Answer:
The area in factored form is [tex]A=(x+2)(x-5)[/tex].
The area in standard form is [tex]A=x^2-3x-10[/tex].
Step-by-step explanation:
The area of a rectangle is length times width.
So the area here is (x+2)(x-5).
They are probably not looking for A=(x+2)(x-5) because it requires too little work.
They probably want A in standard form instead of factored form.
Let's use foil:
First x(x)=x^2
Outer: x(-5)=-5x
Inner: 2(x)=2x
Last: 2(-5)=-10
---------------------Adding together: [tex]x^2-3x-10[/tex].
The area in factored form is [tex]A=(x+2)(x-5)[/tex].
The area in standard form is [tex]A=x^2-3x-10[/tex].
Final answer:
The equation describing the area of the rectangle in terms of x, given the sides x + 2 and x - 5, is A = x² - 3x - 10.
Explanation:
To find the equation that describes the area, A, of a rectangle in terms of x, we use the formula for the area of a rectangle, which is length times width. Given that the length is x + 2 and the width is x - 5, the equation for the area A in terms of x is A = (x + 2)(x - 5).
To express A as a polynomial, we can expand this equation:
A = x(x - 5) + 2(x - 5)
A = x² - 5x + 2x - 10
A = x² - 3x - 10
Therefore, the equation that describes the area of the rectangle in terms of x is A = x² - 3x - 10.
which of the following are necessary when proving that the diagonals of a rectangle are congruent check all that apply
Answer:
Opposite sides are congruent; All right angles are congruent
Step-by-step explanation:
Find the slope and the y-intercept of the equation y-36x - 1) = 0
Answer:
the slope: m = 36the y-intercept: b = 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation
[tex]y-36x-1=0[/tex] add 36x and 1 to both sides
[tex]y-36x+36x-1+1=36x+1[/tex]
[tex]y=36x+1[/tex]
Therefore
the slope: m = 36
the y-intercept: b = 1
Francesca drew point (-2,-10) on the terminal ray of angle x which is in standard position she found values for the six trigonometric functions using the steps below
Answer:
She made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also results in incorrect cosecant, secant, and tangent functions.
Step-by-step explanation:
Francesca made her first error in step 3 because her sine, cosine, and tangent trigonometric ratio values are incorrect.
How to work with trigonometric ratios?The correct steps to use in this regards are as follows;
Step 1;
A unit circle is shown. A ray intersects point (-2, -10) in quadrant 3. θ is the angle formed by the ray and the x-axis in quadrant 1.
Step 2;
r = √[(-2)² + (-10)²] = √104 = 2√26
Step 3;
cos θ = -2/(2√26) = -1/√26 = -(√26)/26
sin θ = -10/(2√26) =-5/√26 = -5(√26)/26
tan θ = -10/-2 = 5
sec θ = 1/sin θ = 1/-(√26)/26 = -26/√26
cosec θ = 1/cos θ = 1/-5(√26)/26 = -(√26)/5
cot θ = 1/tan θ = 1/5
Thus, Francesca made her first error in step 3 because the correct sine, cosine, and tangent ratios above differ from hers which was incorrect which lead to incorrect values of cosecant, secant, and tangent functions.
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A baseball diamond is actually a square with sides of 90 feet. If a runner tries to steal second base how far must the catcher at home plate throw to get the runner out given this information explain why runners more often try to steal second base than third
Answer:
126.5 ft
Step-by-step explanation:
It's further for the catcher to throw to
The catcher must throw approximately 127.3 feet to get a runner out at second base on a square baseball diamond. The Pythagorean theorem is used to calculate the diagonal from home plate to second base. Runners often try to steal second base due to the longer throw required and being in scoring position.
Explanation:The question involves calculating the distance a catcher must throw the ball to get a runner out at second base on a baseball diamond, which is a square with sides of 90 feet. To find this distance, we must determine the diagonal of the square, as the catcher throws the ball from one corner (home plate) to the opposite corner (second base). Applying the Pythagorean theorem to the square, the diagonal distance D is given by D = √(90² + 90²). So, D = √(8100 + 8100) = √16200 feet, which approximately equals 127.3 feet. Runners are inclined to steal second base more often because it is generally easier to steal with the catcher having to make a longer throw, and once on second base, the runner is in scoring position with two bases potentially available to advance.
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#1 2 diamond rings and 4 silver rings cost $1,440. A diamond ring and a silver ring cost $660. How much does a silver ring cost?
#2 Logan and Izzy had the same number of stickers. After Izzy gave him 72 stickers, Logan had three times as many stickers as Izzy. How many stickers did they have altogether?
#3 David and Amrita had an equal number of marbles. After Armita gave 50 marbles to David he had 5 times as many marbles as her. Find the total number of marbles they
Answer:
1. multiply (2) by -2 and add to (1)
-2x-2y=-1320
add to (1) we get
4y-2y=1440-1320
2y=120
y= $60 cost of silver ring.
2. Multiplying (distributive property, we get the equivalent equation
x+72=3x-216
Adding 216 to both sides of the equal sign, we get
x+72+216=3x-216+216 --> x+288=3x
Subtracting x from both sides, we get
x+288-x=3x-x --> 288=2x
Logan and Izzy had initially had 188 stickers between the two of them.
3.
a = d before Anna gives away 50 marbles.
5 (a-50) = a +50 after Anna gives away 50 marbles.
5a - 250 = a + 50
4a = 300
a = 75
Anna has 75 marbles at the beginning and so did David.
Together they have 150 marbles.
Please answer quickly
Combine like terms to create an equivalent expression.
-1/2 (−3y+10) It is meant to be negitave 1 over 2
Answer: 3y/2 - 5
Step-by-step explanation:
Expand
-(-3y/2 + 5)
Simplify the brackets
3y/2 - 5
Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 + 2x = 17
need the awnswer now!!
Answer:
x = -5.24 or x = 3.24Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(8)\\\\x^2+2x=17\\\\x^2+(2)(x)(1)=17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(1)+1^2}_{(*)}=17+1^2\\\\(x+1)^2=18\iff x+1=\pm\sqrt{18}\qquad\text{subtract 1 from both sides}\\\\x=-1\pm\sqrt{18}\\\\x\approx-1-4.24=-5.24\ \vee\ x\approx-1+4.24=3.24[/tex]
what is the eqaution of a vertical line passing through (-5,-2)?
Answer:
x=-5
Step-by-step explanation:
Vertical lines have the same x value all the time. They are of the form x=
Since it passes through the point (-5,-2) the x value must be -5
x=-5
Henry buys a large boat for the summer, however he cannot pay the full amount of $32,000 at
once. He puts a down payment of $14,000 for the boat and receives a loan for the rest of the
payment of the boat. The loan has an interest rate of 5.5% and is to be paid out over 4 years.
What is Henry’s monthly payment, and how much does he end up paying for the boat overall?
Answer:
Monthly Payment = $457.5
Total amount Henry end up paying for the boat overall = $35,960
Step-by-step explanation:
Total Amount to be paid = $32,000
Down Payment = $ 14,000
Interest rate = 5.5%
Total time for Amount to be paid = 4 years
Rest of the payment to be paid = 32,000 - 14,000
= 18000
Amount of interest = P*r*t
P= Principal Amount
r = rate
t = time
Putting values
Amount of interest= 0.055 *18000*4 = 3960
Total Remaining payment = 18000+3960 = 21,960
As Payment to be paid in 4 years, So number of months = 4*12 = 48 months
Monthly payment = Total Payment / Months = 21,960/48 = 457.5
So, Monthly Payment = $457.5
Total amount Henry end up paying for the boat overall = Down Payment + Remaining Payment
=14,000+21960
= 35960
So, Total amount Henry end up paying for the boat overall = $35,960
3. Find all the zeroes of the polynomial x4 + 2x3 - 8x2 - 18x - 9, if two of its zeroes are 3
and -3.
Answer:
2b2t
Step-by-step explanation:
2b2t
Answer:
x = 3, x = - 3, x = - 1 with multiplicity 2
Step-by-step explanation:
Given that x = 3 and x = - 3 are zeros then
(x - 3) and (x + 3) are factors and
(x - 3)(x + 3) = x² - 9 ← is a factor
Using long division to divide the polynomial by x² - 9 gives
quotient = x² + 2x + 1 = (x + 1)² and equating to zero
(x + 1)² = 0 ⇒ x + 1 = 0 ⇒ x = - 1 with multiplicity 2
Hence the zeros of the polynomial are
x = 3, x = - 3, x = - 1 with multiplicity 2
Which expression is equivalent to (7+4i) +(8+I)?
Answer: B) 15 + 5i
Step-by-step explanation:
(7 + 4i) + (8 + i)
Add like terms: (7 + 8) + (4i + i)
Simplify: 15 + 5i.
Simplify the following expression.
x4 + 3x2 - 2x* -5x2 - x + x2 + x +1+7x4
Answer: 8x^4+x^3-4x^2+1
Step-by-step explanation:
To simplify this polynomial expression, we first combine like terms. The simplified expression will be 8x^4 - x + 1.
Explanation:The expression provided in your question is a polynomial that contains terms with variables raised to different powers. In simplifying this kind of polynomial, you first need to combine like terms, which are those terms that have the same variable and the same exponent.
Therefore, let's organize and combine like terms: x4 - 2x + x and 3x2 - 5x2 + x2 and . As a result, we get 8x4, or 8x to the power of 4, -x, and 1. Thus, the final simplified expression is: 8x4 - x + 1
Hope this helps in your understanding of simplifying polynomials!
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.
In which quadrants do solutions for the inequal
the inequality
[tex]y \leqslant \frac{2}{3}x - 4[/tex]
exist.
A.I, III, and IV
B.I, II, and III
C.I and IV
D.All four quadrants
Answer:
A.I, III, and IVStep-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
If m > 0, then the function is increased
If m < 0, then the function is decreased
We have
[tex]m=\dfrac{2}{3}>0[/tex] - the function is increased
[tex]b=-4[/tex] - the y-intercept is -4 → (0, -4)
Therefore the line passes through III, IV and I quadrant.
========================================
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
========================================
We have [tex]y\leq\dfrac{2}{3}x-4[/tex] → ≤ - shaded region below the line.
Therefore the inequal the inequality exist in I, III and IV quadrant.
Look at the picture.
The inequality exists in quadrants A.I, III, and IV.
The answer is option A
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the line
slope(m)=tan∅=y axis/x axis.
If m > 0, then the function is increased
If m < 0, then the function is decreased
=function is increased
=y-intercept is -4 = (0, -4)
Therefor the line passes through III, IV and I quadrant.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
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Could you guys please help me with number 1
Answer:
Option B 6 30 am
Step-by-step explanation:
step 1
Sum all the times
(45+5+10+30+15)=115 minutes
Convert minutes to hours
we know that
60 minutes = 1 hour
so
115 minutes=60+55= 1 hour 55 minutes
Subtract 1 hour 55 minutes from 8 25 am
(8 25 am)-(1 hour 55 minutes)=(8 25 am-1 hour)-(55 minutes)
=7 25 am-55 minutes
=7 25 am-(25+30) minutes
=(725 am-25 minutes)-(30 minutes)
7 00 am-30 minutes
=6 30 am
Martin builds a right square pyramid using
straws. A diagram of the pyramid and its net
are shown.
What is the surface area of the pyramid?
Enter the answer in the box.
Answer:
360 ft^2
Step-by-step explanation:
The surface area of a right square pyramid can be found using the formula: [tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex]
In this formula:
a = base edge (the length of the sides of the square)h = height of the pyramidIn this diagram, the base edge length is 10 ft and the height of the square pyramid is 12 ft. Substitute these values into the formula to find the surface area.
[tex]a^2+2a\sqrt{\frac{a^2}{4}+h^2}[/tex][tex](10)^2+2(10)\sqrt{\frac{(10)^2}{4}+(12)^2[/tex]Simplify this expression. Start by evaluating the exponents then rewrite the expression.
[tex](100)+2(10)\sqrt{\frac{(100)}{4}+(144)[/tex]Now evaluate inside the radical sign.
[tex](100)+2(10)\sqrt{(25)+(144)[/tex][tex](100)+2(10)\sqrt{169[/tex]Multiply 2 and 10 together (we're following the rules of PEMDAS).
[tex](100)+(20)\sqrt{169[/tex]Find the square root of 169 then multiply that by 20.
[tex](100)+(20)(13)[/tex][tex](100)+(260)[/tex]Finish the problem by adding 100 and 260 together.
[tex]100 +260=360[/tex]The surface area of the pyramid is [tex]\boxed{\text {360 ft}^2}[/tex].
What is the standard form
See attachment for the answer.
What is the perimeter of AYXZ?
3.5 in.
5.3 in.
6.4 in.
7.8 in.
Answer: The perimeter of ΔYXZ6.4
Answer:6.4
Step-by-step explanation:
A triangle has two sides of lengths 5 and 12. What value could the length of the third side be?
Answer:
Third side must be greater than 7 and less than 17
Step-by-step explanation:
If a triangle has two sides of lengths 5 and 12, the value for the length of the third side be greater than 7 and less than 17.
-3|x - 3|= -6
what to do, what to do :/
Answer:
X=5, X=1
Step-by-step explanation:
Okay so the | means absolute value and it is similar to a parentheses, except everything inside it becomes positive. Since there is a variable (x) inside it, you will have two scenarios then, one where everything inside is positive and where it's negative (so -3x +9 = -6 and 3x -9 =-6) You then solve for x in both equations.
Answer:
x=5 x=1
Step-by-step explanation:
-3|x - 3|= -6
Divide each side by -3
-3|x - 3|/-3= -6/-3
|x - 3|= 2
To get rid of the absolute value signs, we get two equations, one positive and one negative
x-3 =2 x-3 = -2
Add 3 to each side
x-3+3 = 2+3 x-3+3 = -2 +3
x =5 x = 1
Please help me I have to turn in by 8:00
Answer:
A 2
Step-by-step explanation:
When we divide x by 9 there is some whole number we will call y plus a remainder of 4
x/9 = y remainder 4
Writing this in fraction form
x/9 = y + 4/9
Multiplying each side by 9
9*x/9 = 9* y + 4/9 *9
x = 9y +4
Multiply each side by 2
2x = 2*(9y+4)
2x = 18y +8
Add 3 to each side
2x+3 = 18y +8+3
2x+3 = 18y +11
Divide each side by 9
(2x+3)/9 = 18y/9 +11/9
= 2y + 9/9 +2/9
=(2y+1 + 2/9)
We know y is a whole number and 1 is a whole number so we can ignore 2y +1 when looking for a remainder)
2/9 is a fraction
Taking this back from fraction form to remainder from
(2y+1) remainder 2
The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 ln (9t + 4), where y is the number of mowers sold. How many mowers will be sold 4.5 years after a model is introduced?
Answer:
20875
Step-by-step explanation:
Given:
y = 5500 ln (9t + 4
y is number of mowers sold
t is years after a particular model is introduced
f(t)= 9t+4
How many mowers will be sold 4.5 years after a model is introduced?
t=4.5
putting t=4.5 in given function we get,
y= 5500ln(9(4.5) +4)
= 20875.19
20875 mowers will be sold 4.5 years after a model is introduced!
In the diagram of circle o, what is the measure of ZABC?
O 30°
O 40°
O 50°
O 60
Answer:
30°
Step-by-step explanation:
Line AB and BC are tangents to the given circle.
[tex] \angle \: ABC = \frac{1}{2} ( 210 - 150)[/tex]
[tex] \angle \: ABC = \frac{1}{2} (60) = 30 \degree[/tex]
Alternatively, <ABC and <AOC are supplementary because AB and BC are tangents.
[tex] \angle \: ABC + 150 \degree = 180 \degree[/tex]
[tex] \angle \: ABC = 180 \degree - 150 \degree = 30 \degree[/tex]
The correct choice is A.
Answer:30
Step-by-step explanation:
The digits I through 4 are randomly arranged to create
a four-digit number. What is the probability that the number formed is not divisible by 4?
The probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.
To calculate the probability that the four-digit number formed is not divisible by 4, we need to determine the total number of possible arrangements of the digits I through 4 and then find the number of arrangements that are not divisible by 4.
Total number of arrangements:
Since there are four digits (I, 2, 3, 4), there are 4! (4 factorial) ways to arrange them without repetition.
4! = 4 × 3 × 2 × 1 = 24
Now, let's find the arrangements that are not divisible by 4:
For a number to be divisible by 4, the last two digits must form a number divisible by 4. The possible combinations of the last two digits that are divisible by 4 are: 12, 24, and 32.
So, we have three combinations (12, 24, and 32) where the number formed is divisible by 4.
Now, to find the arrangements that are not divisible by 4, subtract these three combinations from the total:
Arrangements not divisible by 4 = Total arrangements - Divisible by 4 arrangements
Arrangements not divisible by 4 = 24 - 3 = 21
Now, we can calculate the probability:
Probability = (Number of arrangements not divisible by 4) / (Total number of arrangements)
Probability = 21 / 24
Probability ≈ 0.875
So, the probability that the four-digit number formed is not divisible by 4 is approximately 0.875 or 87.5%.
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_____ are ______ midsegments of ΔWXY.
What is the perimeter of ΔWXY?
11.57 cm
12.22 cm
12.46 cm
14.50 cm
Answer:
The perimeter of Δ WXY is 14.50 cm ⇒ the last answer
Step-by-step explanation:
* Lets explain how to solve the problem
- There is a fact in any triangle; the segment joining the midpoints of
two side of a triangle is parallel to the 3rd side and half its length
* Lets use this fact to solve the problem
- In Δ WXY
∵ Q is the midpoint of WX
∵ R is the midpoint of XY
∵ S is the midpoint of YW
- By using the fact above
∴ QR = 1/2 WY
∴ RS = 1/2 WX
∴ SQ = 1/2 XY
- Lets calculate the length of the sides of Δ WXY
∵ QR = 1/2 WY
∵ QR = 2.93
∴ 2.93 = 1/2 WY ⇒ multiply both sides by 2
∴ WY = 5.86 cm
∵ RS = 1/2 WX
∵ RS = 2.04
∴ 2.04 = 1/2 WX ⇒ multiply both sides by 2
∴ WX = 4.08 cm
∵ SQ = 1/2 XY
∵ SQ = 2.28
∴ 2.28 = 1/2 XY ⇒ multiply both sides by 2
∴ XY = 4.56 cm
- Lets find the perimeter of Δ WXY
∵ The perimeter of Δ WXY = WX + XY + YW
∴ The perimeter of Δ WXY = 5.86 + 4.08 + 4.56 = 14.50
* The perimeter of Δ WXY is 14.50 cm
In this exercise we have to use the knowledge of the perimeter of a figure to calculate its value, and then:
Letter D
So from some information given in the statement and in the image, we can say that:
Q is the midpoint of WXR is the midpoint of XYS is the midpoint of YWSo solving, you will have to:
[tex]QR = 1/2 WY\\RS = 1/2 WX\\SQ = 1/2 XY[/tex]
Now with both information we can calculate the perimeter value as:
[tex]QR = 1/2 WY\\QR = 2.93\\2.93 = 1/2 WY\\ WY = 5.86 cm\\RS = 1/2 WX\\ RS = 2.04\\2.04 = 1/2 WX\\WX = 4.08 cm\\SQ = 1/2 XY\\SQ = 2.28\\2.28 = 1/2 XY \\XY = 4.56 cm\\ WXY = WX + XY + YW\\WXY = 5.86 + 4.08 + 4.56 = 14.50[/tex]
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I’ve been stuck on this for a while now can someone please help me out please
Step-by-step explanation:
i think its 4.2m^2+1.5n
Answer:
4.2m^2+1.5n
Step-by-step explanation:
1.7m^2 + 6.5n - 4n + 2.5m^2 - n
First, rearrange the numbers so that they can be added or subtracted with their like terms.
It would look like this:
(1.7m^2 + 2.5m^2) + (6.5n - 4n - n)
All you have to do is solve from here
this would simplify into:
4.2m^2+1.5n
Hope this helped!
Approximately how many milligrams of sodium
remain after 8.4 years?
no your wrong its 85.2
A cylindrial hole is cut through the cylinder below.
below. The larger Cylinder has a diameter of 14 mm and a height of 25 mm. If the diameter of the hole is 10 mm, find the volume of the solid.
Answer:
V=1884 Cubic mm
Step-by-step explanation:
We know that the volume of the Sphere is given by the formula
[tex]V= \pi r^2h[/tex]
Where r is the radius and h is the height of the cylinder
We are asked to determine the radius of the hollow cylinder , which will be the difference of the solid cylinder and the cylinder being carved out.
[tex]V=V_1-V_2[/tex]
[tex]V=\pi r_1^2 \times h-\pi r_2^2 \times h[/tex]
[tex]V=\pi \times h \times (r_1^2-r_2^2)[/tex]
Where
[tex]V_1[/tex] is the the volume of solid cylinder with radius [tex]r_1[/tex] and height h
[tex]V_2[/tex] is the volume of the cylinder being carved out with radius [tex]r_2[/tex] and height h
where
[tex]r_1 = 7[/tex] mm ( Half of the bigger diameter )
[tex]r_2 = 5[/tex] mm ( Half of the inner diameter )
[tex]h=25[/tex] mm
Putting these values in the formula for V we get
[tex]V=\pi \times 25\times (7^2-5^2)[/tex]
[tex]V=3.14 \times 25 \times(49-25)[/tex]
[tex]V=3.14 \times 25 \times 24[/tex]
[tex]V= 1884[/tex]
Solve for x: 2 over 5 (x − 2) = 4x. (1 point) 2 over 9 9 negative 2 over 9 negative 9 over 2
Answer:
x=-2/9 or
x = negative 2 over 9
Step-by-step explanation:
We need to solve:
[tex]\frac{2}{5}(x-2)=4x[/tex]
and find the value of x.
Solving:
[tex]\frac{2}{5}(x-2)=4x\\\frac{2x}{5}-\frac{4}{5}=4x\\ Adding \,\,4/5\,\,on\,\,both\,\,sides\\\frac{2x}{5}-\frac{4}{5}+\frac{4}{5}=4x+\frac{4}{5}\\\frac{2x}{5}=4x+\frac{4}{5}\\subtract \,\,4x\,\,from both sides\\\frac{2x}{5}-4x=\frac{4}{5}\\\frac{2x-20x}{5}=\frac{4}{5}\\\frac{-18x}{5}=\frac{4}{5}\\-18x=\frac{4}{5}*5\\-18x=4\\x=\frac{4}{-18}\\x=\frac{-2}{9}[/tex]
x=-2/9 or
x = negative 2 over 9
Please answer this correctly
Answer:
3/10
Step-by-step explanation:
because the pattern is -0.15;
9/10= 0.9
3/4= 0.75
3/5= 0.6
9/20= 0.45
3/10= 0.3
Help with number 3 it might be hard to read but it is possible
Answer:
This is B because as we can see the X axis increases in value to y decreases making it negetive
Answer:
the answer is B because the X axis increases in value as y decreases making it negative
Step-by-step explanation: