Answer:
x = - 7, x = 5
Step-by-step explanation:
To find the zeros equate f(x) to zero, that is
x² + 2x - 35 = 0
To factorise the quadratic
Consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (+ 2)
The factors are + 7 and - 5, since
7 × - 5 = 35 and 7 - 5 = + 2, hence
(x + 7)(x - 5) = 0
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 5 = 0 ⇒ x = 5
ANSWER
[tex]x = - 7 \: or \: x = 5[/tex]
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} + 2x - 35[/tex]
To find the zeros, we equate the function to zero.
[tex] {x}^{2} + 2x - 35 = 0[/tex]
Split the middle term to obtain,
[tex]{x}^{2} + 7x - 5x- 35 = 0[/tex]
Factor by grouping:
[tex]{x}(x + 7) - 5(x + 7)= 0[/tex]
[tex](x + 7)(x - 5) = 0[/tex]
[tex](x + 7) = 0 \: or \: (x - 5) = 0[/tex]
.
[tex]x = - 7 \: or \: x = 5[/tex]
Please help I need it
There’s an app called Socratic it will help u with the steps
Question 1:
For this case we have to simplify the following expression:
[tex]\sqrt {54n ^ 7}[/tex]
We can rewrite the 54 as:
[tex]54 = 9 * 6 = 3 ^ 2 * 6[/tex]
In addition, we have to:
[tex]n ^ 7 = n ^ 6 * n[/tex] (According to the multiplication of powers of the same base)
Also, by definition of properties of powers and roots we have to:
\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})
Then, we can rewrite the expression as:
[tex]\sqrt {3 ^ 2 * n ^ 6 * 6 * n} =\\3n ^ 3 \sqrt {6n}[/tex]
Answer:
Option C
Question 2:
For this case we have by definition, that a perfect square is the result of multiplying a number by itself. Also, the perfect squares are the numbers that have exact square roots.
So:
2 and 10 are not perfect squares.
Answer:
Option A and D
Question 3:
For this case we must simplify the following expression:
[tex]\sqrt {75x ^ 2 * y ^ 4}[/tex]
We can rewrite the 75 as:[tex]75 = 25 * 3 = 5 ^ 2 * 3[/tex]
Also we have that by definition of properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ (\frac {m} {n})[/tex]
So, we rewrite the expression:
[tex]\sqrt {5 ^ 2 * x ^ 2 * y ^ 4 * 3} =\\5xy ^ 2 \sqrt {3}[/tex]
Answer:
Option B
You want to buy the biggest TV you can to fit into the space above your fireplace. The space where you want to put the TV measures 30 inches high and 43 inches wide. Given that television screens are measured by their diagonal distance across the screen, what size TV should you buy? Round to the nearest inch.
30^2+43^2= x^2
900 +1849= 2749
sqr root of 2749 = x
the answer is about 52 in.
The size of the TV will be equal to 52 inches.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.
Given that the space where you want to put the TV measures 30 inches high and 43 inches wide.
The size of the TV will be calculated as,
30²+43²= x²
900 +1849= 2749
√2749 = x
x = 52 inches
Therefore, the size of the TV will be equal to 52 inches.
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Enter the degree of the polynomial below .
the degree of the polynomial would be 10.
the degree of the above polynomial is (a)10
Need help with all of this please
Answer:
Step-by-step explanation:
In a right angled triangle, we have perpendicular, hypotenuse and base.
The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.
Applying formulas we can find the values:
the formulas are : cos (Ф) = Base / hypotenuse
sin (Ф) = Perpendicular / hypotenuse
tan (Ф) = Perpendicular / Base
11. cos z
cos z = Base / hypotenuse
cos z = 12/15
12. cos C
cos C = base / hypotenuse
cos C = 38/45
13. tan C
tan C = Perpendicular/ Base
tan C = 40/30
14. tan A
tan A = Perpendicular/ Base
tan A = 21/20
15. tan C
tan C = Perpendicular/ Base
tan C = 12/35
16. tan X
tan X = Perpendicular/ Base
tan X = 30/40
17. sin Z
Sin Z = Perpendicular / Hypotenuse
sin Z = 35/37
18. sin z = Perpendicular / Hypotenuse
sin z = 30/50
Figure GHTA below is a parallelogram. = 6 cm, = 8 cm, and the measure of = 60°. Find the area.
Answer:
The area of parallelogram GHTA is [tex]41.568 cm^2[/tex].
Step-by-step explanation:
Given parallelogram GHTA
GH = 8 cm =-AT
GA = 6 cm
∠ GAT =∠ GHT = 60°
To find = Area of parallelogram
Solution:
Draw perpendicular GO on the base AT.
In ΔGOA
[tex]\sin 60^o=\frac{GO}{GA}=\frac{GO}{6 cm}[/tex]
(sin 60°=0.8660)
GO = 5.196 cm
Area of the parallelogram: GO × AT
[tex]=5.196 cm\times 8 cm =41.568 cm^2[/tex]
The area of parallelogram GHTA is [tex]41.568 cm^2[/tex].
The answer would be D 48V3 cm ^2
the v is the root btw
The volume of a right circular cone is 2,279.64 in cubed. If the height of the cone is 18 in, what is the diameter of the cone? (Use pi = 3.14)
A. 22 in
B. 60.5 in
C. 11 in
D. 121 in
ANSWER
A. 22 in
EXPLANATION
The volume of a cone is calculated using the formula:
[tex]Volume = \frac{1}{3} \times \pi {r}^{2} h[/tex]
It was given that: the volume is 2,279.64 in³
The height of the cylinder is also given as: h=18 in.
We substitute, the given values into the formula to get:
[tex]2279.64= \frac{1}{3} \times (3.14) \times {r}^{2} \times 18[/tex]
[tex]2279.64= 18.84 {r}^{2} [/tex]
[tex] {r}^{2} = \frac{2279.64}{18.84} [/tex]
[tex] {r}^{2} = 121[/tex]
We take positive square root to get;
[tex]r = \sqrt{121} [/tex]
[tex]r = 11in[/tex]
Therefore the diameter is 2(11) which is equal to 22 inches.
twenty two percent of the large pieces of mail that Rachel received this week were magazines and the rest were catalogs. Of the catalogs, 36 percent were for clothing. To the nearest whole percent, what is the probability that a randomly chosen large piece of Rachels mail was a clothing catalog?
Answer:
28%
Step-by-step explanation:
78 x .36 = 28.08
Answer:
B. 28%
Step-by-step explanation:
Right on edge.
19)
Solve the quadratic equation x2 − 18x + 81 = 64 for x.
A)
x = 17 or x = 1
B)
x = 11 or x = −5
C)
x = 9 or x = −8
D)
x = 2 or x = 9
Answer:
{1, 17}
Step-by-step explanation:
x2 − 18x + 81 = 64 can be rewritten as x² - 18x + 81 = 64.
Next, x² - 18x + 81 can be rewritten as (x - 9)²
so that we now have:
(x - 9)² = 64.
Taking the sqrt of both sides, we get
x - 9 = ± 8
Then one root is x = 9 + 8 = 17, and the other is x = 9 - 8 = 1.
{1, 17} is the set of roots
Answer:
A.) x=17 or x=1
Step-by-step explanation:
Which expression is equivalent to -9-(-4 1/3)?
A. 9-(-4 1/3)
B. -9+4 1/3
C. -4 1/3-(-9)
D. -4 1/3 + (-9)
Answer:
B. -9+4 1/3
Step-by-step explanation:
If you distribute -1 to -4 1/3 and just bring down the -9, you'd end up with
-9+4 1/3.
The to this question is b I hope this is helpful
what is the quotient of these
Answer:
the answer is C
Step-by-step explanation:
x2−162x2−9x+42x2+14x+244x+4
=4x3+4x2−64x−644x4+10x3−70x2−160x+96
=2x3+2x2−32x−322x4+5x3−35x2−80x+48
=2(x+1)(x+4)(x−4)(2x−1)(x+3)(x+4)(x−4)
=2x+22x2+5x−3
Find the common ratio for the following sequence. 1/2, -1/4, 1/8, -1/16, ... - 2 - 2
Answer:
The common ratio for the given geometric sequence is -1/2.
Step-by-step explanation:
The common ratio in a geometric sequence is simply the number that multiplies one term to arrive at the next term. From the sequence given, we can let the common ratio be x and determine its value using any of the following set of equations;
1/2 * x = -1/4
-1/4 * x = 1/8
1/8 * x = -1/16
using the first equation;
1/2 * x = -1/4
we divide both sides by 1/2 to solve for x.
x = (-1/4)/(1/2)
x = -1/4 * 2
x = -1/2
Thus, the common ratio for the given geometric sequence is -1/2.
Answer:
Common ratio is -1/2
Step-by-step explanation:
Common ratio is the amount between each number in a geometric sequence.
It is called the common ratio because it is the same to each number.
Common ratio is the ratio between two successive numbers in a geometric sequence.
Common is a gotten by either division or multiplication.
Therefore in the case above
1/2 x -1/2 = -1/4 ......
-1/4 x -1/2 = 1/8 ......
1/8 x -1/2 = -1/16 ....etc
Therefore our common ratio is -1/2
A principal of $5,350 is placed in an account that earns 3.5% interest. If the interest is compounded annually, how much money will be in the account at the end of 4 years?
a.
$5,760.06
b.
$5,537.25
c.
$6,099.00
d.
$6,139.25
Please select the best answer from the choices provided
A
B
C
D
Answer:
Option D. [tex]\$6,139.25[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=4\ years\\ P=\$5,350\\ r=0.035\\n=1[/tex]
substitute in the formula above
[tex]A=\$5,350(1+\frac{0.035}{1})^{1*4}[/tex]
[tex]A=\$5,350(1.035)^{4}=\$6,139.25[/tex]
Final answer:
The future amount of money in the account after 4 years with annual compound interest is approximately $6,139.25, which is option D.
Explanation:
The student's question pertains to the calculation of compound interest over a period of 4 years on a principal amount at a given interest rate. To calculate compound interest, we use the formula A = P(1 + r)^n, where A is the total amount after n periods, P is the principal amount, r is the annual interest rate (as a decimal), and n is the number of years the money is compounded. Applying this formula:
P = $5,350 (the principal amount)
r = 0.035 (since 3.5% as a decimal is 0.035)
n = 4 (compounding for 4 years)
Using the formula:
A = $5,350(1 + 0.035)^4
A = $5,350(1.035)^4
A = $5,350 * 1.14888281
A ≈ $6,139.25
Thus, the amount of money in the account at the end of 4 years, with compound interest, will be approximately $6,139.25, which corresponds to option D.
Find the measure of angle 1
Answer:
38°
Step-by-step explanation:
Angles in a triangle add up to 180° and opposite angles are equal, therefore 180°-104°=76°
76°÷2=38°
I think this is correct :)
Answer:
The correct answer is <1 = 38°
Step-by-step explanation:
From the figure we can see a parallelogram.
Opposite angles of a parallelogram are equal.
To find the measure of <1
From the figure we get <1 + <2 = <3 + <4
<1 = <2
<1 + <2 + <3 + <4 = 360 - (2 * 104)
= 360 - 208 = 152
<1 + <2 = 152/2 = 76°
<1 = <2 = 76/2 = 38°
Therefore measure of <1 = 38°
Which is the range of the function f(x) = 1/7 (9)x
It looks incomplete, but all linear functions are going to have *ALL REAL NUMBERS*.
If one of the zero of polynomial x^2-4x+1 is 2+ root3 write the other zero
Answer:
2 - √3Step-by-step explanation:
If the polynomial is degree 2, then it has 2, 1 or 0 zeros.
If the polynomial is degree 2 and the zeros are 2 irrational numbers, then they are in the form a + b√c and a - b√c.
Therefore if one of the zero is 2 + √3, then the other zero is 2 - √3.
whats 8.99 rounded to 1 decimal place??
8.99 rounded to 1 decimal place is 9.0, since the number after the decimal is 9, which is 5 or over, hence, the rounding up.
Explanation:In mathematics, rounding means to replace a number with an approximate value that has a shorter, simpler, or more explicit representation. To round the number 8.99 to 1 decimal place, you need to look at the second number after the decimal point. Since that number is 9, which is 5 or over, we round up the first number after the decimal point, which is 8. Thus, 8.99 rounded to 1 decimal place is 9.0.
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Find equation of the line
Answer:
4, 1
Step-by-step explanation:
The equation of the given line in slope-intercept form, y = 4x + 1.
What is the Equation of a Line?If a line has a slope of m, and a y-intercept of b, the equation of the line in slope-intercept form is y = mx + b.
The slope of the line = rise/run = 8/2
Slope (m) = 4
The y-intercept (b) = 1
Substitute m = 4 and b = 1 into y = mx + b
y = 4x + 1
The equation is y = 4x + 1
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CAN ANYONE HELP ME WITH THIS PROBLEM!!!!!!! THANK YOU
Answer:
24 cubic feet
Step-by-step explanation:
The formula is V = Length x width x height
the first has a length of 2, a width of 2 and a height of 2 = 8 cubic feet
The second has a length of 4, a width of 2 and a height of 2 = 16 cubic feet
8 + 16 = 24 cubic feet
Write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3. Include all of your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution
ANSWER
[tex]y-1= \frac{1}{3} (x- 6)[/tex]
EXPLANATION
We want to write the point-slope form of the line that passes through (6, 1) and is perpendicular to a line with a slope of -3.
The slope of this line is negative reciprocal of -3.
[tex]m = - \frac{1}{ - 3} = \frac{1}{3} [/tex]
The point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point and the slope to get;
[tex]y-1= \frac{1}{3} (x- 6)[/tex]
Answer:
y - 1 = 1/3*(x - 6)
Step-by-step explanation:
point-slope form of a line:
y - y1 = m*(x - x1)
where x1 and y1 are the coordinates of the point included in the line and m is its slope.
Two lines are perpendicular when the multiplication of their slopes is equal to -1. In this case,
m*(-3) = -1
m = 1/3
Replacing this slope and the coordinates of point (6, 1) we get:
y - 1 = 1/3*(x - 6)
89, 81, 85, 82, 89, and 89. What is your grade to the nearest whole number
Answer:
86%
Step-by-step explanation:
For all values of x, which expression is equivalent to 9(2x+9)+2(2x+9)
Answer:
22x + 99
Step-by-step explanation:
Given
9(2x + 9) + 2(2x +9) ← factor out (2x + 9) from each term
= (2x + 9)(9 + 2)
= 11(2x + 9) ← distribute parenthesis
= 22x + 99
Here's two ways you can solve this exercise: you can expand the multiplications and sum like terms:
[tex]9(2x+9)+2(2x+9) = 18x+81+4x+18 = 22x+99[/tex]
Or you can factor the parenthesis:
[tex]9(2x+9)+2(2x+9) = (2x+9)(9+2) = 11(2x+9) = 22x+99[/tex]
What is the addictive inverse of the polynomial
Answer:
if p(x) is the given polynomial then -p(x) represents its additive inverse.
Step-by-step explanation:
We need to explain about what is the addictive inverse of the polynomial.
We know that additive inverse of a polynomial is basically another polynomial that adds to the given polynomial to give result 0.
which can be done by take opposite sign of each term in the given polynomial.
For example if p(x) is the given polynomial then -p(x) represents its additive inverse.
The square of a number is three times the number itself. What is the number?
x^2 = x3
x^2 - 3x = 0
x(x - 3) = 0
x = 0 and x -3 = 0 or x = 3
x cannot equal zero, therefore the answer is three
The numbers that when squared equal to three times themselves are 0 and 3. This is found by solving the quadratic equation x² = 3x, which factors to x(x - 3) = 0.
To express this mathematically, we let 'x' represent the number, so the equation becomes x² = 3x. This is a quadratic equation that can be solved by rearranging the terms and factoring, resulting in x(x - 3) = 0. Applying the Zero Product Property, we have two potential solutions for x: 0 or 3. Therefore, the numbers that fit the condition are 0 and 3.
need help click on me
The answers are: A and C
Write x^2 + 6x -7 in the form (x+a)^2 +b where a and b are integers please
Answer:
[tex](x + 3) {}^{2} - 16[/tex]
Step-by-step explanation:
[tex] {x}^{2} + 6x - 7 = (x + 3) {}^{2} - (3) {}^{2} - 7 \\ = (x + 3) {}^{2} - 16[/tex]
The equation x^2 + 6x - 7 can be written in the form (x+a)^2 + b as (x + 3)^2 - 16 by completing the square.
Explanation:To solve this, we will complete the square for the polynomial x^2 + 6x - 7. The equation (x+a)^2 + b involves squaring a binomial (x+a) and adding a constant. Completing the square can convert x^2 + 6x - 7 to this form.
Step 1: Half of the coefficient of x is (6/2)=3 so a=3. Then we square a to get a^2 = 9.
Step 2: We adjust the original equation by subtracting and adding a^2 within it: (x^2 + 6x + 9) - 9 - 7.
Step 3: Simplify the equation to get (x + 3)^2 - 16, which is the form we desired.
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Idk this please help me on this
Three sides adds up to 3ft squared.
Answer:18
Step-by-step explanation:I did the question and got it right
Mike biked 6 3/4 miles, and Noah biked 4 1/2 miles. How many times the length of Noah's bike ride was mike's bike ride? Please show the steps.
Thank you,
Answer:
1.5 times
Step-by-step explanation:
6.75/4.5 = 1.5
To find out how many times longer Mike's ride was than Noah's, you first need to convert the mixed fractions to improper fractions. Then you divide the length of Mike's ride by Noah's ride length. The result is 1.5, meaning Mike’s bike ride was 1.5 times longer than Noah’s.
Explanation:This problem falls under the category of division of fractions. The question is asking for how many times longer Mike's ride was than Noah's. In order to do this, we must divide the length of Mike's ride by the length of Noah's ride.
First, we convert the mixed fractions to improper fractions. Mike biked 6 3/4 = 27/4 miles, and Noah biked 4 1/2 = 9/2 miles.
To find how many times longer Mike's ride was than Noah's, we divide 27/4 by 9/2. This is equivalent to multiplying 27/4 by the reciprocal of 9/2 (which is 2/9).
When we perform this multiplication, we get (27/4) * (2/9) = (27 * 2) / (4 * 9) = 54 / 36. The result is 1.5, so this means Mike’s bike ride was 1.5 times longer than Noah’s bike ride.
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what is the square root of 104
Answer:
diabeties
Step-by-step explanation:
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The square root of 104 is approximately 10.198039, which can be confirmed using a calculator. It’s not a perfect square, so rounding it to 10.2 is often sufficient for practical purposes.
To find the square root of 104, we will use a calculator since it's not a perfect square. The square root of 104 is approximately 10.198039.
Here’s a step-by-step approach:
Understand that the square root of a number n is a value that, when multiplied by itself, gives n.Use a calculator to compute the square root of 104, which approximately equals 10.198039.We can confirm this by squaring 10.198039, which should approximately give us 104.The exact value includes more decimal places, so for most purposes, you can round it to an appropriate value, such as 10.2 for simplicity.
3a=9 What does a equal
Answer:
a=3
Step-by-step explanation:
3x3=9
Answer: a=3
Step-by-step explanation: 3*3=9
If y is directly proportional to x and y = 5 when x =2, what is the value of y when x=6
Answer:
y=15
Step-by-step explanation:
The formula for direct variation is
y = kx
5 =k*2
Solve for k
Divide by 2
5/2 = k
y = 5/2 x
Now we substitute x=6
y = 5/2(6)
y = 15
Answer:
y = 15
Step-by-step explanation:
If the variables are directly proportional, increasing one by a factor of 3 will mean the other one also increases by a factor of 3.
6 is 3 times 2, so the value of y will be 3 times 5, or 15.
___
You can write the relation as a proportion:
y/x = 5/2 = ?/6
Multiplying by 6 gives ...
(5/2)·6 = ? = 15
___
Or, you can bother with an equation relating x and y:
y = kx
5 = k·2 . . . plug in the given values and solve for k
5/2 = k . . . divide by 2
Then ...
y = (5/2)·6 = 15 . . . . same as the proportion, above.
If you rearrange this to y = 5·(6/2) then you see the relation described at the beginning of this solution. The new value of y is the old value multiplied by the factor by which x changes.