Answer:
x = -1
Step-by-step explanation:
Both tables show a function value of 9 for x = -1.
x = -1 is the solution to f(x) = g(x), since f(-1) = 9 = g(-1).
A mother is five times as old as her daughter. In 6 years, the mother will be three times as old as her daughter. How old is each now?
Answer: daughter = 6 years
mother = 30 years
Step-by-step explanation:
Let the daughter's age be x and the mother's age be y , then from the first statement
y = 5x .......................... equation 1
In 6 years time , the mother will be y + 6 and the daughter will be x + 6 ,from the second statement , we have
y + 6 = 3 ( x + 6 )
y + 6 = 3x + 18 ..................................... equation 2
substituting equation 1 into equation 2 , we have
5x + 6 = 3x + 18
5x - 3x = 18 - 6
2x = 12
x = 6
Therefore , the daughter's age is 6 years ,then the mother's age will be 6x5 = 30 years
Simplify 13x + 2y - 10x -7y
Answer:
3x-5y
Step-by-step explanation:
Combine like terms
To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. The simplified expression is 3x - 5y.
Explanation:To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. Start by combining the x terms and then combine the y terms.
13x - 10x = 3x
2y - 7y = -5y
Therefore, the simplified expression is "3x - 5y."
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The radius of a sphere is 6 units.Which expression represents the volume of the sphere, in cubic units?
Answer:
V=(4/3)πr^3
Step-by-step explanation:
This is the equation to find the volume of a sphere
V=(4/3)πr^3
than plug in 6 for x, and solve
The volume of a sphere with a radius of 6 units is represented by the expression [tex]\frac{4}{3}[/tex] πr³, which calculates to V = [tex]\frac{4}{3}[/tex] π(6)³, cubic units. If two such spheres combine, the volume doubles, and the new radius is the cube root of the new volume.
The expression that represents the volume of a sphere with a given radius in cubic units is given by the formula V = [tex]\frac{4}{3}[/tex] πr³. For a sphere with a radius of 6 units, you can substitute the value of the radius into this formula to calculate the volume.
The calculated volume V would be V = [tex]\frac{4}{3}[/tex] π(6)³, which simplifies to V = [tex]\frac{4}{3}[/tex] π(216), or V = 288π cubic units. Therefore, the volume of the sphere is 288 times π cubic units.
Are you cyclist travels at a rate of 1.8 km/min. how far will the cycle is travel in 48 minutes
Answer:
86.4 km
Step-by-step explanation:
Since the cyclist travels 1.8km in a minute, he will travel 48 times that in 48 minutes:
[tex]48*1.8 = 86.4[/tex]
A paper hat is folded into the shape of a kite, as shown.
A kite is shown. The left and right angles are right angles. The sides above the right angles are (3 x + 5) inches and (5 x + 1) inches. The sides below the right angle are (2 x + 1) inches and 5 inches.
What total length of ribbon is needed to line the two long sides of the hat?
Answer:
D is correct
Step-by-step explanation:
The total length of ribbon needed to line the two long sides of the hat is 22 inches.
Given that, the sides above the right angles are (3x + 5) inches and (5x + 1) inches. The sides below the right angle are (2x + 1) inches and 5 inches.
What are the properties of kites?A kite is a quadrilateral that has 2 pairs of equal adjacent sides. The angles where the adjacent pairs of sides meet are equal.
Now, (3x + 5)=(5x + 1)
⇒x=2
2x+1=5
⇒x=2
Thus, (3x + 5)=11 inches
Now, 11+11=22 inches
Therefore, the required answer is 22 inches.
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For all values of X, Which expression is equivalent to 2x+5-x+3x+x-2
Answer:
=5x+3
Step-by-step explanation:
Hope this helps!
Answer:
annnnnnn
Step-by-step explanation:
u r wronggggggggggggggggggggggggggg
A group of friends went to the movies. Movie tickets cost $8.50 each. One of the group bought some food for $6.50. The group spent a total of $57.50. Write and solve an equation to determine how many tickets were bought. Let t represent the number of tickets.
Answer:
Equation: [tex]8.5t+6.5=57.5[/tex]
Solution: [tex]t=6[/tex]
Step-by-step explanation:
Let be "t" the number of movie tickets bought by the group of friends.
According to the information given in the exercise, the price of each movie ticket is: $8.50.
Then, you can represent the amount (in dollars) the group of friends spent in movie tickets, with this expression:
[tex]8.5t[/tex]
You know that one person spent $6.50, then the expression that represents the total amount (in dollars) the group of friends spent in food and movie tickets, is:
[tex]8.5t+6.5[/tex]
Since that total amount spent is given in the exercise, you can write the following equation to determine how many tickets were bought:
[tex]8.5t+6.5=57.5[/tex]
Finally, you can solve for "t" in order to find the solution of the equation. This is:
[tex]8.5t=57.5-6.5\\\\t=\frac{51}{8.5}\\\\t=6[/tex]
Final answer:
The group purchased 6 movie tickets. The equation formulated to determine this is t × $8.50 + $6.50 = $57.50, where t stands for the number of tickets. Subtracting the food cost and dividing the remainder by the ticket cost gives us the answer.
Explanation:
To determine how many movie tickets were bought by the group, we can set up the following equation:
t × $8.50 + $6.50 = $57.50
Here, t represents the number of tickets. The cost of one movie ticket is $8.50 and the cost of the food is $6.50. The total amount spent by the group is $57.50.
To solve for t, subtract the cost of the food from the total amount:
$57.50 - $6.50 = $51
Now divide the remaining amount by the cost of one ticket to find the number of tickets:
$51 ÷ $8.50 = 6
Therefore, the group purchased 6 movie tickets.
Which number(s) below belong to the solution set of the inequality? Check all
that apply.
X+9=26
A. 234
B. 3
C. 17
D. 35
E. 52
F. 26
please anyone help ?!
What is a quarter til 1:00
Answer:
12:45
Step-by-step explanation:
quik maths
Answer:12:45
Step-by-step explanation:
All tickets for a concert are the same price the tickets agency as a fixed fee to every order a person to order six tickets paid 135 another person who orders three tickets paid 75 right in equation relating to the total cost to the number of tickets purchased in slope intercept form
x will represent the number of tickets.
y will represent the fixed fee given by the ticket agency
6x + y = 135
3x + y = 75
To solve, we can use the process of elimination by multiplying the second equation by -2 so that 6y will cancel:
-6x - 2y = -150
+6y + y = 135
Now we simplify by adding/subtracting:
-y = -15 or y = 15
Plug the value of y into any of the two equations and solve for x. I will use the second equation:
3x + 15 = 75
3x = 60
x = 20
To set this up in slope intercept form (y = mx + b), we need to identify what m and b are.
m is x because it is not a fixed number, and b is y because it is a fixed number (price of “fixed” fee). This brings us to y = 20x + 15
How did i get the decimal in 16.2 by dividing by 48.6 and 3
What is the area of the rectangle?
A. 60 units^2
B. 66 units ^2
C. 70 units^2
D. 74 units^2
Answer:
D
Step-by-step explanation:
Please look at the attached picture for full solution.
Method 1 is using the shoelace method to find the area of the rectangle. Shoelace method can be used to find the areas of any polygons given their coordinates. The coordinates have to be taken in an anticlockwise order and ending with the first coordinate.
Method 2 is making use of the distance formula of two points. The formula is as shown below:
[tex] \sqrt{(x1 - x2) ^{2} + (y1 - y2)^{2} } [/tex]
Having found the distance of the length and breadth of the rectangle, you can now find its area since area of rectangle= length × breadth.
The physician tells a woman who usually drinks 5 cups of coffee daily to cut down on her coffee consumption by 75%. If this woman is compliant with the physician's instruction, how many ounces of coffee is she allowed daily?
Answer:
Step-by-step explanation:
5 cups per day.....1 cup = 8oz.....so 5 cups = (5 * 8) = 40 oz
cut down by 75%....means ur only drinking 25%
25% of 40 oz =
0.25(40) = 10 oz per day <===
What is the value of the expression below? (Four-fifths + three-fifths) + 3.5 times 5
Answer:
21
Step-by-step explanation:
Answer:
18 and 9/10
Step-by-step explanation:
if you add 4/5+3/5=7/5 or 1.4. 3.5*5=17.5, then you add them together to get 18.9 or in the fraction version= 18 and 9/10
What is the diameter of a hemisphere with a volume of 60570
The diameter of hemisphere is 61.4 units
Solution:
Given that, volume of hemisphere is 60570 cubic units
To find: Diameter of hemisphere
The formula for volume of hemisphere is given as:
[tex]V = \frac{2}{3} \pi r^3[/tex]
Where, "r" is the radius of hemisphere
Substituting the values we get,
[tex]60570 = \frac{2}{3} \times 3.14 \times r^3\\\\60570 = 2.093 \times r^3\\\\r^3 = \frac{60570}{2.093}\\\\r^3 = 28939.32\\\\\text{Take cube root on both sides }\\\\r = \sqrt[3]{28939.32} \\\\r = 30.7017248 \approx 30.7[/tex]
We know diameter is twice of radius
[tex]Diameter = 2 \times radius\\\\Diameter = 2 \times 30.7\\\\Diameter = 61.4[/tex]
Thus diameter of hemisphere is 61.4 units
The diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].
To find the diameter of a hemisphere with a volume of [tex]\( 60,570 \, \text{cm}^3 \)[/tex], we can follow these steps:
Step 1: Write a hemisphere's volume formula.
A hemisphere's volume (V) is determined by:
[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]
where ( r ) is the radius.
Step 2: Set up the equation with the given volume
Given [tex]\( V = 60,570 \, \text{cm}^3 \)[/tex], we substitute into the formula:
[tex]\[ 60,570 = \frac{2}{3} \pi r^3 \][/tex]
Step 3: Find the value of [tex]\( r^3 \)[/tex]
First, isolate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = \frac{60,570 \times 3}{2 \pi} \][/tex]
Step 4: Calculate the value inside the equation
[tex]\[ r^3 = \frac{181,710}{2 \pi} \approx \frac{181,710}{6.2832} \approx 28,931.89 \][/tex]
Step 5: Solve for ( r )
Take the cube root of both sides to find ( r ):
[tex]\[ r = \sqrt[3]{28,931.89} \approx 30.1 \][/tex]
Step 6: Calculate the diameter
Two times the radius is the diameter (D):
[tex]\[ D = 2r \approx 2 \times 30.1 = 60.2 \][/tex]
Thus, the diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].
Complete Question:
What is the diameter of a hemisphere with a volume of 60570 [tex]cm^{3}[/tex] , to the nearest tenth of a centimeter?
how to simplify (2√5)²
(2√5 )²
= 2√5 × 2√5
= 4×5
= 20
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Simplify (3a 2) 3.
.
Answer: [tex]27a^6[/tex]
Step-by-step explanation:
The question is not clear. So, assuming that the expression you need to simplify is this one:
[tex](3a^2)^3[/tex]
You need to remember a property called "Power of a power property". This property states the following:
[tex](b^m)^n=b^{(m*n)}=b^{(mn)}[/tex]
Therefore, you need to apply the Power of a power property explained before, in order to simplify the expression provided in the exercise, multiplying the exponents inside the parentheses by the exponent outside of the parentheses. Then:
[tex](3a^2)^3=3^{(1*3)}a^{(2*3)}=3^3a^6[/tex]
Now, you must remember that:
[tex]3^3=3*3*3=27[/tex]
Finally, you get:
[tex]=27 a^6[/tex]
A Line passes through the point (-1,-2) and is perpendicular to the line with the equation y= -x - 1 what’s the equation of the line
Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 1 ← is in slope- intercept form
with slope m = - 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1, thus
y = x + c ← is the partial equation of the perpendicular line
To find c substitute (- 1, - 2) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = x - 1 ← equation of perpendicular line
Nina worked 32 hours this week. She earned a total of 360. How much does she make per hour? Write and solve equation.
Nina makes 11.25 per hour.
Step-by-step explanation:
Given,
Number of hours worked by Nina = 32 hours
Amount earned by Nina = 360
Let,
x represent the amount earned by Nina per hour.
Amount per hour * Number of hours = Amount earned
[tex]32*x=360\\32x=360[/tex]
Dividing both sides by 32
[tex]\frac{32x}{32}=\frac{360}{32}\\x=11.25[/tex]
Nina makes 11.25 per hour.
Keywords: variable, equation
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Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
___
0.802
A factory makes sheets of metal that are 2/3 of an inch thick. If a worker at the factory makes a stack of 8 of the sheets, how many inches thick will the stack be?
Write your answer as a fraction or as a whole or mixed number.
The thickness of a stack of 8 sheets of metal, each 2/3 of an inch thick, is 5 1/3 inches.
To determine the thickness of a stack of 8 sheets of metal that are each 2/3 of an inch thick, we simply multiply the thickness of one sheet by the number of sheets in the stack:
(2/3 inch/sheet) x 8 sheets = (2/3) x 8
Now, we simplify the expression by multiplying 2 by 8 which equals 16, and then we keep the same denominator:
16/3 inches
This fraction can also be converted to a mixed number:
5 1/3 inches
So, the stack will be 5 1/3 inches thick.
A certain television is advertised as a 5-inch TV (the diagonal length). If the width of
the TV is 4 inches, how many inches tall is the TV?
Answer:
TV is 3 inches tall.
Step-by-step explanation:
Given: Diagonal length of TV is 5 inch
Width of TV is 4 inches.
Considering TV to be in rectangle shape.
Lets assume the TV height to be "x"
Diagonal form a right angle triangle as shown on picture attached.
∴ using pathagorean theoram to find the height of TV.
[tex]h^{2} = a^{2} + b^{2}[/tex], where h is hypotenous, a is width or adjacent and b is height or opposite side.
∴ [tex]5^{2} = 4^{2} + x^{2}[/tex]
⇒[tex]25= 16+x^{2}[/tex]
subtracting both side by 16
⇒[tex]25-16= x^{2}[/tex]
⇒[tex]x^{2} = 9[/tex]
Taking sqaure root on both side.
Remember, √a²= a
⇒[tex]x= \sqrt{9}[/tex]
∴[tex]x= 3[/tex]
Hence, the height of TV is 3 inches.
250 surveyed. 15 do not like pizza. 66% like pizza and burritos. 30% do not like burritos. Fill in the two way frequency table to show the results of the survey.
Answer:
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
Step-by-step explanation:
250 people are surveyed. 15 of them do not like pizza, then
250 - 15 = 235 like pizza.
30% do not like burritos. 30% of 250 is
[tex]250\cdot 0.3=75[/tex] people which do not like burritos and 250 - 75 = 175 people like burritos.
Then the incomplete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&&&175\\\text{Do not like burritos}&&&75\\ \text{Total}&235&15&250\end{array}[/tex]
66% like pizza and burritos. Then
[tex]250\cdot 0.66=165[/tex] people like pizza and burritos.
Hence,
[tex]235-165=70[/tex] people like pizza and do not like burritos
[tex]175-165=10[/tex] people like burritos and do not like pizza
[tex]250-165-70-10=5[/tex] people do not like pizza and do not like burritos
Hence the complete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
What is the value of h?
O h= 1.5
Oh=9
0 h = 10
0 h = 13.5
Answer:
The answer is 9 on edgggggggggggg
Step-by-step explanation:
Based on the information given, the value of h is 9.
Firstly, it should be noted that the sum of the angles that are on a straight line is 180°.
In this case, we'll have to equate both values that are given and this will be:
3h + 18° + 15h = 180°
Collect like terms
3h + 15h = 180° - 18°
18h = 162°
Divide both sides by 18
18h/18 = 162°/18
h = 9
Therefore, the value of h will be 9
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The area of the following rectangle is 24 square units.
Write an equation that can be used to find the value of n.
Solve the equation to find the value of n. In your answer, show all of your work.
Answer:
Step-by-step explanation:
Area of rectangle A = L × W
Length L = n - 3
Width = 2
Area = 24square unit
:- 24 = (n - 3)2
24 = 2n - 6 ...... This the equation
24 + 6 = 2n
30 = 2n
n = 30/2
n = 15
At a party, 4 identical tables are placed side by side as shown. The dimensions of one table are given.
2.5x - 3 and x
Which expressions represent the perimeter of the rectangle formed by all the tables together? Choose all that apply.
10x - 12 + x + 10x - 12 + x
8(2.5x - 3) + 5x
2(10x - 12) + 2x
4(2.5x - 3) + x
2(11x - 12)
*There is more than one answer. Please look at the image and please tell me is I’m correct in the ones I chose*
Answer:
The answer is the first choice: 10x - 12 + x + 10x - 12 + x
Step-by-step explanation:
Let the length of a table 2.5x - 3 and let the width of the table be x.
Four tables with identical dimensions are placed together.
So we can say that width of the new table formed by placing the four tables side to side will be the same as the width of one table, that is x.
And the two sides of the new table which will represent the width will be the width of one table at one end and the width of the table at the other end, that is x + x.length
Now as we saw before there are are two widths which are part of the perimeter there are also two lengths which are part of the perimeter.
The perimeter of a table is given by (2 × length) + (2 × width).
Now one length of the new table will be equal to (4 × length of one table) = 4 × (2.5 x - 3) = 10x -12
Therefore perimeter of the new table is given from the formula of the perimeter = Length + width + Length + width
= 10x - 12 + x + 10x -12 + x
A home owner is building a square patio and will cover the patio with square tiles. Each tile has an area of 256 square inches and costs $3.45 each. The home owner has \$500 to spend on tiles. Calculate how many tiles the home owner can buy. Find the side length
(in feet) of the largest patio the home owner can build.
Answer:
The homeowner can buy 144 tiles maximum.
Side length = 16 feet.
Step-by-step explanation:
The cost of each tile is $3.45.
So, at $500, the homeowner can buy [tex]\frac{500}{3.45} = 144.92[/tex] ≈ 144 number of tiles. {As the number of tiles can not be a fraction.}
Since each tile is a square with area 256 square inches, so the homeowner can arrange the tiles in 12 by 12 arrangements.
Each tile has side length = √256 = 16 inches.
So, the side length of the largest patio is (16 × 12) inches = 16 feet. (Since, 1 foot = 12 inches). (Answer)
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8° when staring at the top of the statue. Then the person looks down at an angle of 14° when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
Answer:
The statue is 22.24 ft tall.Step-by-step explanation:
The given question says that, the man is standing 50 ft away from the statue.
Looking at the top of the statue, the angle of elevation is 8°.
Hence, where the man is standing, from that horizontal plane, the distance of the top of the statue is [tex]50 tan 8°[/tex].
Similarly, looking down towards the base, the angle is 14°.
Hence, the height from the base of the statue to the horizontal plane, where the man is standing is [tex]50 tan 14°[/tex].
The total height of the statue is [tex]50 tan 8° + 50 tan 14° = 50( tan 8° + tan 14°)[/tex] = 22.24475804 ≅22.24 ft.
fill in the blank by applying the indicated property of the real numbers (do not simplify the expression)
(24+1)+92=______
Answer: [tex]=24+(1+92)[/tex]
Step-by-step explanation:
For this exercise you need to remember a property called "Associative Property".
The Associative Property states that it does not matter how you group the numbers, because you will always obtained the same result.
For Additiion, the Associentive property states the following:
[tex]a + (b + c) = (a + b) + c[/tex]
Where "a", "b" and "c" are Real numbers.
In this case you have:
[tex](24+1)+92[/tex]
As you can notice, the number 24 and the number 1 are grouped inside the parentheses, but you can also regroup the numbers 1 and 92 using parentheses and you will have the same result.
Therefore, based on the Associative Property explained before, you can conclude that:
[tex](24+1)+92=24+(1+92)[/tex]