Answer:
$147,000
Step-by-step explanation:
After 1st year:
we need to increase 150,000 by 4%. That means the value would be 150,000 multiplied by 1.04. So:
150,000 * 1.04 = 156,000
After 2nd year:
The new appreciated value of 156,000 will now suffer a loss of 6%. So we need to find the new value by multiplying 156,000 by 0.94 (6% loss). So:
156,000 * 0.94 = 146,640
To the nearest 1000, this would be $147,000
Charlie jogs 3 miles south and then 4 miles west. If Charlie were to jog straight home, without changing direction, how far would he have to jog?
Answer:
He would to jog 5 miles to go direct to his home
Step-by-step explanation:
* Lets explain how to solve the problem
- Charlie jogs 3 miles south and then 4 miles west
- We need to know if Charlie were to jog straight home, without
changing direction how far he have to jog
- Remember: the East-west line is perpendicular to the north-south line
∵ He jogs 3 miles south
∵ He jogs 4 miles west
∵ South ⊥ west
- We can consider that the west and east distance with the straight
distance to home formed a right triangle its legs are the south and
west distance and the straight distance is its hypotenuse
∴ By using Pythagoras Theorem we can find the straight distance
- Remember: In Pythagoras Theorem [tex]c=\sqrt{a^{2}+b^{2}}[/tex]
where c is the hypotenuse , a and b are the legs of the right Δ
∴ The straight distance = [tex]\sqrt{(3)^{2}+(4)^{2}}\sqrt{9+16}=\sqrt{25}=5[/tex]
∴ He would to jog 5 miles to go direct to his home
What is the volume of this rectangular prism?
Answer:
It would be A.
Step-by-step explanation:
It is a because you multiply 2 and 2 to get 4 then multiply 4 and 7 to get 28cm cubed
Answer:
Answer: A 28 cm^3
Step-by-step explanation:
Multiply your three values together to get your volume
Hope this is helpful! :)
If f(x) = 2x2 +5/(x-2), complete the following statement:
f(3) = ___
Answer: The answer is 19
Step-by-step explanation:
If [tex]f(x) = 2x^{2} + \frac{5}{x-2}[/tex], Then
[tex]f(x) = 2*3^{2} + \frac{5}{3-2}[/tex]
[tex]f(x) = 2*9 + \frac{5}{1}[/tex]
[tex]f(x) = 18 + 1 =19[/tex]
A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.
Plz give me a step by step answer i need to figure this out.
Answer:
Step-by-step explanation:
$ 0.68 type →85lb
$ 0.20 type →35lb
Hey!
-----------------------------------------------
Let $0.68 per pound beans be (b)
Let $0.20 per pound beans be (p)
-----------------------------------------------
~Total amount of pounds:
b + p = 120
~Total cost
b + p = 120 × 0.54
b + p = 64.8
~Expression
0.68b + 0.20p = 64.8
~Multiply 10 to both sides
0.68b * 10 + 0.20p * 10 = 64.8 * 10
~Simplify
6.8b + 2p = 648
~Divide 2 to both sides
6.8b/2 + 2p/2 = 648/2
~Simplify
3.4b + p = 324
~Subtract
3.4b + p = 324
- b + p = 120
~Simplify
2.4b = 204
~Divide 2.4 to both sides
2.4b/2.4 = 204/2.4
~Value of b
b = 85
~New expression
85 + p = 120
~Subtract 85 to both sides
85 + p - 85 = 120 - 85
~Value of p
p = 35
-----------------------------------------------
[tex]\large\boxed{Of~the~0.68~dollars~per~pound~there~are~85~pounds!}\\\large\boxed{Of~the~0.20~dollars~per~pound~there~are~35~pounds!}[/tex]
-----------------------------------------------
My answer is reasonable because 85 + 35 equals 120 pounds.
~If we check
85 * 0.68 = 57.8
35 * 0.2 = 7
57.8 + 7 = 64.8
We get 64.8 which we can say it is correct because if we go back into our work we can see that we used the expression b + p = 64.8 which in this case by checking our work our answer is reasonable.
-----------------------------------------------
Hope This Helped! Good Luck!
write 6X10X10X10X10 with an exponent.
Answer:
6 × 10 × 10 ×10 × 10 = [tex]6 \times 10^{4}[/tex]
Step-by-step explanation:
The exponent of any number shows that how many times that number can be used in multiplication. It is the power raised to any number which show the number of times that number is raised by.
6 × 10 × 10 ×10 × 10
Here 10 is multiplied 4 times, therefore the exponent of 10 is 4.
∴ 6 × 10 × 10 ×10 × 10 = [tex]6 \times 10^{4}[/tex]
Final answer:
The expression 6X10X10X10X10 written with an exponent is 6x10⁴, indicating that 10 is multiplied by itself four times and then multiplied by 6.
Explanation:
To write 6X10X10X10X10 with an exponent, we identify the repeated multiplication of 10s. Since there are four 10s multiplied together, we use the exponent 4 to represent this, and the expression becomes 6x10⁴. This is because when you have repeated multiplication of the same number, you can express that number raised to the power of how many times it is multiplied by itself.
Quick help guys thanks :)
Answer:
[tex]\large\boxed{t^{-58}u^{-88}v^{-71}w^{-1}}[/tex]
Step-by-step explanation:
[tex]\dfrac{tuv^4w^0}{t^{59}u^{89}v^{75}w}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=t^{1-59}u^{1-89}v^{4-75}w^{0-1}=t^{-58}u^{-88}v^{-71}w^{-1}[/tex]
Consumer price index is an
Answer:
The Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them
Which pair of fractions are proportional? A)36/54 and 6/9 B)6/7and 16/21 C) 21/36and 21/42 D) 14/35 and 21/42
Option A
Answer:
[tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex] are proportional.
Solution:
If two fractions are equal, than it is said to be in proportion.
Case 1:
Consider option A
Given fractions are [tex]\frac{36}{54} \text { and } \frac{6}{9}[/tex]
[tex]\frac{36}{54}=\frac{9 \times 2 \times 2}{9 \times 2 \times 3}=\frac{2}{3} \text { and } \frac{6}{9}=\frac{2 \times 3}{3 \times 3}=\frac{2}{3}[/tex]
Hence both the fractions are equal. So they are propotional.
Case 2:
Consider option 2
Given fractions [tex]\frac{6}{7} \text { and } \frac{16}{21}[/tex] cannot be simplified further. Also both the fractions are not equal. So they are not propotional.
Case 3:
Consider option 3
Given fractions are [tex]\frac{21}{36} \text { and } \frac{21}{42}[/tex]
[tex]\frac{21}{36}=\frac{7 \times 3}{6 \times 6}=\frac{7}{12} \text { and } \frac{21}{42}=\frac{7 \times 3}{6 \times 7}=\frac{1}{2}[/tex]
Hence [tex]\frac{7}{12} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
Case 4:
Consider option 4
Given fractions are [tex]\frac{14}{35} \text { and } \frac{21}{42}[/tex]
[tex]\frac{14}{35}=\frac{7 \times 2}{7 \times 5}=\frac{2}{5} \text { and } \frac{21}{42}=\frac{7 \times 3}{7 \times 6}=\frac{1}{2}[/tex]
Hence [tex]\frac{2}{5} \text { and } \frac{1}{2}[/tex] are not equal. Hence they are not propotional.
The answer for the given question is option A
A line passes through the point (6,3) and has a slope of 3/2. Write an equation point-slope for this line.
Step-by-step explanation:
Given :- The line passes through the point ( 6 , 3 ) and has a slope of 3/2
• Also , to form an equation when a point through which line passes and slope of line is given we use the formula ;
( y - y1 ) = m ( x - x1 )
Where , y and x are variables and
( x1 , y1 ) are the points through which line passes also, m = slope of the required line
Here , x1 = 6 and y1 = 3
also, m = 3/2
[ Refer to the attached file for further process ]
Hey!
-------------------------
Formula:
y - y1 = m(x - x1)
-------------------------
We Know:
x = 6
y = 3
m = 3/2
-------------------------
Answer:
y - 3 = 3/2(x - 6)
-------------------------
Hope This Helped! Good Luck!
A line is drawn so that it passes through the points (3, 4) and (4,1).
What is the slope of the line
Answer:
-2
Step-by-step explanation:
the formula to find slope with two points is y2-y1/x2-x1.
for this problem it would be solved as follows:
1-3/4-3
-2/1 = -2
The slope of a line is the change in the y values over the corresponding x values.
The slope of the line that passes through (3, 4) and (4,1) is -3
Given that:
[tex](x_1,y_1) = (3,4)[/tex]
[tex](x_2,y_2) = (4,1)[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{1-4}{4-3}[/tex]
[tex]m = \frac{-3}{1}[/tex]
[tex]m = -3[/tex]
Hence, the slope is -3.
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Nick bought a music player. The price was $172, and the sales tax rate was 7 percent. How much sales tax did Nick pay when he bought the
music player?
A.
$7.20
B. $12.04
C.
$12.45
Answer:
B
Step-by-step explanation:
7% of 172 is 12.04
Solve the system of equations below. x − y = 6 3x − 2y = 22
The solution for system of equations x-y=6 ,3 x-2 y=22 is x = 10 and y = 4
Solution:
Using substitution method of algebraic equations,
x - y = 6 --------equation 1
3x - 2y = 22 --------equation 2
Multiplying equation 1 by 2, equation 1 becomes
2 x - 2 y = 12
Multiplying equation 2 by -1, equation 2 becomes,
-3 x + 2 y = -22
Solving,
2 x - 2 y = 12
-3 x + 2 y = -22
-x = -10
x = 10
Substitute x = 10 in equation 1, 10 - y = 6
y = 10 -6
y = 4
Answer:
10,4
Step-by-step explanation:
^^
Nine increased by the product of a number and 2 is less than or equal to 27.
