he length of the shortest side is 32
Similar triangles and scale factorsGiven the length if the sides of the triangle to be 8, 15 and 17. If the longest side of a similar triangle is 51, then the scale factor will be expressed as:
Scale factor = 51/17
Scale factor = 4
For the shortest side;
Length = 8 * scale factor
Length = 8 * 4
Length = 32
Hence the length of the shortest side is 32
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Write a number that is greater than 1 in scientific notation. explain how you know it is greater than 1
The positive power of 10 shows that the number is greater than 1.
What is scientific notation?A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less.
Given:
number that is greater than 1 in scientific notation.
So, to get know the number is greater than 1 we can tell it by seeing the power of 10.
If the powers of 10 is positive then the number is also greater than 10.
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Six times the sum of a number and 9 equals 8
Write in equation
Find the equation of the line l where l is perpendicular to y=2/5x and passes through the points (5,2)
The stores below each have the same snowboard for an original price of $189.59. At which store can you get the snowboard for the lowest price?
Answer:
D. You can get the lowest price at Store C.
Step-by-step explanation:
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I need help! THIS IS NOT MULTIPLE CHOICE!!!! The time needed to roast a chicken depends on its weight. Allow at least 20 min/lb for a chicken weighing as much as 6 lb. Allow at least 15 min/lb for a chicken weighing more than 6 lb. a. Write two inequalities to represent the time needed to roast a chicken. b. Graph the inequalities.
The sum of two integers is 9 their difference is 5 what are the two integers
The values of the two integers are 7 and 2 respectively.
Let the two integers be a and b respectively.In this exercise, you're required to determine two integers from the given word problem.
Thus, we would write a mathematical (algebraic expression) for the sentence.
Translating the word problem into an algebraic expression, we have;
The sum of two integers is 9;
[tex]a + b =9[/tex] ....equation 1.
The difference between the two integers is 5;
[tex]a - b = 5[/tex] equation 2.
Solving the systems of linear equations by using the elimination method, we have:
[tex]2a = 14[/tex]
Dividing both sides by 2, we have:
[tex]a = \frac{14}{2}[/tex]
a = 7
To find the value of y:
[tex]a + b =9\\\\7 +b=9\\\\b =9-7[/tex]
b = 2
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A building that is 15 meters tall casts a shadow that is 6 meters long. at the same time, a tree casts a shadow that is 9 meters long. how tall is the tree
Final answer:
To determine the height of the tree, we use proportions based on the shadow lengths. Since the building is 15 meters tall with a 6-meter shadow and the tree's shadow is 9 meters, the height of the tree is found to be 22.5 meters.
Explanation:
You're asking how to find the height of a tree based on its shadow's length using similar triangles. The building is 15 meters tall and casts a 6-meter-long shadow. We can set up a proportion since the tree and the building have the same sun angle, thus their heights and shadows are in proportion. We will compare the building's height to its shadow, and then set this ratio equal to the tree's height to its shadow.
Using the formula for proportions:
Building height / Building shadow = Tree height / Tree shadow
Which translates to:
15 meters / 6 meters = Tree height / 9 meters
Now we solve for the Tree height:
Tree height = (15 meters / 6 meters) * 9 meters = 22.5 meters
The height of the tree is 22.5 meters.
create a real world problem that represents 5/6 + 1/8.
Answer:
me and my friend are buying some pie im pay for it so i get 5/6 and he gets 1/8 how much pie did we buy
1/8 =6/48
5/6= 40/48
so the answer is 46/48 or 23/24
Step-by-step explanation:
assume that y varies inversely with x. if y=27 when x=12, find x when y=-12.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
A coat hanger is in the shape of isosceles triangle ABC shown in the figure. Sides AB and BC are congruent.
if m<BAC=22, then m<ABC= ?
Answer: m∠ABC=136°
Step-by-step explanation:
In the given figure we have a coat hanger is in the shape of isosceles triangle ABC.
Sides AB and BC are congruent.
The isosceles theorem says that the angles opposite to the equal sides of a triangle are equal.
Therefore, in ΔABC, we have
m∠BAC=m∠BCA
If m∠BAC=22°, then m∠BCA= 22°
By angle sum property , we have
m∠BAC+m∠BCA+m∠ABC=180°
⇒22°+22°+m∠ABC=180°
⇒m∠ABC+44°=180°
⇒m∠ABC=180°-44°=136°
⇒m∠ABC=136°
Therefore, If m∠BAC=22°, then m∠ABC=136°
A rectangle is 3 units wide and 4 units long. How long is its diagonal
Choose the product. 4p^3 3(p 2^ + 8p - 3)
4p^5 + 12p^4 + 7p^3
4p^6 + 44p^3
4p^3 - 12p^2 +32p^4
4p^5 + 32p^4 -12p^3
Answer: The correct option is
(D) [tex]4p^5+32p^4-12p^3.[/tex]
Step-by-step explanation: We are given to choose the correct expression for the following product :
[tex]P=4p^3(p^2+8p-3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the above product, we need to multiply 4p³ with every term within the bracket.
The required product (i) is
[tex]P\\\\=4p^3(p^2+8p-3)\\\\=4p^{3+2}+32p^{3+1}-12p^3\\\\=4p^5+32p^4-12p^3.[/tex]
Thus, the required product is [tex]4p^5+32p^4-12p^3.[/tex]
Option (D) is CORRECT.
Suppose g(x) = f(x + 2) – 3. Which statement best compares the graph of g(x) with the graph of f(x)?
Answer:
B. the graph of g(x) is shifted 2 units right and 3 units up
Step-by-step explanation:
just got it right
We conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. Option D is the correct answer.
The given function is g(x) = f(x + 2) – 3.
What is a function?A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.
To shift a function right:
Subtract inside the function's argument. For example, f(x)-b is basically f(x) shifted b units to the right.
Subtracting inside the function's argument moves you to the right.
So, g(x) = f(x – 2) means f(x) is shifted two units to the right.
To move a function down:
Subtract outside the function. For example, f(x)-b is basically f(x) moved down 3 units.
So, g(x) = f(x – 2) + 3 means, f(x) is moved 3 units down.
Therefore, we conclude that g(x) = f(x – 2) + 3 means the graph of g(x) is shifted 2 units right and 3 units down. So, option D is the correct answer.
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A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh 68.7 cm2 161.7 cm2 381.3 cm2 450.0 cm2
Answer:
Option B is the correct answer.
Step-by-step explanation:
We have one side = 27.6 cm
Hypotenuse = 30 cm
Length of remaining side [tex]=\sqrt{30^2-27.6^2}=11.76cm[/tex]
Area of right angled triangle [tex]=\frac{1}{2}\times \texttt{Product of lengths of 2 sides other than hypotenuse}[/tex]
Area [tex]=\frac{1}{2}\times 27.6\times 11.76=161.7cm^2[/tex]
Option B is the correct answer.
To rent a certain meeting room, a college charges a reservation fee of $37 and an additional fee of $6.70 per hour. the chemistry club wants to spend less than $90.60 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use t for the number of hours the meeting room is rented, and solve your inequality for t .
Julio's father is 4 times as old as Julio. The sum of their ages is no less than 55.
What is the youngest age Julio can be?
Enter your answer in the box.
years
Jack's overtime wage is $3 per hour more than his regular hourly wage. He worked for 5 hours at his regular wage and 4 hours at the overtime wage. He earned $66. Find his regular
What is the value of the expression? ( 5/2 ) ^2 +3/4 ^3
5/2 ^2 = 6 1/4 = 6.25
3/4^3 = 27/64 = 0.4201875
6 1/4 + 27/64 = 6 43/64 (mixed number)
6.25 +0.421875 = 6.671875 (decimal)
not sure what format you need, since the question was in fraction form, I think you need to answer using a mixed number though.
A cyclist rides her bike at a speed of 12 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 5 minutes? Do not round your answers.
A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
What is the initial value of the exponential function shown on the graph
Answer:
The initial value of the exponential function is 2
Step-by-step explanation:
A function is a mathematical relation in which we input the values of a domain that generate the output values of a range.
Initial value of the function is the output value of the function when the input is x =0.
As shown in the graph:
The exponential function cut at the point (0, 2)
where;
y=2 when x=0.
Therefore, the initial value for the exponential as shown in the figure is, 2.
The sum of two numbers is 28. one number is 14 more. find the numbers
Which table represents a linear function?
The equation y= 3x relates the number of points resulting from three-point baskets.
What is the constant of proportionality in this equation?
A.1
B.3
C.x
D.y
Answer:
3
Step-by-step explanation:
How can you find a unit rate when given a rate?
Power Glen Elementary School has a plant sale to raise money for a local charity. Each plant costs 3$. It is sold for $10 a) What would be the output if the sold these many plants 10,20,30,40,50 b)How many plants have to be sold to collect $500 c) How many plants have to be sold to be able to give the charity $500?
The polynomial function y = x3 -3x2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
A) The function has one imaginary zero.
B) The function has one real zero and two imaginary zeros.
C) The function has one real zero and one imaginary zero.
D) The function has one imaginary zero and two real zeros.
The correct answer is
D) The function has one imaginary zero and two real zeros.
x = 3, 4i, -4i
Write a conditional statement. Write the converse, inverse and contrapositve for your statement and determine the truth value of each. If a statement’s truth value is false, give a counterexample.
Find the 10th term of the sequence defined by the given rule:f(n)=sqrt n+2
We are given the equation:
f(n)=sqrt n+2
To get the 10th term of the series, we simply have to substitute the value of 10 into the equation, n = 10. So that:
f (10) = sqrt (10 + 2)
f (10) = sqrt (12)
f (10) = 3.46
How do I write the interval(s) for which f(x) is greater than or equal to 0 (interval notation)
To write intervals where f(x) is greater than or equal to 0, solve the equation f(x) >= 0 for x. The solutions are then expressed in interval notation. For instance, x >= 3 is written as [3, infinity).
To write the interval for which f(x) is greater than or equal to 0 in interval notation, you first need to establish where the function is above or touching the x-axis. With algebraic functions, you simply solve the equation f(x) >= 0 for x to find where the function is non-negative. You then write these solutions in interval notation. For example, if your solution was x >= 3, you would write this in interval notation as [3, infinity). Also, keep in mind that round brackets ( ) are used when the number is not included in the interval while square brackets [ ] are used when the number is included.
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