If the coordinates of two points are (x_1,y_1) and (x_2,y_2), the distance between them is given by the formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute for the coordinates: (-12,1) and (12,-1):
[tex]\begin{gathered} d=\sqrt[]{(12-(-12))^2+(-1-1)^2} \\ =\sqrt[]{(12+12)^2+(-2)^2} \\ =\sqrt[]{(24)^2+4} \\ =\sqrt[]{576+4} \\ =\sqrt[]{580} \\ =2\cdot\sqrt[]{145} \\ \approx24.08318916\ldots \end{gathered}[/tex]Therefore, the distance between (-12,1) and (12,-1) is approximately 24.08.
Translate the sentence into an EQUATION
Answer:
4c+8 = 2
Step-by-step explanation:
Making an equation
Eight more than ( than means it comes after the next part)
the product of a number and 4 (Product means multiply)
4c
Eight more than (more than means add)
4c+8
is equal to 2 means equals
4c+8 = 2
Simplify the following expressions (10)
The given expression is,
[tex](3y^2-1)(2y^2-5y+8)[/tex]Using distributive property( A (B+C)=AB+BC),
[tex](3y^2-1)(2y^2-5y+8)=3y^2(2y^2-5y+8)-1(2y^2-5y+8)[/tex]Again using distributive property in RHS of above equation,
[tex]\begin{gathered} (3y^2-1)(2y^2-5y+8)=3y^2\times2y^2+3y^2\times(-5y)+3y^2\times8)-2y^2+5y-8 \\ (As\text{ }x^ax^b=x^{a+b}) \\ =6y^4-15y^3+24y^2-2y^2+5y-8 \\ =6y^4-15y^3+22y^2+5y-8 \end{gathered}[/tex]Therefore, the simplified expression is,
[tex]6y^4-15y^3+22y^2+5y-8[/tex]Need help answering this
Let's multiply the following polynomial:
[tex]\text{ \lparen5x}^2\text{ + y\rparen\lparen x}^2\text{ -2y\rparen}[/tex]We get,
[tex]\text{ \lparen5x}^2\text{ + y\rparen\lparen x}^2\text{ - 2y\rparen= \lparen5x}^2)(\text{x}^2)\text{ + \lparen5x}^2)(-\text{2y\rparen+ \lparen y\rparen\lparen x}^2)\text{ + \lparen y\rparen\lparen-2y\rparen}[/tex][tex]\text{ = 5x}^4\text{ - 10x}^2y\text{ + x}^2y\text{ - 2y}^2[/tex][tex]\text{ = 5x}^4\text{ - 9x}^2y\text{ - 2y}^2[/tex]If the inequality y < 3x – 4 is graphed in the xy - plane above, which quadrant contains no solutions to the inequality? (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Q8uadrant IV
Answer:
T
(B) Quadrant II
xplanation:
Firstly, let us plot the graph of the inequality;
[tex]y<3x-4[/tex]We can plot the graph as:
From the graph of the inequality, we can see that the solution to the inequality are only contained in the Quadrant I, Quadrant III and Quadrant IV. So, And the is no solution in the Quadrant II.
Therefore, the Quadrant that contains no solutions to the inequality is Quadrant II
What is the value of the expression? (−52)2+3^3/4
Answer:
If [tex]3^\frac{3}{4}[/tex] , ≈ -101.7205
If [tex]\frac{3^3}{4}[/tex] , = -389/4
Step-by-step explanation:
If [tex]3^\frac{3}{4}[/tex] :
[tex](-52)2+3^{\frac{3}{4} } =[/tex]
[tex]-104+\sqrt[4]{3^{3} }=-104+\sqrt[4]{27}=-101.7205[/tex]
If [tex]\frac{3^3}{4}[/tex] :
[tex](-52)2+ \frac{3^3}{4} =[/tex]
[tex]-104+\frac{27}{4} =-\frac{416}{4}+\frac{27}{4} =-\frac{389}{4}[/tex]
Question 5 (5 points)
What is the value of b?
3(b + 4) + 5b = 44
11
4
2
9
Answer:
4
Step-by-step explanation:
[tex]3(b+4)+5b=44 \\ \\ 3b+12+5b=44 \\ \\ 8b+12=44 \\ \\ 8b=32 \\ \\ b=4[/tex]
please help me please
Observe that the sequence increases by adding three units. It's an arithmetic sequence.
Let's use the arithmetic sequence formula.
[tex]f(n)_{}=f(1)_{}+(n-1)d[/tex]Where, f(1) = 7, d = 3. Let's replace these values.
[tex]\begin{gathered} f(n)=7+(n-1)\cdot3 \\ f(n)=7+3n-3 \\ f(n)=3n+4 \end{gathered}[/tex]Hence, the answer is D.What is the solution of 2 + 2 =
Solve for a
6s + 50s - 60 = 5428
Answer:
s= 98
Step-by-step explanation:
Answer: s=98
Step-by-step explanation: 6s+50s-60=5428
Combine like terms: 56s-60=5428
Move -60 to the other side: 56s=5488
Divide: 5488/56 =98
s=98
Simplify the expression: −(1/5)^−2.
Answer:
-(1/5)^-2
-5²
-25
Step-by-step explanation:
.....
Solve the equation for y. 5x + y = 9
Isolate y.
5x + y = 9
5x + y - 5x = 9 - 5x
y = 9 - 5x
5. Solve: x² – 3x – 18 = 0a. x= -6, x= 3b. X = 6, X = -3c. X = -9, x = 2d. x = 9, X = -2
Write out the equation
[tex]undefined[/tex]Fill in the blank with a value so that the solution will be as indicated. Each blank can be a different value. Then explain how you know.
Considering the given systems of equations, the expressions to obtain the desired results are filled as follows:
No solution: -2x + 5 + 11x = 9x + 6. (11 and 6 fill the blanks). One solution: -2x + 5 + 8x = 9x + 6. (8 and 6 fill the blanks). Infinitely many solutions: -2x + 5 + 11x = 9x + 5. (11 and 5 fill the blanks). When does a system of equations has no solution?A system of equations will have no solution if it can be written in the following format:
0x = constant different of 0.
Hence:
-2x + 5 + 11x = 9x + 6(the final number can be any number different of 5)
As:
9x + 5 = 9x + 6
0x = 1 -> division by 0 does not exist, hence no solution.
When does a system of equations has one solution?A system of equations will have one solution if it can be written in the following format:
cx = d, c different of 0.
Hence:
-2x + 5 + 8x = 9x + 6(the final number on the left side can be any number different of 11)
6x + 5 = 9x + 6
-3x = 1
x = -1/3 (lone solution).
When does a system of equations has infinitely many solutions?A system of equations will have infinitely many solutions if it can be written in the following format:
0x = 0.
Hence:
-2x + 5 + 11x = 9x + 5
9x + 5 = 9x + 5
0x = 0 (0/0 results in any value).
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The house that David bills for his cat cat is a cube with an edge length of 4 ft to how to use the volume formula V equals x exponent 3 find the volume of the house
The volume of house built by David for cat is 64 ft³.
Firstly representing the mentioned statement about volume as mathematical expression. Exponent is the power of variable or constant. So, volume = x³, where x is the edge length.
As the edge length of house of car is given, we will keep the value in formula to find the volume of house.
V = 4³
Taking cube of the value on Right Hand Side of the equation
V = 4×4×4
Performing multiplication on Right Hand Side of the equation
V = 64 ft³
Thus, the volume of the house of cat is 64 ft³.
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Harry puts money into an account which pays 6% compound interest per year. If he puts £23000 in the account for 5 years how much more interest will he earn altogether?
The interest that Harry will earn altogether if he puts £23000 in the account for 5 years is £386,538,000.
Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. For an amount, compound interest is computed using both the principal and accrued interest. This is the primary difference between compound and simple interest.
Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
In mathematics, compound interest is frequently referred to as C.I.
It is possible to compute interest using both the initial principle and interest that has accumulated over time.
Compound interest is calculated mathematically as Amount - Principal, where
Amount = Principal*(1 + (r/n))t, where r is the rate of interest, n is the number of times interest is compounded annually, and t is the number of years, and Principal is the initial amount deposited.
Given, Principal = £23000
Rate of interest = 6%
Number of times interest is compounded per year = 1
Number of years = 5
Using above literature, Amount = 23000(1 + (6/1))^5 = 23000*16807 = £ 386,561,000.
Thus, Compound Interest = £386,561,000 - £23000 = £386,538,000.
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an item is 65$ and is 20% off what is the new price
Answer: $52
Step-by-step explanation:
Answer:
$52
Step-by-step explanation:
1/2 + P = -3 help I can’t figure this out and I don’t know how to do it
Answer:
p = -3 1/2
Step-by-step explanation:
1/2 - 1/2 + P = -3 - 1/2
-3 - 1/2 would be -3 1/2
So,
p = -3 1/2
Answer:
P= -3.5
Step-by-step explanation:
1/2+P=-3
move 1/2 over
P=-3-1/2
simplify
P=-6/2-1/2
P=-7/2=-3.5=-3 1/2
Recall the Pythagorean theorem, , where a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse. Apply the Pythagorean theorem to right triangle . Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar. By counting square units, the length of side is 8 units, and the length of side is units. By the Pythagorean theorem, the length of the hypotenuse, side , is units.
Supposing that the other square has a length of 6 units, applying the Pythagorean Theorem, it is found that:
The length of the hypotenuse side is of 10 units.
What is the Pythagorean Theorem?The Pythagorean Theorem is a geometry axiom that relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In the context of this problem, we have that the legs have lengths defined as follows:
One leg is of 6 units.The other leg is of 8 units.Hence the length of the hypotenuse can be found as follows:
h² = 6² + 8²
h² = 36 + 64
h² = 100
h = sqrt(100)
h = 10 units.
What is the missing information?
This problem is incomplete and could not be found on any search engine, hence we are going to suppose that the other leg of the triangle has a length of 6 units.
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what does B equal???
Answer:b = 2
Step-by-step explanation:
Hello, I need some assistance with this homework question please for precalculusHW Q37
Given the function, we are asked to find a graph that is symmetric about the y-axis.
Explanation
Functions can be symmetrical about the y-axis, which means that if we reflect their graph, about the y-axis we will get the same graph. In the above question, the answer is
Answer:
[tex]y=|x|[/tex]Let u = (1, −1, 3, 5) and v = (2, 1, 0, −3). Find scalars a and
b so that au + bv = (1, −4, 9, 18).
The value of the scalars a = 3 , and b = -1 .
In the question ,
it is given that
u = (1, −1, 3, 5) and v = (2, 1, 0, −3)
and the equation au + bv = (1, −4, 9, 18)
Substituting the first value of u that is u=1 and substituting the first value of v that is v=2 ,
we get a+2b=1 ....(i)
Now , Substituting the second value of u that is u= -1 and substituting the second value of v that is v=1 ,
we get -a+b= -4 ...(ii)
Solving the equations (i) and (ii)
Adding both the equations we get
a-a+2b+b=1-4
3b= -3
b= -1
a+2b=1
put b= -1
a+2(-1)=1
a-2=1
a=3.
Therefore , the value of the scalars a = 3 , and b = -1 .
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Information is given about a polynomial f(x)
whose coefficients are real numbers. Find the
remaining zeros of f.
Degree 4; zeros: i, - 6+ i
The remaining zero(s) of fis(are)
(Use a comma to separate answers
as needed.)
Answer:
Step-by-step explanation:
If 1/2 p = -5, then the value of p is
(a)-10
b) 10 c) 0 d) 2
Answer:
a
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] p = - 5 ( multiply both sides by 2 to clear the fraction )
p = 2 × - 5 = - 10
Answer: a -10
Step-by-step explanation:
[tex]\frac{1}{2} *\frac{-10}{1}[/tex]
-10 divided by 2 is -5
answer the unknown Angles
Answer:
p=45°, q=45°, s=112.5°
Step-by-step explanation:
Because the triangle is an isosceles right triangle, [tex]p=q=45^{\circ}[/tex].
In the top triangle, because of the isosceles triangle, the other two angles are each 67.5°.
Therefore, because angles that add to form a straight angle add to 180°, s=112.5°.
Can you please help me, I'm not really good at geometry, please and thank you!
Circle and Point
Option B and D are the correct answers.
Graph the polynomial function. Note x- and y-intercepts, multiplicity, and end behavior.h(x) = (x − 1)3(x + 2)2
Given:
[tex]h\left(x\right)=\left(x-1\right)^3\left(x+2\right)^2[/tex]To graph the given polynomial function, we can plug in any values of x to find values of h(x). The graph is shown below:
We also note that the x-intercept is the point on the x-axis, while the y-intercept is the point on the y-axis. Hence,
x-intercepts: (1,0), (-2,0)
y-intercept: (0,-4)
Tt can also be noted that (x − 1) occurs 3 times while (x+2) occurs 2 times. Hence, x=1 has a multiplicity 3, while x=-2 has a multiplicity 2.
aased on the graph, the end behavior would be:
[tex]as\text{ x}\rightarrow+\infty,h(x)\rightarrow+\infty,\text{ and as x}\rightarrow-\infty,h(x)\rightarrow-\infty[/tex]Question in file need this ASAP for homework
The calculation of the value 3/4 - 2/6 is 5/12.
How to calculate the fraction?It should be noted that the question relates to the subtraction of fraction. This will be illustrated as:
= 3/4 - 2/6
It should be noted that the lowest common multiple of 4 and 6 is 12. This will be illustrated as:
= 3/4 - 2/6
= 9/12 - 4/12
= 5/12
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Set up a proportion and solve.
If 4 containers of yogurt cost $2.00, find the cost of 5 containers of yogurt.
Five containers of yogurt will cost what?
Answer: $2.5 for 5 containers of yogurt
Step-by-step explanation:
To set up a proportion for this problem, we will have the 4 containers on the left with the 5 containers on the right and the container amount in the numerator with the dollar amount in the denominator. Let x be the unknown amount that we are solving for.
[tex]\dispalystyle \frac{4\text{ containers}}{\$2} =\frac{5\text{ containers}}{\$x}[/tex]
Now, we will cross-multiply and isolate the variable using inverse operations.
4 * x = 2 * 5
4x = 10
x = $2.5
Bakery has 46 batches of cupcakes each week. How many individual cupcakes do they make each week
Answer:
1,104 cupcakes
Step-by-step explanation:
46 batches, 24 cupcakes per batch.
Multiplying 46 by 24 gives 1,104 cupcakes.
yesssssssssssssssssssssss
Answer:
Yes?
Step-by-step explanation:
Did you figure out a problem and you are celebrating?