Answer:
Step-by-step explanation:
[tex]\sqrt{x} Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\sqrt{(5-3)^{2}+(6-k)^{2}}=2\sqrt{2}\\\\\sqrt{(2)^{2}+[(6)^{2}-(2*6*k)+(k)^{2}]}=2\sqrt{2}\\\\\sqrt{4+[36-12k+k^{2}]}=2\sqrt{2}\\\\\sqrt{40-12k+k^{2}}=2\sqrt{2}\\[/tex]
Take square both side
[tex]40-12k+k^{2}=(2\sqrt{2})^{2}\\\\40-12k+k^{2}=4*2\\\\40-12k+k^{2}=8\\\\k^{2}-12k+40-8=0\\\\k^{2}-12k+32=0\\[/tex]
Factorize,
Sum = -12
Product = 32
Factors = -8 , -4
k² - 8k - 4k + (-8)*(-4) = 0
k(k - 8) - 4(k - 8) = 0
(k - 8)(k - 4) = 0
k = 8 or 4
The points are (3,k) and (5,6).
Given, distance = 2√2 units
Applying distance formula,
Distance = √(x2-x1)^2 + (y2-y1)^2
2√2 = √(x2-x1)^2 + (y2-y1)^2
Squaring both sides,
(2√2)^2 = [√(x2-x1)^2 + (y2-y1)^2]^2
8 = (x2-x1)^2 + (y2-y1)^2
8 = (5-3)^2 + (6-k)^2
8 = 2^2 + (6^2 - 2x6xk + k^2)
8 = 4 + 36 - 12k + k^2
8 = 40 - 12k + k^2
= k^2 - 12k + 32 = 0
On factorising,
=> k^2 - 4k - 8k + 32 = 0
=> k(k-4) -8(k-4) = 0
=> (k-4)(k-8) = 0
=> k-4 = 0 , k-8 = 0
=> k = 4 , k = 8
(14)+(-11) plz help idk what it is
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
(14)+(-11)=3
the sum of ages of Ali and Adam is 45 years. if Ali is 5 years younger than Adam what is their ages
Answer:
Ali is 20
Adam is 25
Step-by-step explanation:
Isabelle is mixing red paint with blue paint to make purple paint. She adds of a fluid ounce of red to of a fluid ounce of blue to make fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
A.
fluid ounce
B.
fluid ounce
C.
fluid ounce
D.
fluid ounces
Answer: the correct answer will be 27/31
Step-by-step explanation:
which expression is equivalent to
Answer:
3
Step-by-step explanation:
"" = x^(0.5*(-2))*y^(-0.25*(-2))*z^(-2) = x^(-1)*y^(0.5)*z^(-2) =
(1/x^1)*y^(0.5)*(1/z^2) = 3
Answer:
Third one.
Step-by-step explanation:
The exponent negative 2 applies to all that's in the bracket. So, x^1/2 times exponent negative 2 equals x to the power negative one. And y to the power negative half and z to the power negative 2. Therefore, x^-1 = 1/x and y^1/2 remains same and z^-2 = 1/ z^2.
The base of an isosceles triangle is one and a half times the length of the other two sides. A smaller triangle has a perimeter that is half the perimeter of the first. Write an expression for the perimeter of the smaller triangle and combine like terms. What is the simplified expression?
0.75s
2.5s
1.75s
5s
Step-by-step explanation:
Isosceles means that two sides are equal.
if the base is 1½s the other two sides will be ½s and½s
thus perimeter=1½+½+½ =2½s
smaller triangle:
perimeter=½(1½s+½s+½s)
=½(2½s)
=1¼s convert to decimal
=1.75s
The simplified expression of the given situation is 1.75s.
The correct option is C.
What is an isosceles triangle?A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.
Given:
The base of an isosceles triangle is one and a half times the length of the other two sides.
Let s represents the side of the triangle.
The base = ([tex]1\frac{1}{2}[/tex])s = 3s/2
So, the other two sides are s and s.
So, the perimeter,
= 3s/2 + s/+ s
= 7s/2
A smaller triangle has a perimeter that is half the perimeter of the first.
That means,
the perimeter of the smaller triangle,
= 1/2(7s/2)
= 7s/4
= (1.75)s
Therefore, (1.75)s is the required expression.
