Answer:tall
Step-by-step explanation:
tall
Solve the inequality 2x<8
The solution to the inequality 2x<8 is x<4.
Step-by-step explanation:
Given inequality is;
2x < 8
For solving this inequality, we will divide both sides by 2 to find the value of x, therefore;
Dividing both sides by 2
[tex]\frac{2x}{2}<\frac{8}{2}\\x<4[/tex]
It means that x is less than four.
Thus,
The solution to the inequality 2x<8 is x<4.
Keywords: inequality, division
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X÷3.7=5? Need help.
Answer:
x = 18.5
Step-by-step explanation:
Multiply 5 and 3.7.
Which equals 18.5.
Check: 18.5 / 3.7 = 5.√
Is the quotient for 215.6÷0 7 greater than or less than 215.06?
308 is greater than 215.06
Solution:
Given data: 215.6 ÷ 0.7
Let us first convert the fraction without decimal.
To remove a decimal point multiply and divide the fraction by 10.
[tex]\frac{215.6}{0.7}=\frac{215.6\times10}{0.7\times10}[/tex]
[tex]=\frac{2156}{7}[/tex]
If we divide 2156 by 7, we get quotient as 308.
Now, to compare the quotient with the number 215.06.
308 > 215.06
Hence, 308 is greater than 215.06.
It is greater than 215.06.
The calculation is as follows:[tex]= 215.06 \div 0.7[/tex]
= 308
This 308 should be more or greater than 215.06
Therefore we can conclude that It is greater than 215.06.
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make a question similar to the one below:
for example:
Solve this quadratic equation: x^2 = 81
and then solve it and explain how you did it.
Answer:
two solutions : 9 ; -9
Step-by-step explanation:
x²=81
means : x² - 81 =0 but 81 = 9²
use identity ; a² - b² = (a-b)(a+b)
x² -9² = 0 : (x-9)(x+9)=0
x-9=0 or x+9 = 0
x =9 or x = -9
Mrs. Jones asked Janae which perfect square comes between 100 and 144. Janae said that 120 is the perfect square becau
10-12=120. Is Janae correct? Bro please I’m dum
No, 120 is not a perfect square because you can't multiply a whole number by itself to get 120.
Yes, because 120 is an even number and all even numbers are perfect squares.
No, because the next perfect square is 125,
No, because there are no perfect squares between 100 and 144.22.
Answer:
Its the first option.
Step-by-step explanation:
120 is not a perfect square.
Its close to one though - 121 is a perfect square ( 11 * 11 = 121).
Answer:
a
Step-by-step explanation:
I toolk the test (: :)
In the figure below, ray was constructed starting from rays and . By using a compass D and G were marked equidistant from E on rays and . The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:
According to the construction described ∠ DEF ≅ ∠GEF by SSS congruence theorem
How to show that the two angles are congruent
Statement Reason
DE ≅ GE given
DF ≅ GF given
EF ≅ FE reflexive property
Δ DEF ≅ Δ GEF SSS congruence theorem
∠ DEF ≅ ∠GEF CPCTC
what is y+4=2(2x-1)
Answer:
y= 2(2x-1) -4
Step-by-step explanation:
you subtract 4 from both sides and it cancel outs at the y side(because 4-4 is 0) leaving just y.
Coordinate of 2x+6y=12 and 4x-3y=9
Answer:
The coordinate to the given equations is (3,1)
Step-by-step explanation:
Given equation is [tex]2x+6y=12\hfill (1)[/tex]
and [tex]4x-3y=9\hfill (2)[/tex]
To find the coordinate of the given equations :
Multiply the equation (2) into 2 we get
[tex]8x-6y=18\hfill (3)[/tex]
Now adding the equations (1) and (3) we get
[tex]2x+6y=12[/tex]
[tex]8x-6y=18[/tex]
_______________
[tex]10x=30[/tex]
[tex]x=\frac{30}{10}[/tex]
Therefore x=3
Substitute x=3 in (1)
2(3)+6y=12
6y=12-6
[tex]y=\frac{6}{6}[/tex]
Therefore y=1
The coordinate to the given equations is (3,1)
To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations using the method of substitution. The coordinates of the intersection point are (3, 1).
Explanation:To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations by using the method of substitution or elimination. Let's use the method of substitution:
From the first equation, solve for x: x = (12-6y)/2 = 6-3y.Substitute this value of x into the second equation: 4(6-3y)-3y=9.Simplify and solve for y: 24-12y-3y=9.Combine like terms: -15y = -15.Divide both sides by -15: y = 1.Substitute this value of y into either of the original equations to find x. Let's use the first equation: 2x + 6(1) = 12.Simplify and solve for x: 2x + 6 = 12, 2x = 6, x = 3.The coordinates of the intersection point are (3, 1).
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Can someone plz help!!!
Which of the following possibilities will form a triangle?
A: side 15 cm, side =7cm , side =7cm
B: side =14cm,side=6cm,side=8cm
C: side=14cm,side=6cm, side=7cm
D: side=15cm , side =7cm,side =9cm
=============================================
Explanation:
A triangle is only possible if you can add two sides and have that sum be larger than the third side. This is the triangle inequality theorem.
Choice A is ruled out because the second and third sides add to 7+7 = 14, but that's not larger than the first side 15.
Choice B is a similar story: 6+8 = 14 is not larger than 14 (the first side)
Choice C as well: 6+7 = 13 is not larger than 14
------
Choice D is the answer because
15+7 > 9
15+9 > 7
7+9 > 15
These three inequalities show that picking any two sides of this triangle, then adding them up, leads to a sum larger than the third side.
Caleb has an assignment to draw a contour map. What type of landform is he most likely drawing?
A- a creek
B- a valley
C- a hill
D- a shoreline
The type of land form that Caleb most likely draws is a hill. The answer is option C- a hill.
Step-by-step explanation:
Contour lines are drawn to represent the changes in the elevation which helps to know the slope of the figure drawn.If the contour lines are drawn close, then steeper the figure is. And more distant the lines are drawn, then less steep the figure is.Here, the lines seem to be likely circle in shape. The distance of the outermost contour line is 20 ft. The next inner lines will have reduced values of 20 ft.Therefore, the elevation gets reduced from higher to lower points which provides a diagram of a hill. Since there is no continuous high and low elevations, this cannot be a valley (a range of mountains).Furthermore, The contour diagram for option A and D such as creek(water stream) or shoreline will have different and mixed values of elevations that seems to be a messy structure of contour lines.The correct answer is option C. He most likely drawing a hill.
Contour maps are used to represent the topography or elevation of an area using contour lines. Contour lines connect points of equal elevation above a reference level (usually sea level).
A hill is typically represented on a contour map by concentric closed contour lines, with higher elevations towards the center and lower elevations towards the periphery.
Which equation demonstrates the distributive property?
A) 36 + 9 = 45
B) 36 + 9 = 3(12 + 3)
C) 36 x 9 = 9 x 36
D) (12 + 3)3 = 3(12 + 3)
Answer:
B) 36 + 9 = 3(12 + 3)
Step-by-step explanation:
The distributive property of multiplication over addition is:
a(b + c) = ab + ac
This is demonstrated by switching the sides of option B) 36 + 9 = 3(12 + 3)
Answer:
B
Step-by-step explanation:
B Because 12*3 = 36 and 3*3 =9
Lexie is making a scale drawing of a soccer field that is 120 yards long and 80 yards wide. If the field in Lexie’s drawing is 30 centimeters wide, how long should the field be in the drawing?
9514 1404 393
Answer:
45 cm
Step-by-step explanation:
The ratio of length to width is the same for the drawing as for the field.
length/width = L/(30 cm) = (120 yd)/(80 yd)
L = (30 cm)(3/2) = 45 cm . . . . . . multiply by 30 cm and simplify
The field should be 45 cm long on the drawing.
Final answer:
The soccer field in Lexie's scale drawing should be 45 centimeters long, using a scale factor based on the given width of 30 centimeters and the real soccer field's dimensions.
Explanation:
Lexie is scaling a real soccer field to a drawing, with the real field's dimensions being 120 yards long and 80 yards wide. When converting these dimensions to a scale drawing where the width is 30 centimeters, we need to find the drawing's length. To do this, we will use a scale factor.
First, we find the actual scale factor based on the given dimensions:
Actual width of soccer field = 80 yards
Width in the drawing = 30 centimeters
To convert yards to centimeters, we need to know that 1 yard equals 91.44 centimeters. Given this, the actual width in centimeters is 80 yards * 91.44 cm/yard = 7312 centimeters.
Now, we calculate the scale factor:
Scale factor = Width in the drawing / Actual width in centimeters = 30 cm / 7312 cm
Using this scale factor, we can find the length for the drawing:
Actual length of soccer field = 120 yards
Actual length in centimeters = 120 yards × 91.44 cm/yard = 10972.8 centimeters
Length in the drawing = Actual length in centimeters × Scale factor = 10972.8 cm × (30 cm / 7312 cm)
Calculating this gives us:
Length in the drawing = 45 centimeters
Therefore, the length of the soccer field in Lexie's drawing should be 45 centimeters.
Solve kx + 12 = 3kx for x.
[tex]
kx+12=3kx \\
12=2kx \\
x=\frac{12}{2k} \\
x=\frac{6}{k}
[/tex]
Hope this helps.
Answer: x=6/k
Step-by-step explanation:
kx + 12 = 3kx and subtract k from both sides
12=3kx-kx then simplify
12=2kx, now divide both sides by two
12/2=kx simplify again
6=kx divide next
6/k=x finally, switch sides to get x=6/k
Hope this helps, have a BLESSED and wonderful day, as well as a safe one!
-Cutiepatutie ☺❀❤
WILL GIVE BRAINLIEST!!! Which expression is equivalent to one over four n − 16? (5 points) one over four (n − 4) one over four (n − 64) 4(n − 4) 4(n − 64)
Answer:
The correct answer is 1/4(n - 64).
Step-by-step explanation:
1/4n - 16 Write Original expression
0.25n -16 Simplify the fraction
0.25(n - 64) Distribute(take out) 0.25 from n-16
1/4(n - 64)
At eagle bay it cost $12 per hour to rent a Canoe Nate and his friends rented a canoe for 4 hours and paid $68. Write and solve a linear equation to find the cost to rent the canoe for 7 hours
The cost to rent the canoe for 7 hours is $ 104
Solution:
At eagle bay it cost $12 per hour to rent a Canoe
Nate and his friends rented a canoe for 4 hours and paid $68
Let "x" be the number of hours rented
We can solve use the point slope equation
[tex]y-y_1 = m(x-x_1)[/tex]
Where, "m" is the rate of change
[tex](x_1, y_1)[/tex] is the sample point
From given,
m = 12
[tex](x_1, y_1) = (4, 68)[/tex]
Therefore,
[tex]y - 68 = 12(x-4)[/tex]
[tex]y - 68 = 12x -48\\\\y = 12x -48+68\\\\y = 12x + 20[/tex]
Thus the linear equation is found
Here, "y" represents the amount paid for "x" hours
Find the cost to rent the canoe for 7 hours
Substitute x = 7 in linear equation
y = 12(7) + 20
y = 84 + 20
y = 104
Thus cost to rent the canoe for 7 hours is $ 104
To find the cost to rent the canoe for 7 hours, we can use the equation: Cost = Rate x Time. Given that the rate is $12 per hour and the time is 4 hours, the cost can be calculated as $68. Therefore, the cost to rent the canoe for 7 hours would be $119.
Explanation:To find the cost to rent the canoe for 7 hours, we can use the equation:
Cost = Rate x Time
Given that the rate is $12 per hour and the time is 4 hours, we can substitute these values into the equation:
68 = 12 x 4
Solving for the rate, we get:
Rate = 68 ÷ 4
Therefore, the rate is $17 per hour. To find the cost to rent the canoe for 7 hours, we can multiply the rate by the time:
Cost = Rate x Time = 17 x 7 = $119
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A pet store usually keeps 12 birds per cage, and
there are 7 birds in the cage now. The equation
7 + x = 12 can be used to find the remaining
number of birds x that can be placed in the
cage. What is the solution of the equation?
