Answer:
x = - 3, x = 1
Step-by-step explanation:
x² + 2x - 3 = 0
consider the factors of the constant term (- 3) which sum to give the coefficient of the x- term (+ 2)
the factors are + 3 and - 1 , since
3 × - 1 = - 3 and + 3 - 1 = + 2 , then
(x + 3)(x - 1) = 0 ← in factored form
equate each factor to zero and solve for x
x + 3 = 0 ( subtract 3 from both sides )
x = - 3
x - 1 = 0 ( add 1 to both sides )
x = 1
solutions are x = - 3 , x = 1
what are the roots of the equation
Answer:
Step-by-step explanation:
The roots (sometimes also called "zeros") of an equation are the values of for which the equation is satisfied.
Felipe rented a truck for one day. There was a base fee of $17.95, and there was an additional charge of 86 cents for each mile driven. Felipe had to pay $270.79 when he returned the truck. For how many miles did he drive the truck?
Answer:
421.4 miles
Step-by-step explanation:
Numner of miles= ($270.79-$17.95)/86 cents
= $252.84/$0.60
=421.4 miles
please help i need this done as soon as possible will mark brainly!!!!!!!!
Answer: the function's y-intercept, 64°F
Step-by-step explanation:
Since "t" represents time, if we set t = 0 to find the initial temperature (0 minutes), we find the function's y-intercept.
To find the initial temperature, we will set t = 0. When we do this, we are finding the y-intercept which is the same as the constant value.
[tex]y=-\frac{1}{40}t^2+t+64[/tex]
[tex]y=-\frac{1}{40}(0)^2+(0)+64[/tex]
[tex]y=64[/tex]
64°F
What is the intermediate step in the form(x+a)^2=b as a result of completing the square for the following equation?
X^2-8x+32=12x-4
Answer:
To complete the square for the equation X^2-8x+32=12x-4, we first need to move all the constant terms to one side of the equation and all the variable terms to the other side.
X^2 - 8x - 12x + 32 = -4
Next, we can simplify the equation by combining like terms:
X^2 - 20x + 32 = -4
Then, we can add a constant term to both sides of the equation such that the left side becomes a perfect square trinomial:
X^2 - 20x + 100 = 64
Finally, we can write the left side of the equation in the form (x - a)^2, where a is a constant:
(X - 10)^2 = 64
Therefore, the intermediate step in the form (x + a)^2 = b as a result of completing the square for the equation X^2 - 8x + 32 = 12x - 4 is (X - 10)^2 = 64.
Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids will he need to make a perfect cube? What will be the dimensions of the cube?
Answer:
Step-by-step explanation:Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids will he need to make a perfect cube? What will be the dimensions of the cube?
An arctic ecologist measures the thickness of an ice floe. The thickness is 0.039 m. What is the thickness in centimeters? Write your answer as a decimal.
The thickness of the ice floe is 3.9 centimeters.
Given that an ice floe's thickness is measured by an arctic ecologist. It measures 0.039 m thick.
We need to determine the thickness in centimeters,
Using the concept of unit conversion,
Since there are 100 centimeters in a meters, you must multiply the figure by 100 to convert from meters to centimeters.
The ice floe's thickness is 0.039 m, which may be converted to centimeters as follows:
100 cm/m times 0.039 m equals 3.9 cm.
The ice floe is 3.9 centimeters thick as a result.
Hence the thickness of the ice floe is 3.9 centimeters.
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can I get some help with finding this volume
Answer: 216 cm³
Step-by-step explanation:
>Break the shape up into 2 separate shapes so we can work with shapes we know (rectangular prisms/ blocks)
>Let's call the bottom left small block, Shape 1
>Let's call the bigger block on right, Shape 2
Volume for rectangular prism = Length x width x height
Shape 1:
length = 4
width = (6-4) =2
height = (12-9) = 3
V = (4)(2)(3) =24
Shape 2:
length= 4
width = 4
height = 12
V= (4)(4)(12)
V=192
Total volume = 24+192 =216 cm³
3 and 2/4 as a percent
3 and 2/4 converted as a percent is 3.50%.
What is a percentage?
Percent means 'out of 100'. Think of any measurement or object split into one hundred equal bits. Each bit is one percent of the whole thing.
Given the question above, we need to convert 3 and 2/4 as a percent.
So,
[tex]\sf \dfrac{2}{4} =0.50[/tex]
[tex]3+0.50[/tex]
[tex]=3.50\%[/tex]
Hence 3 and 2/4 converted as a percent is 3.50%.
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Bromine-82 has a half-life of about 35 hours.
After 140 hours, how many milliliters of an 80 mL sample will remain?
65 mL
20 mL
10 mL
5 mL
Answer:
[tex]\huge\boxed{\sf 5 \ mL}[/tex]
Step-by-step explanation:
Amount of Br-82 = 80 mL
Half-life = 35 hours
Total time = 140 hours
No. of half lives spent:= Total time / Half-life
= 140 / 35
= 4 half lives
After 1st half life:= 80 / 2
= 40 mL
After 2nd half life:= 40 / 2
= 20 mL
After 3rd half life:= 20 / 2
= 10 mL
After 4th half life:= 10 / 2
= 5 mL[tex]\rule[225]{225}{2}[/tex]
Is the following shape a square? How do you know?
D.
2
PREVIOUS
"B
A. There is not enough information to determine
B. Yes, the opposite sides are parallel, and all sides are the same
length.
C. No, because the sides are not congruent
D. No, because opposite sides are not parallel
Answer:
B
Step-by-step explanation:
A square have 4 side that are all the same so its B
¿Cuál es el volumen, en metros cúbicos, de un prisma rectangular con una altura de
17 m, un ancho de 14 m y una longitud de 11 m?
Answer:
V = 2618 cubic meters
Step-by-step explanation:
multiply the three dimensions to obtain volume
(17)(14)(11) = 2618 m3
Hope this helps
Find the missing coordinate in the ordered pair ( -1 , b )
if it is a solution to the equation 5x-3y=10
a -7
b-5
c-4
d 4
e o
.
Answer:
To find the missing coordinate in the ordered pair (-1, b), we can substitute the value of x into the equation 5x-3y=10. This gives us 5(-1)-3y=10. Solving for y, we get -5-3y=10, -3y=15, and y=-5. Therefore, the missing coordinate in the ordered pair (-1, b) is -5. The correct answer is b) -5.
2+2 how to do first year rough
Follow the guided instructions below to rotate the figure 270° counter-clockwise
about the origin.
Click and drag to draw a line through the yellow center and the vertex on
the circle.
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If you need assistance with rotating a figure or performing any specific task, please provide a detailed description or explain the steps involved, and I'll do my best to guide you through the process.
Joshua is 5 ft tall and casts an 8-ft shadow. he is standing next to Jason, who casts a 10 shadow. write a proportion that could be used ti determine Jason's height do not solve
The proportion that can be used to determine Jason's height based on the relationship between the lengths of their shadows is J/8 = H/10.
Given that Joshua is 5 ft tall and casts an 8-ft shadow.
He is standing next to Jason, who casts a 10 shadow.
We have to find a proportion that could be used to determine Jason's height
Let's denote Joshua's height as J and Jason's height as H.
We can set up the proportion by taking the height by shadow
J/8 = H/10
Hence, J/8 = H/10 is the proportion can be used to determine Jason's height based on the relationship between the lengths of their shadows.
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2. How are wealth and savings related?
Savings play a crucial role in wealth creation and financial security while savings alone may not determine an individual's overall wealth
Wealth and savings are closely related concepts and often go hand in hand.
Savings refer to the portion of income or resources that individuals or households set aside for future use or to meet financial goals.
It represents the act of not spending all of one's income and instead preserving a portion for later use.
Wealth, on the other hand, refers to the total accumulated assets, possessions, and financial resources that an individual or household possesses.
It encompasses not only the current income and savings but also the value of investments, properties, and other assets.
Savings contribute to the accumulation of wealth over time.
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Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
Compute the MIRR statistic for Project J and advise whether to accept or reject the project with the cash flows shown as follows if the
appropriate cost of capital is 10 percent.
Project J
Time
Cash Flow
e
1,000
1
$300
2
$1,480
3
500 $300
Save & Exit
5
100
Submit
To compute the Modified Internal Rate of Return (MIRR) for Project J, we need to calculate the present value of cash inflows and outflows separately and then determine the discount rate that equates the present value of outflows with the future value of inflows.
The cash flows for Project J are as follows:
Time 0: Initial investment: -$1,000
Time 1: Cash inflow: $300
Time 2: Cash inflow: $1,480
Time 3: Cash inflow: $500
Time 5: Cash inflow: $100
First, let's calculate the present value (PV) of outflows (the initial investment):
PV(outflows) = -$1,000 (since it's an outflow at time 0)
Next, let's calculate the future value (FV) of inflows (cash inflows at times 1, 2, 3, and 5):
FV(inflows) = $300 + $1,480 + $500 + $100 = $2,380
Now, we can use the MIRR formula to compute the MIRR statistic:
MIRR = (FV(inflows) / PV(outflows))^(1/n) - 1
Where n is the number of periods (5 in this case).
MIRR = ($2,380 / -$1,000)^(1/5) - 1
MIRR = 1.5189 - 1
MIRR = 0.5189 or 51.89%
Given that the cost of capital is 10 percent, the MIRR is higher than the cost of capital. Therefore, we would advise accepting Project J because the MIRR is greater than the cost of capital, indicating that the project is expected to generate a return higher than the required rate of return.
I just need an explanation on how to solve the second one in the middle
Answer: C AND D
Step-by-step explanation:
Cross multiply C to get 59.82D=2512.44 and divide to get $42.
Cross multiply D to get the same thing as C.
If you cross multiply A or B you won’t get a correct conversion.
Is a triangle with side lengths 21,20 and 29 a right triangle show why or why not .
Step-by-step explanation:
Yes, we can determine whether a triangle is a right triangle or not by using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.
Let's label the sides of the triangle as follows: side a = 21, side b = 20, and side c = 29 (where c represents the hypotenuse). Now, we can use the Pythagorean Theorem to check whether the triangle is a right triangle or not:
c^2 = a^2 + b^2
Substituting in the given values, we get:
29^2 = 21^2 + 20^2
841 = 441 + 400
841 = 841
As the equation is true, we can conclude that the triangle is a right triangle.
What is true about the graph below? Select SIX TRUE statements
Select ALL TRUE statements
A) There are no zeroes
B) There is one zero
C) There are two zeroes
D) The vertex is (1, 14)
E) The vertex is (14, 1)
F) The vertex is (2, 14)
G) The vertex is (14, 2)
H) The axis of symmetry is x = 1
I) The axis of symmetry is x = 2
J) The "a" of the parabola is positive
K) The "a" of the parabola is negative
M) The parabola has a minimum
N) The parabola has a maximum
O) The zeroes are -2 and 6
P) The zeroes are 1 and 6
Q) The zero is 6
R) The zero is 14
Step-by-step explanation:
Remember that, this is quadratic function graph.
Let's analyze fact the graph. We get :
There are two roots/zeroes Two roots are x1 = -2 , x2 = 6Vertex is maximum value of parabola (2,14)Symmetry function is x = 2 (you can show that, x-axis from vertex)"a" parabola indicated negativeThe parabola with "a" negative, thus have maximum value (show that vertex is (2,14))Conclusion :
The true statements are C,F,I,K,N,O (6 statements are shown)
Subject : Mathematics
Level : JHS
Chapter : Quadratic Functions
What is the square root of 598?
the square root of 598 is 24.4540385
PLEASE HELP-TIMED-40pts!!
Answer each question individually
___________________________
2. The list below shows the number of computer games a store sold each day for the
first 11 days it was open.
27, 28, 29, 35, 35, 36, 37, 42, 43, 46, 79
a) Find the five-number summary for the data. Show your work.
b) use your results from part A to display the data on a box plot
c)use your box plot from part b to find the interquartile range (IQR) of the data
The five-number summary of the data are:
Minimum: 27Q1: 32Median: 36Q3: 42.5Maximum: 79.The interquartile range (IQR) of the data is 10.5.
What are the five-number summary?We will arrange the data in ascending order first [tex]27, 28, 29, 35, 35, 36, 37, 42, 43, 46, 79[/tex]
Minimum: The smallest value is 27.
First Quartile (Q1):
We have an 11 odd number of data points (11), Q1 is the median of the first five numbers: 27, 28, 29, 35, 35.
The median of this subset is (29 + 35)/2 = 32.
Median (Q2): The middle value of the data set which is 36.
Third Quartile (Q3): The median of the upper half of the data. Q3 is the median of the last five numbers: 37, 42, 43, 46, 79. The median of this subset is (42 + 43)/2 = 42.5
Maximum: The largest value is 79.
The interquartile range (IQR) is calculated as Q3 minus Q1.
Using values from part a:
IQR = Q3 - Q1
IQR = 42.5 - 32
= 10.5.
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Determine which integer will make the inequality 4x + 6 < 2x + 12 false. S:{1} S:{-1} S:{4} S:{-4}
Answer:
S:{4}
Step-by-step explanation:
The inequality is
4x + 6 < 2x + 12
Subtract 2x from both sides:
4x - 2x + 6 < 2x - 2x + 12
2x + 6 < 12
Subtract 6 from both sides:
2x + 6 - 6 < 12 - 6
2x < 6
Divide both sides by 2
x < 3
So any value of x such that x ≥ 3 will make this statement false
In the answer choices, the only value that satisfies this conditionis the value 4
for $3.98 you can get a salad, a main course, and a dessert at the cafeteria. If you have a choice of 3 different salads, 4 different main courses, and 6 different desserts. then how many meals can you get for $3.98
There are 72 different meals that you can get for $3.98
How many different meals can you get for $3.98?We know that for $3.98 you can get a salad, a main course, and a dessert at the cafeteria.
The total number of different meals that you can get, is equal to the product between the number of options for each one of the selections, such that the selections (and correspondent options) are:
Salad ---> 3 different options.Main course ---> 4 different options.Dessert ---> 6 different options.Then the total number of different meals is:
M = 3*4*6
M = 72
That is the number of different meals.
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The point F( – 3, – 6) is translated 4 units right and 2 units up. What are the coordinates of the resulting point, F
Answer:The answer is (1, -4)
Step-by-step explanation:
A lumber company is interested in seeing if the number of board feet per has decreased since moving to a new location of timber. In the past, the company has an average 93 board feet per tree. The company believes that the production has decreased changing locations, a random sample of 25 trees yields mean of 89 with standard deviation of 2.Assuming normality of the data, test the hypothesis at a 10 % level of significance.
There is sufficient evidence to suggest that the mean board feet per tree has decreased since moving to the new location of timber.
According to the information,
Set up the following hypothesis test:
Null hypothesis: The mean board feet per tree is still 93.
Alternative hypothesis: The mean board feet per tree is less than 93.
Here,
We can use a one-sample t-test to test this hypothesis.
The test statistic can be calculated as:
t = (sample mean - hypothesized mean)/(sample standard deviation/square root of sample size)
⇒ t = (89 - 93)/(2/sqrt(25))
⇒ t = -5.00
The degrees of freedom for this test are 24.
Using a t-distribution table,
we can find the critical t-value for a one-tailed test with 24 degrees of freedom and a 10% level of significance.
The critical t-value is -1.317.
Since our calculated t-value (-5.00) is less than the critical t-value (-1.317), we can reject the null hypothesis in favor of the alternative hypothesis.
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the area of a triangle is 16cm^2, if the base of the triangle is two less than its height. find the base and the height
Answer:
The base of the triangle is 4cm and the height is 6cm
Question 1 of 10 Solve - 5 < 4x + 3 <= 7 x > - 2orx <= 1 B. x < - 2orx < 4 O C.-2 and x <= 1 D. x > 2 and x < 4
For the inequality -5 < 4x + 3 ≤ 7 the combined solution are x < -2 and x ≤ 1.
To solve the inequality -5 < 4x + 3 ≤ 7, we need to consider two separate inequalities:
Solve the inequality -5 < 4x + 3:
-5 < 4x + 3
Subtract 3 from both sides:
-5 - 3 < 4x
-8 < 4x
Divide both sides by 4
-8/4 > x
-2 > x
x < -2.
Now let's solve the inequality 4x + 3 ≤ 7:
4x + 3 ≤ 7
Subtract 3 from both sides:
4x ≤ 7 - 3
4x ≤ 4
Divide both sides by 4:
x ≤ 1
Therefore, the combined solution is x < -2 and x ≤ 1.
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A jar has dimes and nickels. The number of dimes is four less than seven times the number of nickels. Let n represent the number of nickels. Write an expression for the number of dimes.
Answer:
d = 7n -4
Step-by-step explanation:
d is number of dimes, n is number of nickels.
7 X number of nickels = 7n.
4 less than that is 7n - 4.
so d = 7n -4.