Answer:
The smaller number is 22
The larger number is 30
Step-by-step explanation:
L + S = 52
L = S + 8
Set both equations equal to L.
S + 8 = -S + 52
+S +S
2S + 8 = 52
- 8 - 8
2S = 44
S = 22
To find the larger number, plug 22 in as S into the equations.
L = 30
Final answer:
The two numbers are 22 and 30, with the smaller number being 22 and the larger one being 30 (which is 8 more than the smaller number).
Explanation:
The sum of two numbers is 52, and the larger number is 8 more than the smaller number. Let's denote the smaller number as x and the larger number as x + 8. The equation to represent their sum is:
x + (x + 8) = 52
By combining like terms, the equation simplifies to:
2x + 8 = 52
Subtract 8 from both sides of the equation to isolate the term with x:
2x = 44
Divide by 2 to solve for x:
x = 22
Now that we have the value of the smaller number, we can find the larger number:
x + 8 = 22 + 8 = 30
So, the two numbers are 22 and 30.
Write the mixed number -7 1/7 as an improper fraction.
Answer:
-50/7
Step-by-step explanation:
-7 1/7=-50/7
Because 7*7+1=49+1=50, and don't forget the negative sign.
Please help me understand this step by step. FOR BRAINLIEST
Evaluate x^2 + 2x - 4 if x= -4
Answer:
Step-by-step explani think its power 10 wizard cards
ation:
Answer:
Step-by-step explanation:
classify the triangle by its angels :
A. acute
B. right
C. obtuse
D. scalene
Answer:
B. right
Step-by-step explanation:
In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.
When solving the equation 27.75n + 5.50= 144.25 , what can you do to get 27.75n by itself on one side of the equation?
Answer:
Subtract 5.5 from both sides
Or
Add -5.50 to both sides
Step-by-step explanation:
The given equation is :
27.75n + 5.50= 144.25
To get 27.75n on one side of the equation.
We subtract 5.50 from both sides to get:
27.75n + 5.50-5.50= 144.25-5.50
This simplifies to:
27.75n= 138.75
Therefore the answer is subtract 5.50 from both sides
Riley is saving up to buy a new television. She needs a total of $1,212.61. Riley has saved $200.30 already and earns $77.87 per week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Riley will need to work approximately 13 weeks to save enough money to buy a new television.
Explanation:Riley needs to save $1,212.61 to buy a new television and already has $200.30, meaning she requires an additional $1,212.61 - $200.30 = $1,012.31. As her weekly earning is $77.87, she must save for several weeks to accumulate the required amount. To find the number of weeks, divide the total amount she needs to save by her weekly earnings. Therefore: $1,012.31 / $77.87 = approximately 13 weeks. Therefore, Riley will need to work for about 13 weeks to accumulate the required amount to purchase the television.
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13. A shop owner spent $540 to purchase a stock of
computer keyboards. If the price of each keyboard
had been reduced by $2, he could have bought 3
more keyboards. Find the price of one keyboard.
The original price of one keyboard was $20.
Let's denote the original price of one keyboard as x.
The shop owner spent $540 to purchase a stock of computer keyboards. Therefore, the number of keyboards he purchased can be calculated as [tex]\( \frac{540}{x} \)[/tex].
If the price of each keyboard had been reduced by $2, the new price of one keyboard would be x - 2.
With this reduced price, the shop owner could have bought 3 more keyboards, so the total number of keyboards he could have purchased is [tex]\( \frac{540}{x-2} \)[/tex].
We are given that this value is 3 more keyboards than the original purchase, so we can set up the equation:
[tex]\[\frac{540}{x-2} = \frac{540}{x} + 3\][/tex]
To solve this equation, we first clear the fractions by multiplying both sides by (x(x-2):
[tex]\[540x = 540(x-2) + 3x(x-2)\][/tex]
Expanding and simplifying:
[tex]\[540x = 540x - 1080 + 3x^2 - 6x\][/tex]
[tex]\[0 = 3x^2 - 6x - 1080\][/tex]
Now, let's solve this quadratic equation for x.
Dividing both sides by 3:
[tex]\[x^2 - 2x - 360 = 0\][/tex]
Now, we can use the quadratic formula to solve for x:
[tex]\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\][/tex]
Where a = 1, b = -2, and c = -360:
[tex]\[x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \times 1 \times (-360)}}{2 \times 1}\][/tex]
[tex]\[x = \frac{2 \pm \sqrt{4 + 1440}}{2}\][/tex]
[tex]\[x = \frac{2 \pm \sqrt{1444}}{2}\][/tex]
[tex]\[x = \frac{2 \pm 38}{2}\][/tex]
So, x can be either:
[tex]\[x = \frac{2 + 38}{2} = \frac{40}{2} = 20\][/tex]
or
[tex]\[x = \frac{2 - 38}{2} = \frac{-36}{2} = -18\][/tex]
Since the price of a keyboard cannot be negative, the only valid solution is x = 20.
Therefore, the original price of one keyboard is $20.
Please answer as soon as possible.
Answer:
9(4 +3)5(9 +5)8(2+9)Step-by-step explanation:
Problems like these are aided immensely by your knowledge of multiplication tables.
1) 36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6
27 = 1·27 = 3·9
The greatest common factor is 9, so the sum can be written as 9(4+3).
__
2) 45 = 1·45 = 3·15 = 5·9
25 = 1·25 = 5·5
The greatest common factor is 5, so the sum can be written as 5(9+5).
__
3) 16 = 1·16 = 2·8 = 4·4
72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9
The greatest common factor is 8, so the sum can be written as 8(2+9).
yea i’m confused so like help?
Answer:
0,1 is greater because...
Answer:0,1
Step-by-step explanation:
The function y = log (x) is translated 1 unit right and 2 units down. Which is the graph of the translated function?
On a coordinate plane, a curve starts at (negative 1, negative 5) and curves up into quadrant 1. It approaches y = 1.
On a coordinate plane, a curve starts at (1, negative 4) and curves upwards. It approaches y = negative 1.
On a coordinate plane, a curve starts at (negative 1, negative 1) and curves up into quadrant 1. It approaches y = 5.
On a coordinate plane, a curve starts at (1, negative 3) and curves up into quadrant 1. It approaches y = 5.
See the graph below
Explanation:
We need to remember the following rules:
[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]
Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:
[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]
Below you can see the graph. The red one is the original function while the blue one is the translated one.
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Answer:
B
Step-by-step explanation:
Took test on edge
Given: f(x) = +5 and g(x) = x - 2.
What are the restrictions of the domain of f(g(x))?
O X=-5
O X=-3
o * 2
o There are no restrictions.
Answer:
14838388÷+113
Step-by-step explanation:
because it has two zeros
Answer:
its b
Step-by-step explanation:trust
Recipe for cookies calls for 3 1/4 cups of sugar Amy has already put three and one nights cup how many more cups so she need to put in
Answer:
So she need [tex]\frac{5}{36}\ cups[/tex] more to put in.
Step-by-step explanation:
Given:
Recipe for cookies calls for 3 1/4 cups of sugar.
Amy has already put three and one nine cups.
Now, to find the number of cups she need to put in.
Number of cups of sugar for recipe calls = [tex]3\frac{1}{4} =\frac{13}{4}\ cups.[/tex]
Amy has already put = [tex]3\frac{1}{9} =\frac{28}{9}\ cups.[/tex]
So, to get the number of cups she need to put in we subtract number of cups of sugar for recipe calls from number of cups of sugar for recipe calls:
[tex]\frac{13}{4} -\frac{28}{9}[/tex]
Subtracting by taking the same denominator:
[tex]=\frac{117-112}{36}[/tex]
[tex]=\frac{5}{36}[/tex]
Therefore, so she need [tex]\frac{5}{36}\ cups[/tex] more to put in.
Solve:
The total cost (C) in dollars for building an office of x square feet is given
by the function C(x) = 107,500 + 150x.
If the total cost was $385,000.00, how many square feet was the office?
Answer:
x=1850
Step-by-step explanation:
C(x) is a stand-in for total cost
since we are given the total cost we can replace the variable with its value
385000=107500+150x
now all we have to do is solve
start by subtracting 107500 from both sides
385000=107500+150x
277500=150x
now we finish solving by dividing both sides by 150
277500=150x
x=1850
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which polynomial represents the sum below? (3x^2+3) + (3x^2+x+4) A) 6x^2+x+12 B) 9x^2+x+7 C) 6x^@+x+7 d)9x^2+x+12
Answer:
Step-by-step explanation:
3x^2 + 3 + 3x^2 + x + 4....combine like terms
6x^2 + x + 7 <===
There are 100 students at a swim meet. Every 3rd finisher in the race receives a medal. Every 5th finisher gets a ribbon. How many people will receive a medal AND ribbon.
Final answer:
Calculating the least common multiple (LCM) of 3 and 5 to determine that 6 students will receive both a medal and a ribbon at a swim meet of 100 students.
Explanation:
To find the number of students at the swim meet who will receive both a medal and a ribbon, we need to look for the common multiples of 3 and 5, as medals are given to every 3rd finisher and ribbons to every 5th finisher. The least common multiple (LCM) of 3 and 5 is 15, which means every 15th student will receive both a medal and a ribbon. Since there are 100 students, we simply divide 100 by 15 and then take the integer part of the result, because we can't have a fraction of a person.
100 ÷ 15 equals approximately 6.66. The integer part is 6, which means 6 students will receive both a medal and a ribbon.
Ikyjah’s cat is stuck up a tree. To rescue it, he places the base of a 10 ft ladder 3 ft away from the base of the tree. What is the height of the branch which the cat is stuck on?
The height of the branch is 9.54 ft
Step-by-step explanation:
Apply Pythagorean relationship in this question where the length of the ladder is the hypotenuse, and the distance from the tree base is the shortest side.Finding the height will be;
a²+b²=c²
a²+3²=10²
a²=10²-3²
a²=100-9
a²=91
a=√91=9.54 ft
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Which graph shows the solution to the system of linear inequalities? y < 2x – 5 y > –3x + 1 On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the right of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the right of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded. On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (0, 1) and (1, negative 2). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (0, negative 5) and (2, negative 1). Everything to the left of the line is shaded.
The graph representing the solution to the system of inequalities y < 2x - 5 and y > -3x + 1 would have a dashed line for the first inequality and a solid line for the second one, with the intersected shading to the left of the lines.
Explanation:The student's question centers around identifying which graph depicts the solution to the given system of linear inequalities: y < 2x - 5 and y > -3x + 1. The solution to a system of inequalities is represented by the area of intersection between the two shaded regions of the graphs. The first inequality, y < 2x - 5, is a line with a positive slope that passes through (0, -5) and the shading is below the line because 'y' is less than the expression on the right. The second inequality, y > -3x + 1, is a line with a negative slope that passes through (0, 1), and the shading is above the line because 'y' is greater than the expression on the right. Based on these conditions, the correct graph would be the one with a dashed line (indicating 'less than' or 'greater than' but not 'equal to') for the first equation and a solid line (indicating 'less than or equal to' or 'greater than or equal to') for the second equation where the shading on the left side of the lines intersect.
Remember, the slope of a line indicates how steep the line is and is calculated by rise over run. The y-intercept of a line is where the line crosses the y-axis. These key features, along with the type of inequality symbol, determine where and how to shade the graph for a system of linear inequalities.
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A politician’s support grew from 42% by 3 percentage points to 45%. What percent (relative) change is this?
Answer:
The percent (relative) change is 7.14 percent (%).
Step-by-step explanation:
We are given that the original support value is at 42%.
Then the support increased by 3%, to reach 45%.
We want the Percentage Change (i.e. relative) change of this increase, which can be computed as:
[tex]\frac{X_{F}-X_{O}}{X_{O}}*100[/tex]
where [tex]X_{F}[/tex] is the final value reached
[tex]X_{O}[/tex] is the original value
So plugging in our known values and computing we have:
[tex]\frac{45-42}{42}*100= \frac{3}{42}*100 = 0.071428*100=7.14[/tex] percent increase.
Now lets go back and check if we are correct.
[tex]42+42\frac{7.14}{100}=42+2.9988=42+3=45[/tex]
So it works!
When you calculate the area, what measurement are you finding?
A
Area measures the distance around the outside of a given shape.
B
Area measures the amount of any certain single unit (inches, feet, miles, etc.) that can be contained inside the flat plane of a given shape.
Answer:
B
Area measures the amount of any certain single unit (inches, feet, miles, etc.) that can be contained inside the flat plane of a given shape.
Step-by-step explanation:
PLEASE HELP 15 POINTS.
the lines a and b intersect at point D. What is the value of z? Enter your answer in the box. z = Lines a and b intersect at point D. Acute vertical angles measure five z plus eight degrees and four z plus twenty degrees.
Answer:
[tex]z=12[/tex]
Step-by-step explanation:
The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.
Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.
Congruent angles have equal measures.
Hence,
[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]
Answer:
12
Step-by-step explanation:
16-(-12)=
As soon as possible please
A regular polygon has an interior angle of 165 degrees. How many sides does it have?
Answer:
24
Step-by-step explanation:
First find the exterior angle: 180 - 165 = 15
Then 360 ÷ 15 because 360 divided by he exterior angle of a regular polygon is equal to the number of sides.
Answer:
Hello, 24
Step-by-step explanation:
Ingerior angle = 165
Exterior angle = 180 - 165 = 15
The sum of exterior angles of any polygon is 360
Number of sides = 360/15 = 24 A polygon is any two dimensional shape formed with the straight lines. Triangles, pentagons, quadrilaterals, and hexagons are all examples of the polygons. The name itself tells as to how many sides the shape has. For example, a triangle has three sides, whereas a quadrilateral has four sides.
Thus, when the regular polygon have if each of its interior angle is 165° then,
The corresponding exterior angle must be 180-165 = 15°
The sum of ALL the exterior angles is 360°
Sides of exterior angles is 360/15 = 24
Therefore the number of sides a regular polygon will have is 24 Have a Awesome Day!
The number of cars Gary sold each month was 12, 5, 9, 11, 14, and 10.
What was Gary's median number of sales per month?
o
10.2
0
0 0
Answer:
11.5
Step-by-step explanation:
(11+12)/2=11.5
Which postulate proves that the two triangles are congruent?
A. SAS
B. SSS
C.AA
D.ASA
Answer:
B. SSS
Step-by-step explanation:
All of the sides are the same
SSS postulate proves that the two triangles are congruent.
What is Congruency of Triangle?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) ASA (angle-side-angle)Given:
From the figure we have two triangles named as FED and CBA
Now, In triangles FED and CBA
FE = AC
ED = BA
FD = BC
So, by SSS Congruency Criteria triangles FED and CBA are Congruent.
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what is 2(8x-3) -4(3x-5)=19
Answer:
5/4
Step-by-step explanation:
2(8x-3)-4(3x-5)=19
16x-6-12x+20=19
16x-12x-6+20=19
4x+14=19
4x=19-14
4x=5
x=5/4
Which values of x is the solution set of the inequality 7 (x+1) > -14?
The solution of given inequality is: [tex]x>-3[/tex]
Solution:
Given inequality is:
[tex]7(x+1)>-14[/tex]
We have to find the value of "x"
Let us solve the given inequality
Divide both sides of inequality by 7
[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]
Simplify the above expression
[tex](x+1)>-2[/tex]
[tex]x+1>-2[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]
[tex]x+1-1>-2-1\\\\x>-3[/tex]
Thus the value of x is [tex]x>-3[/tex]
Identify all factors of the expression 〖4x〗^2+17x-15.
The factors of given expression are: -5 and 3/4
Step-by-step explanation:
Given equation is:
[tex]4x^2+17x-15[/tex]
Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15
[tex]4x^2+20x-3x-15[/tex]
[tex]= 4x(x+5) - 3(x+5)[/tex]
[tex]=(4x-3)(x+5)[/tex]
Now
[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]
[tex]x+5 = 0\\x = -5[/tex]
Hence,
The factors of given expression are: -5 and 3/4
Keywords: Quadratic equation, factors
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Data is often displayed using numbers and categories.
Which types of graphs are most appropriate for displaying categorical data? Check all of the boxes that apply.
the graphs picture is not provided (incomplete question. explanation:
Answer:bar graphs and pie charts
Step-by-step explanation:
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15/12, 0.4, 42%, 0.416 least to greatest
A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars
A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?
Answer:
There were 69 adults and 284 seniors
Solution:
Let "a" be the number of adults
Let "s" be the number of seniors
Cost of 1 adult = $ 8
Cost of 1 senior = $ 4
On a particular day when 353 people paid an admission
Therefore,
number of adults + number of seniors = 353
a + s = 353
a = 353 - s ---------- eqn 1
The total receipts were 1688 dollars
Therefore, we frame a equation as:
number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688
[tex]a \times 8 + s \times 4 = 1688[/tex]
8a + 4s = 1688 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
8(353 - s) + 4s = 1688
2824 -8s + 4s = 1688
4s = 2824 - 1688
4s = 1136
s = 284Substitute s = 284 in eqn 1
a = 353 - 284
a = 69Thus there were 69 adults and 284 seniors in movie theater
there were 55 adults and 284 seniors who paid admission.
Let's denote:
- ( A ) as the number of adults.
- ( S ) as the number of seniors.
Given:
- The price for adults is $9.
- The price for seniors is $5.
- The total number of people who paid admission is 339.
- The total receipts were $1915.
We can set up a system of equations based on the given information:
1. The total number of people who paid admission:
[tex]\[ A + S = 339 \][/tex]
2. The total receipts:
[tex]\[ 9A + 5S = 1915 \][/tex]
Now, we can solve this system of equations.
Let's solve equation 1 for one of the variables (let's solve for ( A )):
[tex]\[ A = 339 - S \][/tex]
Now, substitute this expression for( A ) into equation 2:
[tex]\[ 9(339 - S) + 5S = 1915 \][/tex]
Now, solve for \( S \):
[tex]\[ 3051 - 9S + 5S = 1915 \][/tex]
[tex]\[ -4S = 1915 - 3051 \][/tex]
[tex]\[ -4S = -1136 \][/tex]
[tex]\[ S = \frac{-1136}{-4} \][/tex]
[tex]\[ S = 284 \][/tex]
Now, we can find ( A ) using the value of ( S ) we found:
[tex]\[ A = 339 - 284 \][/tex]
[tex]\[ A = 55 \][/tex]
So, there were 55 adults and 284 seniors who paid admission.
complete question given below:
A movie theater charges 9$ for adults and 5 for seniors.on a particular day when 339 people paid an admission,the total receipts were 1915$ how many who paid were adults and how many who paid were seniors
Which statement could be used to explain why the function h(x) = x has an inverse relation that is also a function?
Answer:
Since h(x) is a one-to-one function, this means its inverse is also a function
Step-by-step explanation:
The key idea here is knowing that a function needs to be a 'many - to -one' operation (Many could also include one-to-one functions. The key if that for any x, there is only one f(x) value).
This means that for a function to have an inverse, it needs to be one-to-one. Since the domain and range switch when we look at inverse relations, and so if we have a many-to-one function, then it's inverse would be one-to-many. But we need it to be one-to-one. So the original function would need to be one-to-one.
However the short answer is to just know the 'theorem' which says that a function has an inverse function if and only if it is a one-to-one function.
Answer: c, the graph of the inverse of h(x) passes through the horizontal line test.
Step-by-step explanation:
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