10. How many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will
reach a point on the house 36 feet from the ground? Draw a picture!
The distance from the base of the ladder to the house is 15 ft.
How to find the side of a right triangle?The length of the ladder is 39 ft.
The ladder is placed to reach a point on the house 36 feet from the ground.
This situation forms a right angle triangle.
The distance from the base of the ladder to the house is as follows:
The distance from the base of the ladder to the house is the other leg of the right angle triangle.
The ladder length is the hypotenuse of the right triangle.
Hence, using Pythagoras theorem,
39² - 36² = b²
b² = 1521 - 1296
b² = 225
b = √225
b = 15 ft
Therefore, the distance is 15 ft.
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Matthew, Enos and Simon share 16 slices of pizza in the ratio 5: 1:2. How many slices of pizza does Simon have?
Simon had 4 slices of the total pizza.
What is fraction?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
There are several fraction examples in daily life, including:
1. If a pizza is split into two equal pieces, each piece represents half of the entire pizza.
2. Each piece of a watermelon slice that is divided into three equal pieces makes up one-third of the whole.
In this question , the ratios given are 5 : 1 : 2
Thus the total is 5 + 1 + 2 = 8
Since Simon's share is 2/8 th of the total
Thus the required fraction is 2 / 8 × 16
On solving further we get;
2 × 2
= 4 slices
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1.9 Which of the following expressions is equal to -12? Select ALL that apply.
A.-15-3
B.-13-(-1)
C.-8-4
D.-3-(-9)
E.5-17
F. 6-(-6)
213313
The expressions that are equal to -12 are present in Options(B,C, and E).
Solutions of the given expressions are:
A. -15-3
To Add two negative numbers together, start by adding the absolute value of each number together and precede it with a negative sign.
-15-3 = -18
B. -13-(-1)
Proceed by opening the parentheses and modifying the sign in front of it.
-13-(-1) = -13 + 1 = -12
C. -8-4 = -12
D. -3-(-9) = -3 + 9 = 6
E. 5-17
Use the sign of the larger number and subtract to determine the sum of a negative and a positive number.
5-17 = -12
F. 6-(-6) = 6 + 6 =12
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how many horseshoes are needed to fit 5 horses
Answer:
20 horseshoes
Step-by-step explanation:
How many horseshoes are needed to fit 5 horses?
5 horses with 4 hooves each:
5 × 4 = 20 horseshoes
Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
CD
From the given figure, it can be seen that there are two circles with centers A and B respectively.
The circle with the center A is larger in size than the circle with center B. Points P, Q and E lie on the surface of the circle having center A and R, S, C and T points lie on the circle having center B.
Circle A and Circle B's connection
Circle A's size is more significant than Circle B's size.
As a result, circle A's radius exceeds circle B's radius.
The connection between segments
1.
Let M be the location where Segment QT and ER intersect.
Additionally, tangents from an outside point to a circle have identical lengths.
QM = ME———— (1)
MT=MR————(2)
Including (1) and (2)
MR + ME = QM + MT
Q T=ER
2.
Tangents from an exterior point to a circle have identical lengths.
We may write the following segments are equal using this property.
UP=U Q
Z C=ZR
V C=VS
NR=NS
KC=K T
What are Tangents?
A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:
As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):
Utilizing the differentiation principles, determine the gradient function's derivative.
To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate
Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).
Circle's Tangent
A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.
Geometric Tangent
Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.
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Find x if:
B is between A and C
AB=x+5
BC= 2(x-3); and
AB BC
Answer:
If B is between A and C, then AB = BC.
x + 5 = 2(x - 3)
x + 5 = 2x - 6
x = 11
Which numbers are greater than 59 1/3
592/10
59 4/12
59 2/3
179/3
The numbers that are greater than 59 1/3 are; C: 59 2/3 and D: 179/3
How to interpret Inequalities?We want to find the numbers that are greater than 59 ¹/₃.
Now, the given fraction is written in mixed fraction. Looking at the fraction side, we can see that 1/3 can be written as 0.333. Thus;
59 ¹/₃ = 59.333
When we talk about the inequality greater than, we are simply referring to sayin that a figure is more than another figure which could be given or not given.
Looking at the given options, let us rewrite each of the mixed or improper fractions in decimal form to get;
59 ²/₁₀ converted to decimal form gives 59.2
59 ⁴/₁₂ = 59 ¹/₃ converted to decimal form gives 59.333
59 ²/₃ converted to decimal form gives 59.667
179/3 = 59 ²/₃ converted to decimal form gives 59.667
Comparing the options to the given number in the question, we can conclude that 59 2/3 and 179/3 are greater than 59 1/3
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What is the value of x − 9 if x = −24?
Answer:
If x= -24
then the equation will be = -24-9
= -24+ -9
= -33
Therefore the value of x-9 when x=-24 is 33
The circumference of a circle of diameter 3,5 cm is 11 cm. What is the circumference of a circle of diameter 42 cm?
Answer ... cm
The circumference of a circle with diameter of 42 cm is 131.88 cm
How to find the circumference of a circle?The circumference of a circle of diameter 3.5 cm is 11 cm.
The circumference of a circle of diameter 42 cm can be found as follows:
Therefore,
circumference of a circle = 2πr
where
r = radius of the circleHence,
diameter = 42 cm
radius = 42 / 2
radius = 21 cm
circumference of a circle = 2 × 3.14 × 21
circumference of a circle = 42 × 3.14
circumference of a circle = 131.88 cm
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Which of the following best defines an output? (4 points)
Question 1 options:
1)
An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
2)
An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
3)
An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
4)
An output is a set of ordered pairs in which no y-value repeats.
Answer:
i go with the first one cause
Step-by-step explanation:
its the only true one
WILL GIVE POINTS! I just need someone to help with the rest
I think the first blank is "Given", the third is "Angle addition postulate", And the 6th is "90 degrees". Check this?
∠FED and ∠DEW are complementary because it is a sum of 90 degrees.
By the law of addition of complementary angles, m∠FED + m∠DEW = 90°
m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.
By the substitution property of equality, m∠FEW = 90°.
The ∠FEW is a right angle by the definition of right angles.
How to Interpret Complementary Angles?Complementary Angles defined as angles that sum up to 90 degrees.
Now, we are given that;
∠FED and ∠DEW are complementary.
We want to prove that ∠FEW is a right angle. Thus;
∠FED and ∠DEW are complementary because it is a sum of 90 degrees.
By the law of addition of complementary angles, we can say that;
m∠FED + m∠DEW = 90°
Also,
m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.
By the substitution property of equality, m∠FEW = 90°.
The ∠FEW is a right angle by the definition of right angles.
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It took a plane 2 hours to fly from Dallas to New York with the headwind and 1.5 hours to return with the tailwind. If the speed of the wind was 30 mph, how far apart are the two cities?
Please help
The distance between in two cities is 360 miles.
Given,
It took a plane 2 hours to fly from Dallas to New York
The headwind and 1.5 hours to return with the tailwind.
and, the speed of the wind was 30 mph.
To find the how far apart are the two cities?
Now, According to the question:
Let speed of be x
Speed of wind be c
Also note D = RT, where
D is distance and R is rate and T is time
For First Leg:
we can write:
(x - c) × 2 = D
2x - 2c = D
For Second Leg:
we can write:
(x+ c) × 1.5 = D
1.5x + 1.5c = D
We can equate and write:
2x - 2c = 1.5x + 1.5c
0.5x = 3.5c
We know Speed of Wind, c, is 30, so we have:
0.5x = 3.5(30)
0.5x = 105
x = 105/0.5 = 210 [speed of airplane]
We know distance is
D = 2x - 2c
D = 2(210) - 2(30)
D = 420 - 60
D = 360 miles
Hence, The distance between in two cities is 360 miles.
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Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities y>-2x-4 and y
Answer:
We want to imagine where the shading should be, and with that determine which point is a solution for both inequalities. We will see that the solution is the point (7, -8)
Step-by-step explanation:
Interpreting inequalities:
In this case, the inqualities are:
y < -x + 1
y < (-1/2)*x - 1
You can see that in both cases, y is smaller than the line, thus, for both inequalities, we must shade the part that is below the lines.
With that in mind, the region of solution will be the region that is below both lines at the same time, and that region will be the "triangle" that you can see at the middle below the horizontal axis.
Now that we know the region of solutions, we only need to see which point belongs there, from the given options the only that belongs to that region is the point (7, -8), which means that this point is a solution for both inequalities.
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Write the domain as an inequality and range as inequality
The domain of the graph as an inequality is
0 ≤ x ≤ ∞The range of the graph as an inequality is
5 < y ≤ ∞How to find the domain and the range of the graphThe domain of a graph is a term that refers to the input values of the graph. The input values are usually in the x axis and this is why we use x in defining the domain
The extreme of the curve on the left side shows the vertex on the x axis is 0 and the curve ended with an arrow showing it is tending to infinity
The range represents the values in the y axis. The curve started at the point y = -5 with a hollow dot. In inequality, a hollow dot means the number is not included hence we use less than.
The graph continued with an arrow this means it tends to infinity
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banks normally charge a monthly service fee to customers for servicing their bank account. This fee can often be avoided, which of the following are common reasons for the bank to waive their monthly fee.
Select one or more:
a.
If you open two checking accounts with the same bank they won't charge a monthly fee
b.
If a student links their account to a parent's account the bank will waive the monthly fee
c.
If you go overdrawn the bank will waive the monthly service fee and charge you an overdraft fee instead.
d.
If you ask your employer to direct deposit your salary into your bank account the bank will waive the monthly fee
e.
If you keep a minimum required balance in the account the bank will waive the monthly fee
f.
If you ask the bank to waive their monthly service fee they will agree to
The common reasons for the bank to waive their monthly fee are :
a. If you open two checking accounts with the same bank they won't charge a monthly fee.
d. If you ask your employer to direct deposit your salary into your bank account the bank will waive the monthly fee
e. If you keep a minimum required balance in the account the bank will waive the monthly fee
What is monthly fee?Monthly fee can be defined as the fee a bank or financial institution charge their customers for services they rendered to their customers example of this monthly fees is account maintenance fees.
A bank can decide to waived a customer monthly fees or charges when the customer open two checking account with the bank or when a customer make use of a direct deposit as well as when a customer maintain a enough balance or maintain minimum balance in their bank account.
Therefore the correct options are A, D, C.
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witch is greater 38 7/12 or 463/12
Answer:
they're the same !
Step-by-step explanation:
38*12= 456
456+7=463
hope this helps!!!
Does this graph represent a function? Why are why not?
No, because it fails vertical line test.
What is vertical line test?
Vertical line test is defined as a method used to find if the given equation or graph represents a function or not. The vertical line test states that a vertical line needs to cuts the graph of a function (equation) at only one point, for it to represent a function.
Hence, in the given graph, the function intercepts the y- axis at two points, therefore, it fails vertical line test.
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Farmer Bob is going out to feed the cattle. He feeds seven pounds of cowchow to each cow. He uses at least 84 pounds of cowchow every time he feeds. Write an inequality and solve to find how many cows farmer Bob has
Each cow receives seven pounds of cow chow from Bob. Every time he feeds, farmer Bob uses at least 84 pounds of cow chow, which means that each time he feeds, 12 cows in total.
What is the concept of Unitary Method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Cow chow fed to each cow by the farmer =7 pounds
Total cow chow used by the farmer to feed the cows every time = 84 pounds
Total cow chow used = no. of cows *cow chow fed to each cow
No. of cows = Total cow chow / cow chow fed to each cow
= 84/7
=12
No. of cows = 12
Therefore, 84 pounds of cow chow is used to feed 12 cows each time.
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-9/2 + 5/12
Due soon
Answer:
-49/12
Step-by-step explanation:
-2+(-6) is units from -2, in the
direction.
-2+(-6) is -3 unit(s) from -2. in the negative direction.
Answer:
-8
Step-by-step explanation:
6 + 2 = 8,just make 8 negative
Whats the answer to 1 1/2 X 3 2/3
Answer:
5 1/2 or 5.5
Step-by-step explanation:
First, we can convert these values to improper fractions, where the numerator is larger than the denominator.
Then, we'd get:
3/2 x 11/3
Now, we can multiply the numerators and denominators, and we would get the answer of 33/6
When we convert 33/6 to a mixed number, we get 5 3/6, which can then be further simplified to 5 1/2 OR 5.5 (whichever you prefer)
Answer:
5 1/2
Step-by-step explanation:
1 1/2×3 2/3
[tex](2 \times 1 + 1) \times (3 \times 3 + 2) \\ [/tex]
3/2×11/3
33/6
=5 1/2
20. A work crew is building a new biking path that will be 28 miles long. Each day,
the crew builds 0.5 mile of the path. Write an expression for the length of the bike
path left to build at any point during the construction. Explain what your variable
represents.
PLEASE HELP
The most appropriate choice for linear equation will be given by-
[tex]l = 28 - 0.5d[/tex] is the required expression for the length of the bike
path left to build at any point during the construction.
[tex]l[/tex] is the length of the bike path left to build at any point during the construction
[tex]d[/tex] is the number of days
What is Linear equation?
A one degree equation is called a linear equation.
Here,
Let the length of the bike path left to build at any point during the construction be [tex]l[/tex] and the number of days be [tex]d[/tex]
In one day, the crew build 0.5 miles of the path
In d days, the crew can build [tex]0.5 \times d[/tex] miles of the path
Length of path left to construct after [tex]d[/tex] days = [tex]28-0.5d[/tex]
By the problem,
[tex]l = 28 - 0.5d[/tex]
This is the required expression for the length of the bike
path left to build at any point during the construction.
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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{2x-7} =1[/tex]
X and Y varies inversely. X equals 10 when Y equals 20. What does X equal when Y is 40?
A. 10
B. 8
C. 20
D. 5
E. 15
I will give you 50 points. NO LINKS
Solve for x, ty/ wlc!
[tex]\sf 3+6x=2x+27[/tex]
3 + 6x = 2x + 27
Move the 2x on the left side with changed sign and the 3 on the right side with changed sign aswell.
6x - 2x = 27 - 3
4x = 24
Now devide 24 by 4.
x = 24 : 6 = 4
Answer:
[tex]\bf x=6[/tex]Step-by-step explanation:
[tex]\bf 3 + 6x = 2x + 27[/tex]
Subtract 3 from both sides:-
[tex]\bf 3+6x-3=2x+27-3[/tex]
Simplify:-
[tex]\bf 6x=2x+24[/tex]
Subtract 2x from both sides:-
[tex]\bf 6x-2x=2x+24-2x[/tex]
Simplify:-
[tex]\bf 4x=24[/tex]
Divide both sides by 4:-
[tex]\bf \cfrac{4x}{4}=\cfrac{24}{4}[/tex]
Simplify:-
[tex]\bf x=6[/tex]
_____________________
Clare wants to make an open-top box by cutting out corners of a 30 inch by 25 inch piece of poster board and then folding up the sides. The volume `V\left(x\right)` in cubic inches of the open-top box is a function of the side length `x` in inches of the square cutouts.
c) Use the Distributive Property or an Area Diagram to find the product and rewrite your polynomial.
Your original V(x)=4x^{3}-110x^{2}+750x
Your new polynomial:
V(x)=
Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches of box. The volume V(x)=4x³-110x²+750x.
Given that,
Clare plans to fold up the sides of a poster board that is 30 inches by 25 inches and trim the corners to create an open-top box. The open-top box's volume, "V(x)," in cubic inches, depends on the square cuts' side length, "x," in inches.
Length =30 inch
Width=25 inch
The box's size changes when x is taken out of the container.
Length=30-2x
Width=25-2x
Height=x
Because x is eliminated from both ends, we subtract 2x.
The volume is then determined as follows:
V(x)=length×width×height
V(x)=(30-2x)×(25-2x)×x
V(x)=(30-2x)×(25x-2x²)
V(x)=750x-110x²+4x³
V(x)=4x³-110x²+750x
Therefore, the volume V(x)=4x³-110x²+750x.
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Explain why 3.14 is rational, but is not.
π
The number 3.14 is a rational number because it can be written as [tex]\frac{314}{100}[/tex].
What is rational number?p/q of two integers with q 0 can be used to represent a number as a rational number in mathematics. The set of rational numbers also contains all of the integers, which can each be expressed as a quotient with the integer as the numerator and 1 as the denominator. A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
Given that,
3.14 is rational number
Here, 3.14 can be written as [tex]\frac{314}{100}[/tex].
3.14 can be written as fraction, whereas pie cannot be written in fraction form.
Therefore, 3.14 is a rational numbers but pie is not a rational number.
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john measured two pieces of strings. one piece measured 7/12 m and the other measured 4/7 m. sect the true statement about the lenghts of john strings.
John measured two pieces of string. One piece measured \dfrac7{12}\text{ m}127 mstart fraction, 7, divided by, 12, end fraction, start text, space, m, end text and the other measured \dfrac47\text{ m}74 mstart fraction, 4, divided by, 7, end fraction, start text, space, m, end text.
Please show your work.
What is this solution?
8+(-7)^2-(7∙-2+1)
janice was given a piggy bank on her seventh birthday, and she put it to use immediately. each time she puts one or more coins into the piggy bank, she keeps track of the number of coins she has collected to date and the accumulated value of her collection. janice collects only nickels, dimes, and quarters. six months after her seventh birthday, janice looked at her record and ascertained that she had collected 540 coins, which were worth $60. janice counted 100 quarters in her savings. how many nickels and dimes are in her collection?
The number of dimes and nickels in her collection are 296 and 108 respectively.
How to find the number of nickels and dimes?She had collected 540 coins. which were worth $60.
She counted 100 quarters in her saving.
The number of dimes and nickel in her collection can be solved as follows:
Therefore,
let
x = number of dimes
y = number of nickels
number of quarters = 100
Therefore,
x + y + 100 = 504
x + y = 504 - 100
x + y = 404
Hence,
0.1x + 0.05y + 100(0.25) = 60
0.1x + 0.05y = 60 - 25
0.1x + 0.05y = 35
combine the equation
x + y = 404
0.1x + 0.05y = 35
Multiply equation(i) by 0.1
0.1x + 0.1y = 40.4
0.1x + 0.05y = 35
subtract equation(ii) from equation(i)
0.05y = 5.4
divide both sides by 0.05
y = 5.4 / 0.05
y = 108
x = 404 - 108
x = 296
Therefore,
Number of dimes = 296
Number of nickels = 108
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