Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
Explain the equation.An equation is a mathematical representation of two identical variables, one on each side of a "equals" sign. Common difficulties can be solved using equations. We commonly seek pre algebra help to resolve problems in real life. Pre-algebra is the fundamental building block of mathematics.
Here,
[tex](x + 2)^{2}[/tex] / [tex]a^{2}[/tex] + [tex](y-5)^{2}[/tex] /[tex]b^{2}[/tex] -=1 is (h, k).
the ellipse's nucleus
The major axis is the larger of the two axes, which are 2a and 26.
(H, a, k) and (H, k, b) are the vertices. Vertices are those along the major axis in this case, and covertices are those along the minor axis.
[tex](x + 2)^{2}[/tex]/16 + [tex](y-5)^{2}[/tex] /20 =1
can be written as
[tex](x + 2)^{2}[/tex]/ [tex]4^{2}[/tex] + [tex](y-5)^{2}[/tex] /(2√/5)2
hence centre is (-2, 5), maor axis is 2 x 2√√5 = 4√√5 and minor axis
is 2 x 4 = 8
Vertices are ( 2,5 25), or ( 2,5 25) and ( 2,5 + 25), while covertices are ( 2 4, 5) and ( 6,5), respectively.
As a result of the presence of a vertical major axis, eccentricity e and focii are
(h, k ± be). e is given by the relation a2 = b2(1 − e2) i.e.
=> e = [tex]\sqrt{1 - \frac{a^{2} }{b^{2}} }[/tex]
a2= 16 and b2= 62
=> e = 1/√5
Focii (-2,5 ± (2√5 x 1/√5)
or (-2,5±2) i.e. (-2, 7) and (-2, 3).
Therefore , the solution of the given problem of equation comes out to be Focii (-2,5 ± (2√5 x 1/√5) and vertex ( − 2,5 ± 2√√5).
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Find the value of x.
Answer: x = 4
Step-by-step explanation:
Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.
This means that:
[tex](4x-1)=15[/tex]
Simplify and solve for x.
[tex]4x-1=15\\4x=16\\x=4[/tex]
So, x = 4
-(x - 13) = 10(x + 9)
3) At the grocery store, the bags of oranges weigh 4 1/3 pounds. How much would 2 1/2 bags of oranges weigh?
Answer:7 7/8. pounds.
Step-by-step explanation:
What is the equation of a line with the slope of 3 that goes through the
point (0,-7)?
9514 1404 393
Answer:
y = 3x -7
Step-by-step explanation:
The given point is the y-intercept, so we can write the equation in slope-intercept form.
y = mx + b . . . . . line with slope m through point (0, b)
For your slope and point, the equation is ...
y = 3x -7
write a word problem and make and explain a math drawing for 4×3/4=?
Answer:u cheating like a mfka lol
Step-by-step explanation:dwd
Solve the system of equations -x-y=-2 and 5x + 7y= 28 by combining the
equations.
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
What is equation?The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given :
=> -x-y=-2
=> 5x + 7y= 28
So ,
=>x = 2-y
thus,
=> 5(2-y) + 7y =28
=> 10 -5y + 7y =28
=> 10 -2y = 28
=> -2y = 18
=> y =-9
and
=> x = 2 - (-9)
=> x = 11
Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.
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Determine whether the relation is a function.
A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Answer:
C
Step-by-step explanation:
1 pound sand for 1 2/3 pounds gravel.
1 pound gravel for 2/5 pound cement.
3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =
= 5 pounds gravel.
5 pounds gravel = 5 × 2/5 = 2 pounds of cement
How many pounds of almonds priced $5.35 per pound should be mixed with peanuts worth $3.75 per pound in order to obtain 20 pounds of mixture that will sell for $4.50 per pound?
10.625 pounds of peanuts mixed with almonds priced $5.35 perpound
what is a pounds?Weight is measured in pounds. 16 ounces or 0.453592 kilos make up one pound.
Let's name the weight in pounds of almonds and peanuts that we need x.
We are aware that our ultimate goal is to produce 20 pounds of the mixture, which will sell for $4.50 each pound. The mixture will therefore cost 20 * $4.50, or $90, in total.
Additionally, we are aware that peanuts cost $3.75 per pound and almonds cost $5.35 per pound.
As a result, the price of the almonds we use is 5.35x, while the price of the peanuts we use is 3.75(20 - x) = 75 - 3.75x.
We may create an equation since our goal is to produce a mixture that costs $90 in total:
5.35x + (75 - 3.75x) = 90
When we simplify this equation, we get:
1.6x + 75 = 90
75 is subtracted from both sides to produced
1.6x = 15
By multiplying both sides by 1.6, we get:
x = 9.375
To create a mixture that will sell for $4.50 per pound, we must combine around 9.375 pounds of almonds with (20 - 9.375) = 10.625 pounds of peanuts
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A tourism website claims travelers can see Europe for $75 a day. If a tourist saved $1,875 for a vacation, how many days can he spend in Europe?
A train traveled 250 mi in 2 hours. If it traveled at the same rate of speed how long would it take the train to travel 600 mi
4.8
Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.
Jessie is building a cabinet door, which is pictured below. The center of the cabinet door is 12 inches by 16 inches, and the border of the cabinet door has a width of x inches. The entire cabinet door has an area of exactly 396 square inches.
Clockwise from the top, the picture reads, x, 12 inches, 16 inches, x, Figure not drawn to scale.
Write an equation in standard form that can be used to find x , the width of the border.
Answer:
[tex]x^2+14x-51=0[/tex]
Step-by-step explanation:
Since the entire cabinet door is a rectangle, its area is given by:
[tex]A=w\ell[/tex]
The center of the cabinet door measures 12 inches by 16 inches.
And the border of the cabinet door has a width of x inches.
Therefore, the total width of the cabinet door will be (12 + 2x).
Likewise, the total length of the cabinet door will be (16 + 2x).
Thus, the area of the entire cabinet door will be:
[tex]A=(2x+12)(2x+16)[/tex]
We are given that this entire area is 396 square inches. Thus:
[tex]396=(2x+12)(2x+16)[/tex]
Simplify. We can factor out a two from both of the factors on the right-hand side:
[tex]396=2(x+6)(2)(x+8)[/tex]
So:
[tex]396=4(x+6)(x+8)[/tex]
Dividing both sides by four yields:
[tex]99=(x+6)(x+8)[/tex]
Distribute the right-hand side:
[tex]x^2+14x+48=99[/tex]
Therefore, our equation in standard form is:
[tex]x^2+14x-51=0[/tex]
Edit:
We want to find the width of the board. So, we simply have to solve for x. We previously obtained:
[tex]x^2+14x-51=0[/tex]
We can factor:
[tex](x+17)(x-3)=0[/tex]
By the Zero Product Property:
[tex]x+17=0\text{ or } x-3=0[/tex]
Solve for both cases:
[tex]x=-17\text{ or } x=3[/tex]
Length/width cannot be negative. So, we can reject the first solution.
Thus, our only solution is:
[tex]x=3[/tex]
The width of the border of the cabinet door is 3 inches.
This means that the total length of the cabinet is 16 + 2(3) = 22 inches, and the total width of the cabinet is 12 + 2(3) = 18 inches.
PLEASE HELP ME ASAP NOW PLEASE
The lines with a slope larger than f(x) are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which one is the linear equation shown on the graph?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
First, you can see that the line crosses the y-axis at y = -4, so the line is something like:
y = a*x - 4
And we can see that it crosses the x-axis at x = 2, then we can write the equation:
0 = a*2 - 4
4 = a*2
4/2 = a
2 = a
So the linear equation on the graph is:
y = 2*x - 4
The slope is 2, the linear equations with a slope larger than that are:
option 4) y = (25/3)*x - 1/2
option 5) (4/5)*y - 16x = -1/2
Which can be rewritten as:
y = (5/4)*16x - (5/4)*(1/2)
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The graphs of lines a and b are shown on the coordinate
plane. Write the equation on the line provided for each line.
Then solve the system of equations using any method.
The equation of line a is.
The equation of line b is.
Solution
From the graph we got two equations of line -3x+ y -9 =0 and x+y-7 =0
and solution of these equations are x = -1/2 and y= 15/2
what is equation of line?An algebraic expression that represents a number of points which creates a line in the XY coordinate system or another coordinate plane.
What is the equation of lines shown in the graph?
we are given a graph containing two equations of line named a and b. The lines are plotted in XY coordinate system.
From the graph, we can detect two locations of point (5, 6) and (1, -6) for line a and detect two location of point (1, 6) and (6, 1) for line b.
As per the formula for equation of straight line, a line passes through two points can be written as y-y₁ = [(y₂-y₁) / (x₂-x₁)] × (x- x₁)
hence, line a can be written as (y- 6) = [(-6 -6) / (1-5)] × (x- 5)
y-6 = 3(x-5)
y-6 = 3x -15
y-3x -9 = 0
In the next, line b can be written as (y-6) = [(1-6) / (6-1)] × (x-1)
y-6 = -1(x-1)
y-6 = -x+1
x+ y -7 =0
now, we get two equations, -3x+ y -9 =0
x+ y - 7 =0
Solving these two equations by addition method, we get x= -1/2 and y = 15/2
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express a decade as a percentage of a century
Jamie has 18/5 cups of frosting she uses 2/5 cups of frosting for each cupcake how many cupcakes will Savannah be able to frost
Answer:
9
Step-by-step explanation:
18/5 ÷ 2/5 = 18/5 x 5/2 = 9
Combine the like terms to create an equivalent expression.
4r + 14 - r - 6 =
[tex]4r + 14 - r - 6[/tex]
Combine Like Terms:
[tex](4r-r)+(14-6)[/tex]
[tex]=\fbox{3r + 8}[/tex]
At a state fair, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. Describe a model that you could use to simulate randomly choosing an exhibit to visit.
Answer:
10:12:8
Step-by-step explanation:
so, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. so it would look like this 10:12:8
hello- need help on this :)
Find the surface area of the rectangular prism
Answer:
200 is your answer
Step-by-step explanation:
First, multiply:
8 × 5 × 4 = 160
Then, multiply:
4 × 5 × 2 = 40
Next, add them up.
160 + 40 = 200
Lastly, have a great day!
Please helppp can’t figure this one out. Keep getting 8.1
1. choices : never. always. sometimes
2. choices: never. always. sometimes
3.choices: variables. coefficient. exponents
4:choices: variables. coefficient. exponents
5. choices: not closed. closed
please help
The product of f(x) and g(x) is always a polynomial. By the definition of
polynomials the product of polynomials is always a polynomial because
the coefficient are real numbers and the exponents are whole
numbers. Real numbers and whole numbers are closed under addition
and subtraction.
What is Polynomial?A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.
Here f(x) and g(x) are two given polynomial,
let f(x) = x+1 ang g(x) = x-1
f(x).g(x) = (x+1)(x-1).
f(x).g(x) = x²-1.
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find an equation for the line that passes through the points (-6,-3) and (4,5).
The equation of the line that passes through the points (- 6, - 3) and (4, 5) is y = (4 / 5) · x.
How to determine the equation of the line from two points
In this question we have the knowledge of two points, of which we must derive the equation of a line, whose definition is shown below:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - y-InterceptThe slope of the line can be determined by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.First, determine the slope of the line:
m = [5 - (- 3)] / [4 - (- 6)]
m = 8 / 10
m = 4 / 5
Second, determine the intercept of the line:
b = y - m · x
b = 5 - (4 / 5) · 4
b = 5 - 5
b = 0
Third, write the equation of the line:
y = (4 / 5) · x
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What is the value of B for the following triangular prism? Remember that there are 10 millimeters in a centimeter
Answer:
B
Step-by-step explanation:
1) transform mm in cm
12 : 10 = 1,2 cm
2) find the base area
base area = (leg 1 x leg 2)/2 = (1,2 x 4,5)/2 = 2,7 cm^2
did not mean to press answer sorry
Please need help ASAP, 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed.
(1). ΔIJH ≅ ΔKHJ, by SSS criterion,
and (2) we need, ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove ΔTNS ≅ ΔUHS, by HL criterion.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
We have the triangle:
ΔIJH ≅ ΔKHJ.
To prove the congruent by SSS:
We have to show that three sides of the triangle are congruent to three sides of the other triangle.
Here,
IJ ≅ KH.
IH ≅ JH, Given.
And both triangles share the same side JH.
So,
JH ≅ JH
So, ΔIJH ≅ ΔKHJ, by SSS criterion.
ΔTNS ≅ ΔUHS.
To prove the congruent by HL:
We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.
So, we need;
ΔTNS and ΔUHS are right-triangles.
S is the mid-point.
So,
SN ≅ SH.
ST ≅ US
So, ΔTNS ≅ ΔUHS, by HL criterion.
Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;
ΔTNS and ΔUHS are right-triangles and S is the mid-point.
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What is an equation of the line that passes through the points (-3, -1) and
(-6, 3)?
Answer:
y = -3/4x -1.5
Step-by-step explanation:
-6+3 = -3
3+1 = 4
-3/4
y = -3/4x +b
3 = -3/4(-6) +b
3 = 4.5 +b
b = -1.5
y = -3/4x -1.5
Answer:
y=-4 /3x– -5
Step-by-step explanation:
mrk me brainliest
Which expression is equivalent to -3(x+4)(x-6)-(x^2+8x-10)?
Answer:-4x^2-2x+46.
Step-by-step explanation:
To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:
(-3)(x+4)(x-6)-(x^2+8x-10)
Then, you can distribute the -3 to the terms inside the first set of parentheses:
(-3x-12)(x-6)-(x^2+8x-10)
Then, you can combine like terms:
-3x^2+6x+36-x^2-8x+10
This simplifies to:
-4x^2-2x+46
Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.
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Suppose that you want to begin saving money to buy a house valued at $300,000. The bank recommends that you have a 20% down payment before it approves a loan for the remaining difference. How much money do you need to save before you will be approved for a loan? What is the remaining difference that you will need to borrow?
Answer:
$60,000 as down payment and remaining difference for loan is 300,000 - 60,000 = $240,000.
The money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000
What is a percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
What is a loan?A loan is money, property, or other material goods given to another party in exchange for future repayment of the loan value amount with interest.
Given value of the house is $300,000.
The bank recommends that you have a 20% down payment before it approves a loan i.e. is $300,000× 20% = $60,000
The remaining difference that you will need to borrow is $300,000 - $60,000= $2,40,000
Thus the money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000
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The price of premium fuel has increased from 289.7 cents per litre to 297.9 cents per litre. Calculate the percentage increase
Answer:
≈ 2.76%
Step-by-step explanation:
Price increase
297.9 - 289.7 = 8
% increase
8/289.7 * 100 = 2.7614773904%
≈ 2.76%
1. choices: m-n m+n. m x n
2. choices: two. one. m. n.
3. choices: one. two. zero
4.choices: one. two. zero.
5. choices: first and last. first. last. middle
The initial polynomial result will include several terms, but after simplification, there may only be one or two terms left.
Polynomial's will be in which form?Each polynomial must be considered to be in standard form. The initial multiplication will result in a total of m and n terms since each of the m terms of the first polynomial will be multiplied by each of the n terms of the second.
When the sum is simplified, some of those elements may be combined, resulting in a final product with only one or two terms.
1. 2 × b = 2b . . . . . each has 1 term; the result has 1 term.
2. (x -a)(x +a) = x² -ax + ax -a² (2×2=4 terms) = x² -a² . . . . the results has 2 terms.
3. (x -a)(x³ +x) = x⁴ -ax³ + x² -ax . . . the results has 2×2 = 4 terms
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