Answer:
a=-3
Step-by-step explanation:
5a+a=-10-8
6a=-18
a=-18/6
a=-3
Answer:
a = -3
Step-by-step explanation:
This is a linear equation in one variable that has a constant term and a variable term on each side of the equal sign. It can be solved in 3 steps, so can be called a "3-step equation."
The three steps involve separating the variable and constant terms, then dividing by the variable's coefficient.
__
-a -10 = 5a +8 . . . . . . given
step 1To separate the variable and constant terms, we eliminate one of the variable terms by adding its opposite to both sides of the equation. It is generally convenient to choose the variable term with the lowest coefficient value. When we add the opposite of that to both sides of the equation, the resulting variable term will have a positive coefficient. (Dealing with positive numbers generally reduces errors.)
Here the two variable terms are -a and 5a. The coefficient -1 is less than the coefficient 5, so we choose to add the opposite of -a to both sides.
-a +a -10 = 5a +a +8 . . . . . add a to both sides
-10 = 6a +8 . . . . . . . . . . . simplify
step 2Now there is only one variable term, but it has a constant added to it. We can eliminate that constant by adding its opposite.
-10 -8 = 6a +8 -8 . . . . . add -8 to both sides
-18 = 6a . . . . . . . . . . . simplify
step 3This equation gives us the value of a multiple of the variable (6a). To get the variable by itself, we multiply by the reciprocal of the variable's coefficient. The product of the coefficient and its reciprocal is 1, so we will have the variable alone.
Multiplying by 1/6 is the same as dividing by 6. Often, it is easier to think in terms of division. However, when the coefficient is a fraction, it can be useful to think in terms of multiplying by the reciprocal of that fraction.
(1/6)(-18) = (1/6)(6a) . . . . . . multiply by 1/6
-3 = a . . . . . . . . . . . . . . . simplify
The solution to the equation is a = -3.
_____
Additional comment
When we say "add" or "multiply" the equation by some number, we mean that operation to be performed on both sides of the equation. The properties of equality say we can do whatever we like to an equation, as long as we do the same thing to both sides of the equation.
A function is defined by x)- What is f(-8)?
0-2
N FIC
02
02
Which equations graph as circles?
x² + x + y² = 4
2x + x + y² = 8
x² + y² = 5
x² + x + y = 6
x² + y² + y = 1
Answer:
A, C, and D
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
Factor x³ + x² + x + 1 by grouping. What is the resulting expression?
○ (x²)(x + 1)
O (x² + 1)(x)
O (x² + 1)(x + 1)
O (x³ + 1)(x + 1)
Work Shown:
x³ + x² + x + 1
(x³ + x²) + (x + 1)
x²(x+1) + 1(x + 1)
(x² + 1)(x + 1)
The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.
The factored form of x³ + x² + x + 1 is (x²+1)(x+1).
What is Factorization?A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.
We have,
x³ + x² + x + 1
Now, making groups as
(x³ + x²) + (x + 1)
= x² (x + 1) + (x+1)
= (x²+1)(x+1)
So, resulting expression is (x²+1)(x+1).
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A conveyor belt carries supplies from the first floor to the second floor, which is 39 feet higher.
The belt makes a 60° angle with the ground. How far do the supplies travel from one end of
the conveyor belt to the other to the nearest foot? If the belt moves at 70 ft./min., how long
does it take the supplies to move to the second floor to the nearest tenth of a minute?
O 68 ft.; 1.0 min.
O55 ft.; 0.8 min.
O 45 ft.; 0.6 min.
O23 ft.; 0.3 min.
The supplies travelled 45ft and it took 0.6min to get to the next floor.
What is trigonometry?Trigonometry is the branch of mathematics dealing with the relationship between the sides of a triangle and the angles.
Analysis:
The supplies distance travelled, distance of first floor from second floor and the ground form a right angled triangle.
so that sin 60 = 39/distance travelled by supplies
distance travelled by supplies = 39/sin 60 = 39/0.866 = 45 feet.
speed = distance / time
time = distance / speed = 45/70 = 0.6 min
In conclusion, the distance and time time taken for the supplies to get to the next floor is 45feet and 0.6 min respectively.
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What is the area of a circular fountain that has a 6 ft. diameter?
A. 18.84 ft2
B. 28.26 ft2
C. 9.42 ft2
D. 254.34 ft2
Answer: B. 28.26 ft2
Step-by-step explanation: I did this in school and got it right.
Answer:
B. 28.26 ft²
Explanation:
Area of Circle = π(radius)²Here given:
diameter: 6 ftradius = diameter/2 = 6/2 = 3 ftArea of the fountain:
3.14(3)² = 28.26 ft²Find the measure of one interior angle of a regular polygon with 13 sides
Answer:
152.3 approximately
Step-by-step explanation:
A polygon with 13 sides (and angles too) would be called tridecagon
Now, the sum of interior angles in a polygon is calculated by dividing the number of angles minus 2 by 180 [(n-2)*180]
(13-2)/180 = 1.980 and to find what is the measure of one angle, we divide the sum by the number of angles the polygon has
1.980/13 = 152.3 approximately
A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). What are the values of h and v? To find the value of a, subtract the y-coordinate of the vertex from the y coordinate of the point on the parabola that is 1 unit to the right of the vertex. Find the value of A for the parabola
The value of a is 1/4 and the value of h and k is (2,-7/4)
What is a Parabola ?A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.
(x-h)² = 4a(y-k)
It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).
Therefore
(x -2)² = 4a(y +2)
The parabola passes through the point (3,-1)
(3-2)² = 4*a(-1+2)
1 = 4 a
a = 1/4
Now to determine the value of focus point , (h,k)
(h = 2)
k = - 2 +1/4 = -7/4
Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)
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Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles
Answer:
52° & 78°Step-by-step explanation
Two angles of a triangle are in the ratio of 2:3 if the third angle is 50 degree find the other two angles
the sum of the interior angles in a triangle is 180°
so
180 - 50 = 130°
130 : 5 = 26° (unit)
26 * 2 = 52°
26 * 3 = 78°
--------------
check
50 + 52 + 78 = 180°------------
2 : 3 = 52 : 780.66666666666 = 0.66666666666The answer is good
Simplify!! Please!!!
Answer:
.................................................
Step-by-step explanation:
edge 2022
In a school in florida, 60% of the students stay in the school's dormitory and 40% stay with their families. the school records show that 30% of the students living in the dormitory and 20% of the students living with their families obtain as on exams. if a student chosen at random from the school receives as, the probability that the student lives in the school dormitory is .
Answer: 9/13
Step-by-step explanation:
plato classes
Iman has 48 months to save $18,000, the maximum amount he estimates his first year of college will cost. he does not want to depend on interest, and does not consider interest when determining his minimum monthly savings goal. what is the minimum amount he should save per month to achieve his goal? $350.00 $375.00 $425.00 $450.00
Answer:
$ 375 / month
Step-by-step explanation:
$ 18 000 / 48 months = 375 /month
The minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.
Given that:
Number of months = 48
Monthly savings = $18,000
The minimum amount to save per month can be calculated by dividing the total amount by the number of months:
Minimum monthly savings goal = Total amount to save / Number of months
Minimum monthly savings goal = $18,000 / 48
Minimum monthly savings goal ≈ $375.00
Therefore, the minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.
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how do i do this could you show step by step please?
The value of x from the given right triangle in rational form is 14√
SOH CAH TOA identityThis is a way of determining the sides and angles of a right triangles
From the given triangle
Opposite = 7√4 = 14
Hypotenuse = x
acute angle = 45 degrees
Using the theorem
sin 45 = 14/x
x = 14/sin45
x = 14√2
Hence the value of x from the given right triangle in rational form is 14√2
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What is the the slope and y-intercept in the equation and what do both mean in context of the problem? y= 0.98x + 1.44
Answer:
The slope is 0.98 and the y-intercept is 1.44.
Step-by-step explanation:
The equation is a linear equation in the Slope-Intercept form y=mx+b. It’s called this because it identifies the slope m and the point on the y-axis at which the line intersects.
Help ASAP!
Solve the following linear system by graphing. 7x – 2y = −4
Y=−5
a (-2,-5)
b (-6,0)
c (1,5)
d (7,-4)
HELP PLEASE ILL MAKE YOU THE BRAINIEST What is the area of the regular polygon?
Based on the calculations, the area of this regular polygon (hexagon) is equal to 24 m².
How to calculate the area of a regular polygon?Mathematically, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.Note: The apothem of a regular polygon is half the length of one side.
Therefore, Length = 2 × 2 = 4 meter.
Substituting the parameters into the formula, we have;
Area = (6 × 4 × 2)/2
Area = 48/2
Area = 24 m².
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Can someone help me withthe full page I will offer a lot of points
#1
Scale ratio
10ft/1in#2
Unknown is actual length
So the ratio is
x/0.75#3
The proportion is
x/0.75=10/1#4
Must be multiplied with 0.75
#5
x=0.75(10)x=7.5ftActual length is 7.5ft
Answer:
Question 1
Given scale: 1 in = 10 ft
[tex]\textsf{Therefore, the scale as a ratio}=\sf \dfrac{\boxed{10}\:ft}{\boxed{1}\:in}[/tex]
Question 2
The ratio of the garden's actual length to its length in the drawing:
[tex]\sf \dfrac{x\:ft}{0.75\:in}[/tex]
Question 3
Therefore, the proportion is:
[tex]\sf \dfrac{10\:ft}{1\:in}=\dfrac{x\:ft}{0.75\:in}[/tex]
Question 4
Multiply both sides of the proportion by 0.75 to find x
Question 5
[tex]\begin{aligned}\textsf{Proportion}: \quad \quad \;\sf \dfrac{10\:ft}{1\:in} & = \sf \dfrac{x\:ft}{0.75\:in}\\\\\textsf{Mulitply both sides by 0.75}: \quad \sf 0.75\cdot \dfrac{10}{1} & = \sf 0.75 \cdot \dfrac{x}{0.75}\\\\\textsf{Simplify}: \quad \quad \quad \sf 7.5 & = \sf x\end{aligned}[/tex]
Therefore, the actual length of the garden is 7.5 ft
sin 30° right triangle
Answer:
The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides.
...
Related Links
Sin 0 Degree Trigonometry Formulas
Inverse Cosine Law of Sines Formula
You are going to visit a relative out of town and want to go to the gym while visiting. Hunkey Heros charges a registration fee of $50 plus a monthly fee of $20. Zipity-zapity- zap-that-fat charges $70 to join, but only $10 per month. After how many months do the gyms cost the same? a) Declare your variables:
c) Solve
b) Write a system of equations:
The number of months when the gyms cost the same is 5 months.
When would the cost be the same?Total cost of joining the gym = registration fee + (cost per month x number of months)
Hunkey Heros = $50 + $20m Zipity-zapity- zap-that-fat = $70 + $10mWhen the gyms costs are the same, the two above equations would be equal to each other:
50 + 20m = 70 + 10m
20m - 10m = 70 - 20
10m = 50
m = 50 / 10
m = 5
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Please help urgent!!!
Which statement about the functions is true?
The minimum value of f(x) is less than the minimum value of g(x).
f(x) and g(x) intersect at exactly one point.
f(x) and g(x) have the same y-intercept.
The x-intercepts of f(x) are common to those of g(x) .
The x-intercepts of f(x) are common to those of g(x) .
What is x-intercept?
The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
Choice 2 is not true. Point B is not on the parabola.
Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.
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PLEASE HELP I’LL MAKE YOU THE BRAINIEST
write the ratio for tan A
Answer:
tan A = 5/12
Step-by-step explanation:
The tangent ratio is equal to the length of the side opposite of the angle over the length of the side adjacent to the angle. If we are finding tangent in respect to angle A, the opposite side would be line CB with a length of 5. The adjacent side is line AC with a length of 12. Therefore, the tan A ratio is 5/12.
PLA HELP ME ITS DUE TOMORROW
Step-by-step explanation:
To Find the number of people in the survey = 36+28+14+12+10 => 94The least prefer mode of transportation is Taxi , as we can see is is preferred by 10 peoples.Most preferred transportation is Bus which was preferred by 36 people.Number of persons who prefer to ride the motorcycle is 12.FIND AREA OF THE FIGURE
when receiving this kind of questions, you just need to find a figure that you can calculate the area of or split the figure in multiple figures that you can calculate.
Sqrt -1+2 using a+bi
[tex]\sqrt{-1} + 2 = i+2 = 2+i[/tex]
the length of a line is y centimetres write down an expressions in terms of y for the length of the line in millimetres
Answer:
L=10y
Step-by-step explanation:
1cm=10mm
Hence, the length in millimeters will be 10 times the value in cm.
What does the t-coordinate of the solution to this system represent? the time at which the ball and the dog hit the ground the time at which the ball and the dog begin moving the time at which the ball and the dog's mouth are at the same height
The t-coordinate of the solution to this system represents C. the time at which the ball and the dog's mouth are at the same height.
How to explain the coordiante?
A coordinate time scale is a time standard designed for use as the time coordinate in the calculation.
When Laurie throws a tennis ball toward her dog from a height, the t-coordinate of the solution to this system represents the time at which the ball and the dog's mouth are at the same height
The complete question is:
Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground. What does the t-coordinate of the solution to this system represent?
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Answer:
C
Step-by-step explanation:
I got it right
2x(x-5)-x(3+2x)=26
help me pls
Answer:
x=−2
Step-by-step explanation:
hope it helps yaa
Using the net below, find the surface area
of the triangular prism.
am
6 cm
7 cm
7 cm
4 cm
4 cm
Surface Area = [?] cm²
The surface area of the triangular prism is 153 cm².
What is a triangular prism?Imagine you have a triangle. Now, extend it upward to form a stack of triangles atop one another. The triangular prism is a new three-dimensional object.Typically, when we refer to a triangle prism, we mean one whose stack faces upward; in this case, we are referring to a right triangular prism.The area of the triangular prism is equal to the sum of the areas of the rectangle and the triangle, hence the prism's area will be,Area = A + B + C
=(9 × 15) + (0.5×6×3) + (0.5×6×3)
= 135 + 9 + 9
= 153 cm²
Hence, the surface area of the triangular prism is 153 cm².
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Which of the following is an equivalent expression to the expression
a4
A
a12
B
C
7
Q12
2
HELP.
Answer:
D is the correct option.
All the best!
Please help me with this question....
Answer:
A x+2 would move the coordinate 2 units to the right while (x)+2 would move the coordinate 2 up and 2 to the right
Step-by-step explanation:
sorry i couldnt do the second part i ran out of time
People in two sample groups were asked to identify their favorite kind of pizza. study the results and circle a generalization
Answer:
Group B
Step-by-step explanation:
You can see even with the same total group b likes the most topppings