Answers
------- * ----- - ----------- * --- = --------------------
7 (x+5) (x + 5) 7 7( x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
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Related Questions
What is the peremeter of this polygon? (With picture)
Answers
so.. simply, use the distance formula, to get their length an add them up, and that's the perimeter of the polygon.
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 2}})\quad % (c,d) &({{ 2}}\quad ,&{{ 4}})\\ &({{ 2}}\quad ,&{{ 4}})\quad % (c,d) &({{ 3}}\quad ,&{{ -2}})\\ &({{ 3}}\quad ,&{{ -2}})\quad % (c,d) &({{ -2}}\quad ,&{{ -3}})\\ &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ -1}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]
[tex]\bf -------------------------------\\\\ d=\sqrt{[2-(-1)]^2+(4-2)^2}\implies d=\sqrt{(2+1)^2+(2)^2} \\\\\\ d=\sqrt{3^2+2^2}\implies \boxed{d=\sqrt{13}}\\\\ -------------------------------\\\\ d=\sqrt{(3-2)^2+(-2-4)^2}\implies d=\sqrt{1^2+(-6)^2}\implies \boxed{d=\sqrt{37}}\\\\ -------------------------------\\\\ d=\sqrt{(-2-3)^2+[-3-(-2)]^2}\implies d=\sqrt{(-5)^2+(-3+2)^2} \\\\\\ d=\sqrt{(-5)^2+(-1)^2}\implies \boxed{d=\sqrt{26}}[/tex]
[tex]\\\\ -------------------------------\\\\ d=\sqrt{[-1-(-2)]^2+[2-(-3)]^2}\implies d=\sqrt{(-1+2)^2+(2+3)^2} \\\\\\ d=\sqrt{(1)^2+(5)^2}\implies \boxed{d=\sqrt{26}}[/tex]
so, those are their lengths, sum them all up, that's the polygon's perimeter.
For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
e ≥ 50 or e ≤ 100
e > 50 or e < 100
50 < e < 100
50 ≤ e ≤ 100
Answers
50 ≤ e ≤ 100
Answer:
The answer is D.
Step-by-step explanation:
We know this because it is an "and" problem because it is numbers in between, not outside.
We also know it is "no less" or "no more" than 50 or 100. so we use a less than and equal too. Not just a less than sign.
Really hoped this helped, kind of in a test right now so just giving a brief way of how to figure this stuff out.
Continue and have fun learning!
Which is equivalent to 5√1,215^x?
A)243x
B)1,215^1/5x
C)1,215^1/5x
D)243^1/x
Answers
Answer:
Option C is correct
The expression [tex](1215)^{\frac{1}{5}x}[/tex] is equivalent to [tex]\sqrt[5]{1215^x}[/tex]
Step-by-step explanation:
Simplify the radical Expression: [tex]\sqrt[5]{1215^x}[/tex]
A radical expression can be written by using the exponents and also using the following procedure:
[tex]\sqrt[n]{x} = x^{\frac{1}{n}}[/tex]
when x be non-negative then n can be any index
when x is negative, then n can be odd.
The following radical expression can be written as:
[tex]\sqrt[5]{1215^x} = (1215^x)^{\frac{1}{5}}[/tex] = [tex](1215)^{\frac{1}{5}x}[/tex]
Therefore, the expression [tex](1215)^{\frac{1}{5}x}[/tex] is equivalent to [tex]\sqrt[5]{1215^x}[/tex]
the area of Juan's garden after he adds a border x feet wide is equal to (3+2x)(6+2x) which polynomial represents the area of Juan's garden?
A. 4x^4+30x+18
B. 4x^2+22x+27
C. 4x^2+18x+18
D. 4x^2+6x+18
Answers
18 + 6x + 12x + 4x² =
4x² + 18x + 18
a scale model of a school building is 5 inches tall. If the building is 100 feet tall, find the scale of the model
Answers
Answer with Step-by-step explanation:
A scale model of a school building is 5 inches tall.
Actual size of the school building is 100 feet.
1 feet=12 inches
100 feet=12×100 inches
= 1200 inches
5 inch is representing 1200 inches
1 inch represents 1200/5 inches
1 inch represents 240 inches
or 1 inch represents 12×20 inch
or 1 inch represents 20 feet
Scale of the model is:
1 inch represents 240 inches
1 inch represents 20 feet
Which graph shows a triangle and its reflection image over the x-axis?
A. first picture
B. 2nd picture
C. picture 3
D. picture 4
A. is wrong
Answers
To make sure we're on the same page, I'm attaching your fourth drawing below. It's the result of taking a triangle and reflecting it over the horizontal x axis. Think of it like mirroring an image.
Answer-
In picture 4, the triangle is reflected over x axis.
Solution-
While reflecting a point over x axis, (x, y) → (x, -y) rule is followed.
Only the sign of y-coordinate is changed, keeping x-coordinate intact.
In the first picture, though the image is reflected, but it is reflected over y axis.
In the second picture, the image is first reflected over y axis, then it is translated 1 unit down.
We rotating a point 90° clockwise, (x, y) → (y. -x) rule is followed.
In the third picture, the triangle is rotated 90° clockwise and then translated 1 unit to right.
But, in case of the fourth picture, the figure is reflected over x axis. Only the y coordinates sign are changed, all the x coordinates are same as before.
The price of a community pool membership has a one-time sign-up fee and a monthly fee. The price can be modeled by the function y = 20x + 50, where x is the number of months.
What is the slope, and what does it represent?
Answers
Answer:
The answer is 20 and it represents the monthly fee.
Step-by-step explanation:
How many years will it take $1,000 invested at 7% interest to earn $280?
Answers
280/70 = 4
It will take 4 years.
what is the length of a circle that has a central angle of 98 degrees and 6 cm rounded to the nearest 100th. using 3.14
Answers
so...
If we take pi to be 3.14,
Arc length = 2(3.14)(6) * 98/360
= 37.68 * 98/360 = 10.26 cm
a game spinner has regions that are numbered 1 through 8. if the spinner is used twice, what is the probability that the first number is a 3 and the second is a 7?
Answers
P(3) = 1/8
P(7) = 1/8
(1/8) * (1/8) = 1/64
The probability that the first number is a 3 and the second is a 7 is 1/64
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
spinner had region numbered from 1 to 8
So, the probability on the spinner has an equally likely chance of being selected= 1/8.
P(3) = 1/8
P(7) = 1/8
Thus, probability that the first number is a 3 and the second is a 7
=(1/8) * (1/8)
= 1/64
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Which of the following is a solution of x2 + 5x = −2?
5 plus or minus the square root of 33 divided by two.
5 plus or minus the square root of 17 divided by two
negative 5 plus or minus the square root of 33 divided by two.
negative 5 plus or minus the square root of 17 divided by two.
Answers
x^2 + 5x + 2 = 0
x = -b (+-) sqrt (b^2 - 4ac) / 2a
a = 1, b = 5, and c = 2
x = -5 (+-) sqrt (5^2 - 4(1)(2)) / 2(1)
x = -5 (+-) sqrt (25 - 8) / 2
x = -5 (+-) sqrt (17) / 2
answer is : negative 5 plus or minus the square root of 17 divided by 2
Answer:
negative 5 plus or minus the square root of 17 divided by two: [tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
Step-by-step explanation:
We have the equation
[tex]x^2+5x=-2[/tex]
[tex]x^2+5x+2=0[/tex].
To solve it, we are going to use the general formula. This formula is used to find the solutions of quadratic equations.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
where a is the coefficient of [tex]x^2[/tex], in this case a=1, b is the coefficient of x, in this case b=5 and c is the independent term, in this case c=2.
[tex]x=\frac{-5\pm\sqrt{5^2-4(1)(2)}}{2(1)}[/tex]
[tex]x=\frac{-5\pm\sqrt{25-8}}{2}[/tex]
[tex]x=\frac{-5\pm\sqrt{17}}{2}[/tex].
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6 find the toal area of the pyramid
Answers
so.. then we end up with the a 30, 60, 90 angles triangle, and thus we apply the 30-60-90 rule, to get the apothem.
now the area of a regular polygon is just (1/2) (apothem)(perimeter).
now, we know the apothem, the perimeter of the hexagon is just 4+4+4+4+4+4. So, just get those values, plug them in to get the area of the hexagonal base.
if you look at the picture bottom-side, the slant-height of the pyramid, is just the altitude/height of the triangular face. So, you really have 6 triangles whose base is 4 and height is 6, and you know how to get the area of a triangle.
so, just get the area of the base, plus the area of the triangular faces, sum them up, and that's the total area of the hexagonal pyramid.
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Answers
Translation 7 units right gives E(4, 4), F(8, 3), G(10, 6), and H(8, 6) as shown in brown in the diagram below
Reflection on the y-axis gives E(3, 4), F(-1, 3), G(-3, 6) and H(-1, 6) as shown in green in the diagram below
Reflection on the x-axis gives E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) as shown in red in the diagram below
Translation 5 units down gives E(-3, -1), F(1, -2, G(3, 1) and H(1, 1) as shown in purple in the diagram below
Answer:
Answers a little bit more simplified, all credit to the expert :)
E(4, 4), F(8, 3), G(10, 6) and H(8, 6) <-----> a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) <-----> a reflection across the y-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) <-----> a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1) and H(1, 1) <-----> a translation 5 units down
Step-by-step explanation:
Identify all the sets to which 0.41567 belongs. Choose from rational,irrational,whole,and integer
Answers
... rational because it can be expressed as a fraction (e.g., 41567/100000)
... not irrational for the same reason
... not whole (obviously)
... not integer (obviously)
Answer:
1.) D
2.) C
3.) C
4.) B
5.) A
6.) D
7.) A
8.) D
9.) A
10.) D
Step-by-step explanation:
What is a quartic function with only the two real zeros given?
x = -4 and x = -1
A.
y = x4 + 5x3 + 5x2 + 5x + 4
B.
y = x4 - 5x3 - 5x2 - 5x - 4
C.
y = -x4 + 5x3 + 5x2 + 5x + 4
D.
y = x4 + 5x3 + 5x2 + 5x - 5
Answers
So, you need to factor the polynomials given or divide them by (x+1)(x+4).
(x+1)(x+4) = x^2 + 5x + 4
Using the first function you get:
(x^4 + 5x^3 + 5x^2 + 5x + 4) / ( x^2 + 5x + 4) = x^2 + 1
And you know that x^2 + 1 does not have a real solution, so the function
x^4 + 5x^3 + x^2 + x + 4 has the two real solutions given, x = -1 and x = -4, and two not real solutions.
Now you know that the answer is the first option.
If you want to check the other functions you just must divide and analyze the quotient obtained.
Answer: option A. x^4 + 5x^3 + 5x^2 + 5x + 4.
How can ΔABC be mapped to ΔXYZ?
First, translate .
Next, rotate ΔABC about B to align the sides and angles.
Answers
To map ΔABC to ΔXYZ, you need to translate the triangle and then rotate it about a point.
Explanation:In order to map ΔABC to ΔXYZ, you can follow these steps:
First, translate ΔABC by moving it horizontally and vertically to a new position.Next, rotate ΔABC about point B to align the sides and angles with ΔXYZ.By performing these steps, you can map one triangle to another.
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Identify the values of a, b, and c that would be used in the quadratic formula to solve the equation 3x2− 5x + 5 = 0. A. a = 3, b = 5, c = 5 B. a = 3, b = −5, c = 5 C. a = 5, b = −5, c = 0 D. a = −3, b = 5, c = −5
Answers
a=3 b=-5 c=5
A. a = 3, b = 5, c = 5
B. a = 3, b = −5, c = 5
C. a = 5, b = −5, c = 0
D. a = −3, b = 5, c = −5
answer is B
Find the missing value. Show your work
(GEOMETRY, PLEASE HELP!!)
Answers
y=12sin51 units
y≈9.33 units (to nearest hundredth of a unit)
...
tanα=12/5
α=arctan2.4°
α≈67.38° (to nearest hundredth of a degree)
...
tan13=x/24
x=24tan13 units
x≈5.54 units (to nearest hundredth of a unit)
...
sin20=10/x
x=10/sin20 units
x≈29.24 units (to nearest hundredth of a unit)
Why is it difficult to measure circumference accurately? answers?
Answers
One of either the circumference or distance across is not rational. If you have a bit of string precisely 1 inch long and you make it into an idealize circle, the distance across of that circle will be an irrational value. You could try to measure it, however regardless of how precisely you measured it, it would in any case not be very sufficiently precise. So, you can never know precisely what the diameter is just by measuring.
What's more, on the off chance that you took that string and made a width with it, the circumference would be irrational and you could never have the capacity to measure the circumference precisely enough. Whatever you quantified would be close however not correct.
A cell phone company orders 500 new phones from a manufacturer. If the probability of a phone being defective is 2.6%, predict how many of the phones are likely to be defective. Round to the nearest whole number.
A.)16 phones
B.)11 phones
C.)13 phones
D.)130 phones
Answers
0.026(500) = 13 <==
Boating across a river, the current moves you downstream. Instead of going directly across the river, the boat moves at a 10 degree angle. If the river is 420 feet across, how far downstream will you end up?
Answers
To solve this problem, we use the tan function. The distance across the river is the adjacent side, the distance drownstream is the opposite side while the direction of the boat is the hypotenuse.
tan θ = opposite side / adjacent side
tan 10 = opposite side / 420 ft
opposite side = 74.06 ft
Therefore the boat will move about 74 ft downstream.
What would you do to isolate the variable in the equation below, using only one step? x + 5 = -12 Select one: a. Add 5 to both sides of the equation. b. Subtract 5 from both sides of the equation. c. Add 12 to both sides of the equation. d. Subtract 12 from both sides of the equation.
Answers
To isolate the variable in x + 5 = -12, subtract 5 from both sides of the equation. This leads to the equation x = -12 - 5.
Explanation:In order to isolate the variable x in the equation x + 5 = -12, you should subtract 5 from both sides of the equation. This gives us the equation in a simplified form that allows us to determine the value of x. The idea here is to cancel out the +5 on the left side by subtracting 5 from both sides, resulting in x = -12 - 5. Hence, the answer is option b.
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Describe the relationship between the segments made when secant lines intersect outside a circle. Use the following image as reference.
Answers
Let the measure of ar DC be 2a, then m(DAC)=m(DBC)=a, since angles DAC and DBC are both inscribed angles intercepting arc DC.
m(P)=b.
Then triangles APC and BPD are similar, because they have 2 pairs of common angles.
from the similarity of APC and BPD, we can write the ratios:
[tex] \frac{AP}{BP} = \frac{PC}{PD} = \frac{AC}{BD} [/tex]
Can someone please answer this for me I'm begging
Answers
As we know the length of circle is 2π*r in this case r = 8.2
The arc JM is 1/4 length of the whole circle so arc JM = (2π*8.2)*(1/4) = 2π*8.2/4 = π*8.2/2 = π*4.1
if we assume that π=3.14 the answer will be 3.14 * 4.1 = 12.874.... And as the answer needs to be rounded to the nearest tenth it will be 12.874≈12.9
So the answer will be 12.9
Consider the trinomial x2 – 9x + 18. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?
Answers
AC = 18
Factors of AC: 1 * 18, 2 * 9, 3 * 6, -1 * -18, -2 * -9, -3 * -6
Sum to -9: 19, 11, 9, -19, -11, -9
(x - 3)(x - 6)
The required pair of number are -3 and -6
The factored form of the trinomial is (x-3) and (x-6)
The standard form of a quadratic equation is expressed as:
[tex]ax^2+bx+c=0[/tex]
Given the expression [tex]x^2 - 9x + 18.[/tex]
[tex]a=1\\b=-9\\c=18[/tex]
We are to get two values that we must add to get b, and that we will multiply that will give c.
The given values are -6 and -3
Check:
[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]
Factorize the trinomial
[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]
Hence the factored form of the trinomial is (x-3) and (x-6).
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Can someone please help me
Answers
B = area of base
h = height of cylinder
It turns out that
V = B*h
In a similar way to that of a cube
If we know that V = 84pi and h = 7, then we can plug those values into the formula above, and solve for B
V = B*h
84pi = B*7
84pi/7 = B*7/7 ... divide both sides by 7
12pi = B
B = 12pi
Therefore the base is 12pi square units
what is the average rate of change for this quadratic function please help
Answers
---------------------------------------------------
---------------------------------------------------
Explanation:
When x = 0, the value of y is y = -6. You can see this as you draw a vertical line through x = 0. This vertical line is the y axis. The parabola crosses the y axis at -6. This point is the y intercept.
When x = 3, the value of y is y = 0. This is one of the two x intercepts. An x intercept is a location where the graph crosses the x axis.
So we have the two points (0,-6) and (3,0). Let's find the slope of the line through these two points
(x1,y1) = (0,-6)
(x2,y2) = (3,0)
Slope:
m = (y2-y1)/(x2-x1)
m = (0-(-6))/(3-0)
m = (0+6)/(3-0)
m = 6/3
m = 2
The slope of the line through those two point is m = 2.
WILL GIVE A BRAINLIEST IF UR RIGHT!!
Evaluate f(–2) in the given function below.
f(x)= 3x-3 if -5 ≤ x < 3 x+4 if 3 ≤ x ≤ 12
A.
–6
B.
–3
C.
2
D.
–9
Answers
f(-2)=3(-2)-3
f(-2)=-6-3=-9
so D is correct
PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?
3y − x = −6
4y − x = 44
3y + x = −6
4y + x = 44
3y − 3x = −6
4y − 4x = 44
3y + 3x = −6
4y + 4x = 44
Answers
ur 2 equations are :
y = 1/3x - 2 and y = 1/4x + 11...but we need them in standard form...
y = 1/3x - 2
-1/3x + y = -2 ..multiply by 3
-x + 3y = -6.....or 3y - x = -6 <==
y = 1/4x + 11
-1/4x + y = 11 ...multiply by 4
-x + 4y = 44 or 4y - x = 44 <==
The system of equations are 3y − x = −6 and 4y − x = 4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
One third x − 2 = one fourth x + 11
1/3x - 2 = 1/4x + 11
Now let us take y as 1/3x - 2
y= 1/3x - 2
3y=x-6
Subtract x on both sides
3y-x=-6
and Let us consider the right side equation
y=1/4x + 11
4y=x+44
Subtract x on both sides
4y-x=44
Hence, the system of equations are 3y − x = −6 and 4y − x = 44
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A recipe for pastry has flour, butter and water mixed in the ratio 24 : 8 : 3 if fiona follows the recipe and uses 3 cups of flour, how many cups of butter should she use?
Answers
Ratio = amount of flour / amount of butter
Ratio = 24 / 3 = 8
This means that there is 8 cups of flour in every cup of butter.
Amount of butter = (3 cups of flour) x (1 cup of butter / 8 cups of flour)
Amount of butter = 3/8 cups of butter
Hence, the amount of butter needed is 3/8 cups.
The same can be done in order to determine the amount of water needed to be mixed for the recipe.
Fiona should use 1 cup of butter when using 3 cups of flour, according to the recipe's ratio of 24:8:3 for flour to butter to water.
Explanation:The question asks how much butter Fiona should use if she's using 3 cups of flour and the recipe calls for flour, butter, and water in the ratio of 24:8:3. To solve this, we take the ratio for butter (which is 8) and divide it by the flour ratio (which is 24), then multiply by the number of cups of flour Fiona is using (which is 3 cups).
Step-by-step Solution:
Write down the original ratio: 24 parts flour : 8 parts butter : 3 parts water.Calculate the ratio of butter to flour, which is 8/24. This simplifies to 1/3.Since Fiona is using 3 cups of flour, multiply the simplified butter ratio by the amount of flour: (1/3) * 3 cups = 1 cup. Thus, she would need 1 cup of butter.