\frac{sina}{A}[/tex] = [tex]\frac{sinc}{C}[/tex]
sina/500 = sin60/482
482 sina = 500 sin60
sina = [tex]\frac{500 sin60}{482}[/tex]
sina = 0.8983
a = sin^-1(0.8983)
a = 63.94 degrees
2 + (-25) =?
NO LINKS OR I WILL REPORT!! 10 POINTS PLEASE ANSWER!
Answer:
-23
Step-by-step explanation:
Answer:
-23
Step-by-step explanation:
When you do positive-negative you subtract the 2 numbers then take the sign of the number that had the highest absolute value.
25-2=23
The absolute value of -25 is 25
(|-25| = 25)
And the absolute value of 2 is 2
(|2| = 2)
25 > 2
So it would be -23
What is the volume of this cone?
Answer:
r=6.1cm
volume=1/3πr^2
=1/3×22/7×6.1^2
=818.62/21
=38.98cm^3
A teacher writes four numbers on the board as shown blow
1
0
4
3
She asked the students to form 4-digit number, and subtract from 4310.
Write two possible solutions
Answer:
909 and 3267
Step-by-step explanation:
There are a total of 24 possible combinations using these 4 digits. This means that any one of these combinations subtracted from 4310 would be a possible solution. Therefore, we can create the following 2 combinations (below in bold) and subtract them from 4310 to get two possible solutions...
4310 - 3401 = 909
4310 - 1043 = 3267
Finally, we have two possible solutions which would be 909 and 3267
Determine the surface area of the shape below.
Try this option:
1. the required surface area consists of: A=A₁+A₂+A₃, where
2. A₁=pi*r*l - the surface of the cone:
pi=3.14; r=4/2=2 cm; l=sqrt(6²+2²)=2√10≈6.33 (cm);
A₁=3.14*2*6.33=39.74 (cm²).
3. A₂=a²-pi*r² - the surface of the top plane:
A₂=36-3.14*4=23.43 (cm²).
4. A₃=5*a² - the surface of the five planes of the given cube:
A₃=5*6²=180 (cm²).
5. the required area:
A=39.74+23.43+180=243.17 (cm²).
Answer: 243.17
what is the Average of -8, -1, -3
Answer:
[tex] = \frac{ - 8 - 1 - 3}{3} \\ = \frac{ - 12}{3} \\ = - 4[/tex]
MARKING BRAINLIEST
PLS HELP
Answer:
-7
Step-by-step explanation:
Domain is simply another way of saying input values. Input values are literally just x values (Any place on the x bar. Range is the same but instead of x values it is for y values.
Which of the following functions best describes this graph?
A. Y = (x-3)(x + 4)
B. y = x^2-5x +6
C. y = x^2 -9x+18
D. y - (x+3)(x +6)
Answer:
(A). y = ( x - 3 ) ( x + 4 )
Step-by-step explanation:
Given that x= -3, what is the value of 2ײ - x + 5?
Answer:
26
Step-by-step explanation:
2(9)-(-3)+5
2(9)+3+5
18+8
26
Answer:
26
Step-by-step explanation:
2x^2 -x+5
x=-3
2(-3)^2 -(-3)+5
2(9)-(-3)+5
18-(-3)+5
negative multiplied by negative is positive so you have
18+3+5= 26
Have a nice day :)
Write and solve the equation for the following situation:
Angles 1 and 2 are complementary. The measure of angle 1 is 16° larger than the measure of angle 2.
A.) x + 16 = 90
B.) x + (x + 16) = 90
C.) 2x + 16 = 90 (NOT CORRECT)
D.) x + 16 = 180
WILL GIVE BRAINLIST
Answer:
B.) x + (x + 16) = 90
2x+16=90
2x=90-16
x=74/2
x=37
Find the volume of the cylinder. Use 3.14 for π. Round to the nearest tenth.
Answer:
62.8 m^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
V = (3.14) ( 2)^2 *5
V = 62.8 m^2
Answer:
V = 62.8 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cylinder Formula: V = πr²h
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify variables
r = 2 cm
h = 5 cm
Step 2: Find Volume
Substitute in variables [Volume of a Cylinder Formula]: V = (3.14)(2 cm)²(5 cm)Evaluate exponents: V = (3.14)(4 cm²)(5 cm)Multiply: V = (12.56 cm²)(5 cm)Multiply: V = 62.8 cm³The following chart shows a store’s coat sales for two years. Identify the percent increase in total sales and the percent increase in sales of jackets. Then find which percent of increase is greater and by how much greater it is than the other. (Round your answer to the nearest tenth.) a. Sales of jackets increased 3.6 percentage points faster than total coat sales. b. Sales of jackets increased 18.8 percentage points faster than total coat sales. c. Total coat sales increased 8.1 percentage points faster than sales of jackets. d. Total coat sales increased 24.5 percentage points faster than sales of jackets. Please select the best answer from the choices provided A B C D
Answer:
The answer is "Option b"
Step-by-step explanation:
Please find the complete question in the attached file.
In 2006:
Top coats= 297
Parkas= 210
Jackets =213
Raincoats=137
Trench coats =103
Total: [tex]297+210+213+137+103=960[/tex]
In 2007:
Top coats =223
Parkas = 210
Jackets= 285
Raincoats = 259,
Trench coats =127
Total: [tex]223+210+285+259+127=1,104[/tex]
Calculating the percentage of the increasing total sales:
[tex]\to \frac{1,104-960}{960}\times 100=15\%[/tex]
Calculating the percentage of the increasing sales of the trench coats: [tex]\to \frac{127-103}{103}\times 100 \approx 23.3\%[/tex]
Because [tex]23.3\%- 15\%=8.3\%[/tex] sales of the Trench coats increase by 8.3% point is faster than the total coat sales.
Answer:
B
Step-by-step explanation:
plssplsplsplspls answer fast bc its a map and I can't wait for way too long
Answer:
Part A: 1
Part B: -4
Step-by-step explanation:
In a coordinate [tex](x,y)[/tex], the x-coordinate represents the input of a function and the y-coordinate represents the output.
Part A:
We're looking for the point the line passes through with an x-coordinate (input) of -3. This point is (-3,1) and therefore the output is 1 when the input is -3.
Part B:
We're looking for the point the line passes through with a y-coordinate (output) of 2. This point is (-4,2) and therefore an input of -4 yields an output of 2.
Answer:
A) 1
B -4
well, need to write at least 20 characters... have a nice day :)
Match the statement with the appropriate reason for the proof above. Answers may be used more than once. You will have to fill in the blanks for 3
and 9 so you know the reason to match it with, but you are not picking solutions for 3 and 9
Answer:
Step-by-step explanation:
From the given question, the following statements and reasons can be matched;
Statement Reason
1. <1 and <2 are linear pair Given
2. <1 and <2 are supplementary Linear pair postulate
3. <1 ≅ <2
4. <1 ≈ <2 Given
5. m<1 = m<2 Substitution POE
6. m<1 + m<2 = [tex]180^{o}[/tex] Def of supplementary angles
7. 2(m<1) = [tex]180^{o}[/tex] Simplify/ Combine like terms
8. m<1 = [tex]90^{o}[/tex] Definition of right angle
9. 2(m<2) = [tex]180^{o}[/tex]
10. g ⊥ h Def of perpendicular lines
if 4/5x - -3/4=0 then x=
Tell whether the triangle with the given side lengths is a right triangle. Y/N question
Answer:
yes , it is a right triangle.
Step-by-step explanation:
according to the pythagoras theorem to be the right angled triangle the sum of square of two smaller sides of triangle must be equal to the square of it's hypotenuse.
Here , 65 is largest side so it is hypotenuse and other two sides are the legs of the triangle.
pythagoras theorem:
a^2 + b^2 = c^2
16^2 + 63^2 = 65^2
256 + 3969 = 4225
4225 = 4225
since both sides are equal it can be concluded that the given side lengths d forms a right triangle.
Keelie has a triangular-shaped card. The lengths of its sides are 4.4 cm, 5.5 cm, and 6.6 cm. Is the card a right triangle?
Answer:
No
Step-by-step explanation:
We can use the Pytaghorean theorem to verify it
4.4^2 + 5.5^2 = 6.6^2
19.36 + 30.25 = 43.56
49.61 = 43.56 (false)
What is organic chemistry??
How do I find RS? I've been having great trouble with questions like this recently.
Answer:
5
Step-by-step explanation:
We can solve by solving for x
2x-6 + 1 + x-4 = 18
3x-9=18
3x=27
x=9
Plug in 9 for x in Segment RS and you get (9) - 4 = 5
Hope this Helps!
Please Mark Me Brainliest!
:)
Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a probability of detecting a missile attack. Use the binomial probability distribution to answer the following questions. a. What is the probability that a single detection system will detect an attack
Answer:
0.8 is the probability that a single detection system will detect a missile attack.
Step-by-step explanation:
The perimeter of a rectangular painting is 344 centimeters. If the width of the painting is 79 centimeters, what is its width?
Answer:
the equation is 2(l+w) so we do 2(93+w)=344 getting the answer of 79
Step-by-step explanation:
i think im 100 percent correct i took the test on flvs if I'm wrong just let me know
Someone PLEASE help me !!
1. five times the product of two numbers x any y, divided by a third number z. what is the algebriac expression?
2. Seven times the product of two numbers x and y, less five, divided by thrice a third number z, what is the algebriac expression?
3. Half the product of two numbers x and y, minus five times a third number z. what is the algebriac expression?
4. three times a number x, minus four times a second number y, divided by seven times a third number. whats the algebriac expression?
Answer:
no lo entiendo lo que escribiste
Answer:
1.5(x+y)/z
2. 7(x+y)-5/3z
3.1/2(x+y)-5
4. 3x-4y/7z
What is the transformation shown in the graph?
270° rotation
reflection
180° rotation
90° rotation
i got it wrong and had 90° rotation
find the x-coordinate of the vertex of the function given below. y = x^2 + 12x + 21
Answer:
(-2,13;-0,02)
and
(-9,87;-0,02)