The value of b that causes the system of equations to have infinite solutions is -6.
How to find the solution to the given system of equations?For that, we will try solving it first using the method of substitution in which we express one variable in another variable's form and then you can substitute this value in another equation to get a linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.
In the given problem, our equations are:
y = 6x + b
-3x + (1/2)^y = -3
So the value of b needs to be such that these two equations must be equal.
In the second equation:
[tex](1/2)^y = -3 + 3x\\y = -3^2 + 3x^2 \\y = -6 + 6x[/tex]
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is -6.
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Answer:
-6
Step-by-step explanation:
trust
Find the radius and circumference of a circle with an area of 28.26.
Answer:
Radius = 3
Circumference = 18.84
Step-by-step explanation:
A = πr²
28.26 = 3.14r²
√9 = √r²
3 = r
C = 2πr
C = (2)(3.14)(3)
C = 18.84
Find the value of xx, yy, and zz in the rhombus below
Answer:
(0,6), (0,4), (0,-10)
Step-by-step explanation:
#x
-3x+6+72=180-3x+78=180-3x=102x=-34.#y
-y+4=72-y=68y=-68#z
-z-10+72=180-z+62=180-z=118z=-118can someone do this for me please?! Just the answer pls
Answer:
1. Center: (-4,3) Radius: 4
2. C
3. C (x^2 + (y+4)^2 = 16)
4. 50 miles
Step-by-step explanation:
1. Look up how to read equations of circles
2.Soh Cah Toa
3. equations of circles again
4. Pythagorean Theorem
Choose the graph below that matches the equation: =2/3 + 5
It is TRUE, so shade on the SAME side as (0,0)
Giving 40 points!!! please help
Select the correct answer.
What are the solutions of this quadratic equation?
x²+4=8x+5
A.
x = 8 + √34
B.
* = 8 + 2√17
C.
x=4 ± √7
D. x=4 ± √17
Answer:
[tex]\textsf{D.} \quad x=4 \pm \sqrt{17}[/tex]
Step-by-step explanation:
Rearrange the equation so it equals zero:
[tex]\begin{aligned} x^2+4 & =8x+5 \\ \implies x^2+4-8x-5 & = 0\\x^2-8x-1&=0\end{aligned}[/tex]
Now use the quadratic formula to solve for x:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]a=1, \quad b=-8, \quad c=-1[/tex]
[tex]\implies x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(-1)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{8 \pm \sqrt{68}}{2}[/tex]
[tex]\implies x=\dfrac{8 \pm \sqrt{4\cdot 17}}{2}[/tex]
[tex]\implies x=\dfrac{8 \pm \sqrt{4}\sqrt{17}}{2}[/tex]
[tex]\implies x=\dfrac{8 \pm 2\sqrt{17}}{2}[/tex]
[tex]\implies x=4 \pm \sqrt{17}[/tex]
There are two numbers which add up to 17. if one number is 13 more than the other, find the two numbers.
Answer:
15, 2
Step-by-step explanation:
Number one: 15
Number two: 2
Well 15 is 13 more than two meaning this is correct.
By eliminating numbers, I was able to find a range of possible numbers which eliminated all the others. Then using that range I found out the number.
The first number is 2 and the second number will be 15.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
There are two numbers that add up to 17.
If one number is 13 more than the other.
Then the two numbers will be
Let the first number be x. Then the second number will be x + 13
x + x + 13 = 17
2x + 13 = 17
2x = 4
x = 2
The first number is 2 and the second number will be 15.
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Help. I will give brainliest if correct.
A. -4/3
B. -3/4
C. 10/17
D. 17/10
The correct option is option B.
The common difference between given data is -3/4.
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Here, given points;
x₁ = 1 , x₂ = 2 and y₁ = -3.75 , y₂ = -4.5
Now,
d = (y₂ - y₁)/(x₂-x₁)
d = (-4.5 - (-3.75))/(2 - 1)
d = -0.75 / 1
d = - 75/100
d = -3/4
Thus, The correct option is option B. The common difference between given data is -3/4.
