Answer:
The numbers are 93, 94, 95 and 96
Step-by-step explanation:
Four consecutive integers add up to 378.
Let the first number be x
Second number will be x+1
Third number will be x+2
And the fourth number will be x+3
These four numbers add up to 378
Which means, we add them up
x + (x+1) + (x+2) + (x+3)=378
x+x+1+x+2+x+3= 378
Collect like terms
4x+6=378
4x= 378-6
4x=372
Divide both sides by 4
x=378/4
x=93
The first number is 93
The second number is x+1 = 93+1= 94
The third number is x+2= 93+2= 95
The fourth number is x+3= 93+3=96
Add up the four numbers
93+94+95+96 = 378
please help me with this problem
Answer: The answer would be the third option 4/4 x 6 = 6
Answer:
4/4 x 6 = 6
Step-by-step explanation:
This is the answer because 4/4 is one which means 1 x 6 = 6 so they are the same.
Which experssions are equivalent to 5(1/3x+7)-3(1/2x-4)?
Helpppppppppppppppppp
Option D:
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]
Solution:
Given expression is [tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex].
To find the product of the expression:
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)[/tex]
Multiply each term of the first term with each term of the 2nd term.
[tex]=y^{2}\left(8 y^{2}+y+1\right) +3 y\left(8 y^{2}+y+1\right) +7\left(8 y^{2}+y+1\right)[/tex]
Using the exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]
[tex]=\left(8 y^{4}+y^3+y^2\right) +\left(24 y^{3}+3y^2+3y\right) +\left(56 y^{2}+7y+7\right)[/tex]
[tex]=8 y^{4}+y^3+y^2+24 y^{3}+3y^2+3y+56 y^{2}+7y+7[/tex]
Arrange the terms with same power.
[tex]=8 y^{4}+y^3+24 y^{3}+y^2+3y^2+56 y^{2}+7y+3y+7[/tex]
[tex]=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]
Hence option D is the correct answer.
[tex]\left(y^{2}+3 y+7\right)\left(8 y^{2}+y+1\right)=8 y^{4}+25 y^{3}+60 y^{2}+10y+7[/tex]
PLEASE HELP QUICK!!!!! WORTH 50 POINTS!!!!!!! Explain how to solve the equation. StartFraction c over 6 EndFraction = 9
Answer:
Solve by undoing the division by multiplying by 6 on both sides of the equation. The solution is c = 54. Check the solution by substituting 54 for the variable in the original equation and then simplify. 9 = 9 is true, so 54 is the solution.
Step-by-step explanation:
The value of c is 54.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 7 is an equation.
We have,
c/6 = 9
Solve for c.
c/6 = 9
Multiply 6 on both sides.
c = 9 x 6
c = 54
Thus,
c is 54.
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Evan enjoys eating fresh fruits and vegetables. This
year, he decided to grow his own garden. The diagram
shows the dimensions of his garden
He fills his garden with enriched topsoil at a height of 2
inches. How much topsoil does Evan use?
48 in
cubic inches
24 in
Answer:
[tex]2304 \ in^3[/tex]
Step-by-step explanation:
Given the surface dimensions of the garden as 24 inches by 48 inches:
#Calculate surface area of the garden's top:
[tex]A=lw\\\\=48\times 24\\\\=1152 in^2[/tex]
Given the soil's thickness is 2 Inches, we multiply this thickness by the garden's surface area to get volume of soil used:
[tex]V=tA, t-thickness, A=Area=1152 \ in^2\\\\=2 \ in \times 1152\ in^2\\\\=2304 \ in^3[/tex]
Hence, the amount of soil used is 2304 cubic inches.
Answer: those are right!
Hope this helps ❤️
What is the value of x?
The value of x is 8√2.
Step-by-step explanation:
From the right triangle,
The angles are 90°, 45° and the third angle is unknown.Third angle = 180° - (90°+45°) = 45°The measure of third angle is 45°The length of the side opposite to angle 45° is a=8.
Therefore, the value of y opposite to angle 45° is also 8.(b=8)
Using Pythagorean theorem,
The length of hypotenuse is c ⇒ c² = a²+b²
c² = 8²+8²
c² = 64+64 = 128
c = √128
c = √64[tex]\times[/tex]2
c = 8√2
In the diagram ABCD is a rectangle and PQ is parralell to AD
For the given rectangles, [tex]f=4[/tex] cm and [tex]g = 6[/tex] cm.
Step-by-step explanation:
Step 1:
The area of a rectangle is calculated by multiplying its length with its width. Both the rectangles APQD and PBCQ have the same width.
The second rectangle PBCQ has a length of 9 cm. Its area is determined by subtracting the area of APQD from the area of ABCD.
The area of the rectangle PQBC [tex]= 60 - 24 = 36[/tex] [tex]cm^{2}[/tex].
Step 2:
The length of rectangle PBCQ is 9 cm and the area is 36 [tex]cm^{2}[/tex] so the width can be determined.
[tex]Width = \frac{area}{length} = \frac{36}{9} = 4[/tex] cm. So [tex]f=4[/tex] cm.
Step 3:
The width of the rectangle APQD is also 4cm.
The width of the rectangle APQD is 4 cm and the area is 24 [tex]cm^{2}[/tex].
[tex]length = \frac{area}{width} = \frac{24}{4} = 6[/tex] cm. So [tex]g = 6[/tex] cm.
Luna buys a shirt that costs $15.65. She gives the cashier $20 and receives $3.25 in change. What is the percent error in the amount of change she was given?
The error in the amount of change she was 25.28%.
Step-by-step explanation:
Given,
The actual price = 15.65$
The amount Luna gives to cashier = 20$
The change she receives = c = 3.25$
The actual amount of changes = x = total amount - actual price:
20$ - 15.65$ = 4.35
The percentage of error can be found using: [tex]\frac{x-c}{x}[/tex]
By putting the values in equation, we get
=> [tex]\frac{4.35 - 3.25}{4.35} * 100[/tex]
=> [tex]\frac{1.10}{4.35} * 100[/tex]
=> 25.28 %
Hence, the error in the amount of change she was 25.28%.
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
To determine the percent error in the amount of change Luna was given, we need to compare the actual change received to the correct change she should have received.
Step 1: Calculate the Correct Change
Luna gave the cashier $20 for a shirt that costs $15.65. The correct amount of change should be:
[tex]\[\text{Correct Change} = 20 - 15.65 = 4.35 \, \text{dollars}\][/tex]
Step 2: Calculate the Error
The cashier gave Luna $3.25 instead of $4.35. The error in the change given is:
[tex]\[\text{Error} = \text{Correct Change} - \text{Actual Change Given} = 4.35 - 3.25 = 1.10 \, \text{dollars}\][/tex]
Step 3: Calculate the Percent Error
Percent error is given by the formula:
[tex]\[\text{Percent Error} = \left( \frac{\text{Error}}{\text{Correct Change}} \right) \times 100\][/tex]
Substitute the values into the formula:
[tex]\[\text{Percent Error} = \left( \frac{1.10}{4.35} \right) \times 100\][/tex]
Perform the division:
[tex]\[\frac{1.10}{4.35} \approx 0.2529\][/tex]
Convert to a percentage:
[tex]\[0.2529 \times 100 \approx 25.29\%\][/tex]
The percent error in the amount of change Luna was given is:
[tex]\[\boxed{25.29\%}\][/tex]
In 20 years, Sam will be 2 times Mary's age. 20 years ago Sam was 4 times Mary's age. How old are Sam and Mary now?
Answer:
in 20 years Sam = 32 = same as Mary so 20 years before Mary was 12 and Sam was 4 times older when she was 48. Sam is now 48 and Mary is 48.
Step-by-step explanation:
Anna has a rectangular that is 33 inches and 75 inches. Find the perímeter of the rectangular in yards
Answer:
6 yards
Step-by-step explanation:
Perimeter of a rectangle: 2a + 2b
2(33) + 2(75)
66 + 150
216 inches
216/12 gives us feet
18/3 gives us yards
6 yards
Answer: 6 yards
Make sure to pick ALL and It needs To BE CoRRECt
Answer:
(a): 9x + 45
Option A, 9(x + 5) because it distributes into 9x + 45
Option B, 9 * x + 9 * 5 because it multiplies into 9x + 45
(b): 13 + 9y - 3 - y
Option D, 8y + 10 because it combines into this number
2. what value of b makes the following equation true
3. which statement is true about the value of
Answer:
2. 10
3. D. 1 for all n
Step-by-step explanation:
2. The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^b = 1/a^-b
__
[tex]\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}[/tex]
The value of n is 10.
__
3. Using the above rules of exponents, the expression simplifies to ...
6^(-n+n) = 6^0 = 1
The value is 1 for any n.
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
The initial values and rates of change for Mr. Allen's and Mr. Jessup's payment plans can be compared based on the given information.
1. Initial Values:
- Mr. Allen's initial amount S: $560
- Mr. Jessup's initial amount: $400
Difference in initial values: $560 - $400 = $160
Mr. Allen's initial value is $160 more than Mr. Jessup's.
2. Rates of Change:
- Mr. Allen's rate of change: $80 per month
- Mr. Jessup's rate of change: $40 per month
The rate of change represents the amount by which the owed amount decreases each month. Mr. Allen's rate of change is greater because he pays off $80 per month, while Mr. Jessup pays off $40 per month.
In summary:
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
Complete question:
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Month 0 1 2 3 4 5 6 7
Amount Mr. Allen Owes (S) 560 480 400 320 240 160 80 0
Mr. Jessup buys a new computer for $400. He makes monthly payments of $40 until the computer is paid for. Compare the initial values and rates of change of each function.
You can graph both functions to show that the amount Mr. Allen owes starts at $560 and decreases $80 per month. The amount that Mr. Jessup owes starts at $400 and decreases $40 each month.
Mr. Allen's initial value is $160 more than Mr. Jessup's. Mr. Allen's rate of change is greater than Mr. Jessup's rate of change.
To calculate Peter's monthly expenses, add up the amounts in row 5 of the table. Compare the total expenses with different salaries to determine if Peter can meet them. Advise Peter to create a budget and prioritize expenses if he wants to move out.
Explanation:To calculate Peter's monthly expenses, we need to add up all the amounts in row 5 of the table. Assuming each amount represents a monthly expense, we can sum them up to get the total monthly expenses. To determine if Peter can meet his expenses with different salaries, we compare the total expenses with each salary. If the salary is greater than or equal to the total expenses, Peter can meet his expenses. If the salary is less than the total expenses, Peter cannot meet his expenses.
If Peter wants to move out of his parent's house, I would advise him to create a budget and prioritize his expenses. He should also consider finding ways to increase his income or reduce his expenses to make moving out more affordable.
Translate the phrase into an algebraic expression. 9 more than x
Answer: 9+x
Step-by-step explanation:
If you have x apples, and you need nine more, you would need to ADD 9 and "x".
a dog and a cat together weigh 27 pounds if the dog's weight is an odd number and if he weighs twice as much as she does how much do each weight.
Answer:
Dog: 9 pounds
Cat: 18 pounds
Step-by-step explanation:
x + y= 27
y = 2x
2x + x = 27
3x = 27
x = 9
y = 2x = 18
The five-number summary for the number of accounts managed by each sales manager at Force Inc. is shown in the following table. \text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 353535 454545 505050 656565 858585 The five-number summary suggests that about 50\%50%50, percent of sales managers at Force Inc. manage fewer than what number of accounts?
The median is is the midpoint of the data. This means half is below 50 and half is above 50.
The answer would be they handle less than 50 accounts.
50% of sales managers at Force Inc. manages fewer than 50( = the median given) number of accounts.
Given that:
[tex]Min = 35\\Q_1 = 45\\Median = 50\\Q_3 = 65\\Maximum = 85[/tex]
These 5 numbers summary tells the partition of data or quartiles with endpoints as minimum and maximum.
The median is a point for which the counts of data lying above it is equal to the counts of data lying below it.
Since the question asks about :
50% Sales managers manage < ? number of accounts
and since 50% of data lie below and above the median which is 50 given in the table.
Thus we have:
50% of the Sales manager at Force Inc. managing fewer than 50(the median given) number of accounts.
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3x+4y-6z=-60
7x-5y+z=-37
2x+3y-z=-29
Answer:
{x,y,z}={-8,-3,4}
Step-by-step explanation:
Why do basic exponential functions always have a horizontal asymptote at y = 0?
Answer:
becouse the value of the exponential function cant go negative... there is no exponent that makes a number negative if the base is positive..
Step-by-step explanation:
Basic exponential functions have a horizontal asymptote at y = 0 because as the input x increases, the output of the function approaches zero but never touches it due to exponential decay.
Explanation:Basic exponential functions always have a horizontal asymptote at y = 0 because as the value of x becomes very large, the value of the exponential function approaches zero. This is due to the nature of exponential decay, where the function's rate of change decreases exponentially. Exponential functions are of the form f(x) = a^x, where a is a positive constant different from 1. When a is less than 1, the function represents exponential decay, and as x approaches infinity, f(x) approaches zero, but never actually reaches it, hence creating a horizontal asymptote at y = 0.
1.
Simplify: 2.6 x 8.4-5.4
A. 2.32
B. 7.8
C. 16.44
D. 21.3
Answer:
b
Step-by-step explanation:
HELP PLEASE BE QUICK
Answer:
8
Step-by-step explanation:
Area of a circle = πr^2
64π / π = πr^2 / π
sqrt(64) = sqrt(r^2)
8 = r
Answer: 8
what is 9/7+5/8 as a fraction
Answer:9/7+5/8=72/56+35/56
Step-by-step explanation:9/7 times 8 by both 9 and 7 and times 7 by both 5 and 8 and you will get your answer
Answer:
[tex]1\frac{51}{56}[/tex]
Step-by-step explanation:
In order to find the answer to this question you will have to find the common denominator, (CD) multiply the denominators by the amount it takes to receive the common deliminator then do the same with the numerators without finding the common numerator, and then add the two numerators together and reduce if needed.
[tex]\frac{9}{7} +\frac{5}{8}[/tex]
Find the common denominator:
[tex]CD=56[/tex]
[tex]9\times 8 =72[/tex]
[tex]7 \times 8 = 56[/tex]
[tex]= \frac{72}{56}[/tex]
Do the same with the second fraction:
[tex]5\times7=35[/tex]
[tex]8\times7=56[/tex]
[tex]=\frac{35}{56}[/tex]
Then you would have:
[tex]\frac{72}{56} +\frac{35}{56}[/tex]
Add the numerators:
[tex]72+35=107[/tex]
[tex]=\frac{107}{56}[/tex]
Turn the improper fraction into a mixed number:
[tex]\frac{107}{56} = 1\frac{51}{56}[/tex]
You get this by dividing 107 by 56 which should give you 1 with the remainder of 51 and you keep the denominator the same.
[tex]=1\frac{51}{56}[/tex]
Hope this helps.
How many liters are in 8 quarts?
Answer:
7.57082 liters
Step-by-step explanation:
Write the equation of the ellipse that has a center at
(-2, – 6), a vertex at (-8, – 6), and a covertex at
(-2, -3)
Check the picture below.
[tex]\bf \textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]
Final answer:
The equation of the ellipse is (x+2)²/36 + (y+6)²/9 = 1, where the center is at (-2, -6), the vertex is at (-8, -6), and the covertex is at (-2, -3).
Explanation:
The equation of an ellipse with a center at (-2, -6), a vertex at (-8, -6), and a covertex at (-2, -3) can be determined using the standard form of the ellipse equation, which is (x-h)²/a² + (y-k)²/b² = 1, where (h,k) is the center, a is the distance from the center to a vertex along the major axis, and b is the distance from the center to a covertex along the minor axis. In this case, the major axis is horizontal because the vertex has the same y-coordinate as the center. Thus, a = 6 (the distance from the center to the vertex) and b = 3 (the distance from the center to the covertex).
The equation becomes: (x+2)²/6² + (y+6)²/3² = 1. Simplified, this is (x+2)²/36 + (y+6)²/9 = 1.
Divide. Reduce the answer to lowest terms. 3/7 / 1 1/6
first off let's convert the mixed fraction to an improper fraction and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{6}}\implies \cfrac{1\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{7}{6}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \frac{3}{7}~~}{\frac{7}{6}}\implies \cfrac{3}{7}\cdot \cfrac{6}{7}\implies \cfrac{18}{49}[/tex]
what is the measure of a? ab=15, bc=15,ac=15
Answer:
5 or 3
Step-by-step explanation:
Mary delivers 32 newspapers to her costumers in 25 minutes these deliveries represent 64% of her costumers
Gaby would like to order a Cobb salad and a drink. What is the minimum amount of money she will have to borrow?(Total money they have is $50 and a Cobb salad costs $8.95 a drink costs $1.55)
Answer:
Gaby do not need to borrow money and they are left with $39.5
Step-by-step explanation:
We are given the following in the question:
Total money = $50
Cost of a Cobb salad = $8.95
Cost of a drink = $1.55
Order: A Cobb salad and a drink
Cost of order =
[tex]= 8.95 + 1.55\\=\$10.5[/tex]
Thus, the total cost of order is $10.5
Money left =
= Total money - Order bill
[tex]=50 - 10.5\\=\$ 39.5[/tex]
Thus, Gaby do not need to borrow money and they are left with $39.5.
PAGE 11
2) 4x+2(x*3)=6x-6
A x=0
B x=6
C INFINITE SOLUTIONS
D NO SOLUTION
ye boi its A | SMART BOIS
A water park conducted a study to investigate the relationship between outdoor temperature and the number of park visitors. The correlating linear model is shown, where x represents the number of degrees over 70°F, and y represents the number of park visitors.
y= 42 + 15x
What is the correct interpretation of the y-intercept?
A.
When the temperature is 70°F, the park can expect 0 visitors.
B.
When the temperature is 70°F, the park can expect 42 visitors.
C.
When the temperature is 70°F, the park can expect 57 visitors.
D.
When the temperature is 70°F, the park can expect 15 visitors.
Answer:
b) When the temperature is 70°F, the park can expect 42 visitors.
Step-by-step explanation:
Given that y represents the number of park visitors and x is the number of degrees over 70°F. The equation of the model is given as:
y = 42 + 15x
The general equation of a straight line plotted y against x with an intercept(c) on the y-axis and a slope(m) is given by the equation:
y = mx + c
comparing y = mx + c with y = 42 + 15x, the slope of the line y = 42 + 15x is 15 and its intercept on the y axis is 42.
This means that at temperature 70°F, x is 0.
therefore y = 42 + 15(0) = 42
Therefore when the temperature is 70°F, the park can expect 42 visitors.
Solve the word problems. Round the answer to the nearest tenth.
Mark is on his way home for work. He drives 35 miles due North and then 42 miles due west. Find the shortest distance he can cover to reach home early.
54.7 miles
54.785 miles
547 miles
54 miles
Option A:
The shortest distance Mark can cover to reach home early is 54.7 miles.
Solution:
Towards North = 35 miles
Towards West = 42 miles
Using Pythagoras theorem,
In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.
Let x be the hypotenuse.
[tex]x^2=35^2+42^2[/tex]
[tex]x^2=1225+1764[/tex]
[tex]x^2=2989[/tex]
Taking square root on both sides, we get
[tex]\sqrt{x^2}=\sqrt {2989}[/tex]
x = 54.67
x = 54.7
The shortest distance Mark can cover to reach home early is 54.7 miles.
Option A is the correct answer.