Using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
Consider the largest number as x and the smallest number as y
The sum of two numbers is 96
The equation will be
x+y = 96
x = 96-y
The difference of the two numbers 42
x-y = 42
Use the substitution method here
Substitute the value of x in the second equation
x-y =42
(96-y)-y =42
96-2y = 42
-2y = 42-96
-2y = -54
y = 27
Substitute the value of y in the first equation
x+y = 96
x+27 = 96
x = 96-27
x = 69
Hence, using the substitution method, if sum of two numbers is 96 and difference of the two numbers is 42, then the two numbers are 69 and 27
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helppppppp 20 points
C) Triangle ABC is equilateral.
E) Segment AB is the same length as segment AC because they are both radii of the same circle centered at point A.
F) Segment AB is the same length as segment BC because they are both radii of the same circle centered at point B.
What are Euclid's Axioms?Euclidean geometry, sometimes referred to as Euclid's geometry is the study of solid and flat shapes based on many axioms and theorems. The assumptions of the evident universal truths that have not been verified are known as Euclid's axioms or common conceptions.In the given figure,
A and B are the centres of the two intersecting circles.
In a circle having centre at A, we have
AC = AB = radius
In a circle having centre at B, we have
BC = BA = radius
According to Euclid's first axiom, things that are equal to the same thing are equal to one another.
Therefore, AC = AB = BC
Hence, the triangle is an equilateral triangle.
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A turkey casserole (30 servings) uses 3.75 pounds of turkey breast. To scale the recipe for 50 servings, how much turkey would be needed?
A turkey casserole (30 servings) uses 3.75 pounds of the turkey breast. To scale the recipe for 50 servings we need 6.75 pounds turkey.
What is a pound?The currency of the United Kingdom and nine of its affiliated territories is called sterling (stg; ISO code: GBP). The primary unit of sterling is the pound (sign: £), while the term "pound" is also frequently used to refer to the British pound or pound sterling in foreign settings.
The oldest currency that is still in the circulation and has been used continuously since its origin is sterling. After US dollar, the euro, and the Japanese yen, it is currently the fourth most traded currency on the foreign exchange market. It makes up basket of currencies used to determine the value of IMF special drawing rights along with other three currencies and the renminbi. Midway through 2021, sterling is also fourth most-held reserve currency in global reserves.
if 30 servings uses = 3.75 pounds
then, 1 serving = 3.75 pounds/ 30
50 servings = [tex]\frac{3.75}{30} * 50[/tex]= 6.25 pounds
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Two more than the quotient of a number and 4 is equal to 9.
The condition "two more than the quotient of a number and 4 is equal to 9" gives the number 28.
What is defined as the term division?Each component of a division equation has its own name.
Dividend: A dividend would be the number divided during the division process.Divisor: The divisor is the number through which the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Dividend = Divisor x Quotient + Remainder
For the given problem;
Two more than the quotient of a number and 4 is equal to 9.
Let the number be n;
n/4 + 2 = 9
Simplifying;
n/4 = 9 - 2
n/4 = 7
n = 7×4
n = 28
Thus, the value of the number is found as 28.
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18. Given J(x. -8) and K(-1,-5) and the graph
of line / below, find the value of x so that
JK \\1.
answer: solutions is x = - 2
11) Increase 763.685 by 0.1
Answer: its 243
Step-by-step explanation:
If I have .81 gallon and I have 2.41 gallon what is the ratio between the two
Answer:
[tex]\frac{81}{241}[/tex]
Step-by-step explanation:
multiply both numbers by 100. 241 is prime so you cannot reduce it further.
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of -2,-1, and 5, and a y-intercept of -10.
Answer:
y = x³ -2x² -13x -10
Step-by-step explanation:
You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.
Polynomial factorsA polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...
p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)
Expanding this gives ...
p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10
This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.
The polynomial function is ...
y = x³ -2x² -13x -10
Solve for x.
√x + 20 = 9
Answer:
x = 61
Step-by-step explanation:
sqrt = square root
sqrt(x + 20) = 9 square both sides to cancel out sqrt
x + 20 = 81 subtract 20 to get x alone
x = 61
Find the x-and y-intercepts of the line:3x - 4y = 12A.x-int: (-4,0)y-int: (0,3)B. x-int: (4,0)y-int: (0, -3)C. x-int: (0,4)y-int:(-3,0)D. x-int: (0,-4)y-int: (3,0)
To find the x-intercept, simply but y=0 in the equation given and solve for x
That is;
3x - 4y = 12
3x - 4(0) = 12
3x = 12
Divide both-side of the equation by 3
x= 4
The x-intercept is;
(4, 0)
To find the y-intercept, simply put y=0 in the equation given and then solve for y
That is;
3x - 4y = 12
3(0) - 4y = 12
-4y = 12
Divide both-side of the equation by -4
y = -3
The y-intercept is (0, -3)
Hence, the correct option is B.
x-int: (4,0)
y-int: (0, -3)
You reflect the triangle below over the x-axis.
The coordinates of P' are ( , )
Answer:
P' (- 5, 3 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x , - y ) , then
P (- 5, - 3 ) → P' (- 5, 3 )
Distribute the following perfect square: 6x(8x - 9y)² = ?
Answer:
384x² - 486xy²
Step-by-step explanation:
I think this is the answer all I did us first i solved the brackets then I multiplied them by 6x
A small publishing company Is planning to publish a new book. The production costs will Include one-time fixed costs (such as editing) and varlable costs (such as printing). The one-time fixed costs will total $49,590. The varlable costs will be $9.25 per book. The publisher will sell the finished product to bookstores at a price of $20.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
4408 books must to be produced so that production costs is equal to sales money.
What is production cost?
Production costs refers to the direct and indirect costs that come from manufacturing a product. Production costs usually include expenses, such as labor, raw materials and manufacturing supplies. Cost of products sold are the production costs incurred on goods that is actually sold in a certain specified period
Let the no. of books= X
Cost = 9.25X + 49590
revenue = 20.50X
20.50X = 9.25X+ 49590
20.50X - 9.25X = 49590
11.25X = 49590
X = 4408
4408 books must to be produced so that production costs is equal to sales money
We can Check by:
cost = 9.25(4408) + 49590
= 40774+ 49590
cost = 90364
revenue = 20.5(4408)
revenue = 90364
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????????????????????
Answer:
536
Explanation:
rom the given table:
If an individual and spouse enroll in the low deductible plan, the monthly premium will be $536.
Fill in the blanks below.
Find the slope of the line passing through the points (6, 4) and (6, -7).
slope:
Find the slope of the line passing through the points (-9,-5) and (-9, 5).
slope:
The entered points (6,4) and (6,-7) belong to a vertical line, There is no slope and The entered points (-9,-5) and (-9,5)belong to a vertical line. There is no slope.
How to find slope of the coordinates ?The slope, which is essentially how slanted a line is, might be positive, negative, zero, or both (x1,y1) and (x2,y2). The slope equation is (y2 - y1) / (x2 - x1). A vertical line is formed by the points entered. Nothing slopes.Formula: x = 6.
Angle (θ)=90°
Location (d) = 11
(x)=0 Distance between x's
d = (y2 + x2) = (-112 + 02) = 121 = 11 is the distance between y's (y)=11.
A vertical line is formed by the points entered. Nothing slopes.Formula: x = -9.
Location (d) = 10
(x)=0 Distance between x's
Distance between y's (d) = y2 + x2 = 102 + 02 = 100 = 10
A vertical line, on the other hand, will have an ill-defined slope since the x-coordinates are constant. As a result, there will be a division-by-zero error when using the formula.To more learn about coordinates refers to:
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15x=75Write which property of equality you used.
1) Given this equality,
15x = 75 Divide both sides by 15
x=5
2) Then we can write that since x = 5 and 15x = 75 we have here is the Division Property of Equality.
