Answer: y = (x - 1) (7x + 5)
Step-by-step explanation:
y = 7x² - 2x - 5 Use the slip and slide method.
y = x² - 2x - 35 Factor
y = (x - 7) (x + 5) Slide 7 back in, divide -7 by 7 to get -1. Slip 7 into (x + 5).
y = (x - 1) (7x + 5)
The factorized form of the quadratic equation is y = (7x+5)(x - 1).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
To factor the quadratic function, we need to find two binomials whose product is equal to the given quadratic. Here's one way to factor y = 7x² - 2x - 5:
First, we need to find two numbers whose product is 7(-5) = -35 and whose sum is -2. These numbers are -7 and 5, since (-7)(5) = -35 and (-7) + 5 = -2.
Next, we use these two numbers to split the middle term of the quadratic:
y = 7x² - 7x + 5x - 5
Notice that we have a common factor of 7x in the first two terms and a common factor of 5 in the last two terms. We can factor these out to get:
y = 7x(x - 1) + 5(x - 1)
Now, we have a common factor of (x - 1), which we can factor out to get the factored form:
y = (7x + 5)(x - 1)
Therefore, the correct answer is: y = (7x+5)(x - 1).
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if cos^4+cos^2=1 prove that cot^4a-cot^2a=1
Step-by-step explanation:
We can solve this kind of trigonometric problem
easily by the followings method :
Given :
cos^4a + cos^2a = 1
or, cos4^a = 1 - cos^2a
Therefore; cos^4a = sin^2a
Again,
To prove: cot^4a - cot^2a = 1
L.H.S = Cot^4a - cot^2a
= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a
= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a
= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a
= 1 - cos^2a ÷ Sin^2a
= Sin^2a ÷ Sin^2a
= 1 = R.H.S proved.
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I’m having trouble understanding how to solve this someone please help ASAP thank you!
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this problem in order.
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Answer:
Answer is 71.95°
Step-by-step explanation:
Cosine formula is
a^2=b^2+c^2-2bc(cosA)
cos A =b^2+c^2-a^2/2bc
if a= 119,b=94,c=173
cos A=94^2+173^2-119^2/2(94*173)
=8836+29,929-14,161/2(16,262)
=38765-14,161/32,524
=24604/32,524
=0.7564
cos A=0.7564
cos^-1=40.85°.that's for angle A.
Using the same formula
B=31.1°
C=180-(40.85+31.1)
C=180-71.95
C=108.05
Since angle on a straight line is 180
therefore x is 71.95
Also the sum of angles A and B
12. How many grams is of of 800 g?
[tex] \frac{3}{8} [/tex]
of 800 g ?
Answer:
800
Step-by-step explanation:it's cuz g represents
Given the quadrilateral below is a rhombus, solve for the length of the side of the rhombus.
Answer:
7.21
Step-by-step explanation:
There is a formula to find the area of a side of a rhombus given 2 diagonals.
It is: [tex]\frac{\sqrt{p^{2}+q^{2} } }{2}[/tex]
64 + 144 = 208
[tex]\sqrt{208}[/tex] = 14.42
14.42 / 2 =
7.21
The circumference of a circle is 237 cm.
What is the area, in square centimeters?
Express your answer in terms of T.
Answer:
Circumference of a circle = 2 pie r
237 = 2 * pie * r
237 / 2 * Pie
118.5/ pie = r
118.5 = Pie*r
Area of circle = Pie *r²
= Pie r * r
= 118.5 * 118.5/ Pie
= 118.5 * 118.5 / pie
= 14042.25/ pie
taking value of pie = 3.14
= 4472.05 sq. cm
PLEASE HELP. FUNCTIONS AND RELATIONS. PROVIDE ANSWER OPTION A,B,C OR D? THANKS!!
Step-by-step explanation:
please mark me as brainlest
The additive inverse of an element of x of a set is the number, which when added to x gives the answer 0. In the set {-3, -2, -1, 0, 1, 2, 3}, what is the additive inverse of -2?
Answer:
2
Step-by-step explanation:
the additive inverse of - 2 is 2 , since
- 2 + 2 = 0
You’re planning to place an order from an online boutique. Leggings are $12 each and shipping is a flat rate of $5. Write an expression that represents the total cost of your order (not including tax) based on the number of leggings (l) you buy.
Answer:
For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.
Step-by-step explanation:
It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as
C = 12x + 5
This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.
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p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.
Step-by-step explanation:
If a variables varies jointly, we can just divide it by the other variables in relation to it.
For example, since p variables jointly as q and square of r, then
[tex] \frac{p}{q {r}^{2} } = k[/tex]
where k is a constant
First, let find k. Substitute p= 200
q= 2, and r=3.
[tex] \frac{200}{2(3) {}^{2} } = k[/tex]
[tex] \frac{200}{18} = k[/tex]
[tex] \frac{100}{9} = k[/tex]
Now, since we know our constant, let find p.
[tex] \frac{p}{q {r}^{2} } = \frac{100}{9} [/tex]
Q is 5, and r is 2.
[tex] \frac{p}{5( {2}^{2}) } = \frac{100}{9} [/tex]
[tex] \frac{p}{20} = \frac{100}{9} [/tex]
[tex]p = \frac{2000}{9} [/tex]
Find the distance-
Which shows the values inputted into the distance formula?
*See photo*
Answer:
A.
Step-by-step explanation:
As shown in the question we can interpret the following:
[tex]x_{1} = -2\\y_{1} = 1\\x_{2} = 5\\y_{2} = -4[/tex]
Now all we have to do is plug these values into the equation, and so we find that A. is the correct answer.
In the diagram Below
Answer:
∠UTC = 55°∠UCD = 70°∠BCT = 55°Step-by-step explanation:
In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.
__
UTC∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair
∠UTC = 180° -125° = 55°
__
UCD∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair
∠UCD = 180° -110° = 70°
__
BCT∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles
Can anyone help me with this
Fnd the value of x.
x = ?
Answer:
X=62 degrees
Step-by-step explanation:
The solution is in the image
Answer:
62°
Step-by-step explanation:
We know that the sum of the interior angles in a triangle is added up to 180°.
Therefore,
68.5° + 49.5° + x = 180°
118° + x° = 180°
x = 180° - 118°
x = 62°
Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.
D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.
Answer:
The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
The function g(x) = ∛(x -3) is positive at the interval x > 3
Complete questionGiven g(x) = ∛(x -3), on what interval is the function positive?
How to determine the positive interval?The function is given as:
g(x) = ∛(x -3)
Set the radicand to positive
x - 3 > 0
Add 3 to both sides
x > 3
Hence, the function is positive at the interval x > 3
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Jamar is attempting to factor the expression 15x^2-16x-15. In his first step, he rewrites the expression as 15x^2-25x+9x-15. Which of the following statements in true about Jamar’s work?
A. Jamar's first step is correct. He should continue to factor the expression.
B. The two middle coefficients add to the correct number, but do not multiply to the correct number.
C. The two middle coefficients multiply to the correct number, but do not add to the correct number.
D. The two middle coefficients do not add or multiply to the correct number.
Jamar's first step is correct. He should continue to factor the expression. Then the correct option is A.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
Jamar is attempting to factor the expression 15x² – 16x – 15.
In his first step, he rewrites the expression as 15x² – 25x + 9x – 15.
Jamar's first step is correct. He should continue to factor the expression.
Then the correct option is A.
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can someone please help mee
Answer:
x = -2y
y-intercept: ( 0, 0 ) and slope: [tex] \frac{1}{2} [/tex]
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)
Answer:
the graph of f(x)= -2-10x+16
Answer:
the vertex would be (-5,41)
Step-by-step explanation:
You just plug the -5 back into the equation to get 41
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. persons taking a 70-hour review course average a score of 780. based on these two data points, create a linear equation for the function that describes how score varies as a function of time. use this function to predict an average score for persons taking a 43-hour review course. round your answer to the tenths place.
Answer:
Answer for linear equation: y=4x+500 and Avg score for persons taking 43-hour review course is 672
x(3y - 2)
Multiply this problem
Answer:
3xy-2x
Step-by-step explanation:
Distribute x to both 3y and -2: 3y*x-2*x.
1. Decide if the following is a properly formed syllogism. If you are going to wrap Holly’s gift, you need wrapping paper. If you need wrapping paper, you have to go to the store. Therefore, if you go to the store, then you’re going to wrap Holly’s gift.
A) This is a syllogism.
B) This is not a syllogism.
This is not a syllogism. Hence option B is correct.
What is a syllogism?A logical structure for a formal argument that includes a major, minor, and conclusion.
This syllogism cannot be concluded without a given statement.
You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.
Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism
Hence option B is correct.
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Answer:
This is not a syllogism
Step-by-step explanation:
I took the quiz. :)
How do u solve 3/8+1/8-2/7+1/4
Answer:
13/28
Step-by-step explanation:
using pemdas we can determine that the equation is directly solves from left to right
so
first
we have
3/8 + 1/8
which is 4/8
you can simplify this to 1/2
then you have 1/2 - 2/7
you must make them have the same numerator
you can multiple 1/2 by 7/7 and 2/7 by 2/2
7/14 - 4/14 = 3/14
now you must add 3/14 and 1/4
but you to make them have the same numerator
so you multiply 3/14 by 2/2 and 1/4 by 7/7
6/28 + 7/28 = 13/28
that is your final answer
Please help me
Find the values of x and y
(12x +15)°=75° .…(शिर्षभिमुख कोण भएर)
or, 12x+15=75
or, 12x=75-15
or, 12x=60
or, x=60÷12
or, x=5
(6y-27)°=105° .…(शिर्षभिमुख कोण भएर)
or, 6y-27=105
or, 6y=105+27
or, 6y=132
or, y=132÷6
or, y=22
Can you solve these questions and explain them for me? Thank you
Step-by-step explanation:
When folding up the box, x will be the height
(30-2x) will be the length
(25-2x) will be the width so
[tex]v(x) = x(30 - 2x)(25 - 2x)[/tex]
b. First, we can't have negative length or zero length so x must be Positve.
Set the other binomial equal to 0.
[tex]30 - 2x > 0[/tex]
[tex] - 2x > - 30[/tex]
[tex]x < 15[/tex]
[tex]25 - 2x > 0[/tex]
[tex] - 2x > - 25[/tex]
[tex]x < 12.5[/tex]
So our domain is
(0,12.5), meaning our value of x must be greater than 0 and less than 12.5
Hi 6 questions ! They are practice so shouldn’t be to hard!
Please fine the slope through the given points
Answer:
1. 1
2. 6/5
5. 0
6. -1/2
9. -1
10. 0
Step-by-step explanation:
Well you should just the slope formula (y2-y1)/(x2-x1)
1. (8-5)/(0-(-3)) = 3/3 = 1
2. (-3-(-9))/(4-(-1)) = 6/5
5. (3 - 3) / (0-2.5) = 0/(-2.5) = 0
6. (0-(-4))/(0-8) = 4/(-8) = -1/2
9. (4-1)/(9-12) = 3/(-3) = -1
10. (7-7) / (1-(-5)) = 0/6 = 0
Which statement about the polynomial function g(x) is true?
1If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
2If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
3If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
4If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.
When leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
What is a Polynomial Function ?Functions of independent variable in which the variable can appear more than once with different powers.
[tex]\rm g(x) = a_n x^n + a_{n-1}x^{n-1} + ................+ a_o[/tex]
Let this represents the polynomial function
where [tex]\rm a_n \; is\;the \;leading \; coefficient \; a_o \; is \;the\;last \;term[/tex]
Then the according to rational root theorem ,
The root of the function is given by
[tex]\rm \dfrac{p}{q} = \dfrac{factor \;of\; the\; last\; term}{factor \;of \;the\; leading coefficient}[/tex]
So when leading coefficient is 1 , the root will be an integer for g(x) = 0
Option 4 is the right answer.
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Please help! Which of the following would result in an integer?
Answer:
B
Step-by-step explanation:
Cube root of 27 is 3, which is in integer
In which funtion is x=2 mapped to 32?
The function g(x)=4(x+3)² - 68 is mapped to 32.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given are the following functions:
f(x)= - 3x² - 4
g(x)= 4(x+3)²-68
f(x)= 3x
f(x)= 2x-62
To get the mapped function, we substitute the value of x in all function,
a) f(x)=-3x²- 4
Put x=2,
f(2)= -3 (2)² - 4
f(2)= -16
It is not mapped.
b) g(x)=4(x+3)² - 68
Put x=2,
g(2) = 4(2+3)² - 68
g(x) =32
It is mapped to 32.
c) f(x)=3x
Put x=2,
f(2) = 3 x 2 =6
It is not mapped.
d) f(x)=2x - 62
Put x=2,
f(2) =2x2 -62
f(2) = -58
It is not mapped.
Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.
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Students are selling T-shirts for a school fundraiser. The table shows the amount they raise from the T-shirt sales.
Shirts Sold 1 2 3 4
Amount Raised (dollars) 4 8 12 16
Complete each statement.
The amount raised ? proportional to the number of shirts sold.
is
is not
Answer:..
Step-by-step explanation: what is is not?
Answer:
1. is
2. amount raised, number of shirts sold
3. dependent, independent
4. 4
5. 4x
Step-by-step explanation:
A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?
I need some help on this one, anyone know?
The number of combinations will be 6 for even numbers.
What is the combination?The arrangement of the different things or numbers in a number of ways is called the combination.
Given that:-
A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?The total sample numbers are from 0 to 5 which are 0,1,2,3,4,5.
The even numbers are 0,2,4.
The combinations will be given by:-
C = 3!
C = 3 x 2 x1
C = 6
Therefore the number of combinations will be 6 for even numbers.
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A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there
Step-by-step explanation:
Ultimately we know:
Men = * 5
Women = * 2
Children =
We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.
Children - 41
Women - 41 x 2 = 82
Men - 41 x 5 = 205
205 + 41 + 82 = 328
So your answer is 41