Answers
The value of x in the given figure is 10.
What is Pythagoras' Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry.According to this statement, the areas of the squares on the other two sides add to the area of the square whose side is the hypotenuse.In the given triangle,
∠ADC = ∠BDC = 90°
Hence the triangles ΔACD and ΔBCD are right-angle triangles. Thus we can apply Pythagoras' theorem in both triangles.
So in ΔACD,
CB² = BD² + DC²
And in ΔBCD,
CA² = AD²+ DC²
But, CA = 15 and CB = x + 5
So, (x + 5)² = BD² + DC²
15² = AD² + DC²
⇒225 = AD² + DC²
Here, BD = AD as given in the figure
Replacing BD with AD in the first equation we get,
(x + 5)² = AD² + DC²
Now, equate the values of AD² + DC² to obtain the value of x,
(x + 5)² = 225
⇒ x² + 25 + 10x = 225
⇒ x² + 10x - 200 = 0
⇒ x² + 20x - 10x - 200 = 0
⇒x(x + 20) - 10(x + 20) = 0
⇒(x + 20)(x - 10) = 0
Thus x = -20, 10
Hence the value of x is 10.
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Related Questions
16
4 points
(A.2A)
You are a part of a sports team that has at least 5 players but no more than 9 on a team. Your cleats for the team cost $15 each and can be represented by the function f(x) 15x where x
is the number of cleats. What is the range of this scenario?
RANGE:
Answers
The range of the function, f(x), that gives the total cost of the cleats of given that each cleat costs $15 and the number of cleats, x, is 5 ≤ x ≤ 9 is RANGE: [75, 135]
What is the range of a function?The range of a function is the set containing the output values that are obtainable with the function.
The given parameters are;
The number of players, n, in the sports team is; 5 ≤ n ≤ 9
The given cost of one cleat = $14
The function that represents the total cost of the cleats for the team is f(x) = 15•x
Given that each team member is given one cleat, we have;
Number of cleats is 5 ≤ x ≤ 9
The range of values for the total cost of the cleats is therefore;
15 × 5 ≤ f(x) ≤ 15 × 9
75 ≤ f(x) ≤ 135, which using interval notation gives;
RANGE: [75, 135]
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A bag contains 6 red marbles and 4 yellow marbles. A marble is drawn at random and not replaced. Two further draws are made, again without replacement.
What is the probability of drawing at least one red marble?
Answers
Answer:
6/10
Step-by-step explanation:
I think, however I may be very wrong, sorry.
Answer:
[tex]\sf \dfrac{29}{30}[/tex]
Step-by-step explanation:
A bag contains:
6 red marbles.4 yellow marbles.Therefore, the total number of marbles in the bag is 10 marbles.
The possible outcomes for drawing 3 marbles (without replacement) are:
R R RR R YR Y RR Y YY R RY R YY Y RY Y YTherefore, the only outcome where at least one red marble is not drawn is {Y Y Y}.
To find the probability of drawing at least one red marble, subtract the probability of drawing 3 yellow marbles from one.
The probability of drawing 3 yellow marbles without replacement is:
[tex]\implies\sf P(3\; yellow \;marbles)=\dfrac{4}{10} \times \dfrac{3}{9} \times \dfrac{2}{8}=\dfrac{24}{720}=\dfrac{1}{30}[/tex]
Therefore, the probability of drawing at least one red marble is:
[tex]\implies \sf P(At\;least\;one\;red\;marble)=1-\dfrac{1}{30}=\dfrac{29}{30}[/tex]
This can be confirmed by drawing a tree diagram (see attached).
To find the probability of drawing at least one red marble, add the probabilities at the end of each relevant final branch:
[tex]\begin{aligned}\implies \sf P(At\;least\;one\;red\;marble)&=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{10}\\\\&=\dfrac{4}{6}+\dfrac{3}{10}\\\\&=\dfrac{20}{30}+\dfrac{9}{30}\\\\&=\dfrac{29}{30}\end{aligned}[/tex]
350 in standard form
Answers
Answer:
3.5 * 10^2
Step-by-step explanation:
So you start with 350.
What you do is take the decimal from the beginning of 350 and move it to the left.
350.0 -> 35.0-> 3.5
And you move the decimal until you get only one number in front of the decimal.
Then you take the number of times you moved the decimal and put it with ten so in this case it would be. 10^2.
Making the final answer: 3.5 * 10^2
-4 -3 -2 -1
3+
2+
-2
Y
-3
-4
What is the slope of the line?
2 3
4
Answers
Answer:
-1/2
Step-by-step explanation:
A cup of fruit contains 12 graps and 3 strawberries Compare strawberries to the total number of fruit
Answers
Answer:
There are 3 strawberries and the total number of fruit is 15, so 3:15 is the ratio, or 3/15.
Step-by-step explanation:
The total number is all of the fruits added together, so 12 + 3.
The 3 means the number of strawberries, so you just put them together into a ratio.
Hope this helps.
Mark as brainliest please
standard to slope intercept form
Answers
Answer:
y=-5x+7
Step-by-step explanation:
15x+3y=21
(15x+3y)/3=21/3
5x+y=7
5x+y-5x=7-5x
y=-5x+7
yeah
i'm probably wrong but its my best
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 5x + 7[/tex]
____________________________________
The given equation is :
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 15x + 3y = 21[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: 3y = 21 - 15x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{21}{3} - \frac{15}{3} x[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = - 5x + 7[/tex]
That's the required equation in slope intercept form, with slope (m) = -5, and y - intercept = 7
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A = x + y - 7 solve for x
Answers
mark brainleist
Perimeter Given Coordinates
Oct 15, 11:32:13 AM
The points E(7,-5), F(7, 2), G(4, 8), and H(4, 1) form parallelogram EFGH. Plot
he points then click the "Graph Quadrilateral" button. Then find the perimeter of the
parallelogram. Round your answer to the nearest tenth if necessary.
4
Answers
Perimeter of the parallelogram which points are E(7,-5), F(7, 2), G(4, 8), and H(4, 1) = 24 units.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
A parallelogram is a shape with only two dimensions. It has four sides, two parallel pairs of which make up each side. The lengths of the parallel sides are also the same. The form is not a parallelogram if the lengths of the parallel sides are not equal.
Properties of parallelograms
Opposite sides are congruent (AB = DC).Opposite angels are congruent (D = B).Consecutive angles are supplementary (A + D = 180°).If one angle is right, then all angles are right.The diagonals of a parallelogram bisect each other.Given points are
E(7,-5),
F(7, 2),
G(4, 8), and
H(4, 1)
Perimeter of the parallelogram EFGH=2(EF+FG)
Distance between two points(x₁ , y₁) and (x₂ , y₂ ) can be calculated using the formula
√(x₂ - x₁ )² + (y₂ - y₁)²
Hence ,length of EF =
√(7 - 7 )² + (2 - (-5))²
=√49
=7units
And length of FG =
√(4 - 7 )² + (8 - 4)²
= √16 + 9
= √25
=5units
Hence, Perimeter of the parallelogram EFGH=2(EF+FG)=2(5+7)=24units
We have form parallelogram EFGH. For the result see the attachment-
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Answer:
27.4 units
Step-by-step explanation:
Given parallelogram EFGH with vertices E(7,-5), F(7, 2), G(4, 8), and H(4, 1), you want to know its perimeter.
Distance between two pointsThe distance between two points can be found from their coordinates using the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
ApplicationThe distance between points F and G is ...
d = √((4 -7)² +(8 -2)²) = √(9 +36) = √45 ≈ 6.708
The distance between points E and F will be the difference of their y-coordinates:
d = √((7 -7)² +(2 -(-5))²) = √(0 +7²) = 7
PerimeterSince opposite sides of a parallelogram are the same length, the perimeter is twice the sum of two adjacent sides:
P = 2(EF +FG)
P = 2(7 +6.708) = 2(13.708) = 27.416
The perimeter of EFGH is about 27.4 units.
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving SM = RN, given RM = SN and ∠MRS = ∠NSR. Submit the entire proof to your instructor.Given:RM = SN∠MRS = ∠NSRProve:SM = RNSTATEMENTREASON1.1.2.2. Reflexive Property3.3.4.4.
Answers
EXPLANATION:
Given;
We are given two triangles labeled MRS and NSR.
Required;
We are required touse the information provided rto rove tside SM is equal to side RN.
Solution;
[tex]RM=SN---Given[/tex][tex]RS=SR---Reflexive\text{ }property[/tex][tex]\angle MRS=\angle NSR---Congruent\text{ }angles[/tex][tex]\begin{gathered} \Delta MRS\cong\Delta NSR---SAS \\ \end{gathered}[/tex]If two sides and the included angle of one triangle are congruent to the corresponding parts of a second triangle, then we can conclude that both triangles are congruent.
Therefore;
[tex]SM=RN[/tex]Simpilfy the variable expression below as much as you can :
7x+(5*6)z
NEED ANSWER ASAP THANK YOU!!!!
Answers
Answer:
7x + 30z
Step-by-step explanation:
7x +(5*6)z
= 7x + 30z
9,999 divided by 9
Two answers
Answers
Answer:
1111...................... ................
I need help with this please thank you
Answers
∠UXS = 135° is the value on transversal line.
What is a transversal angle?
When a transversal splits two parallel lines, the two intersections create a number of angles. Transversal angles are what those are.A transversal is a line that crosses a network of lines, according to the definition. Transversals include, for instance, a line that crosses a set of two parallel lines.A transversal line is one that crosses two other lines at two different locations.Line l meets a and b in the picture below at two different locations, P and Q. Line l is the transversal line as an outcome.∠RXU = 45°
∠UXS = ?
As we know that a line make 180 degree angle on it.
So, ∠UXS + ∠RXU = 180°
∠UXS = 180° - ∠RXU
∠UXS = 180° - 45°
= 135°
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2. Niayla and Hamilton each have a job selling aardvark habitats. Hamilton gets paid a
flat fee of 350 dollars plus 50 dollars for each habitat he sells. Niayla gets paid a
flat fee of 500 dollars 40 dollars for each habitat she sells. How many habitats
must Niayla and Hamilton sell to make an equal amount of money.
Answers
Considering the equation of selling habitat between Niayla and Hamilton, the number of habitats that Niayla and Hamilton must sell to make an equal amount of money is 15
How to determine the number of habitats that Niayla and Hamilton must sell to make equal amountinformation gotten from the question include
Hamilton gets paid a flat fee of 350 dollars plus 50 dollars for each habitat he sells
Niayla gets paid a flat fee of 500 dollars 40 dollars for each habitat she sells
The equation as described is a linear function and is represented by the form. y = mx + c
where:
y = total amount made
x = number of habitat sold
m = cost per habitat
c =flat fee
some interpretation on the information from the question include
for Hamilton
y = 50x + 350
for Niayla
y' = 40x + 500
To make equal amounts y = y'
50x + 350 = 40x + 500
500 - 350 = 50x - 40x
150 = 10x
x = 150 / 10
x = 15
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Write the function for the graph.
Answers
The correct option is option B that is the function f(x) = 3 (4)ˣ.
A function may be defined as an expression in which for every input variable x there is only one output variable y. The input variable is known as independent variable and output variable is known as dependent variable. We need to find the function for the given graph. We have two points on the graph so we will satisfy the points in the options given options. The points are (0, 3) and (1, 12).
The first option is
f(x) = 3 (12)ˣ, after putting point (1, 12)
12 ≠ 3 (12), so it is not required function.
The second option is
f(x) = 3 (4)ˣ, after putting points (0, 3) and (1, 12)
3 = 3 and 12 = 12, so it is the required function.
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two is subtracted from a number, and then the diffrence is divided by 3. the result is 30
Answers
Answer:
Two is subtracted by a number:
n - 2
And then the difference is divided by 3:
(n - 2) / 3
The result is 30:
(n - 2) / 3 = 30
(n - 2 ) / 3 = 30
(n - 2) = 30 • 3
n - 2 = 90
n = 90 + 2
n = 92
The number is 92
In ΔSTU, \text{m}\angle S = (6x-15)^{\circ}m∠S=(6x−15)
∘
, \text{m}\angle T = (2x-2)^{\circ}m∠T=(2x−2)
∘
, and \text{m}\angle U = (4x-7)^{\circ}m∠U=(4x−7)
∘
. What is the value of x?x?
Answers
The value that makes the triangle a valid triangle is x = 17
What are angles?Angles are formed when two or more lines intersect.
This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of x?The given parameters are
Shape = Triangle STU
Angle S = 6x - 15
Angle T = 2x - 2
Angle U = 4x - 7
The sum of angles in a triangle is 180 degrees
This means that
Angle S + Angle T + Angle U = 180
Substitute the known values in the above equation
So, we have the following:
6x - 15 + 2x - 2 + 4x - 7 = 180
Evaluate the like terms in the equation
So, we have the following:
12x = 180 + 15 + 2 + 7
Evaluate the like terms in the equation
So, we have the following:
12x = 204
Divide by 2
x = 17
Hence, the value of x is 17
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1. The area in square feet of a rectangular field is 2x2+x-15. If the length of
the field, in feet, is x + 3 what is the width in terms of x?
A. 2x+3
B. 2x-5
C. 2r-3
D. 2x+5
Answers
Answer: B. 2x-5
Step-by-step explanation:
Decompose the polynomial into factors:
[tex]2x^2+x-15=\\\\2x^2+6x-5x-15=\\\\2x(x+3)-5(x+3)=\\\\(x+3)(2x-5)[/tex]
[tex]S=length*width\\\\The \ lenght=x+3\\\\Hence,\ \\\\The \ width=2x-5[/tex]
How is solving 2x + c= d similar to solving 2x + 1= 9 for x?
Answers
Solving 2x+c = d is similar to solving 2x+1 = 9 because both the equations have similar pattern.
According to the question,
We have thee following two equations:
2x+c = d ....(1)
2x+1 = 9 ....(2)
Now, note in these equations that in equation 2 we have two different values of c and d. We have the value of c as 1 and d as 9.
Further, solving these two equations would be same because of the following:
For equation 1, we have:
2x+c = d
2x = d-c
x = (d-c)/2
For equation 2, we have:
2x+1 = 9
2x = 9-1
x = (9-1)/2
Now, observe that in finding the values of x in both the equations we have similar solutions except the fact that in equation 2 we have two values of c and d.
Hence, solving 2x+c = d and 2x+1 = 9 is similar.
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what is -10+3x>-16 inequality notation
Answers
The Inequality notation of the given equation 10+3x>-16 is x > -2
What is Inequality notation?
A mathematical statement known as an inequality expresses the relationship between two quantities while indicating that they are not completely equal. The four symbols used to represent inequality are. ≥, >,<, and ≤.
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare the two values in inequality. Less than (or less than and equal to), greater than (and greater than or equal to), and also not equal to signs are used in place of the equal sign.
Consider the above equation.
-10 +3x > -16
Add 10 on both sides.
= -10+3x+10> -16+10
= 3x> -6
Divide by 3 to equation into both sides.
= [tex]\frac{3x}{3} > \frac{-6}{3}[/tex]
= x > -2
Inequality notation is x > -2
Interval Notation: [−2,∞)
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twice a number is no more than 7 units from 13
Answers
2x = 20
2x = 6
x = 10 or x = 3
Which expression is equal to???
Answers
Solve please brainliest
Answers
just find it from the graph its not that hard
goodluck :)
seven more than three times a number is 25 what is the number? please help asap thank u so much
Answers
Answer:
n = 10
Step-by-step explanation:
(10 * 3) + 7 = 37
Answer: 6
Step-by-step explanation:
With these type of problems, it is best to work backwards.
