To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.
To eliminate the y terms from the equations,
first equation: 4x - 3y = 34, and
second equation: 3x + 2y = 17,
we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).
That is, for :
the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.
the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.
Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.
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(y ^ 4 * y ^ n)/(y ^ 2) = y ^ - 3 Find the value of n. (2 marks)
Answer:
n = -5
Step-by-step explanation:
Given:
[tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]
Multiply both sides by y²:
[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]
[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies y^{4+n}=y^{-3+2}[/tex]
[tex]\implies y^{4+n}=y^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 4+n=-1[/tex]
Solve for n by subtracting 4 from both sides:
[tex]\implies 4+n-4=-1-4[/tex]
[tex]\implies n=-5[/tex]
Answer:
n = - 5
===========
Given equation:
[tex]\dfrac{y^4*y^n}{y^2} =y^{-3}[/tex]Solve it for n:
[tex]y^{4+n-2}=y^{-3}[/tex] [tex]y^{2+n}=y^{-3}[/tex][tex]2+n=-3[/tex][tex]n=-3-2[/tex][tex]n=-5[/tex]===========
Used properties:
[tex]a^b*a^c=a^{b+c}[/tex] product of exponents with same base[tex]a^b/a^c=a^{b-c}[/tex] division of exponents with same baseIf [tex]a^b=a^c[/tex] then [tex]b = c[/tex] equal exponents with same base4
Find the measure of x.
X
12°
X = = [?]
Round to the nearest hundredth.
The measure of x will be 18.81 units.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
The given information are;
Perpendicular = 4
Base = x
Then, Tan ∅ = Perpendicular /Base
Tan 12 = 4/x
x = 4 /0.212
x = 18.818
Hence, the measure of x will be 18.81 units.
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What is 21% of 456? Calculate the percentages. Make sure to show all your work!
Answer:
21% of 456 = 0.21 x 400 + 0.21 x 50 + 0.21 x 6 = 95.76
Step-by-step explanation:
A regular polygon has 18 sides.
What is the size of each of its interior angles?
Give your answer in degrees (º).
Answer:
160 degrees.
Step-by-step explanation: The interior angle of a polygon formula. S=(n-2) x 180/n. The equation would look like p=(18-2) x 180/18=160.
if 17 is 32 than what does 17+17+17+17+17=?
Answer:
The answer is 160
Step-by-step explanation:
Comment
There really should be no answer to this. It sort of destroys the meaning of equality. However, you might be working in different bases. I'll assume that, but the base will be a fraction, which brings up other problems.
Solution
You have 5 17s there. So you will need five 32s. 5 * 32 = 160
The answer is 160
Given: ΔABC
Prove: m∠ZAB = m∠ACB + m∠CBA
Triangle A C B is shown with its exterior angles. Line A B extends through point X. Line A C extends through point Y. Line C A extends through point X.
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
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Answer:
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
✔ angle addition postulate
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
✔ of the triangle angle sum theorem
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
✔ subtraction property
.
Step-by-step explanation:
What are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
The value of (x,y) is (1.2 , -4.7) , Option D is the right answer.
The complete question is
On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)
What are Coordinates ?Coordinates are the location of a point in an (x,y) plot.
The given data is
Coordinates of
A = (7,-2)
B = (-8,-9)
m:n = 5:8
The coordinates of partition has to be determined
The formula used is
[tex]\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)[/tex]
(x,y ) = (1.2 , -4.7)
Therefore Option D is the correct answer.
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I will give brainiest to the first person who responds BUT only if the answer is correct
Answer:
70 cm2??
Step-by-step explanation:
The area of the rectangle: 50 cm2
The area of the triangle: About 20 cm2
50 cm2 + 20 cm2 +
what is the domain and the range of this function
Answer:
D: -5 ≤ x < 1
R: -4 ≤ y < 7
Step-by-step explanation:
The x values go between -5 and 1. The closed circle on -5 means it is included. The open circle on 1 means it is not included.
The y values go between -4 and 7. The closed circle means -4 is included, the open circle means the 7 is not included.
Factor: 117n + 90
Show your work don’t solve for n
To factor an expression, we can identify common factors between each terms, and take them out.
Solving the Question117n + 90
Both terms have the common factor of 9. Factor this out:
= 9(13n + 10)
13 and 10 do not have a common factor. Therefore, this is the final factored expression.
Answer9(13n + 10)
The tree diagram represents an experiment consisting of two trials. (Enter the probability to the hundredths place. Do not round.)
.6, A, .3, C, .7, D,
.4, B, .2, C, .8, D
P(D) = [ ? ]
please no links
Answer:
0.74
Step-by-step explanation:
A tree diagram is a visual way of showing combinations of two or more events. The outcome of each branch is labelled at the end of the branch line and its probability is written alongside the branch.
To calculate the probabilities of each combination, follow the branches and multiply the probabilities together.
There are two possible combinations to get a final outcome of D:
A and D = 0.6 × 0.7 = 0.42B and D = 0.4 × 0.8 = 0.32Therefore, the probability of D is:
⇒ P(D) = P(A and D) OR P(B and D):
⇒ P(D) = 0.42 + 0.32
⇒ P(D) = 0.74
Which expression is equivalent to 4 √10 ?
(૧/x
0 x ²
022
○ +³² (+ √/x)
0 +5
To eliminate the × terms and solve for y in the fewest steps by which constants should be equations be multiplied by before adding the equations together
To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
In this instance, you can do the following steps:
Start with the original equations:
Equation 1: 2x + 3y = 8
Equation 2: 3x - 2y = 4
To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:
Multiply Equation 1 by 2:
2(2x + 3y) = 2(8)
4x + 6y = 16
Multiply Equation 2 by 3:
3(3x - 2y) = 3(4)
9x - 6y = 12
Now, add the two modified equations together to eliminate the y terms:
(4x + 6y) + (9x - 6y) = 16 + 12
4x + 9x + 6y - 6y = 28
13x = 28
Finally, solve for x by dividing both sides of the equation by 13:
x = 28/13
Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x
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The probable question may be:
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.
What is the missing reason in the proof?
given
transitive property
alternate interior angles theorem
converse alternate interior angles theorem
In parallelogram WXYZ, with diagonal XZ, m∠WXZ = 81° and m∠WZX = 28°. What is the measure of ∠XYZ?
A.
62°
B.
90°
C.
71°
D.
109°
The measure of angle XYZ in the parallelogram is: 71°.
What are the Opposite Angles of a Parallelogram?In a parallelogram, the angles that are opposite each other are congruent.
Find m∠XWZ using the triangle sum theorem:
m∠XWZ = 180 - m∠WXZ - m∠WZX
m∠XWZ = 180 - 81 - 28
m∠XWZ = 71°
m∠XWZ = m∠XYZ [opposite angles are congruent]
m∠XYZ = 71°
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Answer:
71°
Step-by-step explanation:
I got it right on Edmentum
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The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.
What is the surface area of the solid cone requiring paint to the nearest square centimeter?
The surface area of the solid cone requiring paint rounded to the nearest whole number is ___________ square centimeters.
Answer:
111 cm^2
Step-by-step explanation:
h = 11.4
d = 5 so r (radius) = 2.5
Surface Area of a Cone Formula: πr^2 + πrs
s represents the slant height of the cone, lets represent this with a drawing.
We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.
a^2 + b^2 = c^2
These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.
s = √(11.4^2 + 2.5^2) so s = 11.67
now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs
π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2
The surface area of the solid cone requiring paint will be 111 square cm.
What is the surface area of a cone?Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.
Then the lateral surface area of the cone will be
SA = πrl + πr²
Then the slant height is given as
l² = r² + h²
The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.
Then the radius of the base circle will be
r = 5 / 2
r = 2.5 cm
The length of the slant height will be
l² = 11.4² + 2.5²
l² = 136.21
l = 11.67
Then the surface area of the solid cone requiring paint will be
SA = π × 2.5 × 11.67 + π × 2.5²
SA = 29.18π + 6.25π
SA = 35.43π
SA = 111.3
SA ≈ 111 square cm
The surface area of the solid cone requiring paint will be 111 square cm.
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Which criterion can be used to prove abc and adc are congruent? triangles, abc and acd, are plotted on a grid that share a common side ac. angles cad and acb are marked congruent. angles cab and acd are marked congruent. a. sss b. aaa c. sas d. asa
The correct answer is option D which is ASA ( Angle - Side - Angle).
What is congruency?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In triangles ABC and ADC,
Angles BCA and DAC are congruent (from the diagram);
Angles BAC and DCA are congruent (from the diagram);
AC is congruent AC (by reflexive property).
So, the triangles ABC and CDA are congruent with the ASA postulate.
ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Therefore the correct answer is option D which is ASA ( Angle - Side - Angle).
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Mr. K's math class is 1 {1}{4} hours long. After working problems on the board for 55 minutes {11}{12}hour), he gave the students the rest of the class period to work on homework. How long did students have to work on homework? Write your answer in simplest form.
The number of hours that students have to work on homework will be 1/3 hours.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
Mr. K's maths class is 1 and 1/4 hours long.
After working problems on the board for 55 minutes or 11 / 12 hour.
He gave the students the rest of the class period to work on homework.
Then the number of hours that students have to work on homework will be
⇒ 1 + 1/4 - 11/12
⇒ 5 / 4 - 11/ 12
⇒ (15 - 11) / 12
⇒ 4/12
⇒ 1/3 hours
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I need math help. I don’t understand the question.
Answer:
A.) 132.3 mm Hg
B.) 49 years old
Step-by-step explanation:
[tex]P= 0.006y^{2} -0.01y+119[/tex]
P = blood pressure
y = age in years
A.) Solution
To find: P
Given: y = 48
[tex]P= 0.006y^{2} -0.01y+119[/tex]
P = 0.006 x 48 x 48 - 0.01 x 48 + 119
P = 0.006 x 2,304 - 0.48 + 119
P = 13.824 - 0.48 + 119
P = 132.344 ⇒ 132.3
B.) Solution
To find: y
Given: P = 132.92
[tex]P= 0.006y^{2} -0.01y+119[/tex]
[tex]132.92= 0.006y^{2} -0.01y+119[/tex]
[tex]0.006y^{2} -0.01y-13.92[/tex]
.......................................................
Answer: 49 years old
the interest paid for borrowing qn amount of money for 3yrs at the rate of 4%is n108 find the amount of the money borrowed
Answer:
$864.94
Step-by-step explanation:
So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x where r is the growth rate (interest rate)
So the equation can be written as
[tex]m= P(1.04)^t[/tex] where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount
[tex]I = P(1.04)^t-P[/tex] where I represents the interest paid.
plug the values into the equation
[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]
find the surface area of the composite figure
The total area of the given composite figure is 84.8 ft²
How to find the area of a composite figure?We are given;
Area of Triangle = 5.6 ft²
Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²
Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)
Area of rectangles = 14.4 + 16 + 43.2
Area of rectangles = 73.6 ft²
Total area of composite figure = 73.6 ft² + 11.2 ft²
Total area of composite figure = 84.8 ft²
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Fernando purchased 1 pound of dried cranberries and 4 pounds of almonds to make a trail mix. Cranberries cost $4 per pound and almonds cost $5 per pound. What is the price per pound of the trail mix? $
Answer:
$24
Step-by-step explanation:
Cranberries needed: 1 pound
Cost of 1 pound = $4
Almonds needed: 4 pound
Cost of 1 pound = $5
4 x 5 = $20
20 + 4 = $24
Answer:
4.80
Step-by-step explanation:
Find the minimum value of the following equation:
(Please provide detailed explanations, no links)
Answer:
×=11
Step-by-step explanation:
2×-4×+27-5=0
-2×+22=0
-2×=-22
×=11
Add the equations. Two-Variable Systems: Elimination (question is linked with the screenshot below)
Answer:
2y = 24Given -
5x - y = (-1)
-5x + 3y = 25
To find - Summation of this
5x - y = (-1)
+ (-5x) + 3y = 25
adding both the equation we get,
5x +(-5x) - y + 3y = (-1) + 25
0 + 2y = 24
2y = 24.
Answer:
2y = 24
Step-by-step explanation:
5x – y = -1
+ - 5x + 3y = 25
2y = 24
Hence, A. 2y = 24 is the right answer.
The area of a rectangle is represented by the expression 6x³y5. Which of the following could be the
dimensions of the rectangle?
The length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The area of a rectangle is represented by the expression [tex]6x^3y^5[/tex].
The area of the rectangle = [tex]2x^2y^2 \times 3xy^3[/tex]
= [tex]6x^3y^5[/tex]
So, the length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]
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= 1/2 (u+v)t
Where s is the distance traveled by an object (in meters) with an initial velocity u (in m/s) and final velocity (in m/s).
seconds later.
Find s when u is 8 m/s, vis 12 m/s, and t is 5 seconds.
A. 50 m
B. 78 m
C. 100 m
D. 156 m
The distance travelled by an object is 50 m.
What is Distance?The distance between two points is the length of the path connecting them.
Here, given equation of distance
S = 1/2 (u + v)t
Where s is the distance traveled by an object (in meters)
initial velocity u (in m/s)
final velocity v (in m/s).
t in seconds.
Now, given values are;
u = 8 m/s ; v = 12 m/s ; t = 5 sec.
S = 1/2 (8 + 12)5
S = 1/2 (20)5
S = 100/2
S = 50 m.
Thus, the distance travelled by an object is 50 m.
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can u Help me now pls
A boat travels 333 km in 7 hours with a constant speed how far can it travel in 6 hours with the same speed
Answer:
258 km
Step-by-step explanation:
We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.
Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km
its math can you help out
Answer:
81
Step-by-step explanation:
27 people will tell 3 people each. 3x27=81
Answer:
81
Step-by-step explanation:
Answer two questions about system a and b
Answer:
Question 1: A. Replace one equation with a multiple of the other equation
Question 2: B. No
Step-by-step explanation:
1) How can we get System B from System A?
Choose 1 answer:
A. Replace one equation with a multiple of the other equation
B. Replace one equation with a multiple of itself
C. Swap the left-hand sides of both equations
D. Swap the order of the equations
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
The answer to both questions is in bold and in the "Answer" section.
Hope this helps!
If not, I am sorry.
