Answer:
The integers are 4 and 7 or -2 and 1.
Step-by-step explanation:
You can make a system of equations with the description of the two integers.
1. x = y + 3
2. 2x + 2 = y^2
The simplest and the fastest way to solve this system in this case is substitution. You can substitute x for y + 3 in the second equation.
1. x = y + 3
2. 2(y + 3) + 2 = y^2
Now simplify and solve the second one. For convenience, I will just disregard the first equation for now.
2y + 6 + 2 = y^2
y^2 - 2y - 8 = 0
You can factor this equation to solve for y.
(y - 4) (y + 2) = 0
y = 4, y = -2
Now we can substitute the value of y for x in the first equation.
x = 7, x = 1
The two expressions to find the value of the two integers.
M = 3N
2M = N² - 2
N = 6.3 and M = 18.9
The two integers are 6.3 and 18.9
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Smaller integer = M
Larger integer = N
Now,
An integer is three more than another integer.
This can be written as,
M = 3N ____(1)
Twice the larger integer is two less than the square of the smaller integer.
This can be written as,
2M = N² - 2 ______(2)
From (1) and (2) we get,
2(3N) = N² - 2
6N = N² - 2
N² - 2 - 6N = 0
N² - 6N - 2 = 0
This is a quadratic equation.
The roots of this quadratic equation are 6.32 and -0.31 (neglected)
N = 6.32
N = 6.3
Now,
M = 3N
M = 3 x 6.3
M = 18.9
Thus,
The two integers are 6.3 and 18.9
Learn more about expressions here:
https://brainly.com/question/3118662
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How to do this question plz?
Answer:
Ratio of George age to Carl's age to Alex age = 1 : 12 : 4
Step-by-step explanation:
Let the age of Alex = A years
Age of George = G years
And age of Carl = C years
"Alex is 12 years older than George"
A = G + 12 ------(1)
"Carl is 3 times older than Alex"
C = 3A
C = 3(G + 12)
C = 3G + 36 ------(2)
"Sum of their ages is 68 years"
A + G + C = 68 ------(3)
By substituting the values of A and G in equation (3)
G + 12 + G + 3G + 36 = 68
5G + 48 = 68
5G = 20
G = 4 years
From equation (1),
A = 4 + 12 = 16 years
From equation
C = 3(4) + 36
C = 12 + 36
C = 48 years
Ratio of their ages = G : C : A
= 4 : 48 : 16
= 1 : 12 : 4
The three legs of a triangle measure 18, 46, and 3x-5. What are the possible values of x?
a.28
b.11
c. 45
d. 13
Answer:
9. 64
10. 21
11. A (I believe)
Step-by-step explanation:
The first two were simple math problems, however 11. was a bit more complicated and I used logic to find the numbers that best fit into the problem. I am not sure that it is the right answer and if I were you I would wait for someone else to answer this question.
Can someone please help me I really need help please help me thank you
Answer:
(-1,-1), (2,1), (5,3)
Step-by-step explanation:
We can use the formula: rise/run to solve x and y. Since we know the slope is 2/3, 2 will be rise (going up on y axis), and 3 will be run (moving right on x axis).
We are given the point, (2,1) which we can use to find the 2 points that are needed. By using rise/run, we can find the highest point which is (5,3)
How to get the highest point:
(2 + 3, 1 + 2)
Now we can find the lowest point: (-1,-1)
(2 - 3, 1 - 2)
5-3x>6
Please helppppo please hellppppppp
Step-by-step explanation:
5-3x>6
-3x>1
x<-1/3
got it?
Answer:
2x<6
Step-by-step explanation:
What is the length of arc FE?
Answer:
4.42
Step-by-step explanation:
Angles A and C are identical because the two circles are similar.
The arc length formula is s = rФ, where r is the radius and Ф is the central angle.
If we know s and r, then the central angle Ф is s/r, or, in this case,
Ф = 8.84/5.
Now let's find the length of the arc EF: s = rФ becomes:
s = (2.5)(8.84/5) = 4.42
Twelve members of a band purchase one beverage each during a break at practice. Exactly 5 of the 12 members bought bottled water. At this rate, how many band members would you expect to buy bottled water, if all 168 members purchase a beverage?
Answer:
70
Step-by-step explanation:
You have to use ratios. If 5 of 12 members bought water, then x of 168 members will buy water.
[tex]\frac{5}{12} = \frac{x}{168}\\12x = 840\\x = 70[/tex]
70 members will buy bottled water.
Helppp!!!! please!!!
Answer:
[tex]128m^{2}[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2} (\frac{b}{h} )\\A=\frac{1}{2} (\frac{8}{8} )\\A=\frac{1}{2} (64)\\A= 32 m^{2} \\[/tex]
So, the area of 1 triangle is 32m^2.
To find the whole area, you will have to multiply 32 by 4.
Hence, your answer is [tex]128m^{2}[/tex]
EXTRA POINTS! Evaluate the expression 7x2y, when x = 3 and y = 4. A.168 B.252 C.336 D.794
Answer:
A
Step-by-step explanation:
Put the values of x and y into the expression, then multiply the values.
7 x 3 x 2 x 4 = 168
Answer:
B. 252
Step-by-step explanation:
[tex]7x^2y[/tex]
Put x as 3 and y as 4.
[tex]7\left(3\right)^2\left(4\right)[/tex]
Evaluate.
[tex]7(9)(4)[/tex]
[tex]=252[/tex]
Identify the fallacies of relevance, weak induction, presumption, ambiguity, and illicit transference committed by the following arguments, giving a brief explanation for your answer. If no fallacy is committed, write "no fallacy." When I visited Dr. Ames about my cholesterol, she insisted that I go on a statin drug. She says everybody should be on a statin. And when I saw Dr. Collins for depression, he prescribed Prozac. And when the Prozac gave me nausea, he prescribed Zofran to stop the nausea. Doctors are all the same. They all take their orders from the pharmaceutical industry.
Answer:
Hasty generalization fallacy
Step-by-step explanation:
Fallacy can be said to be a reasoning which leads to the wrong interpretation of a statement or an argument. Although some people intentionally make fallacious statements just to score cheap points or to please the listening audience, but some make fallacious unknowingly, either due to carelessness or by being lackadaisical.
In this case the writer, without enough investigation and proof, comes to a very hasty conclusion that "all doctors are the same". This is termed a hasty conclusion because the writer only had dealings with just two docotors(Dr. Ames and Dr. Collins). So saying all doctors are the same just because of two instance is a rather rash statement.
Therefore, the fallacy commited by the writer here is a fallacy of hasty generalization.
Hasty generalization fallacy occurs when someone has a limited information on a population but makes a conclusion based on a larger population than he/she should.
Simplest form w^3-w(w^2+2w-1)+2w
Answer:
[tex] - 2 {w}^{2} + 3w[/tex]Solution,
[tex] {w}^{3} - w( {w}^{2} + 2w - 1) + 2w \\ = {w}^{3} - {w}^{3} - 2 {w}^{2} + w + 2w \\ = - 2 {w}^{2} + 3w[/tex]
Some rules:
[tex]( + ) \times ( + ) \ = ( + ) \\ ( - ) \times ( + ) = ( - ) \\ ( + ) \times ( - ) = ( - ) \\ ( - ) \times ( - ) = ( + )[/tex]
Hope this helps...
Good luck on your assignment..
what is the y intercept of the line x -72 -54 -35 y 25 13 1
Answer:
can you retype the equation
I think it is not correctly typed
HELP ME PLEASE PLEASE IM BEGGING
Answer:
FALSE, (2, 9) is not a solution to the set of inequalities given.
Step-by-step explanation:
Simply replace x by 2 and y by 9 in the inequalities and see if the inequality is true or not:
irst inequality:
[tex]y\geq 4x\\9\geq 4\,(2)\\9\geq 8[/tex]
so thi inequality is verified as true since 9 is larger or equal than 8
Now the second inequality:
[tex]y<x+2\\9<(2)+2\\9<4[/tex]
This is FALSE since 9 is larger than 4 (not smaller)
Therefore the answer to the question is FALSE, (2, 9) is not a solution to the set of inequalities given.
What is sixty dollars increased by fifteen percent?
Answer:
$69 dollars.
Step-by-step explanation:
$60 dollars increased by 15% is the same as:
60 + 60(.15) = 60(1.15) = $69
HELP ASAP HELP PLEASE ASAP
Answer:
WXYZ can not be a rectangle because consecutive sides are not perpendicular to each other.
Step-by-step explanation:
The given vertices are W(-4,3), X(1,5), Y(3,1) and Z(-2,-1).
Plot these points on coordinate plane and draw the quadrilateral as shown below.
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using this formula, we get
[tex]m_{WX}=\dfrac{5-3}{1-(-4)}=\dfrac{2}{5}[/tex]
[tex]m_{XY}=\dfrac{1-5}{3-1}=\dfrac{-4}{2}=-2[/tex]
Now,
[tex]m_{WX}\times =\dfrac{2}{5}\times (-2)=-\dfrac{4}{5}\neq -1[/tex]
Here, WX and XY are two consecutive sides of quadrilateral but the product of their slopes is not equal to -1. It means they are not perpendicular to each other.
Since, all interior angles of a rectangle are right angles, therefore, WXYZ can not be a rectangle.
A wooden clock is made in the shape of a triangular pyramid. The net of the pyramid is shown. A triangular pyramid. The base has a base of 8 inches and height of 6.9 inches. The 3 sides have a base of 8 inches and height of 7.4 inches. [Not drawn to scale] How much wood is needed to build the clock?
Answer:
116.4 Square Inches
Step-by-step explanation:
Base Area of the Triangular Pyramid
[tex]=\dfrac12 \times 8 \times 6.9\\\\=27.6$ square inches[/tex]
Surface Area of the three sides
[tex]=3 \times \dfrac12 \times 8 \times 7.4\\\\=88.8$ square inches[/tex]
Therefore, the area of wood needed to build the clock
=27.6+88.8
=116.4 Square Inches
Answer:
C
Step-by-step explanation:
I hope it helps
For every 1000 hits a channel gets it makes £16 from ad revenue. How much will the channel make from each hit?
Hi there! Hopefully this helps!
The answer is: 0.016
Here is how I got that answer:
16/1000=0.016
Answer:
Step-by-step explanation:
£16÷1000=0.016p
Which expression can be used to determine the slope of the linear function represented in the table?
X
0
y
5
9
4
9-5
4-0
4-0
O9-5
5-0
9-4
.
9-4
Answer:
Option (1)
Step-by-step explanation:
This question is incomplete; find the complete question in the attachment.
Given table represents a linear function.
Two ordered pairs given in the table (0, 5) and (4, 9) pass through the function .
If the two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] lie on a line,
Slope of the line will be = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the linear function represented by the table = [tex]\frac{9-5}{4-0}[/tex]
Therefore, Option (1) will be the correct option.
Henry wants to double a cake recipe that uses 2 cups and 10 tbsp of flour. How much flour will he need?
9514 1404 393
Answer:
5 cups and 4 tbsp
Step-by-step explanation:
Double the quantity (2 c, 10 T) is ...
2 × (2 c, 10 T) = (4 c, 20 T)
A cup is equal to 16 tablespoons, so this quantity can be rewritten as ...
(5 c, 4 T)
Five cups and four tablespoons of flour are needed for the double recipe.
Kirk bought 2 1/4 punds of lemons. He used 1/4 of the lemons to make lemonade. Kirk completed his work and found that he hsed 9 pounds of lemons . Did hs do rhe work correctly?
Answer:
How could he have used 9 lbs of lemons when he only went and bought 2 1/4 lbs? So, his work was NOT correct.
Step-by-step explanation:
Answer:
it is d
Step-by-step explanation:
got it right
The Mississippi River flows at a rate of 16,790 cubic meters per second. Choose the best approximation of the flow rate of the Mississippi River. Choose 1 answer: A:2 * 10^3 B: 2*10^4
Answer:
B, 2(10^4)
Step-by-step explanation:
2(10^3)= 2000
2(10^4)= 20000
2(10^4) Is closer to 16790 than 2(10^3)
The origin is at (1, 1): that is, the origin is at position 1 on the x-axis and at position 1 on the y-axis.
Answer: What is the question? If you could be more specific I could try to help but there is no question here.
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
just did it
This is probbaility, please just help me. i've been stuck forever!
Your answer would be 0.14 to the nearest hundredth.
The question P(Walk to school | Senior) is asking for the probability that a student walks to school given that they're a senior. Therefore we have to count how many total senior students there are, which is 35.
To form the probability, we then need to see how many of these 35 students walk to school, which we're given as 5. Thus, the probability is 5/35 which simplifies to 1/7.
1/7 as a decimal is 0.1429, which, when rounded to the nearest hundredth, gives us 0.14.
I hope this helps! Let me know if you have any questions :)
Please please helpppp helppp helppp❤️
Answer:
774 km
Step-by-step explanation:
Actual distance
[tex] =\frac{4.3}{100000} \times 18000000 \\ \\ = 4.3 \times 180 \\ = 774 \: km[/tex]
1)
4136 mm = 4136/1000 = 4.136 m = 4.14 m
2)
Since 1 yard = 91.44 cm
Hence, 14.7 yard = 14.7*
91.44 = 1,344.168 cm = 1344 cm
3)
342 inches = 9 yards, 1 ft, 6 inches.
In the triangles, HG = MP and GK = PN. Triangles H G K and M P N are shown. Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters. Sides H G and M P are congruent. Sides G K and P N are congruent. Which statement about the sides and angles is true?
Answer:
m∠G > m∠P
Step-by-step explanation:
Given that:
HG = MP and GK = PN., Side H K has a length of 15 millimeters. Side M N has a length of 11 millimeters.
The triangle law for unequal sides states that if two sides are unequal. the angle opposite the longer side is greater than the angle opposite the shorter side. Since side HK has a length of 15 millimeters and Side MN has a length of 11 millimeters, the angle opposite side HK (which is m∠G) is greater than the angle opposite side MN (which is m∠P). That is m∠G > m∠P.
Answer:
A.
Step-by-step explanation:
Which of the following numbers is not part of the solution to x ≤ -2? * -2 * -2.45 * -8 * -1.76
Answer:
-1.76
Step-by-step explanation:
-2 is equal to -2, so it works (greater or less than -2)
-2.45 is less than -2, so it works
-8 is less than -2, so it works
-1.75 is greater than -2, so it doesn't work
Line segment ON is perpendicular to line segment ML.
What is the length of chord ML?
A) 20 units
B) 24 units
C) 26 units
D) 30 units
Answer:
24 units
Step-by-step explanation:
OM = ON, so
OP= 13-8
That means OP is 5.
Using the Pythagorean Theorom to find MP:
5^2+b^2=13^2
25+b^2=169
b^2=169-25
b^2=144
B=12
This means MP =12. ML is twice as long as MP. 12x2=24
The answer is B. 24 units
Andre types 208 words in 4 minutes. Noah types 342 words and 6 minutes.who types faster explain?
Answer:
Noah
Step-by-step explanation:
Find how many words each person types in one minute. Andre types 208/4=52 words/min and Noah types 342/6=57 words/min. The answer is Noah.
Answer:
noah types faster
Step-by-step explanation:
Andre
208 words/ 4 minutes =
52 words per minute
Noah
342 words / 6 minutes = 57 words per minute
Match each polynomial expression to its additive inverse.
6x²-x-2
6x2 - x+2
6x2 - x+2
6x2 + x + 2
6x²+x-2
6x2 + x-2
6x2+x-2
-6,2-x+2
Answer:
Step-by-step explanation:
To find the additive inverse of polynomial expression, flip the sign of each term.
6x² ----> -6x²
-x -----> +x
-2 -----> +2
Additive inverse:
-6x² + x + 2
If f(x)=8-10x and g(x)=5x+4, what is he value of (fg)(-2)
Answer:
168
Step-by-step explanation:
We would like to multiply these two expressions together and then substitute -2 in for x to solve.
f(x) * g(x) = (8 - 10x) * (5x + 4)
We will use FOIL (first, outer, inner last):
(8 - 10x) * (5x + 4) = 8 * 5x + 8 * 4 + (-10x) * 5x + (-10x) * 4
Combining terms, we get:
f(x) * g(x) = 32 - 50x²
Plug -2 in for x:
32 - 50 * (-2)² = 32 - 50 * 4 = 32 - 200 = -168
The answer is thus 168.
~ an aesthetics lover
Can someone help me with this question please?
Answer:
If the ratio of edge lengths is 3:5, I'm going to assume that the perimeters are going with the same ratio.
Therefore, the ratio would be 345:575.
Hope this is right and helps :)