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27 131 Marks
Altogether, I have 10 bags of sweets.
The mean number of sweets in the bags is 42.
The table shows how many sweets there are in 9 of the bags.
Number of sweets
in a bag
Frequency
39 1
40 2
41 5
42 0
43 1
How many sweets are in the 10th bag?
Answer:
The number of sweets in the 10th bag is 53
Step-by-step explanation:
Given
Let the Number of sweets in a bag be represented by x and frequency be represented by f
The table is as follows
x F
39 1
40 2
41 5
42 0
43 1
Mean = 42
Required
How many sweets are in the 10th bag?
Represent the number of sweets in the 10th bag by y;
The table becomes
x F
39 1
40 2
41 5
42 0
43 1
y 1
The mean of observation is calculated using the following formula;
Mean = ∑fx/∑f
Where ∑ means summation
fx means f * x; i.e. product of frequency and number of sweets
f represents frequency;
Calculating ∑fx
∑fx = 39 * 1 + 40 * 2 + 41 * 5 + 42 * 0 + 43 * 1 + y * 1
∑fx = 39 + 80+ 205 + 0 + 43 + y
∑fx = 367 + y
Calcuating ∑f
∑f = 1 + 2 + 5 + 0 + 1 + 1
∑f = 10
Recall that
Mean = ∑fx/∑f and Mean = 42;
So, Mean = ∑fx/∑f becomes
[tex]42 = \frac{367 + y}{10}[/tex]
Multiply both sides by 10
[tex]42 * 10 = \frac{367 + y}{10} * 10[/tex]
[tex]420 = 367 + y[/tex]
Subtract 367 from both sides
[tex]420 - 367= 367 -367 + y[/tex]
[tex]53 = y[/tex]
[tex]y = 53[/tex]
Hence, the number of sweets in the 10th bag is 53
The total number of sweets in the 10th bag is 53 and this can be determined by using the formula of the mean.
Given :
The total number of bags is 10.The mean number of sweets in the bags is 42.The table shows how many sweets there are in 9 of the bags.The following steps can be used in order to determine the total number of sweets in the 10th bag:
Step 1 - The formula of the mean can be used in order to determine the total number of sweets in the 10th bag.
Step 2 - The formula of mean is given below:
[tex]{\rm Mean}= \dfrac{\sum f \times x}{\sum f}[/tex]
Step 3 - Now, substitute the values of the known terms from the given table in the above expression.
[tex]{\rm Mean}= \dfrac{39 \times 1+40 \times 2+41 \times 5+42 \times 0+43 \times 1+y \times 1}{1+2+5+0+1+1}[/tex]
Step 4 - Simplify the above expression.
[tex]\begin{aligned}\\42&= \dfrac{367+y }{10}\\y &=53 \\\end{aligned}[/tex]
So, the total number of sweets in the 10th bag is 53.
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The length of the unknown slide is?
Answer: 10.8
Step-by-step explanation:
We can use the Pythagorean Theorem to solve this.
a^2 + b^2 = c^2
6^2 = 36
9^2 = 81
36 + 81 = 117
square root of 117 is 10.8
If 2x - 9y = 14 and 6x = 42 +y, what is the value of the product xy?
Answer:
The product x time y is zero (0)
Step-by-step explanation:
Notice that you are given a system of two equations with two unknowns, so, let's proceed to find the unknowns by the method of substitution (easiest since it is very simple to find "y" in terms of 'x" from the second equation).
Then we use that expression to substitute for "y" in the first equation and solve for x:
[tex]6x=42+y\\y=6x-42\\Then:\\2x-9y=14\\can\,\,be\,\,written\,\,as:\\2x-9(6x-42)=14\\2x-54x+372=14\\-52x=-364\\x=(-364)/(-52)\\x=7[/tex]
Now we use this result in the substitution equation to find the value of "y":
[tex]y=6x-42\\y=6\,(7)-42\\y=42-42\\y=0[/tex]
Then, the product x times y is: 7 times 0 = 0
The product renders zero (0)
Compare and contrast :
1. Directed graph and indirected graph
2 Weighted and unweighted graph
(02.03)At a dog shelter, a 26-pound bag of dog food will feed 40 dogs. How many dogs would you expect to feed with a 13-pound bag of dog food? (Input only whole numbers.)
38. A painting without its frame has
a width 2.5 times its height, h,
in inches. Its frame is 3 in. wide
all along its perimeter. What is
an expression for the area of the
framed painting in terms of h?
Simplify your expression, and write
it in standard form.
Answer:
1.5*w^2 + 15*w + 36
Step-by-step explanation:
We have to make the width of the portrait be 'w'
in addition to that the height of the frameless portrait (h) = 1.5 times its width, i.e. 1.5 * w
Frame width is 3 inches on all sides.
Therefore the area of the framed portrait is the total area of the portrait plus the area of the frame. The figure representing the above scenario is shown below.
I enclose a figure that allows us to see the problem better, the area of the rectangle ABCD is the area of the framed portrait.
From the figure, we have to:
AB = 3 + w + 3 = w + 6
BC = 3 + h + 3 = h + 6 = 1.5 * 2 +6
We know that the area of the rectangle ABCD is given as the product of the length AB and the width BC. Thus,
Area = (w + 6) * (1.5 * w + 6)
Area = 1.5 * w ^ 2 + 6 * w + 9 * w + 36
Area = 1.5*w^2 + 15*w + 36
That is, the expression for the framed portrait area in terms of the width 'w' is:
1.5*w^2 + 15*w + 36
Can you explain the example 4 pls
Answer:
x = -3/4
Step-by-step explanation:
15/4 - 7x = 9
When solving these types of equations, you want to isolate the variable
Subtract 15/4 from both sides to get
-7x = 21/4
Divide both sides by -7 to get
x = -3/4
Answer:
x = -3/4
Step-by-step explanation:
find the initial value of the function x + 3y = 18
The ordered pair (a, b) gives the location of point P on the coordinate plane. The value of aaa is 0, but b is not zero. Where could point P be located on the coordinate plane?
Answer:
On the y-axis line
Step-by-step explanation:
Given the location (a,b) of the point P on the coordinated plane.
If a=0
Then the location of P on the x-axis is at x=0
Since b is not equal to zero, b could be positive or negative.
Therefore, the point P could be located on the positive y-axis or the negative y-axis,
It must be exactly on the line.
A certain brand of candy is sold by weight, with a 3 oz bag costing $0.75. if a bag of this candy costs $2.00, what does it weight
Answer:It weights 8 oz.
Step-by-step explanation:
[tex]\frac{3}{0.75} = \frac{x}{2}[/tex] solve by cross product
0.75x = 6 now divide both sides by 0.75
x= 8
How many observations are accounted for in the stem and leaf graph?
A) 5
B) 7
C) 18
D) 19
Answer:
C) 18
Step-by-step explanation:
numbers are 100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49
perform the indicated operation 5/11 + 9/11
Answer:
It would be 14/11
when you make it a mixed number, it'll be 1 3/11
Step-by-step explanation:
You can't simplify it more than 3/11 so
1 3/11
Cancel mom please help me with this I’m stuck and I don’t know how to do this
Answer:
20
Step-by-step explanation:
The triangles are similar so we can use ratios
8 32
--- = -----
8+5 32+x
Using cross products
8(32+x) = 32(13)
Divide each side by 8
(32+x) = 32(13)/8
32+x = 4*13
32+x =52
Subtract 32
x = 20
Quadrilaterals ABCD and PQRS shown below are two similar figures.
Find the values of x and y.
Answer:
x = 12, y = 16
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{AD}{PS}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values
[tex]\frac{20}{2x+6}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )
18(2x + 6) = 540 ( divide both sides by 18 )
2x + 6 = 30 ( subtract 6 from both sides )
2x = 24 ( divide both sides by 2 )
x = 12
-------------------------------------------
and
[tex]\frac{AB}{PQ}[/tex] = [tex]\frac{DC}{SR}[/tex] , substitute values
[tex]\frac{y}{24}[/tex] = [tex]\frac{18}{27}[/tex] ( cross- multiply )
27y = 432 ( divide both sides by 27 )
y = 16
f(n) = 9+ 5n; 64
determine which term produces the given answer?
