Answer:
Let the cost of orange be X and cost of cherry be y
3x + 9y = 78
8x + 4y = 58
Solving equation using elimination method
multiplying eq 1 with 8 and eq 2 with 3
8(3x + 9y ) = 78(8)
3( 8x + 4y) = 3(58)
24x + 72 y = 624
24x + 12y = 174
subtracting,
60 y = 450
y = 7.5
3x + 9(7.5) = 78
3x + 67.5 = 78
3x = 78 - 67.5
3x = 10.5
x = 3.5
Box of orange = $3.5 Box of cherry = $7.5Write an equation in slope intercept form with the given information.
Slope = 4 and goes through point (3,0)
Answer:
y = 4x - 12
Step-by-step explanation:
Jean had $25.86 in her pocket. If shoes cost $7.50 a pair plus 10% of tax. How many pairs can she buy?
Answer:
3 pairs
Step-by-step explanation:
10% of 7.50 is 0.75. So one pair will cost $8.25. Now, 25.86/8.25 and you get 3 pairs
Answer:
[tex]\fbox {3 pairs}[/tex]
Step-by-step explanation:
Cost of 3 pairs with tax :
⇒ 7.50 × 3
⇒ 22.50
* Adding tax *
⇒ 22.50 + 22.5 (0.1)
⇒ 22.50 + 2.25
⇒ 24.75
∴ Since 24.75 is less than 25.86, Jean can buy 3 pairs of shoes.
help me with this question please, thank you !
Answer:
2
Step-by-step explanation:
[(27divided by (-3)-9] divided by [15-21}
=[-9-9] divided by 3
= 6divided by 3 = 2
if answer is correct so mark me as brain lest :-)
What is the difference between the answers when numbers are switched in a subtraction?
Which of the following is a like radical to 3/7x?
4 (3√√7x)
O
O √Tx
0 x(³√7)
0 7√√√x
Answer:
Like radicals are those terms that are similar, just like like terms. From this concept we find that option A is correct. 4[∛(7x)] and ∛(7x) are like radicals.
Step-by-step explanation:
Mathematically, like radicals are just like like terms. For example,
x, 2x, -10x, , 7.3x are like terms because the power of x in each case is 1.
xy², -9xy², 13y²x are like terms because the total power of each expression is 3.
Similarly, like radicals are:
√2, -5√2, 1.1√2, etc.
Hence, from the given options, like radical to ∛(7x) is: 4[(7x)].
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A delivery of 5 large boxes and 3 small boxes has a total mass of 137 kilograms. A delivery of 2 large boxes and 6 small boxes has a total mass of 128 kilograms. What is the mass of each type of box?
Answer:
Large boxes are 18.25 kg
Small boxes are 15.25 kg
Step-by-step explanation:
This is a system of equations. You need to set up each equation first.
I am assigning x to be big boxes and y to be small boxes.
5x + 3y = 137
2x + 6y = 128
To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.
-2 ( 5x + 3y = 137)
2x + 6y = 128
Distribute the -2 to everything in the parentheses in the first equation.
-10x - 6y = -274
2x + 6y = 128
Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:
-8x = -146
Solve for x by dividing by -8.
x = 18.25
Now plug that into one of the original equations.
2(18.25) + 6y = 128.
36.5 + 6y = 128 Subtract 36.5 from each side
-36.5 -36.5
6y = 91.5 Divide by 6 to solve
y = 15.25
Determine the equation of a cubic polynomial function with roots at (3,0), (2,0) and (-4,0) that also passes through the point (1,30).
Step-by-step explanation:
Step 1: Setting Up the Factors
Our roots are 3, 2, and -4 so
our factors are
[tex](x - 3)(x - 2)(x + 4)[/tex]
Step 2: Initial Test to see if the result equal 30
Let a be a constant, such we have
[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]
Plug in. 1 for x.
[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]
[tex]a( - 2)( - 1)(5) = 30[/tex]
[tex]a(10) = 30[/tex]
[tex]a = 3[/tex]
So our equation is
[tex]3(x - 3)(x - 2)(x + 4)[/tex]
Or if you want it simplifed
[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]
Answer:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
Step-by-step explanation:
General form of a cubic polynomial function with 3 roots:
[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]
where:
a is some constant to be foundb, c and d are the roots of the functionGiven roots:
(3, 0)(2, 0)(-4, 0)Substitute the given roots into the general form of the function:
[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]
[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]
To find the value of a, substitute the given point (1, 30) into the equation:
[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]
Therefore, the equation of the cubic polynomial function is:
[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]
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What is 2 1/2 x 1 3/4 x 3/4
Answer:
45/32 or 1.40
Step-by-step explanation:
Answer:
3 9/32 or 105/32
Step-by-step explanation:
2 1/2 = 5/2, 1 3/4 = 7/4
5/2 * 7/4 = 35/8
35/8 * 3/4 = 105/32
105/32 = 3 9/32
Brainliest, please :)
PLEASE HELP - image attachment below, thanks! :)
Need help to understand how to do this.
Answer: -1(x+2)^2+10
Step-by-step explanation:
1. The coefficient of -x^2 is just the number in front, which in this case would be a = -1 So now the function is -1(x^2+4x)+6 since negative one has been factored out of the first two terms.
2. Half of the coefficient of x would be 2 since x has a coefficient of 4, and half pf 4 is 2. Squared, it is 4. That will be added inside the bracket. Subtracted on the outside is the same equation but multiplied by a, which we found out was -1 in the beginning. So, the function becomes -1(x^2+4x+4)+6-(-4).
3. Factor the inside equation to find that it’ll become (x+2)^2, and simplify the outside to get 10. The function will now be;
f(x)=-1(x+2)^2+10
Hope that made sense and make sure to check just in case I did the math wrong :]
What else would need to be congruent to show that ABC = XYZ by ASA
Answer:
Option d
Step-by-step explanation:
BC = YZ
AC cannot be equal to XZ else it will be SAA congruency
Solve the following simultaneous equations. x + y = 3
x -y = 1
Answer:
x = 2, y = 1 or (2, 1)
Step-by-step explanation:
Solving by elimination method :
x + y + (x - y) = 3 + 12x = 4x = 22 - y = 1y = 1The solution is : x = 2, y = 1 or (2, 1)
Does this graph represent a function? Why or why not?
10.
8
6
4
2
-10 8 6 4 2
88
-8
10
2468 10
A. No, because it fails the vertical line test.
O B. No, because it is not a straight line.
OC. Yes, because it passes the horizontal line test.
OD. Yes, because it passes the vertical line test.
Answer:
D
Step-by-step explanation:
The graph in the picture given is obviously a function of f(x) = x^3 which answers whether the graph is a function or not. In addition, the answer the part on why it's a graph, it's because it passes the vertical line test.
work out the surface area of a cylinder when the height = 18cm and the volume = 1715cm cubed
We need radius
πr²h=1715πr²(18)=1715r²=30.3r=5.5cmNow
LSA
2πrh2π(5.5)(18)11(18)(3.14)198(3.14)622.72cm²Answer:
813.4 cm² (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
h = 18cmV = 1715 cm³Use the Volume of a Cylinder formula and the given values to find the radius of the cylinder:
[tex]\implies \sf 1715=\pi r^2 (18)[/tex]
[tex]\implies \sf r^2=\dfrac{1715}{18 \pi}[/tex]
[tex]\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}[/tex]
Surface Area of a Cylinder
[tex]\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Substitute the given value of h and the found value of r into the formula and solve for SA:
[tex]\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)[/tex]
[tex]\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]
[tex]\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]
[tex]\implies \sf SA=813.3908956...[/tex]
Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)
Solve for x. Round to the nearest tenth, if necessary
The value of x in the triangle to the nearest tenth is calculated as; 1.1
How to use trigonometric ratios?
We have different trigonometric ratios such as;
sin θ = opp/hyp
cos θ = adj/hyp
tan θ = opp/adja
Thus, from the given triangle we can use the formula for cos θ to get the value of x. Thus;
cos 41° = 0.8/x
x = 0.8/cos 41
x = 1.06
To the nearest tenth, we have x = 1.1
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Suppose y varies inversely as x, and y = 16 when x = 1/2. Find y when x = 17.
Finding the proportionality constant :
y = k/x16 = k/(1/2)k = 8Finding y when x = 17 :
y = 8/(17)y = 8/17The value of y is 8/17 when x = 17.
The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -8 ≤ x ≤ 8?
The average rate of change of the function is -35/16.
How to find the average rate of change of the function?We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ 8.
so
at x₁ = -8, f(x₁) = f(-8) = 30
at x₂ = 8, f(x₂) = f(8) = -5
Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [f(8) - f(-8) ] / [8-(-8)]
= [-5 - (30)] / [16]
= [-35] / 16
Therefore, the average rate of change of the function is -35/16.
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Solve: −0.06+7.6p<−127.74
A. p<−42.6
B. p<−34.57
C. p>−16.8
D. p<−16.8
Answer:
D
Step-by-step explanation:
- 0.06 + 7.6p < - 127.74 ( add 0.06 to both sides )
7.6p < - 127.68 ( divide both sides by 7.6 )
p < - 16.8
Sandhu lights a candle at 6 pm. It is 30 cm high. At 7pm, the candle is 27 cm high. At 8pm, it is 24cm high. a) How many cm does the candle burn down every hour? b) How high is the candle at 11 pm?
Please help worth my math
a)QM and PM
b)QMN and NMQ
c)M
The chart below shows the distribution of the number of books in a library.Sahira chooses a random sample from the library and records the type of books in the chart below.
Answer:
you have jbjhgbjhih7g6ginyfygino
What is the inverse of this function?
f(x) = -√x +3₁ x ≥ −3
f-¹(x) =
2-
-
for x ≤
Answer:
f(x)^-1=x^2-3
Step-by-step explanation:
So I'm assuming you meant to include the 3 in the radical as well which would make sense given the domain restriction. To find the inverse you simply swap the x and y since the inverse function is when the domain and range are swapped.
[tex]y=-\sqrt{x+3}\\x=-\sqrt{y+3}\\-x=\sqrt{y+3}\\(-x)^2=y+3\\x^2-3=y\\f(x)^{-1}=x^2-3[/tex]
It is given that x² - y² = 30 and x - y = 5. Find the value of (x + y)².
Answer:
36
Step-by-step explanation:
when solving for two variables, we need to find one variable in terms of the other.
so, we can turn:
x - y = 5
into
x - y = 5
+ y + y
x = y + 5
Then, we can substitute "x" in the given equation with "y + 5"
x² - y² = 30
(y+5)² - y² = 30
(y + 5)(y + 5)
F: y² O: +5y I: +5y L: 25 {foil}
y² + 10y + 25 - y² = 30 {cancel y² - y²}
10y + 25 = 30
-25 -25
10y = 5
÷10 ÷10
y = 0.5
x = y + 5
x = 0.5 + 5
x = 5.5
check:
(5.5)² - (0.5)²
30.25 - 0.25 = 30
30 = 30
(TRUE)
now, we must find the value of:
(5.5 + 0.5)²
= (6)²
= 36
So, the value of (x + y)² is found to be 36
hope this helps!!
Answer:
(x + y)² = 36
Step-by-step explanation:
x² - y² ← is a difference of squares and factors as
(x - y)(x + y) , then
5(x + y) = x² - y² = 30 ( divide both sides by 5 )
(x + y) = 6 , then
(x + y)² = 6² = 36
Assume that the notation (a,r,s,t) means multiply q and r, then add the product to s and (2,6,4,8)+(4,7,2,6)? Please show work and choose one of the choices like e f g or h
=============================================
Work Shown:
[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (2,6,4,8) = \frac{2*6 + 4}{8}\\\\\perp (2,6,4,8) = \frac{12 + 4}{8}\\\\\perp (2,6,4,8) = \frac{16}{8}\\\\\perp (2,6,4,8) = 2\\\\[/tex]
Let m = 2 so we can use this result later.
[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (4,7,2,6) = \frac{4*7 + 2}{6}\\\\\perp (4,7,2,6) = \frac{28 + 2}{6}\\\\\perp (4,7,2,6) = \frac{30}{6}\\\\\perp (4,7,2,6) = 5\\\\[/tex]
Let n = 5 so we can use this result later.
Add the two results.
m+n = 2 + 5 = 7.0 is the final answer.
PLEASE HELP (not good at math)
Answer:
-7,-6,-5 are the values when x=0,1,2
Step-by-step explanation:
please mark me as brainlest
Answer:
Step-by-step explanation:
y =x - 7
Substitute x = 0 and find the y-value
y = 0 - 7
y = -7
(0,-7)
Substitute x = 1,
y = 1 - 7
y = - 6
(1,-6)
Substitute x = 2,
y = 2 - 7
y = -5
(2,-5)
14x - 12 = 16
PLS HELP HURRY
Answer:
[tex]\fbox {x = 2}[/tex]
Step-by-step explanation:
Given :
14x - 12 = 16
Add 12 to each side :
14x - 12 + 12 = 16 + 12
14x = 28
Divide each side by 14 :
14x/14 = 28/14
x = 2
Someone pls help I don’t really understand graphing
The two-way frequency table below shows the preferred communication method of employees at a company
The percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is 20.48%
Complete questionThe two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.
See attachment
What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?
A. 44.79% B. 20.48% C. 48.84% D. 67.19%
How to determine the percentage of employee that prefers email?From the attached image, we have:
Email 8 or more = 43
The total number of employees in the company is
Total = 210
So, the percentage that prefers email is
Percentage = 43/210 * 100%
Evaluate
Percentage = 20.48%
Hence, the percentage of employees is 20.48%
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PLLLEAASSEE HELP ME!!
AND IF YOU DON"T MIND EXPLANING TO ME HOW TO SLOVE THESIS TYPE OF PROBLEMS CAUSE IM SO CONFUSED
Answer:
75 Seconds
Step-by-step explanation:
First divide 90,000 by 16 then square root that answer for 75 and when you plug it in you'll end up with -90,000 + 90,000
find the maxium value of 16x+ 96y
follow p