STEP - STEP EXPLANATION:
Trying to factor by splitting the middle term
Factoring 4x2-19x-5
The first term is, 4x2 its coefficient is 4 .
The middle term is, -19x its coefficient is -19 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 4 • -5 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -19 .
-20 + 1 = -19 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -20 and 1
4x2 - 20x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(4x+1) • (x-5)
Which is the desired factorization
Equation at the end of step
2
:
(x - 5) • (4x + 1) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
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Answer: 2329 cups
Step-by-step explanation:
Make an equation and you will have c (total number of cups at the end)=2000-125-127+1719-356-782+0= 2329. So the total number of cups at the end of the week is 2329. Hope this helps!
Which of the following is equivalent to 3(x + 5) - 6 ?
Answer:
3x5 is 15, 15-6 is 9
Step-by-step explanation:
7 cm
5.2 cm
6 cm
6 cm
6 cm
Answer:
m24,m249,m416,kar98k
Step-by-step explanation:
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Mia wants to rent a paddleboat in Forest Park. The boathouse charges a 7$ fee, plus an hourly rate of 6$. For how long did Mia rent a paddleboat if she paid a total of 43$?
Answer:
6 hours.
Step-by-step explanation:
since the boat house charges 7 dollars we can subtract that from 43
43-7=36
since we have 36 left and the fee per hour is 6 we can devide
36÷6=6
division 54 /7.5 plz answer this
Answer:
turn the decimal into a whole number by multiplying by 10, 100 (what you do to one number you must do to the other)
multiply both by 10 it then becomes
540/75 = 7.2
it's easier to divide whole numbers and is the same answer as 54/7.5
Janet had a sheet of paper that was 4 inches long the area was 40 inch square what is the width of the paper.
Answer:
10 inches
Step-by-step explanation:
Area is qual to length times width.
A = lw
Rearrange this to find width.
w = A/l
Now plug in your known numbers and simplify.
w = 40/4
w = 10
How to classify triangles by its sides and by its angles help pls
Step-by-step explanation:
triangle with 2 sides of equal lengths= isoceles
triangle with 3 sides of equal lengths= equilateral
Answer:
if the two sides are congruent, then it's an isosceles triangle.
all angles congruent and it's an equilateral.
all angles unequal and it's a scalene.
if all the angle measures are less than 90 degrees, then it's acute, but more than 90 degrees would be obtuse.
What is the rate of change for y=2x+10
Answer:
its 2
The general rate of change can be found by using the difference quotient formula. To find the average rate of change over an interval, enter a function with an interval
divide the decimal 134.55 by the decimal 0.5
Answer:
269.1
Step-by-step explanation:
Please help
A 108 square cm
B 63 square cm
C 139.5 square cm
D 171 square cm
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The length of a planet's orbit around a star is approximately 29,870,000 km.
It takes the planet about 1670 Earth days to complete a full orbit.
What is the planet's average speed in kmh-' to 3sf?
Answer:
745 k/hr
Step-by-step explanation:
mathematically, 1 day = 24 hours
1670 days = 1670 * 24 = 40,080 hours
The speed is thus;
(29,870,000)/40,080 = 745.259
= 745 km/h
Halley’s Comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000 miles. What is the maximum distance from the comet to the sun? Round to the nearest whole number.
Answer:
1582480848 miles
Step-by-step explanation:
The maximum distance is another vertex of the major axis
1,636,484,848 miles - 54,004,000 miles = 1582480848 miles
Based on the calculations, the maximum distance from the Comet to the Sun is equal to 1,582,480,848 miles.
How to calculate the maximum distance from the Comet to the Sun?In this scenario, the elliptical orbit of the Comet with respect to the Sun at one focus and a major axis is equal to 1,636,484,848 miles. Also, the closest it came to the Sun is 54,004,000 miles.
Thus, we would divide the length of the major axis by the distance between the Comet and the Sun as follows:
Maximum distance = 1,636,484,848/54,004,000
Maximum distance = 1,582,480,848 miles.
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Solve the equation y=x2 −81
Mary's tube of red paint is five sevenths full and her blue paint is four sevenths full. How much red and blue paint does Mary have in total? Use the benchmark fraction one half, 1, and 0 to help you estimate each answer before you solve it.
Answer:
We know that:
Mary has 5/7 of the red paint tube
And she also has 4/7 of the blue paint tube.
How much paint does she have in total?
Well, we only need to add these fractions.
5/7 + 4/7 = 9/7
We can rewrite the 9 as 7 + 2, then we get:
9/7 = (7 + 2)/7 = 7/7 + 2/7 = 1 + 2/7
This means that, in total, she has a complete tube and two sevents of other.
Jasmine is buying cakes for a party. One chocolate cake costs $7, and one lemon cake
costs $5. If Jasmine needs to buy 18 cakes and has $110 to spend, how many lemon
cakes can she buy?
Set up and solve a system of linear equations to model how to determine the number
of lemon cakes Jasmine can buy for the party.
Answer:
Step-by-step explanation: Am not sure if this is the answer you guys are looking for but my in 9th grade and this is how my math teacher taught me how to do it.
one chocolate cake=?=x
one lemon cake=?=y
$270 spent
need to buy total of 18 cakes
1-chocolate cake =$7
lemon cake = $5
cakes 18=x+y
money $110=$7x+$5y
When i graphed it on the demos calculator i got (10,8).
So 10= the number of chocolate cake brought and 4= the number of lemon cake brought
Write the equation of the shown line in slope intercept form. I need help please!
Answer:
y = 1/4x -2
Step-by-step explanation:
Slope intercept from is y = mx + b
m is the slope (rise/run) and this one is one over four.
The y-intercept is b and this line crosses the y-axis at -2.
Help me quickly just give the answer
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Divide by 2
32/2 = 16
Therefore-
16 books per box
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Caesar gets coffee from his local coffee shop when he has time in the morning. The coffee shop sells a ceramic refill mug for $8.95. Each refill costs $1.50. Last month Caesar spent $26.95 on a mug and refills.
Write an equation that you can use to find the number of refills Caesar purchased.
a.8.95r + 1.50= 26.95
b.8.95 + 1.50r= 26.95
c8.95 + 1.50 = 26.95r
How many refills did he buy? Solve the equation
What is the value of X in the equation?
Answer:
Whoa!! Dat is waaay too long
Can anyone help?? Basic algebra-
Answer:
-7x+4y=15
Perpendicular lines have slopes with a product of -1
Step-by-step explanation:
Help due soon!
Walker is planning a summer vacation. He wants to visit Petrified National Forest and Meteor Crater, Arizona, the 50,000-year-old impact site of a large meteor. On a map with a scale where 2 inches equals 75 miles, the two areas are about 1 1/2 inches apart. What is the distance between Petrified National Forest and Meteor Crater?
Answer:
56.25 miles
Step-by-step explanation:
2 inches=75 miles
1 inch=37.5
1/2 inch=18.75
37.5+18.75=56.25
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if 2×2=4 and 4×4=8. What is 8×8?
Answer:
64
Step-by-step explanation:
Someone Asist me with this pleaseeee
Answer: it's the last one It's not a function
Step-by-step explanation
(d + 3) + (5d +4)=?
Help
Answer:
[tex]6d + 7[/tex]
Step-by-step explanation:
just add the like terms and remove the parthenses
d+ 5d = 6d
and 3+4 =7
6d + 7
Answer:
6d + 7
Step-by-step explanation:
Solve the equation 6(x + 2) = 3(2x + 4).How many solutions are there? Show your work
A can of beans has surface area 337 cm2. It's heights is 11cm. What is the radius of the circular top?
Answer:
3.66 cm
Step-by-step explanation:
r = Radius of cylinder
h = Height of the cylinder = 11 cm
A = Total surface area of the cylinder = [tex]337\ \text{cm}^2[/tex]
Total surface area of a cylinder is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r(r+h)\\\Rightarrow \dfrac{A}{2\pi}=r^2+rh\\\Rightarrow r^2+rh-\dfrac{A}{2\pi}=0\\\Rightarrow r^2+11r-\dfrac{337}{2\pi}=0\\\Rightarrow r^2+11r-53.64=0\\\Rightarrow 100r^2+1100r-5364=0\\\Rightarrow r=\dfrac{-1100\pm \sqrt{1100^2-4\times 100\left(-5364\right)}}{2\times 100}\\\Rightarrow r=3.66,-14.65[/tex]
So, the radius of the circular top is 3.66 cm.
£600 is invested into a savings account paying
5% compound interest per year. How much is in
the account after three years
Answer:
£694.575
Step-by-step explanation:
Using the formula for calculating the compound interest expressed as;
A = P(1+r)^t
P is the principal = £600
r is the rate = 5% = 0.05
t is the time = 3 years
Substitute into the formula;
A = 600(1+0.05)^3
A = 600(1.05)^3
A = 600(1.157625)
A = 694.575
hence the amount in the account after 3 years is £694.575
Which expression is equivalent to (-4y - x) - (3y - 9x)
Answer: -7y+8x
Step-by-step explanation: I assume you mean to simplify
Step 1: Remove parentheses : -4y - x - (3y - 9x)
Step 2: -(3y - 9x) = -3y + 9x
Step 3: Simplify: -4y - x - 3y +9x
Step 4: Answer: -7y+8x
Please help !!
Solve for x:
-2
-2/3
-3/2
-3
Answer:
x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given 2 intersecting chords, then the product of the parts of one chord is equal to the product of the parts of the other chord, that is
18x = 9 × 3 = 27 ( divide both sides by 18 )
x = [tex]\frac{27}{18}[/tex] = [tex]\frac{3}{2}[/tex]
At a local gardening store, there is a small group of plants located near the gardening
supplies, and the remainder of the plants are arranged in equal-sized rows in the field
behind the store. The function 9(x) = 18x+23 represents the total number of plants at the
gardening store if there are x rows of plants in the field. What is the value of g(27)), the
total number of plants when there are 27 rows?
Answer:
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Step-by-step explauuuuuuuuuuu
The required number of plants from the function is 509 when there are 27 rows.
Given that,
The function g(x) = 18x+23 represents the total number of plants at the gardening store if there are x rows of plants in the field. What is the value of g(27) is to be determined.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Number of plants,
g(x) = 18x+23
Since the number of rows is 27
Now, the number of plants,
g(27) = 27 * 18 + 23
g(27) = 486 + 23
g(27) = 509
Thus, The required number of plants from the function is 509 when there are 27 rows.
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