Answer:
[tex] - 25 + ( - 18) \\ - 25 - 18 \\ = - 43[/tex]
hope this helps you....
For similar triangles, the side lengths are proportional. So, you can write a proportion relating the two pairs of vertical and horizontal side lengths. For the line y = 2x, a triangle can be drawn 2 units up and 1 unit right from the origin.
Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.
Answer:
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The corresponding vertical sides are y and 2
The corresponding horizontal lines are x and 1
so
The proportion is equal to
[tex]\frac{y}{2}=\frac{x}{1}[/tex]
an animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog. Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday. Nick found a record showing that there were a total of 34 cats and dogs on Wednesday. How many cats were at the shelter on Wednesday?
Answer:
There were 9 cats at the shelter on Wednesday.
Step-by-step explanation:
Given:
An animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.
Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday.
Nick found a record showing that there were a total of 34 cats and dogs on Wednesday.
Now, to find the number of cats at the shelter on Wednesday.
Let the number of cats be [tex]x[/tex].
And let the number of dogs be [tex]y[/tex].
So, total number of dogs:
[tex]x+y=34.[/tex]
[tex]y=34-x.[/tex]......( 1 )
As given animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.
Now, total money animal shelter spent on Wednesday:
[tex]3x+5.50y=164.50[/tex]
Putting the value of equation ( 1 ) in the place of [tex]y[/tex] :
⇒ [tex]3x+5.50(34-x)=164.50[/tex]
⇒ [tex]3x+187-5.50x=164.50[/tex]
⇒ [tex]187-2.50x=164.50[/tex]
Adding [tex]2.50x[/tex] on both the sides we get:
⇒ [tex]187=164.50+2.50x[/tex]
Subtracting 164.50 on both sides we get:
⇒ [tex]22.50=2.50x[/tex]
Dividing by 2.50 on both sides we get:
⇒ [tex]9=x[/tex]
⇒ [tex]x=9.[/tex]
The number of cats = 9.
Therefore, there were 9 cats at the shelter on Wednesday.
x^2-5x=14 solve for x
Answer:
x=7, -2.
Step-by-step explanation:
x^2-5x=14
x^2-5x-14=0
factor out the trinomial,
(x-7)(x+2)=0
zero property,
x-7=0, x+2=0,
x=0+7=7,
x=0-2=-2
Answer:
x = - 2, x = 7
Step-by-step explanation:
Given
x² - 5x = 14 ( subtract 14 from both sides )
x² - 5x - 14 = 0 ← in standard form
Consider the factors of the constant term (- 14) which sum to give the coefficient of the x- term (- 5)
The factors are - 7 and + 2, since
- 7 × 2 = - 14 and - 7 + 2 = - 5, thus
(x - 7)(x + 2) = 0
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 7 = 0 ⇒ x = 7
What is the value of log 7 343?–3 -1/3 1/3 3
Answer: 3
Step-by-step explanation:
Given :
[tex]Log_{7}[/tex] 343
We need to write 343 in index form of 7.
343 is the same as [tex]7^{3}[/tex] , replacing 343 with [tex]7^{3}[/tex] , we have
[tex]Log_{7}[/tex] [tex]7^{3}[/tex]
Recall one on the law of Logarithm :
[tex]Log_{a}[/tex][tex]b^{c}[/tex] can be written as c [tex]Log_{a}[/tex]b
So, [tex]Log_{7}[/tex] [tex]7^{3}[/tex] can be written as ;
3[tex]Log_{7}[/tex] 7
Also from the laws of Logarithms , [tex]Log_{a}[/tex] a = 1
so , Log_{7}[/tex] 7 = 1
The solution then becomes
3 x 1 = 3
Therefore :
[tex]Log_{7}[/tex] 343 = 3
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
X + 10y = 29
x - y = 7
Answer:
x = 9, y = 2
Step-by-step explanation:
Given the 2 equations
x + 10y = 29 → (1)
x - y = 7 → (2)
Subtracting (2) from (1) term by term will eliminate the term in x
(x - x) + (10y - (- y)) = (29 - 7), that is
11y = 22 ( divide both sides by 11 )
y = 2
Substitute y = 2 in either of the 2 equations
Substituting in (2)
x - 2 = 7 ( add 2 to both sides )
x = 9
A force of 200 N is exerted on
an object of mass 40 kg that is
located on a sheet of perfectly
smooth ice. Calculate the
acceleration of the object.
The acceleration of the object is 5 m/s^2
Step-by-step explanation:
Given
Mass of object = m = 40 kg
Force = F = 200 N
Newton's 2nd law states that:
[tex]F = ma[/tex]
As we have to find the acceleration
[tex]a = \frac{F}{m}[/tex]
Putting the values
[tex]a = \frac{200}{40}\\a = 5\ ms^{-2}[/tex]
The acceleration of the object is 5 m/s^2
Keywords: Force, acceleration
Learn more about force at:
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To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. Using the given force of 200 N and mass of 40 kg, we can determine that the acceleration of the object is 5 m/s^2.
Explanation:To calculate the acceleration of the object, we can use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
First, we need to determine the net force acting on the object. In this case, it is given as 200 N.Next, we need to determine the mass of the object, which is given as 40 kg.Using the formula: acceleration = net force / mass, we can substitute the given values to find the acceleration.Substituting the values, we get: acceleration = 200 N / 40 kg = 5 m/s^2.Therefore, the acceleration of the object is 5 m/s^2.
Learn more about Calculating acceleration here:https://brainly.com/question/32817533
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MNOP is a parallelogram. U is any point on side OP. Show that ar( MUN)= ar ( Δ △ PUM)+ar( UNO) △
Answer:
The Proof is below.
Step-by-step explanation:
Given:
[]MNOP is a Parallelogram
U is any point on side OP
To Show:
ar(Δ MUN)= ar ( Δ PUM)+ar (Δ UNO)
Proof:
Theorem:
If a triangle and parallelogram are on the same base and have the same altitude, the area of the triangle will be half that of the parallelogram.
If they have same altitude, they will lie between the same parallels.
Hence the area of the triangle will be equal to half that of the parallelogram.
Area of Parallelogram will be twice of Area of Triangle
∴ [tex]\textrm{Area of Parallelogram MNOP}=2\times (area\ of\ Triangle\ MUN)[/tex].............( 1 )
Also,
[tex]\textrm{Area of Parallelogram MNOP}=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
Substituting equation 1 we get
[tex]2\times Ar(MUN)=Ar(MUN) + Ar(PUM)+ Ar(UNO)[/tex]
[tex]2\times Ar(MUN)-Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]
[tex]Ar(MUN) = Ar(PUM)+ Ar(UNO)[/tex]...........Proved
the dollar bills below show the money that Sam has saved
Answer:
Can I please have more details on what your question is?
Step-by-step explanation:
Which expression represents 8 less than two times X?
OA) 2x - 8
OB) 8 - 2x
OC) 8x - 2
OD) 2-8x
Answer:
Therefore the expression is option A)
[tex]2x-8[/tex]
Step-by-step explanation:
Given:
Statement as ' 8 less than two times X'
To Find :
Expression for the statement
'8 less than two times X'
Solution:
[tex]Two\ times\ 'x'\ means=2\times x[/tex]
Now 8 less than two times X means Subtract 8 from '2x'
[tex]2x-8[/tex]
Therefore the expression is option A)
[tex]2x-8[/tex]
Does somebody know how to do this?
Answer:
Total length of running track is 371.24 m .
Step-by-step explanation:
Total running track = Running track around straight region + running track around curved region.
Running track around straight region = 2 × length of straight region
= 2×82 m
= 164 m
Running track around curved region = 2 × length of curved region
= 2 × π × radius of curved region
= 2 × 3.14 × 33 m
= 207.24 m
Therefore , total length of running track = 164 + 207.24 m
= 371.24 m
Given: △ABC, AB=5 sqrt 2 m∠A=45°, m∠C=30° Find: BC and AC will give brainliest!!! By the way the answer is not 5 and 3.66
Answer:
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
Step-by-step explanation:
Consider a Δ ABC with
m∠ A = 45°
m∠ C = 30°
AB = c = 5√2
To Find:
BC = a = ?
AC = c = ?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\\\\45+30+\angle B=180\\\ttherefore m\angle B =180-75=105\°[/tex]
We know in a Triangle Sine Rule Says that,
In Δ ABC,
[tex]\frac{a}{\sin A}= \frac{b}{\sin B}= \frac{c}{\sin C}[/tex]
substituting the given values we get
[tex]\frac{a}{\sin 45}= \frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}[/tex]
∴ [tex]\frac{a}{\sin 45}= \frac{5\sqrt{2} }{\sin 30}\\\\a=\sin 45\times \frac{5\sqrt{2} }{\sin 30}\\\\a=\frac{1}{\sqrt{2} }\times \frac{5\sqrt{2} }{0.5} \\\\\\a=\frac{5}{0.5} =10\\\therefore BC = a = 10\ units[/tex]
Similarly for 'b',
[tex]\frac{b}{\sin 105}= \frac{5\sqrt{2} }{\sin 30}\\\frac{b}{0.9659}= \frac{5\sqrt{2} }{0.5}\\\\b=0.9659\times \frac{5\sqrt{2} }{0.5}\\\\b=\frac{6.8301}{0.5} \\\\b=13.66\\\therefore AC = b =13.66\ units\\[/tex]
Therefore,
[tex]BC=a=10\ units\\\\AC=b=13.66\ units[/tex]
By using the Law of Sines, side BC of the triangle is found to be approximately 10 m, and AC is approximately 8.66 m. These calculations take into account the given lengths and angles of triangle ABC.
Explanation:To find the lengths of sides BC and AC in triangle ABC with given angles and side AB, we will employ trigonometry and the properties of triangles. Since the sum of the angles in any triangle is 180 degrees, we know that m∠B = 180° - 45° - 30° = 105°. With this information, we can use the Law of Sines, which states:
[tex]\(\frac{AB}{\sin(C)} = \frac{BC}{\sin(A)} = \frac{AC}{\sin(B)}\)[/tex]
From the given, AB = 5√2 m, m∠A = 45°, and m∠C = 30°, we know that:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{BC}{\sin(45°)}\)[/tex]
[tex]Knowing \ that\ \(\sin(30 ) = 0.5\) and \(\sin(45) = \frac{\sqrt{2}}{2}\), we can find BC:[/tex]
[tex]BC = \(\frac{5\sqrt{2}}{0.5} \times \frac{\sqrt{2}}{2}\) = 5√2 \times \sqrt{2} = 10 m[/tex]
Now, to find AC, we set up the ratio:
[tex]\(\frac{5\sqrt{2}}{\sin(30°)} = \frac{AC}{\sin(105°)}\)[/tex]
Solving for AC, we get:
[tex]AC = 5\sqrt{2} \times \frac{\sin(105°)}{0.5}[/tex]
Since \(\sin(105°)\) is not a standard angle, we can use the sine sum identity where [tex]\(\sin(105) = \sin(60 + 45\),[/tex]which gives us:
[tex]AC = 10 \times (\(\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2} + \frac{1}{2}\times\frac{\sqrt{2}}{2}\)) = 10 \times (\(\frac{\sqrt{6} + \sqrt{2}}{4}\))[/tex]
AC ≈ 8.66 m
What is the slope of the line represented by the equation y= -1/2x+1/4
Answer:
-1/2
Step-by-step explanation:
The format your equation in is called slope-intercept form:
y=mx+b
m stands for slope, the slope basically determines how much the line is tilted. b stands for the y intercept, the y intercept is when the line intercepts with the y axis.
Your equation is:
y= -1/2x+1/4
y= m x+ b
A number increased by five is equivalent to twice the same number decreased by seven
Answer:
The unknown number is 12.
Step-by-step explanation:
Let the unknown number be 'x'
Given:
A number increased by 5 is equivalent to twice the same number decreased by 7.
So, 'x' increased by 5 means add 5 to 'x'. This gives [tex]x+5[/tex]
Now, [tex]x+5[/tex] is equivalent to twice of 'x' decreased by 7.
Twice of 'x' means 2 times of 'x' which is [tex]2x[/tex]
'2x' decreased by 7 means subtract 7 from '2x'. This gives,
[tex]2x-7[/tex]
Now, [tex]x+5[/tex] and [tex]2x-7[/tex] are equivalent meaning they are equal. So,
[tex]x+5=2x-7\\5+7=2x-x\\12=x\\x=12[/tex]
Therefore, the unknown number is 12.
For what value of R does the equation have a solution of X = 9.5?
7 (5x - R) + 3r = 173.5
Show how you got your answer step-by-step.
Answer:
r=39.75
Step-by-step explanation:
7(5*9.5-R)+3r=173.5
7(47.5-R)+3r=173.5
332.5-7R+3r=173.5
332.5-4r=173.5
4r=332.5-173.5
4r=159
r=159/4
r=39.75
Step-by-step explanation:
7 (5x - R) + 3r = 173.5
let x = 9.5 as given
solve for R
substitute the value of x=9.5 into the equation:
7 (5 * 9.5 - R) + 3R = 173.5
7 (47.5 - R) + 3R = 173.5 expand
332.5 - 7R + 3R = 173.5 combine similar terms
332.5 - 173.5 = 7R - 3R simplify
159 = 4R divide 4 on each side
R = 159/4 simplify
R = 39.75
Ted likes to run long distances. He can run
20 km start text, space, k, m, end text in
95 minutes. He wants to know how many kilometers
(k)left parenthesis, k, right parenthesis he will go if he runs at the same pace for
285 minutes
Answer:
Step-by-step explanation:
20 km to 95 minutes = x km to 285 minutes
20 / 95 = x / 285.....cross multiply
(95)(x) = (20)(285)
95x = 5700
x = 5700/95
x = 60 km <======
PLEASE HELP ASAP
The function f(x) = 800(1.09)3x shows the growth due to interest that Jim earns on an investment. The steps to calculate an equivalent function are shown below:
[Step 1] f(x) = 800(1.09)3x
[Step 2] f(x) = 800(1.093)x
[Step 3] f(x) = 800(1.09 ⋅ 3)x
[Step 4] f(x) = 800(3.27)x
Which of the following is the first incorrect step?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answer:
The in the calculation the step 3 is the first incorrect step.
Step-by-step explanation:
The function [tex]f(x) = 800(1.09)^{3x}[/tex] shows the growth due to interest that Jim earns on an investment.
To get an equivalent function we are given the following steps:
[Step 1] [tex]f(x) = 800(1.09)^{3x}[/tex]
[Step 2] [tex]f(x) = 800(1.09^{3}) ^{x}[/tex]
[Step 3] [tex]f(x) = 800(1.09 \times 3)^{x}[/tex]
[Step 4] [tex]f(x) = 800(3.27)^{x}[/tex]
The in the calculation the step 3 is the first incorrect step.
And this will be [tex]1.09^{3} = (1.09)^{3} = 1.295 \neq 3.27[/tex] (Answer)
Step 3
It is multiplying three instead of doing 9x9x9 she did 9x3
What's x for 12x+1=4x+9
Nevermind someone already answered it.
Solve the following system of equations using the substitution method. x=2y2x+5y=9
Answer:
x=2, y=1. (2, 1).
Step-by-step explanation:
x=2y
2x+5y=9
-------------
2(2y)+5y=9
4y+5y=9
9y=9
y=9/9
y=1
x=2(1)=2
Force moved 350 boxes from the old school to the new school. Then, she moved 160 more. There are 220 boxes left to move. How many boxes needed moved to begin with?
Answer:
730
Step-by-step explanation:
Answer:
350+160+220 = 730
Step-by-step explanation:
There were 730 boxes. After moving 350 boxes out of 730 boxes, there were left 380 boxes. Again after moving 160 boxes out of 380 boxes, there were remained 220 boxes.
What's 286 divided by 20??
Thanks if you help! :)
Answer:
14.3
Step-by-step explanation:
percent: 14.3%
decimal: 14.3
fraction: 14 3/10
Answer:
I got 143/10 ;-;
But as a decimal it's 143.0 and percent is 14.3%
The Ferris wheel has a radius of 70 feet. The distance between the wheel and the ground is 4 feet. The rectangular coordinate system shown has its origin on the ground directly below the center of the wheel. Write the equation of the circular wheel. (JUSTIFY)
Show your work. i will give brainliest.
Answer:
The equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
Step-by-step explanation:
Given :
Radius of Ferris wheel r = 70 feet.
The distance between the wheel and the ground = 4 feet.
Also, the rectangular coordinate system shown has its origin on the ground directly below the center of the wheel.
So the x coordinate of center of wheel must be 0 , and y coordinate = 70 + 4 = 74
Thus, Coordinates of center = (0,74)
The equation of circle is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Now center (h,k) = (0,74) and r = 70 , we get
[tex]x^2+(y-74)^2=(70)^2[/tex]
Hence, the equation of the circular wheel is [tex]x^2+(y-74)^2=(70)^2[/tex].
solve and explain how you got your answer
-3(c-1) = 33
Answer:
Step-by-step explanation:
-3(c-1) = 33
c - 1 = 33/ -3
c -1 = -11
c = -11 +1
c = -10
Answer:
-10
Step-by-step explanation:
-3 (c-1 ) = 33
Divide both sides by -3
c-1 = -11
Add 1 to both sides
c = -10
• #93 ) You are testing a circuit at the factory you work
for. The load draws 1,800 watts of power and has a
voltage of 10 volts. What is the current in amps?
• A. 8.2
•B. 1,790
• C. 1,810
• D. 180
•E. 18,000
Answer:
The current flowing through the circuit is 180 ampere .
Step-by-step explanation:
Given as :
The measurement of load = p = 1800 watt
The voltage of the circuit= v = 10 volts
Let the current = i amperes
Now, As we know
Power = The electric power is define as the voltage drop at the terminal of electric circuit and the product of electric current passing through the circuit
i.e power = voltage × current
where power in watt
voltage in volt
current in ampere
Or, p = v × i
Now, From the definition of power
i = [tex]\dfrac{p }{v}[/tex]
Or, i = [tex]\dfrac{1800}{10}[/tex]
∴ i = 180 ampere
So, The current flowing through the circuit = i = 180 ampere
Hence, The current flowing through the circuit is 180 ampere . Answer
If sin yº = -and tan yº = 1, what is the value of cos y
Answer:
The value of cos y° is -1
Step-by-step explanation:
Given as Trigonometrical functions as :
sin y° = - 1
tan y° = 1
Let The value of cos y° = x
Now, As we know
tan [tex]\theta[/tex] = [tex]\dfrac{sin \theta }{cos \theta }[/tex]
So, tan y° = [tex]\dfrac{sin y^{\circ}}{cos y^{\circ}}[/tex]
∴ cos y° = [tex]\dfrac{sin y^{\circ}}{tan y^{\circ}}[/tex]
Or, x = [tex]\dfrac{-1}{1}[/tex]
i.e, x = - 1
So, The value of cos y° = x = -1
Hence, The value of cos y° is -1 Answer
if the sides of a square are lengthened by 3 m, the area becomes 81 m2. Find the length of a side of the original square.
Answer:
The length of a side of the original square is 6 meters
Step-by-step explanation:
Let
x ----> the length side of the original square
The area of a square is equal to
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem
The new length side of the square is [tex]b=(x+3)\ m[/tex] and the area is [tex]A=81\ m^2[/tex]
so
[tex](x+3)^2=81[/tex]
solve for x
take square root both sides
[tex](x+3)=9[/tex]
[tex]x=9-3=6\ m[/tex]
Use the following figure to answer the question.
∠ 1 and ∠ 2 are supplementary angles.
True
False
Answer:
True
Step-by-step explanation:
Because angles on a straight line are supplementary and these anglea <1 and <2 are supplementary angles
Answer: True
Step-by-step explanation:
The length of a rectangle is 5 centimeters less than its width What are the dimensions of the rectangle if its area is 66 square centimeters?
The length of the rectangle is
The width of the rectangle is
Answer:
length of rectangle=6cm
width of rectangle=11cm
Step-by-step explanation:
let, width of rectangle=x
length of rectangle=x-5
area of rectangle=[tex]length\times(width)[/tex]
given area of rectangle=66
so 66=[tex]x\times(x-5)[/tex]
66=x^2-5x
x^2-11x+6x-66=0
x(x-11)+6(x-11)=0
(x+6)(x-11)=0
x=-6,11
here x=11 is acceptable
length of rectangle=x-5=11-5=6cm
length of rectangle=6cm
width of rectangle=11cm answer
A book on the clearance rack was marked down 65% from $21.95. Approximately, how much was the book discounted?
Answer:
$7.6825
Step-by-step explanation:
65%=0.65
0.65*21.95=14.2675
21.95-14.2675=7.6825
Answer:
7.6825
Step-by-step explanation:
Tony makes a phone call at a pay phone. The charge is 25 cents for the first four minutes,and 19 cents for each additional minute. Tony has $2.10 in change in his pocket. Write an inequality that can be used to find m, the maximum number of whole minutes he can talk on the phone
At Ashley's Hats, 75% of the 84 hats are baseball caps. How many baseball caps are there?
Answer:
63
Step-by-step explanation:
85 * .75 = 63 hats