Answer:
the 11th term
Step-by-step explanation:
f(n) = 9+ 5n;
Let f(n) =64
64 = 9+5n
Subtract 9 from each side
64-9 = 9+5n-9
55 = 5n
Divide each side by 5
55/5 = 5n/5
11= n
I need help pleaseeee
Answer:
8.4375
Step-by-step explanation:
multiply 2.5 times 2.25 times 1.5
lenght x width x height
The function has a y-intercept of (0, 4) and a multiplier of 0.8. 1) Whats the initial value? 2) Is it exponential growth or decay? 3) What is the exponential equation?
Answer:
1) 4
2) exponential decay
3) [tex]y = 4(0.8)^x[/tex]
Step-by-step explanation:
1) The initial value or an exponential function is the y-intercept.
Let us consider a standard exponential function of the form y(x) = a•bˣ , if you put in x = 0 (initial value) we get:
y(0) = a•bˣ = a•b⁰ = a•1 = a , so the y-intercept is a , which is called the initial value.
Therefore the y intercept is 4
2) Since the multiplier is greater than 0 and less than one, it is an exponential decay
3) standard exponential function of the form y(x) = a•bˣ, at (0,4),
4 = a(b)⁰
a = 4
b = multiplier = 0.8
Therefore: [tex]y = 4(0.8)^x[/tex]
what is a slope of the line?
Answer
0
Step-by-step explanation:
A horizontal line has a slope of 0 always
which phrase represents the algebraic expression 3p + 6
Answer:9p
Step-by-step explanation:
Choose the highest common factor (HCF) of 6xy^3 and 9x^2y
A= x^2y^3
B= 3xy
C= 54x^3y^4
D=18x^2y^3
Answer:
B= 3xy
Step-by-step explanation:
6xy^3= 2ₓ3ₓ x ₓyₓyₓy
9x^2y= 3ₓ3ₓ x ₓ x ₓ y
common factors = 3, x , y
HCF: 3 ₓ x ₓ y
=3xy
PLEASE GIMMI ANSWER ASAP
Sharon wants to buy a shirt that cost 40$. The sales tax is 5%. How much is the sales tax. What is her total cost for the shirt.
100% + 5% = 105 %
105/100 x 40$ = 42$
Answer:
hi the answer is 2$
Step-by-step explanation:
40 divided by 10 is 4 divided by 2 is 2
tell me if you need any more help please mark as brainliest
Let f(x) = 4x3 + 3x2 − 20x − 15 and g(x) = 4x + 3. Find f of x over g of x.
x2 − 5
4x2 + x
x2 − 5x
4x2 + 12
Answer:
not B
Step-by-step explanation:
I took the test
what is the solution to the system of equation below Y equals -1/3 X +6 and X equals -6
Answer:
y = 8
Step-by-step explanation:
y= [tex]\frac{1}{3} x[/tex] + 6
[tex]x[/tex] = -6
y=([tex]\frac{1}{3}[/tex] x 6) + 6
y= 2+6 = 8
I need help really bad plsss
Answer:
0
Step-by-step explanation:
(f-g)(x) = 12-sqrt(x)
plugging in 144, we get 12 - 12 = 0
one could also do f(x)-g(x) which would yield 24-24=0
PLS HELP ILL MARK YOU BRAINLIEST 45 POINT Part A: Create a fourth-degree polynomial with three terms in standard form. How do you know it is in standard form? Part B: Explain the closure property as it relates to addition of polynomials. Give an example.
Answer:
A fourth degree polynomial:
[tex]2x^{4} + 10x^{3} + 21[/tex]
The closure property in relation to addition of polynomials means that any polynomials added together will result in another polynomial. For example
(10x^2 + 12) + (x^2 + 6) = 11x^2 + 18
This demonstrates closure because 11x^2 + 18 is also a polynomial
Step-by-step explanation:
Part A: [tex]x^{4}+2x+20[/tex] is a fourth degree polynomial with three terms and it proved that it is in standard form
Part B: Closure property has been proved in the addition of polynomials
What is Polynomial?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Part A
Example of fourth degree polynomial with three terms is
[tex]x^{4}+2x+20[/tex]
The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on
Hence, it is a standard form
Part B
The closure property in relation to addition of polynomials means that any polynomials added together will result in another polynomial
Example
(2x+6)+(5x+2)= 7x+8
Hence, the Closure property has been proved in the addition of polynomial
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