Answer:
D. 16, 9, 8
Step-by-step explanation:
sum of any two sides of triangles must be greater than the third side
only the fourth option follows this rule
Rosie just moved to new york city and makes $2,700 per month at her new job. each month, she pays $2,000 for rent, $100 for the subway, and $200 for groceries. she saves $100 a month for a rainy day. how much can she spend on other things?
Answer:
2700 - 2000 = 700 - 100 = 600 - 200 = 400 - 100 = 300
300 dollars
You are pouring canned sodas Into a cylindrical pitcher. Each can
of soda is 12 cm tall and has a diameter of 6.5 cm. The pitcher is
36 cm tall and has a diameter of 20 cm. How many cans of soda
will the pitcher hold?
Answer: 28.40 cans of soda
Step-by-step explanation:
Volume of cylinder: pi * r^2 * h
Volume of the can of soda = pi * 3.25^2 * 12 = 126.75 pi
Volume of the cylindrical pitcher = pi * 10^2 * 36 = 3600 pi
3600/126.75: 28.40 cans of soda
Answer:
28 whole soda cans or 28.4 soda cans (rounding to nearest tenth)
Step-by-step explanation:
The soda cans and the pitcher can be modeled as cylinders.
Volume of a cylinder
[tex]\sf Volume=\pi r^2h[/tex]
where:
r is the radiush is the heightDiameter of circle
[tex]\sf d= 2r[/tex]
[tex]\sf \implies r=\dfrac{1}{2}d[/tex]
Volume of Soda can
Given values:
d = 6.5 ⇒ r = 3.25 cmh = 12 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (3.25)^2 \cdot 12\\ & = \sf 126.75 \pi \:\:cm^3\end{aligned}[/tex]
Volume of Pitcher
Given values:
d = 20 ⇒ r = 10 cmh = 36 cm[tex]\begin{aligned}\sf \implies Volume & = \sf \pi (10)^2 \cdot 36\\ & = \sf 3600 \pi \:\:cm^3\end{aligned}[/tex]
To calculate how many cans of soda the pitcher will hold, divide the volume of the pitcher by the volume of one soda can:
[tex]\begin{aligned}\implies \textsf{Number of soda cans} & = \dfrac{\textsf{Volume of Pitcher}}{\textsf{Volume of one soda can}}\\\\&= \sf\dfrac{3600 \pi}{126.75 \pi}\\\\& = \sf 28.402366...\end{aligned}[/tex]
Therefore, the pitcher can hold 28 soda cans (nearest whole can), or 28.4 soda cans (nearest tenth).
find the inverse matrix or type "none". (use decimals) {11 -5 3 -1}
The inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
The inverse of a matrix A is calculated by the formula:
A' = (1/|A|)(Adj A),
where A' represents the inverse of matrix A,
|A| represents the determinant value of matrix A, and
Adj A represents the Adjoin matrix of matrix A.
So, to calculate the inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] , we will first calculate its Adj.
Adj = [tex]\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}[/tex]= [tex]\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex].
Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.
Therefore A' = (1/|A|)(Adj A),
or, A' = [tex](1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex] ,
or, A' = [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
Therefore, the inverse of the matrix [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .
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Find m given that the three angles of a triangle are (m plus18),(2m plus 28)and (3m plus 47)degree find all the angles
The value of m is 14.5 and the three angles of the triangle are 32.5°, 57°, and 90.5°.
How the angles of a triangle are related?There are three angles in a triangle. Consider as ∠A, ∠B, and ∠C.
The sum of all the three angles gives 180° in a triangle. I.e.,
∠A + ∠B + ∠C = 180°.
Calculation:The given triangle has three angles,
(m + 18)° , (2m + 28)°, and (3m + 47)°
On adding all these and equating to 180°,
(m + 18)° + (2m + 28)° + (3m + 47)° = 180°
⇒ 6m + 93 = 180
⇒ 6m = 180 - 93
⇒ 6m = 87
∴ m = 14.5
Then, the values of the three angles are:
(m + 18)° = (14.5 + 18)° = 32.5°
(2m + 28)° = (2 × 14.5 + 28)° = 57°
(3m + 47)° = (3 × 14.5 + 47)° = 90.5°
Therefore, the angles of the given triangle are 32.5°, 57°, and 90.5°.
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"-3pq^2+q^3" if p=2.9 and q=-1.3
7
Step-by-step explanation:
p = 1, q = 72 =49, q = 7
ookrndodnepwkpqq
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\mathbf{-3pq^2 + q^3}[/tex]
[tex]\mathbf{= -3(2.9)(-1.3)^2 + (-1.3)^3}[/tex]
[tex]\mathbf{= -3(2.9)(-1.3)^2 - 1.3^3}[/tex]
[tex]\mathbf{= -8.7(-1.3)^2 - 1.3^3}[/tex]
[tex]\mathbf{= -8.7(1.69) - 2.197}[/tex]
=[tex]\mathbf{ -14.703 -2.197}[/tex]
[tex]\mathbf{= -16.9}[/tex]
[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{-16.9}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
Using the Addition Method, solve for x in the following system of linear equations.
2y + x = 4
y - 3x = 2
a.) x = 1
b.) x = 2
c.) x = 8
d.) x = 0
Answer:
c. x=8
Step-by-step explanation:
make me a brain list.
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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we can tell that side DE is parallel to side....
A) AB
B) We can't be sure it's parallel to any side
By the converse of the basic proportionality theorem, we can say DE║AB.
We need to check whether DE is parallel to AB.
What is the converse of the basic proportionality theorem?If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
In triangle ABC, we can see on side AC, D is midpoint (∵AD=DC) and on side BC, E is midpoint (∵BE=CE).
Therefore, by the converse of the basic proportionality theorem, we can say DE║AB.
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The proof is shown below:
What is Mid point theorem?The line segment joining the mid points of any two sides of a triangle is parallel to the third side.
△ABC in which D and E are the mid points of AB and AC,.
If D and E are the mid points of AB and AC,
then AD=DB and AE=EC.
Thus,
AD/DB = AE/ EC
by the converse of Thales theorem, DE∥BC.
As, by theorem we can say that DE∥BC.
So, there is no other side parallel to DE.
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A circular swimming pool has a diameter of 8 m and a depth of 2 m. What is the volume of the swimming pool?
he table shows a probability distribution for predicting how many people will come through the door of a fast food restaurant during the lunch hour. Each event represents the number of people for a ten-minute interval.
Use the six randomly generated numbers 18, 38, 87, 16, 56, and 5 to predict the number of people coming in during the lunch hour.
The number of people coming in during the lunch hour is 160
How to determine the number of people?The complete question is in the attached image
The random numbers are given as:
18, 38, 87, 16, 56, and 5
Regroup the numbers
Number Group Probability
5, 16, 18 1 - 20 3/6
38, 56 21 - 60 2/6
56 61 - 90 1/6
Based on the individual numbers and the probability table, we have:
X 20 30 40
P 3/6 2/6 1/6
The expected value is:
[tex]E(x) = \sum xp[/tex]
This gives
E(x) = 20 * 3/6 + 30 * 2/6 * 40 * 1/6
Evaluate
E(x) = 160/6
There are six ten-minute intervals.
So, we have:
People = 6 * 160/6
Evaluate
People = 160
Hence, the number of people coming in during the lunch hour is 160
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1. Taking your eyes off the road for ____ seconds at 60 miles per hour means you have traveled blindly for half the length of a football field.
Answer:
4.09 seconds
Step-by-step explanation:
simplify miles per hour to feet per second how many feet is a mile and how many seconds are in an hour you end up with 88 fps from 60 mph
now simply a football field is 360 feet so 360/88 is 4.09090909 etc
Your eyes off the road for 4.09 seconds.
What is speed?The rate of change of position of an object in any direction is called the speed.
Given that, Taking your eyes off the road for how many seconds at 60 miles per hour means you have travelled blindly for half the length of a football field,
Converting 60 mph into fps
60 mph = 88 fps
The length of a football field = 360 ft
Time = 350/88
= 4.09 seconds.
Hence, you travelled for 4.09 seconds.
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Solve this identity, where the angles involved are acute angles.
[tex] \dfrac{\tan\theta}{1 -\cot\theta } + \dfrac{\cot\theta}{1 -\tan \theta } = 1 + \sec \theta \cosec\theta[/tex]
[tex]\therefore \sf{ LHS = \dfrac{tan \theta}{1 – cot \theta } + \dfrac{cot \theta}{1 – tan \theta}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{tan \theta}{1 – \dfrac{1}{tan \theta}} + \dfrac{ \dfrac{1}{tan \theta}}{1 – tan \theta} }[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{ LHS = \dfrac{ tan^{2} \theta }{tan \theta – 1} + \dfrac{1}{tan \theta (1–tan \theta) } }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{tan^{2} \theta}{tan \theta–1} – \dfrac{1}{tan \theta(tan \theta – 1 )}}[/tex]
[tex]\\[/tex]
[tex]\therefore \sf{LHS = \dfrac{tan^{3}\theta–1}{tan \theta(tan \theta –1)}}[/tex]
[tex]\\[/tex]
[tex]\therefore\sf{LHS = \dfrac{tan^{3}\theta–(1)^{3}}{tan\theta(tan\theta–1)}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{ (tan \theta -1)(tan^{2}\theta+tan\theta .1 + (1)^{2})} {tan \theta (tan\theta(tan \theta –1 )}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(tan^{2} \theta×tan\theta .1+1)}{tan \theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{(sec^{2}\theta+tan\theta)}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{sec^{2}\theta}{tan\theta} + \dfrac{tan \theta}{tan\theta}}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = sec^{2}\theta \times cot \theta + 1 }[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \dfrac{1}{cos^{2}\theta} \times \dfrac{cos \theta }{sin\theta}+1}[/tex]
[tex]\\[/tex]
[tex] \therefore\sf{ LHS = \left( \dfrac{ 1}{cos \theta} \times \dfrac{1}{sin \theta} \right) + 1}[/tex]
∴ LHS = 1 + secθ.cosecθ = RHS━━━━━━━━━━━━━━━━━━━━━━━We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
How to solve Trigonometric Identities?We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
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Which of the following is the correct definition for dependent events? A. Two events are dependent if they have no outcomes in common and cannot occur at the same time. B. Two events are dependent if they have outcomes in common and can occur at the same time. C. Two events are dependent if the outcome of the first event does not affect the outcome of the second event. D. Two events are dependent if the outcome of the first event affects the outcome of the second event.
The correct definition of dependent events is two events are dependent if the outcome of the first event affects the outcome of the second event.
What are dependent events?Two events are dependent if the outcome of one of the event depends on the outcome of the first event. An example of a dependent event is if it rains, the floor would be wet.
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Simplify (-8a¹b) (3a³b).
a) -24a7b²
b) -5a7b²
c) -5a¹26
d) -24a¹26²
Find the total surface area of this triangular prism.
Answer:
A ≈ 1194.5
The total surface area is 1194.53.
a = 24
b = 30
c = 7
h = 18
Find all solutions to the equation in the interval [0,2pi]. Enter the solutions in increasing order. sin 2x = sin x
please explain how you got the answer
Step-by-step explanation:
[tex]sin2x=sinx\\sin2x-sinx=0\\2*sinx*cosx-sinx=0\\sinx*(2*cosx-1)-0\\sinx=0 \\x=\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_1=0\ \ \ \ x_2=\pi .\\2*cosx-1=0\\2*cosx=1\ |:2\\cosx=\frac{1}{2} \\x=б\frac{\pi }{3} +2\pi n\ \ \ \ \ x\in[0;2\pi ]\ \ \ \ \Rightarrow\\x_3=\frac{\pi }{3} \ \ \ \ \ x_4=\frac{5\pi }{3}.\\[/tex]
[tex]Answer: x=0,\ \frac{\pi }{3} ,\ 1\pi ,\ \frac{5\pi }{3} .[/tex]
Consider u = ⟨5, –2⟩ and v = ⟨10, –4⟩. what is the relationship between u and v?
Answer:
v = 2u
Step-by-step explanation:
note that
2u = 2 (5, - 2 ) ← multiply each component by 2
= (10, - 4) = v , then
v = 2u
David is making a rectangular exercise yard for his turtle, Ralph. The perimeter of the yard is
16x² + 12x +18
3x
2x² + 6x +9
3x
inches in total. The length of the yard measures
inches. Find an expression to represent the measure of the width in inches
yd=
yd=
16x2+12x+18=3x=2x2+6x+9=3x=
sorry i try
Answer:
D
Step-by-step explanation:
Rachel and Jennifer are taking the same biology class. They have a test in about a week during an 8-9AM class period. Both plan to study for about 5 hours, but because of different work schedules, Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam. What do you predict about their scores
Rachel should perform better because of the spacing effect.
Given,
Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam.
What do you predict about their scores?
Rachel should perform better because of the spacing effect.
The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation.
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Using the two way table(in pic) what percentage of the students that do NOT like to travel out of state like camping? Round to the nearest whole percent. Thank you 3
A. 32>
B. 34>
C. 38%
D. 42%
Using it's concept, it is found that the percentage of the students that do NOT like to travel out of state that like camping is:
B. 34%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, there are 112 students that do not like traveling out of the state, and of those, 38 like camping, hence the percentage is:
[tex]P = \frac{38}{112} \times 100\% = 34\%[/tex]
Hence option B is correct.
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If f(x) = 4x - 8 and g(x) = 5x + 6, find (f+ g)(x).
Answer:
9x - 2
Step-by-step explanation:
f(x) = 4x - 8
g(x) = 5x + 6
because it's (f + g)(x), we can simply add the functions together
{note: don't get thrown off by the (x) being separate parentheses--distributing the x first can help it look familiar:
(x)(f + g)
fx + gx,
it's the same thing}
(4x - 8) + (5x + 6)
here, we want to combine like terms to simplify:
4x + 5x - 8 + 6
4x + 5x - 2
9x - 2
So, (f + g)(x) = 9x - 2
hope this helps!! have a lovely day :)
Question 10 How many cubic yards of sand will it take to fill a child's play area that measures 10 yards long, 8 yards wide, and 1/3 yard deep
Answer:
26.6 cubic yards
Step-by-step explanation:
Remark
What you have is a rectangle prism. It has an easy enough formula.
Formula
V = L *w * h
Givens
L = 10 yards
w = 8 yards
h = 1/3 yards
Solution
V = L*w*h
V = 10 * 8 * 1/3
V = 26.66 yds^3
The function f(x) = three-fourths(10)–x is reflected across the x-axis to create the function g(x). which ordered pair is on g(x)?
The ordered pair that is on g(x) is (2, -3/400)
determine the ordered pair:
The function is given as:
f(x)=3/4(10)∧-x
The rule of reflection across the x-axis is:
g(x) = -f(x)
So, we have:
g(x) = -3/4(10)∧-x
Set x = 2.
So, we have:
g(2) = -3/4(10)∧-2
Evaluate the exponent
g(2) = -3/4 * 1/100
Evaluate the product
g(2) = -3/400
This means that:
(x, y) = (2, -3/400)
Hence, the ordered pair that is on g(x) is (2, -3/400)
Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.
Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).
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Write an equation that represents the line.
Use exact numbers.
The equation of the line passing through the points is y = x + 2
How to determine the equation?The points are (-1, 1) and (4, 6).
The slope is calculated using:
m= (y2 - y1)/(x2 - x1)
So, we have:
m = (6 - 1)/(4 + 1)
Evaluate
m = 1
The equation of the line is then calculated as:
y = m(x -x1) + y1
This gives
y = 1 *(x + 1) + 1
Evaluate
y = x + 2
Hence, the equation of the line passing through the points is y = x + 2
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julia typed 410 words in five minutes in her keyboarding class at this rate how many words could she type in 13 minutes
Answer:
1066
Step-by-step explanation:
5 mins = 410 words
410/5 = 82 so she is typing 82 words a minute
Then do 82 times 13
Which triangles could not be similar to triangle ABC ?
triangle a b c where angle b is a right angle. side a b is 15 cm. side b c is 8 cm. side a c is 17 cm.
Select each correct answer.
(See image for details.)
Similar triangles are those triangles whose corresponding sides are in the same ratio. The triangles that are similar to ΔABC are ΔDEF and ΔJKL.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
For two triangles to be similar there sides should be in the same ratio.
For ΔABC ~ ΔMNO,
AB/MN should be equal to BC/NO,
AB/MN = 15/35 = 0.4286
BC/NO = 8/12 = 0.66
Thus, there are not similar triangles.
For ΔABC ~ ΔDEF,
AB/MN should be equal to BC/NO,
AB/DE = 15/22.5 = 0.66
BC/EF = 8/12 = 0.66
Thus, there are similar triangles.
For ΔABC ~ ΔGHI,
AB/GH should be equal to BC/HI,
AB/MN = 15/77 = 0.1948
BC/NO = 8/36 = 0.222
Thus, there are not similar triangles.
For ΔABC ~ ΔJKL,
AB/MN should be equal to BC/NO,
AB/JK = 15/60 = 0.250.25
BC/KL = 8/32 = 0.66
Thus, there are similar triangles.
Hence, the triangles that are similar to ΔABC are ΔDEF and ΔJKL.
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Event A has a probability of occurring of 4/5 . Event B has a probability of occurring of 1/3. If events A and B are independent of one another, what is the probability of both events occurring?
The probability of both events occurring is 4/15
How to determine the probability?The given parameters are:
P(A) = 4/5
P(B) = 1/3
Because the events are independent, we have:
p(A and B) = P(A) * P(B)
This gives
P(A and B) = 4/5 * 1/3
Evaluate
P(A and B) = 4/15
Hence, the probability of both events occurring is 4/15
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An isosceles triangle has a vertex angle of 21.21°. two sides of the triangle are each 17.91 ft long. find the area of the triangle.
The Area of triangle is A= 58.02 (ft)^2
According to statement
Let
B is the measure of the vertex angle of the isosceles triangle ABC
A and C is the two congruent sides of the isosceles triangle ABC
we know that
The area of a triangle applying the law of sines is equal to the
A= 1/2 *AC *SinB
we have
A=C= 17.91 ft
And
B= 21.21
Substitute these values in the formula
A= 1/2* 17.91* 17.91 * Sin(21.21)
A= 58.02 (ft)^2
So, the Area of triangle is A= 58.02 (ft)^2
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In the following exercises, multiply the binomials. Use any method.
244. (x − 7)(x − 2)
Multiplying the binomials, we have (x - 7)(x - 2) = x² - 9x + 14.
How to Multiply Binomials?Applying the distribution property of multiplication, the given binomials, (x - 7)(x - 2) can be multiplied as shown below:
(x - 7)(x - 2)
x(x - 2) -7(x - 2)
x² - 2x - 7x + 14
x² - 9x + 14
Therefore, (x - 7)(x - 2) = x² - 9x + 14.
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Answer:
Hence the expression [tex]$$(x-7)(x-2)=x^2-9x-14$$[/tex]
Step-by-step explanation:
The given expression is (x-7)(x-2).
We have to multiply the given expression.
Multiply the (x-7) by-2, multiply the (x-7) by x then add like terms.
[tex]$$\frac{\begin{matrix}{} & {} & x & - & 7 \\ \times & {} & x & - & 2 \\ \end{matrix}}[/tex]
____________
[tex]{\frac{\begin{matrix}{} & - & 2x & - & 14 \\ {{x}^2} & - & 7x & {} & {} \\ \end{matrix}}{\begin{matrix}{{x}^2} & - & 9x & - & 14 \\ \end{matrix}}}$$[/tex]
What is the solution to the system of equations? "-6x2/5y=8" 1/2x+3y=29
(10, –2)
(10, 2)
(2, 10)
(–2, 10)
The answer choice which represents a solution to the system of equations is; (–2, 10).
Which answer choice is a solution to the systems of equations?The system of equations as given in the task content is;
-6x - (2/5)y = 8
(1/2)x +3y = 29
Hence, by making x subject in equation 1 and substitution; we have;
x = (-0.4y -8)/6
Hence; (0.4y -8)/12 + 3y = 29.
(0.4y -8) + 36y = 348
35.6y = 356
y = 10
and x = (-0.4(10) -8)/6 = -2.
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