Answers
Answer:
10.58
Step-by-step explanation:
We are here given a right angled triangle in which two of the sides are 16 and 12 and we are interested in finding the third side x . We will use Pythagoras theorem here according to which the sum of squares of base and perpendicular is equal to the square of hypotenuse. so that,
[tex]\longrightarrow\sf h^2 = p^2+b^2\\ [/tex]
[tex]\longrightarrow\sf x^2 + 12^2 = 16^2\\ [/tex]
[tex]\longrightarrow\sf x^2 = 256 - 144\\ [/tex]
[tex]\longrightarrow\sf x =\sqrt{ 112}=\boxed{10.58} [/tex]
and we are done!
-Rishabh
Answer:
[tex]x=4\sqrt{7}=10.6\; \sf (nearest\;tenth)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
a = xb = 12c = 16Substitute the given values into Pythagoras Theorem formula and solve for x:
[tex]\implies x^2+12^2=16^2[/tex]
[tex]\implies x^2+144=256[/tex]
[tex]\implies x^2=112[/tex]
[tex]\implies x=\sqrt{112}[/tex]
[tex]\implies x=\sqrt{16 \cdot 7}[/tex]
[tex]\implies x=\sqrt{16} \sqrt{7}[/tex]
[tex]\implies x=4\sqrt{7}[/tex]
[tex]\implies x=10.6\; \sf (nearest\;tenth)[/tex]
Related Questions
Find the polynomial function of the graph.
Answers
A polynomial, which is a mathematical expression. Numerous monomials, which are mathematical expressions, are gathered together in it.
What is meant by polynomial function?When a variable in an equation like the quadratic equation, cubic equation, etc. has only non-negative integer powers or only positive integer exponents, the function is said to be polynomial.
When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).
An expression in mathematics known as a polynomial. It is a collection of several monomials, which are mathematical expressions. That is, a quantity, a variable, or the result of a quantity and multiple variables.
Polynomial equations are equations that contain variables, exponents, and coefficients.
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1. How many faces, vertices, and edges do the pyramids have? Name at least
three patterns you notice.
Answers
Pyramid have faces=n triangles & 1 n-sided polygon
Edges=2n
vertices=n + 1
What are edges?An edge is a line segment that serves as a transition between two faces. It is also sometimes referred to as the line segment that connects two vertices.
What are vertices?The location where two or more edges intersect is the formal definition of the vertex in mathematics. The corner points are called vertices.
What are faces?A solid's face refers to each unique flat surface. Solids have multiple faces.
The number of faces in a pyramid is equal to one more than the base's polygon's number of sides.
faces = n triangles & 1 n-sided polygon
One more than the number of sides at the base of the polygon makes up the number of vertices in a pyramid.
hence, vertices = n + 1
Two times the number of sides at the base of a polygon equals the number of edges on a pyramid.
Therefore, edges = 2n
A pyramid has n triangles & 1 n-sided polygon Faces
A pyramid has 2n Edges.
A pyramid has n + 1 Vertices.
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Select the correct answer.
Sides of three square rooms measure 13 feet each, and sides of two square rooms measure 15 feet each. Which expression shows the total area of
these five rooms?
Answers
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
We know that a square has 4 sides of the same length, meaning that the length and the width are the same length. You can solve for the area of the first three rooms with a length of 13 feet using an equation like this:
(13 × 13) × 3
Now, for the other two rooms with the length of 15 feet:
(15 × 15) × 2
Simply add them together.
([13 × 13] × 3) + ([15 × 15] × 2)
Simplified, the expression would look like this:
(169 × 3) + (225 × 2) = 957
Therefore, the expression that shows the total area of these five rooms would look like this: ([13 × 13] × 3) + ([15 × 15] × 2), or it being simplified would look like this: (169 × 3) + (225 × 2) = 957
Whitney drinks 1,500 mL of water each day troy drinks 1.8 L of water each day
Who drinks more water?
By how much water?
Answers
The person who drinks more water between Whitney and Troy is Troy.
Troy drinks 0.3liters of water more than Whitney.How to convert millimeters to liters?Quantity of water Whitney drinks daily = 1500 ml
1000 milliliters = 1 liter
1500 milliliters = 1.5 litres
Quantity of water Troy drinks daily = 1.8L
The person who drinks more water= Quantity of water Troy drinks daily - Quantity of water Whitney drinks daily
= 1.8L - 1.5L
= 0.3L
In conclusion, Troy drinks 0.3 liters more water than Whitney.
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Evaluate the square root of 9 + 4√5 in the form c + √d
Answers
Step-by-step explanation:
Here we are interested in finding the square root of [tex] 9 +4\sqrt5[/tex] . So , we have
[tex]\longrightarrow \sqrt{ 9+4\sqrt5}[/tex]
We can write it as ,
[tex]\longrightarrow \sqrt{ 5 + 4 + 4\sqrt5} [/tex]
This can be again rewritten as ,
[tex]\longrightarrow\sqrt{ (\sqrt5)^2+2^2+ 2(2)(\sqrt5) } [/tex]
Now this in the form of [tex] a^2+b^2+2ab [/tex] form which is the square of [tex] (a+b)[/tex] . So that,
[tex]\longrightarrow \sqrt{ (2+\sqrt5)^2}[/tex]
Simplify the root ,
[tex]\longrightarrow 2 + \sqrt5[/tex]
Hence we got our answer in the form of [tex] c +\sqrt{d}[/tex]
And we are done!
—Rishabh
What is the expression 1/5
Answers
Answer:
"1/5" is the expression of "one divided by 5", because fractions can represent division as well as a ratio.
Answer:
one divided by 5 I think (Sorry if I'm wrong!)
How many meters are in 28% of 15 km?
Answers
Answer:
15*280 = 4,200 m
Step-by-step explanation:
Since it's metric, you don't need to do much except multiply the 15 km by 280 m which is 28% of 1000 m.
f f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
12
14
36
38
Answers
Answer:
(b) 14
Step-by-step explanation:
You want the difference of functions f(x) = 3x² +1 and g(x) = 1 -x when x=2.
DifferenceThe notation (f -g)(x) means f(x) -g(x). Then (f -g)(2) is ...
f(2) -g(2) = (3·2² +1) -(1 -2) = 13 -(-1) = 14
The value of (f -g)(2) is 14.
I REALLY NEED HELP! I DOMT UNDERSTAND
Answers
Answer:
P = 0.886 (88.6%)
Step-by-step explanation:
Of the 44 students there are 5 who do not apply to be chosen
[tex]P=\frac{44-5}{44} =\frac{39}{44} =0.886[/tex]
P = (0.886)(100) = 88.6%
Hope this helps.
Exact quotient: 216.6/38
Answers
Answer:
5.7
Step-by-step explanation:
216.6/38=5.7
Express Bearing & word problems
Answers
The side lengths of trigonometry a, b, and c are determined by the traveled distances, and the internal angles of the triangle are A, B, and C.
what is trigonometry ?Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.
Here,
Given :
The sine rule or cosine rule, c2=a2+b2-2ab. cos(C), may be used to solve the issue if bearings between three sites result in the formation of a non-right-angled triangle between them.
The side lengths a, b, and c are determined by the traveled distances, and the internal angles of the triangle are A, B, and C.
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The complete question is " For what reason the cosine rule is used in trigonometry ?"
please solve il give brainlest
Answers
Answer:
x ≥ 8
Step-by-step explanation:
It will take 8 hours. The underline underneath represents “greater than or equal to”
Answer:
Inqueality: 2.5cx greater than or equal to -20c
Solved: x greater than or equal to 8.
Diana says that the quadrilateral on the right is a rhombus.
Melissa says that the quadrilateral on the left is a rhombus. Who is correct?
An image shows two quadrilaterals. They are facing different directions, but each of them has two pairs of opposite sides that are parallel and equal in length.
A.
Diana is correct. Only the quadrilateral on the right has two pairs of parallel sides and all sides the same length.
B.
Melissa is correct. Only the quadrilateral on the left has two pairs of parallel sides and all sides the same length.
C.
Both are correct. Both quadrilaterals have two pairs of parallel sides and all sides the same length.
D.
Neither is correct. Neither figure has all sides the same length.
Answers
Both are correct. Both quadrilaterals have two pairs of parallel sides and all sides are the same length. Option C is correct.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
Here,
The question seems to be incomplete, so we assume that both figures are congruent figures,
As mentioned in the question, Diana says that the quadrilateral on the right is a rhombus and Melissa says that the quadrilateral on the left is a rhombus. Besides their statements both figures will be rhombus then as both figures are similar and have two pairs of opposite sides that are parallel and equal in length.
Thus, option C is correct.
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What is the slope-intercept form for y-1=4/5(x+5)?
Answers
Answer:
y = 4/5x + 1
Step-by-step explanation:
In triangle IJK , O is the intersection of the three medians . If IN = 12 find IK. please help
Answers
Answer:
IK = 24
Step-by-step explanation:
Since is says that O is the point of intersection of the three medians (also known as centroid) the segment JN which passes through a vertex of the triangle, would have to be a median to segment IK.
Medians divide a segment into two congruent parts, so IN = NK = 12 as we are given IN = 12.
IK is the sum of the measure of IN and NK, so in other words:
IK = IN + NK = 12 + 12 = 24
HELP ME OUTTTTT...........
Answers
The required measure of the segment ST is 2(a + b).
What is the midpoint?Midpoint is that point on the line whose distance from both ends of the line is equal.
Here,
Draw segment ST, put point Y where a line bisects the segment ST,
SY = a + b
Since y is the midpoint of the line ST, so,
ST = SY + YT [SY = YT]
ST = a + b + a + b
ST = 2[a + b]
Thus, the required measure of the segment ST is 2(a + b).
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Deena bought some shirts at the store for $9 each and received a $25 discount. Her total bill was $74. Find the number of shirts she bought
Answers
Answer:
11
Step-by-step explanation:
If we know that she paid $74, and the discount is $25, we need to figure out the total price of the shirts before the discount.
74 + 25 = 99
Now that we know she spent $99 on shirts, we can divide that by 9 to get the number of shirts purchased.
99 ÷ 9 = 11
Therefore, she bought 11 shirts.
A student doing a research paper on acquired immune deficiency syn-
drome (AIDS) learns that 1/6 of the people with AIDS are in their 20s.
Because the latency period between the time of the HIV infection and
the onset of AIDS is about 10 years, most of these people were infected
as teenagers. If there are 133,758 cases of AIDS, how many were prob-
ably infected as teenagers?
Answers
If there are 133,758 cases of AIDS, 22,293 were probably infected as teenagers.
What do you mean by research paper?A research paper is a written work that presents the results of original research or provides an in-depth analysis of a particular topic or issue. Research papers are typically written by scholars, academics, or students, and are commonly submitted as part of a course assignment, a doctoral or master's degree requirement, or for publication in a scholarly journal.
A research paper typically includes several key elements: an introduction that provides background information on the topic and sets the stage for the rest of the paper; a literature review that summarizes existing research on the topic; the methodology section that describes the methods used to conduct the research; the results section that presents the findings of the research; and a discussion or conclusion section that interprets the results and places them in the context of the broader field of study.
The writing style of a research paper is usually formal and objective, with a focus on clearly and accurately communicating the results of the research. Research papers often include citations and references to other works, which demonstrate the writer's familiarity with the literature and support the validity of their findings.
If 1/6 of the people with AIDS are in their 20s, then 1/6 of 133,758 cases is 133,758 / 6 = 22,293 cases.
These 22,293 people with AIDS in their 20s were probably infected as teenagers, so the answer is 22, 293 cases were probably infected as teenagers.
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Can someone please give me the answer I really don’t get this
Answers
A transition known as a dilation enlarges or reduces an object by a certain amount. Using a scale factor of 2, we can dilate a triangle.
What exactly does it mean to "dilate" a triangle?I One way to make related figures is through dilation. By multiplying distances by the scale factor, each point is drawn farther away from the central point D. In the event when the scale factor is greater than 1, outward. The triangle's shape can be modified by moving the points A, B, and C.Assume that in the coordinate plane, the origin (0, 0) serves as the center of dilation. The original triangle's coordinates are multiplied by the scale factor (if it is 1/2) at each point if the scale factor. Multiply by half after a scale factor of 1/2 dilation. By multiplying the coordinates of each vertex by the scale factor, a triangle can be enlarged by a factor of 2/3. The new coordinates will be (2/3x, 2/3y), for instance, if the vertex's coordinates are (x, y).The complete question is,
How can a triangle be widened by two and three?
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1. What percentage of seventh-grade students prefer hamburgers or hotdogs for lunch ?
2. What percentage of eighth graders prefer pizza or hot dogs for lunch?
3. What percentage of the students in both grades prefer hot dogs for lunch?
Answers
Identify the key features of the graph of the function g(x)= log 2 (x-1)+2
Answers
The key features of the graph of the function would be
1) Domain - (1, infinity).
2) The range of the function is (2, infinity).
3) The graph of the function is a monotonically increasing function.
4) The graph of the function is asymptotic to the x-axis as it approaches x = 1.
5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.
6) The graph is a shifted version of the function log2(x) by 2 units upward.
What is the graph of the function?
The graph of a function is a visual representation of the relationship between the inputs and outputs of the function. It is a diagram that shows the set of all possible points (x,y) that satisfy the equation of the function y = f(x) or in the case of a multivariable function y = f(x,z).
The graph of the function g(x) = log2(x-1) + 2 has several key features. Some of these features include:
1) The domain of the function is (1, infinity) since the logarithm is defined for x>0 and x-1 >0.
2) The range of the function is (2, infinity) since the minimum value of log2(x-1) + 2 is 2.
3) The graph of the function is a monotonically increasing function, meaning that as the input x gets larger, the output g(x) also increases.
4) The graph of the function is asymptotic to the x-axis as it approaches x = 1. This means that as x gets closer to 1, the graph of the function gets closer to the x-axis but never touches it.
5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.
6) The graph is a shifted version of the function log2(x) by 2 units upward.
Hence, the key features of the graph of the function would be
1) Domain - (1, infinity).
2) The range of the function is (2, infinity).
3) The graph of the function is a monotonically increasing function.
4) The graph of the function is asymptotic to the x-axis as it approaches x = 1.
5) The graph is a straight line, that is passing through the point (1,2) and has a slope of 1.
6) The graph is a shifted version of the function log2(x) by 2 units upward.
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If f(x) = 8 – 10x and g(x) = 5x + 4, what is the value of (fg)(–2)?
Answers
Answer:
(fg)(-2) = 18
Step-by-step explanation:
f(x) = 8 – 10x
g(x) = 5x + 4
To find (fg)(-2) or f(g(-2)), first let's find g(-2) by subbing -2 in for x in g(x):
g(x) = 5x +4
g(-2) = 5(-1) +4 = -5+4 = -1
Knowing g(-2)=-1, we can now find f(g(-2)) by subbing -1 in for x in f(x):
f(x) = 8 – 10x
f(-1) = 8 - 10(-1) = 8+10 =18
13. Find the value of x.
127°
112
108
120°
X=
Answers
The value of x is 73°
Sum of interior angles in Polygon:A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges.
The geometric shape known as a pentagon has five sides and five angles. Penta here means five, and gon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's internal angles add up to 540°.
Here we have a five-sided Polygon
And the angles are 127°, 112°, 108°, 120°, and x°
As we know the sum of angles = 540°
=> 127° + 112° + 108° + 120° + x° = 540°
=> 467° + x° = 540°
=> x° = 540° - 467°
=> x° = 73°
Therefore,
The value of x is 73°
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Complete question:
Find the value of 'x' in the given Polygon.
helpp pleaseeeeeeeeeeeeee
Answers
The table that represents the situation when a mattress store is having a sale and are 30% off will be D. Table D.
How to calculate the sales price?From the information given, the table that represents the situation when a mattress store is having a sale and are 30% off.
In this case, Nate wants to know the sale price of the matress that is regularly $1000.
The price after the discount will be:
= $1000 - (30% × $1000).
= $1000 - $300
= $700
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after 25% increase in price the new price is 300.what was the increased price
Answers
Answer:
Step-by-step explanation:
187.5
Select all the algebraic expressions equivalent to m5/n5
A: (mn–1)5
b: (mn)5
C :[(mn2)]–3
d: (mn)–5
e: m5n–5
Answers
6/10 drivers look at their phone while driving. 3/10 drivers are having a conversation and look at their phone while driving. What is the probability that a driver is having a conversation while driving?
Answers
0.5 is the probability that a driver is having a conversation while driving.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, 6/10 drivers look at their phones while driving. 3/10 drivers are having a conversation and looking at their phones while driving.
Let P(A) be the probability of drivers looking at their phones while driving.
and P(B) be the probability of drivers looking at their phones while driving.
Since:
P(A) = 0.6
P(A ∩ B) = 0.3
P(B) = (P(A ∩ B))/ P(A)
P(B) = 0.3/0.6
P(B) = 1/2
therefore, the probability that a driver is having a conversation while driving is 0.5.
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Class: Directions: Create a function table to model the relationship HW 4-1: Creating Function (x,y) X 5 Y = -4x A Y 1
Answers
Answer:
abeni suq ae
Step-by-step explanation:
help
Graph g(x)=4cosx .
Use 3.14 for π .
Answers
5 because the value of pi is 3.14 and therfore the graph must be a rational and a multiple of 3
Graph the 3 lines k, l, and m based on the following
information: Line k is parallel to line / and perpendicular to
line m. Line k passes through the origin (0, 0) and has a slope
of ½. Line m intersects line k at the point (4, 2). Line / has a y-
intercept of 4. Graph and label the 3 lines. Circle the letter of
the statement below which is false. Explain why it is false.
Answers
Step-by-step explanation:
If l and k are lines in the xy-plane, is the product of the slopes of l and k equal to -1 ?
(1) Line l passes through the origin and the point (1,2).
(2) Line k has x-intercept 4 and y-intercept 2