1) Irene places a mirror on the ground 24ft from base of an oak tree.she walks backward until she can see the top of the tree in the middle of the mirror. At that point, Irene’s eyes are 5.5 above the ground, and her feet are 4 ft from the mirror.How tall is the oak tree?
Answer:
Oak tree is 33 ft tall.
Step-by-step explanation:
We know that Irene places a mirror on the ground and walks backwards such that the mirror is in between her and the oak tree (as shown in the attached picture).
Given the distance of Irene's eyes from ground, distance between oak tree and mirror and distance between mirror and Irene, we are to find the height of the tree.
For this, we will use the ratio method:
[tex]\frac{T}{24} =\frac{5.5}{4}[/tex]
T = 33 ft
The perimeter of a rectangle is 18 feet, and the area of the rectangle is 20 square feet. What is the width of the rectangle?
4 ft or 5 ft
i think thats right
Answer:
The width can be 5 ft or the width can be 4 ft
Step-by-step explanation:
Perimeter = 2 (l+w) for a rectangle
Area = l*w for a rectangle
Using perimeter
18 = 2(l+w)
Divide by 2
18/2 = 2/2 (l+w)
9 = l+w
Solving for l
9-w = l
Using area
20 = l*w
Substituing for l
20 = (9-w) * w
20 = 9w - w^2
Subtract 20 from each side
20-20 =-w^2 +9w -20
0 = -w^2 +9w -20
Multiply by -1
0 = w^2 -9w+20
Factor
0 = (w-5) (w-4)
Using the zero product property
w-5 = 0 w-4 = 0
w= 5 w=4
The width can be 5 ft or the width can be 4 ft
Choose the triangle that seems to be congruent to the given one
The triangle that seems to be congruent to the given one is triangle EFA.
Here's why:
Both triangles have three straight sides.
Both triangles have the same angles at corresponding vertices. For example, the angle at vertex E in triangle EFA is congruent to the angle at vertex A in the given triangle, and the angle at vertex F in triangle EFA is congruent to the angle at vertex C in the given triangle.
The corresponding sides of the triangles have the same lengths. For example, side EF in triangle EFA is congruent to side AC in the given triangle, and side FA in triangle EFA is congruent to side CB in the given triangle.
Therefore, based on the properties of congruence, triangle EFA is congruent to the given triangle.
Use the graph of the function y=4^x to answer the following questions
The domain of a function is all the x-values which it passes through. The function is a continuous exponential function, and therefore, it will contain every x value. The answer is:
The domain of the function is negative infinity to positive infinity.
Hope this helps!!
The domain of a function is the set of input values, the function can take.
The domain of the function is negative infinity to positive infinity,
The function is given as:
[tex]\mathbf{y = 4^x}[/tex]
The function is an exponential function, and there are no restriction as to the input values of an exponential function.
i.e: [tex]\mathbf{(-\infty, \infty)}[/tex]
Hence, the domain of the function is negative infinity to positive infinity,
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The sum of one-third of a number and three-fourths of the number exceeds that number by one.
Which equation could be used to find the number?
1/3n = 3/4n + 1
1/3n + n 3/4= n - 1
1/3n + n 3/4= n + 1
The answer would be...
1/3n + 3/4n = n + 1
^^^That would be the last option
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
The correct answer is last option
1/3n + n 3/4= n + 1
Step-by-step explanation:
It is given that,the sum of one-third of a number and three-fourths of the number exceeds that number by one
To find the correct option
Let 'n' be the number, one- third of the number = 1/3(n)
three - fourths of the number = 3/(4n)
Therefore the equation becomes,
1/(n) + 3/4(n) = n + 1
Therefore the correct answer is last option
Solve 9x + 4 = 11 for x using the change of base formula log base b of y equals log y over log b.
Answer:
[tex]x = \frac{7}{9} [/tex]
Step-by-step explanation:
[tex]9x + 4 = 11 \\ \\ 1. \: 9x = 11 - 4 \\ 2. \: 9x = 7 \\ x = \frac{7}{9} [/tex]
Answer with explanation:
The given equation in one variable is:
→ 9 x +4 =11
Subtracting 4 from both sides
→9 x +4 -4=11 -4
→ 9 x=7
Taking log on both sides
→log ( 9 x)= log 7-----log having base 10 is considered.
→ log 9 + log x= log 7
→ 0.95424 + log x= 0.8450
→ log x=0.8450 - 0.9542
→ log x= -0.1092
[tex]\rightarrow\frac{\log x}{\log 10}=-0.1092\\\\\rightarrow \log x=-0.1092 \times \log 10\\\\\rightarrow \log x=\log 10^{-0.1092}\\\\\rightarrow x=10^{-0.1092}\\\\\rightarrow x=0.77767\\\\x=0.778[/tex]
Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1. Btw the variable I used was "f".
Answer:
$[tex]4f[/tex]
Step-by-step explanation:
Let's assume [tex]f[/tex] represents the number of pounds of fruit.
We need to multiply the number of pounds of fruit by the cost per pound.
This is $[tex]f * 4[/tex], or in a simpler form, $[tex]4f[/tex].
In this context, the variable 'f' represents the number of pounds of fruit. In the expression '4f', it means that for every pound of fruit, which costs $4, you multiply the number of pounds by that price to get the total cost.
Explanation:The problem is asking us to provide an equation for the total cost of fruit based on the cost per pound, which is $4. As you identified the variable 'f' in the previous question, let's use that to stand for the number of pounds of fruit.
The written expression for the total cost would then be 4f. This expression says that the total cost is four times the number of fruit pounds ('f') purchased
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The following system has a solution of x=-5, y=9, z=11.
4x+y+z=12
-4x-y-z=-10
5y-z=9
Please select the best answer from the choices provided
T
F
Answer:
Step-by-step explanation:
false
One solution of x^2-25=0 is 5. What is the
other solution?
Enter the correct answer.
Answer:
The other solution: x = -5Step-by-step explanation:
[tex]x^2-25=x^2-5^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-5)(x+5)\\\\x^2-25=0\to(x-5)(x+5)=0\iff x-5=0\ \vee\ x+5=0\\\\x-5=0\qquad\text{add 5 to both sides}\\x=5\\\\x+5=0\qquad\text{subtract 5 from both sides}\\x=-5[/tex]
Step by step 24-3x=-27
For this case we have the following equation:
[tex]24-3x = -27[/tex]
To solve we follow the steps below:
We subtract 24 from both sides of the equation:
[tex]-3x = -27-24\\-3x = -51[/tex]
We divide between -3 on both sides of the equation:
[tex]x = \frac {-51} {- 3}\\x = 17[/tex]
The value of x is 17
Answer:
[tex]x = 17[/tex]
Answer:
[tex]\boxed{x=17}[/tex]
Step-by-step explanation:
Subtract by 24 from both sides.
[tex]24-3x-24=-27-24[/tex]
Simplify
[tex]-27-24=-51[/tex]
[tex]-3x=-51[/tex]
Divide by -3 from both sides.
[tex]\frac{-3x}{-3}=\frac{-51}{-3}[/tex]
Simplify to find the answer.
[tex]-51\div-3=17[/tex]
[tex]x=17[/tex], is the correct answer.
Y= -(x-1)(x+3) has how many roots
Answer:
two
Step-by-step explanation:
Two
x - 1 = 0
x = 1
x + 3 = 0
x = - 3
You can see them for your self. The roots are the points where the graph cuts the x axis.
(1,0) and
(-3,0)
What is the greatest common factor of 28 and 60
Answer:
4 is your answer.
Step-by-step explanation:
You would break down both numbers into their factors.
28 is divisible by 1,2,4,7,14,and 28
60 is divisible by 1,2,3,4,5,6,10,12,15,20,30, and 60
find the common pairs: (1,1), (2,2), (4,4) Both numbers have these as factors, so find the largest one.
The greatest common factor (GCF) of 28 and 60 is 4.
To find the Greatest Common Factor GCF of two numbers, we need to determine the largest number that divides both numbers without leaving a remainder. One way to find the GCF of 28 and 60 is to list the factors of each number and identify the largest factor that they have in common.
The factors of 28 are 1, 2, 4, 7, 14, and 28.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The largest factor that 28 and 60 have in common is 4.
Therefore, the GCF of 28 and 60 is 4.
Another way to find the GCF of two numbers is to use prime factorization. To do this, we need to express each number as a product of its prime factors.
The prime factorization of 28 is 2² x 7, and the prime factorization of 60 is 2² x 3 x 5. To find the GCF, we take the product of the common prime factors with the smallest exponents, which in this case is 2². Therefore, the GCF of 28 and 60 is 2², which is equal to 4.
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What is the total surface area of the square pyramid?
Answer:
144 in^2
Step-by-step explanation:
There are four triangular sides to this square pyramid. According to the area-of-a-triangle formula, A = (1/2)(b)(h), which here is A = (1/2)(8 in)(5 in) = 20 in^2.
Thus, the total lateral (side) area is 4(20 in^2) = 80 in^2.
The area of the bottom is (8 in)^2, or 64 in^2.
Thus, the total surface area is 80 in^2 + 64 in^2, or 144 in^2.
Answer:
144
Step-by-step explanation:
x^2 + mx + n = 0, m and n are integers. The only possible value for x is -3. What is the value of m?
plz the solution is necessary
Thanks
Answer:
The value of m is 3
Step-by-step explanation:
we have
[tex]x^{2}+mx+n=0[/tex]
step 1
Find the value of n
For x=0
[tex]0^{2}+m(0)+n=0[/tex]
[tex]n=0[/tex]
step 2
Find the value of m
For x=-3
substitute
[tex]x^{2}+mx=0[/tex]
[tex](-3)^{2}+m(-3)=0[/tex]
[tex]9-3m=0[/tex]
[tex]3m=9[/tex]
[tex]m=3[/tex]
A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed, what range of weights would 99.7% of the dogs have?
Approximately 26–34 pounds
Approximately 24–36 pounds
Approximately 28–32 pounds
Approximately 29–31 pounds
Answer:
Option 2 - Approximately 24–36 pounds
Step-by-step explanation:
Given : A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed.
To find : What range of weights would 99.7% of the dogs have?
Solution :
The range of 99.7% will lie between the mean ± 3 standard deviations.
We have given,
Mean weight of Eskimo dogs is [tex]\mu=30[/tex]
Standard deviation of Eskimo dogs is [tex]\sigma=2[/tex]
The range of weights would 99.7% of the dogs have,
[tex]R=\mu\pm3\sigma[/tex]
[tex]R=30\pm3(2)[/tex]
[tex]R=30\pm6[/tex]
[tex]R=30+6,30-6[/tex]
[tex]R=36,24[/tex]
Therefore, The range is approximately, 24 - 36 pounds.
So, Option 2 is correct.
Answer:
B: Approximately 24–36 pounds
Step-by-step explanation:
Given f(x) = x squared - 1 and g(x) = x+ 2, what is the value of h(-2) where h(x) = f(g(x))?
Answer: [tex]h(-2)=-1[/tex]
Step-by-step explanation:
We need to find [tex]f(g(x))[/tex]. Substitute the function [tex]g(x)[/tex] into the function [tex]f(x)[/tex]:
[tex]f(g(x)) = (x+ 2)^2- 1[/tex]
Now, we know that the function [tex]h(x)[/tex] is [tex]h(x)=f(g(x))[/tex], then:
[tex]h(x)=(x+ 2)^2- 1[/tex]
In order to find the value of [tex]h(-2)[/tex], we must substitute [tex]x=-2[/tex] into the function [tex]h(x)=(x+ 2)^2- 1[/tex].
Therefore, the value of [tex]h(-2)[/tex] is:
[tex]h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1[/tex]
Which expressions are equivalent to the one below? Check all that apply. Log^7 1 * Log^5 25
Answer:
B if you mean log_7 (1)*log_ 5 (25)
Step-by-step explanation:
I think you mean 7 and 5 as bases... like
log_7(1)*log_5(25)
log_7(1)=0 because 7^0=1
log_5(25)=2 because 5^2=25
So you have to perform the following operation 0*2=0
so 0 is definitely one answer
1 and 5*7 are definitely not equal to 0
let's look at last choice now
log_7(7)=1 because 7^1=7
so D is equivalent to saying 2*1 which is 2 not 0
so only one choice works and it is B
I need some help in this question
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48, …
f (n + 1) = –3 f(n )
f (n + 1) = 3 f(n )
f (n + 1) = –2 f(n )
f (n + 1) = 2 f(n)
Answer:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
Step-by-step explanation:
The given sequence is; 3, –6, 12, –24, 48, …
The first term of this sequence is
[tex]f(1)=3[/tex]
There is a common ratio of [tex]r=\frac{-6}{3}=-2[/tex]
We can actually use any other two consecutive terms in the sequence to obtain the common ratio.
The recursive formula is given by:
[tex]f(n)=r\cdot f(n-1)[/tex]
We plug in the common ratio to get:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
Answer:
The answer is C
Step-by-step explanation:
What is the true solution to 2 In 4x= 2 In 8?
Answer:
1
Step-by-step explanation:
[tex] ln4x = 2 ln8 \div 2 \\ ln4x = ln4 \\ x = 1[/tex]
Hope it helps you...☺
Answer:
x = 2
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ n logx
• log x = log y ⇒ x = y
Given
2 ln 4x = 2 ln 8
ln (4x)² = ln 8²
ln 16x² = ln 64, hence
16x² = 64 ( divide both sides by 16 )
x² = 4 ( take the square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
If f(x) = 4x - 3 and g(x) = x + 4, find (f - g) (x)
[tex](f-g)(x)=4x-3-(x+4)=4x-3-x-4=3x-7[/tex]
which expression is equivalent to (2^1/2 2^3/4)^2
Answer:
[tex]\sqrt{2^5}[/tex]
Step-by-step explanation:
[tex]2^{1/2}[/tex] × [tex]2^{3/4}[/tex] = [tex]2^{5/4}[/tex]
([tex]2^{5/4}[/tex])² = [tex]2^{5/2}[/tex] = [tex]\sqrt{2^5}[/tex]
Answer:
[tex]\large\boxed{\sqrt{2^5}}[/tex]
Step-by-step explanation:
[tex]\bigg(2^\frac{1}{2}\cdot2^\frac{3}{4}\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{\frac{1}{2}+\frac{3}{4}}\bigg)^2\qquad\left/\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{1\cdot2}{2\cdot2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\right/\\\\=\bigg(2^\frac{5}{4}\bigg)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{\frac{5}{4}\cdot2}\\\\=2^{\frac{5}{2}}\qquad\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\=\sqrt{2^5}[/tex]
which graph represents the solutions for x^2+x-12>0
To find the answer, we can use the method of finding x- intercepts by solving the equation.
To solve the equation:
x^2 + x -12> 0
by using cross method,
we can find that 3 x -4 = -12
(x-3)(x+4) = 0
Therefore, x = 3 or x=-4
Hope it helps!
graph C represents the solutions for x^2+x-12>0
What are inequalities?Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to find which graph represents the solution ?The given inequality is :
x^2+x-12>0
Now factorizing the expression we get,
(x-3)(x+4)>0
⇒ x>3 and x<-4
Clearly graph C represents the solutions.
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simplify root45 - root20 +4root5
Answer:
( -3√5)
Step-by-step explanation:
√45 - √20 - 4√5 = √5*3*3 - √2*2*5 - 4√5
= 3√5 - 2√5 - 4√5
= √5 (3 - 2 - 4)
= ( -3√5)
The intensity, or loudness, of a sound can be measured in decibels (dB), according to the equation I(dB)=10log[1/10], where I is the intensity of a given sound and I0 is the threshold of a hearing intensity. What is the intensity, in decibles, [I(dB)], when I=10^32(I0)? Round to the nearest whole number.
Answer:
C. 320
Step-by-step explanation:
According to it's formula, the intensity when [tex]l = 10^{32}[/tex] is of 440 db.
What is the formula for the intensity of a sound?The intensity of a sound l is given by:
[tex]L(l) = 10\log{\left(\frac{l}{l_0}\right)}[/tex]
In which [tex]l_0 = 10^{-12}[/tex] is the threshold of a hearing intensity.
In this problem, we have that the sound is of [tex]l = 10^{32}[/tex], hence:
[tex]L(l) = 10\log{\left(\frac{10^{32}}{10^{-12}}\right)} = 10\log{10^{44}} = 10 \times 44 = 440[/tex]
Hence, the intensity of the sound is of 440 db.
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The city sales and use tax collected on taxable items in falles, Texas is 8.25%. The tax you must Pay depends on the price of the item you are purchasing. Determine the sales tax you must Pay on the following items.
sales tax alone = 0.99, 2.06, 16.5, 1237.5 for the items
Which of the following is not equal to sin(-230°)?
sin(130°)
-sin(-50°)
sin(50°)
sin(-50°)
Answer:
sin(-50°) is not equal to sin(-230°)
Step-by-step explanation:
You will be required to use a scientific calculator for this.
Step 1 : Find out the value of sin(-230°)
sin(-230°) = 0.766
Step 2 : Find out all the other values and see if they are 0.766 or not.
sin(130°) = 0.766 (It is equal to sin(-230°))
-sin(-50°) = 0.766 (It is equal to sin(-230°))
sin(50°) = 0.766 (It is equal to sin(-230°))
sin(-50°) = -0.766 (It is not equal to sin(-230°))
!!
Answer:
sin(-230°) =sin(50°)
Step-by-step explanation:
1) sin(-a) = -sina
note : 2) sina = sinb : a=b or a+b =180°
in this exercice :
sin(-230°) = - sin(230°) = - sin(-50°)=- (-sin(50°)) =sin(50°) because :
sin(230°) = sin(-50°) because ; 230°+(-50°) =180°
sin(230°) = -sin(50°)
a line segment AD, contains B&C such that C is between A and D, and B is between A and C. if AB=6, BD=23, and AB=CD, find the length of segment AD.
Answer:
AD = 29
Step-by-step explanation:
Note that
AD = AB + BD = 6 + 23 = 29
Combine the following expressions.
3\sqrt{27x^3}-2\sqrt{12x^3}
A) 19x
B) 5x
C) 13x
The correct answer is: B) 5x √3x
I just did the test, trust me it is B.
The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].None of the options are correct.
What exactly is simplification?Simplifying is making something easier to do or comprehend, as well as making something less difficult.
The following expression is given ;
[tex]3\sqrt{27x^3}-2\sqrt{12x^3}[/tex]
Simplify the given expression;
[tex]3\sqrt{27x^3}-2\sqrt{12x^3} \\\\ 3 \times 3x \sqrt {3x} -2 \times 2x \sqrt{3x}\\\\ 9x \sqrt {3x}-4x\sqrt{3x}\\\\\ 5x\sqrt{3x}[/tex]
The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].
Hence one of the options is correct.
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Solve for x. Round your answer to the nearest hundredth.
15.56x - 200 < 758.92
Answer: x<61.63
Step-by-step explanation: Add 200 to both sides, giving you 15.56x<958.92 .
Than divide by 15.56 giving you x< x<61.627249
Round to the nearest hundredth giving you x<61.63
Answer: 61.63
Step-by-step explanation:
The given inequality : [tex]15.56x - 200 < 758.92[/tex]
Adding 200 on both the sides , we get
[tex]15.56x < 758.92+ 200\\\\\Rightarrow\ 15.56x <958.92 [/tex]
Dividing 15.56 on both the sides , we get
[tex]\dfrac{15.56x}{15.56}<\dfrac{958.92}{15.56}\\\\\Rightarrow\ x<61.6272493573\approx61.63[/tex]
Hence, the value of x (to the nearest hundredth) = 61.63