Answer: The numbers are 1 and 3.
Step-by-step explanation:
Let x = smaller number , y= larger number.
As per given,
[tex]x=\dfrac{y}{3}[/tex] ...(i)
[tex]x+y=y^2-5[/tex] ...(ii)
Put value of x from (i) in (ii)
[tex]\dfrac{y}{3}+y=y^2-5\\\\\Rightarrow\ \dfrac43y=y^2-5\\\\\Rightarrow\ 3y^2-4y-15=0\\\\\Rightarrow\ 3y^2-9y+5y-15=0\\\\\Rightarrow\ 3y(y-3)+5(y-3)=0\\\\\Rightarrow\ (y-3)(3y+5)=0\\\\\Rightarrow\ y=3 \ \ or\ y=\dfrac{-5}{3}[/tex]
Since numbers are positive , so y=3 is correct.
And x will be 1 [from (i)]
Hence, the numbers are 1 and 3.
Can someone please help me solve this (7th grade math)
Answer: 8x = 72
Step-by-step explanation:
and in case you need to go any further at any point, x = 9
Kelly needs a gross pay of at least $945 a week to pay the bills. Her job is commission and she gets 7.5% for the first $1250 and 13% after that. How much does she need to sell a week to cover the cost of her bills?
Answer:
b and c
Step-by-step explanation:
Kate has 48 softballs. She wants to divide them evenly among b softball bags. Which expression represents how many softballs she should put into each bag?
Answer:
Softballs = (48/b)
Step-by-step explanation:
Given that,
Total number of softballs = 48
She wants to divide them evenly among b softball bags.
We need to find an expression that represents how many softballs she should put into each bag.
As it is dividing among b softball, it means we divide 48 and b. So,
[tex]s=\dfrac{48}{b}[/tex]
Hence, the required expression is (48/b).
simplify the expression
Answer:
-88
Step-by-step explanation:
If a=2, we can say that -[tex]a^{2}[/tex] would be -4.
Secondly, if a=2 and b=-6 we can assume that 4ab would become -48.
Finally, if b=-6 we can say that -[tex]b^{2}[/tex] would become -36.
Adding all of those up gives you -88, your answer.
A triangle has one side that measures 1 foot and another side that measures 20 inches. What are possible lengths of the third side? (Select all that apply.)
6 inches
13 inches
28 inches
36 inches
Answer:
The correct options for the possible lengths of the third side are;
13 inches
28 inches
Step-by-step explanation:
The given lengths of two sides of the triangle are;
The length of one side of the triangle = 1 foot = 12 inches
The length of the other side of the triangle = 20 inches
The question can be solved by the triangle inequality theorem as follows;
A + B > C
B + C > A
A + C > B
Let the given sides be A = 12 inches and B = 20 inches
We have;
12 + 20 = 32 > C
Therefore, by the triangle inequality theorem, the third side, 'C', is less than 32 inches
Similarly, when C = 6 inches, we have;
A + C = 12 + 6 = 18 < B = 20
Therefore, the third side cannot be 6 inches
when C = 13 inches, we have;
A + C = 12 + 13 = 25 > B = 20
Therefore, the third side can be 13 inches
when C = 28 inches, we have;
A + C = 12 + 28 = 30 > B = 20
Therefore, the third side can be 28 inches
Based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.
The Triangle Inequality Theorem
The triangle inequality theorem states that, sum of the length of any two sides of a given triangle = length of the third side.
Given the measures,
1 ft = 12 iches20 inchesThe possible third side must make the three set of numbers conform to the triangle inequality theorem.
Thus, for 13 inches, we have:
13 + 12 > 20; 12 + 20 > 13; 20 + 13 > 12
Also, for 28 inches, we have:
28 + 12 > 20; 12 + 20 > 28; 20 + 28 > 12
Therefore, based on the triangle inequality theorem, the possible lengths of the third side of the triangle are: 13 inches and 28 inches.
Learn more about triangle inequality theorem on:
https://brainly.com/question/26037134
Identify the figure below. Select all names that apply.
Image shows a four-sided figure with opposite sides parallel and equal in length.
A.
quadrilateral
B.
parallelogram
C.
rhombus
D.
square
E.
trapezoid
Answer:
b and d
Step-by-step explanation:
1:
Segment EG is an angle bisector of angle FGH. Abraham wrote a proof to show
that triangle HEG is congruent to triangle FEG.
2
3
5
6
G
1. Side EG is congruent to side EG because they're the same segment.
2. Angle EGH is congruent to angle EGF because segment EG is an angle
bisector of angle FGH.
3. Angle H EG is congruent to angle FEG because segment EG is an angle
bisector of angle FGH.
Answer:
Angle FEG
Step-by-step explanation:
Can y’all please help me I hope you have a wonderful day and I would really appreciate if you could answer this question for me!
Describe this number line and the numbers and fractions shown.
Answer:
Where?
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
Graph the equation y = -x^2+ 8x – 15 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation –x^2 + 8x – 15 = 0.
Answer:
Graph below
Step-by-step explanation:
Graph of the Quadratic Function
We are given the function:
[tex]y=f(x)=-x^2+8x-15[/tex]
Select 5 values of x={2,3,4,5,6}
And calculate the corresponding values of y:
[tex]f(2)=-2^2+8*2-15=-4+16-15=-3[/tex]
[tex]f(3)=-3^2+8*3-15=-9+24-15=0[/tex]
[tex]f(4)=-4^2+8*4-15=-16+32-15=1[/tex]
[tex]f(5)=-5^2+8*5-15=-25+40-15=0[/tex]
[tex]f(6)=-6^2+8*6-15=-36+48-15=-3[/tex]
We have obtained the points
(2,-3) (3,0) (4,1) (5,0) (6,-3)
Now we plot them in the graph below.
It can be noted three remarkable points:
The vertex is located at (4,1)The roots are located at (3,0) and (5,0)The roots of the equation
[tex]-x^2+8x-15=0[/tex]
Are x=3 and x=5.
If you minus a positive number from a negative number is the diffirance a positive number, or a negative number? For example: 5 - ( -2 ) would this problem be positive negative. Also would you add or subtract because there is an negative number?
Answer:
positive + positive is negative
negative+ positive = negative ii think
Step-by-step explanation:
If the value of 3/4÷x is a whole number, which number is the value of x ?
Answer:
1/8
Step-by-step explanation:
Find the area of triangle ABC.
Give your answer correct to 1 decimal
Answer:
let
a=9cm
b=8cm
c=10cm
Step-by-step explanation:
now
s=(a+b+c)/2=(9+8+10)/2=13.5
area of traingle=√(s(s-a)(s-b)(s-c))=√(13.5(13.5-9)(13.5-8)(13.5-10))=34.197cm²
(PLEASE HELP ME)
Which of the following equations is correct?
Please help me thank you so much!!
Answer:
B
Step-by-step explanation:
Distributive property: a*(b + c)= (a*b) + (a*c)
[tex]\frac{3}{4}*(\frac{1}{2}+\frac{-2}{5})=\frac{3}{4}*\frac{1}{2}+\frac{3}{4}*\frac{-2}{5}\\\\=\frac{3}{8}+\frac{-6}{20}\\\\=\frac{3*5}{8*5}+\frac{-6*2}{20*2}\\\\=\frac{15}{20}+\frac{-12}{40}\\\\=\frac{15-12}{40}\\\\=\frac{3}{40}[/tex]
what is x? please help
Answer:
29
Step-by-step explanation:
This is a right triangle because it has the small square in the corner.
And when you have a right triangle the angle with the square in it is ALWAYS going to be 90 degrees.
It gave you one of the angle measurements which is 61.
90+61=151
And When you add all the angle measurements of a triangle it will ALWAYS be a total of 180 no matter what kind of triangle it is.
To find "x" you subtract the sum of the two angles you you know from 180.
180-151=29
Alexis simplified 14/42 to 1/3 by using the greatest common factor (GCF) of 14 and 42
What number did alexis use?
A. 2
B. 14
C.42
D. 84
Answer: 14
Step-by-step explanation:
You had a bag of fruit snacks that you shared with 2 friends. Each of you got no fewer than 5 fruit snacks. The inequality x ÷ 3 ≥ 5 NEED ASAP
solve the inequality to find the number of fruit snacks that were in the bag
Help me please I don't know how to solve this problem.
Find the given trigonometric ratio in the problem below.
Answer:
cosC = 30/50
Step-by-step explanation:
Before you find cosC, you should know that:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
You should also know that trigonometric ratios work for only right triangles.
If cosine = adjacent side/hypotenuse, then:
cosC = 30/50
cosC = 0.6
If rounding to the nearest four decimals, it should be 0.6000.
A cylinder with a height of 6 1/2 inches (in.) and a diameter of 5 inches is shown. What is the volume of the cylinder, in cubic inches? (Use 3.14 for π.) cubic inches. Round to the nearest inch!
Answer:
i dont know for sure but I think it would be 0.07
Solve for x
9
X+4
12
2x
units
please help me please will give brainliest
please show your work
Answer:
step 2
Step-by-step explanation:
When you subtract an expression from another expression, you need to distribute the (-) sign.
step 1 (6x³ + 8x² - 7x) - (2x³ - 16x² + 3x - 24)
step 2 6x³ + 8x² - 7x - 2x³ + 16x² - 3x + 24
step 3 4x³ + 24x² - 10x + 24
2x + y = 11
3x - y = 4
Answer:
[tex]x=3,y=5[/tex]Step-by-step explanation:
Add the equations together and solve for x.
[tex](2x + y )+ (3x - y) = 11 + 4[/tex]
[tex]5x=15[/tex]
[tex]x=3[/tex]
Use equation [tex]2x+y=11[/tex] to solve for y.
[tex]2(3) +y=11[/tex]
[tex]6+y=11[/tex]
[tex]y=11-6[/tex]
[tex]y=5[/tex]
Someone tell me the first hundred digits of pi
Answer:
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825
Step-by-step explanation:
Answer: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
Step-by-step explanation:
how do i find thhe greatest common factor?
Answer:
lets say you needed to find the greates comon factor of 20 and 5, you need to find the closest number they both go into, so 20. or if it was 3 and 10 it would be 30 because it is the closest thing they both go into, i hope i am right i am so sorry if i am wrong.
A figure is made up of one square and one triangle. The square has a side Length of 13 feet. The triangle has a base of 13 feet and a height of 8.2 feet. What is the total area of the figure.
) Which expression is equivalent to 1/3b - 7?
A scale drawing of a building shows 1 inch = 8 feet. How many feet are represented by 3 ¾ inches on the drawing?
Answer:
30 feet
Step-by-step explanation:
3x8=24 ft
3/4x*8= 6 ft
Can 80°, 75 and 20° form a triangle Justify
Select one:
0
a. No
b. Yes
c. None
Answer:
A. No
Step-by-step explanation:
We know that the sum of the angles of a triangle is always equal to 180°. The sum of the angles of a triangle is not equal to 180° in this equation. Hence, we cannot form a triangle.
Find the sum of5x^2-3x+2 and 3x^2-4x-1
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplifying
(3x + -2)(4x + -1) = 0
Reorder the terms:
(-2 + 3x)(4x + -1) = 0
Reorder the terms:
(-2 + 3x)(-1 + 4x) = 0
Multiply (-2 + 3x) * (-1 + 4x)
(-2(-1 + 4x) + 3x * (-1 + 4x)) = 0
((-1 * -2 + 4x * -2) + 3x * (-1 + 4x)) = 0
((2 + -8x) + 3x * (-1 + 4x)) = 0
(2 + -8x + (-1 * 3x + 4x * 3x)) = 0
(2 + -8x + (-3x + 12x2)) = 0
Combine like terms: -8x + -3x = -11x
(2 + -11x + 12x2) = 0
Solving
2 + -11x + 12x2 = 0
Solving for variable 'x'.
Factor a trinomial.
(1 + -4x)(2 + -3x) = 0
Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve:
Simplifying
1 + -4x = 0
Solving
1 + -4x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1
Combine like terms: 0 + -1 = -1
-4x = -1
Divide each side by '-4'.
x = 0.25
Simplifying
x = 0.25
Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:
Simplifying
2 + -3x = 0
Solving
2 + -3x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2
Combine like terms: 0 + -2 = -2
-3x = -2
Divide each side by '-3'.
x = 0.6666666667
Simplifying
x = 0.6666666667
Solution
x = {0.25, 0.6666666667}
2.) 5x^2-3x=2
We move all terms to the left:
5x^2-3x-(2)=0
a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=49−−√=7
x1=−b−Δ√2a=−(−3)−72∗5=−410=−2/5
x2=−b+Δ√2a=−(−3)+72∗5=1010=1