Let's call the smaller number "x" and the larger number "y." Since 7 is added to the larger number, y + 7 = 4x. Since 28 is added to the smaller number, x + 28 = 2y.
We can solve this system of equations by substituting the first equation into the second equation to eliminate one of the variables:
x + 28 = 2(y + 7)
x + 28 = 2y + 14
x - 2y = -14
Then, we can substitute the second equation into the first equation to eliminate the other variable:
y + 7 = 4(x + 28)
y + 7 = 4x + 112
y - 4x = -105
Now we have a system of two equations in two variables, which we can solve using methods such as substitution or elimination. Let's use substitution:
x - 2y = -14
y - 4x = -105
If we solve the second equation for y, we get y = 4x - 105. Substituting this expression into the first equation gives:
x - 2(4x - 105) = -14
x - 8x + 210 = -14
-7x = -224
x = 32
Substituting this value back into the expression for y gives us y = 4(32) - 105 = 107.
Therefore, the two numbers are x = 32 and y = 107. If 7 is added to the larger number, the value obtained is 107 + 7 = 114, which is four times the smaller number (32). If 28 is added to the smaller number, the value obtained is 32 + 28 = 60, which is twice the larger number (107).
Which table represents a linear function?
X
1
2
3
4
X
1
2
234
1
2
3
4
X12
A5951
y
y
-5
10
-15
20
SLE 888SK
10
20
40
-5
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times then the table 4 represents a linear function.
What is meant by linear functions?An algebraic equation with simply a constant and a first-order (linear) term, such as y = mx + b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
The slope-intercept form of the equation for a linear function. As a result, it is written as f(x) = mx + b, where b is the line's y-intercept and m is the slope. Tables with a constant rate of change are represented by linear functions.
Table 4 represents a linear function
From the given tables, only table 4 represent a linear function.
As x's values change by 1, the matching y's values change by 5. This is why.
The table exists represented as:
x y
1 -5
2 0
3 5
4 10
Therefore, table 4 represents a linear function.
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What is 5x-2+7x-5 simplified?
Answer:
12x -7
Step-by-step explanation:
If light strikes a plate mirror at a 36° angle of incidence, what would you expect the resulting angle of reflection to be?
According to the angle of incidence, the angle of reflection will also be 36°
Angle of incidence:
In math it means the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.
Given,
Here we need to find the If light strikes a plate mirror at a 36° angle of incidence, then what would you expect the resulting angle of reflection to be.
Here we know that, the incident ray, the reflected ray and the normal ray at the point of incidence all lies in the same plane.
Then the angle of incidence is equal to the angle of reflection
And it can be written as,
=> Angle of incidence = angle of reflection
As per the 2nd law given above, we say that if a light ray incident at 45°, then the reflected angle will also be 45°
Here we know that the value of,
=> Angle of incidence = 36°
Therefore, the Angle of reflection = 36°
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Hello please graph this with steps thank you
Graph f(x)=-x^4+1
The graph of the quartic function f(x) = -x⁴ + 1 is attached below with points at (-1 ,0), (0, 1) and (1, 0)
Graph of a Quartic ExpressionQuartic polynomials are continuous curves like the cubic polynomials. This means that you can draw the graph of the quartic without lifting your pencil from the page. There are no holes or jumps in the curve but, unlike the cubic graph, a graph of the quartic looks like a W or an M.
The general form of quartics of this form is y = a(x − h)⁴ + k The turning point is at (h, k). When sketching quartic graphs of the form y = a(x − h)⁴ + k, first identify the turning point. To add further detail to the graph, the x-axis and y-axis intercepts are found.
In this function given;
f(x) = -x⁴ + 1
This quartic function has points at (-1 ,0), (0, 1) and (1, 0)
Kindly find the attached graph below
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if you look at the results section of a psychology research article, two signs that scores are significantly different are that (a) the error bars of the groups will not overlap, and (b) the p-value will be less than 0.05.
If Two signs that scores are significantly different then (a) the error bars of group will not overlap
Error bars are graphical representations of data variability that are used to indicate the error or uncertainty in a reported measurement on graphs.
The estimated error in a measurement is indicated by error bars. In other words, an error bar represents the degree of uncertainty in a value.
When the standard deviation error bars overlap significantly, it is an indication that the difference is not statistically significant. To reach a conclusion, you must conduct a statistical test.
When the standard deviation error bars overlap even less, it indicates that the difference is unlikely to be statistically significant.
For significantly different group , we also have p-value greater than 0.05
So, Option (b) is incorrect.
Hence, (a) The error bars of the groups will not overlap is correct
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I submitted y=13 I wouldn't work so what can it be?
Answer:
[tex]\huge\boxed{\sf y = \pm 13}[/tex]
Step-by-step explanation:
Given that,
y² = 169
Take sq. root on both sides
√y² = √169
y = ±13So,
y = 13 OR y = -13
[tex]\rule[225]{225}{2}[/tex]
Answer:
b) y = + 13
Step-by-step explanation:
Now we have to,
→ find the required value of y.
The problem is,
→ y² = 169
Let's solve the problem,
→ y² = 169
→ y = √(169)
→ [ y = + 13 ]
Hence, the answer is + 13.
When we say, "a system of linear equations works", what does that really mean?
The linear equations (the system) are productive members of society and are able to hold a steady full time job working 40
hours a week.
The linear equations (the system) share one or more ordered pairs (x,y) when graphed.
The linear equations (the system) have nothing in common.
The linear equations (the system) have the same y-intercept when graphed.
When we say, "a system of linear equations works" it means that the linear equations share one or more ordered pairs (x,y) when graphed.
Why are linear functions used?In many practical applications in daily life, linear equations are a crucial tool in science. They enable scientists to, among other things, make predictions, compute rates, and characterize relationships between two variables in the physical world. In order to see trends, linear equations are often graphed.
What are four types of linear functions?Slope intercept form, direct variation, point slope form and standard form are four types of linear functions.
When we have a system of linear equations and when we solve them simultaneously we get one or more ordered pair depending upon the variable in system.
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COMPLETE THE PROOF! MY FINAL IS TMRW AT 8 AM!!!!
Given: segment QP is congruent to segment RS and segment QP is parallel to segment RS.
Prove: segment QR is parallel to segment PS.
A two-column method be that can used to prove that segment QR is parallel to segment PS is presented as follows;
Statement [tex]{}[/tex] Reasons
1. [tex]\overline{QP}[/tex] ≅ [tex]\overline{RS}[/tex] 1. Given
2. [tex]\overline{QP}[/tex] ║ [tex]\overline{RS}[/tex] [tex]{}[/tex] 2. Given
3. ∠PRQ ≅ ∠RPS [tex]{}[/tex] 3. Alt. int. angles theorem
∠QPR ≅ ∠PRS [tex]{}[/tex]
4. ∠PRQ = ∠RPS [tex]{}[/tex] 4. Definition of congruency
∠QPR = ∠PRS
5. ∠QRS = ∠PRQ + ∠PRS [tex]{}[/tex] 5. Angle addition postulate
∠QPS = ∠QPR + ∠RPS
6. ∠PRQ + ∠PRS = ∠QPR + ∠RPS [tex]{}[/tex] 6. Substitution property
7. ∠QRP = ∠QPS [tex]{}[/tex] 7. Transitive property
8. [tex]\overline{PR}[/tex] ≅ [tex]\overline{PR}[/tex] [tex]{}[/tex] [tex]{}[/tex] 8. Reflexive property
9. ΔQRP ≅ ΔSPR [tex]{}[/tex] 9. ASA congruency rule
10. ∠PQR ≅ ∠PSR [tex]{}[/tex] 10. CPCTC
11. ∠PQR = ∠PSR [tex]{}[/tex] 11. Definition of congruency
12. QRSP is a parallelogram [tex]{}[/tex] 12. Parallelogram opp. int. ∠s theorem
13. [tex]\overline{QR}[/tex] ║ [tex]\overline{PS}[/tex] [tex]{}[/tex] 13. Properties of a parallelogram
What is a parallelogram?A parallelogram is a quadrilateral that has opposite parallel sides.
The details of the reasons used to prove that the segment [tex]\overline{QR}[/tex] is parallel to segment [tex]\overline{PS}[/tex] are as follows;
Alt. int. angles theorem
The alternate interior angles theorem states that the alternate interior angles formed between two parallel lines and their common transversal are congruent
Definition of congruency
Two geometric figures are congruent if they have the same measurements.
Angle addition postulate
The angle addition postulate states that the measure of an angle ∠A, which is formed by two adjacent angles ∠B and ∠C, is the same as the sum of the measures of the two angles, ∠A = ∠B + ∠C
Substitution property
The substitution property of equality states that if a variable, a = another variable, b, a = b, then b can be plugged into expressions and equations to substitute for a and the values of the expressions and sides of equations remain the same.
Transitive property
The transitive property of equality states that if a = b, and b = c, then a = c
Reflexive property
The reflexive property of congruency states that a geometric figure is congruent to its self
ASA congruency rule
The Angle-Side-Angle congruency rule states that if two angles and the included side of one triangle are congruent to the two angles and included side of another triangle, then the two triangles are congruent.
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent
Parallelogram opp. int. ∠s theorem
The parallelogram opposite interior angles theorem states that the opposite interior angles of a parallelogram are congruent.
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Calculate the quotient and enter it below.
19 ÷ (-1)
Answer here
Answer:
-19
Step-by-step explanation:
Use a calculator
Can you help me thank you
Answer:
A.) [tex]\frac{1}{5^6}[/tex]
Step-by-step explanation:
To simplify [tex](5^2)^3[/tex], use the exponent rule that states [tex](a^m)^n=a^{mn}[/tex]
So,
[tex](5^2)^3=5^{2*3}=5^6[/tex]
Use the same exponent rule to begin simplifying [tex](5^4)^{-3}[/tex]:
[tex](5^4)^{-3}=5^{4*(-3)}=5^{-12}[/tex]
To further simplify [tex]5^{-12}[/tex], use the exponent rule that states [tex]a^{-m}=\frac{1}{a^m}[/tex]
So,
[tex]5^{-12}=\frac{1}{5^{12}}[/tex]
Then multiply the two new expressions as indicated in the original problem:
[tex](5^6)(\frac{1}{5^{12}})=\frac{5^6}{5^12}=\frac{1}{5^6}[/tex]
Alternatively, you could use the exponent rule that states [tex]a^m*a^n=a^{m+n}[/tex]
where
[tex]a^m=5^6\\a^n=5^{-12}[/tex]
So,
[tex](5^6)(5^{-12})=5^{6+(-12)}=5^{-6}=\frac{1}{5^6}[/tex]
The stereo normally priced at $299 is on sale for 15%off. Find the discount and the sale price.
Answer: Sale price: $254.15 , Discount: $44.85
Step-by-step explanation:
15% off indicates that the stereo will now cost 85% of what it did originally:
$299(100% – 15%) = $299(85%)
Decimalizing the percentage results in = $299(0.85) = $254.15
Discount= $299 - $254.15 = 44.85
A man is running through a train tunnel. When he is 2/5 of the way through, he hears a train that is approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or runs back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in mph, is he running?
Answer:
12
Step-by-step explanation:
He is running 12
Write a recursive formula for an, the nth term of the sequence 16,-8,4
Answer: If a1 = 16 and a2 = -8, then we can write a recursive formula for the nth term of the sequence as follows:
an = a(n-1)/2
This formula states that the nth term of the sequence is equal to the previous term (n-1) divided by 2. For example, if n = 3, then a3 = a(3-1)/2 = a2/-8/2 = 4.
We can also write this formula in terms of the initial values of the sequence as follows:
a(n) = (-1)^(n-1) * 8
This formula states that the nth term of the sequence is equal to (-1) raised to the power of (n-1), multiplied by 8. This formula will always give the correct value for the nth term of the sequence, regardless of the initial values of the sequence.
A line passes through the point (3, 7) and has a slope of 4.
Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
4y=3x+7
divide both sides by 4
y= 0.75x+1.75
or in fraction
y=3/4x+7/4
£11000 is invested in an account paying 2.25% per annum. How much will interest will be in the account at the end of 4 years?
Answer:
£990
Step-by-step explanation:
£11000 * 2.25% * 4 = £990
Please answer this question
The inequality model of given problem is |5x-4|≤80.
What is inequality model?In mathematics, an inequality is a connection between two expressions or values that are not equal to each other. In mathematics, an inequality depicts the connection between two non-equal values in an algebraic expression. Inequality signs can indicate that one of the two variables is larger than, greater than or equal to, less than, or less than or equal to another value. An inequality is a mathematical connection between two expressions that is represented by one of the following symbols:: "less than or equal to": "less than": "not equal to"
Here,
The provided problem's inequality model is |5x-4|≤80.
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Literal Equations
help asap !!
Answer:
Step-by-step explanation:
2a + 4b = 12c
4b = 12c - 2a
b = 3c - 1/2a
or
b = (6c - a)/2
Suppose DF=34, AC=36, and BC=72
I already got AB and BE I just need DE
2. The Linton family has a circular swimming pool. The radius of the pool is 15 feet_
circumference of the pool? Use 3.17 for
The required circumference of the pool is given as 95.1 feet.
What is the perimeter?Perimeter is the measure of the figure on its circumference. where the circumference of the circle is given as 2πr.
Here,
The Linton family has a swimming pool as of the circular profile.
The radius of the circular swimming pool is 15 feet
π = 3.17
Now,
Circumference of the swimming pool is given as,
= 2πr
Substitute the value in the above formula,
Circumference of the swimming pool = 2 × 3.17 × 15
= 95.1 feet.
Thus, the circumference is 95.1 feet.
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According to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. How many of those households owned a pet? Round to the nearest whole number.
If according to the American Veterinary Medicine Association, 72% of households in Wyoming owned a pet in 2018. There were 278,595 households in Wyoming in 2018. The number of those households that owned a pet is: 200,588.
How to find the number of household who owned a pet?We would be making use of the given data to find the number of household that owned a pet.
Using this formula
Number of household with pet = Percentage of household × Number of household
Let plug in the formula
Number of household with pet = 72% × 278,595
Number of household with pet = 200,588 household
Therefore the Number of household with pet is 200,588.
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Solve the following compound inequality. 5x+7<-3 or 3x-4>11
Answer:
X <-2 or X > 5
Step-by-step explanation:
Find the slope of the line y=14x–1.
Write your answer as an integer or as a simplified proper or improper fraction.
The slope of the line y = 14x – 1 is 14.
To find the slope of a line, we need to know two points on the line. We can choose any two points, as long as they are not the same. For example, we can choose the points (0, -1) and (1, 13):
y = 14x – 1
y = 14(0) – 1 = -1 when x = 0
y = 14(1) – 1 = 13 when x = 1
The slope of the line is the change in y divided by the change in x between these two points. In this case, the change in y is 13 – (-1) = 14, and the change in x is 1 – 0 = 1. Therefore, the slope of the line is 14/1 = 14.
We can also write the slope as a simplified fraction. In this case, 14 is already a simplified fraction, so we don't need to simplify further. Therefore, the slope of the line y = 14x – 1 is 14.
2x + 3 (4x - 3) = 8 - 3x
Answer:
the value of x is 1
Step-by-step explanation:
2x+3(4x-3)=8-3x
2x+12x-9=8-3x
2x+12x+3x=8+9
17x=17
17x/17=17/17.......... divide both side by 17 to get the value of x
x=1......so, the value of x is 1
What is the quotient? 8^2-81/(x-3)(x-9)
The quotient of the given division is (x + 9).
What is synthetic division?
Synthetic division is a technique for performing manual Euclidean division of polynomials in algebra that requires less writing and calculation than long division. Although it is typically taught for division by monic linear polynomials, the technique can be applied to division by any polynomial.
Given: x^2 - 81 / (x - 9)
We have to find the quotient for the given division.
We can find the quotient using synthetic division.
x + 9
[tex]\sqrt[x-9]{x^2-81}[/tex]
- x^2 - 9x
_______________
9x - 81
- 9x - 81
_____________
0
Hence, the quotient of the given division is (x + 9).
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please help me. thanks.
The angles which makes 45° and 90° in square are shown below.
What is square?The square is a 4 sided figure, each side of the square is equal and make a right angle.
The area of square having sided a unit can be given by a² square unit.
Given that,
ABCD is a square,
The angles which are 45°,
∠ CAD, ∠ CAB, ∠ DBA, ∠ DBC, ∠ ACB, ∠ ACD, ∠ BDA, ∠ BDC
The angle which are 90°,
∠ DAB, ∠ ABC, ∠ BCD, ∠ ADC
And central angles also make 90°,
∠ AEB, ∠ BEC, ∠ CED, ∠ DEA
In square there is no angle that neither makes 45° nor 90°.
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Angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and
∠ABC = ∠AED = 90° respectively.
What is a square?Square is a polygon which has 4 sides. All four sides of square are equal length and perpendicular to each other that means the angle between two adjacent side is 90°.
Given that ABCD is a square surface. And diagonal of square creates two isosceles triangles.
So the ∠ABC = ∠BCD = ∠CDA = DAB = 90°
Here, BD and AC are two diagonals of a square ABCD and E is the intersection point of diagonals.
Diagonals cut each other perpendicular.
So, ∠AED = 90° and ∠EAD = ∠EDA = 45°
Now to find ∠BAC;
we have ∠ABC = 90° so from the property of isosceles triangle
∠BAC = ∠BCA = 45°
In isosceles triangle BCD,
∠BCD = 90° and ∠DBC = ∠BDC = 45°
Therefore, the angles categorized in 45° and 90° are ∠DBC = ∠BDC =∠BAC = 45° and ∠ABC = ∠AED = 90° respectively.
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regarding antipoverty programs intended to supplement family income, One adjustment that can be made is to gradually reduce benefits as incomes rise. However, the more gradual the phase-out of benefits, the _____ the burden on taxpayers.
Safety net policies like food assistance, housing assistance, and family tax credits keep millions of Americans from poverty each year and reduce hardship for millions more.
What are some examples of policies that have been created to address poverty in the United States?The interaction of labor supply and demand on the market determines wage rates. The business will hire as much labor as its marginal labor cost equals its marginal labor revenue output.The interaction of labor supply and demand on the market determines wage rates. The business will hire as much labor as its marginal labor cost equals its marginal labor revenue output. The definition of a wage rate is the amount paid to employees. It is one of the major topics covered in human resource studies. It depends on two things: either the amount of production hours or productivity at work. This field of research is called wage rate economics. Wage rates quantify the fundamental compensation for each unit of output or of time.Contrarily, in a wage system, a person is paid according to the current wage rate, which is subject to change.To learn more about demand refer to:
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Please help! Find the measure of angle 1in the rhombus
Answer:
21°
Step-by-step explanation:
Please help me!
Thank you
The required measures of the angle are given as,
∠JKL = 72° ∠MLK = 108° ∠JMK = 36°
∠MJL = 54° ∠KNL = 90°
Given that.
The measure of the rhombus is given, we have to determine the measure of the angles,
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as angle.
Here,
∠JKL= 2 × ∠JKM = 72°
∠MLK = 180 - 2 × ∠JKM = 108°
∠JMK = ∠JKM = 36°
∠MJL = ∠MLK/2 = 54°
The diagonal of the rhombus bisect each other at an angle of 90°
So,
∠KNL = 90°
Thus, all the measure of the angles is shown above.
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an experienced bricklayer can build a small wall in 3 hours. her apprentice can complete the job in 6 hours. find how long it takes if they work together.
For both the experienced bricklayer and her apprentice working together it will take 2 hours to complete the work.
This is type of combined rate or time and work problem. Here, the experienced bricklayer takes 3 hours and apprentice take 6 hours to complete the job. So the experienced bricklayer completes 1/3rd of work in an hour and her apprentice completes 1/6th of work in an hour.
Let us consider they would take x hours to complete the work together. The work done is the summation of product of time taken by each person to do the work and the rate of work done by each person.
x (1/3 + 1/6) = 1
x = 1/(1/3 + 1/6)
=18/9
=2
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A condo is listed for $230,000. After a year, It’s marked down to $200,000. What was the percent change?
Answer:
13.0434782609%
Step-by-step explanation:
200000 - 230000
-----------
230000
x 100% = 13.0434782609% - 100 = 86.9565217
86.9565217 x 230,000 = 200,000