Answer:
12 feets below sea level
Step-by-step explanation:
Initial height = 25 feets above sea levwl
Total descent = 37 feets
Distance traveled below sea level = 37 feets - 25 feets = 12 feets
Hence, Sarah traveled 12 feets below sea level
(1)[3 Pts] The probability of producing a high-quality color print is 0.10. How many prints do you have to produce so that the probability of producing at least one quality print is larger than 0.90
The number of prints that the probability of producing at least one quality print is 22.
Given that the probability of producing a high-quality color print is 0.10.
The binomial distribution summarizes the number of trials or observations when each trial has an equal chance of reaching a certain value. The binomial distribution determines the probability of observing a particular number of positive results in a defined number of tests.
Probability of high-quality color print (P) = 0.1
Probability of producing not high-quality color print (1-P) = 0.9
Assume the no. of prints to produce 'n' and these are produced independently say 'x' be the no. of producing quality prints, which follows a binomial distribution.
The probability function of binomial distribution is
[tex]P(X=x)\left(\begin{array}{l}n\\ x\end{array}\right)P^x(1-P)^{n-x},x=0,1,2,.....,n[/tex]
Given that
P(X≥1)≥0.90
1-P(X=0)≥0.90
1-(1-P)ⁿ≥0.90
1-(0.90)ⁿ≥0.90
(0.90)ⁿ≥0.10
Now, taking log of both sides, we get
nlog(0.90)≥log(0.10)
n(0.1053)≥2.3025
n≥21.86
n≈22
Hence, the probability of producing a high-quality color print is 0.10 and the number of prints to produce so that the probability of producing at least one quality print is larger than 0.90 is 22.
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The tree diagram represents an experiment consisting of two trials
P(D)=?
For the given tree diagram of the experiment consisting of two trials, P(D) = 0.74
A method that can be infinitely repeated and has a clearly defined range of potential outcomes, or sample space, is referred to as an experiment or trial in probability theory. If there are multiple possible outcomes from an experiment, it is considered to be random; if there is just one, it is said to be deterministic.
Calculation of P(D) for the given experiment:
From the first branch of the tree, P(D) = 0.7 × 0.6
P(D) = 0.42
From the second branch of the tree, P(D) = 0.8 × 0.4
P(D) = 0.32
Hence, the probability of getting D in the experiment is,
P(D) = P(D) from first branch of the tree + P(D) from the second branch of the tree
P(D) = 0.42 + 0.32
P(D) = 0.74
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cannonball is shot into the air. its height can be described by the equation h = -5t2 + 40t, where h is the height in feet and t is the time is seconds. when will the cannonball hit the ground?
Answer:
Step-by-step explanation:
hello :
the cannonball hit the ground when h=0
-5t² + 40t=0 means : -5t(t- 8)=0
t=8
C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40 bcpp
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
2
The trapezium, ABCD, has four angles as shown.
All the angles are in degrees.
A
2x + 5
B
3y-20
(i) Show that 7x + 4y = 390.
(ii) Show that 2x + 3y = 195.
PLEASE HELP THIS IS URGENT!!!
Solve for x in the equation x squared 11 x startfraction 121 over 4 endfraction = startfraction 125 over 4 endfraction.
The solutions are { -1,-11}
Lets solve the given equation:
x^2 + 11x + 121/4 = 125/4
Subtracting 125/4 from both sides:
=>x^2 + 11x + 121/4-125/4= 125/4 -125/4
=> x^2 + 11x - (-4/4) = 0
=> x^2 +11x -(-1) = 0
=>x^2 + 11 x + 1 = 0
This is a quadratic equation so we will use the determinant (b^2-4ac)
a = 1
b = 11
c = 1
b^2-4ac = 11^2-4*1*1 = 117
So this equation has two solutions:
x = (-b -/+ √(b^2-4ac) ) / 2a
x = (-11 -/+ √(117) ) / 2
x = (-11 -/+ 3√(13))/ 2
x = -0.91 or x = -10.9
x = -1 or x = -11 ( rounding off)
hence the solutions are { -1,-11}.
