Answer:
12.6 units.
Step-by-step explanation:
According to cosine formula:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Using cosine formula in triangle STU, we get
[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]
[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]
[tex]t^2=25+225-150(0.60)[/tex]
[tex]t^2=160[/tex]
Taking square root on both sides.
[tex]t=\sqrt{160}[/tex]
[tex]t\approx 12.6[/tex]
Therefore, the value of t is 12.6 units.
Chris purchased a tablet for $650. The tablet depreciates at a rate of $25 per month.
Write and simplify an equation that models the value V(m) of the tablet after m months.
Let d equal the final amount it depreciates.
Let m equal the number of months.
Since d is the final amount, we put this at the very end of the equation.
Since it depreciates $25 every month, this number is going to be subtracted from the total price of the tablet ($650).
The final equation comes out too: d = 650 - 25m
Best of Luck!
On March 20, Soren kierkegaard deposited $1000 into his savings account that pays 5.5% interest compounded daily. How much interest will the money earn by April 20?
Hey there! I'm happy to help!
There are 31 days in March, so there are 11 days left in March. We add this to the 20 days in April, giving us 31 total days this interest is compounded.
We could calculate the amount compounded each day for 31 total days, but that would take a long time. Instead, there is a formula we can use to calculate compound interest instead.
[tex]Total= P(1+i)^n\\\\P=Principal Amount\\i=interest rate\\\\n=number of times compounded[/tex]
So, let's plug in those numbers! Remember to convert the percent to a decimal so it works in the equation!
[tex]Total=1000(1+0.055)^3^1\\Total=1000(5.258068609)\\Total=5258.068609[/tex]
Now, we subtract the initial amount just to see how much interest was earned.
5258.068609-1000=4258.07 (rounded to nearest cent).
Therefore, the money will have earned $4,258.07 by April 20.
Have a wonderful day!
Please help I’m being timed!!! When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population. What is the significance of 160,000 in the function? A) the maximum population of the city B) the expected population in 5 years C) the initial population at the time of the estimation D) the amount of increase in the population in 5 years
The correct answer is C) The initial population at the time of the estimation
Explanation:
A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.
Answer:
yes the 3ed answer in correct on ENG 2022
Please help me!! I am struggling... I will not accept nonsense answers!
Answer:
y = 110°
Step-by-step explanation:
The inscribed angle CHF is half the measure of its intercepted arc CDF
The 3 arcs in the circle = 360°, thus
arc CDF = 360° - 160° - 60° = 140°, so
∠ CHF = 0.5 × 140° = 70°
∠ CHF and ∠ y are adjacent angles and supplementary, thus
y = 180° - 70° = 110°
Multiply the polynomial.
(X2+3)(x3-x2+4)
PLEASE HELP!!! ASAP!!!
Answer:
x⁵ - x⁴ + 3x³+ x² + 12Step-by-step explanation:
( x² + 3 ) ( x³ - x² + 4 )
Multiply the second parentheses by each term from the first parentheses
x² ( x³ - x² + 4 ) + 3 ( x³ - x² + 4 )
Distribute x through the parentheses
x⁵ - x⁴ + 4x² + 3 ( x³ - x² + 4 )
Distribute 3 through the parentheses
x⁵ - x⁴ + 4x² + 3x³ - 3x² + 12
Collect like terms
x⁵ - x⁴ + x² + 3x³ + 12
Use the commutative property to reorder the terms
x⁵ - x⁴ + 3x³ + x² + 12
Hope this helps..
Best regards!!
Answer:
x^5-x^4+3x^3+x^2+12
Step-by-step explanation:
Mulitply each term:
x^5-x^4+4x^2+3x^3-3x^2+12
Now simplify.
x^5-x^4+3x^3+x^2+12
I hope this helps....
Please mark me brainliest!!
5t - 3 = 3t - 5 : solve
Answer: -1
Step-by-step explanation:
[tex]5t-3=3t-5[/tex]
Add 3 to both sides.
[tex]5t=3t-2[/tex]
Subtract 3t from both sides.
[tex]2t=-2[/tex]
[tex]t=-1[/tex]
Hope this helps!
Answer: t=-1
Step-by-step explanation:
1) add 3 to both sides
2) subtract 3t from both sides
3) Divide both sides by 2
-2x-3=-9. What does x equal?
Answer:
x=3
Step-by-step explanation:
-2x-3=-9
Add 3 to each side
-2x-3+3=-9+3
-2x = -6
Divide by -2
-2x/-2 = -6/-2
x = 3
Answer:
x =3
Step-by-step explanation:
[tex]-2x-3=-9. \\ - 2x = - 9 + 3 \\ - 2x - 6 \\ \frac{ - 2x}{ - 2} = \frac{ - 6}{ - 2} [/tex]
[tex]x = 3[/tex]
Adult humans have approximately 2.6 red blood cells and 3.92 white blood cells. About how many times greater is the number of red blood cells than white blood cells?
Answer:
1.5 rounded to the nearest tenth
Step-by-step explanation:
To find how much greater WBC are from RBC we do,
3.92 ÷ 2.6
= 1.50769230769
Which is 1.5 rounded to the nearest tenth.
Thus,
there are approximately 1.5 times WBC than RBC.
Hope this helps :)
The 1.5 times greater is the number of red blood cells than white blood cells
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Adult humans have approximately 2.6 red blood cells and 3.92 white blood cells.
To find the number of times greater is the number of red blood cells than white blood cells:
Use division operation,
3.92 / 2.6
= 1.5076
≈ 1.5 rounded to the nearest tenth.
Therefore, the required number is 1.5 times.
To learn more about the division;
https://brainly.com/question/13263114
#SPJ5
Given: ∆ABC, m∠C = 90°
m∠BAC = 2m∠ABC
BC = 24 cm,
AL
− ∠ bisector
Find: AL
Answer: 16 units
Step-by-step explanation:
Given that in triangle ABC, m∠C=90,
it means m∠A +∠B= m∠BAC + m∠ABC = 90
m∠ABC = 90 - m∠BAC
Also given that;m∠BAC = 2m∠ABC
So,
m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC
m∠BAC +2m∠BAC = 180
3m∠BAC = 180
m∠BAC=180/3 = 60
m∠ABC = 60/3 = 30
thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,
AC=24/√3=8√3AL bisects angle A =>m∠LAC=30
ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16
can someone answer the underlined question? (number 9)
Answer:
Slope = -6/7
Step-by-step explanation:
You need to use the formula m = y2 - y1 ÷ x2 - x1
The formula means: slope = the y coordinate of point 2 subtract the y coordinate of point 1, divided by the x coordinate of point 2 subtract the x coordinate of point 1
So,
m = 2 - 5 ÷ 3/2 - (-2)
m = -3 ÷ 7/2
m = -6/7
Hope this helps :)
what is the midpoint of the segment shown below (2 2) (3 5) a. (5/2, 7/2) b. (5, 7) c. (5/2, 7) d. (5, 7/2)
Answer:
[tex]( \frac{5}{2} \: , \frac{7}{2} )[/tex]Option A is the correct option.
Step-by-step explanation:
Let the points be A and B
A ( 2 , 2 ) ------> ( x1 , y1 )
B ( 3 , 5 ) -------> ( x2 , y2)
Now, let's find the mid-point :
Midpoint = [tex] (\frac{x1 + x2}{2} \:, \frac{y1 + y2}{2} )[/tex]
plug the values
[tex] = ( \frac{2 + 3}{2} \: , \frac{2 + 5}{2} )[/tex]
Calculate the sum
[tex] = \: ( \frac{5}{2} \:, \frac{7}{2} )[/tex]
Hope this helps..
Best regards!!
a quadrilateral has angles measuring 56 degrees, 78 degrees, and 90 degrees. how large is the missing angle?
Answer:
Hey there!
Angles in a quadrilateral add to 360 degrees, so we have 56+78+90+x=360
Solving, we see that the missing angle, x, is 136 degrees.
Hope this helps :)
Answer:
Hey.... Ans is 154°
The mate who ans before me HAVE TO FIND x TOO
Step-by-step explanation:
For example take a quadrilateral ABCD (refer to the pic)
Then solution is...
In quadrilateral ABCD
Sum of all sides of a quadrilateral= 360°
=angle A + angle B+ angle C+ angle D=
Given,
Angle A= 56° + angle B=78° + angle C=90° + angle D=x
=56° + 78° + 90° + x. (add all the numbers)
x+226=360° (56+78+90=226)
x=360° - 226°
x=154°
Therefore the largest angle = x = 154°
Hope it helped u!!
If c cars can be parked in each of the four main rows of the parking lot, what is the expression gor the maximum number of cars that can be parked in the parking lot?
Answer:
4c
Step-by-step explanation:
We can say that the maximum number of cars can be represented as:
Maximum number of cars = Total of rows × Number of cars per row
In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:
Maximum number of cars = 4c
the three-dimensional shape that this net represents is _______. The surface area of the figure is _____ square centimeters.
Answer:
Shape - Cube
Area= 864
Step-by-step explanation:
The shape folds to become a cube and all the edges are the same size.
Area of a cube is Length * Width * Height = Area
12*12*12= 864
Answer:
Shape - Cube
Area= 864
Step-by-step explanation:
The shape folds to become a cube and all the edges are the same size.
Area of a cube is Length * Width * Height = Area
12*12*12= 864
what is the first step in writing f(x)=6x^2+5-42x in vertex form? a) factor 6 out of each term. b) factor 6 out of the first two terms. c) write the function in standard form. d) write the trinomial as a binomial squared.
Answer:
Answer c): write the function in standard form
Step-by-step explanation:
To start with, it is important to write the polynomial in standard form, so as to have the two terms with the dependence in x together:
[tex]6x^2-42\,x+5[/tex]
then you extract 6 as a common factor of just the terms with the variable x:
[tex]6(x^2-7x)+5[/tex]
Then proceed to complete the square in the expression inside the parenthesis:
[tex]6(x^2-7x+\frac{49}{4} -\frac{49}{4})+5[/tex]
[tex]6\,((x-\frac{7}{2} )^2-\frac{49}{4} )+5\\6\,(x-\frac{7}{2} )^2-\frac{147}{2}+5\\6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]
Then, the function can be finally be written as:
[tex]f(x)=6\,(x-\frac{7}{2} )^2-\frac{137}{2}[/tex]
in vertex form
Answer:
C.) Write the function in standard form
Step-by-step explanation:
Pls answer the image given
Answer:
[tex]4 \frac{1}{4} [/tex] hours
Step-by-step explanation:
Given,
Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours
Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours
Now, let's find the time that he spent in all:
[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]
Add the whole number and fractional parts of the mixed numbers separately
[tex](1 + 2)( \frac{3}{4} + \frac{1}{2} )[/tex]
Add the numbers
[tex]3 +( \frac{3}{4} + \frac{1}{2} )[/tex]
Add the fractions
[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]
[tex]3 + ( \frac{3 + 2}{4} )[/tex]
[tex]3 + \frac{5}{4} [/tex]
Convert the improper fraction into mixed number
[tex] 3 + 1\frac{1}{4} [/tex]
Write the mixed number as a sum of the whole number and the fractional part
[tex]3 + 1 + \frac{1}{4} [/tex]
Add the numbers
[tex]4 + \frac{1}{4} [/tex]
Write the sum of whole number and the fraction as a mixed number
[tex]4 \frac{1}{4} [/tex] hours
Hope this helps..
Best regards!!
Answer:
4 1/4 hours.
Step-by-step explanation:
1 3/4 + 2 1/2
= 1 + 2 + 3/4 + 1/2
= 3 + 3/4 + 1/2 The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:
3 + 3/4 + 2/4
= 3 + 5/4
= 3 + 1 1/4
= 4 1/4 hours.
two numbers have these properties, both numbers are greater than 8. Their highest common factor is 8. their lowest common mulitiple is 80
Answer:
16 and 40
Step-by-step explanation:
Hello,
We need to find the factors of 80
1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Which can be 2, 2, 2, 2, and 5 (these numbers would go into all the factor completely without any reminder.)
This leaves us with two numbers 2 and 5
If the highest common factor (H.C.F) of both numbers is 8
And the lowest common multiple (L.C.M) = 80
Multiply the numbers by the highest common factor (H.C.F)
2 × 8 = 16
5 × 8 = 40
The numbers are 16 and 40
help again plz.......
1. Find the cube root of the following through
estimation a) 300763 b) 704969 c)
( - 226981)
in which are perfect cube
Answer:
A).300763=+ 67
b) 704969= +87
c)( - 226981)= -61
Step-by-step explanation:
The values of the cube root iyf the given numbers above will be looked up in a calculator and the estimated value will be returned back.
Going through the numbers
A).for 300763
The value of the cube root = +67
B). For 704969
The value of the cube root = +89
C). For ( - 226981)
The value of the cube root= -61
In65 - lnX = 39
What does X=?
Answer:
The answer is 7.47Step-by-step explanation:
In this problem we are going find the natural logarithmic of the numbers involved and solve for x
[tex]ln65-Ln x= 39\\[/tex]
from tables
ln 65= 4.17[tex]4.17-ln x= 39\4.17-39= lnx\\-34.83=lnx\\[/tex]
taking the exponents of both sides we have
[tex]e^-^3^4^.^8^3= x\\x= 7.47[/tex]
What happens to the value of the expression 80-2r80−2r80, minus, 2, r as rrr decreases? Choose 1 answer: Choose 1 answer: (Choice A) A It increases. (Choice B) B It decreases. (Choice C) C It stays the same. Stuck?Watch a video or use a hint.
Answer:
(Choice B) B It decreases.
Step-by-step explanation:
According to the situation, the solution of the value of the expression is as follows
Let us assume
r 80 -2r
5 80 - 10 = 70
4 80 - 8 = 72
3 80 - 6 = 74
2 80 - 4 = 76
1 80 - 2 = 78
As we can from the above calculation that expression value risen if r value decreased
Therefore the correct option is B.
Answer:
It increases
Step-by-step explanation:
John has 14 boxes of apples. Each box holds 12 apples. If 6 of the boxes are full, and 8 of the boxes are half full, how many apples does John have?
Answer:
120
Step-by-step explanation:
12 x 6 = 72
8x(12/2)=48
72+48 =120
plzzz hellpppppp...........
Answer:
Bearing of R from S = S 45° E or 135°
The bearing of R from Q
= S 66.42° w or 246.42°
Step-by-step explanation:
Distance between R and S
RS²= RP²+PS²
RS²= 15²+15²
RS²=225+225
RS= √450
RS= 21.21
Angle at S
21.21= 15/sins
Sin s= 15/21.21
S= sin^-1 15/21.21.
S= 45°
90+45= 135°
Bearing of R from S = S 45° E or 135°
Distance between R and Q
RQ²= PQ²+PR²
RQ²= 35²+15²
RQ²=1225+225
RQ= √1450
RQ= 38.08
RQ= 15/sinQ
SinQ= 15/38.08
SinQ= 0.40
Q=23.58°
90-23.58 = 66.42°
66.42+180= 246.42°
The bearing of R from Q
= S 66.42° w or 246.42°
EF is a median of trapezoid ABCD. What is the value of x?
Answer:
x = 4
Step-by-step explanation:
The midsegment ( median is equal to half the sum of the parallel bases, that is
[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values
[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2
7x - 2 = 26 ( add 2 to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
please help ASAP. Create a quadratic inequality that has this solution: x ≤ -7 or x ≥ -1. Explain your strategy.
Answer: y ≤ x² + 8x + 7
Step-by-step explanation:
x ≤ -7 --> x + 7 ≤ 0
x ≥ -1 --> x + 1 ≥ 0
First, let's figure out the quadratic equation:y = (x + 7)(x + 1)
y = x² + 8x + 7
Next, let's figure out which inequality symbol to use:The quadratic is positive so it is U-shaped
x ≤ -7 and x ≥ -1
means the outside of the U-shaped parabola is shaded
so we need to use the ≤ symbol
Note: if the inequality symbols were reversed, the shading would be inside the U-shaped parabola so we would use the ≥ symbol.
In a school 3/5are boys. In a day 1/6 were absent and 250 boys were present. How many girls are in that school
Answer:
There are 200 girls in that school
Step-by-step explanation:
The correct and complete question is as folly;
In a school 3/5 pupils are boys. One day 1/6 of the boys were absent when 250 boys were present. How many girls are in the school?
SOLUTION
Let the total number of students in the school be x students
Since 3/5 are boys , then the number of girls in the school would be 1-3/5 = 2/5
The number of boys are 3/5 * x = 3x/5
The number of girls are 2/5 * x = 2x/5
Now on a particular day, 1/6 of the boys were absent and 250 boys were present.
What this means is that the fraction of boys present is 1-1/6 = 5/6
Now, 5/6 of the total boys population were present.
Mathematically;
5/6 * 3x/5 = 250
3x/6 = 250
x/2 = 250
x = 2 * 250 = 500
So there are 590 students in the school.
The number of girls in the school is ;
2x/5 = 2/5 * 500 = 200 girls
Use multiplication to solve the proportion
w/4 = 42/24
Answer: w=5
Step-by-step explanation:
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x = 1 x = negative 1 and x = 1 x = 0, x = negative 1, and x = 1
Answer:
x = 1
Step-by-step explanation:
Using the rules of logarithms
log [tex]x^{n}[/tex] ⇔ n log x
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
3[tex]log_{2}[/tex] (2x) = 3
[tex]log_{2}[/tex] (2x)³ = 3
(2x)³ = 2³
8x³ = 8 ( divide both sides by 8 )
x³ = 1 ( take the cube root of both sides )
x = 1
Answer:
x=1 is the correct answer
Step-by-step explanation:
got it right on edge!!!!
What’s a possible value of an integer that is less than 14 units from 29 but no more than or equal to 18
Answer:
15, 16, 17, 18
Step-by-step explanation:
29-14=15
15, 16, 17, 18 are less than or equal to 18
Rationalize the denominator of $\frac{2}{3\sqrt{5} + 2\sqrt{11}}$ and write your answer in the form $\displaystyle \frac{A\sqrt{B} + C\sqrt{D}}{E}$, where $B < D$, the fraction is in lowest terms and all radicals are in simplest radical form. What is $A+B+C+D+E$? PLEASE HELP ME I WILL DO ANYTHING
Answer:
19Step-by-step explanation:
Given the surdic expression [tex]\frac{2}{3\sqrt{5} + 2\sqrt{11}}\\[/tex], to rationalize the expression, we will have to multiply the numerator and denominator of the expression by the conjugate of the denominator as shown;
[tex]= \frac{2}{3\sqrt{5} + 2\sqrt{11}} * \frac{3\sqrt{5} - 2\sqrt{11}}{3\sqrt{5} - 2\sqrt{11}}\\\\= \frac{2(3\sqrt{5} - 2\sqrt{11})}{(3\sqrt{5} + 2\sqrt{11})(3\sqrt{5} - 2\sqrt{11})}\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9\sqrt{25}+6\sqrt{55}- 6\sqrt{55}-4\sqrt{121} } \\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{9(5)-4(11) }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{45-44 }\\\\= \frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex]
Comparing the result [tex]\frac{6\sqrt{5} - 4\sqrt{11} }{1}[/tex] with the expression [tex]\frac{A\sqrt{B} + C\sqrt{D}}{E}[/tex], it can be seen that A = 6, B = 5, C = -4, D = 11 and E = 1
A+B+C+D+E = 6+5+(-4)+11+1
A+B+C+D+E = 11-4+12
A+B+C+D+E = 19
Hence the value of A+B+C+D+E is 19