Answer:
x= 7
Step-by-step explanation:
2x^2=98
\frac{2x^2}{2}=\frac{98}{2}
x^2=49
7^2=49
Final answer:
The solutions to the equation 2x^2 = 98 are x = 7 and x = -7, obtained by isolating the x^2 term and taking the square root of both sides.
Explanation:
To solve the equation 2x^2 = 98, we need to convert it into a standard quadratic equation by bringing the terms to one side of the equals sign, setting it equal to zero:
2x^2 - 98 = 0
Now, we will proceed to solve the quadratic equation. In this simple case, we can find the solutions by factoring or by taking square roots. First, we move the constant to the other side:
2x^2 = 98
Divide both sides by 2 to isolate the x^2 term:
x^2 = 49
To find x, we take the square root of both sides. Do not forget to consider both the positive and negative roots:
x = ±√49
x = ± 7
So the solutions to the equation 2x^2 = 98 are x = 7 and x = -7.
Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x − y = −11
2x + 3y = 5
Option 1)−4x − 9y = −21
−10y = −30
Option 2)4x + 3y = 5
2y = −6
Option 3)7x − 3y = −11
9x = −6
Option 4)12x − 3y = −33
14x = −28
Answer:
Option 4
Step-by-step explanation:
Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:
(2x + 3y = 5 ) * 2 =
4x + 6y = 10
Now, subtract the second equation from the first one:
(4x - y = -11) - (4x + 6y = 10)
4x - 4x = 0
-y - 6y = -7y
-11 - 10 = -21
-7y = -21
Divide both sides by -7:
y = 3
Plug 3 into the first equation as y:
4x - 3 = -11
4x = -11 + 3
4x = -8
x = -2
So x = -2 and y = 3. We need to find one of the options that equals this.
-4x - 9y = -21
-10y = -30
40x - 90y = -210
-90y = -270
40x - 0 = 40x
-90y - - 90y = -90 + 90 = 0y
-210 - -270 = -210 + 270 = 60
40x = 60
x = 1.5
We already know this isn't equivalent because the x value is not the x value of the given equation.
4x + 3y = 5
2y = -6
_______
8x + 6y = 10
6y = -18
8x - 0 = 8x
6y - 6y = 0
10 - -18 = 10 + 18 = 28
8x = 28
x = 3.5
So we know this isn't equivalent because again, the x value isn't the same as the given equation.
7x - 3y = -11
9x = -6
-----------
63x - 27y = -99
63x = -42
----------------
63x - 63x = 0
-27y - 0 = -27y
-99 - - 42 = -99 + 42 = -57
-27y = -57
-9y = -19
9y = 19
y = 19/9
So we know this one isn't equivalent as the y value isn't the same as the given equation.
12x - 3y = -33
14x = -28
x = -28/14 = -2
12(-2) - 3y = -33
-24 - 3y = -33
-3y = -33 + 24
-3y = -9
y = 9/3
y = 3
So x = -2 and y = -3 which is the same as the first equation.
Final answer:
Option 4 is the correct equivalent system for the given linear equations because you can derive the system in Option 4 by multiplying the original system's equations by constants and rearranging them.
Explanation:
We are given the system of linear equations:
4x − y = −112x + 3y = 5To find an equivalent system, each equation from the new system should be derivable from the original system. A common method is to multiply one or both of the original equations by a constant to see if it matches one of the offered options.
Option 4 is the correct choice. Multiplying the first original equation by 3, we get:
(4x − y) ⋅ 3 = −11 ⋅ 312x − 3y = −33And multiplying the second original equation by 7 and rearranging yields:
(2x + 3y) ⋅ 7 = 5 ⋅ 714x + 21y = 3514x = 35 − 21yBut since y = 0 (from 2y = −6, which implies y = −3),14x = 35 − 21(−3)14x = −28The other options cannot be derived from the original system through multiplication or other allowed operations, hence they are not equivalent.
What is the solution to the equation 5/3b^3-2b^2-5 = 2/b^3-2?
a. b = –4 and b = 0
b. b = –4
c. b = 0 and b = 4
d. b = 4
Answer:
The solution to the equation is:
Option c. b=0 and b=4
Step-by-step explanation:
5 / (3b^3-2b^2-5) = 2 / (b^3-2)
Cross multiplication:
5(b^3-2)=2(3b^3-2b^2-5)
Applying distributive property both sides of the equation to eliminate the parentheses:
5(b^3)-5(2)=2(3b^3)-2(2b^2)-2(5)
Multiplying:
5b^3-10=6b^3-4b^2-10
Passing all the terms to the right side of the equation: Subtracting 5b^3 and adding 6 both sides of the equation:
5b^3-10-5b^3+10=6b^3-4b^2-10-5b^3+10
Adding like terms:
0=b^3-4b^2
b^3-4b^2=0
Getting common factor b^2 on the left side of the equation:
b^2 (b^3/b^2-4b^2/b^2)=0
b^2 (b-4) = 0
Two solutions:
(1) b^2=0
Solving for b: Square root both sides of the equation:
sqrt(b^2)=sqrt(0)
Square root:
b=0
(2) b-4=0
Solving for b: Adding 4 both sides of the equation:
b-4+4=0+4
Adding like terms:
b=4
The solution of the equation is: b=0 and b=4 (Option c)
Final answer:
To solve the equation, we can use the quadratic formula and find the solutions for b.
Explanation:
To solve the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2, we need to find the values of b that satisfy the equation. To do this, we can cross-multiply and rearrange the equation to get a quadratic equation in terms of b. Using the quadratic formula, which states that b = (-b ± √(b^2 - 4ac)) / 2a, we can find the solutions for b.
Substituting the values a = 5/3, b = -2, and c = -7 into the quadratic formula, we obtain the solutions b = -4 and b = 0.
Therefore, the solution to the equation 5/3b^3 - 2b^2 - 5 = 2/b^3 - 2 is b = -4 and b = 0.
Tim Invested $5,000 in a savings account for 6 years.He earned $550 over that fine period.What is the interest rate?
Answer:
1.75 %
Step-by-step explanation:
The formula for the future value (FV) of an investment is
FV =PV(1 + r/n)^nt
If the interest is calculated once a year, n = 1, and the formula reduces to
FV = PV(1 +r)^t
5550 = 5000(1 + r)⁶ Divide both sides by 5000
1.110 = (1+r)^6 Take the sixth root of each side
1 + r = 1.0175 Subtract 1 from each side
r = 0.0175 Convert to percent
r = 1.75 %
The interest rate is 1.75 %.
How do you find the slope of a line parallel to y=6x+5
Describe how the number of total triangles in each shape is related to the shape’s number.
Need more info:
Can you give me more info so I can help you better?
I need a step by step solution i need corrections
1/3+3/4=4/12+9/12=13/12=1 and 1/12. (1 1/12)
5/6+2/3=5/6+4/6=9/6=3/2 or 1.5 or 1 and 1/2.
What fo the graphs if lines in the form y=mx have in common?How might they differ
Answer:
654
Step-by-step explanation:
The graphs of lines in the form y=mx always pass through the origin (0, 0). These graphs only differ in the rate of decrease or increase of the lines.
In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be represented by the following mathematical equation:
y = mx
Where:
y represents the y-variable.x represents the x-variable.m is the constant of proportionality.Generally speaking, the characteristics for a graph that shows a proportional relationship or an equation in y = mx form include the following:
"A straight line can be drawn through the points.""The line connecting the points passes through the origin (0, 0)."In conclusion, the difference between the graphs of the form y = mx is the rate of decrease or increase of the lines.
Complete Question:
What do the graphs of lines in the form y=mx have in common? How might they differ?
Solve for d. 20d − 19d + 3d + 4d + 2d = 20
find the greatest common factor of the following monomials 3B + 30 B
Answer:
3B
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values 3B and 30B. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:
3B: 1,3,B
30B: 1, 3, 5, 6, 10, B
Both have 3 and B has factors. Our GCF is these two factors.
Write an expression (4x-2)*6(2x+7) in the standard form of a quadratic expression, ax^2+bx+c. What are the values of the coefficients of each term and the constant term?
Answer:
a=48
b=-192
c=84
Step-by-step explanation:
figure it out yourself :3 jk Idrk
Answer:
see explanation
Step-by-step explanation:
given (4x - 2) × 6(2x + 7), then
= 6(4x - 2)(2x + 7) ← expand factors using FOIL
= 6(8x² + 28x - 4x - 14)
= 6(8x² + 24x - 14) ← distribute
= 48x² + 144x - 84 ← in standard form
with a = 48, b= - 144, c = - 84
Twice the difference of a number and six is the same as six times the number. What is the number?
Answer:
-3
Step-by-step explanation:
2(x-6)= 6(x)
2x-12= 6x
-12=4x
x= -3
Answer: -3
Step-by-step explanation:
2(n - 6) = 6n
2n - 12 = 6n
-2n -2n
-12 = 4n
÷4 ÷4
-3 = n
For each 9 mm of coloured fabric Sarah uses to make her curtains, she also uses 2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form.
Answer:
The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form
Step-by-step explanation:
The ratio indicates how many times one number contains another
The ratio can be written as:
A fraction [tex]\frac{a}{b}[/tex] a : ba to bThe two terms of the ratio must have the same units
∵ Sarah uses 9 mm of colored fabric to make her curtains
∵ She also uses 2 cm of of white fabric
- To express the amount of white fabric to colored fabric as a ratio
you must change the centimeter to millimeter because the
terms of ratio must have the same unit
∵ 1 centimeter = 10 millimeters
∴ 2 centimeters = 2 × 10 = 20 millimeters
∴ She uses 20 millimeters of the white fabric
Now write the ratio between the white fabric and the colored fabric
→ White : colored
→ 20 : 9
∵ 20 and 9 do not have a common factor
∴ The simplest form of the ratio is 20 : 9
The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form
Sarah uses 2 cm of white fabric for every 9 mm of coloured fabric. After converting to the same unit (centimeters), the simplest form of the ratio of white fabric to coloured fabric is approximately 2.22:1.
Explanation:To determine the ratio of the amount of white fabric to coloured fabric Sarah needs for her curtains in its simplest form, we first need to ensure that both fabrics are expressed in the same units. The question states Sarah uses 9 mm of coloured fabric and 2 cm of white fabric. Since there are 10 mm in a cm, 9 mm of coloured fabric can be converted to 0.9 cm.
Now, with both fabric measurements in centimeters, we can write the ratio of white fabric to coloured fabric: 2 cm of white fabric to 0.9 cm of coloured fabric. To find the simplest form of this ratio, we divide both sides by 0.9:
2 cm ÷ 0.9 cm = 2.2222...0.9 cm ÷ 0.9 cm = 1The simplest form of the ratio is therefore 2.2222...:1, which can be rounded and written as approximately 2.22:1, white to coloured fabric.
What is the gcf of 42 and 56
[tex]42=2\cdot21=\boxed2\cdot3\cdot\boxed7\\\\56=2\cdot28=2\cdot2\cdot14=\boxed2\cdot2\cdot2\cdot\boxed7\\\\Answer:\ GCF(42,\ 56)=\boxed2\cdot\boxed7=14[/tex]
Line contains the points (0,4) and (2,0). Show that the points (-25,81) does or does not lie on line
Answer:
(- 25, 81) does not lie on the line
Step-by-step explanation:
We can use the slope m to determine if (- 25, 81) lies on the line or not
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, 0)
m = [tex]\frac{0-4}{2-0}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
now if (- 25, 81) lies on the line then the slope between (- 25, 81) and either of the 2 points on the line should equal - 2
(x₁, y₁ ) = (- 25, 81) and (x₂, y₂ ) = (2, 0)
m = [tex]\frac{0-81}{2+25}[/tex] = [tex]\frac{-81}{27}[/tex] = - 3
The slopes are not equal hence (-25, 81) does not lie on the line
[tex]\text{Step 1:}\\\\\text{Find the equation of the line passing through the points}\\\\\text{The slope-intercept form:}\ y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b).\\\\\text{We have the points:}\\(0,\ 4)-y-intercept\to b=4\\(2,\ 0)-x-intercept\\\\\text{Therefore we have the equation:}\ y=mx+4.\\\\\text{The formula of a slope}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{put the coordinates of the points:}\\\\m=\dfrac{0-4}{2-0}=\dfrac{-4}{2}=-2\\\\\text{Therefore we have}\ \boxed{y=-2x+4}[/tex]
[tex]\text{Step 2:}\\\\\text{Put the coordinates of the point (-25, 81) to the equation of a line}\\\text{and check equality}\\\\y=-2x+4,\ x=-25,\ y=81\\\\-2x+4\to-2(-25)+4=50+4=54\neq81[/tex]
Answer: The point does not lie on a line.7x + 3x + 4 = 24 (Given) 10x + 4 = 24 (Simplify) 10x = 20 (?) x = 2 (Division) What is the missing reason for the argument shown?
A)
addition
B)
division
C)
subtraction
D)
multiplication
Answer:
I think it is A or B Hope this helps
Step-by-step explanation:
Answer:
The answer is C.Subtraction im a math teacher so if right mark brainliest
Step-by-step explanation:
find the center and the radius of the circle with the equation x^2+6x+y^2+4y+12=0
Answer:
(x + 3)² + (y+ 2)² = 1²
Step-by-step explanation:
The standard form for the equation of a circle with centre (a, b) and radius r is
(x - a)² + (y - b)² = r²
x² + 6x + y² + 4y + 12 = 0
Step 1. Subtract the constant from each side
x² + 6x + y² + 4y = -12
Step 2. Complete the squares for x and y
Square half the coefficients of x and y
(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²
Step 3. Write the lhs as squares of binomials
(x + 3)² + (y+ 2)² = -12 + 3² + 2²
Step 4. Convert the rhs to a square
(x + 3)² + (y+ 2)² = -12 + 9 + 4
(x + 3)² + (y+ 2)² = 1
(x + 3)² + (y+ 2)² = 1²
The graph below shows that this is the equation for a circle with
centre (-3, -2) and radius 1.
The center and radius of the given circle are respectively; (-3, -2) and 1
What is the radius of the circle?The standard form for the equation of a circle with it's centre coordinate (a, b) and radius r is given as;
(x - a)² + (y - b)² = r²
Now, we are given the circle equation to be; x² + 6x + y² + 4y + 12 = 0
Let us subtract 12 from both sides to leave only the variables on the left side;
x² + 6x + y² + 4y + 12 - 12 = 0 - 12
x² + 6x + y² + 4y = -12
Now let us complete the squares for variable x and y;
Square half the coefficients of x and y and add to both the x, y and constant to get;
(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 3² + 2²
(x² + 6x + 3²) + (y² + 4y + 2²) = -12 + 9 + 4
(x² + 6x + 3²) + (y² + 4y + 2²) = 1
Write the left hand side as squares of binomial to get;
(x + 3)² + (y+ 2)² = 1
This can be also written as;
(x + 3)² + (y+ 2)² = 1²
Thus, from the general standard form of equation of a circle, we can say that;
centre is at (-3, -2) and radius is 1.
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Mark is making 10 kites.he uses 5yards of ribbon for each kite.he has already made 2 of the kites.how many yards of ribbon will mark need to make the rest of the kites?
Answer:
40 yards
Step-by-step explanation:
8×5≈40
for a snack,the members of an after school club ate five-eighths of 24 bagels. how many bagels did the group eat
Answer: 5/8 × 24 = 15
PLEASE HELP AS FAST AS POSSIBLE!!!!!!!
Find the appropriate answer for each word problem.
a. A group of twelve art students are visiting a local art museum for a field trip. The total cost of admission for the students is $125. What is the cost of admission for each student?
b. The school van can carry twelve passengers at a time. What is the least number of trips the van must make in order to bring 125 passengers to the same location?
c. Charlotte and her mother baked 125 cookies to give as Christmas gifts to their neighbors. If they plan to give a dozen cookies to each neighbor, how many neighbors will receive a gift?
d. Nicholas and Elaine are planning to serve cheesecake for dessert at their wedding and have purchased twelve cheesecakes. If the cheesecakes are divided evenly among the 125 wedding guests, how much cheesecake will each guest receive?
HELP AND PLS SHOW WORK.
please help me i really need it
Answer:
1. (2.923) 2. i don't know what they are asking for but i believe it is the mean so add all of the data up and divide by how many data pieces there are ( there are seven
Answer:
$0.79 x 3.7 would give you 2.923 but since its money it would be $2.92 and 2) im not sure how there the same question if one is dealing with weather and the other with money, Im sorry
What is the degree of x^5-4x+2
Answer:
5
Step-by-step explanation:
The degree of a polynomial is found by identifying the term with the largest exponent. The degree of a term is found by adding all the exponents of the variables of that term.
For example: [tex]3x^{2} yx^{3}[/tex]
The degree of this term is found by adding all the exponents: 2+1+3=6
In the case of a polynomial, it meets the largest degree term
For example: [tex]2x^{2} y+5x^{2} y^{2} z-8x^{4}[/tex]
If we add the exponents of each term, we will have the term with the greatest degree : 5
The degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.
What is the Degree of a Polynomial?The degree of a polynomial can be defined as the largest exponents on any of the variables of a polynomial of the largest sum of exponents, if any of it's term has multiple variables.
Thus: The largest exponent in [tex]x^5-4x+2[/tex] is 5.
Therefore, the degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.
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Suppose the path of a baseball follows the path graphed by the quadratic function ƒ(d) = –0.6d2 + 5.4d + 0.8 where d is the horizontal distance the ball traveled in yards, and ƒ(d) is the height, in yards, of the ball at d horizontal yards. Identify the domain and range that matches this situation.
Answer:
Domain is all real numbers
Range is
[tex]y\le 12.95[/tex]
Step-by-step explanation:
The given function is
[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]
This is a maximum quadratic function therefore the domain is all real numbers.
Let us complete the square to find the vertex.
[tex]f(d)=-0.6(d^2-9d)+0.8[/tex]
[tex]f(d)=-0.6(d^2+9d)+-0.6(\frac{9}{2})^2- -0.6(\frac{9}{2})^2+ 0.8[/tex]
[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{243}{20}+ 0.8[/tex]
[tex]f(d)=-0.6(d-\frac{9}{2})^2+\frac{259}{20}[/tex]
Therefore the range is
[tex]y\le \frac{259}{20}[/tex]
[tex]y\le 12.95[/tex]
See graph
Answer:
Domain:
[tex][0,9.146][/tex]
Range:
[tex][0,12.95][/tex]
Step-by-step explanation:
we are given
a baseball follows the path graphed by the quadratic function
[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]
where
d is the horizontal distance the ball traveled in yards
ƒ(d) is the height, in yards, of the ball at d horizontal yards
Domain:
we know that domain is all possible values of x for which any function is defined
So, for finding domain , we will take smallest x-value to largest x-value
so, we can set f(d)=0 and find zeros
[tex]-0.6d^2+5.4d+0.8=0[/tex]
we can use quadratic formula
[tex]d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]d=\frac{-54\pm \sqrt{54^2-4\left(-6\right)8}}{2\left(-6\right)}[/tex]
[tex]d=-\frac{\sqrt{777}-27}{6},\:d=\frac{27+\sqrt{777}}{6}[/tex]
[tex]d=-0.14579,d=9.146[/tex]
we know that d is a horizontal distance
and distance can never be negative
so, domain will be
[tex][0,9.146][/tex]
Range:
Since, this is quadratic equation
so, it is also equation of parabola
so, firstly we will find vertex of parabola
Suppose, we have
[tex]ax^2+bx+c=0[/tex]
Vertex is
[tex]x=\frac{-b}{2a}[/tex]
so, we can compare
a=-0.6
b=5.4
c=0.8
now, we can find vertex
[tex]x=\frac{-5.4}{2\times -0.6}[/tex]
[tex]d=4.5[/tex]
now, we can find y-value
[tex]f(4.5)=-0.6(4.5)^2+5.4(4.5)+0.8[/tex]
[tex]f(4.5)=12.95[/tex]
we can see
that leading coefficient is -0.6
which is negative
so, parabola opens downward
so, range will be
[tex][0,12.95][/tex]
An arithmetic sequence has a first term of 3 and a fifth term of 31. What is the second term?
Answer:
10
Step-by-step explanation:
let's call the difference in each term d so the sequence would look like
3,(3+d),(3+2d),(3+3d),(3+4d)
notice how in this sequence that (3+4d) is the fifth term so it must equal 31
3+4d=31
4d=28
d=7
now plug this into the second term
(3+(7))
and we see that the second term is 10
The value of the second term will be 10.
Since the arithmetic sequence has a first term of 3 and the fifth term of 31, this can be represented thus:
First term = a = 3
Fifth term = a + 4d = 31.
Substitute the value of a into the second equation.
a + 4d = 31
3 + 4d = 31
4d = 31 - 3
4d = 28.
d = 28/4
d = 7
Therefore, the value of the second term will be:
= a + d
= 3 + 7
= 10
The value of the second term will be 10.
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Helppppp pleaseeeeee
15) Yes, it is a function.
16)
A f(-4)=2
B F(3)= something around -1.75
C f(-5)=0
D f(-2)=4
E f(0)=0
F) -2
17)2(2a+5)=4a+10
a(a+5)=a^2+5a
18) 1
|x| – 7 = 8 plz help me
x = –1 or 1
x = 1
x = 15
x = –15 or 15
[tex]|x|- 7 = 8\\\\|x|=15\\\\x=-15 \vee x=15[/tex]
Answer:
x = –15 or 15
Step-by-step explanation:
|x| – 7 = 8
We need to isolate the absolute value.
Add 7 to each side
|x| – 7+7 = 8+7
|x| = 15
Now to get rid of the absolute values, we take what is inside the absolute values and set it equal to the right hand side. Remember we set it equal to the positive amount and the negative amount.
x=+15 and x=-15
Which answer shows the proper use of additive inverse’s
2a+b+(-b)=2a+0
2a+b=b+2a
2a+b+0=2a+b
(2a)* b=2(a*b)
Answer:
2a+b+(-b)=2a+0
Step-by-step explanation:
Additive inverse
x+ -x =0
Answer:
a would be the answer
Step-by-step explanation: the whole point of additive inverse is to add a negative number. So putting parenthesis around the negative number and then adding it to another number, would be correct. In my opinion it also looks easier to do.
Round 125.3546 to 1 decimal place
Rounding 125.3546 to 1 decimal place involves looking at the second decimal digit (5) and rounding up, resulting in 125.4.
We look at the second decimal digit, which is a 5. Since it is 5 or more, we round the first decimal place up. Therefore, 125.3546 rounded to 1 decimal place is 125.4.
An airplane is at an elevation of 35,000 ft when it its approach to an airport. Its angle of descent is 6°.
What is the distance between the airport and the point on the ground directly below the airplane?
What is the approximate air distance between the plane and the airport?
What would it be answer for 23 points
Answer:
t≤ 2
Step-by-step explanation:
The temperature must be 2F or less
t <=2
t≤ 2
am i correct?? thanks for checking my answer :)
Answer:
no
Step-by-step explanation:
since the y=mx+b format is used here, your b is -5. for this to be correct, your y-int needs to be on -5, not -2 as you have it. Other than that, i believe you are correct
Answer:
no
Step-by-step explanation:
the point has to be on the 5