Answer:
[tex](x+5)(x+2)[/tex]
Step-by-step explanation:
[tex]\textbf{Given that,}\\\\~~~~x^2 +7x +10\\\\=x^2 +5x +2x +10~~~~~~~~~~~~~~~~~~~~;\textbf{Rewrite}~ 7x ~ \textbf{as}~ 5x +2x\\\\=x(x+5) +2(x+5)\\\\=(x+5)(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~;\textbf{Take out the common factor}~ x+5[/tex]
help i need for tomorrow
Answer:
The three bags for 92.50 pounds (offer B)
Step-by-step explanation:
Offer A:
[tex] \frac{35}{2 \times 25} = \frac{35}{50} = .7[/tex]
Offer B:
[tex] \frac{92.50}{3 \times 50} = \frac{92.50}{150} = .617[/tex]
Offer B has the lower unit price.
What is the solution to the system of equation
Answer:
[tex]x=(-2,\frac{5}{3} )[/tex]
Step-by-step explanation:
1) We will use the matrix method to solve this problem.
[tex]\left[\begin{array}{ccc}-2/3&1&3\\1&0&-2\\\end{array}\right][/tex]
2) Swap Row₁ and Row₂ to make row reduction easier.
[tex]\left[\begin{array}{ccc}1&0&-2\\-2/3&1&3\\\end{array}\right][/tex]
3) Apply to Row₂ : Row₂ + [tex]\frac{2}{3}[/tex] Row₁.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\end{array}\right][/tex]
4) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in row echelon form.
The steps below are for back substitution.
5) Apply Row₁ : Row₁ - 0 Row₂.
[tex]\left[\begin{array}{ccc}1&0&-2\0\\0&1&5/3\end{array}\right][/tex]
6) Simplify rows.
[tex]\left[\begin{array}{ccc}1&0&-2\\0&1&5/3\\\end{array}\right][/tex]
Note: The matrix is now in reduced row echelon form.
7) Therefore,
[tex]x=-2\\x=\frac{5}{3}[/tex]
4x² + 6x = 12
Solve by completing square
4x² + 6x = 12
We move all the terms to the left:
a = 4; b = 6; c = -12;Δ = b² - 4acΔ = 6² - 4 · 4 · ( -12 )Δ = 228The value of Δ is greater than zero, so the equation has two solutions
We use the following formulas to compute our solutions:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a }| \ x_{2}=\dfrac{-b+\sqrt{\Delta} }{2a } } \end{gathered}$}[/tex]
The end solution:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b-\sqrt{\Delta} }{2a}=\dfrac{-(6)-2\sqrt{57} }{2*4}=\dfrac{-6-2\sqrt{57} }{8} } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{x_{1}=\dfrac{-b+\sqrt{\Delta} }{2a}=\dfrac{-(6)+2\sqrt{57} }{2*4}=\dfrac{-6+2\sqrt{57} }{8} } \end{gathered}$}[/tex]
{ Pisces04 }Tanya planted seedlings in her garden over the weekend. The instructions that came with the seedlings stated that they need to be planted 0.2 meters apart. Tanya has a measuring tape that has values in centimeters. Help Tanya convert meters to centimeters.
Determine the ratio to use: .
Tanya should plant the saplings 20 centimeters apart.
1 meter is equal to 100 centimeters.
Multiply the given value by the ratio: .
i think they're supposed to be in order i cant figure it out, please help ToT!!
One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
As we know;-
1 meter is 100 cm so 0.2 meters will be calculated as:-
1 meter = 100 cm
0.2 meter = 0.2 x 100 = 20 centimeters.
Therefore One meter is 100 cm so Tanya should plant the saplings 20 centimetres apart.
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ABCD is a square. Triangle DEF is equilateral. Triangle ADE is isosceles with AD = AE. CDF is a straight line. Showing all your steps, calculate the size of angle AEF
Answer:
90°
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
in an equilateral triangle also all 3 angles are equal and therefore 180/3 = 60°.
angle EDF = 60°.
angle DEF = 60°
all angles in a square are 90°.
so, angle ADC = 90°.
and therefore, ADF = 90°.
the angle ADE is then 90-60 = 30°.
the triangle ADE is isoceles (both legs are equal, and both angles of the legs with the baseline are equal).
so, the angle AED = angle ADE = 30°
the angle AEF is then angles AED + DEF = 30 + 60 = 90°
Which ordered pair is included in the solution set to the following system?
y > x2 + 1
y < x2 – x + 1
(–3, 4)
(–2, 6)
(0, 2)
(2, 4)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The ordered pair which will satisfy both the inequalities will be the solution to the system of inequalities. Therefore, let's substitute each solution in the given inequalities,
A.) (–3, 4)
y > x² + 14 > (-3)² + 1
Since the first inequality is not satisfied this is not a part of the solution.
B.) (–2, 6)
y > x² + 16 > (-2)² + 1
6 > 5
y < x² – x + 16 < (-2)² - (-2) + 1
6 < 7
Since both the inequalities are satisfied this is the solution to the given system of inequalities.
C.) (0, 2)
y > x² + 12 > 0 + 1
2 > 1
y < x² – x + 12 < (0)² - (0) + 1
2 < 1
Since the second inequality is not satisfied this is not a part of the solution.
B.) (2,4)
y > x² + 14 > (2)² + 1
4 > 5
Since the first inequality is not satisfied this is not a part of the solution.
Hence, the correct option is B.
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Subtract the equations. Two-Variable Systems: Elimination
(screenshot of the question below)
Answer:
4x = 14
Step-by-step explanation:
7x + 2y = 17
– (3x + 2y = 3)
- - -
4x = 14
So, the correct option is A. 4x = 14
Hope it helps!
PLEASE HELP ASAP!!!!!!!1
Consider the series 1/4+3/2+11/4+4+21/4+....
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series _____ (diverges or converges). You Consider conclude this because the series is _________ (Arithmetic, Geometric and the absolute value of the common ratio is greater than 1, Geometric and the absolute value of the common ratio is less than 1, neither arithmetic nor geometric)
The series diverges. You Consider concluding this because the series is in arithmetic progression.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
where d is the difference and a₁ is the first term of the sequence.
The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,
The series diverges. You Consider conclude this because the series is in arithmetic progression.
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Which is the graph of y = 3√x+1-2?
Answer:
I'm not sure how to interpret "y = 3√x+1-2."
I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2
Step-by-step explanation:
Use the free online app DESMOS. Either enter the equation, or make a table of individual points and plot them as ordered pairs.
GRAPH: See attached image
PLOT: Calculate a few points, mark them on the graph and then connect the dots. I selected a few values of x and calculated y from the equation. Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected. Note that x values less than -1 result in a value of y that includes i, an imaginary number. So the graph ends abruptly at that point.
Sal's Sandwich Shop sells wraps and
sandwiches as part of its lunch specials. The
profit on every sandwich is $2 and the profit on
every wrap is $3. Sal made a profit of $1,470
from lunch specials last month. The equation
2x + 3y = 1,470 represents Sal's profits last
month, where x is the number of sandwich
lunch specials sold and y is the number of wrap
lunch specials sold.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Answer:
it will be something like that
Step-by-step explanation:
u should modify the equation to be
y = (1470-2x)/3
what is the answer in system form
y=-2x
5x-7y=-38
Answer:
x = -2
y = 4
Step-by-step explanation:
To solve the system of equations, you want to plug one equation into the other and then simplify. You can do this by setting one equation equal to a variable (like in the first equation), and then substituting the function into the variable into the second equation.
First Equation: y = -2x
Second Equation: 5x - 7y = -38
5x - 7y = -38 <----- Second equation
5x - 7(-2x) = -38 <----- Plug first equation into "y"
5x + 14x = -38 <----- Multiply -7 and -2x
19x = -38 <----- Add 5x and 14x
x = -2 <----- Divide both sides by 19
Now that you know the value of one variable, you can use it to find the value of the second variable. This can be done by plugging x = -2 in to one of the equations.
y = -2x <----- First equation
y = -2(-2) <----- Plug -2 in "x"
y = 4 <----- Multiply -2 and -2
Find the nth term of the sequence -2,6,14,22...
Answer:
[tex]\boxed{a_{n} = 2(4n - 5)}[/tex]
Step-by-step explanation:
Given :
⇒ a = -2
⇒ d = 14 - 6 = 8
Formula for nth term :
[tex]\boxed {a_{n} = a + (n-1)d}[/tex]
Solving :
⇒ aₙ = -2 + (n - 1)(8)
⇒ aₙ = -2 + 8n - 8
⇒ aₙ = 8n - 10
⇒ aₙ = 2(4n - 5)
Question 3 of 10
What else would need to be congruent to show that AABC= AXYZ by ASA?
B
A
C Z
Y
X
Given:
The nth term of a sequence is given by 3n²
What is the position of the term in the sequence that is the first one with a value greater than 1000?
The 19 th term of the sequence is the first term of the sequence having value greater than 1000.
Given that the n-th term of the sequence is given by,
[tex]a_n=3n^2[/tex]
Let the p-th term be the first term which have value greater than 1000 in the sequence.
The p-th term of the sequence is, [tex]a_p=3p^2[/tex]
According to the condition,
[tex]3p^2 > 1000[/tex]
[tex]\Rightarrow p^2 > \frac{1000}{3}[/tex]
[tex]\Rightarrow p > +\sqrt{\frac{1000}{3}}[/tex], as number of term cannot be negative so we ignore the negative value of square root here
[tex]\Rightarrow p > 18.25\\\Rightarrow p\geq19[/tex]
Hence the first term which has value greater than 1000 is 19 th term of the sequence.
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The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
PLS HELP
Answer:
x+(x+1)+(x+2)=42
3x+3=42
3x=42-3
3x/3=39/3
x=13
Step-by-step explanation:
hope I helped
A number is 5 more than 3 times another number. the sum of the two numbers is 33. as an equation, this is written x 3x 5 = 33, where x represents the smaller number. plug in the numbers from the set {3, 5, 7, 9} to find the value of x. the value of x that holds true for the equation is . so, the smaller number is and the larger number is .
Answer:
Step-by-step explanation:
Equation
x + 3*x + 5 =33
Solution
4x + 5 = 33
x = 3
4*3 + 5 =? 33
12 + 5 = ? 17 x is not 3
x = 5
4*5 + 5 = ? 33
20 + 5 = 25 x is not 5
x = 7
4*7 + 5 =? 33
28 + 5 = 33 x = 7 is the answer
The value of the variable x will be 7 that holds true for the equation.
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.
A number is 5 more than 3 times another number.
The sum of the two numbers is 33.
Let the number be x.
Then the another number will be 3x + 5.
Then the equation will be
x + 3x + 5 = 33
Then the value of x will be
4x + 5 = 33
4x = 28
x = 7
Then the value of the variable x will be 7 that holds true for the equation.
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Parent Functions
Question 4 of 10
On a piece of paper, graph:
{1 if -1 < x≤0
f(x) = {2 if 0 < x≤1
{3 if 1 < x≤2
Then determine which answer choice matches the graph you drew.
The graph of the parent function is given below;
What is Function?The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, the given function is;
1, if -1<x≤0
f(x) = 2, if 0<x≤1
3, if 1<x≤2
Now, the graph of given function is given below.
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Answer:
The correct graph is in the image below
Step-by-step explanation:
Please help me with my math
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for z and x ~
[tex]\qquad \sf \dashrightarrow \: 82 + z = 180[/tex]
[ they form co-interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: z = 180 - 82[/tex]
[tex]\qquad \sf \dashrightarrow \: z = 98 \degree[/tex]
and
[tex]\qquad \sf \dashrightarrow \: z = (5x - 82)[/tex]
[ by Alternate interior angle pair ]
[tex]\qquad \sf \dashrightarrow \: 98 = 5x - 82[/tex]
[tex]\qquad \sf \dashrightarrow \: 5x = 98 + 82[/tex]
[tex]\qquad \sf \dashrightarrow \: 5x = 180[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 180 \div 5[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 36 \degree[/tex]
Answer:
z = 98
x= 36
Step-by-step explanation:
z + 82 = 180 -> due to same side interior angles adding up to 180
z = 180 - 82
z = 98
z = 5x - 82 due to opposite interior angles being equal
98 = 5x - 82
98+82 = 5x - 82+82
180 = 5x
180/5 = 5x/5
36 = x
To check:
z = 5x - 82
(98) = 5(36) - 82
98 = 180 - 82
The ratio table shows the numbet of miles karen can drive for 1,2,3 and 4 gallons of gasoline.Based on the table, How far would she be able to drive on 8 gallons of gasoline
Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:
D(n) = 30n.
She has n = 8 gallons, hence the distance is given by:
D(8) = 30 x 8 = 240 miles.
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Triangle △ABC is reflected across line n to create △ A'B'C', What is the measure of ∠C?
The measure of ∠C is 54°.
To solve the problem :let us assume that line n is a mirror.
∴ ∠A = ∠A' = 59°
∠B = ∠B' = 67°
∠C = ∠C'
According to property of triangles :
Sum of all angles of a triangle is 180°.
∴ A + B + C = 180°
59 + 67 + C = 180
C = [tex]180 - (59 +67)[/tex]
C = 54°
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Answer:
54 degrees
Step-by-step explanation:
Helppppppppp plssssss
Part 1: complete the operations geometrically. vector operations to draw the resultant vector draw 2u + 4v.
Vectors are elements of the vector space, and they can be illustrated by diagrams.
How to draw the vector 2u + 4v?The vector expression is given as:
2u + 4v
Split the vector expressions, as follows:
y1 = 2u
y2 = 4v
Next, we have:
y = y1 + y2
See the attachment for the graph of 2u + 4v.
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Which transformation would be a horizontal reflection and a dilation of scale factor ½ of the L shape?
The transformation which would be a horizontal reflection and a dilation of scale factor ½ of the L shape is as in the attached image.
What is horizontal reflection and dilation?The term horizontal reflection with respect to transformation in mathematical context simple means that the shape is reflected over the vertical axis(y-axis as mirror). The dilation of a scale factor of ½ simply means that the shape reduces to half it's original size.
Hence, it follows that the attached image represents the transformation.
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Carl scored a total of 24 points by making 6 two-point baskets and some three-point baskets. Which equation can be used to find the number of three-pointers he scored, and how many three-point shots did Carl score?
A. 3p + 12 = 24
Carl made 12 three-point baskets.
B. 3p + 12 = 24
Carl made 4 three-point baskets.
C. p + 6 = 24
Carl made 18 three-point baskets.
D. p + 6 = 24
Carl made 30 three-point baskets.
Answer:
A.3p+12=24
Step-by-step explanation:
carl Made 12 three-pint baskets.
if each element in the input is mapped to one element in the output, then the relation is called as a
Answer:
function
Step-by-step explanation:
find the area and perimeter of the figures
Answer:
6x+6 or 4x+10
Step-by-step explanation:
hope u like it
Answer:
a) 196cm^2
b) 225cm^2
c) 180 cm^2
Step-by-step explanation:
a) The figure is a square, so you can use the formula: a = l^2, or area equals length of one side squared.
a = (14cm)^2
a = 196cm^2
b) a = (15cm)^2
a = 225cm^2
c) This one is a parallelogram, so it's trickier. However, we can imagine the figure as a rectangle by taking the small triangle that sticks out on the right and putting it into the gap in the left. Now, we can solve this using the formula for a rectangle: a = l x w.
a = l x w
a = 18cm x 10 cm = 180 cm^2
:)
In triangle ABC, what is the m
Answer: 38°
Using cosine rule,
a² = b² + c² -2bc cos(A)
Insert values from diagram
14² = 18² + 22.8² - 2(18)(22.8) cos(A)
196 = 324 + 519.84 - 820.8 cos(A)
-820.8 cos(A) = 196 - 324 - 519.84
-820.8 cos(A) = -647.84
cos(A) = -647.84/-820.8
A = cos^{-1} (-647.84/-820.8)
A = 37.88°
A ≈ 38°
Answer:
[tex]\boxed {38^{o}}[/tex]
Step-by-step explanation:
Applying Law of Cosines :
⇒ a² = b² + c² - 2bc(cos A)
⇒ 14² = 22.8² + 18² - 2(22.8)(18)(cos A)
⇒ 820.8(cos A) = 519.84 + 324 - 196
⇒ 820.8(cos A) = 647.84
⇒ cos A = 647.84/820.8
⇒ cos A = 0.789278752
⇒ m ∠A = cos⁻¹ (0.789278752)
⇒ m ∠A = 37.88 ≈ 38°
Which equation represents the line that is parallel to y= 3 and passes through (-2,-8) ?
Answer:
y = - 8
Step-by-step explanation:
y = 3 is a horizontal line that includes all of the x coordinates
just need to find parallel
y = - 8
a bag contains 4 white marbles , 7 red marbles , and 5 black marbles. you randomly select 3 marbles from the bag. without replacement.the random variable represents the number of black marbles
What is the factored form of the expression?
24g2 – gh – 10h2
The factored form of the expression is 2(g-h)(12g+5h)
What is a Quadratic Expression ?A quadratic Expression is what can be written in the form of
ax²+bx +c
The given quadratic expression is
24g² -gh -10h²
10g² - 10h² +14g² -gh
10(g+h)(g-h) +14 g(g -h)
(g-h)(10 g +10h +14g)
2(g-h)(12g+5h)
Therefore the factored form of the expression is 2(g-h)(12g+5h).
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