Answer:
y = -4x + 2
Step-by-step explanation:
Given the following data;
Points (x1, y1) = (0, 2)
Perpendicular line = y = ¼x + 5
To find the equation of the straight line passing;
Mathematically, the equation of a straight line is given by the formula: y = mx + c
Where;
m is the slope.x and y are the pointsc is the intercept.From the question, we can deduce that the slope (m) of the perpendicular line is ¼.
y = ¼x + 5 = mx + c
Since the points are perpendicular to the equation of line, it must have a slope that is its negative reciprocal because the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, ¼ = -4
Next, we would write the equation of the straight line using the following formula;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - 2 = -4(x - 0)
y - 2 = -4x - 0
y - 2 = -4x
y = -4x + 2
Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is
Look at image for reference
Answer:
(3)11
Step-by-step explanation:
We are given that
[tex](x^2-12x+35)(x^2+10x+24)=504[/tex]
We have to find the sum of positive roots of the equation.
[tex]x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504[/tex]
[tex]x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504[/tex]
[tex]x^4-2x^3-61x^2+62x+840-504=0[/tex]
[tex]x^4-2x^3-61x^2+62x+336=0[/tex]
Factor of 336
2,3,4,6,8,7,
Let x=2
[tex]2^4-2^4-61(2^2)+62(2)+336\neq0[/tex]
x=2 is not the root of equation
x=-2
[tex](-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0[/tex]
Hence x=-2 is the root of equation.
x+2 is a factor of equation.
x=3
[tex]3^4-2(3^3)-61(3^2)+62(3)+336=0[/tex]
Therefore, x=3 is the root of equation.
[tex](x+2)(x-3)(x^2-x-56)=0[/tex]
[tex](x+2)(x-3)(x^2-8x+7x-56)=0[/tex]
[tex](x+2)(x-3)(x(x-8)+7(x-8))=0[/tex]
[tex](x+2)(x-3)(x-8)(x+7)=0[/tex]
[tex]x-8=0\implies x=8[/tex]
[tex]x+7=0\implies x=-7[/tex]
Positive roots are 3 and 8
Sum of positive roots=3+8=11
Option (3) is true.
Someone please help me with this math problem?
Answer:
The length of the shortest side of the triangle is 10 units.
Step-by-step explanation:
Let a be the shortest side of the isosceles triangle and b be the two congruent sides.
The congruent sides b are each one unit longer than the shortest side. Hence:
[tex]b=a+1[/tex]
The perimeter of the isosceles triangle is given by:
[tex]\displaystyle P_{\Delta}=b+b+a=2b+a[/tex]
This is equivalent to the perimeter of a square whose side lengths are two units shorter than the shortest side of the triangle. Let the side length of the square be s. Hence:
[tex]s=a-2[/tex]
The perimeter of the square is:
[tex]\displaystyle P_{\text{square}}=4s=4(a-2)[/tex]
Since the two perimeters are equivalent:
[tex]2b+a=4(a-2)[/tex]
Substitute for b:
[tex]2(a+1)+a=4(a-2)[/tex]
Solve for a. Distribute:
[tex]2a+2+a=4a-8[/tex]
Simplify:
[tex]3a+2=4a-8[/tex]
Hence:
[tex]a=10[/tex]
The length of the shortest side of the triangle is 10 units.
what expression is equivalent to 96+18
Answer:
114
Step-by-step explanation:
114
What is Write down the equation of the perpendicular line to y=3x+3?
Answer:
[tex]gradient = - \frac{1}{3} \\ { \tt{equation \: is \: y = - \frac{1}{3}x + 3 }}[/tex]
Answer:
The equation of a perpendicular line to
y =( -1/3 )x+b (b is a normal number)
Step-by-step explanation:
1.Use the slope-intercept form to find the slope.
Tap for more steps...
m = 3
2. the perpendicular line to y=3x+3
must have a slope that is the negative reciprocal of the original slope.
thus,
m perpendicular = −1/3
What is the 7th term in the sequence below?
5, 25, 125, 625, …
A. 78,125
B. 15,625
C. 3,125
D. 825
Answer:
its 3125
Step-by-step explanation:
you multiply it by 5 every time
Answer:
C
Step-by-step explanation:
If f(x) = 3x - 2 and g(x) = x2 +1, find (f +9)(x).
Answer:
A. x² + 3x - 1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 3x - 2
g(x) = x² + 1
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = 3x - 2 + x² + 1Combine like terms: (f + g)(x) = x² + 3x - 1Answer:
D. x² + 3x + 1
Step-by-step explanation:
Given :- f ( x ) = 3x - 2 ɑnd g( x) = x² + 1
Find :- ( f + g ) ( x )
Solution :-
plug 3x + 2 ɑs f ɑnd x² + 1 ɑs g in the functions.( f + g ) ( x ) = ( ( 3x - 2 ) + ( x² + 1))
remove unnecessɑry pɑrɑntheses( f + g ) ( x ) = ( 3 x - 2 + x² + 1 )
combine like terms( f + g ) ( x ) = ( x² + 3x - 1 )
what is the answer to this?
two parallel lines are crossed by a transversal.