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The Leader of Zip decrees that the digit 0, since it represents nothing, will no longer be used in any counting number. Only counting numbers without 0 digits are allowed. So the counting numbers in Zip begin 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, . . . , where the tenth counting number is 11. When you write out the first one thousand allowable counting numbers in Zip, what are the last three digits of the final number?
The last three digits of the final number are 109.
A number is an arithmetic value that is used to calculate and represent a quantity.
The digit zero will no longer be utilized in any counting numbers, according to the Leader of Zip, since it stands for nothing. There can only be counting numbers with 1 digit.
From 1 to 11,
11 is the tenth counting number.
So for the case of first 1000 numbers,
Number of permutations =1000/10 =100
Since 101 to 109 contains a zero.
So, 100+9=109
So, 1000+109=1109
Thus, the last number is 1109, and its last three digits are 1,0,9.
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Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. he spent a total of $47.65. the equation that models the problem is 3.95m+8.95b=47.65, where m is the number of magazines and b is the number of books
Hugh bough 4 books.
What is linear equation ?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.The cost of magazines =
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Subtract 11.85 from both sides.
8.95b = 35.8
Divide 8.95 from both sides.
b = 4
Therefore, Hugh bough 4 books.
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The complete question is -
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
Felix’s total credit card balance is described by the following function: f(p) = p(1.30). If Felix owes $2500, what is the total bill plus interest?
$3,250
$32,500
$325
None of the choices are correct.
The total bill plus interest on the credit card is $3,250
What is credit card?
Credit card gives its holder the opportunity to make purchases on credit such that amount spent and the interest that accrues thereon would be paid by the credit card holder at a future time.
In this case, the function shows the relationship between the amount owed and the interest so as to give the outstanding balance.
f(p) = p(1.30)
p=amount owed=$2,500
f(p)=$2,500*(1.30)
f(p)=$3,250
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I need a proper answer and its urgent pls
perimeter of triangle park is x+y+xy meter. Length of two sides are x-z+yx meter and z+x+xz meter find the third side
Answer:
Step-by-step explanation:
hello :
the perimeter of triangle is : P= (x-z+yx)+( z+x+xz)+A
given P=x+y+xy calculate the third side A
x+y+xy = (x-z+yx)+( z+x+xz) so : A=x+y+xy -x+z-yx-z-x-xz....continu
a=
If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The perimeter of the triangle park is x + y + xy meter. The length of the two sides are x - z + yx meter and z + x + xz meter.
Let the third side be 'A'. Then the third length of the triangle is given as,
x + y + xy = (x - z + xy) + (z + x + xz) + A
x + y + xy = x - z + xy + z + x + xz + A
y = x + xz + A
A = y - x - xz
If the perimeter of the triangle park is x + y + xy meter. Then the third length of the triangle will be y - x - xz meters.
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find the mean of 3,2,4,6,5,6,1,7,9,8,10
Answer:
[tex]5\frac{6}{11}[/tex]
Step-by-step explanation:
Number of Values = 11.
Mean = Sum of values / Number of Values
= [tex]\frac{3+2+4+6+5+6+1+7+9+8+10}{11} \\=\frac{61}{11} \\= 5\frac{6}{11}[/tex]
Solve for x: 12x^2 – 6 (a^2 + b^2)x + 3a^2b^2 = 0
Step-by-step explanation:
[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]
Using quadratic formula, we get
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]
Answer: x₁=6b², x₂=6a².
Step-by-step explanation:
[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]
A client has just inherited a property. the deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. the shape is an irregular quadrilateral and the other three sides have distances of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. more importantly, it is known that the front left corner of the property is a right angle.
This exercise involves the construction of a blueprint. To do so, we need to solve for angles using the Cos Rule. See the step by steps procedure below.
What is a blueprint?A blueprint is a masterplan that highlights how a structure will be look like when it is completed.
What is the solution to the above blueprint?Let the dimensions of the property be labelled QRST.Recall that the distance between the two corners are QR = 210 ftOther sides are: 515ft, 232ft, and 542ft going in a clockwise direction.Recall that the front left corner of the property is a right angle.From the above, see attached the first simple quadrilateral QRST (Draft I) that is indicates the above information.
Next Step
We have to derive ∠T, ∠ S, and ∠R.
In order to achieve the above, we must split the quadrilateral into two triangles.
As noted in the image, the quadrilateral is bisected from R to T.
∠R and ∠T are also divided into R1 R2 and T1, T2 respectively.
Next step - Derive ∠T1 and ∠R1 .
To do the above, we must deploy the Pythagoras Theorem. (PT)
PT requires:
TR² = QT² + QR²
TR² = (210)² + (515)²
TR² = 44,100 + 265,225
TR² = 309,325
TR = √309,325
TR = 556.17
Next step, Derive T1
We can derive T1 using the cos rule:
Cos T1 = QR/QT
= 515/556.17
Cos T1 = 0.926
Therefore
T1 = Cos⁻¹(0.926)
T1 = 22.18°
Next we derive R1
R1 = 180° - (90° + 22.18°)
R1 = 67.82°
In ΔTRS, by using Cosine Rule,
Cos T2 = [TS² + QR² - RS²]/2(TS) * (TR)
Cos T2 = [(232)² + (556.16)² - (542)²]/ 2 * (232) x (556.16)
Cost T2 = 69,373.945/258,058
Cost T2 ≈ 0.269
Therefore,
T2 = Cos⁻¹(0.269)
T2 ≈ 74.4°
Applying the same process, we can derive R2
Cos R2 = TR² + RS² - TS²
Cos R2 = [(556.16)² + (542)² - (232)²] / 2 (556.16) * (542)
Cost R2 = 0.911
R2 = Cos ⁻1 (0.911)
R2 = 24.34°
From the above, we can execute the following iterations:
∠S = 180° - (R2 + T2)
= 180 ° - (24.34 + 74.4)
∠C = 81.26°
Likewise:
∠R = R1 + R2
= 67.82 + 24.34
∠B = 92.16°
Lastly:
∠T = T1 + T2
= 22.18 + 74.40
∠T = 96.48°
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Full Question:
A client has just inherited a property. The deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. The shape is an irregular quadrilateral and the other three sides have a distance of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. More importantly, it is known that the front left corner of the property is a right angle.
-Construct a blueprint of the property labeling the measures of all sides and angle of the property.
(2/3)(-9/8)(-4/5)(-1)
Answer: -0.6
Step-by-step explanation:
Triangle L N M is shown. Angle L N M is 90 degrees and angle N M L is 20 degrees. The length of L N is 21.
Use the diagram to complete the statements.
The measure of angle L is
°.
The trigonometric ratio that uses ∠M and LN to solve for NM is
.
The length of NM, to the nearest tenth, is approximately
.
The length of the triangle will be equal to 2.7.
How to calculate the length?It should be noted that that sin will be the opposite divided by the hypothenuse.
The measure of angle L is 20°.
This will be:
sin 20 = LN/8
NM = 8 sin 20
NM = 2.7
In conclusion, NM is 2.7.
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Answer: 2.7
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
A) f(x) = −2x
Domain:
Range:
g(x) = ½x2 + 5
Domain:
Range:
Answer:
Greetings!A) Domain: x∈R or in interval notation (- ∞, ∞)
Range: x∈R or in interval notation (- ∞, ∞)
Thus, they both the domain & the range of the first function are the same.
B) Domain: x∈R or in interval notation (- ∞, ∞)
Range: [-5,∞)
Using it's concepts, the domain and the range of the functions are given as follows:
a) Both all real numbers.
b) Domain all real numbers, range [tex]y \geq 5[/tex].
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, neither function has any impediment, such as an even root or denominator, hence the domain is all real numbers. As for the range, a linear function assumes all real values, while a concave up quadratic function assumes values of the vertex, in this case y = 5, and greater, hence the range of the second function is [tex]y \geq 5[/tex].
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please answer asap with a clear answer
The permutations is computed below.
How to illustrate the permutations?1. Evaluate 9P4
9P4 = 9!/(9 - 4)
= 9!/5!
= (9 × 8 × 7 × 6)
= 3024
2. How many ways can 5 students sit on a row of 15 chairs for a photograph?
= 15!(15 - 5)
= 15!/10!
= (15 × 14 × 13 × 12 × 11)
= 360360
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write an equation for the line through (5,7) parallel to 2x-5y=15
Answer:
I don't know.i don't know
For the graph y = 1 find the slope of a line that is perpendicular to it and the slope of a line parallel to it. Explain your answer with two or more sentences.
The slope of the parallel line is 0 and the slope of the perpendicular line is undefined
How to determine the slope?The equation is given as:
y = 1
A linear equation is represented as:
y = mx + c
Where:
m represents the slope
By comparison, we have:
m = 0
The slope of the parallel line is:
Slope = m
This gives
Slope = 0
The slope of the perpendicular line is:
Slope =-1/m
This gives
Slope = -1/0
Slope = undefined
Hence, the slope of the parallel line is 0 and the slope of the perpendicular line is undefined
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Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
The surface area of the composite figure is 444m².
Given a composite figure which is shown in the question.
The area of a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces.
Firstly, we will find the area of front and end triangles by using the formula
Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.
Here, h=6 and b=16 and substitute these values in the formula, we get
A₁=2×(1/2)×16×6
A₁=2×8×6
A₁=96m²
Now, we will find the area of the left and right side rectangles which joined both the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=10 and b=5 and substitute these values in the formula, we get
A₂=2×10×5
A₂=100m²
Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=16 and b=4 and substitute these values in the formula, we get
A₃=2×16×4
A₃=128m²
Furthermore, we will find the area of the left and right side rectangles which joined by the front and end rectangles.
We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.
here, l=4 and b=5 and substitute these values in the formula, we get
A₄=2×4×5
A₄=40m²
Now, we will find the area of the base of the composite figure which is rectangle.
We will find the area by using the formula Area=l×b.
here, l=16 and b=5 and substitute these values in the formula, we get
A₅=16×5
A₅=80m²
So, the surface area of the given composite figure will be
Surface area=A₁+A₂+A₃+A₄+A₅
Surface area=96m²+100m²+128m²+40m²+80m²
Surface area=444m²
Hence, the surface area of the given composite figure is 444m².
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simplify the expression 2^m/n * 2^n/m
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the LL Theorm.
Question 6
1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)
5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)
Question 7
1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]
2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)
Question 8
1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)
2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)
5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
6) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)
A balloon rises at the rate of 10 ft/sec from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground.
When the balloon, rising at 10 ft/sec, rises to 100 feet, the rate of change of the angle of elevation is 0.05 rad/sec
How can the rate of change of the angle of elevation be found?The rate at which the balloon rises = 10 ft/sec
Horizontal distance of the balloon from the observer, d = 100 feet
Therefore;
[tex] \frac{dy}{dt} = 10[/tex]
The angle of elevation can be presented as follows;
[tex] tan(\theta) = \frac{y}{100} [/tex]
[tex] y = 100 \times tan(\theta) [/tex]
Therefore;
[tex] \frac{dy}{dt} = \mathbf{ 100\cdot sec^2 \frac{d \theta}{dt}} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}= \frac{ \frac{d y}{dt}}{100} \times cos^2 \theta [/tex]
[tex] \mathbf{ \frac{d \theta}{dt}} = \frac{ 10}{100} \times cos^2 \theta [/tex]
When the balloon is 100 ft. from the ground, we have;
cos(theta) = 100/(√(100²+100²) = 1/(√2)Therefore;
[tex] \frac{d \theta}{dt}= \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 [/tex]
[tex] \frac{ 10}{100} \times \left(\frac{1}{\sqrt{2}} \right)^2 = \frac{ 1}{20} [/tex]
Which gives;
[tex] \frac{d \theta}{dt}=\frac{ 1}{20} = 0.05 [/tex]
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If a union member does not pay their union dues, they will not be able to
Answer:
The ¨mandatory dues¨ asked by the unions are not much (practically none), since it´s a voluntary system implemented, normally all the members pay a ¨agency fee¨ but not more than that, this changes depending on the personal involvement with the union.
a natural person can refuse the membership at any moment, without issues, and this way avoid any kind of activity with the union, including contributing with money (dues) or duties.
However, when this happens, the person it´s restricted to certain activities like participate in union elections, general or important meetings, and the contribution in the bargain for the collective elections is banned as well, these as main aspects to highlight.
If one doesn't pay they union dues, they will not be able to participate in collective bargaining with owners.
Only the real representatives of the union could participate in collective bargaining with owner (in which they could negotiate the new term of the salary with the owner). Without paying their dues, they're still haven't been acknowledged as the member of union.
Hope this helps have a great day!
Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. which expression represents the probability that both students chosen are sophomores? startfraction (20 c 6) (19 c 5) over 20 c 2 endfraction startfraction (20 p 6) (19 p 5) over 20 p 2 endfraction
The probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
How to determine the probability expression?The given parameters are
Sophomore = 6Freshmen = 14The total number of people is
n = 20
2 of the 20 people are to be selected.
So, the number of selection is
[tex]n = ^nC_r[/tex]
This gives
[tex]n = ^{20}C_2[/tex]
The expression that represents both students being sophomore is
[tex]n = ^{6}C_2[/tex] --- i.e. 2 students selected from 6
The probability is then represented as:
[tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
Hence, the probability expression is [tex]\frac{^{6}C_2}{^{20}C_2}[/tex]
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Answer:
a
Step-by-step explanation:
edge 2023
Which graph represents the function p(x) = |x-1|?
-3
O
-2-
-3.
O
64-3
3.
2
2
3
O
5
Graph is in the attached image.
EXTRA POINTS
x/4 ÷ 2/3 = 1/5 solve for x
Answer:
x=40
Step-by-step explanation:
first you simplify both sides of the equation, then you isolate the variable
40/4= 10
10 times 3/2 = 15
Find angle V
(2x +29)= (10x-27)
Answer:
137
Step-by-step explanation:
VYXW is a parallelogram.
The opposite angles of a parallelogram are congruent, meaning their angle measurements are equal.
Following this information we can write an equation to find the value of x:
10x - 27 = 2x + 29 transfer like terms to the same side of the equation
10x - 2x = 29 + 27 add/subtract
8x = 56 divide both sides by 8
x = 7 replace x with 7 to find the given angle measures
now, the consecutive angles in a parallelogram are supplementary meaning their sum is equal to 180
m<V + m<W = 180
m<V + 2*7 + 29 = 180
m<V + 43 = 180 subtract 43 from both sides
m<V = 137
A rectangular pen has a length 4 feet greater than its width. Find the area
A. x+4
b. x^2+4x
c. 4x
d. x^2+8x+16
Answer:
b. x^2+4x
Step-by-step explanation:
So since you don't know the width, you can just represent it as a variable, and in this case that variable will be "x". Now using this variable we can use it to represent the length since there is a relationship between the width and length which is given. Since the length is 4 feet greater than the width, we can represent the length as (x+4). Now to find the area, we simply multiply the length * width, which is x * (x+4) = x^2 + 4x
Solve for x. − 15 = 22 x + 7
Answer:
x = - 1
Step-by-step explanation:
- 15 = 22x + 7 ( subtract 7 from both sides )
- 22 = 22x ( divide both sides by 22 )
- 1 = x