The given quadratic expression; 5b² -6b -2 is prime because the discriminant is not a perfect square.
What is the discriminant of the expression?According to the task content; it is required to identify if the expression is prime.
On this note, it follows that the discriminant of the expression can be evaluated as follows;
= 36 -(4× 5 × -2)
= 76.
Hence, the expression is prime since 76 is not a perfect square.
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Pencils cost $0.05. Notebooks cost $0.30. Henry spent $1.40. How many of each did he buy if he bought the same number of pencils and notebooks? A. 3 B. 4 C. 6 D. 8
Answer:
b) 4
Step-by-step explanation:
4 times $0.05 = $0.20
4 times $0.30 = $1.20
then you add the both totals together
0.20 + 1.20= $1.40
A triangle has vertices at (2, 3), (-4, 5), and (-3, 4). What are the coordinates of the vertices
of the image after the translation (x, y) (x + 1, y - 3)?
[tex](2,3) \longrightarrow (2+1, 3-3)=\boxed{(3,0)}\\(-4,5) \longrightarrow (-4+1, 5-3)=\boxed{(-3, 2)}\\(-3,4) \longrightarrow (-3+1, 4-3)=\boxed{(-2, 1)}[/tex]
How is the product of 3 and –2 shown using integer tiles?
3 positive tiles and 2 negative tiles.
3 negative tiles and 2 positive tiles.
3 sets of 2 negative tiles.
3 sets of 2 positive tiles.
let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²
Answer:
[tex]\dfrac a{b^2} + \dfrac b{a^2} = 10[/tex]
Step-by-step explanation:
[tex]\text{Given that, the roots are a,b and } ~ x^2 -4x+2 = 0\\\\\text{So,}\\\\a+b = -\dfrac{-4}1 = 4\\\\ab = \dfrac 21 = 2\\\\\text{Now,}\\\\~~~~~\dfrac a{b^2} + \dfrac b{a^2}\\\\\\=\dfrac{a^3 +b^3}{a^2b^2}\\\\\\=\dfrac{(a+b)^3 -3ab(a+b)}{(ab)^2}\\\\\\=\dfrac{4^3 -3(2)(4)}{2^2}\\\\\\=\dfrac{64-24}{4}\\\\\\=\dfrac{40}{4}\\\\\\=10[/tex]
Answer:
[tex]\dfrac{a}{b^2}+\dfrac{b}{a^2}=10[/tex]
Step-by-step explanation:
Given equation: [tex]x^2-4x+2=0[/tex]
The roots of the given quadratic equation are the values of x when [tex]y=0[/tex].
To find the roots, use the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
[tex]a=1, \quad b=-4, \quad c=2[/tex]
[tex]\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}[/tex]
[tex]\textsf{Let }a=2+\sqrt{2}[/tex]
[tex]\textsf{Let }b=2-\sqrt{2}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}[/tex]
Please help Urgently and need working out!
The table gives information about the height of some trees draw a histogram for the information of some trees
2.3+2.2y uneed to pus the 2 on the 3 and answer is uten
I don’t quite understand this problem could someone help me please
Answer:
[tex]\frac{7\sqrt{65}}{65}[/tex]
Step-by-step explanation:
Cosine is the ratio of the side adjacent to the angle and the right triangle hypotenuse.
[tex]cos[/tex] B = [tex]\frac{7}{\sqrt{65}}[/tex] = [tex]\frac{7\sqrt{65}}{65}[/tex]
Solve | 5+7= 17.
1
O A. x= 15 and x = -15
OB. x= -15 and x = -5
OC. x= -15 and x = 5
OD. x= 15 and x = -5
The solutions of the absolute value equation is determined as 15 and - 5.
Solution to the absolute equationThe solution to the absolute equation is determined as follows;
|x - 5| + 7 = 17
collect similar terms
|x - 5| = 17 - 7
|x - 5| = 10
to resolve the absolute values, form two equations as follows;
x - 5 = 10 and x - 5 = -10
x = 15 and x = -5
Thus, the solutions of the absolute value equation is determined as 15 and - 5.
The complete question is given as;
|x - 5| + 7 = 17
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7x-5=30
I need this explained for me please
Step-by-step explanation:
7x-5=30
Firstly -5 will cross the equality sign and become +5. so we'll have
7x=30+5=35
7x=35 we'll divide both sides by 7
giving u
7x/7=35/7
=x=5
therefore x=5.
CONFIRMATION
7*5-5=30
PLS MARK ME AS BRAINLIEST
Answer:
x = 5.Step-by-step explanation:
Solve for X:
7x - 5 = 30= 7 * x= 7(5)= 35 - 5= 30x = 5.Hence, answer is x = 5.answer the problem please
Answer: Point C is (-2, -2), which is the third option.
Step-by-step explanation:
The midpoint formula is [tex]m=(\frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2})[/tex]
All we have to do is plug in the numbers and solve the fractions from there.
[tex]m=(\frac{-10+6}{2},\frac{-6+2}{2} )[/tex]
[tex](\frac{-4}{2},\frac{-4}{2} )[/tex]
[tex]m=(-2, -2)[/tex]
I hope this helps!!
√324 + 6 √64
what is the answer to this question.
Answer:
66
Step-by-step explanation:
[tex]\sqrt{324} + 6 \sqrt{64}\\\\=\sqrt{18^2} +6 \sqrt{8^2}\\\\=18+6(8)\\\\=18+48\\\\=66[/tex]
Answer:
hmm
Step-by-step explanation:
not enough words to know u steal my points I steal yours kid
( - 37 + 37 ) ÷ - 15 = What is the answerr
Answer:
0
Step-by-step explanation:
[tex]~~~(-37+37 )\div(-15)\\\\=0\div (-15)\\\\=0[/tex]
Answer:
0
Step-by-step explanation:
Following PEMDAS -37+37 is 0 and 0/-15 is also 0
daniel wants to build a sandbox that has a perimeter or 20.5 ft. the length is 5.36 ft. what is the width of the sandbox?
Answer:
20.5 - 5.36
= 15.14/2 (because we are using perimeter, so there are 2 equal lengths and 2 equal widths)
=7.57, therefore the width of the sandbox is 7.57 ft.
Answer:
4.89 ft
Step-by-step explanation:
Perimeter of a rectangle is given by the formula :
P = 2L + 2W
So now we solve for W :
P = 2(L+W)
P/2 = L+W
P/2 - L = W
Now we substitute our P and L into the rearranged formula :
20.5 / 2 - 5.36 = W
10.25 - 5.36 = W
W = 4.89 ft
Hope this helped and brainliest please
Consider the linear system:
[tex]\overrightarrow y'=\begin{bmatrix}-6 & -4 \\12 & 8\end{bmatrix}\overrightarrow y[/tex]
a. Find the eigenvalues and eigenvectors for the coefficient matrix.
b. For each eigenpair in the previous part, form a solution of [tex]\overrightarrow y' = A\overrightarrow y[/tex]. Use [tex]t[/tex] as the independent variable in your answers.
c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions?
a. If A is the coefficient matrix, solve det(A - λI) = 0 for the eigenvalues λ :
[tex]\det\begin{bmatrix}-6-\lambda & -4 \\ 12 & 8-\lambda\end{bmatrix} = (-6-\lambda)(8-\lambda)+48 = 0 \implies \lambda(\lambda-2)=0[/tex]
[tex]\implies \lambda = 0, \lambda = 2[/tex]
Let v = [v₁, v₂]ᵀ be the eigenvector corresponding to λ. Solve Av = λv for v :
[tex]\lambda=0 \implies \begin{bmatrix}-6&-4\\12&8\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 3v_1 + 2v_2 = 0[/tex]
If we pick v₂ = -3, then v₁ = 2, so [2, -3]ᵀ is the eigenvector for λ = 0.
[tex]\lambda = 2 \implies \begin{bmatrix}-8&-4\\12&6\end{bmatrix}\begin{bmatrix}v_1\\v_2\end{bmatrix} = \begin{bmatrix}0\\0\end{bmatrix} \implies 2v_1 + v_2 = 0[/tex]
Let v₁ = 1, so v₂ = -2.
b. λ = 0 and v = [2, -3]ᵀ contributes a constant solution,
[tex]\vec y_1 = e^{\lambda t} v = \begin{bmatrix}2\\-3\end{bmatrix}[/tex]
while λ = 2 and v = [1, -2]ᵀ contribute a solution of the form
[tex]\vec y_2 = e^{\lambda t} v = e^{2t} \begin{bmatrix}1\\-2\end{bmatrix}[/tex]
c. Yes; compute the Wronskian of the two fundamental solutions:
[tex]W(1, e^{2t}) = \det\begin{bmatrix}1 & e^{2t} \\ 0 & 2e^{2t}\end{bmatrix} = 2e^{2t} \neq 0[/tex]
The Wronskian is non-zero, so the solutions are independent.
A line intersects the points (-5,1) and (-2,7). m=2 Write an equation in point slope form using the point (-5,1) y-[?] = ___(x-___)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-5)}}} \implies \cfrac{7 -1}{-2 +5}\implies \cfrac{6}{3}\implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{(-5)})\implies y-1=2(x+5)[/tex]
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
x > 64 and x < 68
x > 64 or x < 68
x < 64 and x < 68
x < 64 or x < 68
Answer:
answer is b
Step-by-step explanation:
because all you need to do is flip the signs.
Which equation matches the graph of the greatest integer function given
below?
Answer: is y=[x]-2
I used this app to help me get the answer too lol
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answer:
Last option, - 1 / 20
Step-by-step explanation:
log x + log (2x-1) = log 6
Answer:
x = 2
Step-by-step explanation:
logx + log(2x - 1) = log 6
Apply log rules,
x(2x - 1) = 6
2x^2 - 1x = 6
x = 2 (true) or x = -3/2 (False)
with full explanation from the internet like before
1/(x-5)+3/(x+2)=4
Solution :
[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
Step-by-step explanation:[tex] \frac{1}{(x - 5)} + \frac{3}{(x - 2)} - 4[/tex]
1. Multiply by LCM[tex]x = 2 + 3( x - 5) = 4 - (x - 5)(x + 2)[/tex]
2. Solve[tex]x = 2 + 3(x - 5) = 4 (x - 5)(x + 2)[/tex][tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]3.Verify SolutionsFind undefined (singularity) points : x=5,x=–2[tex]x = \frac{4 + \sqrt{43} }{2} .x = 4 + \frac{4 - \sqrt{43} }{2} [/tex]
[tex]\\ \rm\Rrightarrow \dfrac{1}{x-5}+\dfrac{3}{x+2}=4[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2+3x-15}{(x-5)(x+2)}=4[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x-5)(x+2)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x(x+2)-5(x+2))[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2+2x-5x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4(x^2-3x-10)[/tex]
[tex]\\ \rm\Rrightarrow 4x-13=4x^2-12x-40[/tex]
[tex]\\ \rm\Rrightarrow 4x^2-16x-53=0[/tex]
On solving we get
[tex]\\ \rm\Rrightarrow x=2\pm\dfrac{69}{2}[/tex]
The ratio of the one leg of
the right triangle to the other
leg of the right triangle must
be 8:7. Determine the
greatest length of one leg of
the right triangle given the
other leg of the right triangle
is 10.5 feet.
Answer:
12 ft
Step-by-step explanation:
We assume right triangle ABC with the right angle being at B. We are given that the ratio of AB/CB = 8/7, and one leg is 10.5. Let's call the other leg is X. We don't know which leg is which so assume both. Then
(a) assume the X leg is the longer
8 / 7 = X / 10.5
(8 * 10.5) / 7= X
X = 12
OR (b) assume the X leg is the shorter
8/7 = 10.5 / X
(8X / 7) = 10.5
8X = 10.5 * 7
8X = 73.5
X = 9.1875
(a) is the greater so (a) wins
he national government would like to start a program that would give states money for flood relief. Which of the following states could most likely benefit from a program like this? Idaho
Oklahoma
Wyoming
Mississippi
The state that would most likely benefit from this program is the Missippi state due to the incidence of floods.
What type of state would benefit the most?States constantly affected by floods would benefit the most.
What states are affected by floods?GeorgiaMissisippiIn the case of Mississippi state, the floods are caused by the Mississippi River.
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Round your answer to the nearest tenth if necessary. Use 3.14 for.
A pan for baking bread is shaped like half a cylinder. It is 16 inches long and 4.5 inches in diameter.
What is the volume of uncooked dough that would fill this pan?
4.5 in.
16 in.
The volume is approximately
in³.
just a little help
Answer:
127.17 in³
Step-by-step explanation:
V = (1/2)πr²h
(1/2)(3.14)(2.25 in)²(16 in)
(1/2)(3.14)(5.0625 in²)(16 in) = 127.17 in³
What is the volume of a cylinder with base radius 2 and height 9?
Answer:
V =113.09734
Step-by-step explanation:
[tex]V=\pi r^{2}[/tex]
[tex]= 2^{2}[/tex] x 9= 113.09734
(which you can technically round to 1)
=113.1
Which choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly?
19+43 = 62
19+11+32= 30+32 = 62
11+9+10+32 20+32 = 52
19+11+32 = 30 +43 = 73
The choice shows 19 + 32 + 11 rewritten correctly using the commutative property and then simplified correctly is option B; 19+11+32= 30+32 = 62.
What is the commutative property of addition?The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.
For two numbers x and y, we have:
x + y = y + x
WE have given
19 + 32 + 11
The sum would be 62.
We know that by commutative property of addition,
For two numbers x and y,
x + y = y + x
Thus, if we take 3 numbers as a,b and c, then:
c + a + b = c + b + a
Similarly,
19 + 32 + 11 = 19+11+32
= 30+32
= 62
Therefore, the option B is the correct answer.
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If f(x) = 2x + 3, what is f(–2)?
Substitute -2 for x
[tex]f( - 2) = 2( - 2) + 3 \\ y = - 4 + 3 \\ y = - 1[/tex]
Hope it helps
Please give brainliest
Answer:
-1
Step-by-step explanation:
Hi student! Let me help you out on this question.
_____________________
To find the value of f(-2), we need to stick in -2 for x.
[tex]\mathsf{f(-2)=2\cdot(-2)+3}[/tex]. Multiply first.
[tex]\mathrm{f(-2)=-4+3}[/tex]. Now simplify completely.
[tex]\mathsf{f(-2)=-1}[/tex]. Which is our final answer.
Hope that this helped you out! have a good day ahead.
Best Wishes!
[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]
◆◈-Greetings!-◆◈
__________________
Translate (13, 4) to the right 5 and up 2
Answer:
(18,6)
Step-by-step explanation:
add 5 units to X and 2 to Y
Click on the pic there will be the question (very easy I’m just lazy lol)
Answer: ......... 14.85
Step-by-step explanation:
4.95 × 3
...
14.85
bros lazy lol
In function notation, f(x)is used instead of the letter ___ to represent the __________ variable.
In function notation, f(x) is used instead of the letter y to represent the output variable.
How to complete the blanks?A function is represented as:
f(x)
The above means that:
The function of x
As a general rule, the function can be rewritten using the letter y (i.e. the output variable)
Hence, the words that complete the blanks are y and output
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FGH and HGJ form a linear pair. Find the measurement of the anglesif FGH=11x and HGJ+(6x-7)
The angles are 121 and 59 degrees, respectively
How to determine the angles?The given parameters are:
FGH = 11x
HGJ = 6x - 7
Linear pair angles add up to 180.
So, we have:
11x + 6x - 7 = 180
Evaluate the like terms
17x = 187
Divide both sides by 17
x = 11
Substitute x = 11 in FGH = 11x and HGJ = 6x - 7
FGH = 11 * 11=121
HGJ = 6 * 11 - 7 = 59
Hence, the angles are 121 and 59 degrees, respectively
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