Answer:
5y + 3= 14
subtract 3 from each side
5y=11
divide each side by 5
5y/5=11/5
y=11/5 or 2.2 or 2 1/5
Hope This Helps!!!
Answer:
2.2
Step-by-step explanation:
Properties needed:
Subtraction Property of EqualityDivision Property of Equality
First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.
5y + 3 = 14
-3 -3
5y = 11
Then we need to divide 5 from both sides (division property of equality) to get y.
[tex]\frac{5y}{5} = \frac{11}{5}[/tex]
And we get 2.2
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Select the correct answer.
Which set of coordinates satisfies the system of equations y=x-3 and y=-2x+1?
Y
w
A
N
9
83
B
-1
-2
3
5
C
3
4
O
Answer: [tex]\left(\frac{4}{3}, -\frac{5}{3} \right)[/tex]
Step-by-step explanation:
Setting the equations equal to each other.
[tex]x-3=-2x+1\\\\3x=4\\\\x=\frac{4}{3}\\\\\implies y=\frac{4}{3}-3=-\frac{5}{3}[/tex]
What is the length of a 90 degree arc of a circle with the radius of 11 cm
There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
Given that a randomly selected person
uses the gym and the track, what is
the probability they do not use the
swimming pool?
A sequence has three terms.
Its term-to-term rule is
multiply by 6 and then add 13
a) The first term of the sequence is -2
Work out the third term.
b) The order of the three terms of the sequence is reversed.
Describe the term-to-term rule of the new sequence.
Answer:
a) The third term is 19
b) The new term-to-term rule is subtract 13 and then divide by 6.
Step-by-step explanation:
First term: -2
Second term: 1 (-2 * 6 = -12 + 13 = 1)
Third term: 19 (1 * 6 = 6 + 13 = 19)
Our reversed sequence is now 19, 1, -2
First term: 19
Second term: 1 (19 - 13 = 6 / 6 = 1)
Third term: -2 (1 - 13 = -12 / 6 = -2)
It's term is -3 it can be divided into 6 points +79
At a gymnastics meet, twenty gymnasts compete for first, second, and third place.
How many ways can first, second, and third place be assigned
There 6840 ways can first, second, and third place be assigned.
What is Permutation?A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
We will use the concept of permutation
[tex]^{20}P_3[/tex]= 20!/ (20-3)!
= 20*19*18*17!/ 17!
= 6840 ways.
Hence, there are 6840 ways.
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Can someone explain this?
Answer:
false
Step-by-step explanation:
if the 2 shorter segments dont add up to be equal or greater to the longest segment, then its impossible for a triangle to be formed :)
Answer:
True
Step-by-step explanation:
General formulas and concepts:
Subject: Geometry
Unit: Triangular Line Segments
Definitions:
Triangle Inequality Theorem
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.Steps:
Use the triangle inequality theorem:
9 + 4 > 11
13 > 11 ⇒ True
9 + 11 > 4
20 > 4 ⇒ True
4 + 11 > 9
15 > 9 ⇒ True
Conclusion:
Because the 3 segments that are given satisfy the statements of the triangle inequality theorem, they can therefore form a triangle.
Check
The tiles on the left contain functions written using function r
g(f) = 2f
f(h) = h - 7
h(g) = -4+g
The input values for each of the given functions are as outlined below.
How to identify input values of functions?Input values are also defined as domain which is the set of input values for which the function is defined. Thus, let us look at each of the given functions;
1) g(f) = 2f. The input value here is f
2) f(h) = h - 7. The input value here is h.
3) h(g) = -4 + g. The input value here is g
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[tex](1/8)^-^3^a=512^3^a[/tex]
The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
How to solve the equation?The equation is given as:
[tex](\frac18)^{-3a} = 512^{3a}[/tex]
Express the equation as a base of 2
[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]
Evaluate the products
[tex]2^{9a} = 2^{27a}[/tex]
Cancel out the common base
9a = 27a
The above equation is not true because [tex]9a \ne 27a[/tex]
Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution
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What is the common ratio between successive terms in the sequence?
27, 9, 9, 1,
3,
of
Answer:
What is the common ratio between successive terms in the sequence?
27, 9, 9, 1,
3,
of
The point stope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1 = (x-12). What is
the standard form of the equation for this line?
