An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 11 inches, and the length of the base is 6
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
What is another way to make 2.98?
Choose 1 answer:
B
1 one +8 tenths +18 hundredths
1 one 19 tenths 8 hundredths
1 one +10 tenths 8 hundredths
Answer:
Below
Step-by-step explanation:
1 + 19/10 + 8/100 = 1 + 1.9 + .08 = 2.98
Can someone help me find the point of intersection for:
2500(1. 25)^t=6000(0. 3)^t
algebraically? thank you.
The point of intersection can be found by setting the equations equal, dividing by the same quantity, taking the natural log, and dividing by ln(1.25).
[tex]2500(1.25^t) = 6000(0.3^t)[/tex]
[tex]2500*1.25^t = 6000*0.3^t[/tex]
Divide both sides by 2500:
[tex]1.25^t = 0.3^t * (6000/2500)[/tex]
Divide both sides by[tex]0.3^t[/tex]:
[tex]1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]
Take the natural log of both sides:
[tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]
Divide both sides by ln(1.25):
[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]
The point of intersection is t = ln((6000/2500) / [tex]0.3^t[/tex]) / ln(1.25).
The point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other and solving for the variable t. For example, if we want to find the point of intersection of [tex]2500(1.25^t) = 6000(0.3^t)[/tex], we can start by setting the two equations equal to each other and dividing both sides by [tex]2500: 1.25^t = 0.3^t * (6000/2500)[/tex]. Then we can divide both sides by[tex]0.3^t: 1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]. We then take the natural log of both sides: [tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]. Finally, we divide both sides by ln(1.25): [tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]. This means that the point of intersection is[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25).[/tex] In conclusion, the point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other, dividing both sides by the same quantity, taking the natural log of both sides, and then dividing both sides by ln(1.25).
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Transcribed image text: Question 4 A certain automotive dealer sells only cars and trucks, and the ratio of cars to trucks on the lotis 11 to 33. If there are currently 51 trucks for sale, how many cars does the dealer have for sale! 34 68 136 272 thierronse
If the ratio of cars to trucks on the lot is 11 to 33 and there are currently 51 trucks for sale, then there are 17 cars for sale
The ratio of cars to truck on the lot = 11 : 33
Total number of trucks for sale = 51 truck
Consider the number of cars for sale = x
Then the ratios will be
11/33 = x / 51
Cross multiply the terms in the equation
33x = 51 × 11
33x = 561
Move 33 to the right hand side of the equation
x = 561 / 33
Divide the terms
x = 17
Therefore, the number of cars does the dealer have for sale is 17
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Forest rangers at a state park have observed a decline in the rate of trees per
acre over a 5-year period. At the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an
average of 42 trees per acre. If this trend continues, how many trees per acre
will there be 412 years from the end of the 5-year observation period?
After 412 years there will be no trees at the state park.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
From the given information,
Slope(m) = (42 - 48)/(5 - 0).
Slope(m) = - 6/5.
b = 48, As y-intercept(0, 48).
Therefore, y = - (6/5)x + 48.
Now, y = - (6/5)×412 + 48.
y = - 446.4 trees per acre, But there will be no trees as it came out to be a negative value.
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In the figure below, B is between A and C, and C is between B and D. If AD=13, BD=7, and BC=3, find AC.
AC =
The length of segment AC is equal to 9.
How to Find the Length of a Segment?Since B is between A and C, we can use the fact that AB + BC = AC. Similarly, since C is between B and D, we can use the fact to state the lengths of the following segments that: CD + BC = BD.
Substituting the given values, we get:
AB + BC = AC
CD + BC = BD
We are given segments BD = 7 and BC = 3, so we can substitute these values:
CD + 3 = 7
Solving for CD, we get:
CD = 7 - 3
CD = 4
Now we can use the fact that AD = AC + CD to solve for the length of segment AC:
AD = AC + CD
13 = AC + 4
AC = 9
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Determine the value of the missing angle using the inverse trig function.
Answer:
x = 59.036°
Step-by-step explanation:
tan (BÂC) = BC/AB
tan= opposite/ adjacent
Then subs AB = 3 BC= 5 BÂC= x into tan (BÂC) = BC/AB
tan(x)=5/3
x= tan^-1 (5/3)
x= 59.036°
which equations for the measures of the unknown angles x and y are correct? check all that apply.(a) x=cos−1(a/c)x=cos−1(a/c)(b) x=sin−1(c/b)x=sin−1(c/b)(c) x=tan−1(c/a)x=tan−1(c/a)(d) y=sin−1(a/c)y=sin−1(a/c)(e)y=cos−1(c/b)y=cos−1(c/b)
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Sin θ = Opposite Side to θ/Hypotenuse
Cos θ = Adjacent Side to θ/Hypotenuse
Tan θ = Opposite Side/Adjacent Side
Cot θ = Adjacent Side/Opposite Side
Sec θ = Hypotenuse/Adjacent Side
Cosec θ = Hypotenuse/Opposite Side
where, Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle)
The inverse ratios start with the ratio and then find the angle that produces this ratio.
(a) x=cos−1(a/c)
(b) x=sin−1(c/b)
(c) x=tan−1(c/a)
(d) y=sin−1(a/c)
(e)y=cos−1(c/b)
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
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Mimi Divided a block of chese weighing 10kg into pieces weighing 5/8 kg how many pieces did she get? (Show Working)
find the missing length
The value of the missing side of the given triangle would be = 12
How to calculate the value of the missing length?To calculate the value of the missing length the Pythagorean formula can be used such as;
c² = a² + b²
where;
C =?
a = 11
b = 5
C² = 11²+5²
= 121 + 25
= 146
C =√ 146
C = 12
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Please help I’ll give brainliest!! What ordered pairs are the solutions of the system of equations shown in the graph
below?
Answer:
(-1,3) and (3,-5)
Step-by-step explanation:
I'm assuming since it is giving no information that it wants where the two graph intersect each other.
So, by the looks of it they intersect at
(-1,3) and (3,-5)
QUESTION FOR FOR LIH04
Determine the intercepts of the line. Do not round your answers. y+1=3(x − 4) x-intercept: (_,_) y-intercept: (_,_)
The intercepts of the line are x intercept: (4.3,0) y-intercept: (0,-13)
How to determine the intercepts of the lineFrom the question, we have the following parameters that can be used in our computation:
y+1=3(x − 4)
To calculate the x-intercept, we set y to 0
So, we have the following representation
0+1=3(x − 4)
This gives
x - 4 = 1/3
So, we have
x = 4.33
To calculate the y-intercept, we set x to 0
So, we have the following representation
y + 1 = 3(0 − 4)
This gives
y + 1 = -12
So, we have
y = -13
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Need help with this question urgent please
Answer:
Step-by-step explanation:
First, add 7 to all parts of the inequality to isolate x.
-10+7 < 3x-7+7 ≤ 5+7
-3 < 3x ≤ 12
Then divide all sides by 3.
-1 < x ≤ 4
So x is greater than -1 but less than or equal to 4.
This can be written as (-1, 4] in interval notation.
Which ordered pair is a solution of the inequality y≤1/3x−6
The ordered pair of the inequality will be (9,-3).
What is inequality?The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
Given that inequality is given as y ≤ 1/3x−6.
The ordered pair can be calculated as:-
y ≤ 1/3x−6
Substitute the value of x equal to 9 and get the value of y,
y ≤ 1/3(9) - 6
y ≤ 3 - 6
y ≤ -3
Hence, the ordered pair will be (9,-3).
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What is the complete square corresponding to x2 – 6x? A. (x – 1.5)2 B. (x – 3)2 C. (x – 4.5)2 D. (x – 9)
Answer:
So the answer is C. (x - 3)^2.
Step-by-step explanation:
The complete square corresponding to x^2 - 6x is (x - 3)^2.
A complete square is a trinomial that can be written in the form (x - a)^2, where a is a constant. To find the complete square of x^2 - 6x, we need to rewrite x^2 - 6x into the form (x - a)^2. We do this by adding and subtracting a constant term to make the trinomial a perfect square.
x^2 - 6x + 9 = (x - 3)^2
So the answer is C. (x - 3)^2.
What is the definition of equivalent ratios?
18.85% of the pupils in Form 2 study craft, 72% study music and 60% study both subjects. What percentage study neither craft nor music?
Answer:
Step-by-step explanation:
Sorry cant help 18.85%
do 3 over 4 and 9 over 12 form a proportion
Answer:
0 over 12
Step-by-step explanation:
3/4 is equal to 9/12
so your basically taking 9/12 from 9/12
Find x
25
38
Please help me
Answer:
x ≈ 40.6
Step-by-step explanation:
using the sine ratio in the right triangle
sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )
x × sin38° = 25 ( divide both sides by sin38° )
x = [tex]\frac{25}{sin38}[/tex] ≈ 40.6 ( to 1 decimal place )
Answer:
x ≈ 40.6 units
(nearest tenth / one decimal place)
Step-by-step explanation:
You can use the law of sines in this situation since you know it is a right triangle because of the right angle, and you have an angle and a corresponding side.
Given this information, you can use the equation:
sin A / a = Sin B / b = Sin C / c
Given: A is 38°, a is 25, C is 90°.
Find: x which is side c
sin A / a = Sin B / b = Sin C / c →
[Substitute the information given]
Sin (38°) / 25 = Sin (90°) / c →
[Use the basic identity of sin(90°)]
Sin (38°) / 25 = 1 / c →
[Use the reciprocal rule]
25 / Sin(38°) = c →
[Rotate the equation]
c = 25 / Sin(38°) →
[Solve]
c = 40.606731137068..
[Reduce to the nearest tenth
(one decimal place) and set c to x]
x ≈ 40.6
The length of a cell phone is 1.41.4 inches and the width is 3.83.8 inches. The company making the cell phone wants to make a new version whose length will be 0.910.91 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
“Log 2x = -1 Solve each equation. Check Answers”
Please help me logs are confusing
Please help with number 2!!! 100 points
Answer:
C
Step-by-step explanation:
Two less than 7 times a number equals 33 = 7x - 2 = 33. Sorry I cant really explain :/
Hope my answer helps!
The sum of two numbers is 22. Two less than three times the smaller number is equal to the larger number x. Find the larger number.
y=6, x=16
you create a system with the two variables and manipulate an equation so that you can substitute in the other to make it a single-variable equation. you then solve for that variable by isolating it and you can solve for the second variable afterwards. hope this helps!
There are 50 teachers in a school. 40% of them are women and the rest are men. If 70% of the women and 80% of the men are married, find the number of unmarried teachers in the school.
Convert 1000000 seconds to hrs, min and seconds
The value of the conversion is;
16, 666. 67 minutes
277.78 hours
What is conversion of units?Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.
From the information given, we have;
10⁶ seconds
But, we have to take note of;
60 seconds = 1 min
Then 10⁶ seconds = x min
cross multiply
x = 16, 666. 67 minutes
Also,
60 minutes = 1 hour
Then 16, 666. 67 minutes = x
cross multiply
x = 277.78 hours
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Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region between line y =3x -6 and line y=-2x+8 and
the x-axis with the help of integration will be 2.88 sq units.
What exactly is integration?
The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).
Integral Fundamental
A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.
From a to b, use ∫f(x)dx
indefinite integral
Integrals are defined without upper and lower limits. It looks like this:
A indefinite Integral is written as:
∫f(x)dx = F(x) + C
Where C might be any constant and the function f(x) is referred to as the integrand.
Now,
As given in image
Area of the region will be =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.
=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x) from x=2.8 to 4.
=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2
=2.88 sq units.
Hence,
The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.
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8. the weights of cows offered at an auction in one region are normally distributed with a mean of 825.0 pounds and a standard deviation of 74.8 pounds. one cattleman only wants to bid on cows that are in the top 5% of weight. what is the lowest weight cow that the cattleman should bid on
The cattleman should bid on cows that weigh at least 944.0 pounds, which is the weight corresponding to the top 5% of the normally distributed weights of cows.
To determine the lowest weight cow that the cattleman should bid on, we need to find the weight that corresponds to the top 5% of the weight distribution.
Using the standard normal distribution, we can find the z-score that corresponds to the top 5% of the distribution as follows:
z = invNorm(0.95) ≈ 1.645
where invNorm is the inverse of the standard normal cumulative distribution function, which can be found using a statistical calculator or a standard normal distribution table.
Next, we can use the z-score formula to convert the z-score to a weight value:
z = (x - μ) / σ
Solving for x, we get:
x = z * σ + μ
Substituting the values given in the problem, we get:
x = 1.645 * 74.8 + 825.0
x ≈ 944.0 pounds
Therefore, the cattleman should bid on cows that weigh at least 944.0 pounds.
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Write a linear function for the data in the table.
X
y
0
8
1
4.5
2
1
3
-2.5
4
-6
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The owner of two hotels is ordering towels. He bought 6 hand towels and 27 bath towels for his hotel in Campbell, spending a total of $255. He also ordered 50 hand towels and 27 bath towels for his hotel in Lowell, spending $343. How much does each towel cost?
A hand towel costs $ ----------, and a bath towel costs $ --------.
Answer:
A handtowel costs $2.00 and a bathtowel is $9.00
Step-by-step explanation:
Let h equal the cost of a handtowel. And let b equal the cost of a bathtowel.
In Campbell, they spent:
255 = 6h + 27b
In Lowell, they spent:
343 = 50h + 27b
Solve the system.
see image.
