Answer: C
Step-by-step explanation:
A 28 foot ladder leans up against a building and reaches the base of a window that is 20 feet high. How far is the base of the ladder from the base of the building? Round your answer to the nearest whole foot
A 16 feet
B 20 feet
C 24 feet
D 34 feet
Answer:
20 feet
Step-by-step explanation:
The distance between base of the ladder from the base of the building is given by option B) 20 feet.
Use the Pythagorean theorem to solve this problem.
The Pythagorean theorem states that in a right-angled triangle,
The square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Length of the ladder = 28 foot
Here, the ladder forms the hypotenuse, and the height of the window (20 feet)
And the distance from the base of the ladder to the base of the building (let's call it x feet) are the other two sides.
So, we have:
Ladder² = Height² + Distance²
28² = 20² + x²
Now, let's solve for x:
x² = 28²- 20²
x² = 784 - 400
x² = 384
Now, take the square root of both sides to find x:
x = √384
x ≈ 19.6 feet
Rounding to the nearest whole foot, the distance from the base of the ladder to the base of the building is 20 feet.
Therefore, the distance between base of the ladder and building is equal to option B) 20 feet.
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PLAEASE HELP ME
If the equation of a line is 2y+3x=3, what is the y intercept of the line?
Answer:
3/2
Step-by-step explanation:
2y+3x=3
This represents a linear equation and the format for a linear equation is
y = mx+b
m = slope
b= y-intercept
we have to subtract 3x from both sides to make this the y=mx+b form
2y=-3x+3
and divide both sides by 2
y = (-3x+3)/2
3/2 or 1.5 is the y-intercept
the constant of a linear equation (or 3) is the y-intercept, if there is no constant then the y-intercept is 0
Answer:
1.5
Step-by-step explanation:
2y+3x=3
Convert to y=mx+b form...
y=mx+b
y(output)
x(input)
x(slope/growth)
b(y int/starting point)
Steps for converting to y=mx+b form:
-subtract 3x from both sides of equal sign
-divide by 2 on both sides
2y+3x = 32y = -3x+3y = -1.5+1.5y = -1.5+1.5
so 1.5 is y int.
:)ur welcome
D and E are points on sides AB and AC respectively of triangle ABC such that DE || BC. If AD = x-1, DB = x – 3, AE = x + 3 and EC = x , the value of x is:
9514 1404 393
Answer:
9
Step-by-step explanation:
The triangles are similar, so corresponding sides are proportional.
AE/AD = EC/DB
(x+3)/(x -1) = x/(x -3)
x^2 -9 = x^2 -x . . . . . . . cross multiply
x = 9 . . . . . . . . . . . add x+9-x^2 to both sides
Select the correct answer.
What are the roots of this equation?
Answer:
Hope this helps!
Step-by-step explanation:
Help help pls pls help help
Multiply the top equation and the bottom by 7.
Answer:
The answer is D: Multiply the top equation by 3 and the bottom equation by 4
Step-by-step explanation:
when you do that, the coefficients for the x on the top and bottom equations both become 12, so you would have to subtract the 2 equations to get rid of x.
how many real solutions does the equation sqrt 2x+4=1/2 x+1 have?
Answer:
unfortunately I do not have the answer, but this is like the only way to tell you something
The 3 real roots of the given equation.
To find the real roots.
What is quadratic equation?Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.
Given that:
The equation are
[tex]\sqrt{2x+4}=\frac{1}{2x} +1\\[/tex]
By squaring both sides
[tex]2x+4=\frac{1}{4x^{2} }+1+\frac{1}{x} \\\\2x-\frac{1}{x}+3=\frac{1}{4x^{2} }\\\\8x^{3}-4x+12x^{2} -1=0\\ \\8x^{3}+12x^{2}-4x -1=0[/tex]
By solving quadratic equation ,Solutions for x
x1 = -1.74543
x2 = -0.17169
x3 = 0.41712
So, the 3 real roots of the given equation.
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If x is 6, then 7x =
Answer:
42
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
x = 6
7x
Step 2: Evaluate
Substitute in variables: 7(6)Multiply: 42Each side of a regular polygon is 2.5 cm in length .The perimeter of the polygon is 12.5 cm .How many sides does the polygon have?
with explanation please.
Answer:
There are 5 sides in the polygon.
Total perimeter of the polygon is 12.5 cm and it is a regular polygon.
Each side of the polygon is 2.5 cm.
So total number of sides is: Total perimeter of the polygon / Length of each side = 12.5 cm/ 2.5 cm = 5
Hence, the polygon has 5 sides and it is a regular pentagon.
Step-by-step explanation:
I hope this is correct, if it isn't please feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
A) m + n
B) 0
C) m - 1
D) -(m+n)
the required answer is 2m- (m-n)(m-1)
Point O is the center of the circle. What is the value of X?