1. Because of the seven more, you subtract 7 from 25. This gives you 18.
2. Then it says three times, this means to divide by 3. 18/3 is 6
3. Your final answer is 6
Proving the answer is 6:
1. 3 [tex]*\\[/tex] 6 = 18
2. 18 + 7 = 25
THERE IS 5 QUESTIONS I NEED TO GET DONE IN TOTAL, BUT IT WONT LET ME PUT MANY PICS IN ONE QUESTION SO PLS GO TO MY ACC AND VIEW THE OTHER 2!!I NEED THIS BY **TODAY**
Answers
Answer:
(-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,-5)
Step-by-step explanation:
see picture
Brandon has seven pieces of chocolate.
He gives Colton one piece and Jill three pieces.
What fraction of chocolate does Brandon have now?
Answers
Answer:
4/7
Step-by-step explanation:
Answer:
Brandon has [tex]\frac{3}{7}[/tex] of the chocolate left with him.
Step-by-step explanation:
Step 1: Identify the fractions
Colton is given one of the seven pieces, so he has [tex]\frac{1}{7}[/tex] of the chocolate.
Jill is given three of the seven pieces, so she has [tex]\frac{3}{7}[/tex] of the chocolate.
Brandon himself had seven pieces at the beginning, so he had [tex]\frac{7}{7}[/tex] (the whole) of the chocolate.
Step 2: Do calculations with the fractions
Collectively, Colton and Jill have taken:
[tex]\frac{1}{7}+\frac{3}{7}\\\\\text{Add the fractions:}\\\frac{1+3}{7}\\\\\text{Calculate:}\\\frac{4}{7}~\text{of the chocolate}[/tex]
So, the fraction that Brandon has currently is:
[tex]\frac{7}{7}-\frac{4}{7}\\\\\text{Subtract the fractions:}\\\frac{7-4}{7}\\\\\text{Calculate:}\\\frac{3}{7}[/tex]
Brandon has [tex]\frac{3}{7}[/tex] of the chocolate left with him.
What is this number in standard form?
sixty-eight and fifty-four thousandths
Answers
Answer:
68.054
Step-by-step explanation:
I don't really have an explanation for this, it just is.
Sixty-eight (68) and fifty-four thousandths (.054, because the thousandths place is the third digit after the decimal point).
191% as a mixed or whole number
Answers
Answer:
1 91/100
Step-by-step explanation:
everything you need is in the picture
goodluck :)
convert 45grade into degree measure
Answers
Answer:
45g = 40.5°
45g = 40° 30′ 0″
If jummai is 12years old and Tunde is 8years old and they share 15bananas in the ratio of their ages how many will each have show calculation
Answers
Jummai and Tunde will each have 9 and 6 bananas respectively.
For the given ratio case we use the sharing ratio criterion to solve the problem.
Jummai is 12 years old.
Tunde is 8 years old.
Their ages are in ratio of;
A = 12 : 8
A = 3 : 2
The ratio's sum is 5.
15 bananas total are available for sharing.
Jummai will have [tex]x\\[/tex] bananas [tex]x[/tex] = (15 x 3/5) = 9
Tunde will have [tex]y[/tex] bananas [tex]y[/tex] = (15 x 2/5) = 6
Jummai and Tunde will each have 9 and 6 bananas with them.
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Which of the following values are solutions to the inequality -5 < 9- 6x?
None
II only.
I and II
O II and III
-6 II. 3
I. - 6
O I only
O III only
I and III
O I, II and III
III. - 1
Answers
The solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.
What is inequality?
In mathematics, the term 'inequality' is defined as a statement or equation with an ordered relationship like greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
-5 < 9- 6x
Adding 5 both the side we get,
5 - 5 < 9 - 6x + 5
⇒ 0 < 14 - 6x
⇒ 14 - 6x > 0
Dividing both the side by 6 we get,
⇒ 14 < 6x
⇒ x > 14/6 = 7/3
or, x ≤ 7/3
this is the required solution of the given inequality.
Thus, the solutions to the inequality -5 < 9 - 6x is x ≤ 7/3.
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