Answer:
Step-by-step explanation:
As the length AB increases, the measure of C increases
As the length AB increases, the measure of C increases.
What is an angle measure?An angle is formed when two lines or rays meet at a single point. The common point is referred to as the vertex. The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.
Angles and sides in relation to one another:
The biggest side and angle of any triangle are in opposition to one another.
The smallest side and angle in every triangle are on opposing sides.
The middle side and middle angle are always in opposition to one another in triangles.
When we extend vertex A further to the left of vertex B,
we increase the side length of AB.
As the length AB increases, the measure of opposite angle increases.
Let C be the angle opposite to AB.
Therefore, as the length AB increases, the measure of C increases.
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A runner can run 3miles in minutes. At this rate, how many 15miles can he run in 45minutes?
15
Answer:
9
Step-by-step explanation:
I believe the question is stating he can run 3 miles in 1 minute? Though it does make sense, here's the breakdown. :)
3 x 45 = 135 Miles total
135 / 15 = 9 "15" miles ran after 45 minutes.
If this is not what you meant to ask, let me know!
Deepak is choosing a password for his phone using letters from the alphabet, A-Z. The password must be four letters long, and he can repeat letters. How many different passwords can he create?
Answer: 26 × 4
Step-by-step explanation: There are 26 letters in the alphabet lettered A through Z.
Deepak is given the choice of picking a four letter password of his liking, using any four letters. Since the letters he uses can be repeated, it is 26 * 4 possibilities, since there are 26 different possibilities of letters from the alphabet he could choose, for 4 times. Also, since letters can be repeated, 26 stays the same. If letters could not be repeated, it would be 26 * 25 * 24 * 23.
Answer:
B. 26⁴
Step-by-step explanation:
If the password is 4 letters long and he can repeat letters then:
1st letter: any one of the 26 letters from the alphabet2nd letter: any one of the 26 letters from the alphabet3rd letter: any one of the 26 letters from the alphabet4th letter: any one of the 26 letters from the alphabetTherefore, to find the total number of passwords he can create, simply multiply the number of permutations for each letter of his password:
⇒ 26 × 26 × 26 × 26 = 26⁴
Which equation can be used to calculate the surface area of the triangular prism net show below?
The net of a rectangular prism. The rectangular sides are 10 centimeters by 13 centimeters, 10 centimeters by 12 centimeters, and 10 centimeters by 5 centimeters. The triangular sides have a base of 5 centimeters and height of 12 centimeters.
[Not drawn to scale]
Surface Area = (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
Surface Area = (one-half) (5) (13) + (one-half) (5) (13) + (13) (10) + (12) (10)
Surface Area = (2) (5) (13) + (5) (10) + (13) (10) + (12) (10)
Surface Area = (one-half) (5) (12) + (one-half) (5) (12) + (5) (10) + (12) (10) + (13) (10)
The equation that can be used to calculate the surface area of the triangular prism net shown below is mathematically given as
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
Which equation can be used to calculate the surface area of the triangular prism net shown?Generally, The region or area that is occupied by the surface of any particular item is referred to as that object's surface area.
In conclusion, the equation surface area of the triangular prism will be one that accommodates all parameters
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
SA = (1/2)(5)(12) + (1/2)(5)(12) + (5)(2) + (12)(2) + (13)(2)
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Use the diagram to complete the statements.
This is circle .
If the distance from A to C is 6 units, then the distance from C to B is units.
A circle is a curve sketched out by a point moving in a plane. If the distance from A to C is 6 units, then the distance from C to B is 6 units.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
If the distance from A to C is 6 units, then the distance from C to B is 6 units. This is because AC and BC are the radii of the circle, therefore, both are equal to each other.
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Answer: c and 6
Step-by-step explanation:
The graph plots four equations. Which pair of equations has (4, 8) as its solution?
(see picture)
Answer:
B and D
Step-by-step explanation:
Both B and D cross over the point (4, 8) therefore they share the solution (4, 8)
Why is the angle of elevation for two parasailing boats traveling at the same speed
The angle of elevation for two parasailing boats traveling at the same speed is equal because they have the same length of tow line.
What is parasailing?Parasailing is also referred to as parascending and it can be defined as a recreational activity which involves a person wearing an open parachute (canopy wing) and gliding through the air, while being towed by a boat.
By critically observing the image shown below, we can infer and logically deduce that the reason why the angle of elevation for two parasailing boats traveling at the same speed is equal, is simply because they have the same length of tow line.
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Complete Question:
Why is the angle of elevation for two parasailing boats traveling at the same speed equal?
Please help! I will give you lots of points!!!
Directions: construct the bisector of the following figures.
Note: please draw them out each on a piece of paper or laptop. Thank you!
A bisector is a line that divides either a given line or an angle into two equal parts. The answer to the given question is in the attachments to this answer.
The process of bisection implies dividing a given angle or line into two equal parts. Thus a bisector should be constructed.
The construction required is as given below:
For figure 1:
With center S and any radius, draw an arc to intersect S and T.Using the end of the arc on SR and a greater radius, draw two arcs.Using the end of the arc on ST and the same radius, draw another arc to intersect the previous arc.Join S to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <RST.For figure 2:
With center u and any radius, draw an arc to intersect T and V.Using the end of the arc on uT and a greater radius, draw two arcs.Using the end of the arc on uV and the same radius, draw another arc to intersect the previous arc.Join u to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <TuV.For figure 3:
With center B and any radius, draw an arc to intersect A and C.Using the end of the arc on AB and a greater radius, draw two arcs.Using the end of the arc on BC and the same radius, draw another arc to intersect the previous arc.Join B to the point of intersection of the arcs by a straight line. Thus this line is the required bisector of <ABC.The required construction is as shown in the attachments to this answer.
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What can you say about the end behavior of the function f(x) = -ln(2x)+4?
A: Both ends increase
B: One end increases and the other approaches a constant
C: One end increases and one end decreases
D: Both ends decrease
The end behavior of the function is the one in option C.
"One end increases and one end decreases"
What can we say about the end behavior?
Here we have the function:
f(x) = -ln(2x) + 4.
Remember that for the natural logarithm, as x tends to zero the function tends to negative infinity.
And as x tends to infinity, the natural logarithm tends to infinity.
So, for our function where we have a negative sign before the logarithm, as x tends to zero the function tends to infinity and as x tends to infinity the function tends to zero.
Then the correct option is C:
"One end increases and one end decreases"
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What mass of solid that has a molar mass of 89.0 g/mol should be added to 100.0 g of benzene to raise the boiling point of benzene by 2.42°C? (The boiling point elevation constant of benzene is 2.53°C•kg/mol.)
Use the equation attached.
2.84 g
8.52 g
21.5 g
93.0 g
The required mass of the solid is 8.52g. Hence option B is correct.
We have,
mb = mass/89.0, ΔTb = 2.42° C and Kb = 2.53°C•kg/mol.
Mass of the object is defined as the space occupied by an object.
Given equation, ΔTb=Kb x mb
2.42 = 2.53 x mb
mb =0.95
mass / 89.0 x 0.1 = 0.95
mass = 8.52 g
Thus, the required mass of the solid is 8.52g.
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Point G lies between points F and H on Line segment F H.
A line contains points F, G, H. The space between F and G is 4 x. The space between G and H is 2 x.
If the length of FH is 18 units, what is the value of x?
3
4
6
12
The value of x is 3 units.
We know that a portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
Given that FH is a line segment and FH = 18 units. G is a point on FH such that FG = 4x units and GH = 2x units.
So, we can write
4x + 2x = 18
i.e. 6x = 18
i.e. x = 18/6 = 3
Then, the value of x is 3 units. So, the first option is correct.
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Answer: A / 3
Step-by-step explanation: edge 2022
If y is inversely proportional to the square root of x and y=−70 when x=49, find y if x=2401.
The value of y when x= 2401 is -10
How to determine the value of x?An inverse variation is represented as:
[tex]y = \frac{k}{\sqrt x}[/tex]
Where k is the proportionality constant
When y = -70, x = 49
So, we have:
[tex]-70 = \frac{k}{\sqrt {49}}[/tex]
Take the square root of 49
[tex]-70 = \frac{k}{7}[/tex]
Multiply through by 7
k = -490
Substitute k = -490 in [tex]y = \frac{k}{\sqrt x}[/tex]
[tex]y = -\frac{490}{\sqrt x}[/tex]
When x =2401, we have
[tex]y = -\frac{490}{\sqrt {2401}}[/tex]
Evaluate the square root
[tex]y = -\frac{490}{49}[/tex]
Divide
y = -10
Hence, the value of y when x= 2401 is -10
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need help with this asap
There is no relationship between the number of hours cycled and the number of hours worked (Option D).
What is a scatterplot?A scatterplot is a graph that is used to show the association between two variables. The relationship between the variables is shown by the use of line of best fit.
From the scatterplot shown, we can conclude that there is no relationship between the number of hours cycled and the number of hours worked (Option D).
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A job order cost sheet for Ryan Company is shown below.
Job No. 92
For 2,000 Units
Date
Direct
Materials
Direct
Labor
Manufacturing
Overhead
Beg. bal. Jan. 1 6,300 7,000 4,900
8 7,000
12 8,000 6,400
25 2,600
27 4,000 3,200
15,900 19,000 14,500
The balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.
What makes up the work in process inventory?The work-in-process inventory is made up of the costs of direct materials, direct labor, and manufacturing overhead at the beginning or end of the period.
Data and Calculations:Work in Process Balance on January 1:
Direct materials $6,300
Direct labor $7,000
Manufacturing overhead $4,900
Total = $18,200
Question Completion?What was the balance in the Work in Process Inventory on January 1 if this was the only unfinished job?
Thus, the balance in the Work in Process Inventory on January 1, if this was the only unfinished job for Ryan Company, is $18,200.
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How do l do this I’m so confused
Answer:
[tex]967.6cm^{2} (1 d.p)[/tex]
Step-by-step explanation:
Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]
Given from the question, r = 7 cm and h = 15cm
Lets Substitute r and h into the formula to find the Total Surface Area of the cylinder.
Total Surface Area of Cylinder = [tex]2\pi (7)(15)+2\pi (7)^{2} \\=210\pi +98\pi \\=308\pi cm^{2} \\=967.6cm^{2} (1 d.p)[/tex]
A table blueprint uses the scale 3 inches :2 feet.If the model is 15 inches long how long is the table!!!!!HURRY
Answer:
I am pretty positive it is thirty if you need work shown just let me know if it is wrong for some reason then I apologize.
Step-by-step explanation:
If the model is 15 inches. Then the length of the table will be 10 feet.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
A table blueprint uses the scale 3 inches :2 feet.
The scale factor will be 2 feet: 3 inches.
If the model is 15 inches.
Then the length of the table will be
⇒ (2 feet/ 3 inches) x 15 inches
⇒ 2 x 5
⇒ 10 feet
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Which choice is equivalent to the expression below? √-12 A. 214√3 B. -12/ C. 12/ OD. -2√3 E. 2/3/
The equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex]\sqrt{-12[/tex]
Express -12 as 4 * -3
[tex]\sqrt{-12} = \sqrt{4 * -3}[/tex]
Expand the expression
[tex]\sqrt{-12} = \sqrt{4} * \sqrt{-3}[/tex]
Take the positive square root of 4
[tex]\sqrt{-12} = 2 * \sqrt{-3}[/tex]
Evaluate the product
[tex]\sqrt{-12} = 2\sqrt{-3}[/tex]
Hence, the equivalent expression of [tex]\sqrt{-12}[/tex] is [tex]2\sqrt{-3}[/tex]
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Solve: x² + x + 1 = 0.
Answer:
[tex]\sf x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]
Explanation:
[tex]\sf Given : x^2 + x + 1 = 0[/tex]
Solve it using quadratic formula
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad \:when\: \: ax^2 + bx + c = 0[/tex]
So, here constants are: a = 1, b = 1, c = 1
When the value's are substituted inside the formula
[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{1^2 - 4(1)(1)} }{2(1)}[/tex]
[tex]\sf \rightarrow x = \dfrac{-1 \pm \sqrt{-3} }{2}[/tex]
[tex]\sf \rightarrow x = \dfrac{-1 \pm i\sqrt{3} }{2}[/tex]
[tex]\sf \rightarrow x = \dfrac{-1 + i\sqrt{3} }{2} \quad or \quad \dfrac{-1 - i\sqrt{3} }{2}[/tex]
The answers are :
x = -1 + √3ix = -1 - √3iThis problem can be solved using the quadratic equation.
x = -1 ± √1² - 4(1)(1) / 2a
x = -1 ± √1 - 4 / 2a
x = -1 ± √-3 / 2a
x = -1 ± i√3 / 2a (∴ i = √-1)
The possible values of x are :
x = -1 + √3ix = -1 - √3iVolume and surface area
Answer:
The volume of the suitcase will be 199.5 [tex]ft^{3}[/tex]
Step-by-step explanation:
To find the volume of a 3D shape (in question, the suitcase) we use the formula length x width x height. With this in mind, we multiply 19 x 7 = 133. Multiply 133 by 1.5, which equals 199.5. With a final answer of 199.5, the volume of the suitcase will be 199.5 [tex]ft^{3}[/tex].
What is the slope and y- intercept in the equation y=4x+6?
The slope is 4 and the y-intercept is 6.
The slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
Attached is an image of the graph.
The equation 8(3x – 2) – 4 = 8x + 4(4x – 3) has what type of solution set?
The type of solution set of the given equation is; "No Solution"
How to find the solution of an equation?Let's solve for x in the given equation;
8(3x - 2) - 4 = 8x + 4(4x - 3)
Expanding the bracket gives;
8(3x) + 8(-2) - 4 = 8x + 4(4x) + 4(-3)
24x - 16 - 4 = 8x + 16x - 12
24x - 20 = 24x - 12
Subtract 24x from both sides to get;
-20 = -12
This is a false equation as both sides are not the same number and as such the type of solution set is "No Solution"
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Given that 1/x+1/y=3 and xy+x+y=4, compute x^2y+xy^2.
Answer:
3
Step-by-step explanation:
[tex]\frac{y+x}{xy} =3\\x+y=3xy\\xy+x+y=4\\xy+3xy=4\\4xy=4\\xy=1\\x^2y+xy^2=xy(x+y)=xy(3xy)=3(xy)^2=3(1)^2=3[/tex]
Answer:
3
Step-by-step explanation:
So we're given: [tex]\frac{1}{x} + \frac{1}{y} = 3[/tex] and that: [tex]xy+x+y=4[/tex]. And now we need to solve for: [tex]x^2y+xy^2[/tex].
Original equation:
[tex]\frac{1}{x} + \frac{1}{y} = 3[/tex]
Multiply both sides by xy
[tex]y+x=3xy[/tex]
Now take this and plug it as x+y into the second equation:
Original equation:
[tex]xy+x+y=4[/tex]
Substitute 3xy as x+y
[tex]xy + 3xy = 4[/tex]
Combine like terms:
[tex]4xy = 4[/tex]
Divide both sides by 4
[tex]xy=1[/tex]
Divide both sides by x:
[tex]y=\frac{1}{x}[/tex]
Original equation:
[tex]x^2y+xy^2[/tex]
Substitute 1/x as y
[tex]x^2(\frac{1}{x})+x(\frac{1}{x})^2[/tex]
Multiply values:
[tex]\frac{x^2}{x}+\frac{x}{x^2}[/tex]
Simplify:
[tex]x+\frac{1}{x}[/tex]
Substitute y as 1/x back into the equation:
[tex]x+y[/tex]
so now we just need to solve for x+y
Look back in steps to see how I got this:
[tex]y+x=3xy[/tex]
Divide both sides by 3
[tex]\frac{x+y}{3}=xy[/tex]
Original equation:
[tex]xy+x+y=4[/tex]
Substitute
[tex]\frac{x+y}{3}+x+y=4[/tex]
Multiply both sides by 3
[tex]x+y+3x+3y=12[/tex]
Combine like terms:
[tex]4x+4y=12[/tex]
Divide both sides by 4
[tex]x+y=3[/tex]
So now we finally arrive to our solution 3!!!!! I swear I felt like I was going in circles, and I was about to just stop trying to solve, because I had no idea what I was doing, sorry if I made some unnecessary intermediate steps.