Because in this case, we divided both sides by 15, which is different from zero to find equivalent equality.
3) So
Given F(x) 3x^2+1, G(x) = 2x - 3, H(x) = xF(G(x))
Given
[tex]f(x)=3x^2+1,g(x)=2x-3,h(x)=x[/tex]Answer
[tex]\begin{gathered} f(g(x))=f(2x-3) \\ =3(2x-3)^2+1 \\ =3(4x^2+9-12x)+1 \\ =12x^2+18-36x+1 \\ =12x^2-36x+19 \end{gathered}[/tex]What is the value of x in the equation x^2 + 2 = 0
Answer:
[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]
- At this point, we can't operate the square root. Let's introduce the imaginary part of a value
From complex numbers;
[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]
Therefore;
[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]
Which of the following is the graph of (g-f)(x)?
The graph (g-f)(x)=-4x complies with the query.
Graph example: What is it?An edge denotes the connection between the x and y vertices and is represented by the pair (x ,y). In the examples that follow, circles stand in for vertices and lines for edges.
The graph indicates that line generated by function f(x) passes through the points (1,-3) and (0,0) and that line similarly passes through the points (1,1) and (0,0).
With the use of the formula Y-Y1 = y2-y1/x2-x1, we can thus determine the equation of the lines (x-x2)
Therefore, the equation of the line produced by the function f(x) y+3= 3-0/0-1 (x-1)
Function f(x) Equals 3x since y+3=-3x+3 y=-3x.
the line drawn by the function g(x) has the equation y=x, hence function g(x)=x.
We now need to figure out, (g-f) (x) = g(x)- f(x) = -3x-x = -4x
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PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
It should be emphasized that a relationship is proportional if its graph is a line that passes through its origin.
How should the information be illustrated?
If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to do this, the ratio is not proportional. The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a relationship is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional. Additionally, if anything is not linear, it is not proportionate.
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A sample of ore is found to be 0.0094 % silver and 0.037 % copper. What is the percentage of matter in the ore that is
neither silver nor copper? Round your answer to the nearest ten thousandth.
The proportion of the ore's composition that is neither silver nor copper is 99.9536 %.
What is percentage ?
Percentage , which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
The ore is found to be 0.0094 % silver and 0.037 % copper.
The percentage of matter in the ore that is
neither silver nor copper is = 100% - 0.0094 % - 0.037 %
= 99.9536 %
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The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet. a. solve the formula for d. b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet
A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variableGiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
(a) We get,
P/64 = 64d/64
d = P/ 64
(b) P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient,
d = 10. 5 ft.
The value is 10.5 feet .
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. The depth of a submerged object if the pressure is 672 pounds per square foot is 10. 5 feet.
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The polynomial passes through the
X-intercepts of (-5, 0), (-3, 0), and (1, 0). The end behavior of the graph is down, up.
Finally, it passes through the point of (3, 14).
The equation of the polynomial is P(x) = 6.86(x + 5) (x + 3) (x - 1)
Given,
x intercepts which the polynomial passes though = (-5, 0), (-3, 0), and (1, 0).
Point = (3, 14).
We have to find the polynomial equation;
A polynomial is defined as;-
P(x) = a(x - c₁) (x - c₂)....(x - cₙ)
Here,
a is a constant
c₁, c₂,...cₙ are the zeros of the polynomial
Here,
-5, -3 and 1 are the zeros of the given polynomial
(x + 5), (x + 3) and (x - 1) are the factors of the given polynomial.
Then the equation of polynomial be like;
P(x) = a(x + 5) (x + 3) (x - 1)
This polynomial passes through point (3, 14)
That is,
14 = a(3 + 5) (3 + 3) (3 - 1)
14 = a x 8 x 6 x 2
14 = 96a
a = 96/14
a = 6.86
Substitute this in equation of polynomial;
That is,
P(x) = 6.86(x + 5) (x + 3) (x - 1)
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ms. smith sharpened 135 pencils. her students used 88 of them how many sharpened pencils does Ms. smith have left.
Answer: 47
Step-by-step explanation:
x + 9.27 = 21
I need help answer this questions
Answer:
x = 11.73 is what i got
Step-by-step explanation:
Plot (−3 1/2, −1 1/4) on the coordinate plane.
The point is located at 3 1/2 points to the left of the origin and 1 1/4 points below the origin
How to plot the point on a coordinate plane?The coordinate of the point on a coordinate plane is given as
Point = (-3 1/2, -1 1/4)
Rewrite the above coordinate as follows:
(x, y) = (-3 1/2, -1 1/4)
Split the coordinates into x and y coordinates
So, we have the following equations
x = -3 1/2
y = -1 1/4
The above means that:
(-3 1/2, -1 1/4) is located at 3 1/2 points to the left of the origin (-3 1/2, -1 1/4) is located 1 1/4 points below the originNext, we plot the points
See attachment for the plot of the points on a coordinate plane
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Order the function from the least steep slope to the steepest slope.
y=2x-3
y = 4x+0.5
y=-2x+3
y=x+42
y=-0.5x+7
How are the given functions ordered based on their slopes?
1. y = -2x+ 3
slope = m= -2
tanФ = -2 -----(1) Least steep slope
Ф = -63.4°
2. y= 3/4x-3
slope = m = 3/4 ------(3)
tanФ = 3/4
Ф= 36.9°
3. y= 4x+0.5
slope = m = 4 ------(5) Steepest
tanФ = 4
Ф = 75.9°
4. y= x+42
slope = m= 1 ------(4)
tanФ= 1
Ф= 45°
5. y = - 0.5x+ 7
slop = m= -0.5 -----(2)
tanФ = -0.5
Ф = -26.56°
What is a slope?
An indication of how steep a line is is its slope. Nowhere on the line there is a different slope as it is constant. The gradient may be used to refer to it.The ratio of vertical change to horizontal change between any two separate points on a line, or any two points, is used to compute slope.Indicating a steeper line is a slope with a higher absolute value.A line can have upward, downward, horizontal, or vertical directions.To learn more about steep slope, refer:
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a city planner wants to build a road perpendicular to D street. What is the slope of the new road?
The slope of the new road is zero.
How to find slope?The slope of a line is the change in y with respect to the change in x.
In other words, the slope of a line is rise over run.
Therefore, the new road the city planner wants to build is perpendicular to the the D street.
(5, 1)(5, 4)
slope of D street = 4 - 1 / 5 - 5
slope of D street = 3 / 0
slope of D street = infinity
An infinite slope is simply a vertical line. Therefore, it is only perpendicular to a horizontal line which will have a slope of 0. Hence, the new road should have a slope of 0.
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Find the value of k for which x=0 and y=8 is a solution of 3x 6y+k=0
Answer:
(-40)
Step-by-step explanation:
therefore, 3x0=0
(6x8)+k=0
40+k=0
k=0-40
k=(-40)
180
94
112
90
68
56
100
(x+18)° is vertical opposite 112° and vertical opposite angles are equal meaning
⇒(x+18)°=112°
x+18°=112°
x=112°-18°
∴x=94°
(2y)° is in a straight line with 112° meaning their sum is 180°
[tex]2y+112=180\\2y=180-112\\2y=68\\\frac{2y}{2} =\frac{68}{2} \\y=34[/tex]
∴y=34°
Solve for x
Your answer must be simplified
-3 < x - 10
The simplified inequality is x > 7.
What is an inequality?
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line. There are multiple notations used to denote various types of inequalities: (i)The symbol a b indicates that an is less than b. (ii)A > b indicates that an is greater than b. In either scenario, a and b are not equal. These are characterized as stringent inequalities because an is either strictly less than or strictly bigger than b. Equivalence is not allowed. In contrast to rigorous inequalities, there are two forms of non-strict inequality relations.
The given inequality -3 < x - 10
or, -3 + 10 < x
or, 7 < x
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