Answer:
[tex]{ \boxed{ \tt{m \angle1 = m \angle5}}} \\ { \tt{m \angle1 = 180 \degree - m \angle6}} \\ { \tt{m \angle1 = 180 \degree - 123.5 \degree}} \\ { \bf{m \angle1 = 56.5 \degree}}[/tex]
When a pair of parallel lines is intersected by a transversal, then
Corresponding angles are equal.
∠2 and ∠6 are corresponding angles.
So, m∠2 = m∠6
=> m∠2 = 123.5°
We know that linear pair of angles are supplementary (180°).
∠1 and ∠2 are linear pair of angles.
So, m∠1 + m∠2 = 180°
=> m∠1 + 123.5° = 180°
=> m∠1 = 180° - 123.5°
=> m∠1 = 56.5°
Select the correct answer.
A distribution center is redesigning two of its shipping boxes. The volume of these two boxes needs to be the same, and their dimensions are shown.
Write a system of equations to represent the volume of each box, y. Which statement describes the number and viability of the systems solutions?
Answer:
The system has two solutions, but only one is viable because the other results in negative side lengths.
Step-by-step explanation:
correct on edmentum or plato
find the area and perimeter of a circle
Answer:
Step-by-step explanation:
r=5 cm
area=πr²
perimeter=2πr
substitute the value of r and calculate.
Answer:
78.54 [tex]cm^{2}[/tex] Area
31.42 cm Circumference/perimeter
Step-by-step explanation:
A = [tex]\pi r^{2}[/tex]
C = 2[tex]\pi[/tex]r
A = [tex]\pi[/tex][tex]5^{2}[/tex]
A = 25[tex]\pi[/tex]
A = 78.54
C = 2[tex]\pi[/tex](5)
C = 10[tex]\pi[/tex]
C = 31.42
____________ was designed to tabulate the 1890 census and used cards with designated areas representing data fields.
Answer:
Hollerith tabulating machine
Step-by-step explanation:
The Hollerith tabulating machine was invented by Herman Hollerith in other to assist in the data processing of the United States 1890 election. This machine was used to read and summarize the information stored on punchcards. This machine paved the way for the development of enhanced models which were employed for accounting and some other aspects related to business management.
In a class of 22 students, 7 are female and 17 have an A in the class. There are 3 students who are male and do not have an A in the class. What is the probability that a student who has an Ais a male?
Answer:
Step-by-step explanation:
total number of students=22
number of female students=7
number of male students=22-7=15
number of male students not having A=3
Number of male students having A=15-3=12
P(male student having A)=12/22=6/11
The probability that a student who has an A is male is approximately 0.632
What is probability?We can use the formula for conditional probability:
P(Male | A) = P(Male and A) / P(A)
We are given that there are 3 male students who do not have an A, so there are 22 - 3 = 19 students who have an A. Of these 19, we do not know how many are male. However, we do know that there are 7 female students, so the number of male students who have an A is:
19 - 7 = 12
Therefore, the probability that a student who has an A is male is:
P(Male | A) = 12 / 19
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor (which is 1 in this case):
P(Male | A) = 12 / 19
So the probability that a student who has an A is male is approximately 0.632.
To know more about probability follow
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ratio and proportion
One of the angle of pair of supplementary angle is 120 degree. find the ratio of pair of supplementary angles.
Answer:
2 : 1
Step-by-step explanation:
Supplementary angles are two angles whose measures add up to 180°
If one of the angle = 120°
The other angle = sum of supplementary angle - one of the angle
= 180° - 120°
= 60°
The other angle = 60°
ratio of pair of supplementary aangle = 120° : 60°
= 120° / 60°
= 2/1
= 2 : 1
ratio of pair of supplementary aangle = 2 : 1
Can someone help with the ones I haven’t answer
Answer:
Step-by-step explanation:
[tex]5) 5\frac{11}{12}+3\frac{5}{6}=5+\frac{11}{12}+3+\frac{5}{6}\\\\ =8 +\frac{11}{12}+\frac{5*2}{6*2}\\\\= 8 +\frac{11}{12}+\frac{10}{12}\\\\=8 +\frac{11+10}{12}\\\\= 8+\frac{21}{12}\\\\=8+ 1\frac{9}{12}\\\\= 9\frac{9}{12}[/tex]
can someone give me the answer for this? __ (5 + 4) = 2 * 5 + 2 * 4
Answer:
The answer is 2_____________________________
2 x 5 = 10
2 x 4 = 8
10 + 8 = 18
______________________________
5 + 4 = 9
_______________________________
_ 9 = 18
18 : 9 = 2
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Please help me with this one I seriously suck at math
Answer:
194
Step-by-step explanation:
Rectangles :
7 x 10 = 70
6 x 10 = 60
4 x 10 = 40
Triangles
[tex]\frac{6x4}{2}[/tex] = 12 (two of them = 24)
70 + 60 + 40 + 24 = 194
is dilated to become LaTeX: g\left(x\right)=\frac{1}{3}\cdot4^x. What is the specific effect on LaTeX: f\left(x\right)
Answer:
f(x) is shrinked
Step-by-step explanation:
Given
[tex]f(x) = 4^x[/tex]
[tex]g\left(x\right)=\frac{1}{3}\cdot4^x[/tex]
Required
The effect of dilation on f(x)
From the given parameters, we have:
[tex]f(x) = 4^x[/tex]
[tex]g\left(x\right)=\frac{1}{3}\cdot4^x[/tex]
On a general term;
[tex]g(x) = k * f(x)[/tex]
So by comparison:
[tex]k = \frac{1}{3}[/tex]
When scale of dilation is less than 1, it means the function is reduced. Hence, the specific effect on f(x) is shrink
the green line below _____ check all that apply
Answer:
A, C, and D
Step-by-step explanation:
Answer:
the answer is A, C And D
Step-by-step explanation:
ADC
which of the following equations describes the line
check all that apply (1,9) (-2, 3) A. y - 1 = 2(X-9) B. Y- 2 = 2(x-3) c. y - 3 = 2(x + 2) D. Y-3 = 2(x - 2) E. y + 2 = 2(x-3) F. - 9 = 2(x - 1)
The equation of the line that connects the two points (1,9) and (-2,3) is,
y = 2x+7
or, y-3=2x+4
or, y-3=2(x+2)
So, option c, is the correct option
Answered by GAUTHMATH
Simplify the expression. (6)8 + (6)3
Answer:
66
Step-by-step explanation:
Use the PEMDAS order. Multiplication comes before addition so it simplifies to 6(8)+(6)3
=48+18
=66
A clothing store offers a free T- shirt when a customer spends $75 or more. Lyndon has already spent $36.95 which statement best represents all of the amounts he can spend to get a free T-shirt
Select the correct answer.
What are the solutions to this quadratic equation?
x^2+13=8x+37
A. x=4+2sr 10
B. x=-4+4sr10
C. x=-2+4sr10
D. x=4+sr10
Answer:
the answer to the question is C
Express y in terms of x in the equation ax + by = c where b is not equal to zero.
HELLLP
Answer:
y=(-ax+c)/b
Step-by-step explanation:
ax+by=c
by=c-ax
by=-ax+c
y=(-ax+c)/b
If f(x) = -3 3 and g(x)= 4x2 + 2x - 4, find (f +g)(x).
Answer:
A. 4x² + 9x/4 - 7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x/4 - 3
g(x) = 4x² + 2x - 4
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = x/4 - 3 + 4x² + 2x - 4Combine like terms: (f + g)(x) = 4x² + 9x/4 - 7If AVB has a measure of 88° and VM is its angle bisector, what is the
measure of AVM?
A. 88°
B. 22°
C. 176°
D. 44
Answer:
B. 22°
Step-by-step explanation:
Angle bisector divides an angle into two equal angles.
Angle AVM = Angle MVM = Angle AVB / 2
Angle AVM = Angle AVB / 2
Angle AVM = 88 / 4
Angle AVM = 22°
Answer:
44
Step-by-step explanation:
Write each as a percent. Use proportions.
7/25, 2/3, 3/8
Answer:
Step-by-step explanation:
[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]
¿cual es el porcentaje de ganancia de un comerciante que vende a $4600 un producto que compró a $4000?(con desarrollo)
Respuesta:
15%
Explicación paso a paso:
Dado :
Precio de compra = $ 4000
Precio de venta = $ 4600
El beneficio obtenido por la venta del artículo:
Precio de venta - precio de compra
$ (4600-4000) = $ 600
El porcentaje de beneficio obtenido:
Beneficio / precio de compra * 100%
600/4000 * 100%
600/4000 * 100%
0,15 * 100%
= 15%
how to determine proofs
Answer:
check footprints and then check finger print the finger print pour powder on it and Trace
simplify the following. (x²+2x)-(x²-7x)
Answer:
9x
Step-by-step explanation:
(x² + 2x) - (x² - 7x) ← distribute parenthesis
= x² + 2x - x² + 7x ← collect like terms
= 9x
Answer:
9x
Step-by-step explanation:
( x ² + 2 x ) - ( x² - 7 x )
Simply the expression
➻ ( x ² + 2 x ) - ( x² - 7 x )Remove unnecessary parantheses
➻ x² + 2x - x² + 7xcombine like terms
➻ x² - x² + 2x + 7x➻ 9x