A driveway 18 ft wide and 36 ft. long is to be paved with concrete 3 in. thick. How many cubic yards of concrete are required?
Answer:
6 yds^3
Step-by-step explanation:
I find these easiest if you put all of the dimensions into yards and then multiply
18 ft = 6 yds
36 ft = 12 yds
3 in = 3/36 yds = 1/12 yds now multiply them together
6 x 12 x 1/12 = 6 yds^3
If you are just given the two points it is the same formula. Find the midpoint between the
points (4,-5) and (-4, 5).
Solution
Let's begin by applying the Midpoint Formula:
(217-22,
+32
2
Looking at our x values first we have:
+(-4))/
And looking at our y values we have:
(-5+
)/2 = (0/
So our midpoint would be the point (
4
/2) =
Given :
Point 1 = (4, -5)Point 2 = (-4, 5)Midpoint formula :
[tex]\boxed {M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})}[/tex]
Let's input the values !
⇒ M = (4 - 4 / 2, -5 + 5 / 2)
⇒ [tex]\boxed {M = (0,0)}[/tex]
The midpoint between the points is (0, 0).
Mrs. evans has 5 spaces in which to display 5 baskets. how many ways can mrs. evans display the baskets?
Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer. The number of ways Mrs Evans can display the 5 baskets is 120.
What is factorial?Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 to that considered integer.
Thus, if we want to take the factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
We usually write it in reverse order because, in calculations, its cancellation comes useful. Thus, we have:
[tex]n! = n \times (n-1) \times \cdots \times 2 \times 1[/tex]
Mrs. evans has 5 spaces in which to display 5 baskets. Therefore, the number of ways Mrs Evans can display the 5 baskets are,
Number of ways = 5! = 5×4×3×2×1 = 120
Hence, the number of ways Mrs Evans can display the 5 baskets is 120.
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(3√5)(10√3) help me pls
Runner A finished 200 meter race in 5/12 of a minute. Runner B ran it in 21/25 of runner A's time. How much time did it take runner B to finish the race?
The time it will take runner B to finish the race is 7/15 of a minutes
FractionRunner A = 200 meters in 5/12 minutesRunner B = 21/25 of runner A timeTime taken by runner B = 21/25 × 5/12 minutes
= (21 × 5) / (25 × 12)
= 105 / 300
= 7/15 minutes
Therefore, it takes runner B 7/15 of a minutes to run the same race as runner A.
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You are training your dog to catch a frisbee. You are playing in a large field, and you are standing next to your dog when you throw the frisbee. If the path of the frisbee is y=-x²
+7x+1 and the path of the dogis modeled by y = 2x + 5, will the dog catch the frisbee? If so, what are the coordinates of the point or points where they meet?
A: Yes, they intersect at the coordinates (1,7) and (4, 13)
B: Yes, they intersect at the coordinates (1,9) and (2, 9)
C: Yes, they intersect at the coordinates (2, 11) and (3, 11)
D: No, the paths do not cross
the intersection points are (1, 7) and (4, 13), So the correct option is A.
Will the dog catch the frisbee?
To see that, we need to see when the two equations:
y = -x²+7x+1
y = 2x + 5
Can be solved simultaneously for a point (x, y). So we need to solve a system of equations.
y = -x²+7x+1
y = 2x + 5
We can rewrite:
-x²+7x+1 = y = 2x + 5
Then we can solve this for x:
-x²+7x+1 = 2x + 5
x² - 5x + 4 = 0
This is just a quadratic equation, the solutions are:
[tex]x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4*(1)*(4)} }{2} \\\\x = \frac{5 \pm 3 }{2}[/tex]
So we have two values of x:
x = (5 + 3)/2 = 4x = (5 - 3)/2 = 1The correspondent values of y are:
y = 2*(4) + 5 = 13
y = 2*(1) + 5 = 7
Then the intersection points are (1, 7) and (4, 13)
Then the correct option is A. The dog will catch the frisbee.
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sketch the graph of f(x)=((x^(3)-1)/(x^(2)-1))
It's easier to sketch if you simplify [tex]f(x)[/tex]. Factorize the numerator and denominator - simple to do with a difference of cubes or squares.
[tex]\dfrac{x^3 - 1}{x^2 - 1} = \dfrac{(x - 1)(x^2 + x + 1)}{(x - 1) (x + 1)}[/tex]
If [tex]x\neq1[/tex], we can cancel the factors of [tex]x-1[/tex]. Note that [tex]f(1)[/tex] itself is undefined. For all intents and purposes, aside from the singularity at [tex]x=1[/tex], the graph of [tex]f(x)[/tex] will look exactly like the graph of
[tex]\dfrac{x^2 + x + 1}{x + 1}[/tex]
Now, rewrite this as
[tex]\dfrac{x(x + 1) + 1}{x + 1}[/tex]
Then when [tex]x\neq-1[/tex] (note that [tex]f(-1)[/tex] is also undefined), we can cancel [tex]x+1[/tex] to reduce this to
[tex]x + \dfrac1{x+1}[/tex]
On its own, the graph of [tex]x[/tex] is a line through the origin. When [tex]x[/tex] is a large number [tex]\frac1{x+1}[/tex] is small. But as [tex]x[/tex] gets closer to -1, the rational term blows up. Effectively, this means the graph of [tex]f(x)[/tex] looks like [tex]\frac1{x+1}[/tex] around [tex]x=-1[/tex], and far enough away it looks like [tex]x[/tex].
See the attached plot for a sketch of these details.
what number could t represent to make the inequality true? 2t+4<-8
2t + 4 < -8
2t < -12
t < -6
For the inequality to be true, t must be a number that is less than -6.
Hope this helps!
how high up a vertical wall will a 26-foot-long extension ladder reach if its base is placed 10 feet away from the wall
Answer:
24ft high
Step-by-step explanation:
Assuming the wall is perpendicular to the ground (so that it forms a right angle, and that when the ladder is placed on the ground and leaned up against the wall that it forms a right triangle), we can use the Pythagorean Theorem to describe the situation mathematically.
The Pythagorean TheoremFor any right triangle (a triangle that has a right angle) the Pythagorean Theorem applies. The Pythagorean Theorem describes the relationship between side lengths as [tex]a^2+b^2=c^2[/tex], where "c" is the length of the "hypotenuse" (the side across from the right angle), and "a" and "b" are the lengths of the "legs" (the other two sides that are touching the right angle). Since addition is commutative, it doesn't matter which leg you pick for side "a" or side "b", it only matters that the hypotenuse must be "c".
Given that the ladder is across from the right angle (the angle formed by the wall and the ground... the two "legs"), the ladder represents the hypotenuse in this situation.
Substituting known values, and solving the equation[tex]a^2+b^2=c^2[/tex]Substitute known values, and simplify...
[tex]a^2+(10)^2=(26)^2[/tex]
[tex]a^2+100=676[/tex]
Subtract 100 from both sides...
[tex](a^2+100)-100=(676)-100[/tex]
[tex]a^2=576[/tex]
Apply the square root property...
[tex]\sqrt{a^2}=\pm \sqrt{576}[/tex]
[tex]a=\pm 24[/tex]
[tex]a=24[/tex] or [tex]a=- 24[/tex]
Since the distance height the ladder will reach is not a negative number, we reject the negative solution. Hence, the ladder will reach 24ft high, if placed 10ft from the base of the wall.