Answer:
5
Step-by-step explanation:
One step equation. You would subtract 7 from 12 to get 5 because x would be alone now.
Which polynomial is factored completely?
4 (4 x Superscript 4 Baseline minus 1)
2 x (y cubed minus 4 y squared + 5y)
3 x (9 x squared + 1)
5 x squared minus 17 x + 14
Answer:
3x(9x^2+1) or C on edge
Step-by-step explanation:
did the test on edge and i got it right :
The polynomial that is factored completely is 5x^2 - 17x + 14, as it can be fully factored into (5x - 7)(x - 2) using the quadratic formula or factoring by inspection.
Explanation:The question requires us to determine which polynomial is factored completely. We have four options to consider.
4(4x^4 - 1) is not factored completely because the expression inside the parentheses is a difference of squares and can be factored further into (2x^2 + 1)(2x^2 - 1).2x(y^3 - 4y^2 + 5y) is not factored completely because the expression inside the parentheses does not factor further in terms of integer coefficients.3x(9x^2 + 1) cannot be factored further since 9x^2 + 1 is a sum of squares, which is not factorable in the set of real numbers.5x^2 - 17x + 14 is a quadratic equation of the form ax^2 + bx + c. By applying the quadratic formula or through factoring by inspection, we find that it factors completely into (5x - 7)(x - 2).Hence, the polynomial that is factored completely is 5x^2 - 17x + 14.
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Angle e measures 126LaTeX: ^\circ∘. What is the measure of LaTeX: \angle∠h?
PLEASE HURRY will give brainliest
Group of answer choices
A 108LaTeX: ^\circ ∘ ∘
B 36LaTeX: ^\circ ∘ ∘
C 126LaTeX: ^\circ ∘
D 54LaTeX: ^\circ
Option C: 126° is the correct answer
Step-by-step explanation:
When two lines intersect, the four angles are formed. The angles vertically opposite with same vertex are called vertical opposite angles.
The opposite vertical angles are equal.
In the given figure, the pairs of vertically opposite angles are e,h and f,g.
Given
∠e = 126°
The measurement of e and h will be equal as they are vertically opposite
So,
m∠e = m∠h
m∠h = 126°
Hence,
Option C: 126° is the correct answer
Keywords: Vertical angles, lines
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What is the next number in the pattern of perfect squares shown below?
1,9, 25, 49 ...
A.36
B.64
C.81
D.121
Answer: 81
Step-by-step explanation:
The pattern of the sequence is :
[tex]1^{2}[/tex] , [tex]3^{2}[/tex] , [tex]5^{2}[/tex] , [tex]7^{2}[/tex] , [tex]9^{2}[/tex] ...
Which will be :
1 , 9 , 25 , 49 , 81 , ...
Therefore , the next pattern in the sequence is 81
For what value of x is the function g(x)=x/1-x NOT defined?
The function is definately defined at x=0 but not x=1.
But its just one part of the coordinate (x,y).
If the value of y or f(x) is considered, you'll see that it is never possible to attain f(x)=0. In other terms (x,y)= (0,0) is not a defined point in the graph of the function because the graph doesnt pass through that point.
Now I hope you understood what I meant!
Conclusion- The above function is not defined at all points in the space having the abscissa or x=1 in the coordinate and also at ordinate or y=0 in the coordinate.nation:
The value of x for which the function g(x)=x/1-x is not defined is at x = 1.
When does a value of a function become undefined?A value of a function becomes not defined when the denominator of that function becomes zero.
The value for which the function becomes zero is given below:The function is g(x)=x/1-x.
We can substitute the different values of x to find which makes the function not defined.
For x = -1:g(-1) = -1/1-(-1)
= -1/2
The function is defined.
For x = 0:g(0) = 0/1-0
= 0
The function is defined.
For x = 1:g(1) = 1/1-1
= 1/0 = not defined
The function is not defined.
For x = 2:g(2) = 2/1-2
= 2/-1 = -2
The function is defined.
Therefore, we have found that the value of x for which the function g(x)=x/1-x is not defined is at x = 1.
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Which of the graphs below correctly solves for x in the equation −x2 − 3x − 1 = −x − 4?
Graph of quadratic opening downward and linear sloping up to the right. They intersect at point negative 4, negative 2 and point 0, 2.
Graph of quadratic opening upward and linear sloping up to the right. They intersect at point 0, 2 and point 4, 6.
Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5.
Graph of quadratic opening upward and linear sloping up to the right. They intersect at point 2, 0.
Answer:
Graph of quadratic opening downward and linear sloping up to the left. They intersect at point negative 3, negative 1 and point 1, negative 5
Step-by-step explanation:
we have
[tex]-x^{2} -3x-1=-x-4[/tex]
we can separate the expression above into two equations
[tex]y=-x^{2} -3x-1[/tex] ----> equation A
This is a quadratic equation ( vertical parabola) open downward (the leading coefficient is negative)
[tex]y=-x-4[/tex] ----> equation B
This is a linear equation with negative slope (decreasing function).so linear sloping up to the left
The solution of the original expression are the x-coordinates of the intersection point both graphs
using a graphing tool
The intersection points are (-3,-1) and (1,-5)
see the attached figure
Answer: C is the correct choice
Step-by-step explanation:
These points are linear.
Find the slope.
x|2|3|4 5 6 7
y 10/15/20 25 30 35
slope = [?]
How to solve 17=-13-8x
Answer:
Explanation:
add 13 to both sides of the equation.
17+13=−8x.
30=−8x.
divde both sides by −8.
30−8=x⇒x=−308=−154.
As a check.
Step-by-step explanation:
Answer:
Step-by-step explanation:
17 = -13 - 8x....add 13 to both sides
17 + 13 = -13 + 13 - 8x
30 = -8x...now divide both sides by -8
-30/8 = (-8/-8)x
-30/8 = x.....reduce
- 15/4 = x <===
ASAP.....................................
What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. Negative three-fourths + one-half A number line going from negative 2 to positive 2 in increments of one-fourth. Negative 1 and one-fourth Negative one-fourth One-fourth 1 and one-fourth
Answer:
C. Negative three-fourths
Step-by-step explanation:
Step-by-step explanation:
Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:
-1 1/4 + 1/2
Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:
-5/4 + 1/2
Taking the LCM of the expression
= (-5+2)/4
= -3/4
Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths
Final answer:
To add negative three-fourths and one-half, we first convert 1/2 to 2/4 to have the same denominator as -3/4. Adding the numerators gives us -1/4 as the sum, which can be visualized on the number line.
Explanation:
The student has asked how to find the sum of the fractions negative three-fourths (-3/4) and one-half (1/2) using a number line and equivalent fractions. To solve this problem intuitively, we can use our understanding of fractions as parts of a whole. First, we need to find a common denominator which is the least common multiple of 4 and 2, which is 4 in this case. So, we convert 1/2 to 2/4 since one half of one-half is one quarter, and then add it to -3/4.
Now, we have -3/4 + 2/4, which simplifies to -1/4 when we add the numerators, -3 and +2. This result can be visually confirmed on a number line. If we start at -3/4 on the number line and move 2/4 (which is half) to the right, we'll end up at -1/4, between -1 and 0.
Through this intuition and number line visualization, we have determined that -3/4 plus 1/2 equals -1/4. This highlights how our intuition about everyday things like parts of a pie or quarters in a dollar can help us with fraction operations like addition and finding common denominators.
Isaac purchased a house for $109,400.00. Every year, Isaac makes improvements so that the value of the house goes up by 3%. Which of the following inequalities can be used to determine the number of years after purchase, t, that the value of Isaac's house will be more than $120,340.00?
The correct inequality is: C. $114,840.00(1 + 0.04)^2 > $115,362.00.
It correctly applies compound interest to determine when the house value exceeds $114,840.00.
To determine the number of years [tex](\( f \))[/tex] after purchase that the value of Isaac's house will be more than $114,840.00, we can use the formula for compound interest.
The formula for compound interest is given by:
[tex]\[ A = P(1 + r)^n \][/tex]
Where:
- A is the future value of the investment/asset.
- P is the initial principal amount (the initial value of the investment/asset).
- r is the annual interest rate (expressed as a decimal).
- n is the number of years the asset is invested for.
In this case:
- [tex]\( P = \$104,400.00 \)[/tex] (the initial value of the house).
- r = 0.04 (the annual rate of increase, which is 4% expressed as a decimal).
- We want to find the value of n when [tex]\( A > \$114,840.00 \)[/tex].
So, the inequality to represent this scenario is:
[tex]\[ \$114,840.00 < \$104,400.00(1 + 0.04)^n \][/tex]
Now, let's compare this inequality with the options provided:
A. [tex]\( \$114,840.00(1 + 0.04)^{n+1} > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( n + 1 \) instead of \( n \)[/tex] in the exponent.
B. [tex]\( \$114,840.00(0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (0.04)^2 \)[/tex] instead of [tex]\( (1 + 0.04)^n \)[/tex].
C. [tex]\( \$114,840.00(1 + 0.04)^2 > \$115,362.00 \)[/tex] - This option is correct. It uses the correct formula for compound interest and compares it to the threshold value of [tex]\$114,840.00[/tex].
D. [tex]\( \$114,840.00(1 - 0.04)^2 > \$115,362.00 \)[/tex] - This option is incorrect because it uses [tex]\( (1 - 0.04)^2 \) instead of \( (1 + 0.04)^n \).[/tex]
Therefore, the correct inequality is option C:
[tex]\[ \$114,840.00(1 + 0.04)^2 > \$115,362.00 \].[/tex]
Correct question is:
Isaac purchased a house for $104,400.00.
Every year, Isaac makes improvements so that the value of the house goes up by 4% Which of the following inequalities can be used to determine the number of years after purchase, f, that the value of Isaac's house will be more than $114,840.00?
[tex]A. $114,840.00(1+0.04)^r+1 > $115,362.00[/tex]
[tex]B. $114,840.00(0.04)^2 > $115,362.00[/tex]
[tex]C. $114,84000(1+0.04)^2 > $115,362.00[/tex]
[tex]D. $114,84000(1-0.04)^2 > $115,362.00[/tex]
A boat travelled 231 km downstream and back. The trip downstream took 11 hours. The trip back took 77 hours. Find the speed of the boat in still water and the speed of the current
Speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
Solution:
From given,
Downstream distance = 213 km
Time taken for downstream = 11 hours
Thus, speed is given as:
[tex]\text{Downstream speed} = \frac{\text{Downstream distance}}{\text{time taken}}[/tex]
[tex]\text{Downstream speed} = \frac{231}{11} = 21[/tex]
Thus downstream speed is 21 km/hr
Also,
Upstream distance = 213 km
Time taken for upstream = 77 hours
Thus, speed is given as:
[tex]\text{Upstream speed} = \frac{\text{Upstream distance}}{\text{time taken}}\\\\\text{Upstream speed} = \frac{231}{77} = 3[/tex]
Thus upstream speed is 3 km/hr
If the speed downstream is "a" km/hr and the speed upstream is "b" km/hr , then:
[tex]\text{Speed in still water } = \frac{1}{2}(a+b)\\\\\text{Speed of current } = \frac{1}{2}(a-b)[/tex]
Here, a = 21 and b = 3
Therefore,
[tex]\text{Speed in still water } = \frac{1}{2}(21+3) = \frac{24}{2} = 12\\\\\text{Speed of current } = \frac{1}{2}(21-3) = \frac{18}{2} = 9[/tex]
Thus speed of boat in still water is 12 km/hr and speed of current is 9 km/hr
The speed of boat in still water is 12 km/hr as:
Let speed of Boat be 'b' and speed of Current be 'c'.
Distance given is 210 miles.
Therefore speed for downstream = 210 ÷ 10=21 mph
speed for upstream =3mph
Now we can form the two equations as :
i) b+c = 21 ......(i) For downstream
ii) b-c = 3.........(ii) For Upstream
Solving by substitution method :
From equation (ii) c = b - 3 Substitute this value of c in equation
(i) we get b + b - 3 = 21
Therefore b = 12. Now substitute the value of b in any of the equations above (i) or (ii) and get c= 9
b= 12 and c = 9.
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Is each product less than 1 equal to 1 or greater than 1 ? 2 x 1/3 5 x 1/3 1/2 x 3
Each multiplication problem was evaluated individually, revealing that two products are greater than 1 and one is less than 1.
When evaluating whether each product is less than 1, equal to 1, or greater than 1, it's important to consider the values being multiplied. Let's examine each multiplication problem provided:
2 x 1/3: Multiplying 2 by one-third gives us 2/3, which is less than 1.
5 x 1/3: Multiplying 5 by one-third gives us 5/3, which simplifies to 1 and 2/3, meaning it is greater than 1.
1/2 x 3: Multiplying one-half by 3 gives us 3/2, which simplifies to 1 and 1/2, so this is also greater than 1.
Write the polynomial function, in standard form, that has zeros -1, -2, and 3.
Answer:
The sum of the roots of a polynomial is 5/3, the product of the same polynomial is -11. Write the polynomial function in standard form.n:
Answer:
f(x) = x³ - 7x - 6
Step-by-step explanation:
Given that the zeros are x = - 1, x = - 2 and x = 3 then the corresponding factors are
(x + 1), (x +2) and (x - 3)
The polynomial is then the product of the factors, that is
f(x) = (x + 1)(x + 2)(x - 3) ← expand the first pair using FOIL
= (x² + 3x + 2)(x - 3) ← distribute
= x³ - 3x² + 3x² - 9x + 2x - 6 ← collect like terms
= x³ - 7x - 6
5/y + 7/x =24
12/y + 2/x =24 ,find the ratio of x to y.
Answer:
Step-by-step explanation:
5/y + 7/x =24.........(1)
12/y + 2/x =24........(2)
Let 1/y = a and 1/x = b
5a + 7b = 24 ...........(3)
12a + 2b = 24...........(4)
Multiply (3) by 2 and (4) by 7
10a + 14b = 48..........(5)
84a + 14b = 168.........(6)
Substracting (5) from (6)
84a - 10a = 168 - 48
74a = 120
a = 120/74
a = 60/37
Putting a = 60/37 in (3)
5a + 7b = 24
5(60/37) + 7b = 24
300/37 + 7b = 24
Multiply each term 37
300 + 259b = 888
259b = 888 - 300
259b = 588
b = 588/259
And a = 1/y
60/37 = 1/y
Cross multiply
60y = 37
y = 37/60
Also
b = 1/x
588/259 = 1/x
Cross multiply
588x = 259
x = 259/588
The ratio of the variables 'x' and 'y' will be 5/7.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of equations is given below.
5/y + 7/x =24
12/y + 2/x =24
Let 1/x = X and 1/y = Y. Then the equation is given as
5Y + 7X = 24 ...1
12Y + 2X = 24 ...2
From equations 1 and 2, then we have
12[(24 - 7X) / 5] + 2X = 24
288 - 84X + 10X = 120
74X = 168
X = 168 / 74
1/x = 168/74
x = 74/168
The value of the variable Y is given as,
12Y + 2(168 / 74) = 24
12Y = 720 / 37
Y = 60/37
1/y = 60/37
y = 37/60
The ratio of the variable 'x' and 'y' will be given as,
Ratio = x / y
Ratio = (74 / 168) / (37 / 60)
Ratio = (74 / 168) x (60 / 37)
Ratio = 5/7
The ratio of the variables 'x' and 'y' will be 5/7.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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4-2 3/5 how can I get the answer to this problem