Answer:
a = 7
Step-by-step explanation:
a - 17 = -10
Add 17 to each side
a - 17+17 = -10+17
a = 7
Answer:
a = 7
Step-by-step explanation:
Add 17 to each side, so it cancels out the -17. It should now looks like this: a = 7I hope this helps!
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.
Step-by-step explanation:
35-inch television is a television whose screen has an hypotenuse ([tex]l[/tex]) of 35 inches and the aspect ratio of 4 : 3 means that 4 inches width per each 3 inches height. And by Pythagorean Theorem:
[tex]r_{l} =\sqrt{r_{w}^{2}+r_{h}^{2}}[/tex]
Where:
[tex]r_{l}[/tex] - Hypotenuse rate, dimensionless.
[tex]r_{w}[/tex] - Width rate, dimensionless.
[tex]r_{h}[/tex] - Height rate, dimensionless.
If [tex]r_{w} = 4\,in[/tex] and [tex]r_{h} = 3\,in[/tex], the hypotenuse rate is:
[tex]r_{l} = \sqrt{4^{2}+3^{2}}[/tex]
[tex]r_{l} = 5[/tex]
The width and height of the old television can be found with the help of trigonometric functions:
Width of 35-inch old television ([tex]w[/tex])
[tex]w = l\cdot \cos \theta[/tex]
[tex]w = l\times\left(\frac{r_{w}}{r_{l}} \right)[/tex]
Height of 35-inch old television ([tex]h[/tex])
[tex]h = l\cdot \sin \theta[/tex]
[tex]h = l\times\left(\frac{r_{h}}{r_{l}} \right)[/tex]
Where [tex]\theta[/tex] is the direction of the hypotenuse with respect to width, measured in sexagesimal degrees.
If [tex]r_{w} = 4[/tex], [tex]r_{h} = 3[/tex] and [tex]r_{l} = 5[/tex] and [tex]l = 35\,in[/tex], the width and height of the old 35-inch television:
[tex]w = (35\,in)\times \left(\frac{4}{5} \right)[/tex]
[tex]w = 28\,in[/tex]
[tex]h =(35\,in)\times \left(\frac{3}{5} \right)[/tex]
[tex]h = 21\,in[/tex]
The width and height of the old 35-inch television are 28 inches and 21 inches, respectively.
Step by step please: x^3+2x^2-5x-6=0
Answer:
x=-1, x=2, x=3
Step-by-step explanation:
Factor the left side of the equation.
(x+1)(x^2+x-6)
(x+1)(x-2)(x-3)
Now set everything equal to 0
x+1=0
x-2=0
x-3=0
Now solve for x
therefore, the answer is x=-1, x=2, x=3
Jose Plans to make a down payment plus monthly payments in order to buy a Harley Davidson motorcycle. At one dealership, he would pay $8,000 down and pay $250 each month. At another dealership, he would pay $10,000 down and pay $125 each month. After how many months would the payment be the same for both dealers? What will that amount be?
a) 16 month
b) $12 000
Step-by-step explanation:$8000 + 250m = $10000 + 125m
250m - 125m = $10000 - $8000
125m = $2000
m = $2000 : 125
m = 16 months
After how many months would the payment be the same for both dealers ?16 months
What will that amount be ?$8000 + $250×16 =
= $8000 + $4000
= $12000
$10000 + $125×16 =
= $10000 + $2000
= $12000
Hi plz just give me an answer. no explanation needed. sorry and thanks
Answer:
B=45
The sum of the interior angle of a triangle is equal to 180
Therefore equate angle A, B and C to 180
then add them to get 135 + c=180
group like terms,135 crosse the equal sign to be negative
which is c=18p-135
c=45
Which image shows a rotation?
Answer:
c is the best answer in my mind
What number needs to be eliminated to solve this equation? 3d = -81
Answer:
You must first divide 3 from both sides.
Step-by-step explanation:
Whenever you solve an equation such as this you are always trying to isolate the variable that is given. In this case we are arriving at the value of d alone.
3d = -81
d = -27
Hope this helps!
Answer:
i believe that 3 needs to be eliminated
Step-by-step explanation:
3d÷3=-81÷3
d=27
hope i helped :D
3.what is 8/30 equal to?
Answer:
4/15Step-by-step explanation:
[tex]\frac{8}{30}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4}{15}[/tex]
A high school athlete ran the 100 meter sprint in 13.245 seconds. what is the time rounded to the nearest tenth. Award is brainliest
The value of each digit in a number is known as the place value. The time rounded to the nearest tenth is 13.2 seconds.
What is the place value of a digit in a number?The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.
Identification of the place value of a digit in a number:
The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10Given the time to run is 13.245, now tenth means the value that is after the decimal. Since the value after the tenth is 4, therefore, the tenth value will remain the same but the numbers after that will be erased.
Hence, the time rounded to the nearest tenth is 13.2 seconds.
Learn more about the Place Value here:
https://brainly.com/question/27734142
#SPJ2
When you roll a dice you are more likely to get a 2 than a 6
Answer:
You are just as likely to get a 2 as a 6
Step-by-step explanation:
There are six sides on a die 1,2,3,4,5,6
Assuming a fair normal die
P(2) = number of 2's / total = 1/6
P(6) = number of 6's / total = 1/6
You are just as likely to get a 2 as a 6
2. The radius of a circle is 9 cm. Find the area of the circle
(Use 3.14 as the approximation of T.)
Answer:
Area of a Circle = 254.34 cm²
Step-by-step explanation:
Area of a Circle = π r²
Area of a Circle = 3.14 * 9²
Area of a Circle = 254.34 cm²
what is a short introduction of the story happy prince?
Answer:
happy prince was born and one day he died
What is the cost of 18 toy cars?
Answer:
$27
Step-by-step explanation:
Assuming this price list, ...
4 toy cars cost 6 dollars
6 toy cars cost 9 dollars
8 toy cars cost 12 dollars
We recognize that 18 cars is 3 times 6 cars, so the cost will be ...
cost of 18 cars = 3(cost of 6 cars) = 3($9) = $27
The cost of 18 toy cars is $27.
What is the midpoint between each pair (-1, -5) and (-5, 9)
==============================================
Explanation:
The x coordinates are -1 and -5. They add to -6. Which is then cut in half to -3
The y coordinates are -5 and 9. They add to 4. This is cut in half to 2.
The midpoint is therefore (-3, 2)
-------
A symbolic way to write this is if you had endpoints (a,b) and (c,d), then the midpoint is [tex]\left(\frac{a+c}{2}, \frac{b+d}{2}\right)[/tex]
Rewrite the number in standard form. 3.4 x 10^8
Answer:
340000000
Step-by-step explanation:
3.4 x 10^8 is in scientific notation.
To change this to standard form you have to multiply 3.4 by 10 to the 8th power. You would be multiplying 3.4 by 10 eight times. It's a positive 8 so you move the decimal point 8 times to the right. If it were a negative then you'd move the decimal to the left.
3.4
↑ moving the decimal 8 times to the right would then make it 340000000Evaluate the expression below when x = 5.
3(2x - 7)
Answer:
9
Step-by-step explanation:
Hello!
They want us to find x when x is 5 so we put 5 in for x
3(2(5) - 7)
Now we follow PEMDAS
3(10 - 7)
3(3) = 9
The answer is 9
Hope this helps!
how do reference angles work and how do you find them?
A 200-degree angle is between 180 and 270 degrees, so the terminal side is in QIII.
Do the operation indicated for that quadrant. Subtract 180 degrees from the angle, which is 200 degrees.
You find that 200 – 180 = 20, so the reference angle is 20 degrees.
hope this helped!
o(*￣▽￣*)ブ
A new Youth Activity Center is being built in Hadleyville. The perimeter of the rectangular playing field is 442 yards. The length of the field is 4 yards less than quadruple the width. What are the dimensions of the playing field?
Answer:
45 yards and 176 yards
Step-by-step explanation:
Perimeter of a rectangular playing field = 2(Length + width)
P = 2(L+W)..................... Equation 1
From the question,
Let the width of the rectangular playing field = x yards,
The the Length = 4x-4 yards.
Given: P = 442 yards.
Substitute these values into equation 1
442 = 2(4x-4+x)
442/2 = 5x-4
221 = 5x-4
5x = 221+4
5x = 225
x = 225/5
x = 45 yards.
Width = 45 yards.
Length = (45×4)-4 yards = 176 yards
Hence the dimensions of the playing field are, 45 yards and 176 yards
[tex] \frac{ {x}^{3} }{x { }^{2} + 2x + 1} [/tex]
Hi! I need help with the problem above. I know the answer to it is x-2+((3x+2)/(x^2+2x+1)), but I need help knowing and understanding the process. I can usually divide polynomials with ease, but I have never had to divide when the divisor is larger than the dividend. Can you please show me how to solve this with long division? Also, if you still have time to help me, how would synthetic division work with this? Thank you in advance!
Since
[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^3}{(x+1)^2}[/tex]
we can perform synthetic division twice, first for
[tex]\dfrac{x^3}{x+1}[/tex]
then dividing the result by [tex]x+1[/tex] again.
... || 1 0 0 0
-1 || -1 1 -1
================
... || 1 -1 1 -1
This translates to
[tex]\dfrac{x^3}{x+1}=x^2-x+1-\dfrac1{x+1}[/tex]
Now divide [tex]x^2-x+1[/tex] by [tex]x+1[/tex]. (Dividing the remainder term by [tex]x+1[/tex] can wait until the end.)
... || 1 -1 1
-1 || -1 2
=============
... || 1 -2 3
or equivalently,
[tex]\dfrac{x^2-x+1}{x+1}=x-2+\dfrac3{x+1}[/tex]
Taking everything together, we have
[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^2-x+1}{x+1}-\dfrac1{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac3{x+1}-\dfrac1{(x+1)^2}[/tex]
Combine the last two fractions:
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3(x+1)-1}{(x+1)^2}[/tex]
[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3x+2}{(x+1)^2}[/tex]
which agrees with the solution we found in your other question.
(There's a variant of synthetic division that works with directly dividing a polynomial by another one of any degree, but it's basically just a condensed version of applying the algorithm for dividing a polynomial twice by a linear one, like we've done here.)
What is an equation of the line that passes through the points (6,2) and (-6, -8)?
Put your answer in fully reduced form.
Step-by-step explanation:
Hey, there!!
Let me simply clear you.
The given points are (6,2) and (-6,-8).
Remember if you are finding the equation of the line passing through point, you will get equation in slope intercept form.
If there is two point you simply use one point formula. {i.e (y-y1)= m(x-x1)} (as the slope will be given too).If you are finding the equation for two points then use double point formula for the equation. { i.e (y-y1) = (y2-y1/x2-x1) × (x-x1)}.As in your question there are two points we must use double point formula,
[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]
[tex]( y - 2) = \frac{ - 8 - 2}{ - 6 - 6} (x - 6)[/tex]
Simplifying them we get,
6(y-2)= 5(x-6)
6y - 12 = 5x -30
Therefore, 5x - 6y - 18 = 0 is the required equation.
Hope it helps.....
Help urgent, which functions are bounded below but not above? Choose all answers that apply.
Answer:
c, e, f, and i
Step-by-step explanation:
a. is bounded above at y = 1 and below at y = 0
b. is unbounded both above and below
c. is bounded below at y = 0 and unbounded above
d. is unbounded both above and below
e. is bounded below at y = 0 and unbounded above
f. is bounded below at y = 0 and unbounded above
g. is bounded below at y = 0 and bounded above at y = 1
h. is unbounded both above and below
i. is bounded below at y = 0 and unbounded above
j. is unbounded both above and below
Rewrite 2/20 : 1/40 as a unit rate
Answer:
[tex]\frac{4}{1}[/tex]
Step-by-step explanation:
Given:
2/20 : 1/40
A). First re-write the ratio as follows;
(i) Change the ratio sign to division (÷). i.e
2/20 ÷ 1/40
(ii) Solve the expression by changing the division to multiplication(×). This also means you will need to swap the numerator and the denominator of the second term. i.e (1 / 40) becomes (40 / 1)
(2/20) × (40 / 1) = [tex]\frac{2}{20}[/tex] × [tex]\frac{40}{1}[/tex] = [tex]\frac{4}{1}[/tex]
B). Now convert the result from above to unit rate. A unit rate is a rate in which the denominator has a value of 1.
So to convert [tex]\frac{4}{1}[/tex] to unit rate, we keep simplifying until the denominator becomes 1.
And since the denominator is already 1, there is no need for further simplification.
Therefore, 2/20 : 1/40 to unit rate is [tex]\frac{4}{1}[/tex]
Answer:4/1
Step-by-step explanation:
I say this because you are supposed to divided it and the answer is 4 then you find the answer choice with a 1 as the denominator and it should say 4/1 and that is the correct answer.
1. Which one does not belong *
O y=(x+4)(x-6)
O y=2x²-88-24
O y=x2+5x-25
O y=x®+3x?-10x-24
Answer:
I believe the answer is 2x² - 88 - 24, since it is the only one with a number in front of the x²
Step-by-step explanation:
y = x² - 2x - 24
y = 2x² - 88 - 24
y = x² + 5x - 25
y = x² + 3x - 10x - 24
whats the pattern 729, -243, 81, -27, 9
Answer:
This is the product of three nines (three factors of 9). 9 × 9 × 9 × 9 = 6561 --> This is the product of four nines (four factors of 9). It's a common mistake among educators to state that 81 is what we get by "multiplying nine by itself twice".
If the rectangle is 38 inches and the length is 12 how much is the width ?
Answer:
width= 3.17
Step-by-step explanation:
Divide 38 (the area) by 12 (the width)
PLEASE I BEG FOR HELP! Find mKNL A. 247 B. 184 C. 196 D. 264
Answer:
D. 264°
Step-by-step explanation:
When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,
60° = 1/2[(18x - 6)° - (5x +17)°]
60° * 2 = (18x - 6 - 5x - 17)°
120° = (13x - 23)°
120 = 13x - 23
120 + 23 = 13x
143 = 13x
143/13 = x
11 = x
x = 11
(18x - 6)° = (18*11-6)°= (198 - 6)° = 192°
(5x +17)° = (5*11 +17)° =(55+17)° = 72°
m (arc KNL) = (18x - 6)° + (5x +17)° = 192° + 72°
m (arc KNL) = 264°
how to solve slope intercept form with 4y=x+3
m = 1/4 = slope
b = 3/4 = y intercept
===================================================
Explanation:
The goal is to solve for y.
Divide both sides by 4 and simplify like so
4y = x+3
4y/4 = (x+3)/4
y = (x+3)/4
y = x/4 + 3/4
y = (1/4)x + 3/4
This equation is in slope intercept form y = mx+b
m = 1/4 is the slope
b = 3/4 is the y intercept
The graph is a straight line that goes through (1,1) and (5,2)
(3x + 5) (x2 – 10x + 2 ).
Answer:
[tex]3x^{3} -25x^{2} -44x+10[/tex]
Step-by-step explanation:
Hello!
To solve this we distribute what in one parenthesis into the other
3x
3x * x^2 = 3x^3
3x * -10x = -30x^2
3x * 2 = 6x
5
5 * x^2 = 5x^2
5 * -10x = -50x
5 * 2 = 10
Now we put like terms together and simplify
3x^3 + 0 = 3x^3
-30x^2 + 5x^2 = 25x^2
6x - 50x = -44x
0 + 10 = 10
Put it all together
3x^3 + 25x^2 - 44x + 10
Hope this helps!
Answer:
3x^3 + 25x^2 - 44x +10
Step-by-step explanation:
To answer this use FOIL
First Outer Inner Last
In this problem start by distributing the 3x
3x^3-30x^2+6x
Next distribute the 5 in the second parenthesis
5x^2 - 50x + 10
Lastly, add like terms (terms that have the same variable and powers)
3x^3 - 25x^2 +6x +10
Which equation represents this proportional relationship
y=3x
y=1/6x
y=6x
y=1/3x
Answer:
I think that, please check it y=3x
what is the equation of the line
Answer:
y = -7
Step-by-step explanation:
the value of -7 is constant at the x coordinates
y = -7
x | y
-8 | -7
-6 | -7
-4 | -7
-2 | -7
0 | -7
2 | -7
4 | -7
6 | -7
8 | -7
Given x=-3, y=6, and z=-4
-15+(-x)+y=
x = -3 , y = 6 , z = -4
Take Given equation :
⇒-15 + (-x) + y = 0
substitute values of x and y
⇒-15 + [- ( -3)] + 6
⇒-15 + (3) + 6
⇒-15 + 9
⇒-6
Hence, value of -15 + (-x) + y = - 6