Answer:
A) All real numbers
B) All real numbers except y = 0
C) All real numbers except x = -7
D) All real numbers except b = 10
Step-by-step explanation:
An expression is defined at all those points at which it does not give the value equal to [tex]\infty[/tex] or does not give the zero by zero form.
i.e. [tex]\frac{0}{0}[/tex] Numerator and Denominator both having zeroes.
Now, let us have a look at the given expressions:
A) 5y+2
Here, Denominator is 1. So, there is no constraint on the value of y.
Hence, at all Real Numbers, the expression is defined.
[tex]B)\ \dfrac{8}{y}[/tex]
Here, denominator is y,
At [tex]y = 0[/tex], the value of expression will approach towards [tex]\infty[/tex]
Hence, this expression is defined at All Real numbers except y = 0
[tex]C)\ \dfrac{1}{x+7}[/tex]
Here, zero by zero form is not possible.
Let us check the value of x where the denominator can be 0 and as a result the expression tends to reach value [tex]\infty[/tex].
x+7=0
At x = -7, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].
Hence, the expression is defined at All real number except x = -7
[tex]D) \dfrac{2b}{10-b}[/tex]
Here zero by zero form is not possible.
Let us check the value of b where the denominator can be 0 and as a result the expression tends to reach value [tex]\infty[/tex].
10-b=0
At b = 10, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].
Hence, the expression is defined at All real number except b = 10
Helpppp pleaseee
What is the solution to -2(8x – 4)< 2x + 5?
Ox>
Ox<
O x > 6
O x<6
Answer:
x> 1/6
Step-by-step explanation:
-2(8x – 4)< 2x + 5
Distribute
-16x +8 < 2x+5
Add 16x to each side
-16x +8+16x < 2x+16x+5
8 < 18x+5
Subtract 5 from each side
8-5 < 18x
3 < 18x
Divide each side by 18
3/18 < 18x/18
1/6 < x
Answer:
[tex]x > \frac{1}{6} [/tex]
First answer is correct.
Step-by-step explanation:
[tex] - 2(8 x - 4) < 2x + 5 \\ - 16x + 8 < 2x + 5 \\ - 16x - 2x < - 8 + 5 \\ - 18x < - 3 \\ \frac{ - 18x}{ - 18} < \frac{ - 3}{ - 18} \\ x > \frac{1}{6} [/tex]
How much x% sugar syrup can you make if you have 100 grams of sugar?
Answer:
100/x/100
Step-by-step explanation:
Step-by-step explanation:
What are the intercepts of the function?
The x-intercepts are
Consider the function f(x) = x2 + 12x + 11.
x-intercepts:
0= x2 + 12x + 11
0 = (x + 1)(x+ 11)
The y-intercept is
y-intercept
f(0) = (0)2 + 12(0) + 11
) Intro
Done
Answer:
see explanation
Step-by-step explanation:
To find the x- intercepts let f(x) = 0, that is
x² + 12x + 11 = 0 ← in standard form
(x + 1)(x + 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 11 = 0 ⇒ x = - 11
The x- intercepts are x = - 11 and x = - 1
To find the y- intercept let x = 0, that is
f(0) = 0² + 12(0) + 11 = 0 + 0 + 11 = 11
The y- intercept is 11
which of the following is equal to the rational expression when x ≠ -1 or -7
Answer:
A.
Step-by-step explanation:
When you simplify the equation down by getting rid of (x + 1) (and that creates a hole in the graph), you should end up with A as your answer.
Which would be appropriate compatible numbers to use to estimate (19 4/5)(4/6)
Answer:
Approximately 10
Step-by-step explanation:
19 / 5 Approximately 4
4 * 4 = 16
16 * 4 / 64
64 / 6 * = Approximately 10 / 10.6 ish
Actual Answer is 10.133
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Which expression is equivalent to (150x-80y+ 50-50x-25y+20)?
20x-214+ 14
20x+ 11y + 14
20x-11y+6
20x+21y+6
Answer:
20x+21y+14
Step-by-step explanation:
Combine like terms:
150x-80y+50-50x-25y+20=
100x-80y+50-25y+20=
100x-105y+50+20=
100x-105y+70
100x-105y+70 can be divided by 5 and get 20x+21y+14.
Answer:a
Step-by-step explanation:
How many roots do u thinn
Answer:
2 roots1 rootStep-by-step explanation:
Each equation is in vertex form, so you can easily determine the number of real roots. The leading coefficient tells you whether the parabola opens upward (positive) or downward (negative).
y = a(x -h)^2 +k
has leading coefficient "a" and vertex (h, k).
__
f(x) = 1/3(x +5)^2 +7
vertex: (-5, 7), opens downward
The vertex is above the x-axis, so there are two real roots.
__
f(x) = -5(x -3)^2
vertex: (3, 0), opens downward
The vertex is on the x-axis, so there is one real root.
Sam bright a Canada saving bond paying 4% interest and a provincial government bond paying 5% interest. He invested a total of $15,000 and earned $690 in interest in the first year. How much did he pay for each bond? PLEASE ANSWER THIS ASAP
Answer:
Money invested in Canada saving bond is $6000.
Money invested in provincial government bond is $9000.
Step-by-step explanation:
First of all, let us have a look at the formula for simple interest:
[tex]SI = \dfrac{P\times R\times T}{100}[/tex]
Where P is the amount invested
R is the rate of interest and
T is the time
We are given here, 2 bonds in which a total of $15000 were invested
Let money invested in Canada saving bond [tex]P_1[/tex], = $x
Rate of interest, [tex]R_1=4\%[/tex]
Time, [tex]T_1 = 1\ year[/tex]
[tex]SI_1 = \dfrac{P_1\times R_1\times T_1}{100}\\\Rightarrow \dfrac{x\times 4\times 1}{100} ..... (1)[/tex]
Let money invested in provincial government bond [tex]P_2[/tex], = $(15000-x)
Rate of interest, [tex]R_2=5\%[/tex]
Time, [tex]T_2 = 1\ year[/tex]
[tex]SI_2 = \dfrac{P_2\times R_2\times T_2}{100}\\\Rightarrow \dfrac{(15000-x)\times 5\times 1}{100} ..... (2)[/tex]
We are given that
[tex]SI_1+SI_2=$690\\\text{Using equations (1) and (2):}\\\\\Rightarrow \dfrac{4x}{100} + \dfrac{(15000-x)\times 5}{100} = 690\\\Rightarrow 4x + (75000-5x) = 69000\\\Rightarrow x = \$6000[/tex]
Money invested in Canada saving bond = $6000
Money invested in provincial government bond = $15000-$6000 = $9000
heklp me again please if you dont mind
Step-by-step explanation:
This is the answer of this question.
terrace buys a new car for 20,000 the value of the car depreciates by 15% each year if f(x) represents the value of the car after x years which function represents the care value
Answer:
f(x)= 20,000[tex](0.85)^{x}[/tex]or 20,000 (0.85) to the power of x.
Step-by-step explanation:
Okay, so based on the question, we know that the car is depreciates its value every year. In case you don't know, when something depreciates, it is becoming smaller or less in value. It comes to a point where the item becomes worthless. Recall, that the formula for an exponential function is y= a(b) to the power of x. A is your initial value or your y-intercept. B is the multiplicative rate of change. Lets put 20,000 for a because that is value of the car that terrace purchased before any depreciation happened. Since it says that it is decaying every year, we don't want to graph how much it is decaying, we want to graph what the value is of the car. So, do 100 percent minus 15 which is 85 percent. You need to change it into decimal, so it is 0.85. Therefore, there is your function.
Hope this helps!
Which equations are correct? Select each correct answer.
Answers:
Option two, 5[tex]y^{4}[/tex](2[tex]y^{5}[/tex]) = 10[tex]y^{9}[/tex] and option 4, 5[tex]x^{3}[/tex](6[tex]x^{4}[/tex]) = 30[tex]x^{7}[/tex]
Step-by-step explanation:
O1 + O3 = incorrect, the powers have been multiplied together. Laws of indices suggest that if you are multiplying powers together, you must add them, not do 4 x 5 or 2 x 2.
Please remember:
2y squared x 3y cubed = 6y to the power 5
Answer:
Solution(s) : Option # 2 and # 4
Step-by-step explanation:
One quick way to identify which solutions are accurate would be adding the exponents of the terms provided ( b, y, c etc ). As you can see in each example two expressions are being multiplied, and hence the exponents of each term are being added.
Therefore the second and fourth example are correct, as 4 + 5 = 9, the co - efficient of y. And 3 + 4 = 7, the co - efficient of x.
Check :
[tex]5y^4\left(2y^5\right)[/tex] = [tex]5\cdot \:2y^{4+5}[/tex] = [tex]5\cdot \:2y^9[/tex] = [tex]10y^9[/tex]
[tex]5x^3\left(6x^4\right)[/tex] = [tex]5\cdot \:6x^{3+4}[/tex] = [tex]5\cdot \:6x^7[/tex] = [tex]30x^7[/tex]
a rectangle has an area of 40 sq units , then length is 6 units greater than the width
Answer:
A=L*W
Let w be width
L=(w+6)
40=(w+6)*w
40= w^{2} +6w
w^{2} +6w-40=0
w^{2}+10w-4w-40=0
w(w+10)-4(w+10)=0
(w-4)(w+10)=0
w=4
Length= 10 units
Width=4 units
Step-by-step explanation:
What is the value of x? [PART 2] A.285˚ B.105˚ C.75˚ D.15˚
Answer:
x = 17
Step-by-step explanation:
The two angles form a straight line so they add to 180 degrees
5x-18 + 4x+45 = 180
Combine like terms
9x +27 = 180
Subtract 27 from each side
9x+27-27 =180-27
9x =153
Divide by 9
9x/9 = 153/9
x =17
WILL GIVE BRAINLIEST Which pairs of rectangles are similar polygons? Select each correct answer. 1)two rectangles. larger rectangle has left side labeled 1225 m and bottom labeled 144 m. the smaller rectangle has left side labeled 3.5 m and bottom side labeled 1.2 m. 2)two rectangles. larger rectangle has left side labeled 13 m and bottom labeled 5 m. the smaller rectangle has left side labeled 5.2 m and bottom side labeled 2.5 m. 3)two rectangles. larger rectangle has left side labeled 18 m and bottom labeled 6 m. the smaller rectangle has left side labeled 4.5 m and bottom side labeled 1.5 m. 4)two rectangles. larger rectangle has left side labeled 40 m and bottom labeled 15 m. the smaller rectangle has left side labeled 8 m and bottom side labeled 3 m.
Answer: Look at the picture :)
The pairs of rectangles that are similar polygons are those in;
1 and 4
For two rectangles to be similar polygons, it means that the ratio of their corresponding sides must be the same.
In question 1;
Ratio of corresponding left sides = 1225/3.5 = 350
Ratio of corresponding bottom sides = 144/1.2 = 120
Ratios do not correspond and as such they are not similar polygons.
In question 2;
Ratio of corresponding left sides = 13/5.2 = 2.5
Ratio of corresponding bottom sides = 5/2.5 = 2
Ratios do not correspond and as such they are not similar polygons.
In question 3;
Ratio of corresponding left sides = 18/4.5 = 4
Ratio of corresponding bottom sides = 6/1.5 = 2l4
Ratios correspond and as such they are similar polygons.
In question 4;
Ratio of corresponding left sides = 40/8 = 5
Ratio of corresponding bottom sides = 15/3 = 5
Ratios correspond and as such they are similar polygons.
Read more at;https://brainly.com/question/20590854
If 3x-5=6x-2 is -1. Then how do I do a check step? :(
Answer:
ok,just substitute the x for -1
3x-5=6x-2
3(-1)-5=6(-1)-2
-3-5 = -6-2
-8 = -8
TRUE
So,the solution is correct.-1 is the correct solution
I hope this help,Please give me the brainliest
Step-by-step explanation:
A blue sqaure is placed inside a large yellow square The centres of the squares are aligned one over the other one side of the square is (3x + 2)cm and the other side is (8 - x)cm the area of the blue square is 36% the area of the yellow square. Find the dstance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Answer:
the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
Step-by-step explanation:
From the information given;
A blue square is placed inside a large yellow square and the centres of the squares are aligned one over the other
So ; if one side of the square is (3x + 2)cm (i.e the blue side)
the other side is (8 - x)cm (i.e the yellow sides)
since the two shapes given are squares ; we can say that:
(3x+2)= (8 - x)
3x +x = 8 -2
4x = 6
x = 6/4
x = 1.5
Let replace x = 1.5 for the sides of the square and find the actual length of the square sides.
So, for the yellow side; we have:
= (8 - x)cm
= (8 - 1.5 ) cm
= 6.5 cm
We all know that the area of the square = l²
then the area of the yellow side = (6.5 cm )²
the area of the yellow side = 42.25 cm²
Let y be the distance between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner
Since the blue region is inside the yellow region; to calculate for the side of the blue region ; we have:
(6.5y -y+y) cm
(6.5 - 2y )cm
The area of the blue side =( (6.5 - 2y )cm)²
The area of the blue side = (6.5 - 2y )² cm²
However; we are also given that :
the area of the blue square is 36% the area of the yellow square.
Thus;
(6.5 - 2y )² = 36/100 × 42.25
(6.5 - 2y )² = 0.36 × 42.25
(6.5 - 2y )² = 15.21
(6.5 - 2y ) = [tex]\sqrt{15.21}[/tex]
(6.5 - 2y ) = 3.9
6.5 - 2y = 3.9
6.5 - 3.9 = 2y
2.6 = 2y
y = 2.6/2
y = 1.3 cm
Therefore , the distance y between the bottom right corner of the blue square and the right side of the yellow square directly next to the corner is 1.3cm
In a 10% sale a jumper costs £36. How much does it usually cost?
A. 40
B. 39.60
C. 32.40
D. 360
Answer:
A. 40
Step-by-step explanation:
CP= x, SP= £36, sale= 10%
SP= CP- 10%= CP*0.9
x*0.9= £36
x= £36/0.9= £40
Find the 14th term of geometric sequence 5,-10,20,...
Answer:
-40960
Step-by-step explanation:
5,-10,20,..
first term= 5 and common ratio= -2
aₙ= a₁*rⁿ⁻¹
a₁₄= 5*(-2)¹³= -40960
Please help! What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 4.5? ^ means squared A.) Perimeter = 46 cm, area = 131.25 cm^2 B.) Perimeter = 126 cm, area = 972 cm^2 C.) Perimeter = 46 cm, area = 972 cm^2 D.) Perimeter = 126 cm, area = 131.25 cm^2
Answer:
B.) Perimeter = 126 cm, area = 972 cm²
Step-by-step explanation:
==>Given:
Rectangle with the following dimensions:
L = 8 cm
W = 6 cm
==>Required:
Perimeter and area of the rectangle if enlarged using a scale factor of 4.5.
==>Solution:
The dimensions of the rectangle when enlarged by a scale factor of 4.5 would be:
L = 8 × 4.5 = 36cm
W = 6 × 4.5 = 27cm
=>Area = L × B
= 36 × 27
Area = 972 cm²
=>Perimeter = 2(L + W)
= 2(36 + 27)
= 2(63)
Perimeter = 126 cm
please help thank you
Answer:
y=5x+15
Step-by-step explanation:
We get y=5x+15 since she charges a one time fee of $15 and $5 every hour.
Answer:
Answer D
Step-by-step explanation:
11(4x+13)+12x-17 PLZ HELP WILL HAVE MORE QUESTIONS. ANSWER ASAP
Answer:
56x + 126
Step-by-step explanation:
Step 1: Distribute
44x + 143 + 12x - 18
Step 2: Combine like terms
56x + 126
[tex]\text{Simplify the expression}\\\\11(4x+13)+12x-17\\\\\text{Use the distributive property}\\\\44x+143+12x-17\\\\\text{Combine like terms}\\\\\boxed{56x+126}[/tex]
Write a compound inequality that represents the situation. All real numbers are at least -6 and at most 3
Answer:
{x ∈ ℝ | -6 ≤ x ≤ 3}
Step-by-step explanation:
For a real number x, numbers that are at least -6 are ...
x ≥ -6
and numbers that are at most 3 are ...
x ≤ 3
This can be written as a compound inequality with x in the middle as ...
-6 ≤ x ≤ 3 . . . . x is a real number
helppppppp pls I don't get itttt
Answer:
c: 5 x 3/5
Step-by-step explanation:
so the is 15 blocks shaded on the 25 grid
so i would work out each fraction answer and find which one makes 15/25
5 x 5/3 = 25/25
3/5 + 3/5 + 3/5 + 3/5 + 3/5 + 3/5 = 21/5
5 x 3/5 = 15/25
hope this helps :)
if the answer is wrong plz comment and i will fix thanks :)
Answer:
c) 5x3/5
Step-by-step explanation:
Look at one of the bars only. We see that 3 blocks out of 5 are colored in.
So that means the fraction is 3/5. But since there are 5 bars, we must multiply the fraction by 5.
Therefore, the answer is c) 5x3/5
hope this helped:)
P.S. If you like the answer, could you mark as brainliest plz?
Angle X measures _____ degrees. Angle Y measures _____ degrees. The value of x is ______ degrees. Tha value of y is _____ degrees.
Answer:
Angle x measures 64 degrees and Angle y also measures 64 degrees. X is 11. The value of y is also 11.
Step-by-step explanation:
Alright, so this triangle is an isosceles triangle since there are lines on two sides meaning they are congruent to each other. So, if the sides are congruent, then the angles are also congruent. Angle y is congruent to angle x. First, lets find what they measure totally. Since they are congruent, we can write the equation with 2x+angle w which is 52=180 because the sum of all angles in a triangle is 180. Subtract 52 from both sides 2x=132 divide both sides by 2, and you get 64. You found what angle x and y equal. Now you can find what the value of x and y. For finding x, 4x+20=64 and for y, 6y-2=64. Isolate each variable, and you get 11 for both the value of x and y.
Find the value of x. 5x+18+2x=5
Answer: x=-1.9
Step-by-step explanation:
[tex]5x+2x=7x[/tex]
[tex]7x+18=5[/tex]
-18 on both sides
[tex]7x=-13[/tex]
divide 7 on both sides
[tex]x=-1.9[/tex]
Answer
X=-1.9solution
[tex]5x + 18 + 2x = 5 \\ or \: 5x + 2x + 18 = 5 \\ or \: 7x + 18 = 5 \\ or7x = 5 - 18 \\ or \: 7x = - 13 \\ \: x = - \frac{13}{7} [/tex]
X=-1.9
hope this helps..
Good luck on your assignment...
I NEED HELP PLEASE, THANKS! :)
Answer: D) reflection over the x-axis, vertical shrink by a factor of 7/8, horizontal shift 3 units to the left, and vertical shift 3 units up.
Step-by-step explanation:
[tex]Consider\ f(x)=Ae^{Bx-C}+D\qquad where[/tex]
A = vertical stretch by a factor of A (|A| < 1 is a vertical shrink)-A = reflection across the x-axisB = horizontal shrink by a factor of 1/BC = horizontal shift C units (positive = right, negative = left)D = vertical shift D units (positive = up,, negative = down)[tex]f(x)=e^x\\\\g(x)=-\dfrac{7}{8}e^{x+3}+3[/tex]
→ A = -(7/8)
The negative sign represents a reflection across the x-axis.
(7/8) < 1 so it is a vertical shrink by a factor of (7/8)
→ C = -3 x +3 = x - (-3)
This is a horizontal shift 3 units to the left.
→ D = +3
This is a vertical shift 3 units up.
for the following geometric sequence find the recursive formula. {1, -3, 9, ...}
Answer:
[tex]g_{n}=g_{n-1} *-3[/tex]
Step-by-step explanation:
A recursive formula is [tex]g_{n}=g_{n-1} *r[/tex]. N is the number of terms and r is the rate of change. R here equals -3 because you are multiplying by -3 eachtime. Therefore, the recursive formula is [tex]g_{n}=g_{n-1} *-3[/tex]
Calculate the area and perimeter of the following ring where
a = 7cm,
b = 14cm
Area of Ring:
Perimeter of Ring:
(its urgent)
Answer:
Area=19
perimeter=21
La suma de las edades de tres personas es 127años. La mayor tiene 30 años mas que la menor y la del intermedio 26 menos que la menor.¿ calcula la edad de la persona mayor'
Answer:
La mayor tiene 61 años.
Step-by-step explanation:
Sea x,y,z la edad de la mayor, intermedio y la menor respectivamente.
Tenemos las siguientes ecuaciones:
[tex]x+y+z=127[/tex] (la suma de las edades es 127)
[tex]x = z+30[/tex] (la mayor tiene 30 años más que la menor)
La frase "y la del intermedio 26 menos que la menor" no tiene sentido, puesto que esto implicaría que la del intermedio es menor que la menor. Luego se asume que la frase ha de ser "y la del intermedio 26 menos que la mayor"
[tex]x-26 = y[/tex] (la del intermedio tiene 26 menos que la mayor).
La segunda ecuación se traduce a x-30 =z. Si reemplazamos todo en la primera ecuación obtenemos
[tex]x+(x-26)+(x-30) = 127[/tex]
Obtenemos la ecuación
[tex]3x-56 = 127[/tex]
Sumando 56 a ambos lados y dividiendo por 3, obtenemos
[tex] x = \frac{127+56}{3} = 61[/tex]
Es decir la mayor tiene 61 años.
determine which function has the greatest rate of change as x approaches infinity f(x)=4x+50, g(x)=3^x-4, h(x)=2x^2+9x-4, there is not enough information to determine the answer
Answer:
g(x)=3^x-4, this one is exponential so it would have the greatest rate of change as x approaches infinity. The first one is a line and the third one is a parabola.
Step-by-step explanation: