[tex]5x+2y = 4~~~~~~~~~~...(i)\\\\7x +3y = 5~~~~~~~~~~...(ii)\\\\\text{Write in AX = B form.}\\\\~~~~~~\begin{bmatrix}5&2\\7&3 \end{bmatrix} \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\begin{bmatrix}5&2\\7&3 \end{bmatrix}^{-1}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-7\\-2&5\end{bmatrix}^{T}}{\begin{vmatrix}5&2\\ 7&3 \end{vmatrix}}\\\\\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\dfrac{\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}}{5(3) -2(7)}\\\\\\[/tex]
[tex]\\\implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 4\\5 \end{bmatrix}\cdot\begin{bmatrix} 3&-2\\-7&5\end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}12-10\\-28+25 \end{bmatrix}\\\\\\ \implies \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix}2\\-3\end{bmatrix}\\\\\\\text{Hence,}~ (x,y) = (2,-3)[/tex]
The selling price of an item is Rs. 690 on which 15% profit is earned by the trader. What is the cost price of the item?
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
≛ Given ≛ ➣Selling Price of an item is Rs. 690➣Profit earned by trader 15%▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
≛ To find ≛ ➣Cost price of the item▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
≛ Formula to be used ≛ ➣here we use profit formulathat is :-
[tex]{ \boxed{✠\underline{ \boxed{ \sf{ \red✰Cost \: price =100 \times \frac{selling \: price}{100 + profit\%} }}}✠}}[/tex]
when selling price and profit "%" is given▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
≛ Assumption ≛ ➣let cost price be "x"▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
≛ let's solve acc to formula≛[tex]\rm{➾x = 100 \times \frac{690}{100 + 15}} \\\rm{➾x \frac{100 \times 690}{100 + 15}~~~~~~~~~~~~~~~ } \\ \rm{➾x = \frac {100 \times \cancel{ 690}}{ \cancel{115}}}~~~~~~~ \\ \rm{➾x = 100 \times 6}~~~~~~~~~~~~~~~ \\ \rm{➾x =106}~~~~~~~~~~~~~~~[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
➣ Hence "x" (Cost price) of the item
[tex] \large{ \boxed{✠\underline{ \boxed{ \sf{ Rs.106\green✓}}}✠}}[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂☘
Hope it helps !
RATIONAL EXPONENTS pls help what do i do??
Answer:
x = 3
Step-by-step explanation:
[tex]26=-1+(27x)^{\frac{3}{4}}[/tex][tex]\implies 26+1=27^{\frac{3}{4}} x^{\frac{3}{4}}[/tex][tex]\implies 27\div 27^{\frac{3}{4}} =x^{\frac{3}{4}}[/tex][tex]\implies 27^{1-\frac{3}{4}} =x^{\frac{3}{4}}[/tex][tex]\implies 27^{\frac{4-3}{4}} =x^{\frac{3}{4}}[/tex][tex]\implies 27^{\frac{1}{\cancel 4}} =x^{\frac{3}{\cancel 4}}[/tex][tex]\implies 27 =x^{3}[/tex][tex]\implies 27^{\frac{1}{3}} =x[/tex][tex]\implies (3^3)^{\frac{1}{3}} =x[/tex][tex]\implies x = 3[/tex]Answer:
x = 3Step-by-step explanation:
[tex]26=-1+\left( 27x\right)^{\frac{3}{4} }[/tex]
[tex]\Longleftrightarrow 27=\left( 27x\right)^{\frac{3}{4} }[/tex]
[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left[ \left( 27x\right)^{\frac{3}{4} } \right]^{\frac{4}{3} }[/tex]
[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =\left( 27x\right)^{\frac{3}{4} \times \frac{4}{3} }[/tex]
[tex]\Longleftrightarrow \left( 27\right)^{\frac{4}{3} } =27x[/tex]
[tex]\Longleftrightarrow x=\frac{27^{\frac{4}{3} } }{27}[/tex]
[tex]\Longleftrightarrow x=27^{\frac{4}{3} -1}[/tex]
[tex]\Longleftrightarrow x=27^{\frac{1}{3} }[/tex]
[tex]\Longleftrightarrow x=\sqrt[3]{27}[/tex]
[tex]\Longleftrightarrow x=3[/tex]
What is the sum of the first 6 terms of the sequence defined by an = 3n - 2?
Answer:
51
Step-by-step explanation:
when n=1
t 1=1when n=2
t2=4
as first term is 1 and second term is 4 so the common difference is 3 ,for 6 term if you put this in formula for sum to the n term you will get 51
t1 =1
d=3
n=6
than S6=51
Ms. Bell's mathematics class consists of 11 sophomores, 7 juniors, and 13 seniors. How many different ways can Ms. Bell create a 3-member committee of juniors if each junior has an equal chance of being selected?
Answer:
35 ways
Step-by-step explanation:
Seven juniors to choose three from
7 C 3 = 7! / ( 4! 3!) = 35
Which of the statements are true about the function f given by f(x) = 100-e? Select all that apply.
a The values of increase when x increases.
b The value off when x = 5 is less than 1.
d
e The value of is never 0.
E
The value of f when x=-1 is a little less than 40.
The y-intercept of the graph off is at (0, 100).
From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.
What is the explanation for the above function?Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:
f(x) = 100 * [tex]e^{-x}[/tex]
Assuming x = -2, we'd have:
100 * 2.7182[tex]^{-2}[/tex]
= 271.82[tex]^{-2}[/tex]
= 0.00001353354
Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.
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Don’t know how to solve
Answer:
Hi,
Step-by-step explanation:
I don't know the name in Enghish but in French it is "une règle de 3"
(may be linear rule)
arc length= 2*π*r/360*100=50*π/9
area= π*r²*100/360=250*π/9
Find f(-3) if f(x)=x^2+2x-1
Simplify the expression. Write your answer as a power.
8¹⁰x8⁴
The simplified expression is
Answer:
[tex]8^{14}[/tex]
Step-by-step explanation:
When we multiply exponents with the same base, the product it the base to the power of the exponents added together. In this case, the base will remain as 8 and the exponent will be 10 + 4 = 14. Therefore, the answer is [tex]8^{14}[/tex].
Answer:
[tex]\large\boxed{\sf \sf 8^{14}}[/tex]
Explanation:
[tex]\rightarrow \sf 8^{10} \ \ x \ \ 8^4[/tex]
apply exponent rule: [tex]\sf \bf a^b\cdot \:a^c=a^{b+c}[/tex]
[tex]\rightarrow \sf 8^{10+4}[/tex]
[tex]\rightarrow \sf 8^{14}[/tex]
Darcy gave her nail technician a $5.10 tip. The tip was 15% of the cost of the manicure. Write an equation to find b, the cost of the manicure.
Question content area bottom
Part 1
If all percents are expressed as decimals, the equation enter your response here can be used to find b, the cost of the manicure.
(Use the operation symbols in the math palette as needed. Type an equation. Use whole numbers or decimals for any numbers in the equation. Do not simplify.)
Answer:
Let b the cost of the manicure
15% of b= 5.10$
15% × b= 5.10$
b= 5.10×100/15
b= 34$
Look at the pattern below.
step 1 step 2 step 3 step 4
How many squares will be in the pattern at the 8th step?
Choose 1 answer:
8 squares
12 squares
B
There will be 36 squares in the 8th step of the pattern
How to determine the number of squares?The pattern and the squares are represented as:
Pattern Squares
1 1
2 3
3 6
4 10
This can be rewritten as:
Pattern Squares
1 1
2 1 + 2
3 1 + 2 +3
4 1 + 2 + 3 +4
So, the number of squares on the 8th pattern is:
8th pattern = 1 + 2 + 3 +4 + 5 + 6 + 7 + 8
Evaluate
8th pattern = 36
Hence, there will be 36 squares in the 8th step
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Can you please help me with this
Answer:
dilation by a factor of 1/3 about the origin
Step-by-step explanation:
Each side of triangle B is 1/3 the length of the corresponding side of triangle A. This tells you dilation using a scale factor of 1/3 is involved.
Lines joining corresponding points of triangles A and B converge on the origin. This tells you the center of dilation is the origin.
The one transformation that maps A to B is ...
dilation by a factor of 1/3 about the origin
_____
Additional comment
No rotation, reflection, or translation are needed, since the triangles have the same orientation, and dilation fully accounts for their relative position.
Can someone help please?
Complete the slope-intercept form of the linear equation that represents the relationship in the table
Answer:
y = 3x - 4
Step-by-step explanation:
The general structure of a line in slope-intercept form is:
y = mx + b
In this form, "m" is the slope and "b" is the y-intercept.
(Step 1)
Before you can determine this equation, you need to find the value of "m". Since you were given the value of two points, you can find this by using the point-slope form. The general structure of the point-slope equation is:
y₁ - y₂ = m(x₁ - x₂)
y₁ - y₂ = m(x₁ - x₂) <---- Point-slope equation
-1 - 8 = m(1 - 4) <---- Insert "x" and "y" values from table
-9 = m(1-4) <---- Simplify left side
-9 = -3m <---- Simplify inside parentheses
3 = m <---- Divide both sides by -3
(Step 2)
Now that you know "m", you can plug it and the "x" and "y" values of one point into the slope-intercept equation to find the value of "b".
y = mx + b <---- Slope-intercept equation
y = 3x + b <---- Plug 3 into "m"
-1 = 3(1) + b <---- Plug "x" and "y" values in
-1 = 3 + b <---- Multiply 3 and 1
-4 = b <---- Subtract 3 from both sides
(Step 3)
Now that you know that m = 3 and b = -4, you can substitute these values into the slope-intercept form to find your final answer. You can check your answer by plugging the "x" values from the table into the equation to verify that you get the correct "y" values.
y = 3x - 4
Question 27(Multiple Choice Worth 1 points)
(01.05 LC)
Which calculation can be used to find the value of p in the equation p³= 8?
Op=√8
Op=3•√8
Op=2•√8
Op=√8
Answer:
Option 1 ========> p = ∛8
Step-by-step explanation:
In order to make p the subject we would need to cube root both sides and would therefore get :
∛(p³) = ∛8
p = ∛8
Just a side not but you wrote the first option wrong but it's fine as you attached an image.
Hope this helped and have a good day
The calculation p=∛8 can be used to find the value of p in the equation p³= 8
What is Expression?An expression is combination of variables, numbers and operators.
The given equation is p³= 8
p to the power of three equal to eight
p is the variable in the given equation
We have to find the value of p from the equation
Take cube root on both the side
∛ p³= ∛8
On left hand side the cube will be cancelled and left with p
p=∛8
Hence, p=∛8 calculation can be used to find the value of p in the equation p³= 8
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HELP PLEASEEE!!!!1!!!!
Answer: 1. Dilation.
Step-by-step explanation: All of these transformations do not change the shape's form except for a dilation. It is nessacary to change the shape, so it is a dilation.
You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water. The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?
Answer:
See below
Step-by-step explanation:
Fill the 5 and pour into the 3 ....this will leave 2 gal in the 5 bucket
empty the 3 bucket and put that 2 gallon in to it.....
then fill the 5 bucket again......pour 1 gallon into the 3 gallon bucket to fill it....then there will be 4 gallons left in the 5 bucket
Please Help I Don't Understand
In general, they're not similar.
In any triangle with side lengths a, b, and c, we have the aptly-named triangle inequality that says the largest side is no larger than the sum of the smaller sides. In other words, if a and b are both smaller than c, then
a + b ≥ c
Suppose x < 12. Then BC corresponds to either YZ or XY.
• If BC corresponds to YZ, then the triangles are similar if and only if
BC/YZ = AB/XY = AC/XZ
x/2 = 9/3 = 12/4 = 3 ⇒ x = 6
• If BC corresponds to XY, then triangle similarity means
BC/XY = AB/YZ = AC/XZ
x/3 = 9/2 = 12/4
but this fails because 9/2 ≠ 12/4 = 3.
Suppose x > 12. Then BC corresponds to XZ, and
x/4 = 12/3 = 9/2
but this also fails because 12/3 = 4 ≠ 9/2.
(We ignore the case of x = 12 because that would make ∆ABC isosceles, and ∆XYZ certainly is not.)
So ∆ABC and ∆XYZ are similar only if x = 6. Under this condition, similarity would follow from the SSS similarity theorem.
Independent Assessment 2
Directions: Use the data in the line graph below to answer the following questions.
Pieces of Bibingka Sold Per Day
60
50
40
30
20
10
0
Monday
Tuesday Wednesday Thursday
1. How many bibingka were sold on
Tuesday and Wednesday?
2. What days have the same number of
bibingka sold?
3 How many more bibingka were sold
on Monday than on Wednesday?
4. What is the average pieces of
bibingka sold for the first three days?
5. In your opinion, what other kind of rice
cake do you prefer to sell? Give your
reason
Pieces of Bibingka Sold
Friday
0000
Answer
Answer
Answer
Answer
Answer
Answer:
are you from Philippines?
Step-by-step explanation:
because I want to know gehe
11+7+(75÷(16+9))+4x(20÷10)+(28-27)
by the way the x in 4x is not a variable it means multiplication
Answer:
30
Step-by-step explanation:
Select the correct answer from each drop-down menu.
Consider the function shown on the graph.
Graph shows a function plotted on a coordinate plane. A curve begins at (minus 1, minus 3) in quadrant 3, rises through (0, minus 2), (3, minus 1), and (8, 0), and exits quadrant 1.
Complete the statements to make them true.
This is the graph of a
function.
The x-intercept of the function is at
The graph described is the graph of a quadratic function.
The x-intercept of the function is at; (8, 0).
What type of function is described by the graph?It follows from the description box of the graph that it begins in the third quadrant, and rises through a series of points in the first quadrant before it exits the first quadrant.
Hence, it follows that the graph is a quadratic function and its x-intercept is at point; (8,0).
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Answer: 1. Square root
2.(8,0)
Step-by-step explanation:
Solve the compound inequality for x and identify the graph of its solution.
x+7 > 3 and x-5≤-1
O A. Solution: x < -4 or x ≥ 4
1 2 3 4 5
OB. Solution: x>-4 and x≤ 4
1
2 3 4 5
OC. Solution: x>-4 and x≤ 4
+
+
-5 -4 -3 -2 -1
1
2
3 4 5
OD. Solution: x²-4 and x < 4
1 2 3 4
5
-5 -4 -3 -2 -1 0
-5 -4 -3 -2 -1 0
0
-5 -4 -3 -2 -1 0
Answer:
x<-4 or x≤4
Step-by-step explanation:
The solution of the inequality is x > -4 and x ≤ 4.
So, the graph B is correct.
Given is an inequality, x+7 > 3 and x-5 ≤ -1, we need to solve and identify the graph,
To solve the compound inequality, let's solve each inequality separately and then find the intersection of the solutions.
Inequality 1: x + 7 > 3
Subtract 7 from both sides:
x > 3 - 7
x > -4
Inequality 2: x - 5 ≤ -1
Add 5 to both sides:
x ≤ -1 + 5
x ≤ 4
Now, we need to find the intersection of the solutions for both inequalities.
Since the conjunction between the two inequalities is "and," we need to find the common solution.
The common solution is the values of x that satisfy both x > -4 and x ≤ 4. From the two inequalities, we can see that the common solution range is from -4 to 4, including -4 but not including 4.
Therefore, the solution to the compound inequality is: -4 < x ≤ 4
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Which of the following equations has infinitely many solutions?
A.
4x + 5(2x + 6) = 14x + 30
B.
5x + 2 = 2x + 6
C.
4(x + 5) + 2 = 6x + 4(x + 2)
D.
4x + 5 = 2
The equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30
How to determine the equation?An equation with infinitely many solutions is represented as:
ax + b = ax + b
This means that both sides of the equation must be the same.
Next, we test the options:
4x + 5(2x + 6) = 14x + 30
Open the bracket
4x + 10x + 30 = 14x + 30
Evaluate the like terms
14x + 30 = 14x + 30
Both sides of the equation must be the same.
Hence, the equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30
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PLEASE HELP THIS IS HARD
What is the measure of AT in 0 below?
A
123
0
97⁰
T
ASAPP!!
If an angle is a central angle, meaning that it goes through the center, then its corresponding arc has the same measure.
AOT is a central angle, which means that AT will have the same measure.
AOT = 97, AT = 97
Answer: A, 97
Hope this helps!
Please help worth
70 points
will mark branlest
Answer:
CE = 3.2 cm
DH = 4.5 cm
Explanation:
Given:
MNPR ≅ CEDH
≅ - means approximately equal
Lengths of the shape:
MN = CE = 3.2 cm
NP = ED = 6.5 cm
PR = DH = 4.5 cm
RM = HC = 9 cm
Which of the following inequalities is graphed on the coordinate plane?
A. y > 30 +5
B. y ≤ 3r +5
C. y < 3x + 5
D. > 31 +5
Based on the scenario above, the inequalities that can be graphed on the coordinate plane is y < 3x + 5.
What is the inequalities about?In graphing inequalities, one can graph inequality on the coordinate plane.
Note that the solutions for a linear inequality can be seen in the area of the coordinate plane. The boundary line used are > ,<, ≥ and ≤.
Note also that the inequalities graphed on the coordinate plane known to be y < 3x + 5 is shown in the image attached. When you look at option A, B and D, you will see that they are incomplete and missing some values but option C gave the correct example of an inequalities.
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Three times the sum of a number and 3 is 3 less than the number times 5. Find the
number.
Answer:
3 * (x + 3) = x * 5 - 3
A spinner is divided into five colored sections that are not of equal size: red, blue,
green, yellow, and purple. The spinner is spun several times, and the results are
recorded below:
Spinner Results
Color Frequency
Red
4
Blue
3
Green
20
Yellow
14
Purple 16
Based on these results, express the probability that the next spin will land on red as a
percent to the nearest whole number.
The probability that the next spin lands on red is
How to determine the probability?The table of values is given as:
Red = 4
Blue = 3
Green = 20
Yellow = 14
Purple = 16
The probability that the next spin lands on red is:
P(Red) = Red/Total
This gives
P(Red) = 4/(4+3+20+14+16)
Evaluate
P(Red) = 7%
Hence, the probability that the next spin lands on red is
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Answer:8%
Step-by-step explanation:
Find the gradient of the curve y =2x³-7x+4when x=-2
By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
How to find the gradient of a functionA gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:
[tex]\nabla f = \frac{df}{dx}[/tex] (1)
Now we proceed to calculate the gradient of the curve:
[tex]\nabla f = 6\cdot x^{2}-7[/tex]
[tex]\nabla f = 6\cdot (-2)^{2}-7[/tex]
[tex]\nabla f = 17[/tex]
By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
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The cost, in dollars, of shipping x computers to
California for sale is 3000+100x. The amount
received when selling these computers is 400x
dollars. What is the least number of computers
that must be shipped and sold so that the
amount received is at least equal to the shipping
cost?
The least number of computers that must be shipped is 10.
What is the least number of computers that must be shipped?In order to determine the least number of computers that must be shipped, the equation that represents the cost of shipping should be equal to the selling price of the computers.
3000 + 100x = 400x
In order to determine the value of x, take the following steps:
3000 = 400x - 100x
3000 = 300x
x = 3000 / 300
x = 10
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