Answer options: 9, 17, 8, 15
Answer:
j4k4
Step-by-step explanation:
k4k4j4h g o4utf75d4s6e Ok xkyai5eziKyeakyz6ozo6syzyl6
An advertising company conducted a survey to determine how often people of different ages shopped online. The table shows the data.
Answer:
Teens who use online shopping sometimes = 6
total number of people who use online shopping sometimes = 20
total percentage of teens using online shopping sometimes = 6/20*100 => 30%
hope it helps
have a nice day
the meal costs $52.95 for 5 people. Jenna ordered a dessert for $2.50. if Jenna deducts this amount from the total how much will each of the other people pay for their meal
Subtract the dessert from the total:
52.95 - 2.50 = 50.45
Now divide that by the number of people:
50.45/5 = 10.09
Each person would pay $10.09
She would pay 10.09 + 2.50 = 12.59
May someone help me out with this. A bit lost here. If anyone knows, and would like to answer, I would gladly appreciate you. Thanks.
Answer:
since they are parallel lines therefore the angles hence formed will also be equal
x+5=2x-7
5+7=2x-x
12=x
hence the ans is 12
plz mark it as brainliest
hi can you answer this question thank you
9514 1404 393
Answer:
2 < x < 24.937
Step-by-step explanation:
Conceptually, the values of x are allowed to be between those that make angle ABC one of zero measure and that make angle ABD a straight angle.
That is ...
0 < 2x-4 < 180 -86
4 < 2x < 98
2 < x < 49
__
However, some study of this geometry convinces us that the largest that angle ABC can be is one that makes ∆ABC isosceles. In that case, AB = CB = DB, and B is the center of the circle through points A, C, and D. Trigonometry can be used to find the value of x in that case.
The radius CB of circle B must be such that the bisector of angle CBD intersects the midpoint of CD:
CB·sin(86°/2) = 14/2
Similarly, the bisector of angle ABC will meet the midpoint of AC:
CB·sin((2x -4)°/2) = 8/2
Equating expressions for CB gives ...
7/sin(43°) = 4/sin((x-2)°)
(x -2)° = arcsin((4/7)sin(43°))
x° = 2° +arcsin(4/7·sin(43°))
x ≈ 24.937
So, a revised upper limit on x puts the range of possible values as ...
2 < x < 24.937
Cora invests $1000 at 5% compounded semi-annually. How long will it take, to the
nearest whole year, for her money to double? Use the formula A=P(1+r/n)^(nt),
where 0.05 and n=2 to find the answer.
It will take years for Cora's money to double when invested at 5%
compounded semi-annually
The solution is
Answer:
15 Years or 14.5 Years
Step-by-step explanation:
According to the Question,
Given That, Cora invests $1000 at Rate of 5% Per Annum. Interest is compounded semi-annually, After What time her money to get double.We Know, the formula A=P(1+r/n)^(nt) (where r=0.05 , p=1000 , A=2000 , n=2)Put the Given value in Formula, We get
2000 = 1000 (1 + 0.05/2) ^ 2t
2 = (1+0.025)^2t
2 = (1.025)^2t ⇔ 1.025^30 = 2.0975 ≈ 2
Thus, 2t = 30 ⇒ t = 15 Years
OR
2 = (1.025)^2t ⇔ 1.025^29 = 2.0464 ≈ 2
Thus, 2t = 29 ⇒ t = 14.5 Years
f (x) = x2 – 5, what is f(1)
Answer:
-3
Step-by-step explanation:
f(x)=x2-5 f(1)
f(1)= (1)2 -5
2-5
-3
Determine the measure of CD from the diagram below.
A
E
809
88
Answer:
88
Step-by-step explanation:
line AC is equal to line DB
A parabola has a vertex at (–5, 0) and passes through the point (–3, 1). Which of the following is the equation of this parabola in the form y=a(x-h)^2+k?
Answer:
y = 1/4(x + 5)^2
Step-by-step explanation:
Using the given equation form;
(h,k) represents the vertex of the parablola
To get the value of a, we use the given point
So we have;
1 = a(-3 + 5)^2 + 0
1 = a(2)^2
4a = 1
a = 1/4
so we have the equation as;
y = 1/4(x+5)^2 + 0
y = 1/4(x + 5)^2
Choose either YES or NO to tell whether the expression is equivalent to 179 x 44
(179 x 40) + (179 x 4)
(100x4)+(70 x 4)+(9 x 4)
4,000 + 2,800 + 360 + 400 + 280 + 36
(100 x 44) + (70 x 44)+ (9 x 44)
179 (4 + 4)
Answer:
Step-by-step explanation:
(179 * 40) + (179 * 4) = 179 *(40 + 4) = 179 * 44
YES
(100 * 4) + 70*4 + 9*4 = 4 * ( 100 +70 + 9) = 4 * 179
No
4000 + 2800 + 360 + 280 +36 = 7876 = 179 *44
YES
(100 *44) + (70*44) + (9*44) = 44 * (100 + 70 +9) = 44 * 179
YES
179 *(4 +4) = 179 * 8
NO
This graph represents a quadratic function. Which expression is a factor of the function's equation?
A 0
B x-4
с. x
D X + 4
The low temperature (t) was 8 Celsius and the high temperature was 16 Celsius, write it as an inequality.
Answer:
8 ≤t≤16
We know the low temperature was 8
8≤ t
And the high was 16
8 ≤t≤16
Step-by-step explanation:
Set up an en equation and use it to solve for x
Answer:
x = 30
Step-by-step explanation:
The 2 angles lie on a straight line and sum to 180° , then
x - 3 + 153 = 180
x + 150 = 180 ( subtract 150 from both sides )
x = 30
Answer:
x = 30
Step-by-step explanation:
180° = total
153° = part
180° - 153° = 27°
Then use the equation to find the value of x
(x - 3) = 27
(x + 3) = +3 Add 3 to both sides!
x = 30
what is 2+a when a=22?
Answer:
24
Step-by-step explanation:
2+a
2 + (22)
= 24
PLZZZ HELP NO LINKS What graph represents the piecewise-defined function?
Answer:
option alphabet c is the answer
A class of 40 pupils voted for their favourite flavour of ice cream. 3/4 of the pupils voted for chocolate, 1/10 of the remaining pupils voted for vanilla and the rest for strawberry. How many voted for strawberry?
Answer:
6 students
Step-by-step explanation:
3/4 = chocolate
1/10 = vanilla
3/4 = 30/40
1/10 = 4/10
30+4=34
40-34 = 6
6 = the number of students that voted for strawberry
A and B contributed 2700 and 1800 respectively to start a business. They agreed to share the profit in the ratio 7:5 respectively. If the profit made was 900, Calculate B's share of the profit.
Answer:
375
Step-by-step explanation:
let the ratio constant be 'x'
=>Profit ratio for A=7x
=>Profit ratio for B=5x
Profit=900 (Given)
Sum of the ratios=7x+5x=12x
Therefore,
Profit ratio for A=(7/12)x900=7x75=525
Profit ratio for B=(5/12)x900=7x75=375
Need help ASAP! Will Give Brainliest!
A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answer:
A) To plot equations in point-slope form, pick one and let x = 0, then solve for y (or -4). That gives you point 1 (0,-4). Then let y = 0 and solve for x (or 2/3). That gives you a second point (2/3,0). Plot the two points and draw the line. Repeat for the second equation (points are (0,-3) and (3/5,0)). Where the lines cross is the solution for both equations.
B) point (1,2) fits both equations.
Step-by-step explanation:
Or solve by brute force...
The solution is where the same X,Y point fits both equations, or Y1 = Y2 and X1 = X2. So the equations in point-slope form (already in point-slope form) equal to each other, solve for X and plug that back into either of the equations to find Y.
6X - 4 = 5X -3
X = 1 so
y = 6X - 4
Y = 6 - 4
Y = 2
13
What is the Pythagorean Theorem?
A) a + b + c
B
a2+b2=c2
a2-b2=c2
D) abc = d
Answer:
a2 +b2=c2
Step-by-step explanation:
......
hope it helps
Answer: its a^2+b^2=c^2
Step-by-step explanation:
What is x equal to????
Answer:
x = 20
Step-by-step explanation:
The 3 arcs UV, VW, WX form a semicircle, so sum to 180° , that is
4x + 2 + x + 78 = 180
5x + 80 = 180 ( subtract 80 from both sides )
5x = 100 ( divide both sides by 5 )
x = 20
Pls help me, I really dont understand
Answer:
-2.5x-.5
[tex]y=\frac{2}{3}x-1[/tex]
draw the dotted line (3/7)x-3 and shade below it
Step-by-step explanation:
First, we need the slope
Use the slope formula:
[tex]\frac{Y_2-Y_1}{X_2-x_1}=\frac{2-(-8)}{-1-3}=\frac{10}{-4}=-2.5[/tex]
so we have
y= -2.5x+b
Solve for b by plugging in coordiantes
-8= -2.5(3)+b
-8= -7.5+b
b= -.5
Put it together and get -2.5x-.5
2.)
A line is parallel to another line if they have the same slope (and different y intercepts)
So in the formula y=mx+b we knowe that m= 2/3
Now it's just a matter of solving for B
plug in the required coordinate to do this
-1=(2/3)*0+b
-1= b
Put it all together to get
[tex]y=\frac{2}{3}x-1[/tex]
3.)
put this into slope intercept form
3x-7y>21
3x-21 > 7y
(3/7)x-3 >y
To graph this just draw a dotted line with the equation (3/7)x-3 and shade everything below it (use de_smos if you're stuck)