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4/9 divided by 18/3 in math because i really don't know so can someone help me please
[tex]\left( \dfrac 49 \right) \div \left( \dfrac{18} 3 \right)\\\\\\=\dfrac 49 \div6\\\\\\=\dfrac 49 \times \dfrac 16\\\\\\=\dfrac{2}{9\times 3}\\\\\\=\dfrac{2}{27}[/tex]
Find the value of x.
x = [?]
Both (x−3)(x+3) and (3−x)(3+x) contain a sum and a difference and have only 3 and x in each factor. If each expression is rewritten in standard form, will the two expressions be the same? Explain or show your reasoning.
The expression is rewritten in standard form and they are not the same due to the negative.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Both (x−3)(x+3) and (3−x)(3+x) contain a sum and a difference and have only 3 and x in each factor.
Let see the equation formed by the factor;
(x−3)(x+3)
= x^2 + 3x - 3x - 9
= x^2 - 9
(3−x)(3+x)
= 9 + 3x - 3x - x^2
= 9 - x^2
The expression is rewritten in standard form and they are not the same due to the negative.
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Answer:
Step-by-step explanation:
What is the relationship between the values m and n plotted on the number
line below?
m
n
H
A. m = n
OB. m> n
OC. m
h
Answer:
C
Step-by-step explanation:
M is less than n because it comes before it in the number line
How many grams are there in 28 kilograms
DL is a perpendicular bisector of chord GA. Identify the diameter.
Solve-2x6x + 9.
A. x > -3
B. x < -5
OC. x>-5
D. x <-3
Step-by-step explanation:
please mark me as brainlest
Answer:
[tex]x < - 5[/tex]
Step-by-step explanation:
[tex] - 2x - 6 > x + 9[/tex]
[tex] - 2x - x > 9 + 6[/tex]
[tex] - 3x > 15[/tex]
[tex] \frac{ - 3x}{ - 3} > \frac{15}{ - 3} [/tex]
[tex]x < - 5[/tex]
harry invests £6000 in a savings account.
the account pays 3.4% compound interest every year.
after 3 years how much will his investment be
Step-by-step explanation:
here,
principal (p)=£6000
Rate (R)=. 3.4%
time (t)=3 yrs
now,
total investment is compound amount i.e CA
here,
[tex]CA = p(1 + \frac{r}{100} ) ^{t} [/tex]
=£6000(1+3.4/100)^3
=£6633.044
here he will get his total investment as £6633.044 in compound interest of 3.4%
PHOTO ATTACHED, please help ASAP, will give brainliest
Find the value of x that will make A||B.
5x + 9
A
B
Entor
6x-2
X =
= [?]
Answer: x=11
Step-by-step explanation:
Set the two equations equal to each other
5x+9 = 6x-2
9=x-2
11=x
x=11
X will need to be 11 in order to make the two equations equal to each other
Translate the shape A four squares right and two squares down.
please don't delete this question iltae668.
What are the coordinates of the vertices of the image?
Pls answer I will mark brainliest
Step-by-step explanation:
I hope this will help you
Answer:
198
Step-by-step explanation:
annie has some sweets. teddy gives her some sweets and she now has 50% more . rosie gives her some sweets and she now has an extra 40% . annie now has 63 sweets. how many did she have originally
Using proportions, considering the amount she received from each person, it is found that Annie had 30 sweets originally.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
Initially, she had n sweets.With the ones she got from Teddy, the amount became 1.5n.With the amount from Rosie, the amount became 1.4 x 1.5 x n.The final amount was of 63, hence:
1.4 x 1.5 x n = 63
n = 63/(1.4 x 1.5)
n = 30.
Annie had 30 sweets originally.
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Please help me!! High school algebra 2 math. Big Ideas Math.
Step-by-step explanation:
We know that,
[tex]\boxed{\sf \sin θ = \dfrac{Opposite \: side}{Hypotenuse}}[/tex]
[tex]\longmapsto \sf \sin 30^{\circ} = \dfrac{x}{12}[/tex]
[tex]\longmapsto \sf \dfrac{1}{2}= \dfrac{x}{12}[/tex]
[tex]\longmapsto \sf \dfrac{1}{2}×12= \dfrac{x}{12}×12[/tex]
[tex]\longmapsto \sf x = 6[/tex]
Answer:
x = 6
Step-by-step explanation:
Hello!
The missing angle is 60°, and is found by subtracting 90° and 30° from 180°.
Using basic triangle theorems of a 30° - 60° - 90° triangle, we know that the leg opposite to 30°, x, is one-half of the hypotenuse.
So:x = 0.5(12)x = 6.The value of x is 6.
The leg opposite to 60° is √3 times the leg opposite to 30°.
Jane earns an annual salary of £14000 and receives
a pay rise of 1.8%
Lenny earns an annual salary of £11000 and
receives a pay rise of 1.7%
Find which of the employees has the larger pay
increase and by how much.
The employee that has the larger pay increase is Jane. Her income is larger by £65.
Which employees has the larger pay increase?Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.
Increase in Jane's salary = £14,000 x 0.018 = £252Increase in Lenny's salary = £11,000 x 0.017 = £187Difference in increase = $252 - £187 = £65To learn more about percentages, please check: https://brainly.com/question/25764815
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The roof of a clock tower is a pentagonal pyramid. Each side of the base is 7 ft long. The slant height is 9 ft. What is the area of the roof?
Answer:
Area = 63ft
Step-by-step explanation:
7*9=63
multiply the base and height
157.5 square feet is the area of the roof.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the roof of a clock tower is a pentagonal pyramid.
a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point
Each side of the base is 7 ft long.
The slant height is 9 ft.
We need to find the area of the roof.
Area=1/2×7×9×5
=315/2
=157.5
Hence, 157.5 square feet is the area of the roof.
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Please help me I need it now please please please
Answer:
1st triangle: missing angle is 100
2nd triangle: missing angles are 50
3rd triangle: missing angle is 90, this is also a right triangle. The hypotenuse on this is the side length that reaches from angle 70 to 20. the other sides are legs
Step-by-step explanation:
4.5 (−6.2)??????
explanation: i'm slow
Answer:
0
Step-by-step explanation:
simplfy: 4.5(6.2) = 0
Multiply 4.5 * 6.2
27.9 = 0
and solve
27.9 = 0
I hope this helps ^^
Answer:
= -27.9
If you mean multiplication, [tex]4.5\times(-6.2)=-27.9[/tex].
The product is negative because the (-)6.2 is negative.
Step-by-step explanation:
HELPPPPPP ITS FOR MY FINALLLL
click the photo below
Answer:
28
Step-by-step explanation:
▪︎ ADE and ABC are similar triangles (AAA)
▪︎ DA = DB + BA = 30 + 12 = 42
▪︎ k = DA / BA = 42 / 12 = 3.5
▪︎ DE = BC * k = 8 * 3.5 = 28
A pre-school has 12 four-year old children and 11 three-year old children. What is the ratio of four-year old
children to three-year old children?
Answer:
12:11
Step-by-step explanation
Answer:
I think it would be 12:11
Step-by-step explanation:
This is because you can't down size the 11
answer dis plsss and explain too
Answer:
113.1 inches
Step-by-step explanation:
The area of a circle can be calculated using the formula [tex]\pi r^{2}[/tex], with r being the radius of the circle.
On this circle, the radius is 12 inches, making the area of the entire circle [tex]\pi 12^{2} =\pi 144[/tex], which is about 452.39.
The shaded area of the circle is 1/4 of the circle, so we use the equation [tex]\frac{452.39}{4}[/tex] to get an area of 113.1 inches.
Hope this helps! :)
The cost of 10 days at healthy gym
Solve for x.
(x−2)^2+2=38
x= ___ or x= ___
Step-by-step explanation:
[tex]( {x - 2)}^{2} + 2 = 38 \\ {x }^{2} + 4 - 2 {x}^{2} + 2 = 38 \\ x = 38 - 2 - 4 \\ x = 32[/tex]
is 23/100 a rational number
Answer:
YES
Step-by-step explanation:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers
- 23 and 100 are both integers
- 23 / 100 = 0.23 which is not a continious decimal
Answer:
Yes,it is.
Step-by-step explanation:
Rational numbers are usually expressed in fractions with both the numerator and denominator greater than zero