The solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The expression is calculated as:-
E = log₅ ( 2 )+ log₅( 10 ) - log₅( 4 )
Use Logarithmic property Loga(x / y ) = Loga(x) - Loga(y)
E = log₅ ( 2 ) + log₅( 10 / 4 )
Use Logarithmic property Loga(x y ) = Loga(x) + Loga(y)
E = log₅ [ 2 x ( 10 / 4 ) ]
E = log₅ ( 5 ) = 1
Therefore, the solution to the expression log₅ ( 2 )+ log₅( 10 ) - log₅( 4 ) is 1. Option B is correct.
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If I=prt, which equation is equivalent to t?
is the sample valid? what percent of students prefer caramel popcorn?
Using the equation, y=10000(0.97)x predict the purchasing power of $10000 ten years later
Answer:
The purchasing power is $7374
Step-by-step explanation:
We are given an equation [tex]y=10000(0.97)^x[/tex]
where,
y represents purchasing power.
x represents the number of years.
We need to find purchasing power of $10000 after 10 years.
Put x=10 into equation and solve for y
[tex]y=10000(0.97)^{10}[/tex]
[tex]y=7374.24\approx 7374[/tex]
After 10 years the purchasing power of $10000 becomes $7374
As we can see the value of the product decrease.
Hence, The purchasing power is $7374
Madison and Centerville are 6 cm apart on a map that has a scale of 1 cm : 11 km. How far apart are the real cities
Final answer:
The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor. Madison and Centerville are 66 km apart in real life.
Explanation:
The actual distance between Madison and Centerville is calculated by multiplying the map distance by the scale factor:
Map distance = 6 cm
Scale factor = 1 cm : 11 km
Actual distance = 6 cm * 11 km = 66 km
Therefore, Madison and Centerville are 66 km apart in real life.
You find that the going rate for a home mortgage with a term of 30 years is 5% APR. The lending agency says that based on your income, your monthly payment can be at most $750 . How much can you borrow?
Your state's bigbucks lottery prize has reached $100,000,000, and you decide to play. you have to pick ve numbers between 1 and 60, and you'll win if your numbers match those drawn by the state. you decide to pick your "lucky" numbers using a random number table. which numbers do you play, based on these random digits? 43680 98750 13092 76561 58712
Please Help the First Answer Will Get Brainliest!!!!!!!!
Question 1 <> Aka <> First Picture
What is the area of this triangle? A = bh/2
A > 24 in²B > 30 in²C > 48 in²D > 96 in²
Question 2 <> Aka <> Second Picture
A company logo is made up of a square and three identical triangles.
What is the area of the logo?
Enter your answer in the box. _________
Question 3 <> Aka <> Third Picture
The figure is made up of 2 rectangles and 2 right triangles.
What is the area of the figure?
A > 173 units^2
B > 253 units^2
C > 277 units^2
D > 325 units^2
QUESTION 1
The area of a triangle is given by
[tex]Area=\frac{1}{2}\times base\times heigth[/tex]
The length of the base of the triangle is [tex]6\:in.[/tex] and the vertical height is [tex]8\:in.[/tex].
We substitute these values into the formula to obtain,
[tex]Area=\frac{1}{2}\times 6\times 8[/tex]
[tex]Area=3\times 8[/tex]
[tex]Area=24\:in^2[/tex]
The area of the triangle is 24 square inches.
The correct answer is A
QUESTION 2
The company logo is made up of three triangles and a square.
The length of the square is [tex]7\:cm[/tex]
The area of a square is given by
[tex]Area=l^2[/tex]
[tex]\Rightarrow Area=7^2[/tex]
[tex]\Rightarrow Area=49cm^2[/tex].
The area of one of the triangles is
[tex]Area=\frac{1}{2}\times base \times height[/tex]
The height of the triangle is [tex]4cm[/tex].
The base of the triangle is on one side of the square, so it is [tex]7cm[/tex].
The area now becomes
[tex]Area=\frac{1}{2}\times 7 \times 4[/tex]
[tex]\Rightarrow Area=7 \times 2[/tex]
[tex]\Rightarrow Area=14cm^2[/tex].
Since there are three identical triangles, we multiply the area of one triangle by 3 to get area of the three triangles.
[tex]Area\:of\:the\:three\:triangles=3\times14=42cm^2[/tex]
The area of the logo is equal to the area of the square plus the area of the three identical triangles.
[tex]Area\:of\:logo=49+42=91cm^2[/tex]
Hence the area of the logo is [tex]91cm^2[/tex]
QUESTION 3
Since the figure is made up of two rectangles and two right triangles, we find their areas and sum them to get the area of the figure.
The area of a rectangle is given by
[tex]Area=l\times w[/tex]
The width of the bigger rectangle is [tex]5[/tex] and the length is [tex]25[/tex].
[tex]Area\:of\:bigger\: rectangle=25\times 5[/tex]
[tex]Area\:of\:bigger\: rectangle=125\:square\:units[/tex]
The width of the smaller rectangle is [tex]8[/tex].
The length of the smaller rectangle is [tex]25-(6+6)=25-12=13[/tex].
[tex]Area\:of\:smaller\: rectangle=13\times 8[/tex]
[tex]Area\:of\:smaller\: rectangle=104\:square\:units[/tex].
The two triangles are identical, so we find the area of one and multiply by 2
[tex]Area\:of\:triangle=\frac{1}{2}\times base \times heigth[/tex]
[tex]Area\:of\:triangle=\frac{1}{2}\times 6 \times 8[/tex]
[tex]Area\:of\:triangle=3 \times 8[/tex]
[tex]Area\:of\:triangle=24\:square\:units[/tex]
[tex]\Rightarrow Area\:of\:the\:two\:triangles=2\times24=48\:square\:units[/tex]
The area of the figure is
[tex]=125+104+48=277\:sqaure\:units[/tex]
The correct answer is C
Kendra bought a magazine for $3.00 and 4 paperback books for $5.00 each. The expression 3+4x5 represents the total cost in dollars of her purchases. What are the terms in this expression?
Answer:
Step-by-step explanation:
When a grizzly bear hibernates, it’s heart rate drops to 10 beats per minute, which is 20% of its normal value. What is a grizzly bear’s normal heart rate when not hibernating?
what is the solution of the equation 1.6m - 4.8 = -1.6m
Answer:
m=1.5
Step-by-step explanation:
I took the test.
At Store 1 I can buy 36 oz of baby formula for $26.62, and at Store 2 I can buy 28 oz of baby formula for $22.42. Which one is a better buy and by how much? A) Store 1 by $0.74 an ounce. B) Store 2 by $0.06 an ounce. C) Store 2 by $0.80 an ounce. D) Store 1 by $0.06 an ounce.
you were wrong, so I got it wrong...
expand the equation 1/3(2/5-2/3w)
You observe one pine tree. if the probability of not being a foxtail pine is equal to 0.06, what is the probability that this tree is a foxtail pine? (calculate to 2 decimals)
Final answer:
The probability that the observed pine tree is a foxtail pine is 0.94 or 94%, calculated by subtracting the probability of it not being a foxtail pine (0.06) from 1.
Explanation:
If the probability of not being a foxtail pine is 0.06, we can find the probability of a tree being a foxtail pine by subtracting this from 1 (since the sum of all probabilities for an event and its complement must equal 1). Therefore, the calculation to find the probability of the tree being a foxtail pine is 1 - 0.06.
Carrying out this subtraction gives us:
1 - 0.06 = 0.94.
Thus, the probability that the observed pine tree is a foxtail pine is 0.94, or 94%, when calculated to two decimals.
Box contains 4 bolts. two of them, labeled #1 and #2 are 5 mm in diameter, and two of them, labeled #3 and #4, are 7 mm in diameter. bolts are randomly selected until a 5 mm bolt is obtained. the outcomes are the sequences of the bolts that can be selected. so one outcome is 1, and another is 342. let x represent the number of bolts selected.
a.find the probability mass function of x.
we built a fence around the back of his yard he built 7 feet of fence every day in July and was finished how long is the fence explain how you got the answer
Mr. Lin baked banana bread for a bake sale to raise money for the math team. He said that he added a spoonful of walnuts for each of the students in his three classes, and that he added more than 250 walnuts. He used the inequality
16w + 24w + 10w > 250 to represent this situation, where w represents the number of walnuts in each spoonful. How many walnuts can be in a spoonful?
Susan been a total of $26 at the State Fair she's mad she spent 9 on food in the rest of the money susan spent on games,g.
There are 14 cars waiting to cross the ferry. The ferry can carry 3 cars at one time. How many trips will the ferry make to get all 14 cars across?
5. What is the value of x to the nearest tenth? The figure is not drawn to scale.
A) x=15.7
B) x=4.4
C) x=13.9
D) x=1.9
The correct option is B) [tex]x=4.4[/tex]. The value of x to the nearest tenth is x=4.4.
To find the value of x, we need to apply the Law of Cosines to the given triangle. The Law of Cosines states that for any triangle with sides [tex]\( a \), \( b \), and \( c \),[/tex] and the angle opposite side c and [tex]\( \gamma \),[/tex] the following relationship holds: [tex]\[ c^2 = a^2 + b^2 - 2ab\cos(\gamma) \][/tex]
Let's denote the sides of the triangle as follows: the side opposite the right angle (hypotenuse) as c, the side opposite the 30-degree angle as b, and the side opposite the 60-degree angle as a. We are given that [tex]\( a = 2x \), \( b = x \), and \( c = 10 \).[/tex]
Using the Pythagorean theorem, we have:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ 10^2 = (2x)^2 + x^2 \][/tex]
[tex]\[ 100 = 4x^2 + x^2 \][/tex]
[tex]\[ 100 = 5x^2 \][/tex]
[tex]\[ x^2 = \frac{100}{5} \][/tex]
[tex]\[ x^2 = 20 \][/tex]
[tex]\[ x = \sqrt{20} \][/tex]
[tex]\[ x = \sqrt{4 \cdot 5} \][/tex]
[tex]\[ x = 2\sqrt{5} \][/tex]
Now, we calculate the numerical value of x:
[tex]\[ x \approx 2 \cdot 2.236 \][/tex]
[tex]\[ x \approx 4.472 \][/tex]
Rounding to the nearest tenth, we get: [tex]\[ x \approx 4.4 \][/tex]
Therefore, the value of x to the nearest tenth is 4.4, which corresponds to option B.
A realtor earns a 0.8% commission on the homes sje sells. Last month, she sold a $380,000 home. How much did the realtor earn as her commission for the sale
Answer:
Her commission for the sale was $3,040
Step-by-step explanation:
A realtor sold a home costs = $380,000
She earns commission on the home she sells = 0.8%
Commission for the sale she earns = 0.8% of 380,000
[tex]\frac{0.8}{100}[/tex] × 380,000
0.008 × 380,000 = 3,040
Her commission for the sale was $3,040
6 friends share 15 oz bag of nuts equally between what two whole numbers of ounces will each person get
Troy is going to Spain and needs to convert his dollars to euros. He knows that when he goes, $5.00 is equivalent to about 3.45 Euros, How many will he get for $125?
Math help!! 5 questions!!! A classmate believes that a triangle can have both right angle and an obtuse angle. Which of the following statements would you use to convince him that he is incorrect. A. Its is not possible because the sum of the angles in the triangle can't exceed 180 d. B. It is not possible because if a triangle has an obtuse triangle , that means all the angles are obtuse angles. C. It is not possible because if a triangle has a right triangle, that means all the angles are right angles. Its is possible. The classmate is correct.
Final answer:
A triangle cannot have both a right angle and an obtuse angle, as the sum of its angles must always equal 180 degrees.
Explanation:
To convince your classmate that a triangle cannot have both a right angle and an obtuse angle, you should explain that according to Euclidean geometry, the sum of the angles in any triangle must equal two right angles, or 180 degrees.
If a triangle has a right angle (90 degrees), then the remaining two angles must sum up to 90 degrees as well. Introducing an obtuse angle, which is any angle greater than 90 degrees, would cause the total sum of the angles to exceed 180 degrees, which is impossible.
Therefore, the correct statement to use would be 'A. It is not possible because the sum of the angles in the triangle can't exceed 180 degrees.'
James has 6 stamps in his stamp collection. Roy has 12 stamps in his stamp collection. James adds 2 stamps to his stamp collection. After James adds these stamps, what is the ratio of the number of stamps in James's collection to the number of stamps in Roy’s collection?
can u show me common core way this problem how to do 5/9 ×3 1/2
Convert a length of 25.0 m to inches.
express your answer numerically in inches.
Answer:
98.4 inches
Step-by-step explanation:
You want the length 25.0 meters expressed in inches.
ConversionThere are 0.254 m in an inch, so the distance d can be found from the proportion ...
d/(25 m) = (1 in)/(0.254 m)
Multiplying by 25 m, we find ...
d = 25/0.254 in ≈ 98.4252 in
The length is about 98.4 inches.
__
Additional comment
The value to convert is given to 3 significant figures. The conversion factor is exact. The answer is appropriately expressed using 3 significant figures.
Caitlin says that AC is the longest segment of fencing becasue it is opposite 68 degrees, the largest angle measure in the figure. Is her reasoning valid?
Caitlin's reasoning is valid; in a triangle, the side opposite the largest angle is indeed the longest, according to the triangle inequality theorem.
Explanation:Caitlin's reasoning that AC is the longest segment of fencing because it is opposite the largest angle measure in the figure is indeed valid. In any triangle, the longest side is always opposite the largest angle. This is due to the fact that the angles in a triangle are directly related to the lengths of their opposite sides.
The triangle side opposite the largest angle is the longest because of the triangle inequality theorem. So, if 68 degrees is the largest angle in the triangular piece of land that Caitlin is fencing, then segment AC, being opposite this angle, would be the longest side.
Caitlin's reasoning is valid based on the principle that in a triangle, the longest side is opposite the largest angle. The length of the third side can be determined using the cosine law or vector addition, depending on the given details.
Explanation:The validity of Caitlin's reasoning is based on a principle in geometry that states the side opposite the largest angle in a triangle is the longest side. This fact is drawn from the Law of Sines which asserts that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. Therefore, if AC is indeed opposite the largest angle, which is 68 degrees, then her reasoning is valid and AC would be the longest segment of fencing.
To calculate the length of the third side, one can use the cosine law or the vector addition method depending on the given information and the context of the question. If the internal angles and lengths of two sides are known, the cosine law allows for the calculation of the third side. In the context of vectors, the resultant vector, which in this case is the third side C, can be calculated by mathematically adding vectors A and B.
1 2/3 × 2 1/3= in fraction form
After the multiplication of the given fraction, the value obtained in terms of a fraction will be equal to 35/9.
What is a fraction?In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.
As per the information available in the question,
The given fraction is,
1 2/3 × 2 1/3
It can also be written as:
5/3 × 7/3 = 35/9 or 3 8/9.
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The expression 17n+11 represents the perimeter of the triangle.
A simplified expression that represents the measure of the third side is
Answer: the answer is 8n
The third side of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n
The perimeter of any shape is total distance around the shape
In the triangle shown:
The perimeter = 17n + 11
The first side = 5n + 6
The second side = 4n + 5
Let the third side be represented by M
The perimeter = (The first side) + (The second side) + (The third side)
Substitute perimeter = 17n + 11, first side = 5n + 6, second side = 4n + 5, and third side = M into the equation above
17n + 11 = (5n + 6) + (4n + 5) + M
M = 17n + 11 - 5n - 6 - 4n - 5
Collect like terms
M = 17n - 5n - 4n + 11 - 6 - 5
M = 8n
Therefore, the third side of a triangle whose perimeter is 17n + 11 and the other two sides are (5n + 6) and (4n + 6) is 8n
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As per an axiom in Euclidean geometry, if points lie in a plane, the containing those points also lies in the same plane?
A) two/plane
B) three/plane
C)two/line
D)three/line
Answer: two, line
Step-by-step explanation: