how do I get from step 3 to step four? please explain.
sin x = opposite over hypotenuse
sin 45° = 50 over x
0.707106781 ≈ 50 over x
(0.707106781)x ≈ 50
x ≈ 70.71
Factor completely: x2 + 6x + 8
* (x + 8)(x + 1)
* (x + 2)(x + 4)
* (x2 + 8)(x + 1)
* Prime
Answer:
(x+2)(x+4)
Step-by-step explanation:
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A group of children are asked whether they prefer vanilla or chocolate ice cream. The data are collected in the table.
How many ways can 6 students desks be arranged in a row permutation or combination?
The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than twice x. solve for x. Round to the nearest whole number.
Answer: The answer is actually 6.
Step-by-step explanation:
The value of x is 6, rounded to the nearest whole number.
To solve for x given the conditions:
1. Define the variables based on the problem:
- Length of the rectangle [tex](\( L \)) = \( x + 2 \)[/tex]
- Width of the rectangle [tex](\( W \)) = \( 2x - 5 \)[/tex]
2. Write the equation for the area of the rectangle:
- Area [tex](\( A \)) = \( L \times W \)[/tex]
- Given that the area is 56 cm², we have:
[tex]\[ (x + 2)(2x - 5) = 56 \][/tex]
3. Expand the equation:
[tex]\[ (x + 2)(2x - 5) = 2x^2 - 5x + 4x - 10 = 2x^2 - x - 10 \][/tex]
4. Set up the equation:
[tex]\[ 2x^2 - x - 10 = 56 \][/tex]
5. Move all terms to one side of the equation to set it to zero:
[tex]\[ 2x^2 - x - 10 - 56 = 0 \] \[ 2x^2 - x - 66 = 0 \][/tex]
6. Solve the quadratic equation using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\ where \( a = 2 \), \( b = -1 \), and \( c = -66 \).[/tex]
7. Calculate the discriminant:
[tex]\[ \Delta = b^2 - 4ac = (-1)^2 - 4(2)(-66) = 1 + 528 = 529 \][/tex]
8. Calculate the roots:
[tex]\[ x = \frac{-(-1) \pm \sqrt{529}}{2(2)} = \frac{1 \pm 23}{4} \][/tex]
So, the solutions are:
[tex]\[ x = \frac{1 + 23}{4} = \frac{24}{4} = 6 \][/tex]
and
[tex]\[ x = \frac{1 - 23}{4} = \frac{-22}{4} = -5.5 \][/tex]
Since x must be a positive value in the context of this problem, we have: x = 6
9. Verify the solution:
Length L = x + 2 = 6 + 2 = 8 cm
Width W = 2x - 5 = 2(6) - 5 = 12 - 5 = 7 cm
Area = [tex]\( 8 \times 7 = 56 \)[/tex] cm², which matches the given area.
Therefore, ( x = 6).
Figure A is reflected over the y-axis and then lowered 6 units. Which sequence describes these transformations.
Elizabeth rode her bike 6 1/2 miles from her house to the library and then another 2 2/5 miles to her friend Milo's house. If Carson's house is 2 1/2 miles beyond Milo's house, how far would she travel from her house to Carson's house?
Answer:
Step-by-step explanation:
11.4
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What is the scale factor when △RST is dilated to △R'S'T'? What is the value of x?
A. Scale factor 0.75, x = 8
B. Scale factor 0.75, x = 4.5
C. Scale factor 1.3, x = 8
D. Scale factor 1.3, x = 4.5
If h(x) = 6 - x, what is the value of ( h o h)(10)?
A line passes through the point , 8−1 and has a slope of −3/4 . Write an equation in slope-intercept form for this line.
Need help ASAP
Which statements are true? Select each correct answer.
40m^6−4=4(10m^6−1)
6m^2+18m=6m^2(1+3m)
32m^4+12m^3=4m^3(8m+3)
15m^3−6m=3m(5m^2−6m)
Marukh can wash the car in 10 minutes. steven can wash the car in 60 minutes. if marukh and steven work together, how long will it take them to wash the car? round your answer to the nearest minute.
Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?
i need help with adding and subtracting fractions
WHAT IS 3/8-3/9 ? I NEED TO SHOW MY WORK
PLEASE HELP ASAP!!!!! LOTS OF POINTS
Answer:
Your answer is D :)
Step-by-step explanation:
No explanation :) <3
Jordan needs 6 3/10 gallons of milk to make 4 1/2 gallons of ice cream. How many gallons of milk will jordan need to make one gallon of ice cream
Answer:
[tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream
Step-by-step explanation:
Using unitary method,
Unitary method is a method use to find the value of a unit quantity.
[tex]6\frac{3} {10}[/tex] gallon of milk needed to make [tex]4\frac{1}{2}[/tex] gallon of milk
[tex]\frac{63}{10}[/tex] gallon of milk needed to make [tex]\frac{9}{2}[/tex] gallon of ice cream
One gallon of ice cream needed = [tex]\frac{63}{10} \times \frac{2}{9}[/tex] gallon of milk
= [tex]\frac{7}{5}[/tex] gallon of milk
= [tex]1\frac{2}{5}[/tex] gallon of milk
Thus, [tex]1\frac{2}{5}[/tex] gallon of milk is needed to make one gallon of ice cream.
The population of a local species of dragon fly can be found using an infinite geometric series where a1=36 and the common ratio is 1/2 write the sum in sigma notation and calculate the sum that will be the upper limit of this population
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box.
central angle theta (in radians) = arc length / radius
So theta = 5.6/8 = 0.7 radians
The central angle measure for a circle with an 8 cm radius and a 5.6 cm intercepted arc length is 0.7 radians.
The question asks to find the measure in radians for the central angle of a circle with a radius of 8 cm and an intercepted arc length of 5.6 cm. To calculate the central angle in radians, we use the formula θ = [tex]\frac{l}{r}[/tex], where θ is the central angle in radians, l is the arc length, and r is the radius of the circle. Substituting the given values, we get θ = [tex]\frac{5.6}{8}[/tex]
Through calculation, θ = 0.7 radians. So, the measure of the central angle that intercepts an arc length of 5.6 cm in a circle with a radius of 8 cm is 0.7 radians.
The next number in the arithmetic sequence 15, 22, 29, ___ is:
A. 34
B. 35
C. 36
D. 37
In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposite to a shorter side.
Answer:
The answer is 72 degrees
Step-by-step explanation:
The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.
1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees
2. ∠ABD= ∠BDC = 36 - alternate interior angles
3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54
4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.
5. 180 - 54*2 = 72 degrees
I hope this helps!
will give brainliest for correct answer
Use the triangle pictured to calculate the following measurements.
Perimeter: p = ___ units Semiperimeter: s = ___units Area: A ≈ ___square
Perimeter is 30 units
Semi-perimeter is 15 units
The Area is 39.7 square units
Given the geometric sequence where a1 = 2 and r = √2 find a9
32
32√2
256
256√2
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
There is a geometric sequence:
where a₁ = 2
r = √2
We need to find a₉:
As we know the formula for "nth term ":
[tex]a_n=ar^{n-1}\\\\a_9=ar^{9-1}\\\\a_9=ar^8\\\\a_9=2\times (\sqrt{2})^8\\\\a_9=32[/tex]
Hence, First option is correct.
Celina says that each of the following expressions is actually a binomial in disguise:(Expressions in picture) For example, she sees that the expression in (i) it is algebraically equivalent to − , which is indeed a binomial. (She is happy to write this as + (−), if you prefer.) Is she right about the remaining four expressions?
All the given expressions are binomials except the expression in (i) which is a trinomial.
What are binomials in expressions?
Binomials can be defined as the expression that contains two variables that are different in terms.
ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴
= 10x⁵-10x⁴+3x⁵-6x⁵
= 7x⁵+10x⁴ (this is an example of a binominal)
iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)
iv.) 5(a-1)-10(a-1)+100(a-1)
= 5a-5-10a+10+100a-100
= 95a - 95 (binomials)
v.) (2πr-πr²)r-(2πr-πr²)2r
= 2πr²-πr³-4πr²+2πr³
= -2πr²+πr³(binomials)
The point of intersection of the lines has an e-coordinate of?
Jerry's beginning balance in his checkbook was $457.56. He made deposits of $20, $80, and $165 and wrote checks for $216.58. His bank charge was $3.50. What was his ending balance for the month? a. $552.10 b. $505.98 c. $722.56 d. $502.48
Which of the binomials below is a factor of this trinomial? 5x2 + 20x + 15
factor X + 1 is the answer
You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
answers :
a.using a paid membership card to buy it at a 10 percent discount
b.buying it online at a 10 percent discount with a $5 shipping charge
c.buying it at a 10 percent discount without sales tax
According to these three facts, which statements are true? - Circle D has center (2, 3) and radius 7. - Circle F is a translation of circle D, 2 units right. - Circle F is a dilation of circle D with a scale factor of 2.
A) Circle F and circle D are similar.
B) The center of circle F is (0, 3).
C) The radius of circle F is 28.
D) Circle F and circle D are congruent.
(Again, you can choose more than one option.)