Find the missing side of the triangle.A. 19−−√ miB. 22–√ miC. 11−−√ miD. 1 mi
Answers
From the right angled triangle given,
To find the missing side, x, of the triangle, Pythagorean theorem is applied
The Pythagorean theorem formula is
[tex]\begin{gathered} (\text{Hyp)}^2=(\text{Opp)}^2+(\text{Adj)}^2 \\ \text{Hyp is the hypotenuse} \\ \text{Opp is the opposite } \\ \text{Adj is the adjacent} \end{gathered}[/tex]The dimensions of the triangle are
[tex]\begin{gathered} \text{Hyp}=\sqrt[]{10}mi \\ \text{Opp}=xmi \\ \text{Adj}=3mi \end{gathered}[/tex]Substituting the values into the Pythagorean theorem formula above,
[tex]\begin{gathered} (\sqrt[]{10})^2=x^2+3^2 \\ 10=x^2+9^{} \\ \text{Collect like terms} \\ x^2=10-9 \\ x^2=1 \\ \text{Square root of both sides} \\ \sqrt[]{x^2}=\sqrt[]{1} \\ x=1 \end{gathered}[/tex]The missing side, x is 1mi
Answer is D
Related Questions
Find the measures of the numbered angles in the figure, shown to the right. Name the theorem that justifies each answer.
Question content area bottom
Part 1
Complete the table below.
Measure
Justification
Answers
The measurement of all four angles is 105°
What is an angle?
When two solid lines or rays intersect at a single endpoint, an angle is created. The vertex about an angle is the location where two points come together.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides are linked at a single end. The arms of just an angle are OA and OB.180° [Linear pair with angles] = m1 + 75°
The opposite angles of either a rectangle are equal: m1 = 180° - 75° = 105° m2 = m1.
[Vertically opposing angles] m2 = m1 = 105° m2 = m3 = 105°
m∠3 = m∠4 = 105° Coordinating angles
As a result, the measurement of all four angles is 105°.
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What is the area of a triangle whose vertices are J(-2, 1), K(0,3), and L(4, -4)?
Enter your answer in the box.
Answers
According to the given coordinates, the area of the triangle is 11 units².
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, the area of the triangle:
The formula for the area of the triangle: 1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
Now, insert the values in the formula as follows
1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|1/2|-2(3+4) + 0(-4-1) + 4(1-3)|1/2|-2(7) + 0(-5) + 4(-2)|1/2|-14 + 0 + -8|1/2|-22|-11Since the area cannot be negative, the area of the triangle will be 11 units².
Therefore, according to the given coordinates, the area of the triangle is 11 units².
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Answer: 11 units squared
Step-by-step explanation: You can use an interactive coordinate plane like I did to plot the points and then find the area.
help pleeeaseee i don’t understand what to do!
Answers
Answer:
The difference of a number and seven ⇒ n - 7
The product of seven and a number ⇒ 7n
The quotient of a number and seven ⇒ n/7
The sum of seven and a number ⇒ n + 7
Step-by-step explanation:
Difference ⇒ subtraction.
Product ⇒ multiplication.
Quotient ⇒ division.
Sum ⇒ addition.
_1) Given: L = √2
M-3√3
N =√16
P = √9
Which expression results in a rational number?
(3) N + P
(4) P+L
(1) L + M
(2) M + N
Answers
The expression that results in rational number is P+N
What is rational numbers?Any integer that can be expressed as p/q, where q ≠ 0, is referred to as rational.
The form of a rational number, which is a type of real number in mathematics, is p/q when q is not equal to 0. Examples of rational numbers include 1/2, 1/5, 3/4, and other such values. For example, any integer is a rational number. The number one can be written as 10,000/10000, -2 over -2, or 1/1.
Here, L = √2
M=3√3
N =√16
P = √9
we know [tex]\sqrt{16} =4 , \sqrt{9} =3[/tex]
only P and N are rational numbers.
P+N = 4+3 = 7/1
which is a rational number.
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Evaluate the expression shown below and write your answer as a mixed number in simplest form.
-5 9/10 divided by 9/10
Answers
The most appropriate choice for fraction will be given by -
The quotient obtained on performing the division is [tex]-6\frac{5}{9}[/tex]
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
We can do addition, subtraction, multiplication and division on fractions.
Here,
The given division is
[tex]-5\frac{9}{10} \div \frac{9}{10}[/tex]
Now,
[tex]-5\frac{9}{10} \div \frac{9}{10}\\\\-\frac{59}{10} \div \frac{9}{10}\\\\-\frac{59}{10} \times \frac{10}{9}\\\\-\frac{59}{9}\\\\-6\frac{5}{9}[/tex]
The quotient obtained on performing the division is [tex]-6\frac{5}{9}[/tex]
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Find the distance between the parallel lines. If necessary, round to the nearest whole number y=2x+7 y=2x-2
Answers
The distance between the two parallel lines are found as 9 units.
What is defined as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and share the same slope. Many pairs of angles are formed when two parallel lines are intersected by some other line known as a transversal.For the given question;
The two equation of the lines are given as;
y = 2x + 7 ; y = 2x - 2
Complaining both equation with standard form of line in point slope form.
y - y1 = m(x - x1)
The equations are in slope intercept form, yielding two points (0,7) and (0,7). (0, -2).
Now, find the distance using the distance formula.
d = √(x₂ - x₁)² + (y₂ - y₁)²
Put the values in the equation.
d = √(0 - 0)² + (-2 - 7)²
d = √(-9)²
d = 9
Thus, the distance between the two parallel lines are found as 9 units.
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Claire is building a rectangular frame to hold her stretched canvas painting. she has 14
feet of wood to build the frame. what is the maximum possible area for the painting?
Answers
The maximum possible area for the rectangular painting is 12.25 square feet.
A crossed rectangle is a quadrilateral that is formed by the two diagonals, two opposed sides, and two opposite corners of a rectangle (therefore only two sides are parallel).
It is a special illustration of an antiparallelogram in which the angles are not all right angles and equal, despite the fact that opposite angles are equal. There are so-called rectangles with opposite sides of equal length and equal angles that aren't right angles in other geometries, such as spherical, elliptic, and hyperbolic ones.Let the length of the painting be x and the width be y.
perimeter of rectangle = 2( x + y )
or,2( x + y ) = 14
or, x+y = 7
or, y = 7-x
Area of the painting in the form of a function
A(x) = x (7 - x)
A(x) = 7x - x²
Now we find the first differentiation of A(x).
A'(x) = 7 -2x
now , A'(x) = 0
or, x = 7 / 2 = 3.5
Area of the frame = 3.5² = 12.25 square feet.
hence the maximum possible area for the frame is 12.25 square feet.
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which cards are equivalent to 2/3 - 1/4 choose all the correct answers
6/12-4/12
8/12-3/12
2/7-1/7
1/7
2/7
5/12
Answers
5th one
are both correct
The triangular prism has a volume 120 yards^3
Please tell me the height of the prism.
Answers
In the picture there is a prism. The volume of the prism is 120 yards³. The prism stands 8 yards height.
Given that,
In the picture there is a prism.
The volume of the prism is 120 yards³.
The base is 6 yards and the length is 5 yards.
We have to find the height of the prism.
Take the height of the prism as h.
The volume of a prism is the space that it occupies.
The formula for volume of the prism is (base×height×length)/2
120=(6×h×5)/2
120×2=30×h
240=30h
h=240/30
h=8
Therefore, The prism stands 8 yards height.
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Given that f(x) = 9 - 2x, find f(3)
a) 1
b) 2
c) 3
d) 4
Answers
IN THE PLACE OF x IN THE EXPRESSION 9-2x PLUG IN 3 AND SIMPLIFY.
[tex]f(3) = 9 - 2(3) \\ f(3) = 9 - 6 \\ f(3) = 3[/tex]
OPTION c) IS THE ANSWER.
A line passes through the point (8, 3) and has a slope of 5/2
Write an equation in slope-intercept form for this line.
Answers
Answer:
y= 5/2x + -17
Step-by-step explanation:
plug in (8,3) into y=mx+b
3=5/2(8) + -17
then solve for b
What is the solution of the inequality − 4 ≤ 4 x + 8 ?
Answers
Answer:
[tex]x \geqslant - 3[/tex]
100 points need asap
Determine the solutions to the equation below. 5|x−2|+3=8
x=1 and x=3
x=−9 and x=13
x=−3 and x=−1
Answers
Answer: X = 1 and X = 3
Step-by-step explanation:
By filling in both the possible X values (1 and 3) you get two equations.
5|1-2| + 3 = 8
5|3-2| + 3 = 8
Both of these equations when simplified equal eight on both sides because the first one has the absolute value of -1 times 5 plus 3 which is eight. The second equation is the same besides the fact that it's the absolute value of 1, not -1 but it makes no difference.
Scale Factor And Scale Drawing
Explain Please
Answers
The explanation of the scalar factor and scalar drawing is given below.
Given that
We have to explain what is scalar factor and scalar drawing.
What is a scalar factor?
To adjust the size of a figure without altering its shape, a scalar factor is a number or conversion factor that is utilized. It is employed to change the size of an object. If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scalar factor can be determined.
The original rectangle's dimensions in the accompanying figure are 3 units and 2 units. The formula: Dimensions of the new shape = Dimensions of the old shape Scalar factor is used to multiply the dimensions by the scalar factor of 3 to produce an expanded figure. The revised dimensions are thus given as 9 units and 6 units, respectively. In a similar manner, we multiply the original dimensions by a scalar factor of half to produce a reduced figure. As a result, the reduced dimensions are given as 1.5 units and 1.
What is a scalar drawing?
An accurate portrayal of an object or location in two dimensions is called a scalar drawing. Scalar drawings include, but are not limited to, maps and floor plans.
The scalar describes the actual length that each length on the scalar graphic corresponds to.
A scalar of "1 inch to 5 miles," for instance, indicates that 1 inch on the figure corresponds to 5 actual miles. If a road is depicted on a drawing as being 2 inches long, it is actually 10 miles long.
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What is the horizontal distance in inches covered by 12 stair steps if each is 11 in. wide?
Answers
The total horizontal distance covered by 12 stair steps is 132 inches.
What is an equation?An equation is an expression that can be used to show the relationship between numbers and variables.
Given that:
Each stair step is 11 inches wideThere are 12 stair stepsTotal horizontal distance = 12 stairs * 11 in/stair = 132 inches
Total horizontal distance is 132 inches
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what is the process of getting 10b+7<8b+7<9b+10 down to -3<b<0 because I have my solution graphed already but I genuinely couldn't track my friend helping me on my homework assignment so can somebody please explain?
Answers
What is the process of getting 10b+7 <8b+7 <9b+10 down to -3 <b <0?
Transforming the inequalities,
(a) Consider 10b+7<8b+7,
10b+7<8b+7
Combining like terms,
10b - 8b < 7-7
2b< 0
Dividing both sides of the inequality by the coefficient of the variable,
b< 0
(b) Consider 8b+7<9b+10,
8b+7<9b+10
Combining like terms,
8b- 9b < 10-7
-b < 3
Dividing both sides of the inequality by the coefficient of the variable,
b > -3
The intersection of the inequality is given by,
-3 < b < 0
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Put decimals numbers in order
Ok, ok I need help with this and it’s due tomorrow and if I don’t complete it until 11:45 PM I’m gonna fail immediately
Answers
Answer:
Least to greatest:
0.03
0.2
0.36
0.38
0.9
Step-by-step explanation:
i don’t get this help lol
Answers
The equation of the parabola using vertex form in the graph is given as; y = (-19/9)(x + 3)².
What is meant by the term parabola?A parabola is a collection of points in a plane which are the same distance apart from a given point and line in that plane. The given point is known as the focus, and the line is known as the directrix. The vertex of the parabola is the midpoint of a perpendicular segment from of the focus to the directrix. The axis of symmetry is the line that connects the vertex and the focus.For the given question;
The curve on the graph in the vertex form is defined by the the equation;
y = a( x – h) 2 + k
Where, (h,k) are the vertex of the curve.
From the graph.
Vertex (h,k) = (-3, 0)
Point = (x, y) = (0, -19)
Put the values in the curve.
y = a( x – h)² + k
-19 = a( 0 – (-3))² + 0
Solving.
a = -19/9
Now, the put the value of a in the equation of parabola.
y = (-19/9)(x + 3)² + 0
y = (-19/9)(x + 3)²
Thus, the equation of the parabola in the graph is given as; y = (-19/9)(x + 3)².
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Can you please help me find the limit and identify any vertical asymptotes? Thanks
Answers
Given: The limit below
[tex]\lim_{x\to7^-}(\frac{1}{x-7})[/tex]To Determine: The limit and the vertical asymptotes
Solution
[tex]\begin{gathered} \lim_{x\to7^-}(\frac{1}{x-7}) \\ \mathrm{For}\:x\:\mathrm{approaching}\:7\:\mathrm{from\:the\:left},\:x<7\quad \Rightarrow \quad \:x-7<0 \\ The\:denominator\:is\:a\:negative\:quantity\:approaching\:0\:from\:the\:left \\ Hence \\ \operatorname{\lim}_{x\to7^-}(\frac{1}{x-7})=-\infty \end{gathered}[/tex]For the vertical asymptote
[tex]\begin{gathered} Vertical-asymptote \\ For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points \\ also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function. \end{gathered}[/tex]The denominator of the rational function given is
[tex]\begin{gathered} denominator:x-7 \\ x-7=0 \\ x=7 \end{gathered}[/tex]Hence:
limit = - ∞
Vertical asymptote: x = 7
work out m and c for the line: y = 6x
Answers
After using equation of line the value of m = 6 and c = 0.
What is a equation of line?
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
Given that,
The equation of line
y = 6x
Compare the given equation by the standard equation of line.
y = mx+c
m = 6 and c = 0
Hence, The value of m = 6 and c = 0.
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Lucia ordered a set of beads. She received 35 beads in all. 7 of the beads were green. What percentage of the beads were green?
Write your answer using a percent sign (%).
Answers
The percentage of the beads were green is 20% .
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
Given that
Total number of beads = 35
In which Number of green beads = 7
Find out What percentage of the beads were green?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
So here total value = 35
Value = 7
Put the values in the formula
(value/total value)100%
= (7/35) × 100 %
= 1/5 × 100 %
= 100 / 5 %
= 20 %
Hence , Twenty percent (20%) of the beads were green.
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factor (GCF) the binomial 25x^2 -15x and find one of its factors.
Answers
The most appropriate choice for factorization will be given by
[tex]\\5x(5x - 3)\\[/tex] is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
What is factorization?
Algebraic expression consist of number and variables connected with addition, subtraction, multiplication and division.
Factorization is the process of breaking of algebraic expression into algebraic expressions of smaller degree.
The algebraic expressions of smaller degree are called factors.
Here,
[tex]25x^2 - 15x\\5x(5x - 3)\\[/tex]
This is the required factorization.
(5x - 3) is one of the factor of [tex]25x^2 - 15x[/tex]
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Alex earns a \$35{,}000$35,000dollar sign, 35, comma, 000 salary in the first year of his career. Each year, he gets a 3\%3%3, percent raise. Which expression gives the total amount Alex has earned in his first nnn years of his career?
Answers
The expression which represents the total amount Alex has earned in his first n years of his career is; F(n) = 35,000 (1.03)^n.
Which expression gives the total amount Alex has earned in his first n years of his career?The expression which represents the total amount earned in n years of Alex's career is to be determined.
Since the percent raise in Alex's earning each year is 3%, it follows that the required expression would be an exponential function.
It is therefore noteworthy to note the standard form of exponential models at this point, 2whuch is as follows;
F(n) = a(b)^n
Hence, the value of a which is the starting value is; 35,000 while b = (100% + 3%) = (1 + 0.03) = 1.03.
The required expression is therefore;
F(n) = 35,000 (1.03)^n.
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Angie Simon is a single palmetto county deputy sheriff. she has $103.92 in federal income tax withheld from her weekly salary. her weekly salary exceeds $645.00. she calms 2 allowances the county computes her federal income tax using the percentage method.
Answers
In this truss bridge, AABC~ AXYZ BASED ON THE GIVEN INFORMATION WHAT IS YZ??A.) 10 FTB.) 20 FTC.) 30 FTD.) 40 FT
Answers
Given that the triangles are similar, then their corresponding sides are in proportion, that is,
[tex]\frac{XY}{AB}=\frac{YZ}{BC}[/tex]Substituting with data:
[tex]\begin{gathered} \frac{40\text{ ft}}{10\text{ ft}}=\frac{YZ}{10\text{ ft}} \\ 40\cdot10=YZ\cdot10 \\ \frac{400}{10}=YZ \\ 40\text{ ft = YZ} \end{gathered}[/tex]Rick used 4-2-3 yards to sew 3-1-2 shirts what is the unit rate of cloth he used in terms of yards per shirt Mathematics 7th grade
Answers
If Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts.
We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.
The unit rate of cloth he used in terms of yards per shirt is found by dividing the 3 1/2 shirts by 4 2/3 yards,
[tex]= 4 \dfrac{2}{3} / 3 \dfrac{1}{2} \\\\ = \dfrac{14}{3} / \dfrac{7}{2} \\\\ = \dfrac{14}{3} \times \dfrac{2}{7} \\\\ = \dfrac{4}{3}[/tex]
Thus, if Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. The unit rate of cloth he used in terms of yards per shirt will be 4/3.
The question is incomplete
The complete question is"Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. What is the unit rate of cloth he used in terms of yards per shirt?"
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If4x-2y=6, then y =?
Answers
4x-2y=6, move the x to the other side by subtracting 4x from both sides
-2y=-4x+6, leave the y by itself and divide by -2, since that’s what y is being multiplied by
you get y=2x-3
16. The greatest distance between the Sun and
greatest distance between the Sun and Saturn
Jupiter is about 8.166 x 10^8 kilometers. The
is about 1.515 x 10⁹ kilometers. What is the
difference of these two distances?
Answers
The difference of the distance given for Sun, Saturn and Jupiter is 6.984 x 10⁸ kilometers.
What is termed as the scientific notations?Every day, we use numbers in our lives. Scientific notation is a method of writing extremely large and extremely small numbers. Scientific notation consists of two parts: a coefficient between 1 and 10 and a power of ten. The mantissa is the difference between the whole part (left of a decimal point) and also the decimal part (right of a decimal point) of the coefficient. The exponent would be positive or negative depending on which way the decimal point is moved.For the given question;
The greatest distance between the Sun and Jupiter is about 8.166 x 10⁸ kilometers.
The greatest distance between the Sun and Saturn is about 1.515 x 10⁹ kilometers.
Write this distance in the form of 10⁸ , the point will shift towards right one decimal.
Sun and Saturn distance = 15.15 x 10⁸ kilometers.
Difference = Sun and Saturn distance - Sun and Jupiter distance
Put the values,
Difference = 15.15 x 10⁸ - 8.166 x 10⁸
Difference = 6.984 x 10⁸ kilometers.
Thus, the difference of the distances is found as 6.984 x 10⁸ kilometers.
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a right triangle has one angle that measures 70°. what is the measure of the other acute angle?
Answers
1. A right triangle is a triangle with an angle measuring 90 degrees
2. 3 angles in a triangle add up to 180 degrees
We have the measurements of 2 angles, and because of 2., we can find the measure of the other acute angle : 180 - 90 - 70 = 20 degrees.
Answer: 20°
Step-by-step explanation:
Right triangle means one angle is 90°
One angle is given, 70°
A triangle adds up to 180°
90° + 70° + X = 180°
160° + X = 180°
X = 20°
how could you determine the number of feet per second a squirrel can run?
Answers
We are asked that how could we determine the number of feet per second a squirrel can run?
Recall that rate (also known as speed) is given by
[tex]r=\frac{d}{t}[/tex]Where d is the distance in feet.
t is
Rate is the speed so then to figure that out you need to divide how many feet it ran by how many seconds so (feet / seconds)= rate / speed
