Answer:
[tex]26[/tex] and [tex]28[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the smaller one of the two even integers ([tex]x > 0[/tex] since both integers are positive.) The larger one of the two consecutive even integer would be [tex](x + 2)[/tex].
The square of the smaller integer would be [tex]x^{2}[/tex].
Five times the larger integer would be [tex]5\, (x + 2)[/tex].
Subtract five times the larger integer from the square of the smaller integer to get [tex](x^{2} - 5\, (x + 2))[/tex].
The value of this expression should be equal to [tex]536[/tex]. In other words:
[tex]x^{2} - 5\, (x + 2) = 536[/tex].
Rewrite and simplify this quadratic equation:
[tex]x^{2} + (-5)\, x + (- 546) = 0[/tex].
[tex]a = 1[/tex].[tex]b = (-5)[/tex].[tex]c = (-546)[/tex]Apply the quadratic formula to find possible values of [tex]x[/tex]:
[tex]\begin{aligned}x_{1} &= \frac{-b + \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{-(-5) + \sqrt{(-5)^{2} - 4 \times 1 \times (-546)}}{2}\\ &= \frac{5 + \sqrt{2209}}{2} \\ &=\frac{5 + 47}{2} \\ &= 26\end{aligned}[/tex].
[tex]\begin{aligned}x_{2} &= \frac{-b - \sqrt{b^{2} - 4\, a\, c}}{2\, a} \\ &= \frac{5 - \sqrt{2209}}{2} \\ &=\frac{5 - 47}{2} \\ &= -21\end{aligned}[/tex].
Since [tex]x > 0[/tex] (both numbers are supposed to be positive), [tex]x = 26[/tex] would be the only valid solution.
Therefore, the two integers would be [tex]x = 26[/tex] and [tex]x + 2 = 28[/tex].
I bought a 4 pack of tissues for $8.80. What was the unit rate?
Answer: 2.2 and/or 2.20 the zero doesn't matter
Step-by-step explanation:
4 goes into 8, 2 times bring the 2 up (4x2=8)
8-8=0
Bring down the next 8
4 goes into 8, 2 times bring the 2 up (4x2=8)
8-8=0
4 goes into 0, 0 times
0-0=0 bring up the 0 or don't
you should get 2.2 and/or 2.20
please help I am confused
Answer: -5
Step-by-step explanation:
Opposite sides of a parallelogram are parallel, and thus have equivalent slopes.
Evaluate the given algebraic expression for x = 7 and y = 3.
Answer: = 2(7 + 3) ^2= 2 * 10^2= 200
Hong purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Hong paid.
Answer:
5n=c
Step-by-step explanation:
the equation 5n=c can represent the total cost Hong would have paid for the notebooks because given that each notebook costs $5, you would multiply 5 by the number of notebooks (n) that Hong would be purchasing, which would bring you to the cost (c) of the notebooks all together
sorry for the delay. hope this helps
Phillip is going to a college where tuition is $7,000 per year. He has a scholarship that pays 75% of tuition. He has a grant that pays $1,500 per year. How much will he need to borrow to pay tuition each year?
What is the volume of this figure? Enter your answer in the box. ft³
Answer:
75 ft³ for K12
Find the perimeter of the shape shown below.
perimeter = turn of the figure
P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36
the triangle has 2 équal sides => isosceles
and 1 angle is 60° so the triangle is equilateral
PLEASE HELP!! 100 POINTS
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b)What is the scale factor? Explain and show your work.
The red figure is the original and the green the dilation. We know this because the dilated points are marked with '.
Therefore, we can see that the dilation is a reduction of the original figure. The figure got smaller in size after the dilation.
To find the scale factor, we'll need to look at a few of the points before and after the dilation.
A = (-4, 4)
A' = (-2, 2)
C = (0, 4)
C' = (0, 2)
---The scale factor will be the same on all the points, which is why I have selected only 2 sets of points to look at.
Now, we can figure out the scale factor by thinking about how -4 got to -2, how 4 got to 2. In this case, it is simply dividing by 2. The scale factor must be in multiplication, so we cannot use division in reporting the scale factor, it must be a fraction.
2 / 4 = 1 / 2
The scale factor, therefore, is 1/2.
Hope this helps!
Answer:
a) A reduction.
b) 0.5 or 1/2
Step-by-step explanation:
a) The new points are indicated by the ' next to the letters. By observing the graph, we can see that new points have lessened, and therefore shrank the dialtion, so it is a reduction.
b) On each point, it is reducted by 0.5.
Point A went down from 4 to 2, which is half of 4.
Point B went down from -2 to -1, which is half of -2.
Point C went down from 4 to 2, which is half of 4.
Point D went down from 8 to 4, which is half of 8.
hope this helps!
PLS HELP :How is energy causing motion or creating a change in this image? (2 points)
(leaves of a plant in the sunlight)
1.Energy from fuel allows the plant to grow and make its own food.
2.Energy from the sun allows the plant to grow and make its own food.
3.Energy from the wind allows the plant to grow and make its own food.
4.Energy from the water allows the plant to grow and make its own food
Answer:
Not entirely sure but im sure its no. 2
Step-by-step explanation:
Answer:
I think it's 2
Step-by-step explanation:
I would really like help with A & B
Check the picture below.
Make sure your calculator is in Degree mode.
y=|x-3|+|x+2|-|x-5| if x < -2
what does y equal
Answer:
y= |x-3|+ |x+2|-|x-5|; x<-2
y=-2
A store is having a clearance special and every item is 10% off. What is the sale price of a $310 suit?
Answer:
$279
Step-by-step explanation:
10% off $310 is $31
310-31 is 279
Answer: the sale price of the suit is $279 or $31 dollars off
Step-by-step explanation:
$310 x 0.10= $31
$310 - $31= $279
I would just like to know what this means and how to do it consistently. Thanks (:
Answer:
This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.
If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.
I hope this helps, but if you need more clarification, please tell me in the comments!
I need help with this problem in math I don’t know how to find the y but I know how to get the slope can someone teach me
Answer:
Use the equation y=mx+b
Step-by-step explanation:
So you know how to get the slop, which is awesome
Now to get y all you have to do is use the equation:
y=mx+b
m being slop
b being y- intercept in this case being 2
so you have y=-2x+2
all you have to do is insert different x values and solve the equation for y and see if they match up together in any of the tables
Marie is making her own website. She has 45 background colors, 130 fonts, and 20 themes to choose from. How many different designs can she create?
Answer:
20 designs
Step-by-step explanation:
Some websites have limited data and bytes to hold, so she might have to have one theme, 5 fonts, and 2 background colors to look nice. 1 × 5 × 2 = 10. Add all the other background colors and fonts and themes and divide them by 10.
Therefore, she can create about 20 designs
On Melissa's 6th birthday, she gets a $6000 CD that earns 7% interest, compounded semiannually. If the CD matures on her 14th birthday, how much money will be available?
if the CD matures on her 14th birthday, that means 8 years after she got it, since she got it in her 6th birthday, so
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &8 \end{cases} \\\\\\ A=6000\left(1+\frac{0.07}{2}\right)^{2\cdot 8}\implies A=6000(1.035)^{16}\implies A\approx 10403.92[/tex]
HELP!! I’m in class I just need help with the fill in blanks segment help me please
Answer:
First Blank: “controlled” Second Blank: "a Different" Third Blank: "the same" Last Blank: "Height of the ramp"
Step-by-step explanation:
Juan has forty dollars in his jacket. Every day he spends half of the money that is in the jacket. On the first day (Monday), he spends $20 leaving him with twenty dollars. On what day will he start with less than $3.00 in his jacket?
A) Friday
B) Thursday
C) Tuesday
D) Saturday
Answer:
FridayStep-by-step explanation:
Monday he is left with 20,
Tuesday he will start with 20 and end with 10
Wednesday he will start with 10 and end with 5
Thursday he will Start with 5 and end with 2.5
Friday Start with 2.5
which is >3
MARK ME AS BRAINLISTAnswer:
D) Friday
Hope it helps...
A school gym has an area of 4,641 square feet and a perimeter of 284 feet. What are the dimensions of the gym?
Answer:
dimensions are 51x91
Step-by-step explanation:
Assuming that the gym is rectangular in shape, then...
l*w=4641
and 2l+2w=284
We have two variables and two equations so to solve this we plug one equation into another.
Solve for one variable:
l*w=4641
w=4641/l
Plug into the other equation...
2l+2(4641/l)=284
Solve
l*(2l+9282/l)=284
2l^2+9282=284l
2l^2-284l+9282=0
Factor the trinomial:
2(l−51)(l−91)=0
l−51=0 or l−91=0(Set factors equal to 0)
l=51 or l=91
now, lets plug it into one of the equations to find w
51*w=4641
w=91, l=51
or...
91*w=4641
w=51, l=91
Answer:
91 ft × 51 ft
Step-by-step explanation:
while the other answer is basically correct, it makes a to at the beginning of the calculation (but the continues correctly).
and it assumes you can find the right factoring of the expression.
so, I will show you here how to generally solve this, even if you cannot find the right factorization :
l×w = 4,641 ft²
w = 4641/l
2l + 2w = 284
2l + 2(4641/l) = 284
2l + 9282/l = 284
2l² + 9282 = 284l
2l² - 284l + 9282 = 0
to make things easier let's divide everything by 2
l² - 142l + 4641 = 0
the general solution to a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = l
a = 1
b = -142
c = 4641
l = (142 ± sqrt((-142)² - 4×1×4641))/(2×1) =
= (142 ± sqrt(20,164 - 18,564))/2 =
= (142 ± sqrt(1600))/2 = (142 ± 40)/2 = 71 ± 20
l1 = 71 + 20 = 91
l2 = 71 - 20 = 51
w1 = 4641/91 = 51
w2 = 4641/51 = 91
so, they are interchangeable (it does not matter which we call length and which width).
the dimensions are 91 ft × 51 ft
The number of goldfish in a tank is 12, and the volume of the tank is 45 cubic feet. What is the density of the tank?
Answer: 0.27
Population density of the species in water:
Population density of a species in the water is given by the expression,
Density =Given in the question,
Number of goldfish in the tank = 12
Volume of the tank = 45 cubic feet
Substitute these values in the expression,
Density =
= 0.267
≈ 0.27 goldfish per cubic feet
Therefore, density of the tank will be 0.27 goldfish per cubic feet.
MIGHT GIVE BRAINLIEST.
Calculator What is the surface area of the square pyramid?
Answer:
I need to know the dimensions to solve
Miranda deposits $100 into a savings account. she decides that she will make one deposit at the end of each month and that she will increase the amount that she deposits by 10% each month.
a. complete the table to show the amount of money miranda deposits at the end of each month for the first 4 months
Using an exponential function, it is found that the amounts deposited at the end of each month are given by:
At the end of the first month, she deposits $110.At the end of the second month, she deposits $121.At the end of the third month, she deposits $133.1.At the end of the fourth month, she deposits $146.41.What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, we have that A(0) = 100, r = 0.1, hence the equation for the amount deposited after t months is:
[tex]A(t) = 100(1.1)^t[/tex]
Then, for each of the first four months:
[tex]A(1) = 100(1.1)^1 = 110[/tex][tex]A(2) = 100(1.1)^2 = 121[/tex][tex]A(3) = 100(1.1)^3 = 133.1[/tex][tex]A(4) = 100(1.1)^4 = 146.41[/tex]More can be learned about exponential functions at https://brainly.com/question/25537936
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole. A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. What is the height of the pole? Round to the nearest hundredth. 12. 00 feet 19. 60 feet 24. 17 feet 38. 40 feet.
The height of the pole from the ground is 19.60 feet round to the nearest hundredth.
How to find the length of longest side in right angle triangle?To find the lenght of longest side in right angle triangle, the Pythagoras theorem is used.
According to this theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
A right triangle with side length 10 feet, hypotenuse of 22 feet, and side of h. Thus, the length of side of h by the Pythagoras theorem can be given as,
[tex]h^2=22^2-10^2\\h=\sqrt{484-100}\\h=\sqrt{384}\\h=19.60\rm\; ft[/tex]
Thus, the height of the pole from the ground is 19.60 feet round to the nearest hundredth.
Learn more about the Pythagoras theorem here;
https://brainly.com/question/343682
When Sally decided to run for class treasurer, she predicted how many votes she would get. After the election, Sally found out she had received 150 votes. She had predicted she would get 20% fewer votes than that. How many votes did Sally predict she would get?
Answer:
3000
because you need to dived it
Is (2,10) a solution to this system of equations?
y = 4x + 2
y = x + 8
Yes or no
Answer:
yes, it is
Step-by-step explanation:
10 = 4(2) + 2
10 = 8 +2
10 = 10
10 = 2 + 8
10 = 10
Answer:
The answer is yes
*View the attached graph to check your answer graphically.*
Step-by-step explanation:
y = 4x + 2
y = x + 8
For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.
First, I will substitute the second equation, for y, in the first equation:
y = 4x + 2
y = x + 8
x + 8 = 4x + 2
Next, subtract 4x from both sides to isolate x:
x + 8 = 4x + 2
-4x -4x
-3x + 8 = 2
Then, subtract 8 from both sides:
-3x + 8 = 2
- 8 - 8
-3x = -6
Now, divide both sides by -3:
-3x = -6
/-3 /-3
x = 2
Now, we find the value of y by substituting 2 for x:
y = 4x + 2
y = 4(2) + 2
y = 8 + 2
y = 10
(x, y) ==> (2, 10)
Therefore, yes (2,10) is a solution to this system of equations.
*View the attached graph to check your answer graphically.*
Hope this helps!
Based on her results, what is the probability that a student randomly picked in her class chose comedy as their favorite?
1. 1/14
2. 2/7
3. 1/2
4. 1/7
Explanation:
8 people picked comedy out of 14+8+2+4 = 28 people total.
8/28 = (4*2)/(4*7) = 2/7 is the probability of randomly selecting someone who picked comedy as their favorite.
Diana is trying to choose a broker who will help her purchase a par value $1,000 corporate bond from deegan pharmaceuticals. broker p charges a commission of 4.4% of the market value of each bond purchased, and broker q charges a flat fee of $32.50 for each bond purchased. if bonds from deegan pharmaceuticals are selling at 104.682, which broker will give diana the better deal, and by how much? a. broker p’s commission will be $9.47 less than broker q’s. b. broker p’s commission will be $27.89 less than broker q’s. c. broker q’s commission will be $13.56 less than broker p’s. d. broker q’s commission will be $11.50 less than broker p’s.
Broker q’s commission with a charge of $32.50 will be $11.50 less than broker p’s commission of 4.4%
What is a bond?A bond is a fixed-income instrument that represents a loan made by an investor to a borrower.
Par value of bond = $1,000
Commission on this by broker p= 4.4% = 1000*(4.4)/100= $44
So, the total price spent to purchase this bond = $1044
Par value of bond = $1,000
Commission on this by broker q= $32.50
So, the total price spent to purchase this bond =1000+32.50 = $1032.50
Difference between both deals = 1044-1032.50 = $11.50
Therefore, broker q’s commission will be $11.50 less than broker p’s.
To get more about bonds visit:
https://brainly.com/question/25965295
Answer:
C. Broker Q's commission will be $13.56 less the Broker P's.
Step-by-step explanation:
I just took the test and got it right.
Evaluate the expression for m = -3.
-4|5 + m|
Type the correct answer in the box. Use numerals instead of words.
Answer:
The answer is -8
-4 l5 +(-3)l
-4 (2) = -8
Answer: Correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Edmentum Answer
Describe the relationship between pi and circles.
Answer:
The circumference (C) of a circle is found by the equation C = 2*[tex]\pi[/tex]*radius
There is a second relationship between [tex]\pi[/tex] and circles. That of the area (A) of the circle which is found by the formula A = [tex]\pi*radius^{2}[/tex]
Step-by-step explanation:
What is 170.6% of 366?
Answer:
624.396
Step-by-step explanation:
I did the math myself XD