Answer:
The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions
Step-by-step explanation:
Given two linear equations as :
2 y - 4 x = 6 .......1
y - 2 x = 7
Or, y = 2 x + 7 .......2
Now, Solving these two equations
Put the value of y from eq 2 into eq1
So, 2 y - 4 x = 6
∴ 2 × (2 x + 7) - 4 x = 6
Or, 4 x + 14 - 4 x = 6
or, (4 x - 4 x) = 6 - 14
i.e 0 = - 8
∵ The expression that comes after solving the two linear equation is independent of variables So , The system of equations has no solutions Answer
Rearrange the equation so n is the independent variable.
m+1= -2(n +6)
m
=
Answer:
n= (-m-13)/2
Step-by-step explanation:
look @ photo
Answer: m=-2n-13
↗️⬆️↖️
Consider this quadratic equation.
x2 + 1 = 2x – 3
Which expression correctly sets up the quadratic formula?
Answer:A
Step-by-step explanation:
The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].
Hence, option A is the correct answer.
What is a Quadratic Equation?Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
Using the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given that;
x² + 1 = 2x – 3
First we re-arrange the the equation.
x² + 1 = 2x - 3
x² - 2x + 1 + 3 = 0
x² - 2x + 4 = 0
Hence;
a = 1b = -2c = 4Next we input this values into the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
x = (-(-2)±√((-2)² - 4(1)(4))) / (2(1))
[tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex]
The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].
Hence, option A is the correct answer.
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In forensic anthropology, the length of the femur bone (the thigh bone) in the skeleton is used to estimate the height of the person when he or she was alive. The height of a person is estimated to be 4 times the length of the femur.22
(a)If the femur bone on a female skeleton measures 15.5 inches, approximately how tall was the
woman?
(b) If the femur bone on a male skeleton measures 17 inches, approximately how tall was the
man?
(C) Write an equation for the height, H. of a person with femur bone of length b.
(d) Graph the equation H with height on the y-axis and bone length on the z-axis. Your graph
should include heights up to 80 inches.
(e) What is the slope of your line? What does it mean in this context?
(f) Use your equation or the graph to estimate the length of your own femur bone. (Be sure to
indicate your height and how you figured out your estimated femur bone length.)
I need the quadratic formula.
Answer:
ax^2+bx+c=0
Step-by-step explanation:
hope this helps
Answer:
[see picture]
Step-by-step explanation:
The formula shown in the picture is the quadratic formula.
When:
[tex]ax^2+bx+c=0[/tex]
a, b, c ≠ 0
x = unknown
Use the distributive property to write an equivalent expresión to 4(6x+5)
Answer: 6(4x + 5)
Step-by-step explanation: 4(6x + 5) 24x + 20
A 20-ft-long wire is used to support a television antaans. The wire is connected to the
antenna 15 ft above the ground. How far away from the base of the tower will the other
end of the wire be located?
Answer:
The distance of base of wire to the base of tower is 13.27 ft
Step-by-step explanation:
Given as :
The measure of wire connected between base ad antenna top = 20 ft
The wire is connected to the antenna on tower at height h = 15 ft above the ground
Let The distance of base of wire to the base of tower = x ft
Let the angle drawn on ground = Ф
Now, According to question
In figure AOB
Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm hypotenuse}[/tex]
i.e SinФ = [tex]\dfrac{\textrm AB}{\textrm BO}[/tex]
Or, SinФ = [tex]\dfrac{\textrm h}{\textrm 20}[/tex]
Or, SinФ = [tex]\dfrac{\textrm 15}{\textrm 20}[/tex]
Or, SinФ = [tex]\dfrac{\textrm 3}{\textrm 4}[/tex]
or, Ф = [tex]sin^{-1}(\frac{3}{4})[/tex]
∴ Ф = 48.5°
Now, Again from figure
Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]
i.e TanФ = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]
Or, Tan 48.5° = [tex]\dfrac{\textrm h}{\textrm x}[/tex]
Or, 1.13 = [tex]\dfrac{\textrm 15}{\textrm x}[/tex]
∴ x = [tex]\dfrac{\textrm 15}{\textrm 1.13}[/tex]
i.e x = 13.27 feet
So, The distance of base of wire to the base of tower = x = 13.27 ft
Hence, The distance of base of wire to the base of tower is 13.27 ft Answer
Final answer:
The other end of the wire will be located approximately √175 ft away from the base of the tower.
Explanation:
To find the distance from the base of the tower to the other end of the wire, we can use the Pythagorean theorem. The wire forms the hypotenuse of a right triangle, with one leg being the height of the antenna and the other leg being the distance from the base of the tower. Let's call this distance 'x'.
Using the Pythagorean theorem, we have:
x² + 15² = 20²
Simplifying this equation, we get:
x² = 20² - 15²
x² = 400 - 225
x² = 175
Taking the square root of both sides, we find:
x = √175
So the other end of the wire will be located approximately √175 ft away from the base of the tower.
A $10,000 deposit at the bank will double in value in 9 years. Give a formula for the accumulated amount t years after the investment is made
Answer:
[tex]S = P(1.08)^{t}[/tex]
Step-by-step explanation:
A $10,000 deposit at the bank will double in value in 9 years.
If the interest is r% and it is compounded each year, then we can write from the formula of compound interest that
[tex]20000 = 10000(1 + \frac{r}{100})^{9}[/tex]
⇒ [tex]2 = (1 + \frac{r}{100})^{9}[/tex]
⇒ [tex]1 + \frac{r}{100} = 1.08[/tex]
⇒ r = 8%
Therefore, the formula for the accumulated amount t years after the investment is made will be
[tex]S = P(1 + \frac{8}{100})^{t} = P(1.08)^{t}[/tex]
where, P is the invested principal and S is the accumulated sum. (Answer)
A person kicks a 4.0-kilogram door with a 48-newton force causing the door to accelerate at 12 meters per second 2 . What is the magnitude of the force exerted by the door on the person? A. 48 N B. 24 N C. 12 N D. 4.0 N
According to Newton's Third Law of Motion, the force exerted by the door on the person who kicks it, is equal and opposite to the force the person exerts on the door, i.e., 48 Newtons.
Explanation:The question asks about the force exerted by a door on a person if the person kicks the door with a certain force. This scenario illustrates Newton's Third Law of Motion, which states: 'For every action, there is an equal and opposite reaction.' So, if the person exerts a force of 48 Newtons on the door, then the door will exert an equal and opposite force of 48 Newtons on the person. Therefore, the answer is A. 48 N.
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There are 12 female students and 18 male students in a class. Which of the following expresses the ratio of female students to male students in simplest form?
A.3/2
B.3 to 2
C.2/3
D.3:2
Answer:
C. 2/3
Step-by-step explanation:
12 female / 18 male
Dividing by 6 we get:
2 female / 3 male
or 2/3
Answer:
C.2/3
Step-by-step explanation:
A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3c > 240. Which graph represents this inequality?
Answer:
Graph 3.
Step-by-step explanation:
Since they need to earn $240 by selling $3 candy bars, they must sell at least 80 candy bars since 240/3 = 80.
With this in mind, selling more than 80 candy bars would be acceptable, but selling less would not which is why the third graph is correct.
Answer:
c
Step-by-step explanation:
Rewrite the function by completing the square.
h(x)= x^2+3x-18
Answer:
Step-by-step explanation:
Simplifying
h(x) = x2 + 3x + -18
Multiply h * x
hx = x2 + 3x + -18
Reorder the terms:
hx = -18 + 3x + x2
Solving
hx = -18 + 3x + x2
Solving for variable 'h'.
Move all terms containing h to the left, all other terms to the right.
Divide each side by 'x'.
h = -18x-1 + 3 + x
Simplifying
h = -18x-1 + 3 + x
Reorder the terms:
h = 3 + -18x-1 + x
Answer:
h(x)= (x+3/2 ) ^2 − 81/4
Step-by-step explanation:
Its correct :)
Which graph represents the function
-10 -3 -6 -4 -
I
4
6
8
10
x
1
0
-10
There are no illustrations, so it is impossible to answer this question. I apologise.
what does -16-3 equal
Answer:
Step-by-step explanation:
it equals -19
Answer:
The value of the given expression [tex]-16-3=-19[/tex]
Step-by-step explanation:
Given expression is [tex]-16-3[/tex]
To find the value of the given expression:
[tex]-16-3=-16-3[/tex]
Now taking the negative sign (-) outside the terms of the above equation we get,
[tex]-16-3=-(16+3)[/tex]
Now apply the algebraic sum to the above expression we get,
[tex]=-19[/tex]
Therefore [tex]=-19[/tex]
The value of the given expression is [tex]-16-3=-19[/tex]
20% tip on a bill of 86.74
Answer:
$17.35
Step-by-step explanation:
86.74*.2
Which system of linear inequalities has the point (2, 1) in its solution set?
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.
y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.
y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 4, negative 2) and (0, 0). Everything below the line is shaded.
Answer:Its C
Step-by-step explanation:
ED 2023
The correct answer is provided by the third system.
To determine which system of linear inequalities includes the point (2, 1), we need to substitute this point into each inequality and check if the inequalities hold true. Let's evaluate each system step-by-step:
System 1
y < -x + 3y [tex]\leq[/tex] 0.5x + 3Evaluating at (2, 1):
1 < -2 + 3 → 1 < 1 (False)1 ≤ 0.5(2) + 3 → 1 ≤ 4 (True)The point (2, 1) does not satisfy the first inequality, so it is not in the solution set for the first system.
System 2
y < -0.5x + 3y < 0.5xEvaluating at (2, 1):
[tex]1 < -0.5(2) + 3 \rightarrow 1 < 2[/tex] (True)[tex]1 < 0.5(2) →\rightarrow 1 < 1[/tex] (False)The point (2, 1) does not satisfy the second inequality, so it is not in the solution set for this system either.
System 3
y [tex]\leq[/tex] -x + 3y [tex]\leq[/tex] 0.5x + 2Evaluating at (2, 1):
[tex]1 \leq -2 + 3 \rightarrow 1 \leq 1[/tex] (True)[tex]1 \leq 0.5(2) + 2 \rightarrow 1 \leq 3[/tex] (True)The point (2, 1) satisfies both inequalities, so it is in the solution set for the third system.
System 4
y < 0.5xy [tex]\leq[/tex] -0.5x + 2Evaluating at (2, 1):
[tex]1 < 0.5(2) \rightarrow 1 < 1[/tex](False)[tex]1 \leq -0.5(2) + 2 \rightarrow 1 \leq 1[/tex] (True)The point (2, 1) does not satisfy the first inequality, so it is not in the solution set for the fourth system.
The system of linear inequalities that includes the point (2, 1) is the third one: y [tex]\leq[/tex] -x + 3, and y [tex]\leq[/tex] 0.5x + 2.
Mr jones is planning to pant grass and place afence in a small area for his dog. The rectagular dimension are 12×15 feet. The grass costs 50 cents per square foot. The small fence costs $8.00 per linear foot.
Answer:
A) The total feet needed for the fence total perimeter is 54 feet
B) The total cost of fence is $432
C) The square feet of grass needed foe the total area is 180 square feet
D) The total cost of the project is $572
Step-by-step explanation:
Given as :
The dimension of rectangular field
Length of rectangular field = L = 12 feet
width of rectangular field = w = 15 feet
The cost of grass per square foot = 50 cents = $0.5 ( ∵ 1 cents = $0.01 )
The cost of small fence = $8 per linear foot
Now, According to question
A ) Let The total feet needed for the fence total perimeter = A feet
∵ Perimeter of rectangular field = 2 × Length + 2 × width
Or, A = 2 × L + 2 × w
Or, A = 2 × 12 feet + 2 × 15 feet
Or, A = 24 feet + 30 feet
∴ A = 54 feet
So, The total feet needed for the fence total perimeter = A = 54 feet
B ) Let The total cost of fence = $B
So, The total cost of fence = The cost of small fence × perimeter of fence
i.e B = $8 × 54 feet
∴ B = $432
So,The total cost of fence = B = $432
C) Let the square feet of grass needed foe the total area = C square feet
∵The Area of rectangular fence = Length × width
Or, The square feet of grass needed foe the total area = Area of rectangular fence = L × w
i.e C = 12 feet × 15 feet
Or, C = 180 feet²
So,The square feet of grass needed foe the total area = C = 180 square feet
D) Let The total cost of grass = $D
∵ The cost of grass per square foot = $0.5
So,Total cost of grass = $0.5 × Area of fence
i.e D = $0.5 × 180 feet²
Or, D = $90
So, The Total cost of grass = D = $90
E) Let the total cost of the project = $E
∵Mr. Jones spend additional $50 for tools
So, The total cost of the project = money spent on tools + total cost of fence + Total cost of grass
i.e E = $50 + B + D
Or, E = $50 + $432 + $90
∴ E = $572
So, The total cost of the project = E = $572
Hence,
A) The total feet needed for the fence total perimeter is 54 feet
B) The total cost of fence is $432
C) The square feet of grass needed foe the total area is 180 square feet
D) The total cost of the project is $572 Answer
suppose you order two pizzas, 2 garlic breads, and one order of barbecue wings. how much change would you receive from $30?
Answer:
$6
The drawings will help
Which function represents the graph below ?
Answer:
The first choice.
Step-by-step explanation:
We only need to know one part of this step function to figure out the answer. The first step is y=-1 if -6<x<=-4, this knocks out the 2nd and 3rd answer choices as they don't follow this equation.
Simplify the following expression. 4 to -11/3 power ÷ 4 to -2/3 power
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}}\implies \cfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\implies 4^{-\frac{11}{3}}\cdot 4^{\frac{2}{3}}\implies 4^{-\frac{11}{3}+\frac{2}{3}} \\\\\\ 4^{-\frac{9}{3}}\implies 4^{-3}\implies \cfrac{1}{4^3}\implies \cfrac{1}{64}[/tex]
in the Venn diagram 60 farms only grow potatoes or sugar beets 4/5 of these 60 farms grow potatoes the number of farms that grow potatoes are 3 times the number that grow sugar beets complete the Venn diagram
To complete the Venn diagram, calculate that 48 out of 60 farms grow potatoes and the remaining 16 grow sugar beets, since the potato farms number is three times the sugar beet farms.
Explanation:The question asks us to complete a Venn diagram with information about how many farms grow potatoes vs sugar beets, given that 60 farms grow one or the other, not both. 4/5 of the 60 farms grow potatoes, which is 48 farms.
Since the number of farms that grow potatoes is three times the number that grow sugar beets,
we can determine the number of sugar beet farms by dividing the number of potato farms by 3, giving us 16 farms growing sugar beets.
Here's the step-by-step solution:
Calculate the number of farms that grow potatoes: 4/5 of 60 = 48.Since the potato farms are three times the sugar beet farms, divide the potato farms by 3 to get the number of sugar beet farms: 48 / 3 = 16.Use these numbers to complete the Venn diagram with the two disjoint sets, one with 48 (potatoes) and the other with 16 (sugar beets).Mike had 2/3 of a cake. He cut 3/4 of the cake to wrap and store in the freezer.
He ate the remaining portion
How much of the cake did he eat
A. 3/4
B. 1/4
C. 1/2
D. 1/8
E. 1/6
E
The portion of cake Mike ate is 1/6.
The numbers given are expressed as fractions. Fractions are numbers that consist of numerators and denominators. For example, in the fraction 2/3, 2 is the numerator and 3 is the denominator.
The first step is to determine which portion of the cake that was stored in the freezer.
Portion kept in the freezer = 2/3 x 3/4 = 1/2
The second step is to determine the amount of cake Mike ate.
2/3 - 1/2
[tex]\frac{4 - 3}{6}[/tex] = [tex]\frac{1}{6}[/tex]
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The portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
The given parameters:
Original fraction of cake Mike possessed = 2/3Fraction of the cake Mike stored = 3/4The portion of the cake that Mike wrapped and stored in the freezer is calculated as follows;
[tex]= \frac{3}{4} \times \frac{2}{3} \\\\= \frac{1}{2}[/tex]
The portion of the cake that Mike ate is calculated as follows;
[tex]remaining = original - portion \ stored\\\\remaining = \frac{2}{3} - \frac{1}{2} = \frac{4 - 3}{6} = \frac{1}{6}[/tex]
Thus, the portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
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For what value of x does 32x – 93x-4?
оооо
the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]
To find the value of x that satisfies the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex], we can use the quadratic formula:
[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
Where:
- a = 32
- b = -93
- c = -4
Now, let's plug these values into the quadratic formula:
[tex]\[ x = \frac{{-(-93) \pm \sqrt{{(-93)^2 - 4 \cdot 32 \cdot (-4)}}}}{{2 \cdot 32}} \]\[ x = \frac{{93 \pm \sqrt{{8649 + 512}}}}{{64}} \]\[ x = \frac{{93 \pm \sqrt{{9161}}}}{{64}} \]\[ x = \frac{{93 \pm 95.7}}{{64}} \][/tex]
Now, we have two possible solutions:
[tex]\[ x_1 = \frac{{93 + 95.7}}{{64}} \]\[ x_2 = \frac{{93 - 95.7}}{{64}} \]\[ x_1 \approx \frac{{188.7}}{{64}} \]\[ x_2 \approx \frac{{-2.7}}{{64}} \]\[ x_1 \approx 2.95 \]\[ x_2 \approx -0.042 \][/tex]
Therefore, the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]
The probable question maybe:
What are the solutions for x in the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex]?
help plz ASAP graph the solution to the inequality on the number line : q < 69.5
Answer:
Step-by-step explanation:
Remember:
If something is:
-equal to a number
-equal to or less then a number
-euqal to or greater than a number
Then you you would use a closed mark with an arrow.
Note: Don't use the arrow for the "equal to" part
If something is greater/less than a number:
Then you would use an open mark with an arrow
So since you're using the inequality q < 69.5,
You would graph it with an open mark with a left arrow, and the open mark must be on the number 69.5
The graph the solution to the given inequality on the number line plotted below.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is q < 69.5.
The result can be shown in multiple forms.
Inequality Form:q<69.5
Interval Notation:(−∞,69.5)
Therefore, the graph the solution to the given inequality on the number line plotted below.
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In the expression ax+bx,a is a decimal and b is a fraction. How do you decide whether to write a as a fraction or b as a decimal?
To decide whether to write a as a fraction or b as a decimal in the expression ax+bx, consider the context of the problem. If dealing with measurements or real-life quantities, write a as a decimal. If dealing with parts of a whole or ratios, write b as a fraction.
Explanation:In the expression ax+bx, a is a decimal and b is a fraction. To decide whether to write a as a fraction or b as a decimal, you can consider the context of the problem or the specific instructions. If the problem involves measurements or real-life quantities, it is more appropriate to write a as a decimal. On the other hand, if the problem deals with parts of a whole or ratios, it is more appropriate to write b as a fraction.
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Whether you write 'a' as a fraction or 'b' as a decimal in the expression ax+bx depends on the context of the problem you're solving. 'a' can be converted to a fraction by expressing the decimal in fractional terms, whereas 'b' can be turned into a decimal by dividing the numerator by the denominator.
Explanation:In the expression ax+bx, where 'a' is a decimal and 'b' is a fraction, deciding whether to write 'a' as a fraction or 'b' as a decimal depends largely on the problem you're solving and what format is most convenient or understandable. To convert 'a' from a decimal to a fraction, you can write the decimal in fractional form. If the denominator is not 100, convert it to a fraction with a denominator of 100, which then allows you to present it as a percentage. On the other hand, to convert 'b' from a fraction to a decimal, you can simply divide the numerator of the fraction by the denominator.
A practical example could be if a=0.5 and b=3/4 in the expression. Here, you can write 'a' as 1/2 (a fraction) and 'b' as 0.75 (a decimal). Therefore, the expression becomes 1/2x + 0.75x.
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Simplify by combining like terms.
3(-2y-9)-2y
Answer: -8y-27
Step-by-step explanation: Simplify the expression.
Hope this helps you out.
Answer:
-8y-27.
Step-by-step explanation:
3(-2y-9)-2y
= 3*-2y+3*-9 -2y
= -6y-27-2y
= -8y-27.
In each table x represents the input value and y represents the output value. Which table does not represent a function of x?
Answer:
D
Step-by-step explanation:
The function of the x in the table is not having a specific pattern apart from repeating 3's.
Choice A: pattern for x +1
pattern for y +1
Choice B:pattern of x -1
pattern for y +1
Choice C: pattern for x +1
pattern for y -0
Choice D:pattern for x -0
pattern for y +1
Therfore D would be the answer.
What would you earn in total commissions on the following sales of $5100 $4876 $5215 $6225 and $5235 if you if you earn a commission rate of 1.5%
Answer:
$5100 would be $76.50
$4876 would be $73.14
$5215 would be $78.23
$6225 would be $93.38
$5235 would be $78.53
Step-by-step explanation:
To find commissions take your sale price and multiply it by your percentage and divide by 100
Answer: $399.77
Step-by-step explanation:
What is the approximate length of a line segment connecting points A and B?
Point A: 3, 6
Point B: 2, -4
Point D: -2, 6
A. 10 units
B. 15 units
C. 13 units
D. 11 units
Answer:
A. [tex]\displaystyle 10\:units[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[-3 + 2]^2 + [-6 - 4]^2} = \sqrt{[-1]^2 + [-10]^2} = \sqrt{1 + 100} = \sqrt{101} ≈ 10,04987562 ≈ 10[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
Final answer:
The approximate length of a line segment connecting points A(3, 6) and B(2, -4) is found using the distance formula and it is approximately 10 units.
Explanation:
To calculate the approximate length of a line segment connecting points A and B, we use the distance formula. The distance formula is derived from the Pythagorean theorem and is:
d = \/((x2 - x1)² + (y2 - y1)²)
Given points, A(3, 6) and B(2, -4), we can plug these coordinates into the formula:
d = \/((2 - 3)² + (-4 - 6)²)
Now, calculate the squares and sum:
d = \/((-1)² + (-10)²)
d = \/(1 + 100)
d = \/(101)
The square root of 101 is approximately 10.05, which is close to 10 units.
Therefore, the approximate length of the line segment connecting points A and B is 10 units, which corresponds to option A.
TEST HELPO AGAIN
What is the final amount in a $1500 account earning .75% compound interest for 6 years?
Answers will include a $ sign and round all answers to hundredths place.
Answer:
The final amount in the account after 6 years at compound interest is $1568.78 .
Step-by-step explanation:
Given as :
The principal amount in account = p = $1500
The rate of compound interest = r = 0.75 %
The time period of the loan = t = 6 years
Let The Amount in account after 6 years = $A
From Compound Interest method
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
I.e A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, A = $1500 × [tex](1+\dfrac{\textrm 0.75}{100})^{\textrm 6}[/tex]
Or, A = $1500 × [tex](1.0075)^{6}[/tex]
Or, A = $1500 × 1.04585
Or, A = $1568.775
So, The final amount= A = $1568.78
Hence The final amount in the account after 6 years at compound interest is $1568.78 . Answer
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours).
Answer: [tex]A(t)=-8t+52[/tex]
Step-by-step explanation:
The missing question is: "What is the Functions formula A(t)=?"The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
According to the data given in the exercise, you know that:
- [tex]A(t)[/tex] represents the area to paint the Hiros' romm as a function of time.
- The rate he painted the room was 8 square meters per hour.
- The area left to paint after 3 hours was 28 m².
Therefore, based on this, you can idenfity that:
1. The slope of the line is:
[tex]m=-8[/tex]
2. One of the point on the line is:
[tex](3,28)[/tex]
So you must substitute the slope and the coordinates of that point into [tex]y=mx+b[/tex] and then solve for "b" in order to find its value:
[tex]28=-8(3)+b\\\\28+24=b\\\\b=52[/tex]
Therefore, you can determine that the function [tex]A(t)[/tex] is:
[tex]A(t)=-8t+52[/tex]