Step-by-step explanation:
Explanation is in the attachmentHope it is helpful to you
The equation 9 y minus 6 x = 36 is written in standard form. What is the first step when writing an equivalent equation which solves for x? Divide both sides of the equation by 36. Multiply both sides of the equation by 6. Add 9y to both sides of the equation. Subtract 9y from both sides of the equation.
Answer:
D. Subtract 9y from both sides of the equation.
Step-by-step explanation:
A. Divide both sides of the equation by 36.
B. Multiply both sides of the equation by 6.
C. Add 9y to both sides of the equation.
D. Subtract 9y from both sides of the equation.
Given:
9y - 6x = 36
To solve for x
Step 1: subtract 9y from both sides
9y - 6x - 9y = 36 - 9y
- 6x = 36 - 9y
Step 2: Divide both sides by -6
- 6x / -6 = (36 - 9y) / - 6
x = (36 - 9y) / - 6
The answer is
x = (36 - 9y) / - 6
Answer:
d
Step-by-step explanation:
y=x²+4x-3 y=5x+3 solve the simultaneous equation
Answer:
(-2, -7) or (3, 18)
Step-by-step explanation:
Start with your 2 equations
y = x^2 + 4x - 3
y = 5x + 3
Because both equal y, we substitute:
x^2 +4x -3 = 5x+ 3
x^2 - x - 6 = 0
Factor:
(x + 2) (x - 3) = 0
Solutions for x: -2 or 3 since if either of the numbers in parentheses is 0, the equation is 0 (0* anything = 0).
Then plug -2 in for x in either equation:
y = 5* -2 + 3
y = -7
So ( -2, -7) is a solution.
Plug 3 in for x in either equation:
y = 5*3 + 3
y = 18
So ( 3 , 18) is a solution.
Hope that helps, let me know if I did anything wrong!
Answer:
(- 2, - 7 ) and (3, 18 )
Step-by-step explanation:
Given the 2 equations
y = x² + 4x - 3 → (1)
y = 5x + 3 → (2)
Substitute y = x² + 4x - 3 into (2)
x² + 4x - 3 = 5x + 3 ( subtract 5x + 3 from both sides )
x² - x - 6 = 0 ← in standard form
(x - 3)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 3 = 0 ⇒ x = 3
Substitute these values into (2) for corresponding values of y
x = - 2 : y = 5(- 2) + 3 = - 10 + 3 = - 7 ⇒ (- 2, - 7 )
x = 3 : y = 5(3) + 3 = 15 + 3 = 18 ⇒ (3, 18 )
Some students were asked how many pens they were carrying in their backpacks. The data is given in this frequency table. What is the mean number of pens carried by these students in their backpacks?
A. 3
B. 3.5
C. 4
D. 4.5
Answer:
4
Step-by-step explanation:
Mean: the sum of all numbers divided by the amount of numbers
In this case it will be the sum of all frequency divided by the amount of pens
Mean = 5 + 7 + 3 + 5 + 3 + 2 / 6
Mean = 25/6
Mean = 4.16
The mean is approximately 4
how many metres are there in ½ of ⅕ km
Step-by-step explanation:
1/5=1/5×1000=200
1/2 of 200
1/2×200=100
write equation!!
twice the difference of a number and seven equals five 
Answer:
Its either 2(A+7=5) or 2(A+7) =5
The sum of three consecutive numbers is 117.what is the largest of the three numbers?write an equation to represent this scenario and solve for the variable
Answer:rrrrrrrr
rrrrrrrrrr
Step-by-step explanation:
rrrrrrrrrrrrrrr
The equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the first number:
The other numbers are:
x+1, x+2
The sum of three consecutive numbers is 117:
x + x+1 + x+2 = 117
3x + 3 = 117
3x = 114
x = 38
x+ 1 = 38+1 = 39
x+2 = 38+2 = 40
Thus, the equation for the scenario is x + x+1 + x+2 = 117 and largest number is 40.
Learn more about the linear equation here:
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A boy borrowed his boat 531 feet out into the ocean. When he looked back he saw the house on a cliff above the beach where he set out. He estimated the angle of elevation was 26 degrees. Estimate to the nearest foot. the height of the house above the water
Answer:
259 ft.
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles. scalene, equilateral, acute, obtuse and right angled triangle.
A right angled triangle is a triangle in which one of the angles is 90 degrees. Trigonometric ratios show the relationship between the angles of a right angle triangle and its sides.
Let h represent the height of the house above water, hence using trigonometric ratios:
tan(26) = h / 531
h = 531 * tan(26)
h = 259 ft.
I will mark you the brainiest for the correct answer, please be correct, Have a good day and take care, thanks. ( VIEW THE IMAGE TO ANSWER).
Mistake in Line 2 : Was in the determining the values for a ,b,c
Mistake in Line 4 : Not taking the square roots of both sides.
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
First Mistake : Line 2
[tex]a = x \\ b = 6 \\ c = 10[/tex]
Second Mistake : Line 4
[tex]136 = {x}^{2} \\ not \\ 136 = x[/tex]
Correct Solution :
[tex] {x}^{2} + {6}^{2} = {10}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ {x}^{2} = 100 - 36 \\ [/tex]
[tex] {x}^{2} = 64 \\ \sqrt{ {x}^{2} } = \sqrt{64} \\ x = 6[/tex]
Help with question 24 the answer is (y-2)(a-b) but I need explain I don’t understand
Answer:
a(y_2)_b(y_2) =a_b)(y_2(
What is the range of the function f(x) = -2(6^x) + 3?
o (-inf,-2]
0 (-inf,3)
O [-2,inf)
O [3,inf)
Answer:
write question in short form
Step-by-step explanation:
There are 5 pears, 10 grapes, and 4 strawberries in a bag. What is the ratio of all pieces of fruits to pears?
Answer:
19: 5
Step-by-step explanation:
Total fruit is 5+10+4 = 19
fruit: pears
19: 5
Answer:
19:5
Step-by-step explanation:
5+10+4= 19
Pears= 5
Which statements are true about finding the difference of the expressions? Select three options
[tex]\frac{3p+1}{6p}[/tex] and [tex]\frac{2p-3}{2px^{2} }[/tex]
A. The common denominator is 6p.
B. The first fraction rewritten with the LCD is [tex]\frac{3px^{2} +p}{6px^{2} }[/tex]
C. The second fraction rewritten with the LCD is [tex]\frac{6p-9}{6p}[/tex]
D. The diffrence is [tex]\frac{3px^{2} -5p+9}{6px^{2} }[/tex]
E. The difference is a rational expression.
Answer:
CAUTION HERE !!!!!
if you suggested edits are accurate the solution would be...
[tex]\frac{3p^2 - 5p+9}{6p^2}[/tex]
that is not one of your choices, but is is almost identical to choice "D"
which is different by [tex]6px^2[/tex] vs [tex]6p^2[/tex]
which i think is your comment ????
Step-by-step explanation:
Ella has two 8-ft. long boards. She
needs to cut pieces that are 15 inches
long. How many 15-inch pieces can
she cut from the two boards?
My sister needs help?
Answer:
Step-by-step explanation:
DB is a diagonal of parallelogram ABCD
What is the measurement of
Please help ASAP
Answer:
m∠DAB+m∠ADC=180
115+ 29 + m∠ADB=180
m∠ADB=180 - 115 -29
= 36°
Use the coordinates of the labeled point to find the point-slope equation of the line.
(12, -1)
Answer:
Choice C.
[tex]y + 1 = - 2(x - 2)[/tex]
Step-by-step explanation:
When converting to
[tex]y = mx + b[/tex]
We are left with:
[tex]y = - 2x + 3[/tex]
Which fits both the x-intercept and y-intercept.
Sipho buys a bread on Monday and eats a third of it. On Tuesday he eats half of what is left over. If the bread is cut in 21 slice how many slice are left for Wednesday?
Answer:
7 slices
Step-by-step explanation:
1/3 of the bread would be seven slices (21/3), and he would be left with 2/3, half of which is 1/3; another seven slices were eaten. On Wednesday, he will have 7 slices left over.
4.
a. The total area of the model is 130 m2. Write an equation to find x. b. Solve the equation by completing the square.
A. (x + 2)(2x + 2) = 130; x = 5.12 m
B. (x + 2)(2x + 2) = 130; x = 6.70 m
C. (x + 2)(x + 2) = 130; x = 9.40 m
D. (x + 2)(2x + 2) = 130; x = 6.58 m
Answer:
(x+2)(2x+2) = 130
x=6.58m
Step-by-step explanation:
The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:
Area = Length * Width
Given
Length = 2 + x + x = 2+2x
Width = 2 + x
Area = 130m²
Substitute the resultng values into the formula;
(2+2x)(2+x)= 130
(x+2)(2x+2) = 130
Expand the bracket:
[tex]2x^2+2x+4x+4=130\\2x^2+6x+4=130\\[/tex]
Divide through by 2
[tex]x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63[/tex]
Complete the square by adding the square of the half of the coefficient of x to both sides:
[tex](x^2+3x+(\frac{3}{2} )^2)=63+(\frac{3}{2} )^2[/tex]
[tex](x+\frac{3}{2} )^2=63 + \frac{9}{4} \\(x+\frac{3}{2} )^2=\frac{252+9}{4} \\(x+\frac{3}{2} )^2=\frac{261}{4}\\(x+\frac{3}{2} )^2=65.25[/tex]
Take the square root of both sides
[tex]\sqrt{(x+(\frac{3}{2} ))^2} = \sqrt{65.25}\\x+\frac{3}{2}= 8.078\\x=8.078-1.5\\x=6.58m[/tex]
Hence the value of x is 6.58m
What is the range of g ( x ) = 3x − 2, if the domain is { − 1, 0, 1, 2 }?
Answer:
range{-5,4)
Step-by-step explanation:
3(-1)-2= -5
3(2)-2=4
help asap! what does sinø=
Answer:
-3/5
Step-by-step explanation:
Pythagorean formula :
x^2 + y^2 = r^2
(-8)^2 + (-6)^2 = r^2
64 + 36 = 100
r^2 = 100
r= 10
sin is the y coordinate over the radius :
-6/10
-3/5
if x=2+√5 find the value of x²-1/x²
Answer:
[tex]{ \tt{ {x}^{2} - \frac{1}{ {x}^{2} } }} \\ = { \tt{ {(2 + \sqrt{5} )}^{2} - \frac{1}{ {(2 + \sqrt{5}) }^{2} } }} \\ = { \tt{ \frac{(2 + \sqrt{5} ) {}^{4} - 1}{ {(2 + \sqrt{5} )}^{2} } }} \\ = { \tt{ \frac{(9 + 4 \sqrt{5}) {}^{2} }{ {(9 + 4\sqrt{5}) }}}} \\ = { \tt{9 + 4 \sqrt{5} }}[/tex]
Answer:
[tex]8\sqrt{5}[/tex]
Step-by-step explanation:
[tex]x = 2 + \sqrt{5}\\\\ x^{2} = (2+ \sqrt{5})^{2} \\\\ \ \ \ \ = 2^{2}+2* \sqrt{5}*2+( \sqrt{5})^{2}\\\\[/tex]
[tex]= 4 + 4 \sqrt{5}+5\\\\= 9+4 \sqrt{5}[/tex]
[tex]\frac{1}{x^{2}}=\frac{1}{9+4\sqrt{5}}\\\\=\frac{1*(9-4\sqrt{5}}{(9+4\sqrt{5})(9-4\sqrt{5})}\\\\=\frac{9-4\sqrt{5}}{9^{2}-(4\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-4^{2}(\sqrt{5})^{2}}\\\\=\frac{9-4\sqrt{5}}{81-16*5}\\\\=\frac{9-4\sqrt{5}}{81-80}\\\\=\frac{9-4\sqrt{5}}{1}\\\\=9-4\sqrt{5}[/tex]
[tex]x^{2}-\frac{1}{x^{2}}= 9 + 4\sqrt{5} -(9 - 4\sqrt{5})\\\\[/tex]
[tex]= 9 + 4\sqrt{5} - 9 + 4\sqrt{5}\\\\= 9 - 9 + 4\sqrt{5} + 4\sqrt{5}\\\\= 8\sqrt{5}[/tex]
HEELLLPPPPPP what’s the answer????????????????????????? HEELLLLLLLPPPPPPPPPPPPPP
Answer:
(-2,-2)
Step-by-step explanation:
x^2 + y^2 = 9
A circle has an equation of the form
(x-h)^2 + (y-k)^2 = r^2
where the center is at ( h,k) and the radius is r
The circle is centered at (0,0) and has a radius 3
The only point entirely within the circle must have points less than 3
(-2,-2)
4.Find the first five terms of the recursive sequence
Answer:
5, 12, 19, 26, 33
Step-by-step explanation:
Using the recursive rule and a₁ = 5 , then
a₂ = a₁ + 7 = 5 + 7 = 12
a₃ = a₂ + 7 = 12 + 7 = 19
a₄ = a₃ + 7 = 19 + 7 = 26
a₅ = a₄ + 7 = 26 + 7 = 33
The first 5 terms are 5, 12, 19, 26, 33
Solve the equation sine Ф=0.6792 for 0°≤Ф≤360
Answer:
42.78⁹, 137.22⁹.
Step-by-step explanation:
sine Ф=0.6792
Angle Ф in the first quadrant = 42.78 degrees.
The sine is also positive in the second quadrant so the second solutio is
180 - 42.78
= 137.33 degres.
How do I solve this math equation: 7=8-p
Answer:
p = 1
Step-by-step explanation:
7 = 8 - p
7 + p = 8
p = 8-7
p = 1
Answered by Gauthmath
What is the solution to this equation?
log_8 16 + 2log_8x =2
The value of x for the given equation [tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2 will be 2 so option (B) must be correct.
What is a logarithm?The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.
In another word, a logarithm is a different way to denote any number.
Given the equation
[tex]log_{8}[/tex](16) + 2[tex]log_{8}[/tex](x) = 2
We know that,
xlogb = log[tex]b^{x}[/tex]
So,
2[tex]log_{8}[/tex](x) = logx²
For the same base
logA + logB = log(AB)
So,
[tex]log_{8}[/tex](16) + [tex]log_{8}[/tex](x)² = 2
[tex]log_{8}[/tex](16x²) = 2
We know that
[tex]log_{a}[/tex](b) = c ⇒ b = [tex]a^{c}[/tex]
so,
[tex]log_{8}[/tex](16x²) = 2 ⇒ 8² = 16x²
x = 2 hence x = 2 will be correct answer.
For more about logarithm
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Solve for x. round to the nearest tenth, if necessary.
Answer:
29
Step-by-step explanation:
all in all it is 180 so 61 + m (which is 90 because it is a right angle)=151
then 180-151=29
Hi I need help with this question please!!! I don’t understand it :/
Answer:
- 22.5
Step-by-step explanation:
Substitute x = 3 into f(x) and x = 16 into h(x) , then
[tex]\frac{1}{2}[/tex] g(3) - h(16)
= [tex]\frac{1}{2}[/tex] × - 3(3)² - (2[tex]\sqrt{16}[/tex] + 1)
= [tex]\frac{1}{2}[/tex] × - 3(9) - (2(4) + 1)
= [tex]\frac{1}{2}[/tex] × - 27 - (8 + 1)
= - 13.5 - 9
= - 22.5
Given a right triangle with an acute angle Θ , if sin Θ = cos Θ , describe what this triangle would look like.
For sinø = cosø, ø = 45°. Because it is right, it is also a right, isosceles triangle
If a = 1/2, then a^2=
(A) -1
(B) 4
(C) 0
(D) 1
Answer:
1/4
Step-by-step explanation:
a^2
Let a= 1/2
(1/2)^2
(1/4)
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the slope between (-2,-2) and (0,-3)
Answer:
Step-by-step explanation:
x1 y1 x2 y2
-2 -2 0 3
ΔY 5
ΔX 2
slope= 2 1/2
B= 3
Y =2.5X +3
