Find the length of BC
Answer:
53.68
Step-by-step explanation:
tan54 = bc/39
bc = 39tan54
Step-by-step explanation:
Hey there!
From the given figure;
Angle CAB = 54°
Side AC = 39
To find: side BC
Taking Angle CAB as reference angle;
Perpendicular (p) = BC = ?
Base (b) = AC = 39
Hypotenuse (h) = AB
Taking the ratio of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep value;
[tex] \tan(54) = \frac{bc}{39} [/tex]
Simplify it;
1.376381*39 = BC
Therefore, BC = 53.678.
Hope it helps!
identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)
Answer:
d. y+8=2(x-4)
Step-by-step explanation:
There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.
Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].
Evaluate 3|x|+2x-1 when x = -5.
Answer:
4
Step-by-step explanation:
To start off, we are going to input our x value into our expression.
3|-5| + 2(-5) - 1
Next, we are going to find the absolute value (always positive) of -5 and multiply 2 and -5.
3(5) - 10 -1
Now, we will multiply 3 and 5.
15 - 10 -1
Finally, we are going to combine our like terms (15, -10, and -1)
4
So! Our final answer for this expression is 4!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
What's the slope and y-intercept of the equation 4x + 2y = 8?
Question 13 options:
m = –2; b = –4
m = 2; b = 4
m = –2; b = 4
m = 2; b = –4
Answer:
m= - 2, b = 4
Step-by-step explanation:
structure of a linear equation
y = mx + c
m = gradient / slope
c = intercept
convert the given equation according to this structure of linear equations
4x+2y = 8
2y = -4x + 8
y = -2x +4
according to this intercept is 4 and slope is -2
Find the surface area of the rectangular prism below.
Answer:
Option B
Step-by-step explanation:
This is the formula :
2(wl+hl+hw)
Step 1 : Take the length, width, and height and substitute the values in.
The required surface area of the rectangular prism is 461.02 square meters (m²).
What is surface area?Surface area is defined as the measure of a region or surface is called as surface area.
The surface area of a rectangular prism can be calculated by adding up the areas of all six faces. The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Substituting the given values, we get:
Surface area = 2(12.3m x 4.3m) + 2(12.3m x 10.7m) + 2(4.3m x 10.7m)
Simplifying the expression gives:
Surface area = 461.02m²
Therefore, the surface area of the rectangular prism is 461.02 square meters (m²).
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ2
Which statement is correct?
Answer:
c is the answer why cause I did it
Given the function f ( x ) = { 6 x − 4 x < 0 6 x − 8 x ≥ 0 Calculate the following values: f ( − 1 ) = f ( 0 ) = f ( 2 ) =
Answer:
[tex]f(-1) = -10[/tex]
[tex]f(0) =- 8[/tex]
[tex]f(2) = 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x - 4[/tex] --- [tex]x < 0[/tex]
[tex]f(x) = 6x - 8<0[/tex] -- [tex]x \ge 0[/tex]
Solving (a); f(-1)
Here [tex]x= -1[/tex]
[tex]-1 < 0[/tex], so:
[tex]f(x) = 6x - 4[/tex]
[tex]f(-1) = 6 *-1 -4[/tex]
[tex]f(-1) = -10[/tex]
Solving (b); f(0)
Here [tex]x = 0[/tex]
[tex]0 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(0) = 6*0 - 8[/tex]
[tex]f(0) =- 8[/tex]
Solving (c) f(2)
Here [tex]x = 2[/tex]
[tex]2 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(2) = 6*2 - 8[/tex]
[tex]f(2) = 4[/tex]
please help me with this on the image
Answer:
200 grams
Step-by-step explanation:
80 grams x grams
-------------- = -------------
6 people 15 people
Using cross products
80 *15 = 6x
1200 = 6x
Divide by 6
1200/6 = 6x/6
200 =x
Quentin is one third the age of his aunt. And 20% older than his sister. If Quentin's sister is 15 years old, how old is his aunt?
Answer:
54
Step-by-step explanation:
20% of 15 is 3 so Quentin is 18 years old
If Quentin is one thrid his Aunt's age that means his aunt is three times older.
18 * 3 = 54
So his Aunt is 54 years old
The age of Quentin's aunt is 54 years if the Quentin is one third the age of his aunt if we solve by making the Quentin's Aunt age as variable x.
What is a equation?
An equation is a formula that expresses the equality of variables.
How to determine age of aunt?
let the age of the aunt is x years.
According to the question the age of Quentin is x/3 years.
The age of Quentin's sister is x/3*100/120
=5x/18
We have been given the age of Quentin's sister is 15 years.
So, 5x/18=15
=x=54 years
Hence the age of aunt is 54 years old.
Learn more about equations at https://brainly.com/question/2972832
#SPJ2
Find each question solutions.Please
Answer:
Dependent variable = Total daily cost
Independent variable = number of items manufactured
2500 ;
9750
Step-by-step explanation:
Given the cost function in. A manufacturing company :
C(x) = 7.25x + 2500 ; Where
C(x) = total daily cost
x = number of items manufactured
The Independent variable is the variable whose value causes a change in the measured variable, this is the number of items manufactured, and the variable which charges as the predictor variable charges is the dependent variable (Total daily cost).
2.)
C(0) ;
C(x) = 7.25x + 2500
Put x = 0
C(0) = 7.25(0) + 2500
Cost = 2500
This is the total daily cost even if no items are produced, this is probably the fixed cost of daily production.
3.)
C(1000)
C(x) = 7.25x + 2500
Put x = 1000
C(0) = 7.25(1000) + 2500
Cost = 7250 + 2500
Cost = 9750
This is the total cost including variable cost of producing 1000 items.
Find the measure of TU
A. 8
B. 12
C. 14
D. 11
Answer:
D. 11
Step-by-step explanation:
First apply the secant-secant theorem to find the value of x.
Thus,
VU(TU + VU) = VW(BW + VW) (secant-secant theorem)
Substitute
(7)(x + 4 + 7) = (9)(-2 + x + 9)
7(x + 11) = 9(7 + x)
7x + 77 = 63 + 9x
Collect like terms
7x - 9x = 63 - 77
-2x = -14
Divide both sides by -2
x = 7
✔️Find TU
TU = x + 4
Substitute get value of x
TU = 7 + 4 = 11
Answer:
11
Step-by-step explanation:
Prove: Quadrilateral ABCD is a parallelogram.
m∠AEB = m∠CED
Answer:
m∠ AEB = m∠ CED ......... By Vertical Angles Theorem.
Step-by-step explanation:
Vertical Angles Theorem: Vertical angle theorem states that vertical angles, angles that are opposite each other and formed by two intersecting lines, are congruent. If two lines intersect each other, we have the two pair of vertical opposite angles. As shown in the figure. Here, ∠ 1 and ∠ 2 are vertical opposite angles, and also they are equal. ∠ 3 and ∠ 4 are also vertical opposite angles, and also they are equal. For, step 3. m∠ AEB = m∠ CED Therefore, the reason for this proof is Vertical Angles Theorem.
Use the integral test to determine whether the series is convergent or divergent. [infinity] n = 2 n2 n3 + 1 Evaluate the following integral. [infinity] 2 x2 x3 + 1 dx
I think the given series is
[tex]\displaystyle\sum_{n=2}^\infty \frac{n^2}{n^3+1}[/tex]
You can use the integral test because the summand is clearly positive and decreasing. Then
[tex]\displaystyle\sum_{n=2}^\infty\frac{n^2}{n^3+1} > \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx[/tex]
Substitute u = x ³ + 1 and du = 3x ² dx, so the integral becomes
[tex]\displaystyle \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx = \frac13\int_9^\infty\frac{\mathrm du}u = \frac13\ln(u)\bigg|_{u=9}^{u\to\infty}[/tex]
As u approaches infinity, we have ln(u) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.
4 times a certain number less two times that's the same number is 10 what is the number
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
Four times the number= 4x
two times the same number= 2x
So we have ,
4x – 2x = 10
2x = 10
x = 5
Therefore the number is 5
plzzzzz helppp i will give brainlyist
Answer:
C. (2)
Step-by-step explanation:
an integer is a WHOLE NUMBER
have an amazing day :)
Answer:
2 is an integer
Step-by-step explanation:
An integer is a whole number, it does not have a fractional part
I need help answering this ASAP
can you zoom in on my pic more or no does it say 1/z
Answer:
Option A. Reciprocal
Answered by GAUTHMATH
Instructions: Find the missing length indicated.
Answer:
x = 65
Step-by-step explanation:
x = √(25×(25+144))
x = √(25×169)
x = 5×13
x = 65
Answered by GAUTHMATH
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft^2. Find the dimensions of the rectangle.
Answer:
7 x 4
Step-by-step explanation:
Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
p(X)=x²+50 then p(2)=
a) 6
b)7
c)8
d)9
Answer:
54
Step-by-step explanation:
p(x)=x^2+50, p(2)=2^2+50=54
P(x) = x² + 50
P(2) = 2² + 50
= 54
P(6) = 6²+50
= 86
P(7) = 7²+ 50
= 99
P(8) = 8²+50
= 114
P(9) = 9²+50
= 131
Answered by Gauthmath must click thanks and mark brainliest
the quotient of (x^4 - 3x^2 + 4x - 3) and a polynomial is (x^2 + x - 3) what is the polynormial
Answer:
Hello,
polynomial is x²-x+1
Step-by-step explanation:
if a=b*c+r then a=c*b+r
Using a long division, see the picture.
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
Jean drove 67 miles per hour for a total of 469 miles on a trip. She used the equation below to calculate the time, t, it would take her to complete the trip.
469 = 67t
What is the constant of proportionality in the equation?
A.
7
B.
67
C.
469
D.
t
9514 1404 393
Answer:
B. 67
Step-by-step explanation:
Miles are proportional to time at some speed. The constant of proportionality is the speed, 67 (miles per hour).
Find the difference between the result of one sixth of product of 10 and 3 multiplied by 4 and 30
Pleas helppppp ;_-((((((
Answer:
10 or -10,
Read the explanation
Step-by-step explanation:
Rewrite this problem as a numerical expression. As per the wording of this problem, there can be two expressions derived.
1. [tex]((\frac{1}{6}(10*3)*4)-30[/tex]
2. [tex]30-((\frac{1}{6}(10*3)*4)[/tex]
Simplify, remember the order of operations. The order of operations is the sequence by which one is supposed to perform operations in a numerical expression. This order is the following:
1. Parenthesis
2. Exponents
3. Multiplication or division
4. Addition or Subtraction
Use this sequence when simplifying and solving the expression:
Expression 1
[tex]((\frac{1}{6}(10*3)*4)-30\\\\=((\frac{1}{6}(30)*4)-30\\\\=(5*4)-30\\\\=20 - 30\\\\= -10[/tex]
Expression 2
[tex]30-((\frac{1}{6}(10*3)*4)\\\\=30-((\frac{1}{6}(30)*4)\\\\=30-(5*4)\\\\= 30-20\\\\= 10[/tex]
five sutracted from x is at most -21 translate the sentence into an inequality?
Which equation results from isolating a radical term and squaring both sides of the equation for the equation
Vc-2-vc=5
Answer:
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Required
Isolate radical, then square both sides
We have:
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Isolate radical
[tex]\sqrt{c - 2} = 5 + \sqrt c[/tex]
Square both sides
[tex](\sqrt{c - 2})^2 = (5 + \sqrt c)^2[/tex]
[tex]c - 2 = 25 + 2 * 5 * \sqrt c + c[/tex]
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. ASA Postulate
Answer:
ACB = JCB
Step-by-step explanation:
ASA means angle - (included) side - angle.
we have one angle confirmed.
we have the connected side BC confirmed (the diagram shows that the side is shared, so it is not only congruent, it is actually identical).
now we need confirmation for the angle at the other end point of that side.
help me with this please
An employee makes $11.20 per hour but is getting a 6.5% increase. What is his new wage per hour to the nearest cent? His new wage per hour is?
Answer:
11.93
Step-by-step explanation:
First find the amount of increase
11.20 *6.5%
11.20 *.065
0.728
Rounding to the nearest cent
.73
Add this to the original wage
11.20+.73
11.93
