The cost of book case be $ 11.6.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0.
Here, let the cost of book case be $ x
and the cost of pencil case be $ y
Now, Helen purchased 3 books and 2 pencils in $ 74.
3x + 2y = 74 .......(i)
Cost of pencil case $ 8 less than the book.
y - 8 = x ............(ii)
put the value of x in equation (i), we get
3(y - 8) + 2y = 74
3y - 24 + 2y = 74
5y = 74 + 24
5y = 98
y = 98/5
y = $ 19.6
put the value of y in equation (ii), we get
x = y -8
x = 19.6 - 8
x = $ 11.6
Thus, the cost of book case be $ 11.6.
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A sector of a circle of radius 14cm containing
an angle 60° is folded to forma cone
Calculate the radius of the base of the circle
}
answer is 2 ⅓
Explanation
Length of arc = circumference of the base of the
cone
is β/360 x 2πR=2πr
make r the subject of formula
r =βR/360
r=60 x 14/360
r=2⅓cm
please mark as brainliest if i am right
A cube has edges measuring 8 centimeters.
Find its surface area.
(please)
State the value of 'x' in this equation, and explain why you know this to be true without doing any calculations. 5X=59
The value of x in the equation is 59/5
How to solve for x?The equation is given as:
5x = 59
Divide both sides by 5
x = 59/5
This means that the value of x in the equation is 59/5
To know if the value is accurate, we simply multiply 5 by 59/5 and we get 59 as in 5x = 59
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Find the measure of angle 1.
5)
AB is a straight line.
A
152⁰
B
Let that angle be x
Linear pairs are supplementary
So
152+x=180x=180-152x=28°5|2x+6|=26...can someone answer this please
Answer:
x = -2/5 or x = -28/5
Step-by-step explanation:
Let's solve your equation step-by-step.
5(|2x+6|)=26
Step 1: Divide both sides by 5.
5(|2x+6|)/5 = 26/5
|2x+6|=26/5
Step 2: Solve Absolute Value.
|2x+6|=26/5
We know either2x+6= 26/5 r2x+6=−26/5
2x + 6 = 26/5(Possibility 1)
2x+6−6= 26/5 - 6 (Subtract 6 from both sides)
2x = -4/5
2x/2 = -4/5/2 (Divide both sides by 2)
x = -2/5
2x + 6=-26/5 (Possibility 2)
2x+6= -26/5 (Simplify both sides of the equation)
2x + 6 - 6 = -26/5 - 6 (Subtract 6 from both sides)
2x = -56/5
2x/2 = -56/5/2(Divide both sides by 2)
x = -28/5
Answer:
x = -2/5 or x = -28/5
Please help! I'm not understanding this question. Giving 75 points! Please provide an explanation as to why that is the answer as well. Thank you!
What is i* if i = 0?
A. 0
B. 6
C. 8
D. 9
E. none of these
Answer:
A, the answer is A
The answer is a because the question say what is I if I = 0. The question basically gave you the answer. In other words the question said, I = 0 what is I? Sorry if this is a bit confusing, I’m not that good at explaining.
Hope this helps!
Mike mixes paint at a hardware store. A certain shade of orange paint is made by
mixing white, red, and yellow paint in a ratio of 4 to 3 to 2. If Mike wants to make 3
gallons of paint that is this shade of orange, how many gallons of red paint will he
need?
Answer: 1 gallon
Step-by-step explanation:
white: red: yellow
4 : 3 : 2
total units: 9 units
total amount: 3 gallons
one unit: 3/9
= 1/3
no of units of red: 3 units
amount of paint needed: 1/3 x 3
= 1 gallon
Using p as the variable for the problem below, solve for p. Submit your answer
as an inequality, using "<=" for < or ">" for ≥ if necessary. Round to two
decimal places.
Hosting a dinner party for 38 people, you plan to serve peach pie for dessert.
Each pie has 8 slices. How many pies must you buy to ensure each guest
gets 1 slice?
Answer:
Step-by-step explanation:
As host, we want to insure each guest has at least one slice of pie. We can say (1 Slice/Guest) and use this as a conversion factor. We also know each pie has 8 slices: (8 Slices/1 Pie). Since this is a conversion factor, we can invert it to (1 Pie/8 Slices). We expect 38 people and want to convert that number of people to the number of pies, p, we need.
p (pies) [tex]\geq[/tex] (38 Guests)*(1 Slice/Guest)*(1 Pie/8 Slices)
We use the [tex]\geq[/tex] sign to note that we need a minimum of pies to be sure everyone is served.
p (pies) [tex]\geq[/tex] (38 )*(1 /)*(1 Pie/8 )
Note how the units cancel:
Guests and Slices both cancel and we are left with pies as the only remaining unit, as we hoped we'd see.
p [tex]\geq[/tex] (38/8) pies
p = 4 +(6/8) pies
Since we cannot purchase 6/8 of a pie, we need to round up to 5 pies.
5 pies, at 8 slices per pie, will provide 40 servings, enough for the 38 guests.
A 1/25 scale model sports car is 5.5 in long. What was the length of the actual car to the nearest in?
Answer: 137.5 in
Step-by-step explanation: All we have to do is multiply 25 to 5.5 to get the original result. Since the scaling is 1/25, it means it is 25 times smaller. Thus, just multiply 25 to 5.5 and you get 137.5 in, the original result.
HELP PLEASE! (will be marking brainliest) What is the measure of FJG?
A. 95
B. 100
C. 105
D. 115
Answer:
105
Step-by-step explanation:
Angles HJG and HJG form a straight line so they add to 180
< HJG + < FJG = 180
75 + <FJG = 180
<FJG = 180-75
<FJG = 105
Answer:
C) 105
Step-by-step explanation:
HJG and KJF are vertical angles so they both equal 75 degrees.
A line is 180 degrees so 180-75=105 so 105 = is FJG
In △ABC, ∠C = 2∠B and ∠A = 540, find the measure of ∠B.
Answer:
B = 42°
Step-by-step explanation:
All of the internal angles of a triangle sum to 180°
x + 2x + 54 = 180
3x = 180 - 54
x = 42 ° which is angle B
If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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−−→AB=(xy)
What values should x an y take?
The values x and y take are 5 and 0 respectively.
We know that in mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way.
The relationships between two or more things are frequently represented by the points on a graph.
In this case, we have to determine the values of x and y.
Notice that in this graph, point A is located at A = 5 and point B is located at B = 0.
So, we can write (A, B) = (x, y) = (5, 0)
Therefore, the values x and y take are 5 and 0 respectively.
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Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
The solution to the exponential expression is as follows:
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} = 2}[/tex][tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)=\dfrac{1}{2}}[/tex][tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex][tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]What are exponential expressions?Exponential expressions are convenient ways to express the mathematical power of a number in short forms.
Simplifying the following expressions given:
1.
[tex]\mathbf{\dfrac{(2\times 3^{-2})^3(5\times 3^2)^2}{(3^{-2})(5\times 2)^2} }[/tex]
Applying the exponent rule: [tex]\mathbf{(a\times b)^n = a^n b^n}[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 5^2\times 81}{3^{-2}\times 5^2\times2^2} }[/tex]
cancel out the common factor, we have:
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 81}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^4}{3^{-2}\times2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{(2\times 3^{-2})^3\times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times 3^6}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 \times \dfrac{1}{729} \times729}{2^2} }[/tex]
[tex]\mathbf{\implies \dfrac{2^3 }{2^2} = 2}[/tex]
2.
[tex]\mathbf{=(3^3)(4^0)^2(3\times 2)^{-3}(2^2)}[/tex]
= [tex]\mathbf{\dfrac{1}{2}}[/tex]
3.
[tex]\mathbf{\dfrac{(3^7\times 4^7)(2 \times 5)^{-3}(5^2)}{12^7\times 5^{-1}\times 2^{-4}} = 2}[/tex]
4.
[tex]\mathbf{\dfrac{(2\times 3)^{-1}\times 2^0}{(2\times 3)^{-1}}= 1}[/tex]
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Using a left endpoint riemann sum approximation with four equal subintervals, the approximate value of integral from 0 to 8 g(x) dx is:
Subdividing [0, 8] into 4 equally-spaced subintervals, each one will have length ∆x = (8 - 0)/4 = 2, and the partition is
[0, 2] U [2, 4] U [4, 6] U [6, 8]
We approximate the integral with a left endpoint sum. The left endpoint of the i-th subinterval is
[tex]\ell_i = 2(i-1)[/tex]
where 1 ≤ i ≤ 4.
Then the integral is approximated by
[tex]\displaystyle \int_0^8 g(x) \, dx \approx \sum_{i=1}^4 g(\ell_i) \Delta x \\\\ = 2 (g(0) + g(2) + g(4) + g(6)) \\\\ = 2 (-1 - 3 - 1.25 - 1.5) = \boxed{-13.5}[/tex]
22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There 22.
(05.07 MC)
The table shows the values of y for different values of x:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The correlation coefficient for the data is −0.9847. Which statement is true about the data in the table? (1 point)
There is no relationship between x and y.
There is a weak negative relationship between x and y.
There is a strong positive relationship between x and y.
There is a strong negative relationship between x and y.
The option fourth "There is a strong negative relationship between x and y" is correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
The options are:
There is no relationship between x and y.There is a weak negative relationship between x and y.There is a strong positive relationship between x and y.There is a strong negative relationship between x and y.We have data:
x 7 8 9 10 11 12 13
y 13 10 7 6 5 3 0
The value of correlation r = -0.9847
As we know the value of r between -1 to +1
If r = 1 (perfect and positive correlation)
if r = -1 (perfect and negative correlation)
We have r = -0.9847
The value is near to -1 which means there is a strong negative relationship between x and y.
Thus, the option fourth "There is a strong negative relationship between x and y" is correct.
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sec(pi/2 -x) =csc x true or false
Answer:
true
Step-by-step explanation:
if you rewrite [tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] with trigonometric identities:
[tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] [tex]=\frac{1}{\sin \left(x\right)}[/tex]
[tex]\frac{1}{\sin \left(x\right)}[/tex] [tex]=\csc \left(x\right)[/tex]
so, yes, [tex]sec\left(\frac{\pi }{2}\:-x\right)[/tex] [tex]=\csc \left(x\right)[/tex]
hope this helps!!
Which of the following is equivalent to
Answer:
The first one
Step-by-step explanation:
[tex]n^{2} - 6n + 9 = (n-3)^{2}\\\\[/tex]
The expression removes the first 9 terms of the summation so the summation goes from 10 to 19
Jada is comparing membership costs for two gyms. What is the difference in membership costs after m months if she joins Be strong instead of Zippy Health Club?
Write an expression for each membership cost for m months and subtract them.
Answer: Difference in membership costs after m months = -($24.96m + $34.94)
Step-by-step explanation:
Cost of Zippy health club = $49.95 + $19.95 per month
Cost of Be strong = $24.99 per month and $10 off the first month
Total cost after m months of Zippy health club = $49.95 + $19.95m
Total cost after m months of Be strong = $24.99 (m - 1) + $ 10
Difference in membership costs after m months ={ $24.99m - $24.99 + $10 ]-[$49.95m + $19.95}
=$(24.99 - 49.95) m -$14.99 - $19.95
= -$24.96m - $34.94
=-($24.96m + $34.94)
So Difference in membership costs after m months =-($24.96m + $34.94)
therefore jada have to pay more if she joins Be strong.
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In your notebook, set up the following subtraction in a vertical format and select the correct answer.
Find 2p 2 + 3p - 4 less - 2p 2 - 3p + 4.
1. 4p2 + 6p + 8
2. 4p2 - 6p - 8
3. 4p2 + 6p - 8
4. 0
The answer is 4p² + 6p - 8 which is subtraction of one equation from the other in vertical format.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have two polynomial:
2p² + 3p - 4 and -2p² - 3p + 4
Subtraction in a vertical format:
2p² + 3p - 4
- -2p² - 3p + 4
-------------------------
Changin sign of the expression -2p² - 3p + 4:
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
Now adding like terms.
2p² + 3p - 4
+ 2p² + 3p - 4
-------------------------
4p² + 6p - 8
Thus, the answer is 4p² + 6p - 8 which is the subtraction of one equation from the other in vertical format.
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I NEED HELP !!! Right now!!!
Answer:
Step-by-step explanation:
If f(x) = √2x, then f'(8) =
Answer:
√2
Step-by-step explanation:
Comment
You have differentiated the given equation. When you do that the x becomes 1. F'(x) is going to be √2 no matter what x is.
What is the midpoint of the segment (-6.-9)(16.5)
Answer:
M=(11,−2)
Step-by-step explanation:
Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]
The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.
Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]
M=(11,−2)
Evaluate the function: g(x) = -x +4 Find: g(b-3)
Answer:
g(b-3) = -b + 7
Step-by-step explanation:
Plug in the value (b-3) as x into the equation
g(b-3) = -(b-3) + 4
distribute the negative sign
g(b-3) = -b + 3 + 4
combine like terms
g(b-3) = -b + 7
The population of a small town was 3,150 last year. After a new factory opened close by, the population increased by 8%. What
is the new population of the town?
The depreciation method that does not initially use the residual value in depreciation calculations is the.
An asset loses value over time as a result of use, damage, or obsolescence.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline.
The depreciation method that does not initially use the residual value in depreciation calculations is the depreciating balance.
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What is the best name for the part of the figure
identified by the arrow?
O line of reflection
O line of symmetry
O plane of reflection
O axis of symmetry
The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have given a three-dimensional figure.
As we can see the arrow is pointing at the plane.
A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.
A plane is a plane of symmetry.
Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
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Rosa has $12.29 and spends $4.85. To the nearest dollar, about how much does she have left?
A $3
B $5
C $7
D $9
This question was confusing 15 for whoever answers
Answer:
Refer to the attached image. I'm not clear on one point. Yes, it is confusing.
Step-by-step explanation:
See attached image.
You are heading to a drive-in movie and will need exact cash at the entrance for everyone in your car to get in. The cost is $6.50 per person. Write an expression that represents the total cash needed for your car based on the number of people, p, in your car.
Answer:
Using the concept of equation of line, we find that the relationship will be
C = $6.5p.
Step-by-step explanation:
If the cost per head is $6.5 and there are p persons entering the car, then the total amount would be $6.5p.
The final equation would resemble the equation of line y = mx + c.
The expression for the total cost C, would be
C = 6.5p.
Here y = C, x = p, m = 6.5 and c = 0.
So, the expression for the total cost will be the equation of line C = 6.5p.
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