The measure of base angles and vertex angle are 133° and 47° respectively.
What is an isosceles triangle ?
A triangle with two equal-length sides is known as an isosceles triangle (/assliz/). The term "equilateral triangle" can refer to a shape with either exactly two sides that are the same length or at least two sides that are the same length, with the latter definition containing the equilateral triangle as an exception.
Let the vertex angle to be 'x'
So, according to the question, the measure of the base angels in an isosceles triangle is 8 less than 3 times the measure of a vertex angle
So, Base angles = (3 × vertex angle) - 8
We know that sum of all angles of a triangle is 180° and the base angles of an isosceles triangle are equal.
∴ Base angles + vertex angle = 180°
(3 × vertex angle) - 8 + x = 180°
3x - 8 + x = 180°
4x = 188°
x = 47°
∴ The vertex angle is 47° and,
Base angles = (3 × vertex angle) - 8
= 3 × 47 - 8
= 141 - 8
= 133°
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The temperature on February 2 in Lake City was 14°F. The temperature in Ellenville the
same day was -6°F. How much warmer was it in Lake City than in Ellenville?
To solve the problem, Gabby subtracted 14 - (-6) and came up with an answer of 8°F. Is
Gabby correct? Why or why not?
Yes, Gabby is correct.
No. The answer should have been 20°F, not 8°F, because subtracting a
negative number is the same as adding its opposite.
No. Gabby should have added -6 + 14 because the temperature in Lake City
was warmer.
Yes, Gabby is correct. Lake city is warmer at 8F than Ellenville.
What is temperature?Temperature is defined as the sum of the kinetic energies of all the atoms or molecules in a substance. The kinetic energy of a substance's constituent particles varies. A distribution can be used to depict the particles' kinetic energy at any particular moment.
How temperature is measured?Temperature is measured in Fahrenheit, Celsius and Kelvin.
As minus sign with the temperature depicts cold and hot and it have to do nothing with the calculation. The correct way is 14-6 = 8f. So Gabby is correct. We will not consider minus sign with six in calculations.
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Select all the equations that represent the line.
Multiple select question.
A)
2x – 3y= –1
B)
2x+3y= –3
C)
3x – 2y=2
D)
y+3= –23(x – 3)
E)
y – 1= –23(x+3)
F)
y+1= –32(x+3)
The equations that represent the line are:
B. 2x + 3y = –3
D. y + 3= –2/3(x – 3)
E. y – 1 = –2/3(x+3)
What is the Equation that Represents a Line?An equation that represents a line whose slope is given as m, and it intercepts the y-axis at b, is expressed in slope-intercept form as y = mx + b.
To find the equation of the given line above, pick two points on the line, (0, -1) and (-3, 1) and find the slope (m):
Slope of the line (m) = change in y / change in x = (1 - (-1)) / (-3 - 0)
Slope of the line (m) = 2 / -3
Slope of the line (m) = -2/3.
The line intercepts the y-axis at -1. This means the y-intercept of the line is b = -1.
To write the equation of the line, substitute m = -2/3 and b = -1 into y = mx + b:
y = -2/3x - 1
It can be rewritten as 2x + 3y = –3 in standard form, or as y + 3= –2/3(x – 3) or y – 1 = –2/3(x+3) in point-slope form.
Therefore the answers are:
B. 2x + 3y = –3
D. y + 3= –2/3(x – 3)
E. y – 1 = –2/3(x+3)
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PLEASE PLEASE PLEASE HELP ASAP
Problem: A freight train leaves Denver at 10:00 pm heading east at 20 mph. Another freight train leaves an hour later from the same station, and also heads east at 25 mph.
What time will the second freight train catch up with the first one?
The second train catches up with the first one at
If another freight train leaves an hour later from the same station and also heads east at 25 mph. The second freight train catches up with the first one by 11:12 pm.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
The relative speed for the given condition is,
=25 mph - 20mph
=5 mph
Relative distance = relative speed × time
Relative distance = 5 mph × 1 hour
Relative distance = 5 miles
The time will the second freight train catch up with the first one is obtained as,
Distance = speed × time
5 miles = 25 mph × t
t = 5 / 25
t=0.2 hour
1 hour = 60 minute
0.2 hour = 60 × 0.2
0.2 hour = 12 minute
=10:00 + 60:00 +12:00
=11:12
Thus, if another freight train leaves an hour later from the same station and also heads east at 25 mph. The second freight train catches up with the first one by 11:12 pm.
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The mass of the Earth is 5.97 × 1024 kg and the mass of Jupiter is 1.90×10²7.
This expression can be used to find the ratio.
What is the ratio of the mass of Earth to the mass of Jupiter?
The ratio of the mass of Earth to the mass of Jupiter is equal to 3.14*10⁻³, thus option B is correct.
What is ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given, the mass of Earth = 5.97*10²⁴ kg
Also, mass of Jupiter = 1.90*10²⁷ kg
Hence, ratio of mass of Earth to Jupiter is calculated by dividing mass of Earth upon the mass of Jupiter.
Ratio = (5.97*10²⁴/1.90*10²⁷ )
= 3.14*10²⁴⁻²⁷
= 3.14*10⁻³
Thus, the ratio of the mass of Earth to the mass of Jupiter is equal to 3.14*10⁻³, thus option B is correct.
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If 3% of a number equals 15, find 12% of that number.
Answer: 60
Step-by-step explanation:
3 / 100 * x = 15
3x = 1500 multiply both sides by 100
x = 500
500x0.12 = 60
The 12 percentage of the number is A = 60
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let's call the number we're looking for N
We can set up an equation based on the information given:
0.03N = 15
To solve for N, we can divide both sides by 0.03:
N = 15 / 0.03
N = 500
So the number we're looking for is 500
Now , the percentage value is = 12 %
And , we can find 12% of that number by multiplying it by 0.12:
A = 0.12 x 500 = 60
Hence , 12% of the number is 60.
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please tiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Answer:
Explanation: Its D.
A fish was swimming 2 1/2 feet below the water's surface at 1:00 p.m. Three hours later, the fish was at a depth that is 3 1/4 feet below where it was at 1:00 p.m. What rational number represents the position of the fish with respect to the water's surface at 4:00 p.m. ?
The fish's position with respect to the water's surface at 4:00 p.m. is 3/4.
What is a fraction?
Any number of equal parts is represented by a fraction, which also means a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Here, we have
Based on the given conditions, formulate: 3 1/4 - 2 1/2
Remove the parentheses: 3 + 1/4 - 2 - 1/2
Reorder and combine like terms: (3-2)+1/4 - 1/2
Calculate the sum or difference: 1+ 1/4 - 1/2
Expand the fraction to get the least common denominator: 4/(1×4) + 1/4 - 2/(2×2)
Calculate the product or quotient: 4+1/4 - 2/(2×2)
Calculate the product or quotient: 4 + 1/4 - 2/4
Write the numerators over the common denominator: 4 + 1 -2/4
Calculate the sum or difference: 5 - 2/4
Calculate the sum or difference: 3/4
Hence, the fish's position with respect to the water's surface at 4:00 p.m. is 3/4.
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This equation has one solution.5(x – 1) + 3x = 7(x + 1)What is the solution?
The solution of the given equation is x = 12. The solution is the value, that satisfies the given equation.
What is a solution for an equation?A solution is a value, that satisfies the equation. A solution is also said to be a root for the equation. Depending upon the degree of the variable, the number of solutions for that equation is defined.Calculation:Given equation is 5(x - 1) + 3x = 7(x + 1)
On simplifying the equation, we get
5(x - 1) + 3x = 7(x + 1) ⇒ 5x - 5 + 3x = 7x + 7
⇒ 8x - 5 = 7x + 7
⇒ 8x - 7x = 7 + 5
⇒ x = 12
Therefore, the solution for the given equation is x = 12.
Here, the power or the degree of the variable x is 1 in the given equation. Thus, it has only one solution.
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one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. find the lengths of the legs of the triangle.
one leg of a right triangle is 6 inches longer than the other leg, and the hypotenuse is 30 inches. Thus,
The lengths of the legs of the triangle are 18 inches,24 inches and 30 inches.
What is triangle?Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given that,
one leg of a right triangle is 6 inches longer than the other leg.
hypotenuse is 30 inches.
Let assume, the other leg be x
It is given that, one leg of a right triangle is 6 inches longer than the other leg. So, One leg = x + 6
Since it is a right angled triangle,
h² = p² + b²
Where, h = hypotenuse
p = perpendicular
B = Base
So, (30)² = (x+6)² + x²
or, x = -24, 18
As, the length of side cannot be negative so x becomes 18.
Thus, x + 6 = 18 + 6 = 24 inches
Hypotenuse = 30 inches
Hence, the lengths of the legs of the triangle are 18 inches, 24 inches and 30 inches.
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f(x)=(5[tex]\sqrt[5]{x}[/tex])^7
The answer to this Question is (5^7)*(x^7/5), the question is based on exponents laws
What are exponent laws?
These are some basic laws in maths that helps us to simplify the complicated expressions easily
Solution:
Here we can first distribute the power 7 to both 5 and 5th root of x by exponent laws
we get 5^7 * 5th root(x)^7
now we know nth root(x) = x ^1/n
we will do the same as
we get 5^7 * x^7/5 which is our required answer and there many more properties of exponents that we study in higher classes
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Select Repeating or Nonrepeating to correctly classify each decimal.
0.192 with a line over the 2
0.314 with a line over the
0.5353...
0.7777
please answer fast
Answer:
[tex]\sf 0.19\overline{2} \quad Repea\:\!ting[/tex]
[tex]\sf 0.\overline{314} \quad Repea\:\!ting[/tex]
0.5353... Repeating
0.7777 Non-repeating
Step-by-step explanation:
A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.
There are three ways to show a repeating decimal:
Several duplicates of the repeating digit or block of digits, followed by an ellipsis, e.g. 0.3333... or 0.123123...A dot or a line above a repeated digit, e.g. [tex]\sf 0.\.{3}[/tex] or [tex]\sf 0.\overline{3}[/tex]A line above a repeating block of multiple digits, e.g. [tex]\sf 0.\overline{123}[/tex][tex]\sf 0.19\overline{2}[/tex]
This is a repeating decimal as the line over the "2" means that this digit repeats forever.
[tex]\sf 0.\overline{314}[/tex]
This is a repeating decimal as the line over the "314" means the group of digits 314 repeats forever, e.g. 0.314314314...
0.5353...
This is a repeating decimal as there are two duplicates of the repeating block of digits "53" followed by an ellipsis.
0.7777
This is non-repeating decimal as there are no dots or lines above any of the digits, nor an ellipsis after the repeating digits.
Is (r-4) a factor of 6r^4-17r^3-46r^2+77r-20? What are the steps and how would you know if it’s a factor?
Answer:
see explanation
Step-by-step explanation:
By the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0
if (r - 4) is a factor then substituting r = 4 into the polynomial should result in it having a value of zero, that is
6[tex]r^{4}[/tex] - 17r³ - 46r² + 77r - 20 ( substitute r = 4 )
= 6[tex](4)^{4}[/tex] - 17(4)³ - 46(4)² + 77(4) - 20
= 6(256) - 17(64) - 46(16) + 308 - 20
= 1536 - 1088 - 736 + 288
= 0
Then (r - 4) is a factor of the polynomial
(04.04 MC)
The graph of two functions is shown.
graph of f of x equals negative x squared plus x and g of x equals x minus 1
If x = −1 is a solution to f(x) = −x2 + x and g(x) = x − 1, why is it also a solution to f(x) = g(x)?
a
It is a solution to f(x) = g(x) because it is the x-intercept of the two graphs.
b
It is a solution to f(x) = g(x) because it is the y-intercept of the two graphs.
c
It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.
d
It is a solution to f(x) = g(x) because both graphs are negative at x = −1.
The correct option is c. It is a solution to f(x) = g(x) because it is the x-coordinate where the two graphs intersect.
How to determine why x = −1 is also a solution to f(x) = g(x)?
x = −1 is also a solution to f(x) = g(x) because it is asking for the values of x that make f(x) equal to g(x). In this case, x = −1 is a value that makes both f(x) and g(x) equal to −1, so it is a solution to the equation f(x) = g(x).
The graph of f(x) = g(x) is simply the set of all points that are on both the graph of f(x) and the graph of g(x)
These points are the points where the two graphs intersect. In this case, the graph of f(x) = g(x) is a single point at x = −1, which is the x-coordinate where the two graphs intersect
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The path of a submarine can be modeled by d=0.012t-5.29t where d is the depth the submarine reaches and t is the number of hours the submarine is submerged
a. find the vertex. Then explain the relevance of this point in the context of this problem. Round to the nearest tenth
b. Find the number of hours the submarine was submerged. round to the nearest tenths.
HELP THIS IS DUE TOMMOROW :((
ALGEBRA 2 (Quadratic equations and functions)
a) The vertex of the problem is given as follows: (220, -583), meaning that the minimum depth reached by the vertex is of 583 after 220 hours.
b) The submarine was submerged for 440.1 hours.
What is the quadratic function?The quadratic function in this problem is defined as follows:
d(t) = 0.012t² - 5.29t.
Which gives the depth of the submarine after t hours.
The coefficients of the equation are given as follows:
a = 0.012, b = -5.29.
Then the t-coordinate of the vertex is given as follows:
t = -b/2a = 5.29/(2(0.012)) = 220.
The minimum depth is then of:
d(220) = 0.012(220)² - 5.29(220) = -583.
This is a concave up parabola, which is the reason why the vertex is a minimum.
The roots of the function are given as follows:
0.012t² - 5.29t = 0
t(0.012t - 5.29) = 0.
Hence:
t = 00.012t - 5.29 = 0 -> t = 5.29/0.012 -> t = 440.1.Meaning that the submarine was submerged for 440.1 hours.
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Help i’m lost please
Answer:
Step-by-step explanation:
A: If she were to travel 1 block every minute it would take 24 minutes because there are 24 blocks but if she were to travel two blocks every minute it would take 12 minutes because 24/2 is 12.
B: 1=24, 2=12, 3=8, 4=6, 6=4, 8=3, 10=2 4/10, 12=2, and 24=1
C: The speed causes the time to change because the faster she goes the quicker she will get there.
D: No, because the time it takes her constantly changes with there being no constant rate.
please help hard question
Answer:
Use Pyramid Formua to get upper height.
And add with 5m lower height.
The ratio of the meaure of the three ide of a triangle i 9:7:5. It perimeter i 191. 1 inche olve for X
If the ratio of the measure of the three sides of the triangle is 9:7:5 and the perimeter is 191.1 inches, then the three sides of the triangle are 81.9 inches, 63.7 inches and 45.5 inches
The ratio of the measure of the three sides of a triangle = 9 : 7 : 5
Then three sides of the triangles = 9x, 7x and 5x
Where x is the constant
The perimeter of the triangle = 191.1
The perimeter of the triangle is the sum of the three sides of the triangle
Then the equation will be
9x + 7x + 5x = 191.1
21x = 191.1
x = 191.1 / 21
x = 9.1
The first side = 9x
= 9 × 9.1
= 81.9 inches
The second side = 7x
= 7 × 9.1
= 63.7 inches
The third side = 5x
= 5 × 9.1
= 45.5 inches
Therefore, the measure of the sides of the triangle is 81.9 inches, 63.7 inches and 45.5 inches
I have solved the question in general, as the given question is incomplete
The complete question is:
The ratio of the measures of the three sides of a triangle is 9:7:5. Its perimeter is 191.1 inches. Find the measure of each side.
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What is the answer for page 785 CPM textbook
Step-by-step explanation:
????????????........
On a certain hot summer's day, 481 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $932.50. How many children and how many adults swam at the public pool that day?
By using simultaneous linear equation, it can be calculated that-
Number of children are 118 and number of adults are 363
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a simultaneous linear equation needs to be solved
Let the number of children be x and number of adults be y
481 people used the public swimming pool.
x + y = 481 ..... (1)
The daily prices are $1.75 for children and $2.00 for adults.
Total price = $(1.75x + 2y)
By the problem,
1.75x + 2y = 932.50
7x + 8y = 3730 .... (2)
Multiplying (1) by 7
7x + 7y = 3367.... (3)
Subtracting (3) from (2)
y = 363
Putting the value of y in (1)
x + 363 = 481
x = 481 - 363
x = 118
Number of children are 118 and number of adults are 363
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Find the value of X.
The value of x is 69°.
What is a quadrilateral?
A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined.
Given that ABCD is a quadrilateral.
The diagonal AC divides the quadrilateral into 2 triangles △ABC and △ACD.
The length of sides AC and CB of the △ABC is same. Thus △ABC is isosceles triangle. Therefore ∠BAC = ∠ABC = x°.
Similarly, the length of sides AC and CD of the △ADC is same. Thus △ADC is isosceles triangle. Therefore ∠CAD = ∠CDA = 66°
Given that ∠DCB = 90°.
∠A = ∠CAD + ∠BAC = 66° + x°
The sum of all interior angle of a quadrilateral is 360°.
Therefore,
∠A + ∠B + ∠C + ∠D = 360°
66° + x° + x° + 90° + 66° = 360°
Add to the like terms:
222 + 2x = 360
Subtract 222 from both sides:
2x = 138
x = 69
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Given that a is a positive integer, show that
√3a(√12a + a√3a)
is always a multiple of 3.
Input note: write the expression in the form 3(...)
Answer:
[tex]3(a^2+2a)[/tex]
Step-by-step explanation:
[tex]\sqrt{3a}(\sqrt{12a}+a\sqrt{3a}) \\ \\ =\sqrt{36a^2}+a\sqrt{9a^2} \\ \\ =6a+a(3a) \\ \\ =3a^2+6a \\ \\ =3(a^2+2a)[/tex]
How much fertilizer is needed for a 200 square-foot garden
Answer:2 to 4 pounds per
Step-by-step explanation:
Express the solutions of -34
For the expression -34 < x < 10, interval notation, builder notation and graphical solution is shown below.
What is number line?A number line is a line on which numbers are pointed at some intervals, it is used to show numerical operations.
The given expression is -34 < x < 10
The interval notation of the expression -34 < x < 10 is given as,
x ∈ (-34, 10)
The builder notation of the expression -34 < x < 10 can be given as,
{x | -34 < x < 10}
The graphical solution of the expression -34 < x < 10 is given below.
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The points on this graph represent a relationship between - and y-values. Which
statement about the relationship is true?
It must be proportional because the points lie in a straight
line.
It cannot be proportional because the y-values are not
whole numbers.
(0,0)
CLEAR CHECK
It must be proportional because each time x increases by
2. y stays the same.
It cannot be proportional because a straight line through
the points does not go through the origin.
The graph cannot be proportional because y stays the same
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that:
As x increases, the values of y remains unchanged
For the graph to be proportional, it must be a straight line that passes through the origin
And the variables must change
Hence, the true statement is the graph cannot be proportional
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Can anyone help with this? My friend's brain cells hurt :')
The required value of n for two similar pentagons is 15/4.
What is Scale factor?The scale factor is a type of measurement which is used to increase or decrease the size of an object keeping its shape as the same. It can be determined by taking the ratio of the new and the original dimension of the object.
The given two pentagons have similar shape because one has been scaled to get the other.
It implies that the ratio of the corresponding sides for them will be equal. It can be written as follows,
5/n = 3(¹/₃)/2(¹/₂)
=> 5/n = (10/3)/(5/2)
=> 5/n = 20/15
=> n = 15/20 × 5
=> n = 15/4
Hence, the value of n for the given pentagon is 15/4.
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PQR is an isosceles triangle in which PQ = PR
M and N are points on PQ and PR such that angle MRQ = angle NQR.
D
Prove that triangles QNR and RMQ are congruent.
R
since we know that PQ and PR are twin sides, well, the angle they each make at the base are also twin angles, Check the picture below.
Carissa works as a babysitter during her summer vacation. She gets paid one rate for daytime hours and a higher rate for nighttime hours. One week, she worked 12 daytime hours and 4 nighttime hours and earned $120. The next week, she earned $60 for a total of 4 daytime hours and 3 nighttime hours. Let x represent the hourly daytime rate and y represent her hourly nighttime rate. 12 x + 4 y = 120. 4 x + 3 y = 60. What is the solution to the system of equations? (3,4) (4, 12) (6, 12) (10, 30).
The solution of the given system of equation is (6, 12). So the option c is correct.
In the given question, Carissa works as a babysitter during her summer vacation.
She gets paid one rate for daytime hours and a higher rate for nighttime hours.
One week, she worked 12 daytime hours and 4 nighttime hours and earned $120.
The next week, she earned $60 for a total of 4 daytime hours and 3 nighttime hours.
Let x represent the hourly daytime rate and y represent her hourly nighttime rate.
The system of equations is
12 x + 4 y = 120……………(1)
4 x + 3 y = 60……………(2)
We have to find the solution to the system of equations.
To find the solution for the system of equation we solve the given equation using elimination method.
Multiply equation by 3 on both sides, we get;
12x + 9y = 180
Subtract equation 3 and 1
12x+9y-(12x+4y)=180-120
12x+9y-12x-4y=60
5y=60
Divide by 5 on both side, we get;
y=12
Now putting the value of y in equation 2
4x+3×12=60
4x+36=60
Subtract 36 on both side, we get
4x=24
Divide by 4 on both side, we get
x=6
Hence, the solution of the given system of equation is (6, 12). So the option c is correct.
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Answer: (6, 12)
Step-by-step explanation: did edge test
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
5% of $1100 = 55
Year given = 7
So, 55 × 7 = 385
She would get after 7 years all total = (1100 + 385) = $1485
27 POINTS
Which graph passes the vertical line test?
Answer:
C
Step-by-step explanation:
If you draw multiple vertical lines through each graph, C is the only graph that touches the line once. Which means it passes the vertical line test.
911: Wang Xiu Ying has 109 dollars in her savings account. She has -21 dollars in her checking account. whats a inequality that compares the correct amount of values.
109 dollars in her savings account is greater than -21 dollars in her checking account, that is 109 > -21. When comparing values that may not be equal that is, when one value is bigger or less than another inequalities are utilised.
What is inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >, <, ≤ or ≥. indicate that the two expressions in an inequality are not always equal.You can add the same amount to each side, take the same amount away from each side, multiply or divide each side by the same positive amount, and so on to solve an inequality. You must flip the inequality symbol if you multiply or divide each side by a negative number.To learn more about inequalities refer :
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