Answer:
x-4y = 8
Step-by-step explanation:
The standard form for the equation of a line is Ax+By=C where A is a positive integer and B and C are integers
First we need to find the slope
m = ( y2-y1)/(x2-x1)
m = (-3-1) / (-4-12)
=-4/-16
= 1/4
The point slope form is
y-1 = 1/4(x-12)
Multiply each side by 4
4(y-1 )= 4*1/4(x-12)
4(y-1) = x-12
4y -4 = x-12
Subtract 4y from each side
4y-4-4y = x-4y -12
-4 = x-4y -12
Add 12 to each side
-4+12 = x-4y -12+12
8 = x-4y
x-4y = 8
The standard form is x-4y = 8
A boy earned $435, $230, and $562 for 3 consecutive months. How much did he earn in the fourth month so that he gets an average earning of $500 in these 4 months?
Answer:
The boy earned $773 in the fourth month.
Step-by-step explanation:
1) First, we need to find the total amount of money he needs so that the average of the 4 months would be 500. We can do this by multiplying 500 and 4 (essentially, we are working backward when trying to find the average) [tex]500*4=2000[/tex] So, we know that the boy needs $2000 total by the end of the fourth month to make the 4-month average $500.
2) Now, we know how much the boy made for the first 3 consecutive months, so add those numbers up. [tex]435+230+562=1227[/tex] So within the first 3 months, the boy made $1227.
3) Finally, we know how much money the boy needs by the end of the fourth month and how much he made by the third, so to figure out how much he earned in the fourth month, we can simply subtract $1227 from $2000. [tex]2000-1227=773[/tex]
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
Answer:
the graph of f(x)= -2-10x+16
Answer:
the vertex would be (-5,41)
Step-by-step explanation:
You just plug the -5 back into the equation to get 41
Identify the conclusion of the conditional statement:
If an animal is a fish, then it lives in the water.
Answer:
Conclusion : it lives in the water
Step-by-step explanation:
Concept :The conclusion of a conditional statement is the result of the hypothesis. The “then” part of an if-then statement is called the conclusion.
therefore, for the given statement,
the 'then' part is 'it lives in the water'
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[tex]\Large\text{HELP ASAP!!!!!}[/tex]
[tex]\boxed{\stackrel\circ\circ\boxed{\textbf{what is the sin of -4\pi /3??$}}\stackrel\circ\circ}[/tex]
[tex]\dfrac{\sqrt{~~} }{[~~]}[/tex] [tex]\text{that's what the answer should look like}[/tex]
[tex]\text{Spam will NOT be tolerated!!!!!}[/tex]
Step-by-step explanation:
Did you mean.
[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]
[tex] \: [/tex]
[tex] = \sin( - \frac{4\pi}{3} ) [/tex]
[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]
[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]
[tex] = \sin( - 4 \times 60 \degree) [/tex]
[tex] = \sin( - 240 \degree) [/tex]
[tex] = \sin(0 - 240 \degree) [/tex]
[tex] = \sin(360 \degree - 240 \degree) [/tex]
[tex] = \sin(120 \degree) [/tex]
[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]
Round each of these numbers to the degree of accuracy shown in brackets. d) 34 766 (nearest hundred) please help me
Answer:
34800
Step-by-step explanation:
As, the nearest hundred to 766 is 800.
What are the slope and the y-intercept of the linear function that is represented by the graph?
answer C is “The slope is Negative three-fourths, and the y-intercept is 3.”
answer D is “The slope is Negative three-fourths, and the y-intercept is 4”
Answer:
“The slope is Negative three-fourths, and the y-intercept is 3.”
Step-by-step explanation:
the graph passes through the points (0 , 3) and (4 , 0)
Then
The slope is :
[tex]=\frac{0-3}{4-0}[/tex]
[tex]=-\frac{3}{4}[/tex]
Since , the graph passes through (0 , 3)
THen the y-intercept is 3.
solve for z z - 6 < 3
Step-by-step explanation:
[tex]z - 6 < 3 \\ z < 3 + 6 \\ z < 9[/tex]
Hope it helps
Z – 6 < 3
Z < 3 + 6
Z < 9
✯Hope this helps✯✿..๑... Ziddi girl ♡..✧Simplify the expression
Answer:
[tex]2*2^1^/^4[/tex]
(≈2.378)
Step-by-step explanation:
we know that:
[tex]a^x*a^y=a^x^+^y[/tex]
[this is the same as multiplying any exponents]
3/4 + 1/2 = 1 + 1/4
if [[tex]a^x*a^y=a^x^+^y[/tex]], then [[tex]a^x^+^y=a^x*a^y[/tex]] must also be true
so,
[tex]2^1^+^1^/^4=2^1*2^1^/^4\\[/tex]
= [tex]2*2^1^/^4[/tex]
([tex]2^1^/^4 = 1.189207115[/tex])
1.189207115 · 2 = 2.37841423001
(rounded to 2.378)
Answer:
[tex]2*2^1^/^4[/tex]
(2.37841)
Explanation:
3/4 + 1/2 = 1 + 1/4
= [tex]2*2^1^/^4[/tex]
([tex]2^1^/^4 = 1.189207115[/tex])
(2)(1.189207115) = 2.37841423001
How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answer:
one solution
(second option listed)
Step-by-step explanation:
We can that these two lines, each representing one equation/function, only meet at one specific value.
In a system of equations, we are essentially looking for a solution that works for both equations.
So, if both lines share a point/value (meaning they intersect), that point is a solution to the system of equations.
Because these lines only overlap at one point, this system of equations has one solution.
Answer:
1 solution (C)
Explanation:
They have one point of intersection.
I’m confused I need help
Answer:
x-intercept: -4
Step-by-step explanation:
It's where the slope intercepts with the x-axis
Answer:
Step-by-step explanation:
x-intercept: the x-value is that when y = 0: (-4, 0).
y-intercept: the y-value when x = 0: (0, 5)
Find the equivalent exponential expression. [(-4)^5]^3
Answer:
[tex]-4^{15}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left[(-4)^5\right]^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (-4)^{(5 \times 3)}[/tex]
[tex]\implies (-4)^{15}[/tex]
[tex]\textsf{Apply exponent rule} \quad (-a)^n=-a^n,\:\: \textsf{ if }n \textsf{ is odd}:[/tex]
[tex]\implies -4^{15}[/tex]
A cell phone plan charges $38 a month, and an additional $12 a month for each gb of data used. write an equation for the monthly cost (y) of the cell phone plan in terms of the number of gb of data used (x).
Answer:
y = 38 + 12x
Step-by-step explanation:
38is fixed cost per month and since the charge is $12 per GB, the variable cost is 12x where x is the GB used
Determine the solution to the system of equations graphed below and explain your reasoning and complete sentences
g(x)=-2x-3
f(x)= |x+1|-4
Answer:
(x, y) = (0, -3)
Step-by-step explanation:
On a graph, the solution to a system of equations is the set of points where the graphs of the equations intersect.
__
solutionThe graphs for this system of equations intersect at the point (0, -3). That point is the only solution for this system of equations.
The solution is (x, y) = (0, -3).
Given lJK , which is an isosceles right triangle, IJ=4 and m
Answer:
[tex]IK = IJ\sqrt{2}[/tex]
Step-by-step explanation:
First, it's an isosceles right triangle, which means there is a 90 degree angle and the two other angles are equal.
To find what the two other angles are, you can set up a quick equation:
let x be angle
90 + 2x = 180, since the sum of the interior angles in a triangle is always 180.
then,
[tex]2x = 90\\x = 45[/tex]
Therefore, the triangle is a 45-45-90 triangle.
You have the measure of IJ, which is one of the legs of the triangle. The way you can find the length of the hypotenuse of a 45-45-90 triangle is by multiplying the length of one of the legs by [tex]\sqrt{2}[/tex].
This means the equation is [tex]IK = IJ\sqrt{2}[/tex]
Answer:
[tex]\sf IK=IJ\sqrt{2}[/tex]
Step-by-step explanation:
The interior angles of a triangle sum to 180°. Therefore, if ΔIJK is an isosceles right triangle where m∠J = 90°:
vertex is m∠J = 90°two base angles are m∠K and m∠ITo calculate the base angles:
⇒ m∠K + m∠I + m∠J = 180°
⇒ m∠K + m∠I + 90° = 180°
⇒ m∠K + m∠I = 90°
⇒ m∠K = m∠I = 45°
Therefore, IJ and JK are the legs of the right triangle and IK is the hypotenuse.
To find the length of the hypotenuse, use Pythagoras' Theorem.
Pythagoras’ Theorem: [tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given:
a = IJ = 4b = JK = 4c = IKSubstitute the given values into the formula and solve for IK:
[tex]\sf \implies IJ^2+JK^2=IK^2[/tex]
[tex]\sf \implies 4^2+4^2=IK^2[/tex]
[tex]\sf \implies IK^2=32[/tex]
[tex]\implies \sf IK=\sqrt{32}[/tex]
[tex]\implies \sf IK=\sqrt{16 \cdot 2}[/tex]
[tex]\implies \sf IK=\sqrt{16}\sqrt{2}[/tex]
[tex]\implies \sf IK=4\sqrt{2}[/tex]
As IJ = 4 then:
[tex]\implies \sf IK=IJ\sqrt{2}[/tex]
Ella has a collection of vintage action figures that is worth $430. If the collection
appreciates at a rate of 4% per year, which equation represents the value of the
collection after 7 years?
The equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
What is an Equation ?An equation is a mathematical statement , where the algebraic expression is equated to another algebraic expression.
It is given that
Ella has a collection of vintage action figures that is worth $430.
collection
appreciates at a rate of 4% per year
equation representing the value of the collection after 7 years is
value of collection = 430 + (0.04 * 430 )* t
value of collection = 430 + (0.04 * 430 )* 7
= $550.4
Therefore the equation representing the value of the collection after 7 years is value of collection = 430 + (0.04 * 430 )* 7 or value of collection = $550.4
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If the rejection region is +1.10, what will be your decision if the z computed value is 2.34
The decision when the z value is within the rejection region is that we'll have to reject the null hypothesis.
What is a rejection region?It should be noted that the rejection region is also known as the critical region. It is the set of values where the null hypothesis is rejected.
When the observed test statistic is in the rejection region, we'll have to reject the null hypothesis and then accept rte alternative hypothesis.
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Find the length of side x in simplest radical form with a rational denominator.
30°
60°
√12
D
The value of x is 10√3 .
The missing figure is attached with the answer
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.
As it is a right angled triangle therefore the trigonometric ratios are applicable
From the given figure sin 60 needs to be determine to find the value of x
sin x = Perpendicular / Hypotenuse
sin 60 = 5 / x
[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]
x = 10√3
Therefore the value of x is 10√3
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Need help urgently please
Answer:
x = -12
y = 3
Step-by-step explanation:
[tex]1/2x + 6(x+15) = 12\\1/2x + 6x + 90 = 12\\6\frac{1}{2} x + 90 = 12\\6\frac{1}{2} x= -78\\x = -12[/tex]
[tex]y = x + 15\\y = -12 + 15\\y = 3[/tex]
Part A Can image 1 be the reflected figure from question 1? Explain your answer.
The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and translation.
Reflection is a rigid transformation, hence it does not affect the size and shape of the object or pre-image.
The resulting reflected image would be congruent to image 1, i.e. have congruent corresponding sides.
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Mr Abdul made tuna and curry potato filling for some puffs.3/5 of the filling he made was tuna and the rest was curry potato.
After he used 1/8kg of the tuna filling and made another 3/4
kg of curry potato filling, he then had equal amounts of tuna filling
and curry potato filling left. How much tuna filling did he make at first?
Give your answer as a mixed number in its simplest form
At first, he made [tex]2\frac{5}{8}[/tex] kg of tuna filling.
Mr Abdul made tuna and curry potato filling for some puffs.
3/5 of the filling he made was tuna and the rest was curry potato.
So, amount of curry potato = 1- 3/5 = 2/5
Ratio of tuna & curry potato = tuna : curry potato
= 3/5 : 2/5 = 3 : 2
Let amount of tuna = 3x & amount of curry potato = 2x
After he used 1/8kg of the tuna filling and made another 3/4 kg of curry potato filling.
According to the question, he then had equal amounts of tuna filling and curry potato filling left.
So, 3x - 1/8 = 2x + 3/4
Multiplying 8 in both sides we get,
⇒ 24x - 1 = 16x +6
⇒ 24x - 16x = 7
⇒ 8x = 7
⇒ x = 7/8
So, 3x = (3×7/8) = 21/8 kg = [tex]2\frac{5}{8}[/tex] tuna filling at first.
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