The simplest form of the expression (x + 7)(3x − 8) is 3x² + 13x - 56
How to determine the simplest form of this expression?The expression is given as:
(x + 7)(3x − 8)
Expand the expression
3x² - 8x + 21x - 56
Evaluate the like terms
3x² + 13x - 56
Hence, the simplest form of the expression (x + 7)(3x − 8) is 3x² + 13x - 56
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100 POINTS SOMEONE PLEASE HELP
A fireman needs to get water to a second-floor fire. His ladder is 33 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest tenth of a degree and show all your work.
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 50°. Will the ladder be safe the way it is positioned? Explain.
Answer:
Answer:
(a) 64°
(b) Yes, it is safe
Step-by-step explanation:
A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.
We solve the above question using the trigonometric function of Sine
sin θ = Opposite side/Hypotenuse sides
θ = Angle formed with the ground = ?
Opposite side = 27 ft
Hypotenuse side = 30 ft
Hence,
sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9
θ = arc sin (0.9)
θ = 64.158067237°
Approximately to the nearest whole number = 64°
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?
From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°
Hence:
64° < 70°
Therefore, the ladder will be safe the way it is positioned.
Answer:
(a) 64°
(b) Yes, it is safe
Step-by-step explanation:
A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.
(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.
We solve the above question using the trigonometric function of Sine
sin θ = Opposite side/Hypotenuse sides
θ = Angle formed with the ground = ?
Opposite side = 27 ft
Hypotenuse side = 30 ft
Hence,
sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9
θ = arc sin (0.9)
θ = 64.158067237°
Approximately to the nearest whole number = 64°
(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?
From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°
Hence:
64° < 70°
Therefore, the ladder will be safe the way it is positioned
What is the volume (in cubic units) of a cylinder with a radius of 5 units and a height of 8 units? Assume that π = 3.14 and round your answer to the nearest tenth when necessary.
Answer:
V = hpir^2 = 12(3.14)(3)^2 = 108(3.14) = 339.1
Step-by-step explanation:
Interest is compounded semianually. Find the amount in the account after the given time.
Answer:
$1,159.69
Step-by-step explanation:
Compound Interest Formula :
A = P (1 + r/n)^(nt)A = amount P = principalr = rate (in decimals)n = number of times compoundedt = number of yearsSolving :
A = (1,000)(1 + 0.05/2)²⁽³⁾A = (1,000)(1.025)⁶A = (1,000)(1.15969342)A = $1,159.69Find the remainder of (h4+ h² - 2) /(h+3).
Answer:
remainder is 88
Step-by-step explanation:
if
[tex]h = 3[/tex]
[tex]f( - 3) = { ( - 3)}^{4} + { (- 3)}^{2} - 2[/tex]
[tex]f( - 3) = 88[/tex]
which is the remainder
Find the value of x in the parallelogram below.
Answer:
x = 25
y = 6
Step-by-step explanation:
In a parallelogram, opposite angles are equal.
2x and 50 are opposite angles,
2x = 50
Divide 2 on both sides,
x = 50 / 2
x = 25
In a parallelogram opposite sides are equal.
y + 5 and 11 are opposite sides,
y + 5 = 11
y = 11 - 5
y = 6
Answer:
x=25
y=6
Step-by-step explanation:
from the diagram,
2x= 50(opposite angles of a parallelogram)
2x= 50
dividing bothsides by 2
2x/2=50/2
x= 25
then,
y+5=11(opposite sides of a parallelogram)
y= 11-5
y= 6
-0.5 = - m/6=
First answer get to be brainliest!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\diamond\large\textsf{\textbf{\underline{Given question:-}}}[/tex]
-0.5=-m/6. what is m?
[tex]\diamond\large\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
❖ First, multiply both sides by 6 to get rid of the fraction:-
▪︎ -0.5*6=-m/6*6
On the RHS, the 6's cancel:-
◆-0.5•6=-m
Multiply:-➪ [tex]\it{-3=-m}[/tex]
Divide by -1 on both sides:-➪ [tex]\it{3=m}[/tex]
❒So we conclude that the value of m is 3.
✥ Good luck with your studies. ✥- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:
m = 3
Step-by-step explanation:
⇒ -0.5 = - m/6
Divide both sides by -1.
⇒ -0.5/-1 = -m/(6 × -1)
⇒ 0.5 = m/6
Multiply both sides by 6.
⇒ 0.5 × 6 = m/6 × 6
⇒ m = 3
The first three terms of a geometric sequence are as follows 80, 40, 20 what are the next 2 terms of the sequence
80 40 20 10 5
Step-by-step explanation: Divide 20 by 40 then 40 by 80 They all are divisible by .5so then times .5 to get the next terms
please help me I have been working on this for 20 minutes
Answer:
First Figure:
Do you see the right triangle in the first figure? It is bisected by the angle x° and 68°. Since all right triangles add to 90°, this makes x° = 90° - 68°.
E.) x° = 90° - 68° -----> x° = 22°
Do you see how you now know the values of 3 out of 4 angles on the straight line? Since all lines add to 180°, the value of y° = 180° - 90° - 22°. Remember, the entire angle value for all right triangles is 90°.
H.) y° = 180° - 90° - 22° -----> y° = 68°
Second Figure:
A similar process can be taken for the second figure.
T.) x° = 180° - 90° - 74° -----> x° = 16°
E.) y = 90° - 50° -----> y° = 40°
Third Figure:
Again, remember that right triangles = 90° and lines = 180°.
C.) w° = 180° - 90° - 31° -----> w° = 59°
R.) x° = 90° - 28° -----> x° = 62°
H.) y° = 180° - w° -----> y° = 180° - 59° -----> y° = 121°
Find the arc length of an arc with a Central angle of 2π/3 radians and a radius of 6 units
Answer:
Step-by-step explanation:
if u answered on the same 1 move on
help me i dont get this
The two-way table that shows the joint and the marginal relative frequencies is:
Aerobic Anaerobic Total
Male 0.48 0.63 0.55
Female 0.52 0.37 0.45
Total 1 1 1
How to make a two-way table from the frequency table?The table is given as:
Aerobic Anaerobic
Male 88 104
Female 96 62
The column total are:
Aerobic = 88 + 96 = 184
Anaerobic = 104+ 62 = 166
So, we have:
Aerobic Anaerobic
Male 88/184 = 0.48 104/166 = 0.63
Female 96/184 = 0.52 62/166 = 0.37
The total count of the table is
Total = 184 + 166 = 350
So, we have:
Aerobic Anaerobic Total
Male 0.48 0.63 (88 + 104)/350 = 0.55
Female 0.52 0.37 (96 + 62)/350 = 0.45
Hence, the two-way table that shows the joint and the marginal relative frequencies is:
Aerobic Anaerobic Total
Male 0.48 0.63 0.55
Female 0.52 0.37 0.45
Total 1 1 1
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Based on the number of males and females doing aerobic and anaerobic respiration, the relative and marginal frequencies can be shown as:
Aerobic Anaerobic Total
Male 47.8% 62.7% 54.9%
Female 52.2% 37.3% 45.1%
100% 100% 100%
What are the relative and marginal frequencies given?The frequencies for males are:
Aerobic = 88 / (88 + 96) Anaerobic = 104 / (104 + 62)
= 47.8% = 62.7%
For females:
Aerobic = 100% - 47.8% Anaerobic = 100 - 62.7%
= 52.2% = 37.3%
Total males frequency: Total females
= (88 + 104) / (88 + 104 + 96 + 62) = 100% - 54.9%
= 54.9% = 45.1%
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Let $a_1$, $a_2$, . . . , $a_{10}$ be an arithmetic sequence. if $a_1 + a_3 + a_5 + a_7 + a_9 = 17$ and $a_2 + a_4 + a_6 + a_8 + a_{10} = 15$, what is the value of $a_1$?
giving brainliest>
Because [tex]a_1[/tex] through [tex]a_{10}[/tex] are in arithmetic progression, there is some fixed number [tex]d[/tex] between consecutive terms. This means we have
[tex]a_2 = a_1 + d[/tex]
[tex]a_3 = a_2 + d = a_1 + 2d[/tex]
[tex]a_4 = a_3 + d = a_1 + 3d[/tex]
and so on, with the general [tex]n[/tex]-th term
[tex]a_n = a_1 + (n-1) d[/tex]
Then we can write each given equation in terms of [tex]a_1[/tex] and [tex]d[/tex] :
[tex]a_1 + a_3 + a_5 + a_7 + a_9 = 17[/tex]
[tex]\implies a_1 + (a_1+2d) + (a_1+4d) + (a_1 + 6d) + (a_1 + 8d) = 17[/tex]
[tex]\implies 5a_1 + 20d = 17[/tex]
and
[tex]a_2 + a_4 + a_6 + a_8 + a_{10} = 15[/tex]
[tex]\implies (a_1+d) + (a_1+3d) + (a_1+5d) + (a_1+7d) + (a_1+9d) = 15[/tex]
[tex]\implies 5a_1+25d= 15[/tex]
Eliminate [tex]d[/tex] and solve for [tex]a_1[/tex] :
[tex]5 (5a_1 + 20d) - 4 (5a_1 + 25d) = 5\times17-4\times15[/tex]
[tex]\implies 5a_1 = 25[/tex]
[tex]\implies \boxed{a_1 = 5}[/tex]
what is 300 in scintifiyc notation?
300 written in scientific notation is 3 × 102.
hope this was helpful.
Step-by-step explanation:
If a slice of pizza is 2 dollars and I have 15 dollars how many pieces of pizza can I get
what is the value of...
4x - x + 5, when x = 3
???
Answer:
The value of 4x-x + 5 when x + 3 is 14
Step-by-step explanation:
4(3)= 12 - 3= 9 + 5= 14
The value of 4x - x + 5 when x = 3 is 14.
To find the value of 4x - x + 5 when x = 3, we substitute the value of x into the expression and simplify.
Plugging in x = 3, we have:
4(3) - 3 + 5
Now let's simplify each term:
4(3) = 12
-3 = -3
Now we can substitute the simplified terms back into the expression:
12 - 3 + 5
Next, we perform the addition and subtraction in order from left to right:
12 - 3 = 9
9 + 5 = 14
Therefore, the value of 4x - x + 5 when x = 3 is 14.
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A taxi charges a flat rate of $2.00, plus an additional $3 per mile. If Erica has at most $20 to spend on the cab ride, how far could she travel? Write an inequality and solve
Answer:
6 miles
Step-by-step explanation:
20.00 - 2.00 = 18
18/3 = 6
she can travel 6 miles
Which expressions are equivalent to the given expression?
√80
80²
☐ 4√10
160²
8√5
4√5
Answer:
4 root 5
Step-by-step explanation:
√80 = √ 16 X √5
√16 = 4
so 4√5
1. what are the amounts of interest and maturity value of a loan for 250,000.00 at 5.5% simple interest for 4 months?
the amount of maturity is 254583
Double tap to add title • AC is the diameter of the circle. Angle AWB is 120 degrees. How big is arc BC? A 1200 B w c D 85
Answer:
Step-by-step explanation:
GIVING BRAINLIEST!!!!!
plane PBC is right answer.
it's a logical answer....
Answer:
Plane PBC
Step-by-step explanation:
Plane PBC contains 4 points : P, B, C, and Q.
The question asks which contains all three of C, Q, and P.
The plane is Plane PBC3 x 5/6 = ? x 1/6
those are fractions btw and what number makes the equation true?
PLEASE NO LINKS
Answer:
15
Step-by-step explanation:
[tex]3 \times \frac{5}{6} = \frac{15}{6} = 15 \times \frac{1}{6} [/tex]
Which expression is equivalent to startfraction 4 f squared over 3 endfraction divided by startfraction 1 over 4 f endfraction? startfraction 16 f cubed over 3 endfraction startfraction f over 3 endfraction startfraction 3 over 16 f cubed endfraction startfraction 3 over f endfraction
The value of the quotient expression [tex]\frac{4f^2}{3} \div \frac{1}{4f}[/tex] is [tex]\frac{16f^3}{3}[/tex]
What is quotient?The quotient of numbers or expressions is the division of a number or expression by another
How to determine the equivalent expression?The expression is given as:
[tex]\frac{4f^2}{3} \div \frac{1}{4f}[/tex]
Rewrite as a product expression
[tex]\frac{4f^2}{3} \times \frac{4f}{1}[/tex]
Evaluate the product of 3 and 1
[tex]\frac{4f^2}{3} \times 4f[/tex]
Evaluate the product of 4f^2 and 4f
[tex]\frac{16f^3}{3}[/tex]
Hence, the value of the quotient expression [tex]\frac{4f^2}{3} \div \frac{1}{4f}[/tex] is [tex]\frac{16f^3}{3}[/tex]
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Answer:
its A
Step-by-step explanation:
On edge its the first answer
solve the equation by completing the square. x²+6x-4=0
Answer:
x = √13 - 3
x = -√13 - 3
Step-by-step explanation:
Given :
x² + 6x - 4 = 0Solving :
x² + 6x + 9 - 9 - 4 = 0 [Adding and subtracting 9](x + 3)² - 13 = 0 [Group the square term together](x + 3)² -13 + 13 = 0 + 13 [Add 13 on both sides]√(x + 3)² = √13 [Taking square root on both sides]x + 3 - 3 = ±√13 - 3 [Subtract 3 from both sides]x = ±√13 - 3Solutions :
x = √13 - 3x = -√13 - 3a. If the swimming pool is 4 feet deep, what is the approximate volume of the swimming pool?
Answer:
64 ft³
Step-by-step explanation:
given that l = 4 ft
Since a swimming pool is like a cube
:- V= l³
V = 4³
V = 64 ft³
I NEED HELP!!!!
[tex]3(7+7i)+i(7+7i)[/tex]
Thanks!:)
Solve the equation:-
[tex]3(7 + 7i) + i(7 + 7i) \\take \: common \: (7 + 7i) \: out\\ (7 + 7i) (3 + i) \: is \: your \: answer [/tex]
Open the equation:-
[tex]3(7 + 7i) + i(7 + 7i) \\ 21 + 21i + 7i + 7 {i}^{2} \\ 7 {i}^{2} + 28i + 21 \: \: answer[/tex]
What is the approximate Volume of the cone below?
Answer:
B - 183 cm3
Step-by-step explanation:
volume of a cone is 1/3 x pi x r^2 x H
Answer:Your answer is going to be D
Step-by-step explanation:
1/3 x 3.14 x 10^2 x 7 =732.66
Ms. Wimbley surveyed the middle school and found out that 70 students want to go to sky zone for the end of the year field trip. This represents 14% of the middle school. How many students are in the middle school?
Answer:
500
Step-by-step explanation:
If 700 is 14%, then x=100%
We do:
700=14%
x=100%
Then, we cross multiply to get
14x=7000
We divide 14 on each side, and get x=7000/14 which is x=500
So there are 500 total students in the middle school
Hope this helped you! If the answer is wrong, please tell me and I will correct it. Also, I would appriceate if you gave me a Brainliest. It means a lot to me :D
find the missing length
Answer:
Step-by-step explanation:
15^2 - 12^2 = a^2
225 - 144 = 81
a^2 = 81
a=9
What is the product (1 – 6i) (-5 – 8i) ?
PLEASE HELP QUICK!!!!!f
Answer:
[tex]-53+22i[/tex]
Step-by-step explanation:
You can simply use the FOIL method, but keep in mind that [tex]i^2=-1[/tex]:
[tex](1-6i)(-5-8i)\\(1)(-5)+(1)(-8i)+(-6i)(-5)+(-6i)(-8i)\\-5-8i+30i+48i^2\\-5+22i+48(-1)\\-5+22i-48\\-53+22i[/tex]
Agree & disagree statements: CIrcles
Circle A has a diameter of 18 inches.
Circle B has a circumference of 36 inches.
write the letter of the card in the correct column next to the letter, write your explanation as to why it belongs in the agree or disagree columns.
1. Circle B has a radius of 18 inches. True or false?
2. Circle B has an area of approximately 103. 14in2. True or false?
3. The distance around Circle A is 20.5 inches longer than Circle B. True or false?
Answer:
1. False
2. True
3. true
Step-by-step explanation:
The first answer is false, the second one is true and the third is true
Find the Surface Area:
A) 200 in^2
B) 300 in^2
C) 500 in^2
D) 400 in^2
Answer: B
Step-by-step explanation: