9514 1404 393
Answer:
x = 39
Step-by-step explanation:
The usual approach is ...
12x -48 = 10x +30 . . . . use the distributive property to eliminate parentheses
2x -48 = 30 . . . . . . . . . subtract 10x from both sides [1]
2x = 78 . . . . . . . . . . . . add 48 to both sides [2]
x = 39 . . . . . . . . . . . . divide both sides by the coefficient of x
The solution is x = 39.
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Check
4(3x -12) = 5(2x +6) . . . . given
4(3·39 -12 = 5(2·39 +6) . . . . substitute for x
4(117 -12) = 5(78 +6) . . . . . . . multiply
4(105) = 5(84) . . . . . . . . . . . . add
420 = 420 . . . . . . . . . . . . . . multiply
The found value of x makes the equation true, so is the solution.
_____
Additional Notes
[1] The point of the solution process is to put the variable on one side of the equal sign and a constant on the other side. To that end, we subtract the smallest variable term from both sides of the equation. The net result is a variable term on one side of the equal sign that has a positive coefficient.
We could have subtracted either of the constant terms first, and subtracted the variable term second. In this latter approach, the variable term subtracted is the one on the same side of the equation as the remaining constant term. Unless care is taken to select the constant on the side of the largest variable term (for subtraction), the net result may be a negative variable term. Technically, that works just as well, but can tend to increase the probability of an error being made.
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[2] We notice that all of the terms in the equation after the last step have the x-coefficient as a common factor. This gives us the opportunity to divide by that coefficient at this stage. Doing this would give x-24=15. Then adding 24 would give the same final solution. Sometimes I like to work equations this way so the variable is "bare" (has a coefficient of 1) sooner, and the numbers are smaller.
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In this discussion, when we talk about subtracting or dividing, we mean the entire equation is involved. The properties of equality tell us the equal sign remains valid if the same operation is performed on both sides of the equation. Our discussion here takes for granted that understanding. We have occasionally said "[do such and such] to both sides". Even where it isn't stated, the "to both sides" always applies.
To which subsets of the real numbers does the number 82 belong?
Answer: the number 82 belongs to the following subsets of the real numbers of Natural Numbers (N), Whole Numbers (W), Integers (I), Rational Numbers (Q), Real Numbers (R)
The number 82 belongs to several subsets of the real numbers as given in the following:
1. Natural Numbers (N): The natural numbers are the set of positive integers starting from 1, i.e.,(1, 2, 3,.......). Since 82 is a positive integer, it belongs to this subset.
2. Whole Numbers (W): The whole numbers are the set of non-negative integers, i.e., ( 0, 1, 2, 3,....). Since 82 is a non-negative integer, it belongs to this subset.
3. Integers (Z): The integers include all positive and negative whole numbers, including zero, i.e., ( -3, -2, -1, 0, 1, 2, 3,...). Since 82 is a whole number, it belongs to this subset.
4. Rational Numbers (Q): The rational numbers are numbers that can be expressed as the quotient of two integers [tex]\( \frac{a}{b} \)[/tex], where a and b are integers and [tex]\( b \neq 0 \)[/tex]. Since 82 can be written as [tex]\( \frac{82}{1} \)[/tex], it belongs to this subset.
5. Real Numbers (R): The real numbers include all the rational and irrational numbers. Since 82 is a rational number, it is also a real number.
How many different ways can you choose a council with exactly 3 sophomores, 1 junior, and 2 seniors?
If Luis earns a base salary of $150.00 every week with an additional 14 % commission on everything he sells .Luis sold $6050.00 worth of items last week. what is Luis's total pay last week
Triangle GHI has the angle measures of G = (2x + 5)°, H = (6x − 10)°,
and I = (x + 5)°. What is the actual measurement of angle H?
The actual measurement of angle H is thus 110 degrees.
To find the actual measurement of angle H in triangle GHI, we can use the fact that the sum of the interior angles in any triangle is always 180 degrees. Given the expressions for angles G, H, and I as G = (2x + 5)", H = (6x − 10)", and I = (x + 5)", we can set up the equation (2x + 5) + (6x - 10) + (x + 5) = 180 to find the value of x. After determining x, we substitute it back into the expression for angle H to get the desired measurement.
Setting up the equation we have:
(2x + 5) + (6x - 10) + (x + 5) = 180
Combine like terms to get 9x = 180
Divide both sides by 9 to find x: x = 20 degrees
Now plug this value into the expression for angle H: H = 6(20) - 10
We find that H = 120 - 10 degrees, so H = 110 degrees
To find the measurement of angle H in triangle GHI, we apply the fact that the sum of angles in a triangle is always 180 degrees. By solving the equation that sets this sum, we find the value of x, and then use it to determine that angle H measures 110 degrees.
Which of the following scenarios has a lower y-intercept than y = 4x + 5 ?
(a.) A 50 gallon tub is draining. Every 2 minutes, the amount of water decreases by 2 gallons.
(b.) Reginaldo had $17 in his account and for every book he buys, it costs him $4.
(c.) Sydney has collected 8 postcards. Each time a friend comes to visit, Sydney gives her a postcard.
(d.) Owen has 3 pets. He receives a new pet each time he has a birthday.
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
4x^2+25y^2=100
[tex]4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\
\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]
Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].
So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].
The area of the circle shown below is 100π. What is the diameter (D) of the circle?
Answer: 20 units
Step-by-step explanation:
We know that the area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.
We are given that the area of the circle = [tex]100\pi[/tex] square units.
[tex]\Rightarrow\ 100\pi=\pi r^2\\\\\Rightarrow\ r^2 =100[/tex]
Taking square root on both the sides , we get
[tex]\\\\\Rightarrow\ r=10[/tex]
The diameter of the circle is given by :-
[tex]d=2r=2(10)=20\text{ units}[/tex]
Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?
$1,021.01
$1,188.66
$991.38
$1,192.39
After 7 years, Abner earned $1575 in simple interest from a CD into which he initially deposited $6000. What was the annual interest rate of the CD?
The annual interest rate of the CD was 3.75 %
Explanation
Simple Interest formula is : [tex] I =P*r*t [/tex] , where [tex] I= [/tex] Amount of interest, [tex] P= [/tex] Principal/Initial amount, [tex] r= [/tex] rate of interest in decimal form and [tex] t= [/tex] time in years
Here Abner earned $1575 in simple interest and he initially deposited $6000. So, [tex] I=1575 [/tex] dollar and [tex] P= 6000 [/tex] dollar
Also given that, [tex] t = 7 [/tex] years
Now according to the formula...
[tex] I= P* r*t\\ \\ 1575= 6000*r*7\\ \\ 1575= 42000*r\\ \\ r= \frac{1575}{42000}= 0.0375 [/tex]
For getting the interest rate in percentage, we will multiply it by 100%. So... (0.0375 × 100) % = 3.75 %
So, the annual interest rate of the CD was 3.75 %
Item 12 a regular triangular pyramid has a base and lateral faces that are congruent equilateral triangles. it has a lateral surface area of 57 square centimeters. what is the surface area of the regular triangular pyramid?
Answer:
76
Step-by-step explanation:
im short on time sorry for no explanation.
Identify the transformations that describe the graph of an even function. Select all that apply.
reflection over the x-axis
reflection over the y-axis
reflection over the line y = x
90° rotation around the origin
180° rotation around the origin
Answer:
reflection over the y-axis
Step-by-step explanation:
Simplify: (10*5+6)(13+2)+19
A company has 200 employees. The company’s owner randomly chose 30 employees for an in-depth survey. Of those surveyed, 12 employees said they work overtime on a regular basis.
What is the best estimate of the percent of the company’s employees who work overtime on a regular basis?
The distance on the number line from 5 to 12 equals 3x – 2. What is the value of x?
A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the probability that he makes it exactly three of his next four free throws is
The probability that a college basketball player makes exactly three of his next four free throws is calculated using binomial probability, resulting in approximately 38.58%.
Explanation:The probability that a college basketball player makes exactly three of his next four free throws, given that he makes 5/6 of his free throws, involves calculating a binomial probability. We have four independent events (four free throws), and we want exactly three successes (made throws) and one failure (missed throw). We use the following formula for the binomial probability:
P(X=k) = C(n, k) × p^k × (1-p)^(n-k)
where:
In this problem:
p = 5/6 (probability of making a throw)(1-p) = 1/6 (probability of missing a throw)n = 4 (total number of free throws)k = 3 (number of free throws made)Plugging in the values:
P(X=3) = C(4, 3) × (5/6)^3 × (1/6)^1
C(4, 3) is 4, since there are four different ways to make three throws and miss one (MMM-M, MM-MM, M-MMM, MMMM-). So the calculation gives:
P(X=3) = 4 × (5/6)^3 × (1/6) = 4 × (125/216) × (1/6) = 500/1296, which simplifies to about 0.3858 or 38.58%.
Therefore, the probability that he makes exactly three of his next four free throws is 0.3858 or 38.58%.
If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not?
Yes, along with the given information, ZX ≅ ZX by the reflexive property.
Yes, the triangles are both obtuse.
No, the sides of the triangles intersect.
No, there is not enough information given.
No, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given information only provides the lengths of two sides and the measures of two angles in the triangles, but we do not know if the third side is congruent, and we cannot assume that it is by the given information.
Additionally, the given information does not specify that one of the congruent sides is included between the congruent angles, which is necessary for the SAS postulate to be used to prove congruence.
Therefore, there is not enough information given to prove that ΔVZX and ΔWXZ are congruent by SAS.
Learn more about congruent triangles here:
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In five consecutive tosses of a coin, what is the probability of not getting a tail until the 5th coin toss?
1 cubic foot of sand weighs 100 lb. a square sandbox with 5 foot sides has a half of a foot of sand in it. how many pounds of sand is sandbox the holding?
The sandbox with 5-foot sides and a half-foot depth of sand is holding 1250 pounds of sand, calculated using the volume of the sand and the known weight per cubic foot.
Explanation:To calculate the weight of sand in the sandbox, we can use the formula for the volume of a cube, which is length × width × height. Given that the sandbox has 5-foot sides and is filled with a half of a foot of sand, the volume × weight of the sand can be calculated as follows:
The volume of sand = 5 ft (length) × 5 ft (width) × 0.5 ft (height) = 12.5 cubic feet.Since 1 cubic foot of sand weighs 100 lb, the total weight of the sand = 12.5 cubic feet × 100 lb/cubic foot = 1250 pounds.Therefore, the sandbox is holding 1250 pounds of sand.
The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.
Which answer is the best estimate of the residual value when x = 1?
−1.5
−0.5
0.5
1.5
I took a test?
1.5 w/out a negative.
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Also saw a lot of struggle to answer the other question,... so in case you need it.
From the graph in the figure attached to the question, The best estimate of the residual value when x = 1 on the graph is 1.5
What is a residual value in the graph?A residual value is an indication of how far a regression line fails to reach a data point vertically. From the graph in the figure attached to the question;
We can see how the regression line lies at the midpoint between 3 to 4 on the vertical axis at x = 1. However, the data point is located at 5, so we have the distance of the residual value to be from the midpoint of 3 to 5 which is equal to 1.5
Learn more about residual value here:
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The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length.
Which polygon is a convex heptagon?
Answer: The correct option is 1.
Explanation:
A polygon is said to be a heptagon if it has 7 vertices, 7 sides and 7 angles. A heptagon is called a convex heptagon if the line connecting the two vertices are lies completely inside the heptagon.
In the figures the black points shows the vertices.
Reason for correct option:
In figure 1 there are 7 angles, 7 sides and 7 vertices and the lines joining any two vertices are lies inside the figure, therefore it is an convex heptagon and option 1 is correct.
Reason for incorrect option:
In figure 2 and 3 the number of vertices and sides are 8, therefore the figure shows the octagon and option 2 and 3 are in correct.
In figure 4 the number of vertices and sides are 7 but there axis a line which connecting the two vertices and lies outside the figure as shown in below figure, therefore the option 4 is incorrect.
Answer:
First picture
Step-by-step explanation:
I WILL MARK BRAINLIEST
what is x???? you HAVE to explain and show for the brainliest!!!!!!
Answer:
x + 64 = 110
x = 46
Step-by-step explanation:
You need to isolate the x, so you need to subtract 64 from 110 ( which is 46 ). By you doing that, you need to now subtract 64 from 64 itself.
Would look like this: x + 64 = 110
- 64 - 64
Which would leave you with x = 46
Find the cosine of both angle A and angle B.
An investment banker is responsible for investing a customer’s money into the greatest interest earning account. The banker has the following options for his customer’s investment: Account A: interest rate = 4.8% term of investment = 10 years interest compounded monthly Account B: interest rate = 4.9% term of investment = 10 years interest compounding continuously Which account, A or B, will earn the customer the greatest amount of interest on his $150,000 investment? In your final answer, include all of your calculations.
A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?
The viewing room at a planetarium is in the shape of a hemisphere. The diameter of the hemisphere is 48 feet. What is the volume of the viewing room?
Answer:
9,216π cubic feet
Step-by-step explanation:
Which point lies outside the circle with equation (x - 2)2 + (y + 3)2 = 4?
(1, -4)
(0, -3)
(2, 0)
(2, -4)
The only point outside of the line is (2, 0)
In order to find if a point is outside, inside or on the line, you simply have to put the number into the equation. If the result is both sides are equal, then it is on the line. If the left side is bigger than the right side, then it is outside of the line. If the right side is bigger than the left, then it is inside of the line. So lets plug in and see where (2, 0) falls.
(x - 2)^2 + (y + 3)^2 = 4
(2 - 2)^2 + (0 + 3)^2 = 4
0^2 + 3^2 = 4
0 + 9 = 4
9 = 4
Since the left side is bigger than the right, we know it is outside of the line
Chaz is constructing the circumscribed circle for △JKL .
Which construction is a correct next step for Chaz?
Open the compass to just more than half the width of JL¯¯¯¯¯ and draw a circle centered at point K.
Open the compass to the width of JL¯¯¯¯¯ and draw a circle centered at point K.
Construct the angle bisector of ∠J .
Construct the perpendicular bisector of JL¯¯¯¯¯ .
The correct next step for him to take in constructing a circumscribed circle for △JKL is to construct: the perpendicular bisector of JL
How can We Construct A Circumscribed Circle of a Triangle?To construct a circumscribed circle for a triangle, the first thing we have to do is to place our compass at the center of one of the sides of the triangle.
This center point can be gotten by constructing a perpendicular bisector to a side of the triangle.
Therefore, the correct next step for him to take in constructing a circumscribed circle for △JKL is to construct: the perpendicular bisector of JL
Learn more about Circumscribed Circle on:
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The cost of renting a car is a flat 26 plus an additiona 0.13 cents per mile that you drive how face can you drive for 99