Use the variable w for the unknown number.
Answer:
x≤9
Step-by-step explanation:
9+2x≤27
1) Subtract both sides by 9:
2x≤18
2) Divide both sides by 2:
x≤9
Final answer:
Translate the verbal statement into an inequality, 9 + 2w ≤ 27, then solve for w by subtracting 9 and dividing by 2 to find w ≤ 9.
Explanation:
The statement 'Nine increased by the product of a number and 2 is less than or equal to 27' can be translated into the following inequality: 9 + 2w ≤ 27, where w represents the unknown number. To solve for w, we will follow these steps:
Subtract 9 from both sides: 2w ≤ 18.
Divide both sides by 2: w ≤ 9.
Therefore, the solution to the inequality is w being any number less than or equal to 9.
A chessboard has an area of 324 square inches. There is a 1 - inch border around 64 squares on the board. What is the length of one side of the region containing a small squares?
The length of one side of the region containing the small squares is 64 inches.
Let x be the length of one side of the region containing the small squares.
The area of the small squares is 64 * 1 = 64 square inches.
The area of the border is (x + 2)^2 - x^2 = 4x + 4 square inches.
Since the area of the small squares and the border is equal to the area of the chessboard, we have:
64 + 4x + 4 = 324
68 + 4x = 324
4x = 256
x = 64
Therefore, the length of one side of the region containing the small squares is 64 inches.
The sales tax on a coat that is priced at $45 is 8%.find the total cost of the coat
Answer:
48.6
Step-by-step explanation:
45 * 1.08 = 48.6
What is the measure of ∠ A C D ? Upper A is labeled as 33 degree and the angle formed at the vertex Upper B is labeled as 117. The angle formed at the vertex Upper A is labeled as 33 degree and the angle formed at the vertex Upper B is labeled as 117 A. 30 ° B. 63 ° C. 147 ° D. 150
To find the measure of angle ACD, subtract the measures of angles ABC and BCD from 180 degrees.
Explanation:To find the measure of angle ACD, we need to subtract the measures of angles ABC and BCD from 180 degrees since the sum of the angles in a triangle is always 180 degrees.
Given that angle ABC measures 117 degrees and angle BCD measures 33 degrees, we have:
∠ACD = 180 degrees - 117 degrees - 33 degrees
= 147 degrees.
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2 Points
What is the slope of the line that contains the points (-2,2) and (3,4)?
Answer:
⅖
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
-2 + 4\2 + 3 = ⅖
I am joyous to assist you anytime.
Determine if the statement is always, sometimes or never true.
An exterior angle of a triangle is 180 degrees.
always
sometimes
never
Answer: It is always.
Step-by-step explanation: In an obtuse angle in a triangle, it will range from 90 degrees to 180, but that angle has to connect to the other two angles (and the other two angles plus the obtuse angle will always be 180 degrees).
Answer:
always
Step-by-step explanation:
6x + 5y = 147
8x + 4y = 156
Answer:
[12, 15]
Step-by-step explanation:
{6x + 5y = 147
{8x + 4y = 156
-¾[8x + 4y = 156]
{6x + 5y = 147
{-6x - 3y = -117 ← New Equation
________________
2y = 30
___ ___
2 2
y = 15 [Plug this back into both equations to get the x-coordinate of 12]; 12 = x
So, using the Elimination Method, what I did here was took the bottom equation and multiplied it by -¾, turning 8x to -6x, canceling out all x-terms. It does not matter which variable you choose to eliminate, as long as you know what you are doing.
I am joyous to assist you anytime.
Which expressions are equivalent to 3x + 2(x − 1) − 4?
Answer:
5- x 6
Step-by-step explanation:
What does this maths sign mean?
Answer:
Step-by-step explanation:
in discrete math, a single vertical line usually means "such that" as it relates to data sets. In this case it looks like a typo.
What is 1,000,000,000x 3,000,000,000
Answer:
Step-by-step explanation: the answer is
3,000,000,000,000,000
Answer:
3e+18
Step-by-step explanation:
to solve the equation 3x-7=x-2, Alex says the first step is to subtract x from both sides. Danny says the first step is to add 7 to both sides.
a.Solve the equation using Alex's method of first subtracting x from both sides.
b.Solve the equation using Danny's method of first adding 7 to both sides.
c.Who is correct, Alex or Danny? Justify your answer.
d. Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.
Answer:
[tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex]3x-7=x-2[/tex]
To find : Solve the equation ?
Solution :
a) Solve the equation using Alex's method of first subtracting x from both sides.
Equation [tex]3x-7=x-2[/tex]
Subtract x from both side,
[tex]3x-7-x=x-2-x[/tex]
[tex]2x-7=-2[/tex]
[tex]2x=-2+7[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
b) Solve the equation using Danny's method of first adding 7 to both sides.
Equation [tex]3x-7=x-2[/tex]
Adding 7 from both side,
[tex]3x-7+7=x-2+7[/tex]
[tex]3x=x+5[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
c) Both are correct in their ways.
d) Is there another correct first step for solving this equation? If so, identify it and use it to solve the equation. If not,explain why not.
Equation [tex]3x-7=x-2[/tex]
We can isolate the terms as like terms place together,
[tex]3x-x=-2+7[/tex]
[tex]2x=5[/tex]
[tex]x=\frac{5}{2}[/tex]
Simplify the following expression. 12a^3b^6c^5/3a^2b^4c^5
A. 4ab^2
B. 9ab^2c
C. 9ab^2
D. 4ab^2c
Answer:
A. 4ab^2.
Step-by-Step Explanation.
12 a^3 b^6 c^5 / 3 a^2 b^4 c^5
Dividing each pairs of terms:
12 / 3 = 4.
a^3 / a^2 = a.
b^6 / b^4 = b^2.
c^5 / c^4 = 1.
So it is 4ab^2.
Point J is on line segment IK. Given JK = 2x – 1, IK = 3x + 2,
and I J = 3x – 5, determine the numerical length of JK.
Answer:
JK=7
Step-by-step explanation:
From the line segment, since J is on it ,it means the line segment is
represented as I J K
from this illustration, we can say that the longest part of the line segment is from I to K
this means that, IJ +JK =IK
making JK the subject,
JK= IK - IJ
but from the question, JK=2x-1 , IK=3x+2 and IJ=3x-5
substituting them in the expression,
2x-1 =3x+2 -(3x-5)
solving for x
2x-1 =3x+2-3x+5
2x-1 =0+7
2x-1 =7
2x=1+7
2x=8
dividing through by 2
2x/2 =8/2
x=4
but the question says we should find the numerical value for JK
but from the line segment,
JK=2x-1
but now we know the value of x to be 2
so substituting it in the formula
JK= 2(4)-1
JK=8-1
JK=7
therefore, the numerical value for JK is 7
The length of JK is found by setting the sum of IJ and JK equal to IK and solving for x. When x=4 is substituted back into the expression for JK, the calculated length of JK is 7 units.
Explanation:To find the numerical length of JK, we can use the fact that IK is the entire line segment, which is the sum of IJ and JK. Therefore, we have the equation IK = IJ + JK. Substituting the given expressions, we get 3x + 2 = (3x - 5) + (2x - 1). Solving for x, we combine like terms and simplify the equation.
First, add the expressions for IJ and JK: (3x - 5) + (2x - 1) = 5x - 6.
Next, set the total length equal to the sum of parts: 3x + 2 = 5x - 6.
Now we solve for x: -2x = -8, leading to x = 4.
Finally, we substitute x back into the expression for JK to find its length: JK = 2(4) - 1 = 8 - 1 = 7.
So, the numerical length of JK is 7 units.
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The product of 2.5 and a number minus 4.7 is 10.3
Answer:
2.5(x-4.7)=10.3
Step-by-step explanation:
what is the value of x in the equation 2(x-3)+9=3(x+1)+x?
Answer:
X=0
Step-by-step explanation:
Since x is on the right side of the equation, switch the sides so it is on the left side of the equation.
3(x+1)+x=2(x−3)+93(x+1)+x=2(x-3)+9
Simplify the left side.
4x+3=2(x−3)+94x+3=2(x-3)+9
Simplify 2(x−3)+92(x-3)+9.
4x+3=2x+34x+3=2x+3
Move all terms containing xx to the left side of the equation.
2x+3=32x+3=3
Move all terms not containing xx to the right side of the equation.
2x=02x=0
Divide each term by 22 and simplify.
x=0
(+30)÷(-10)+(-20)÷(-1)
Mauna Loa, a volcanic mountain in Hawaii stands 4170m above sea level and extends to 13000 m below sea level what is the total height of Mauna Loa
The total height of Mauna Loa is -8,830 meters.
Explanation:The total height of Mauna Loa, a volcanic mountain in Hawaii, can be calculated by adding its height above sea level to its depth below sea level. The mountain stands at 4,170 meters above sea level and extends to a depth of 13,000 meters below sea level. To find the total height, we add these two values: 4,170m + (-13,000m) = -8,830 meters.
What percent of 200 is 0.5?