Answer :-
Value of two integers are 22 and 24Step-by-step explanation:
Given :-
The product of 2 consecutive even integers is 528To Find :-
Value of each integersSolution :-
Let one integer be xother integer be x + 2According to question,
Product of two integers = 528↠ (x)(x + 2) = 528
↠ x² + 2x = 528
↠ x² + 2x - 528 = 0
↠ x² + 24x - 22x - 528 = 0
↠ x(x + 24) - 22 (x + 24) = 0
↠ (x + 24) (x - 22) = 0
↠ x = -24 or 22
Hence,
1st integer = 222nd Integer = 22 + 2 = 24Value of two integers are 22 and 24
Step-by-step explanation:
It is given that, The product of 2 consecutive even integers is 528 and we have to find the value of each integers.
So, Let us assume the 1st consecutive even integer as y and the 2nd as (y + 2)Now, As it is stated in the question that the product of 2 consecutive even integers is 528, So
[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { y(y + 2) = 528 }}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y = 528 }}}} \: \: \\ \\[/tex]
Subtracting both sides by 528 we get :
[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 528 - 528 }}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + 2y - 528= 0 }}}} \: \: \\ \\[/tex]
We have to find two numbers such that,
[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { p + q= 24 }}}} \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf { p \times q= 528 }}}} \: \: \\ \\[/tex]
The two numbers are 24 and 22. So,
[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf { {y}^{2} + (-22y) + 24y - 528= 0 }}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf { {y}(y -22) + 24(y - 22)= 0 }}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf { (y -22) (y + 24)= 0 }}}} \\ \\ [/tex]
Whether, the value of y is (-24) or 22.[tex] \: [/tex]
So, The first consecutive even integer is 22.
Now,
[tex] \\ { \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=y \:+2 \: }}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=2 2+2 \: }}}} \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \pmb{ \sf {Second \: consecutive \: even \: integer=24 }}}} \\ \\ [/tex]
Therefore,
The value of each integer is 22 and 24.15. A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take off point of 2000 feet. How far apart are the take off point and the water tower?
The required distance between the take-off point and the water tower is 1980.1 feet.
Given that,
A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take-off point of 2000 feet.
To determine how far apart are the take-off point and the water tower.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
Now,
The distance flying over inclination is 2000 feet at an angle of 8° with horizontal.
Now,
Required horizontal distance = 2000 * cos 8°
= 1980.1 feet.
Thus, the required distance between the take-off point and the water tower is 1980.1 feet.
Learn more about trigonometry equations here:
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#SPJ2
What are the volume and the surface area of this storage chest?
Answer:
Surface Area: [tex]18ft^3[/tex]
Volume: [tex]44ft^2[/tex]
Step-by-step explanation:
Volume Formula --> base * height
[tex](4.5 * 2) * 2 = 9*2=18ft^3[/tex]
Surface Area Formula --> 2(width*length + height*length + height*width)
[tex]2((2*4.5) + (2*4.5)+(2*2)) = 2(9+9+4) = 2(22) = 44ft^2[/tex]
Answer:
Volume = 18 ft³
Surface area = 44 ft²
Step-by-step explanation:
Volume
Volume of a cuboid = base length × base width × height
Given:
base length = 4.5 ftbase width = 2 ftheight = 2 ftSubstitute given values into formula:
⇒ Volume = 4.5 × 2 × 2 = 18 ft³
Surface Area
Surface area = 2(base width × height) + 2(base length × height) + 2(base length × base width)
=2(2 × 2) + 2(4.5 × 2) + 2(4.5 × 2)
= 8 + 18 + 18
= 44 ft²
Jules draws the incenter of ABC. Which term describes the three segments Jules draws inside the triangle?
a.medians
b.angel bisector
c.altitudes
d.perpendicular bisectors
Answer:
b) angle bisector of angle ABC
Which of the states in the table below has the least area?
State Population in 2020 Population Density (people/mi?) Indiana 6,785,528 186.32 Mississippi 2,961,279 61.14 Iowa 3,190,369 56.69 Arizona 7,151,502 62.74
Indiana
Mississippi
Iowa
Arizona
According to the information in the table, it can be inferred that the state with the least area is Mississippi, with an area of 61.14 square miles.
How to read the table?The table shows the population density of some states in which the number of people and the area of that state are mentioned.
Based on this information, it can be inferred that the state with the fewest number of miles is the one with the smallest area. So Mississippi is the one with the least area.
On the other hand, the one with the largest area would be Indiana which is 186.32 square miles in area.
Learn more about area in: https://brainly.com/question/11952845
Help with this question here please
Answer:
that is 4.6 m that the answer
help it is for calculus
Answer:
I think 2(x^2−y^2)=3x
Answer:
Its 2(x^2-y^2)=3x
Which sentence is correct?A.B.C.D.
Answer: B is correct
Step-by-step explanation:
if you do 2 ÷ 5 you get 0.4. But that isn't an option. So, the only other possibility would be -2 ÷ 5 which gives us -0.4, and that makes sense.
I'm not the greatest at explaining this one but hopefully, this helps!
Show all steps when completing the square to solve 2x^{2} - 4x - 5 = 25.
Answer:
x = 5,-3
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
See attachments
Step-by-step explanation:
Hope this helps! (I hope you can open them)
A cone-shaped container has a height of 240 in. and a radius of 150 in. The cone is filled with a liquid chemical. The chemical evaporates at a rate of 12,000 in³ per week.
How many weeks will it take for all of the chemical to evaporate?
Use 3.14 to approximate pi.
Enter your answer in the box.
____ weeks
The table shows the atomic radii of four elements.
Element Atomic Radii (m)
Potassium 2.2 × 10-7
Argon 7.1 × 10-8
Boron 8.5 × 10-8
Silver 1.6 × 10-7
Which list shows the atomic radii of the elements ordered from greatest to least?
[tex]\sf Potassium \ : \ 2.2 * 10^{-7}[/tex]
[tex]\sf Argon \ : \ 7.1 * 10^{-8}[/tex]
[tex]\sf Boron \ : \ 8.5 * 10^{-8}[/tex]
[tex]\sf Silver \ : \ 1.6 * 10^{-7}[/tex]
greatest to least :
Potassium < Silver < Boron < ArgonThe order is
Potassium>Silver>Boron>ArgonShortcut trick :-
The nature of atomic radii in. periodic table
Decrease in a period from left to right.Increase in a group from up to downwrite an inequality that means 2 times a number (d) plus 3 is less than or equal to 9.
Answer: 2d+3<=9
Step-by-step explanation:2 times a number is 2d plus 3 is +3 less than or equal to is <=
in the figure triangle XYZ is similar to triangle XTU if XT measures 12cm what is the length of TY
Answer:
20
Step-by-step explanation:
It is stated that the triangles in the figure are similar:
We can use the side lengths' proportions to find the length of TY
UT/ZY = XT/TY
(9.6)/16 = 12/TY cross multiply expressions:
192 = (9.6)TY divide both sides by 9.6
20 = TY
According to the Current Population Report of the United States census, 32. 3% of males aged 25 or older have earned a bachelor's degree or higher. Suppose that Nancy works for the city of Peoria, AZ. City officials have asked her to estimate the proportion of males aged 25 or older in Peoria who have earned a bachelor's degree or higher. They have requested that her estimate have confidence level of 95% and a margin of error of 2%, or 0. 2. Determine the sample size n needed for the 95% confidence interval to be no more than 0. 2.
Answer:
i did this on study island
Step-by-step explanation:
If the two acute angles of a right triangle are congruent, then what is the measure of each acute angle?
What is the area of this rectangle?
Answer:
39
Step-by-step explanation:
You find the area by multiplying the length times the height which is what I did 13 x 3 = 39
What are the measures of the interior angles of the triangle?
m∠1 =
°
m∠2 =
°
m∠3 =
°
Answer:
Step-by-step explanation:
a and b are parallel lines. So, alternate interior angles are congruent.
∠2 = 64.8°
∠3 = 30.5°
Sum of all angles of triangle = 180
∠1 + ∠2 + ∠3 = 180
∠1 + 64.8 + 30.5 = 180
∠1 + 95.3 = 180
∠1 = 180 - 95.3
∠1 = 84.7°
-3 x 7 -:- 5 x 1/7
please show the steps :)
is the sign that you mean ÷ ?
if so:
-3×7÷5×1/7
= -21÷5×1/7
=-21/5 × 1/7
= (-21×1) / (5×7)
= -21/35
=-3/5
=-0.6
A Lorry travels for 4 hours at a speed of 58km/h . Work out the travel distance
Answer: The answer is 9.00988 mi/h
Step-by-step explanation: to be simplified it would be 9.0 or 9 miles an hour
what is the sum of 1 To 101 only positive integers pease fast
Answer:
5050
Step-by-step explanation:
sum of first n natural num. = [n(n+1)]/2
sum of first 100 natural num. = (100x101)/2 = 5050
Answer : The sum of 1 to 101 positive integer is 5050
5052 will be sum of 1 to 101 only positive integer
Find the coordinates of A.
Answer:
(-4, 1)
Step-by-step explanation:
Coordinates on the plane are written (x, y), meaning you write where the point is located on the x-axis (across) and then you write where the point is located on the y-axis (up and down).
You can see that A's location on the x-axis is -4, so now we have (-4, y). We can also see that A's location on the y-axis is 1, so we have (-4, 1) as our coordinates of A.
I hope this helps! Have a lovely day!! :)
How do i solve this?
4 Indira makes a wooden box without a lid. All the faces of the box meet at
right angles. Indira plans to paint all surfaces of the box, including the
inside and outside. The interior of the box has length 13 in., width 8 in., and
depth 7 in. Indira can cover up to 1,350 in.? with
5 cup of paint. Will she
need more than 5 cup of paint to cover the box? Explain how you know.
Considering the surface area of the rectangular box, it is found that since it is of 502 in² < 1,350 in², she will not need more than 5 cups of paint.
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and depth d is given by:
S = 2(lw + ld + wd).
In this problem, we have that the dimensions, in inches, are given by l = 13, w = 8, d = 7. Hence, the surface area in in² is given by:
S = 2(13 x 8 + 13 x 7 + 8 x 7) = 502 in².
Since the surface area of the box is of 502 in² < 1,350 in², she will not need more than 5 cups of paint.
More can be learned about the surface area of a rectangular prism at https://brainly.com/question/17223528
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
There are two mystery numbers. The sum of 10 times the first number and 5 times the second number is -15. The sum of 6 times the first number and 2 times the second number is -10. What are the two numbers? please explain
Answer:
-2 and 1
Step-by-step explanation:
The two "mystery numbers" are described by two relations. We can assign variables to those numbers, and write a system of equations that express the given relations.
__
Let x and y represent the first and second mystery numbers, respectively. The first relation tells us ...
10x +5y = -15
The second relation tells us ...
6x +2y = -10
We can reduce both of these equations to lowest terms by factoring out the common factor of 5 from the first one and 2 from the second one:
2x +y = -33x +y = -5__
We are told to solve this using elimination. We can eliminate the y-variable by subtracting the first equation from the second:
(3x +y) -(2x +y) = (-5) -(-3)
x = -2 . . . . . . . . . . simplify
2(-2) +y = -3 . . . . substitute for y
y = 1 . . . . . . . . . . add 4
The two numbers are -2 and 1.
Solve the system of inequalities and indicate all the integers which are in the solution set: The answer isn't an inequality like -5
Answer:
{- 4, - 3, -2, -1, 0, 1, 2, 3}Step-by-step explanation:
Solve each inequality in the system:
3 - 2a < 13 ⇒ 2a > 3 - 13 ⇒ 2a > - 10 ⇒ a > - 55a < 17 ⇒ a < 17/5 ⇒ a < 3.4The solution is:
- 5 < a < 3.4The integer solution set is:
{- 4, - 3, -2, -1, 0, 1, 2, 3}[tex]\\ \rm\rightarrowtail 3-2a<13[/tex]
[tex]\\ \rm\rightarrowtail -2a<10[/tex]
[tex]\\ \rm\rightarrowtail -a<5[/tex]
[tex]\\ \rm\rightarrowtail a>-5[/tex]
And
[tex]\\ \rm\rightarrowtail 5a<17[/tex]
[tex]\\ \rm\rightarrowtail a<17/5[/tex]
[tex]\\ \rm\rightarrowtail a<3\dfrac{2}{5}[/tex]
So
solution set
[tex]\\ \rm\rightarrowtail a\in\left(-5,3\dfrac{2}{5}\right)[/tex]
So
a={-4,-3,-2,-1,0,1,2,3}How do we do this? The sub gave us the wrong work and isn’t explaining it! Help please!!!
Answer:
1) 18b - 3c - 10
2) [tex]1\frac{3}{4}[/tex]g + 7
3) 0.3y
4) -4n - 5
Step-by-step explanation:
1) 16b + 5c - 10 - 8c + 2b
like terms: 16b + 2b = 18b
like terms: 5c - 8c = -3c
like terms: -10
simplified: 18b - 3c - 10
____________
2) 1/2g + 2g - 3/4 g + 7
like terms: 1/2g + 2g - 3/4g
2 1/2 - 3/4
improper fraction > 5/2 > same denom > 10/4
10/4 - 3/4 = 7/4 > mixed number> 1 3/4g
like terms: +7
simplified: 1 3/4g + 7
____________
3) -0.9y + 4.4y - 3.2y
like terms: -0.9y + 4.4y - 3.2y
simplified: 0.3y
____________
4) 4 - 8n + 7n - 3n - 9
like terms: -8n + 7n - 3n = -4n
like terms: 4 - 9 = -5
simplified: -4n - 5
____________
solve for the measure of angle JKL in the diagram below? Show your work and explain the steps you used to solve
Question: calculate the measure of angle JKL, i.e. mJKM+mMKL
Answer:
78°
Step-by-step explanation:
angle JKM is a tangent-chord intersection angle and equals half of the intercepted arc KM of 76°. Thus
mJKM = 76/2 = 38°
angle MKL is an inscribed angle and equals half of the intercepted arc ML of 80°, Thus
mMKL = 80/2 = 40°.
Therefore angle JKL = 38°+40° = 78°.
. It took Erin the same time to drive 21 miles as it took Brent to drive 15 miles. Erin's speed was 10 mph
faster than Brent's speed. How fast did Erin drive?
The speed at which Erin drove from the given parameters was calculated as; 35 mph
How to work with speed rates?
Let Erin's speed rate be X. Now, since it took erin 21 miles, then;
Erin's time = 21/X
Now, erin's speed was 10 mph faster than Brent's speed. Thus;
Brent's speed = (X - 10) mph
Thus, Brents time = 15/(x - 10)
Now, since they took the same time, then we know that;
21/x = 15/(x - 10)
15x = 21x - 210
6x = 210
x = 210/6
x = 35
Thus, Erins speed = 35 mph
Read more about rates at; https://brainly.com/question/12242745
Solve the following system by graphing. 5x+2y=10 4x−y=−18
Answer:
x = -2, y = 10
Step-by-step explanation:
What is the average rate of change?
A. 4
B. 2/5
C. 1
D. 2
Answer:
C) 1
Step-by-step explanation:
The average rate of change remains constant among the 3 given points as [tex]\frac{5-4}{2-1}=1[/tex] and [tex]\frac{10-5}{7-2}=1[/tex], so your answer is C
Pls someone do this its on test
Answer:
they get a 7/24th piece of cake.
Step-by-step explanation:
if we divide 3 1/2 by 12 we get 7/24
we use the 3 1/2 because that is how many cakes there are.
we use 12 because there are 12 boys that want to split the cake equally.
