Answer:
Step-by-step explanation:
Set up a table for a distance = rate × time problem. We are considering the trips taken on Monday and Tuesday.
d = r × t
Monday
Tuesday
Now let's start filling in what we know. First off, Fran went to her Mother's both days. Unless her Mother moved overnight from Monday to Tuesday, the distance from Fran to her mom is the same both days, even though we don't know how far it is. So we will just call that "d".
d = r × t
Monday d =
Tuesday d =
Now we are told about the times it took to get there on both days. Monday took 2.7 hours and Tuesday took 3 hours. Filling in that:
d = r × t
Monday d = × 2.7
Tuesday d = × 3
We're getting there. Now let's look at rates. Again, we don't know her rate (that's what we are solving for!) but we do know that she drove faster on Monday than Tuesday. Tuesday she was 6 miles per hour slower than Monday. Since we don't know Monday's rate, we will call it r. Since we don't know Tuesday's rate, but only that it is 6 mph slower than Monday, we will call it r - 6
d = r × t
Monday d = r × 2.7
Tuesday d = r-6 × 3
Now we have our equations. We know that d = rt. Since the distances are the same, d = d, by the transitive property of equality, we can set the 2 expressions equal to each other:
2.7r = 3(r - 6) and solve for r:
2.7r = 3r - 18
-.3r = -18
r = 60
If r = 60, then that r value goes in for Monday. That means that Tuesday is 60 - 6 which is 54
What was her average speed on Tuesday is 54 mph
Monday
Time = 2.7 hours
Date = r mph
Distance = 4.5r miles
Tuesday
Time = 3 hours
rate = r-6 mph
Distance = 3(r-6) miles
Hence:
Distance = distance
2.7r=3(r-6)
2.7r = 3r - 18
0.3r = 18
r =18/0.3
r 60 mph ( Monday rate)
r-6=60-3 (Tuesday rate)
r-6 = 54 mph (Tuesday rate)
Inconclusion What was her average speed on Tuesday is 54 mph.
Learn more here:
https://brainly.com/question/13238620
Which of the following is the equation for the line of symmetry in this figure?
y = 4
x = 4
y = 3
x = 3
Answer:
x = 3
Step-by-step explanation:
A line of symmetry splits a figure into 2 exact, mirror images of one another. The line here that does that is x = 3
Answer:
x=3
Step-by-step explanation:
Evaluate (5 + 2)2 − 40 + 3 = __________.
NUMERICAL ANSWER EXPECTED!
Answer for Blank 1:
Answer:
-28
Step-by-step explanation:
(5+2) = 7
7 + 2 - 40 = -31
-31 + 3 = -28
What fraction is equal to the percent? Simplify the fraction. 16% =
Answer: 16% as a fraction is 4/25
Step-by-step explanation:
convert 16% into a decimal then put it over 100 and simplify which gives you 4/25
Answer: [tex]=\frac{4}{25}[/tex]
Step-by-step explanation:
First, you need to convert 16% to decimal form. To do this, you must divide it by 100. Then, the numerator will be 16 and the denominator will be 100:
[tex]=\frac{16}{100}[/tex]
And finally, you need to simplify the fraction by reducing it. Notice that the numerator and the denominator can be both divided by 4. Then, dividing by 4 you get:
[tex]=\frac{4}{25}[/tex]
Since the numerator and the denominator cannot be divided by the same number anymore, then the fraction is simplified.
Therefore, the fraction equal to 16% (simplified) is:
[tex]=\frac{4}{25}[/tex]
MA 912. G.1.4
60. What is the slope of a line that passes through the point (-1, 1) and is parallel to a line that passes through
(3.6) and (1, -2)?
Answer:
Step-by-step explanation:
Going from (1, -2) to (3,6), x increases by 2 and y increases by 8. Thus, the slope m of this line is m = rise / run = 8/2 = 4.
I think you meant, "What is the EQUATION of the line that passes through the point (-1, 1) and is parallel to a line that passes through
(3, 6) and (1, -2)? We have seen that this slope is -4.
Starting with the point-slope equation of a line, we have:
y - 6 = -4(x - 3)
Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.
Answer:
y = (1/12)x^2
Step-by-step explanation:
The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).
The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus. Here that distance is p = 3.
Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.
The answer is: y = (1/12)x^2.
The equation of the parabola with focus (a,b) and directrix y=c is
(x−a)2+b2−c2=2(b−c)y
The equation for a parabola with its focus at (0, 3) and a directrix of y = -3 i.e:
The vertex of this parabola is halfway between (0, 3) and the directrix, y = -3; that is, it's at (0, 0).
The applicable equation for this vertical parabola is 4py = x^2, where p is the distance between the vertex and the focus. Here that distance is p = 3.
Thus, 4py = x^2 becomes 4(3)y = x^2, or 12y = x^2, or y = (1/12)x^2.
Learn more about the equation of a parabola with focus and directrix: https://brainly.com/question/12760808
#SPJ2
100 POINTS WILL MARK AS BRAINLIEST HHHHHHHHHHHHHHEEEEEEEEELLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!
Rewrite the parametric equation by eliminating the parameter.
x = 3t+1 and y = t-4
y = 4x-3
y = 2x+5
y = x-13/3
y = x-5/3
You can make one equation equal to t instead of y or x. I decided to make the equation y = t - 4 equal to t
y + 4 = t + (-4 + 4)
t = y + 4
Now in the other equation ( x = 3t + 1) you can replace t with y + 4 and solve for y
x = 3(y + 4) +1
x = 3y + 12 + 1
x = 3y + 13
x - 13 = 3y
y = x/3 -13/3
^^^I assume that's what you meant in the fourth opption when you wrote "y = x - 13/3"
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
The correct option is C) [tex]y=\frac{x-13}{3}[/tex].
Step-by-step explanation:
Consider the provided parametric equations.
[tex]x=3t+1......(1)[/tex]
[tex]y=t-4......(2)[/tex]
The equation (2) can be written as:
[tex]y+4=t[/tex]
Substitute the value of t in equation (1).
[tex]x=3(y+4)+1[/tex]
[tex]x=3y+12+1[/tex]
[tex]x=3y+13[/tex]
[tex]x-13=3y[/tex]
[tex]y=\frac{x-13}{3}[/tex]
Therefore, the correct option is C) [tex]y=\frac{x-13}{3}[/tex].
In the figure. What is the value of x?
180-40-60=80 degrees
1. Find sin? if cos?=1/2 and ? terminates in Quadrant IV. 2. Find cos? if sin?=(?2)/2 and ? terminates in Quadrant I. 3. Find tan? if cos?=-1/2 and ? terminates in Quadrant II. 4. Find tan? if sin?=-1 and 0??<2? radians.
1. [tex]x[/tex] in quadrant IV means [tex]\sin x<0[/tex], so
[tex]\cos^2x+\sin^2x=1\implies\sin x=-\sqrt{1-\cos^2x}=-\dfrac{\sqrt3}2[/tex]
2. [tex]x[/tex] in quadrant I means [tex]\cos x>0[/tex]. Then
[tex]\cos x=\sqrt{1-\sin^2x}=\dfrac{\sqrt2}2[/tex]
3. [tex]x[/tex] in quadrant II means [tex]\sin x>0[/tex]. Then
[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{1-\cos^2x}}{-\frac12}=\dfrac{\frac{\sqrt3}2}{-\frac12}=-\sqrt3[/tex]
4. If [tex]\sin x=-1[/tex], then [tex]\cos x=0[/tex], so [tex]\tan x[/tex] is undefined.
Solve the system of equations. (3x + 4y = 5) (2x - 3y = -8)
A)y = -x = 2
B)x = -1, y = 2
C)x = -4, y = 0
D)x = 3, y = -1
Answer:
the solution is (-1, 2)
Step-by-step explanation:
Let's solve the system
(3x + 4y = 5)
(2x - 3y = -8)
using the method of elimination by addition and subtraction. Notice that if we multiply all terms of the first equation by 3 and all terms of the second by 4, y as a variable will temporarily disappear:
9x + 12y = 15
8x - 12y = -32
-----------------------
17x = - 17, so x = -1.
Replacing x in the second equation by -1, we get:
2(-1) - 3y = -8, or
2 + 3y = 8,
or 3y = 6. Thus, y = 2, and the solution is (-1, 2).
The solution to the given system of equations is x = -1 and y = 2. We found these values using the elimination method, first by making the coefficients of x in both equations the same, then eliminating x and solving for y, and finally substituting y = 2 into the first equation and solving for x.
Explanation:To solve the given system of equations, we can use the elimination method. First, we need to make the coefficients of either x or y the same in both equations. We can do so by multiplying the first equation by 2 and the second equation by 3:
⟹ (3x * 2 + 4y * 2 = 5 * 2) and (2x * 3 - 3y * 3 = -8 * 3)
When simplified, we get:
⟹ 6x + 8y = 10 and 6x - 9y = -24
Now, we subtract the second equation from the first one to eliminate x:
⟹ (6x + 8y) - (6x - 9y) = 10 - (-24)
⟹ 17y = 34
Finally, we solve for y by dividing both sides of the equation by 17:
⟹ y = 34 / 17
⟹ y = 2
Substitute y = 2 into the first original equation:
⟹ 3x + 4 * 2 = 5
⟹ 3x + 8 = 5
⟹ 3x = -3,
On simplifying, we get x = -1. So, the solution to the system is x = -1, y = 2.
Learn more about Elimination Method here:https://brainly.com/question/13877817
#SPJ3
What is the volume of a cone with diameter 21 m and height 4 m?
441π m3 147π m3 220.5π m3 294π m3
For this case we have by definition, that the volume of a cone is given by:
[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]
Where:
A: It is the cone radius
h: It's the height
They tell us that the diameter is 21 m, then the radius is half the diameter, that is: 10.5m. The height is 4m. Substituting the data:
[tex]V = \frac {1} {3} * \pi * (10.5) ^ 2 * 4\\V = \frac {1} {3} * \pi * 110.25 * 4\\V = 147 \pi[/tex].
Finally, the volume of the cube is[tex]147 \pi \ m ^ 3[/tex]
ANswer:
Option B
Answer:
147[tex]\pi[/tex]m^3
Step-by-step explanation:
Malia solved an equation, as shown below: Step 1: 6x = 48 Step 2: x = 48 – 6 Step 3: x = 42 Part A: Is Malia's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. Part B: How many solutions will this equation have?
Answer:
a. the answer is incorrect
b. 1
Step-by-step explanation:
step 1) 6x=48
step 2) 48/6
step 3)x=3
The number which is repeated as a factor in an exponential expression exponent 2. the fixed amount multiplied by a term to get to the next term in a geometric sequence radical expression 3. the (superscript) number in an exponential expression which tells how many times a factor is repeated index 4. a sequence in which there is a common ratio between the terms geometric sequence 5. the small number preceding a radical symbol that indicates the desired root of the radicand rationalize 6. expressions having the same root index and the same radicand like radicals 7. an expression that contains a radical; √7 and √21y are examples of radical expressions term 8. the expression under a radical symbol common ratio 9. eliminate the radical from the denominator of a fraction radicand 10. a set of numbers that follows a pattern, with a specific first number sequence 11. an individual quantity or number in a sequence base
An exponential expression refers to an expression where a base number is raised to a certain power or exponent. The exponent indicates how many times the base number is repeated as a factor. Exponential expressions can be simplified or evaluated using the rules of exponents.
Explanation:In mathematics, an exponential expression refers to an expression where a base number is raised to a certain power, or exponent. The exponent indicates how many times the base number is repeated as a factor. For example, in the expression 23, 2 is the base and 3 is the exponent, so it means that 2 is repeated as a factor three times. Exponential expressions can be simplified or evaluated using the rules of exponents.
For example, in the expression 42, 4 is the base and 2 is the exponent, so it means that 4 is repeated as a factor two times. This can be evaluated as 42 = 4 x 4 = 16.
Exponential expressions are commonly used in various mathematical applications, such as in compound interest, population growth, and scientific calculations.
Learn more about Exponential Arithmetic here:https://brainly.com/question/31870974
#SPJ3
The ratio of Melanie's allowance to Jacob's allowance is 4.1 to20.5.If Jacob gets 5.00 dollars, how much allowance does Melanie get
[tex]\bf \cfrac{Melanie}{Jacob}\qquad \stackrel{ratio}{\cfrac{4.1}{20.5}}\qquad \qquad \cfrac{4.1}{20.5}=\cfrac{m}{5}\implies 20.5=20.5m \\\\\\ \cfrac{20.5}{20.5}=m\implies 1=m[/tex]
Fill in the exponent
Answer:
3
Step-by-step explanation:
12/4 = 3
so
(a^2/b^3)^4 = a^8 / b^12
RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.
The area of rectangle ABCD is 18 square units.
Step 1: Calculate the length of the rectangle.
The length of the rectangle is the distance between points A and B (or C and D). Using the distance formula:
[tex]\[ \text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For the points A(-5,2) and B(-5,4), the length is:
[tex]\[ \text{Length} = \sqrt{(-5 - (-5))^2 + (4 - 2)^2} \][/tex]
[tex]\[ \text{Length} = \sqrt{(0)^2 + (2)^2} \][/tex]
[tex]\[ \text{Length} = \sqrt{0 + 4} \][/tex]
[tex]\[ \text{Length} = \sqrt{4} \][/tex]
[tex]\[ \text{Length} = 2 \][/tex]
Step 2: Calculate the width of the rectangle.
The width of the rectangle is the distance between points B and C (or A and D).
For the points B(-5,4) and C(4,4), the width is:
[tex]\[ \text{Width} = \sqrt{(4 - (-5))^2 + (4 - 4)^2} \][/tex]
[tex]\[ \text{Width} = \sqrt{(4 + 5)^2 + (0)^2} \][/tex]
[tex]\[ \text{Width} = \sqrt{9^2 + 0} \][/tex]
[tex]\[ \text{Width} = \sqrt{81} \][/tex]
[tex]\[ \text{Width} = 9 \][/tex]
Step 3: Calculate the area using length and width.
Now that we have the length and width of the rectangle, we can use the formula:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
[tex]\[ \text{Area} = 2 \times 9 \][/tex]
[tex]\[ \text{Area} = 18 \][/tex]
The length of the rectangle, calculated as the distance between points A and B (or C and D), is 2 units. The width of the rectangle, calculated as the distance between points B and C (or A and D), is 9 units. Multiplying the length and width together gives us the area of the rectangle, which is 18 square units. Therefore, the correct answer is that the area of rectangle ABCD is 18 square units.
Complete question :
RECTANGLE ABCD has vertices A(-5,2) B(-5,4) C(4,4) D(4,2) calculate the area.
Help with this question, please!!
Answer:
∠XMZ = 74°
Step-by-step explanation:
Since the arcs XZ and BC are congruent, then
∠BNC = ∠XMZ ← substitute values
6x - 88 = 3x - 7 ( subtract 3x from both sides )
3x - 88 = - 7 ( add 88 to both sides )
3x = 81 ( divide both sides by 3 )
x = 27
Hence
∠XMZ = 3x - 7 = (3 × 27) - 7 = 81 - 7 = 74°
Which one is it???
4x = 8x − 1
x = three fourths
x = 1
x = 3
x = 6
The correct answer is x = 3.
To solve the equation[tex]4x=8x-1\[/tex] we need to isolate the variable x on one side of the equation. Let's perform the necessary algebraic steps:
First, subtract 4x from both sides of the equation to get all the x terms on one side:
[tex]4x=8x-1\\\8x-4x=1\\4x=1\\x=4-1\\3[/tex]
However, the options provided are numerical values, and [tex]3[/tex] does not match any of the given options. It seems there was a mistake in the options provided or in the interpretation of the equation. The correct solution to the equation 4x = 8x - 1 is indeed x = 3
Drag the correct classification for each graph into the boxes to complete the table.
neither even or odd, odd, even
Answer:
Odd, neither, neither
Step-by-step explanation:
A function is even if f(x) = f(-x). That means that it passes through the origin and is symmetrical about the y-axis.
A function is odd if f(x) = -f(-x). That means that it passes through the origin and is symmetrical about the origin.
The first graph, the line, passes through the origin and is symmetrical about the origin. So it is odd.
The second graph does not pass through the origin, nor is it symmetrical. So it is neither odd nor even.
The third graph does not pass through the origin, nor is it symmetrical about the y-axis. So it is neither odd nor even.
Describe the solutions for this inequality. 2x+9/4?6 A) All values of x that are less than 1 7 8 . B) All values of x that are greater than 1 7 8 . C) All values of x that are less than or equal to 1 7 8 . D) All values of x that are greater than or equal to 1 7 8
Answer:
C
Step-by-step explanation:
The solution for the inequality 2x + 9/4 > 6 is x> 15/8 the all values of the x which is greater than the 15/8
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have inequality:
2x+9/4?6
Here the proper form of inequality is not given, but we can solve the inequality by assuming the inequality is:
2x + 9/4 > 6
2x > 6 - 9/4
2x > 15/4
x > 15/8
From the above procedures we can solve any inequality.
Thus, the solution for the inequality 2x + 9/4 > 6 is x> 15/8 the all values of the x which is greater than the 15/8
Learn more about the inequality here:
brainly.com/question/19491153
#SPJ2
The image of (triangle) ABC is (triangle) A'B'C. What transformations would result in this image?
A.(triangle)ABC is reflected over the y-axis, then is rotated -90° around the origin.
B.(triangle)ABC is reflected over the line y = x.
C.(triangle)ABC is rotated -90° around the origin, then is reflected over the x-axis.
D.(triangle)ABC is rotated 90° around the origin, then is reflected over y-axis.
Answer:
The triangle ABC is reflected over the line y = x ⇒ answer B
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
* Lets find the vertices of ABC and A'B'C' to solve the problem
- In Δ ABC
# A = (5 , -5) , B = (5 , -4) , C = (2 , -4)
- In Δ A'B'C'
# A' = (-5 , 5) , B = (-4 , 5) , C = (-4 , 2)
∵ The image of (5 , -5) is (-5 , 5)
∵ The image of (5 , -4) is (-4 , 5)
∵ The image of (2 , -4) is (-4 , 2)
∴ The point (x , y) is (y , x)
- From the rule above
∴ The triangle ABC is reflected over the line y = x
Answer:
The triangle ABC is reflected over the line y = x ⇒ answer B
Step-by-step explanation:
Marie is purchasing a $108,000 home with a 30 year ortgage at 5.25%. What is her monthly principal and interest payment
Answer:
Monthly interest rate is r=0,004375
Monthly principal c=590,625
Step-by-step explanation:
Monthly interest payment rate :
[tex]r=\frac{5.25}{12}:100=0,0004375[/tex]
Now, we need to find monthly principal payment : [tex]c=\frac{rP}{1-(1+r)^{-N}}[/tex]
Use this rule : [tex]N=30*12=360[/tex]
P=108000
r=0,004375
[tex]c=\frac{0.004375*108000}{1-(1+0.004375)^{-360}} =\frac{472.5}{0.8}=590,625[/tex]
Answer: 596.38
Step-by-step explanation:
The base of a tower with the height of 55 meters is the 37 meters from point A . Find the angle of elevation from point A to the top of the tower .
Answer:
56.07 degrees
Step-by-step explanation:
This is a classic problem involving right triangle trig. We are looking for the angle that has a side opposite it with a measure of 55 m and a side adjacent to it with a measure of 37 m. This is the tangent ratio of the missing angle. Our equation then looks like this:
[tex]tan\theta=\frac{55}{37}[/tex]
To find a missing angle on your calculator in degree mode, hit 2nd then tan and you'll see "tan^-1( " on your display. After the open parenthesis, enter your fraction and hit the enter button to get the angle measure. 56.07°
Answer:47. 72°
Step-by-step explanation:
from the attached figure below; adjacent =37 hypotenuse=55
θ = ?
From trig. formular,
cos θ = adjacent / hypotenuse
cos θ = 37 / 55
cos θ =0. 6727
θ = cos⁻¹ (0. 6727)
θ = 47. 72°
The angle of elavation is 47. 72°
Please help!!!!!!!!!!!!!!
Answer:
51.3°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Tan = Opposite/Adjacent
For angle y, the opposite side is 10 cm, and the adjacent side is 8 cm. Then you have ...
tan(y) = (10 cm)/(8 cm)
y = arctan(1.25) ≈ 51.3402° ≈ 51.3°
One letter is selected from the word "statistics." What is the probability that an "s" or "t" is chosen?
1/5
2/5
1/2
3/5
Answer:
3/5
Step-by-step explanation:
There are 10 letters in the word "statistics".
Out of which, there are 3 s's and 3 t's.
So, the question asks what's the probability to get a S or a T out of 10 letters.
Since the number of S's (3) and the number of T's equal 6, that means you have 6 chances out of 10 to pick an S or a T.
6/10 or if we simplify/reduce it... we get 3/5.
the correct answer is 3/5
The question is asking for the probability of selecting either an 's' or a 't' from the word 'statistics'. To solve this, we need to look at the total number of each letter and the total number of letters in the word. The word 'statistics' has 10 letters in total, with 3 's' letters and 3 't' letters.
To calculate the probability, we add the number of 's' letters to the number of 't' letters, which gives us 6. Then we divide this sum by the total number of letters in the word:
Probability('s' or 't') = (Number of 's' + Number of 't') / Total number of letters
Probability('s' or 't') = (3 + 3) / 10 = 6/10 = 3/5.
Thus, the correct answer is 3/5, meaning there is a 60% chance of picking either an 's' or a 't' from the word 'statistics'.
Help plzzzz I have until 12 am
Answer:
To complete the square move the non-x term to the right
2x^2 + 13x = -20 then divide equation by x^2 coefficient
x^2 + 6.5x = -10
then coefficient of x (which is 6.5) divide by 2 (3.25) square the number
=10.5625 Then add 10.5625 to both sides of the equation:
x^2 + 6.5x + 10.5625 = -10 + 10.5625
x^2 + 6.5x + 10.5625 = .5625
Take the square root of both sides
(x + 3.25)^2 = .75
Step-by-step explanation:
how many solutions does 5x=30 have
For this case we must find the solutions of the following equation;
[tex]5x = 30[/tex]
We clear the value of the variable "x", dividing by 5 on both sides of the equation:
[tex]x = \frac {30} {5}[/tex]
[tex]x = 6[/tex]
Answer:
[tex]x = 6[/tex]
We have a single solution of a linear equation.
Answer:
One solution
Step-by-step explanation:
We are given the following equation and we are to determine the number of solutions this equation has:
[tex] 5 x = 3 0 [/tex]
For that, we will solve it.
Dividing both the sides by 5 to get:
[tex] \frac { 5 x } { 5 } = \frac { 3 0 } { 5 } [/tex]
[tex] x = 6 [/tex]
Therefore, this equation has only one solution.
If (x-2) is a factor of x^3 + bx^2 - 4 , what is the value of b?
Answer:
b= -1
Step-by-step explanation:
Step 1: Find out value of x
x-2 = 0
x= 2
Step 2: Substitute value of x in the equation
x^3 + bx^2- 4 = 0
(2)^3 + b (2)^2 - 4 = 0
8 + 4b - 4=0
4 - 4b = 0
4b = -4
b = -1
How many solutions will the following system of linear equations have? –2x + 4y = –7 y= -1/2x + 5 A. 0 B. 1 C. 2 D. infinite
Answer:
B. 1
Step-by-step explanation:
they only cross at one point... look below
ANSWER
B. 1
EXPLANATION
The given system of equations is;
–2x + 4y = –7
y= -1/2x + 5
We rewrite the first equation is slope intercept form:
4y = 2x–7
[tex]y = \frac{1}{2}x - \frac{7}{4} [/tex]
The two equations have different slopes.
This means that they will intersect at one point in the XY plane.
Hence the system has a unique solution.
You can work at most 20 hours next week. You need to earn at least $90 to cover your weekly expenses. Your dog walking job pays $9.00 per hour and your job as a car wash attendant pays $10.00 per hour. This situation can be represented by a system of inequalities, where x = dog walking hours and y = car washing hours. Identify two possible combinations of hours you can work at both jobs. Create a system of linear inequalities and solve.
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x ----> the dog walking hours
y ----> the car washing hours
we know that
The system of linear inequalities is equal to
[tex]x+y\leq20[/tex] -----> inequality A
[tex]9x+10y\geq 90[/tex] -----> inequality B
Solve the system of inequalities by graphing
The solution is the shaded area
see the attached figure
Two possible combinations of hours are
(10,10) and (0,9)
Verify
For (10,10)
Substitute the value of x and the value of y in both inequalities
Inequality A
[tex]10+10\leq20[/tex]
[tex]20\leq20[/tex] -----> is true
Inequality B
[tex]9(10)+10(10)\geq 90[/tex]
[tex]190\geq 90[/tex] ----> is true
therefore
(10,10) is a possible solution
For (0.9)
Substitute the value of x and the value of y in both inequalities
Inequality A
[tex]0+9\leq20[/tex]
[tex]9\leq20[/tex] -----> is true
Inequality B
[tex]9(0)+10(9)\geq 90[/tex]
[tex]90\geq 90[/tex] ----> is true
therefore
(0,9) is a possible solution
Final answer:
The situation can be described by two inequalities: x + y <= 20 and 9x + 10y >= 90. Two possible combinations of hours that meet these requirements are 0 hours of dog walking and 9 hours of car washing, or 8 hours of dog walking and 2 hours of car washing.
Explanation:
To represent this situation with a system of linear inequalities, we will let x be the number of hours working as a dog walker and y be the number of hours working as a car wash attendant. The two inequalities based on the constraints of the problem are:
x + y \<= 20 (because you can't work more than 20 hours).
9x + 10y >= 90 (because you need to earn at least $90).
Solving this system can be done graphically or algebraically. Let's see two possible solutions:
If you want to work at both jobs, you could work 8 hours dog walking (x=8) and 2 hours at the car wash (y=2). This means you would earn 8*$9 + 2*$10 = $92, which is also enough to cover the expenses.
One serving of rice has 44.9 grams of carbohydrates how many grams of carbohydrates de 2.5 servings of rice have
Answer:
[tex]112.25\ grams\ of\ carbohydrates[/tex]
Step-by-step explanation:
we know that
using proportion
[tex]\frac{1}{44.9}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} =\frac{2.5}{x}\frac{serving\ of\ rice}{grams\ of\ carbohydrates} \\ \\x=44.9*2.5\\ \\x=112.25\ grams\ of\ carbohydrates[/tex]
Answer:
WHAT IS THE ANSWER I CAN'T VEIR THE FILE
Step-by-step explanation: