the height if a triangle is 8 cm shorth than its base. if the are of the trinagle is 24cm^2 find the height of the triangle
The height of the given triangle is 4cm.
Let the base of the triangle be x cm.
It is given that the height of the triangle is 8cm shorter than the base.
∴ Height of the triangle = ( x-8 ) cm
Now,
Formula for the area of a triangle = 1/2 × Base × Height sq units.
It is given that the area of the triangle is 24 cm^2.
Area= 1/2* x(x-8) cm^2
⇒ 1/2 × x(x-8) = 24
⇒ x(x-8) = 48
⇒ [tex]x^{2}[/tex] - 8x -48=0
⇒ [tex]x^{2}[/tex] - 12x + 4x -48 = 0
⇒ x(x -12) +4(x-12) = 0
⇒ ( x-12 )( x + 4) =0
⇒ x= 12 , -4
Since, x is a length so it can not be negative value.
∴ x = 12 cm
Now, height = x-8= 4 cm
Therefore, The height of the given triangle is 4cm.
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Write the equation of a line perpendicular to y=2x−5 that passes through the point (2, -5) in slope-intercept form.
To write the equation of a line that is perpendicular to y = 2x - 5, we need to find the slope of the new line.
As we know, the slope of a line perpendicular to y = 2x - 5 is the negative reciprocal of the slope of y = 2x - 5, which is -1/(2) = -1/2.
To find the equation of the line in slope-intercept form (y = mx + b), we can use the point (2, -5) and the slope of -1/2.
We know that the point (2, -5) belongs to the line, so we can substitute these values into the equation:
y = -1/2x + b
-5 = -1/2(2) + b
-5 = -1 + b
b = -4
So, the equation of the line in slope-intercept form is:
y = -1/2x -4
This is the equation of a line that is perpendicular to y = 2x - 5 and passes through the point (2, -5)
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The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, the fourth number by fourth, and the fifth number by 5. What is the average of the set of increased numbers?
The average of the increased set of numbers is 21
What is the average of a set of numbers?The average, also known as the arithmetic mean is found by adding together, the numbers in a set of numbers, and dividing the sum by the count of the numbers.
The average of the 5 numbers = 18
The amount by which the numbers are increased are as follows;
First number; Increased by one
Second number; Increased by two
Third number; Increased by three
Fourth number; Increased by four
Fifth number; Increased by five
Let a represent the first number, b the second number, c the third number, d, the fourth number, e, the fifth number, we get;
The increased numbers are; a + 1, b + 2, c + 3, d + 4, e + 5
The initial average can be presented as follows;
Initial average = [tex]\frac{a+b+c+d+e}{5} = 18[/tex]
The imncreased average becomes;
New average = [tex]\frac{(a+1)+(b+2)+(c+3)+(d+4)+(e+5)}{5} = \frac{a+b+c+d+e+15}{5}[/tex]
The new average = (a + b + c + d + e + 15)/5 = (a + b + c + d + e)/15 + 15/5
The term (a + b + c + d + e)/15 in the expression on the right for the new average is the initial average and is equivalent to 18, therefore;
(a + b + c + d + e)/15 = 18
The new average = (a + b + c + d + e)/15 + 15/5
(a + b + c + d + e)/15 + 15/5 = 18 + 15/5 = 18 + 3
The new average = 18 + 3 = 21
The average of the increased set of numbers (the new average) is 21
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what is the answer to 12+13
Answer: 25
Step-by-step explanation: 10+10=20 and 2+3=5. 20+5=2
Solve for r²
1
S= Ar^2h
Answer:
I think r^2= 4S/πh
Step-by-step explanation:
S=1/4πr^2h
Multiple 4 on both sides
4S=πr^2h
Divide π and h on both sides
r^2=4S/πh
Sorry if this wrong
in the diagram below of trapezoid RSUT, X is the midpoint and V is the midpoint of SU if RS=30 and XV=44, what is the length of TU
The length of TU in a trapezoid RSUT is 34 units.
How to calculate length of TU in a Trapezoid?To find the length of TU, we can use the midpoint formula. The midpoint formula states that for a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2).
In this case, we know that X is the midpoint of line segment RS and V is the midpoint of line segment SU. So we can set up the following equation:
(RS/2) + (SU/2) = 44
Where (RS/2) = (30/2) = 15 and (SU/2) = TU/2
So we can substitute this into the equation and get:
15 + (TU/2) = 44
To find TU, we can solve this equation by multiplying both sides by 2:
TU = 2(44) - 2(15) = 64 - 30 = 34
So the length of TU is 34 units.
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Which of the following statements is NOT true regarding an expression written in scientific notation in the form of a times 10 Superscript n baseline?
A. The value of a must be greater than or equal to 1 and smaller than 10.
B. The value of n must be an integer.
C. Doubling n results in a doubling of the value of the expression.
D. Doubling a results in a doubling of the value of the expression.
There are 150,000 households in Market City. A local phone repair shop takes a random sample of 50 households and finds that the average number of phones per household from the sample last year that needed to be repaired was 1.05 ± 0.23. Which of the following is an estimate of the total number of phones that needed repairing last year in Market City?
The estimate of the total number of phones that needed repairing last year in Market City is given as follows:
Between 123,000 and 157,500.
How to obtain the estimate?The estimate is obtained applying the proportions in the context of this problem.
The confidence interval is given as follows:
1.05 ± 0.23.
Hence the bounds of the interval are given as follows:
1.05 - 0.23 = 0.82.1.05 + 0.23 = 1.28.Then the amounts out of 150,000 households are given as follows:
0.82 x 150,000 = 123,000.1.05 x 150,000 = 157,500.More can be learned about proportions at brainly.com/question/24372153
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X - 4.65 less than or equal to 0.09
it's an equation not a question
The required given expression is a equation x - 4.65 = 0.09.
What is Equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:In any expression variables and constants are expressed by equal sign,
Then the expression is called equaion.
So, as question says,
x - 4.65 = 0.09
x = 4.74
Thus, It is a equation of value 4.74.
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What is 0.025m in centimeters?
Answer:2.5cm
Step-by-step explanation:1cm =0.01 m
A concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m. The pillars have diameter 0.4m and height 2m. Calculate the total volume of concrete needed to make the beam and the pillars. Round your answer to a sensible level of accuracy.
In a case whereby concrete beam is to rest on two concrete pillars. The beam is a cuboid with sides of length 0.5m, 3m and 0.4m with diameter 0.4m and height 2m. the total volume of concrete needed to make the beam and the pillars is 1.103m^3
How can the concrete needed to make the beam be calculated?The concept here is total volume , then we can calculate this for concrete needed to make the beam and the pillars as:
Vtd = V1 + V2
= V1= lwh
where length l = 0.5m,
width w= 3m
height h= 0.4m.
V1 + V2 = (0.5m* 3m * 0.4m) + 2(π/4 d^2. h)
where h =height 2m
Then V1 + V2 = 1.1026m^3
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A plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The pipe is cut into two sections. One section of pipe is 12 ft. shorter than the other. If 3 of the length of the shorter pipe is 120 ft., how long is the longer piece of the pipe?
If a plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The length of the longer piece of the pipe is: 172 ft.
How to find the length?Let x represent the longer piece
Let x - 12 represent the shorter piece
So,
(3)(x - 12) = 120
Multiply both sides by 4/3
x - 12 = 120 (4/3)
x - 12 = 160
Add 12 to both sides
x = 172 ft (longer piece)
Therefore the length of the longer piece is 172 ft.
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The correct question is:
A plumber has a very long piece of pipe that is used to run city water parallel to a major roadway. The pipe is cut into two sections. One section of the pipe is 12 ft. shorter than the other. If 3/4 of the length of the shorter pipe is 120 ft., how long is the longer piece of the pipe?
the length of the mid segment is:
Check the picture below.
so from the picture below we can say that parallel sides or bases of the trapezoid are AB and DC, that means our midsegment is found halfway of BC and halfway of AD, let's get the midpoints for those and then get their length.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad D(\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 2 +0}{2}~~~ ,~~~ \cfrac{ 0 +3}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies (1~~,~~\frac{3}{2}) \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad C(\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 +2}{2}~~~ ,~~~ \cfrac{ 4 +5}{2} \right) \implies \left(\cfrac{ 8 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies (4~~,~~\frac{9}{2})[/tex]
let's get their distance
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{\frac{3}{2}})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{9}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(4-1)^2 + (\frac{9}{2}-\frac{3}{2})^2}\implies d=\sqrt{3^2 + 3^2}\implies {\Large \begin{array}{llll} \stackrel{midsegment}{ d=\sqrt{18}} \end{array}}[/tex]
4. Analyze and Persevere What is a power that
has the same value as 18? Explain.
The powers that have same value as 1^8 are 1^n, n^0 where n=real number.
What are real numbers?
Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also. At the same time, the imaginary numbers are the un-real numbers, which cannot be expressed in the number line and are commonly used to represent a complex number. Some of the examples of real numbers are 23, -12, 6.99, 5/2, π, and so on.
Now,
As we know anything raised to the power of 1 is always one and 0 raised to the power of anything is also one.
Hence, the powers that have same value as 1^8 are 1^n, n^0 where n=real number.
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I Need Help I’m Desperate i really need it cause it due tmr
The slope is 1.33, the y-intercept is -1 and the equation is y = 1.333x -1.
The solution has been obtained using the slope intercept form.
What is slope intercept form?
The line with slope m and y-intercepts b is the graph of the linear equation y = mx + b. The values of m and c are real integers, and the form of the linear equation is known as the slope-intercept form.
A line's steepness is indicated by its slope, m. Sometimes, a line's slope is also referred to as its gradient. The y-coordinate of the place where the line's graph contacts the y-axis is represented by a line's y-intercept.
We are given graph with straight line.
The two points on the graph are (0,-1) and (3,3)
Let's find the slope(m)
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]m=\frac{3+1 }{3 -0 }[/tex]
m = 4/3
m = 1.333
We know that b = y₁ - x₁(y₂ - y₁)/(x₂ - x₁)
So,
⇒b = (-1) - 0(3 + 1)/(3 - 0)
⇒b = -1 + 0
⇒b = -1
The equation comes out to be
⇒y = mx + b
⇒y = 1.333x -1
Hence, the slope is 1.33, the y-intercept is -1 and the equation is
y = 1.333x -1.
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Since, there are multiple questions, so the question answered above is attached below
Can someone please help
Find the average if another set of three consecutive numbers. What do you notice? Explain why the thing you notice must always work or find a counterexample
The average of three consecutive numbers 17, 18, 19 is 18 and the average of three consecutive numbers -100, -99, -98 is -99
Consider the three consecutive numbers 17, 18, 19.
We find the average number would be found by adding all the terms and dividing by 3:
(17 + 18 + 19)/3
= (54)/3
= 18
consider another example: three consecutive numbers are -100, -99, -98.
Their average would be,
[-100 + (-99) + (-98) ] ÷ 3
= -297 ÷ 3
= -99
We can observe that the average of three consecutive numbers is the second term given in that set.
Let m, m + 1, m + 2 be set of any three consecutive numbers.
The average of these three consecutive numbers would be,
A = [m + (m + 1) + (m + 2)] ÷ 3
A = (3m + 3) ÷ 3
A = 3(m + 1) ÷ 3
A = m + 1
Thus, the rule will always work, as we know that average is the central value of a set of numbers.
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The complete question is:
Consecutive numbers follow one right after the other. An example of three consecutive numbers is 17, 18, and 19. Another example is -100, -99, -98. Choose any set of three consecutive numbers. Find their average. What do you notice? Find the average of another set of three consecutive numbers. What do you notice? Explain why the thing you noticed must always work, or find a counterexample.
Marvin is putting together a business outfit. There are 8 pairs of pants and 7 dress shirts to choose from. How many different outfits can Marvin put together?
Answer:
54
Step-by-step explanation:
This is legit just 8 x 7,
27+____=44
30+____=44
[tex]27 + g = 44 \\ 30 + g = 44[/tex]
How do you solve these equations to set them equal?
The value of g in 27+g=44 is 17 and the value of g in 30+g=44 is 14.
How to solve the mathematical equations:Multiplication, division, addition, and subtraction. A mathematical equation's two sides will remain equal if we add the same integer to each of them.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the equal sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.
= 27 + g = 44
= 27 - 44 = g
g = 17
= 30 + g = 44
= 30 - 44 = g
g = 14
Therefore, the value of g in 27+g=44 is 17 and the value of g in 30+g=44 is 14.
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Show full solution (all steps). Consider the following triangle to answer the questions.
a) Identify the hypotenuse side.
b) Determine the missing side using the
Pythagorean Theorem.
b) Determine the perimeter.
c) Determine the area.
Answer:
a) The hypotenuse side is BC.
b) Using the Pythagorean Theorem, we can determine the missing side: AB = √(AC² - BC²) = √(6² - 4²) = √(36 - 16) = √20 = 4.47.
c) The perimeter of the triangle is AC + BC + AB = 6 + 4 + 4.47 = 14.47.
d) The area of the triangle is ½ × AC × AB = ½ × 6 × 4.47 = 13.7.
Step-by-step explanation:
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. So, for the triangle given, we can use this theorem to calculate the length of side AB, which is the missing side. Then, we can calculate the perimeter of the triangle by adding up all three sides and the area of the triangle by using the formula ½ × AC × AB.
A measure computed from the entire population is called: Select one: a. a statistic. b. a qualitative value. c. a mean. d. a parameter.
A measure computed from the entire population is called a parameter.
The correct answer is an option (d)
We know that a parameter is nothing but a numerical value that describes a certain characteristic of the entire population. It is computed using the population values such as population mean, population variance, etc.
Whereas, a statistic is a numerical value that defines certain characteristic of a sample.
It is computed using the sample values such as the sample mean, sample variance, etc.
A qualitative value or a qualitative data are represented by a name, symbol, or a number code. This data is the data about categorical variables.
And the mean is nothing but the average of a set of values.
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The frequency table shows the results of a survey about favorite exhibits. Find the relative frequency that a randomly selected student's favorite exhibit was either butterflies, or trains, as a percent
Butterfly - 12
Dinosaurs - 25
Planets - 17
Trains - 6
The relative frequency as a percentage is 25.7%.
The ratio (fraction or proportion) of the number of times a data value appears in the set of all outcomes to the total number of outcomes is known as the relative frequency. Divide each frequency by the overall sample size, in this example 20 students, to determine the relative frequencies.
The relative frequency of students who picked either butterflies or trains as their favorite exhibit is 18 (12 + 6) out of a total of 70 students.
The relative frequency as a percentage is 18/70 * 100 = 25.7%.
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Determine if the ordered pair (6, 4) is a solution to the inequality y is less than three fourths times x minus 3.
No, because (6, 4) is above the line
Yes, because (6, 4) is below the line
Yes, because (6, 4) is on the line
No, because (6, 4) is on the line
The ordered pair (6, 4) is not a solution to the inequality
The graph is given below
Option A is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
Ordered pair = (6, 4)
This means,
(6, 4) = (x, y)
Now,
y < 3/4(x - 3)
Substitute (6, 4) = (x, y)
4 < 3/4(6 - 3)
4 < 3/4 x 3
4 < 4
This is not true.
From the graph,
(6, 4) is above the line.
Thus,
The graph is given below
(6, 4) is not a solution.
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. Zachariah has 9 American stamps out of 15 stamps. Khai has 13 American stamps out of 20 stamps. Which statement is correct?
Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.
What is a fraction?Due to the fact that 8 over 14 is more than 11 over 21, Zachariah has a higher ratio of American stamps than Khai.
An element of a number or any number of equal pieces is represented by a fraction.
Given that Khai and Zachariah are stamp collectors.
Zachariah also contains eight of the fourteen American stamps that are available.
Khai contains 11 American stamps out of a total of 21.
Khai equals 8/14 Zachariah equals 11/21
Zachariah has a higher proportion of American stamps than Khai does since 8 over 14 is more than 11 over 21.
After all, we would convert 11/21 and 8/14 into fractions.
Tell them that we would turn their fractional values into decimals and then into percentiles.
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Select the correct answer. Which is the correct solution to the expression 3 + 5^2? You can use a calculator to find the answer. A. 10 B. 13 C. 28 D. 64
Answer:28
Step-by-step explanation:
5x5=25
25+3=28
Answer:
C. 28
Step-by-step explanation:
3 + 5^2
3 + 25 = 28
if the diameter of the output cylinder of a imple hydrolic ytem were greater how would thi affect the output force?
If the diameter of the output cylinder of a simple hydraulic system were greater, this would increase the output force.
In a simple hydraulic system, a small force applied to a small piston (input cylinder) is amplified and transferred to a larger piston (output cylinder) through a fluid. The output force is equal to the input force multiplied by the ratio of the areas of the two pistons. The area of a cylinder is equal to the radius squared times pi. So, if the diameter of the output cylinder is increased, the area of the output cylinder will increase and the output force will be greater.
It's important to note that increasing the diameter of the output cylinder will also increase the volume of the output cylinder, so more fluid will be required to fill the cylinder and the system may need a larger fluid pump or reservoir.
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Select all the equations that are true when x = 6.
6x = 12
17 – x = 11
x ÷ 2 = 3
19 ÷ 3 = x
5 + x = 11
Does someone mind helping me with this question? Thank you!
Answer:
80 pennies
160 nickels
Step-by-step explanation:
.01p + .05n = 8.80 multiply through by 100
p + 5n = 880
2p = n
substitute 2p for n is the bold equation
p + 5(2p) = 880
p + 10p = 880
11p = 880 Divide both sides by 11
p = 80
2p = n
2(80) = n
160 = n
Check:
(.01)(80) + (.05)(160) = 8.80
0.80 + 8 = 8.80
8.80 = 8.80 Checks
Find the product (14)(4)
Answer:
56
Step-by-step explanation:
10 times 4 is 40
4 times 4 is 16
40+16=56
What are the missing angle measures in triangle abc? 1.4° and 88.6° 18.6° and 71.4° 35.5° and 54.5° 44.4° and 45.6°
The missing angle measures in triangle ABC are 35.5° and 54.5°.
We know that,
In the right triangle ABC
∠A +∠B =90° ( by complementary angles)
We find the measure of angle B.
we know that
[tex]tanB = \frac{opposite side angle B}{adjacent side angle B}[/tex]
According to the question,
Opposite side angle B= 7 in
Adjacent side angle B = 5in
So, [tex]tanB = \frac{7}{5}[/tex]
[tex]B = arc tan(\frac{7}{5})[/tex]
B = 54.5°
Then, we find the measure of angle A
A + B = 90°
A = 90°-B
A = 90° - 54.5° ( using subtraction)
A = 35.5°
So, The angles measured in triangle ABC are 35.5° and 54.5°.
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Rectangle ABCD with vertices A(-3,0), B(1, 2),
C(2, 0), and D(-2,-2): k = 3