Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
Select all the equation that depicts one of the properties of exponents
Answer:
1st, 4th and 5th are correct.
Step-by-step explanation:
Find the value of x. The answer is 32 I just need help showing my work.
Answer:
Below.
Step-by-step explanation:
The line of length 48 = 1/2 of the baseline (3x) as the line 48 joins the midpoints of the 2 sloping sides.
1/2 * 3x = 48
multiply both sides by 2:
3x = 96
x = 32.
Dominik uses 20 grams of filling for each dumpling he makes. He has 1500 grams of dumpling filling. The grams F of filling remaining is a function of d, the number of dumplings Dominik makes.
Answer:
75 dumplings
Step-by-step explanation:
1500/20= 75
Answer:
−20d+1500
Step-by-step explanation:
I did it on khan and it worked
Can u please help.......
Using the centroid P on the triangle, the value of QN is 25.5 and PN is 8.5
What is Centroid of a TriangleThe centroid of a triangle is a point located at the intersection of the three medians (the lines that connect the vertices to the midpoints of the opposite sides). The centroid divides each median in two segments that have the same length. It is the center of gravity of the triangle and is the point at which the triangle's three medians intersect.
The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.
In this triangle, the centroid is at P and the QP is 17.
a) QN
The distance between QP is two-thirds the length of QN
The length of QP = 17
QP = 2/3 QN
17 = 2/3 QN
QN = (3 * 17) / 2
QN = 25.5
b) PN
The distance between PN is calculated as;
PN = QN - QP
PN = 25.5 - 17
PN = 8.5
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Please help ASAP ....
Answer:
21 3/4
Step-by-step explanation:
3 times 7 1/4 since the scale is 1:7 1/4. Good luck!! :)
An online furniture store sells chairs for $200 each and tables for $450 each. Every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $4800 worth of chairs and tables. If xx represents the number of tables sold and yy represents the number of chairs sold, write and solve a system of inequalities graphically and determine one possible solution. Inequality 1
Using the provided values and the conditions, The inequality equations required are : [tex]x+y \leq 20[/tex] and [tex]450x+200y \geq 4800[/tex].
What do you mean by equation?An equation is a mathematical statement in which two expressions are set equal to each other. It is typically written using an "=" sign, with the expressions on either side of the sign representing equivalent values. For example, the equation 2 + 2 = 4 states that the value of 2 plus 2 is equal to the value of 4. Equations can be used to express relationships and to solve problems.
What are inequalities?An inequality is a mathematical statement that compares two values or expressions. It is similar to an equation, but instead of using the "=" sign to indicate that the two sides are equal, it uses one of the following symbols: ">", "<", "≥", "≤" to indicate that the two sides are not equal. For example, the inequality 2 + 2 > 4 states that the value of 2 plus 2 is greater than 4. Similarly, the inequality 2 + 2 < 4 states that the value of 2 plus 2 is less than 4. Inequalities can be used to express constraints in a problem or to define a range of solutions. They can also be represented graphically by using a number line.
x= number of tables sold
y= number of chair sold
max furniture in a day = 20
so, [tex]x+y \leq 20[/tex].
least selling amount = 4800
so, [tex]450x+200y \geq 4800[/tex]
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Order the following number from greatet to leat. When entering fraction pleae ue "/". For example 1/2 or 3 2/3
-0. 44, -3/8, -0. 5, -2/5
The order from greatest to least is -3/8> -2/5>-0.44>-0.5
To compare all the numbers, we first convert the numbers to their fractional equivalent.
Therefore, -0.44= -44/100
And -0.5= -5/10
Now, we covert all the numbers to get the same denominator in all the numbers, therefore, let the denominator be 100
Therefore, we multiply -3/8 with 12.5 in both numerator and denominator to get, -37.5/100
Then, we multiply -2/5 with 20 in both numerator and denominator to get, -40/100
and, we multiply -5/10 with 10 in both numerator and denominator to get -50/100
Therefore, with these resultant value we can say that, -37.5/100> -40/100 >-44/100> -50/100
Thus, -3/8> -2/5>-0.44>-0.5
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6(x+4)=30
how do i solve this?
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
C
Step-by-step explanation:
We want to solve the equation:
[tex]x^2+2x+7=0[/tex]
Using the quadratic formula. The quadratic formula is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 2, and c = 7.
Substitute:
[tex]\displaystyle x=\frac{-(2)\pm\sqrt{(2)^2-4(1)(7)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{-2\pm\sqrt{-24}}{2}[/tex]
Simplify the square root:
[tex]\sqrt{-24}=\sqrt{4\cdot 6\cdot -1}=\sqrt{4}\cdot\sqrt{6}\cdot\sqrt{-1}=2i\sqrt{6}[/tex]
Hence:
[tex]\displaystyle x=\frac{-2\pm2i\sqrt{6}}{2}[/tex]
Simplify:
[tex]\displaystyle x=-1\pm i\sqrt{6}[/tex]
Hence, our solutions are:
[tex]\displaystyle x=\left\{-1+i\sqrt{6}, -1-i\sqrt{6}\right\}[/tex]
Our answer is C.
Which angle is a vertical angle to with <7?
Answer: <9
Step-by-step explanation:
Katie says that if a number is a multiple of 8, it is also a multiple of 4. Is Katie correct? Explain.
Katie is correct. Any number that has 4 as a factor will also have 8 as a factor; therefore, any number that has 8 as a factor will have 4 as a factor.
Katie is correct. Since 4 is a factor of 8, any multiple of 8 will also be a multiple of 4.
Katie is incorrect. 80 is a number that has 8 as a factor but not 4.
Katie is incorrect; just because 4 is half of 8 does not mean that a number that has 8 as a factor will also have 4 as a factor. HELP PLS ASAP PLS AND THANK U
Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.
Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4. So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.
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What is the line x =- 4?
The line x= -4 is a vertical line passing through x-axis.
It is a distance of 4 units from the x-axis and is parallel to the y-axis.
Vertical Line in a coordinate plane refers to a line that is perpendicular to the Y-axis. From top to bottom and from bottom to top, it is a straight line. The x-coordinate of every point along this line will be the same. The points of vertical lines include, for instance, (2,0), (3,0), (-4,0), etc. Similar to this, a horizontal line is a line that runs parallel to the x-axis from left to right.
There is no slope to the vertical lines. It follows the y-axis parallel, hence the slope is not known. As a result, the equation for the vertical line that at any point, let's say 'a', crosses the x-axis is:
x = a
where x is a point on the line's coordinate.
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The length of ome material i 8. 3m correct to 1 decimal place. Write the error interval for the length ,x, of the material
The error interval for the length ,x, of the material is [8.25, 8.35)
We know that error interval is nothing but the limits of accuracy when a number has been rounded.
It is the range of possible values that a number could have been before a number was rounded.
Here, The length L of a some material is 8.3 meters.
The length of the material has been rounded to 8.3 to one decimal place.
The number below 8.3 is 8.2 and the number above is 8.4
Consider a half way between 8.2 and 8.3 for the lower bound and half way between 8.3 and 8.4 for the upper bound.
This means, the length of the material must have been between 8.25 meters and 8.35 meters to round to 8.3 meters to one decimal place.
Therefore, the required error interval would be 8.25 ≤ x < 8.35
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PLEASE HELP PIC UPLOAD
If /A and /B are supplementary angles and
m/B = 54, find m/LA.
Therefore , the solution of the given question of triangle comes out to be the only true option is A.
What is Triangle?Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.
Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.
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what is the area of the puzzle pieces above
Answer:
101.25 feet2
Step-by-step explanation:
Area =
b1 + b2 ×h
2
=
16 + 11 × 7.5
2
= 101.25 feet2
Tip if you need this again just go to Area Calculator
Steven bought a video game that was on sale for 30 percent off of the original price. If
the original price of the video game was $29, what was the sales price of the game?
URGENT
The time it takes Susan to drive to work each day is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes.
Approximately what percent of workdays does it take Susan between 38 and 46 minutes to drive to work?
50%
68%
95%
99.7%
Answer:
99.7%
Step-by-step explanation:
the standard deviation is 4 minuet but there is always outliers so thats why its not 100% of the time and the minutes are coverd by the deviation.
Answer:
68%
Step-by-step explanation:
The attached normal table shows area under the standard normal curve that are to the left of a particular z-score.
To find the area between two z-scores, say [tex]z_1 < z_2[/tex], find the area to the left of [tex]z_2[/tex] then subtract the area to the left of [tex]z_1[/tex]. That difference is the area between the two z-scores.
38 minutes has a z-score [tex]z_1=\frac{38-42}{4}=-1[/tex]
46 minutes has a z-score [tex]z_2\frac{46-42}{4}=1[/tex]
Find z= 1.0 in the table. The area in that row is .8413.
Find z=-1.0 in the table. The area in that row is .1587.
The difference, .8413 - .1587 = .6826 is the area under the normal curve between z=-1 and z=1.
.6826 is about 68%
Jackson borrows $400 with an interest rate of 1.5%. How much interest will
he pay after 4 years?
Answer:
$80 in interest for four years. She has to pay back a total of $480
Step-by-step explanation:
ive tried everything and cant get the answer
Answer:
Slope of perpendicular line: 5
Slope of parallel line: -1/5
Step-by-step explanation:
Convert the equation to slope-intercept form (y=mx+b where m is the slope and b is the y-intercept)
x+5y=6
subtract x on both sides
5y=-x+6
divide by 5 on both sides
y=-(1/5)x+6/5
The slope of this equation is the coefficient of x, -1/5.
The slopes of two perpendicular lines are negative reciprocals of each other.
To get the negative reciprocal of a number, flip the numerator and denominator and multiply by -1.
-1/5 becomes 5, so that's the slope of a line perpendicular to our original line.
Parallel lines have the same slope, so that's just -1/5.
Slope of perpendicular line: 5
Slope of parallel line: -1/5
Can zero be negative
Answer: no
Step-by-step explanation:
Zero is neither positive or negative
For items 15 -16 refer to the figure at the right
15. Which is the common side of Ļ BCA and Ļ ACD ?
A. segment BC B. segment CE C. segment AC D. segment CD
16. Which two angles are congruent if segment CD bisects ĻACE
A. Ļ BAC and ĻACE B. Ļ BAC and ĻACD C. Ļ CDE and ĻACE
D. Ļ ACD and ĻCDE
17. What property is described in the statement: AB ≅ AB?
A. transitive B. reflexive C. substitution D. symmetric
18. Which term refers to the collection of axioms or statements about undefined terms?
A. numeral system B. postulates C. axiomatic system D. theorems
19. What basic geometric principle are proven to be true by making connections between accepted definitions?
A. axioms B. postulates C. theorems D. defined terms
20. Which statements are assumed to be true without any proof ?
A. undefined terms B. postulates C. theorems D. defined terms
Answer:
15. C. segment AC
16. D. angles ACD and DCE
17. C. substitution
18. C. axiomatic systems
19. A. Axioms
20. D. Defined Terms
Your colleague’s computer stops working, and no one from the IT department is available to fix it. You have basic knowledge of computer hardware. Which action should you take as an ethical employee?
A.
Initiate help by offering to check the computer.
B.
Start a conversation with your colleague and provide a distraction.
C.
Take a quick break and offer your computer for a short time.
D.
Ignore it because it is beyond your designated scope of work.
Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.
What is a computer hardware?A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.
In Computer technology, there are various examples of a computer hardware and these include the following:
Power supply unit (PSU).Hard-disk driveKeyboardMonitor (screen)MouseMotherboardCentral processing unit (CPU).Network interface card (NIC).Memory moduleBased on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.
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pls i need to know what the answer is!!!
The solution of the equation 3(2m - 1) ≤ 4m + 7 is option A m ≤ 5.
What are inequalities?A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol denotes that the expressions on each side are not equal.
The given inequality is 3(2m - 1) ≤ 4m + 7
Remove the brackets by multiplying 3 with each term inside it:
6m - 3 ≤ 4m + 7
Subtract 4m from both sides of the equation.
6m - 3 - 4m ≤ 4m + 7 - 4m
2m -3 ≤ 7
Add 3 to both sides of the equation.
2m - 3 + 3 ≤ 7 + 3
2m ≤ 10
Divide both sides of the equation with 2.
2m/2 ≤ 10/2
m ≤ 5
Hence the solution of the equation is m ≤ 5, that is option A.
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The following table gives annual life insurance premiums per $1,000 of face value. Use the table to determine the annual premium for a $110,000 5-year term policy for a 22-year-old female. Round your answer to the nearest cent.
Answer: $244.20
Step-by-step explanation:
The amounts listed are per $1,000 of coverage so if the coverage is $110,000, first find the number of $1,000 coverages this entails:
= 110,000 / 1,000
= 110
Then multiply this by the cost per $1,000 for a 22 year old female for a 5 year policy:
= 110 * 2.22
= $244.20
Can someone please help me with this I'm not great with math.
The width of a rectangle is unknown. The length of the rectangle is two more units than its width.
Write a simplified algebraic expression for the area of the rectangle in terms of width (w).
Write your answer in descending order with no spaces. Use w as your variable and use ^ infront of exponents
The algebraic expression for area of rectangle in terms of width(w) is w^2+2w.
What is algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
The expressions are mainly of 4 types that includes:
Monomial Expression: These expressions have only one term.Binomial Expression: These expressions have two terms.Trinomial Expression: These expressions have three terms.Polynomial Expression: These expressions have many terms.Let the width be w.
So, length of rectangle will be w+2
Now, area of rectangle is length*width
Area= (w+2)*w
= w^2+2w
Hence, a simplified algebraic expression for the area of the rectangle in terms of width (w) is w^2+2w.
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Anybodyyy know how to do thisss ???
Answer:
volume of a sphere is ⁴/³π r³
⁴/³ ×3.14 × 23³
3 goes into 3.14 , 1.047 times
4 ×1.047×23³
50939.17
Step-by-step explanation:
hope itade sense
help i have to turn this in today !
Rosa is 402 meters from a tall skyscraper in Chicago. Your line of sight to the top of the skyscraper is a 20 ° elevation angle to the ground. How tall is the skyscraper to the nearest decimal?
Answer:
900 meters
Step-by-step explanation:
If the height of the building (unknown) is opposite of the angle of elevation (20°) and the distance from the building (402 meters) is adjacent to the angle of elevation, then we use the tangent function to find the height of the building:
tanθ=opposite/adjacent
tan(20°)=x/402
402tan(20°)=x
900=x
Therefore, the height of the skyscraper is 900 meters.
10. Find the degree of the monomial. 7m^6n^5
11
6
7
5
Answer:
(a) 11
Step-by-step explanation:
You want the degree of the monomial 7m^6n^5.
DegreeThe degree of a monomial is the sum of the exponents of its variables.
m has an exponent of 6
n has an exponent of 5
The degree is 6+5 = 11.
Please help me with this question
Answer:
-29
Step-by-step explanation:
(−4−3)(2^2)−1
=−7(2^2)−1
=(−7)(4)−1
=−28−1
=−29
Answer:
NEGATIVE 29
Step-by-step explanation:
p
Exponents
Multiply
D
Add
Subtract
So the first exponent is
[tex]2^{2}[/tex] which is 4
So now we have multiply so
4 x ( - 4 + - 3 )
4 x - 4 = - 16
4 x - 3 = - 12
So our new equation is
- 12 - 16 - 1 = - 29 :)
So the answer is NEGATIVE 29
*LOOK AT PICTURE*
A) 8.45 in
B) 3.125 in
C) 6.25 in
D) 62.5 in