Answer:
(3x + 5)(4x - 7)
Step-by-step explanation:
The most common factors of 35 are 5 and 7. The 12 is a nuisance.
We could try 6 and 2 or 3 and 4 or even 12 and 1. You just have to juggle a bit to get the difference to be - x.
I'm going to try 3 and 4 first with 5 and 7. The numbers you get for the middle term have to be quite close.
(3x 5)(4x 7) Oops. It's going to come out first try.
Now you need to get the middle term come to - 1
(3x - 5)(4x + 7)
Just to make it slightly harder, I'll do it the wrong way first.
-5*4x + 3x*7 = - 20x + 21x = x That is close. Only the signs are incorrect.
So try again.
(3x + 5)(4x - 7)
20x - 21x = - x
Steve has a steel barrel with a diameter of 4 feet that can be filled to a depth of 4.3 feet with oil. What is the volume of the barrel?
Use = 3.14
A.
54.008 cubic feet
B.
51.6 cubic feet
C.
78.128 cubic feet
D.
17.708 cubic feet
Answer:
Option A. 54.008 cubic feet
Step-by-step explanation:
we know that
The volume of the barrel is equal to
[tex]V=\pi r^{2}h[/tex] ----> volume of the cylinder
we have
[tex]r=4/2=2\ ft[/tex] ----> the radius is half the diameter
[tex]h=4.3\ ft[/tex] ---> is the depth
[tex]\pi =3.14[/tex]
substitute
[tex]V=(3.14)(2)^{2}(4.3)[/tex]
[tex]V=54.008\ ft^{3}[/tex]
Which graph represents the function f(x) = −|x − 2| − 1? Image for option 1 Image for option 2 Image for option 3 Image for option 4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f\left(x\right)=-\left|x-2\right|-1[/tex]
The function represents an inverted V-shaped graph
The vertex of the function is the point (2,-1)
The y-intercept of the function is the point (0,-3)
The domain is all real numbers -----> (-∞,∞)
The range is all real numbers less than or equal to -1 ----> (-∞,-1]
Using a graphing tool
The graph in the attached figure
Find the distance between 11 and 7 on a
number line.
Enter the correct answer.
F(x) = 1/x g(x)=x-4 can you evaluate (g*f)(0) ? Why or why not?
[tex](g\cdot f)(x)=\dfrac{1}{x}-4[/tex]
[tex]D_{g(f(x))}:x\not =0[/tex]
No, since 0 doesn't belong to the domain.
Sales tax is an everyday example of where _______ are used.
Answer:
percentages
Step-by-step explanation:
Sales tax is an everyday example of where percentages are used.
Sales tax is an everyday example of where percentage math is used.
Given that,
To determine the suitable system that fit the given incomplete statment.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Sale tax is a type of taxation, which is applied to the sale and business of goods and services up to some percentage of the actual revenue generated by the goods and services in the form of some percent of the price of the actual cost of goods and services.
Thus, Sales tax is an everyday example of where percentage math is used.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ6
What is the value of the product (3-2i) (3+2i)
Answer:
[tex]\large\boxed{(3-2i)(3+2i)=13}[/tex]
Step-by-step explanation:
[tex](3-2i)(3+2i)\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=3^2-(2i)^2=9-4i^2\qquad i=\sqrt{-1}\to i^2=-1\\\\=9-4(-1)=9+4=13[/tex]
If f(x)=2x^+1 and g(x)=x^-7, find (f-g)(x)
Answer:
(f-g)(x) = 2x - x^(-7)
Step-by-step explanation:
We know that
f(x) = 2x^+1 = 2x
g(x)=x^-7 = x^(-7)
Then, we just need to subtract both functions
(f-g)(x) = f(x) - g(x) = 2x - x^(-7)
(f-g)(x) = 2x - x^(-7)
Please, see attached images for more information
What is the volume of this prism?
___ units3
Answer:The answer is 189 units 3
Step-by-step explanation:
It is a 3x7x9 prism so you multiply the numbers
Answer:
36
Step-by-step explanation:
find the difference
6-(-4)-(-3)
Answer:
6 - (-4) - (-3) = 13Step-by-step explanation:
Subtracting a number means the same as adding the opposite number.
(-)(-) = (+)
6 - (-4) - (-3)
opposite number to -4 is 4
opposite number to -3 is 3
6 - (-4) - (-3) = 6 + 4 + 3 = 13
Answer:
the correct answer is 13.
Step-by-step explanation:
PLEASE HELP! 8 POINTS!! Find the value
Answer:
-sqrt(3)/2
Step-by-step explanation:
Use double angle identity for sin(2x)
sin(2x)=2sin(x)cos(x)
We are given sin(x)=-1/2 so we already have so far that:
sin(2x)=2(-1/2)cos(x)
sin(2x)=-1*cos(x)
We just need to find cos(x).
x is in the fourth quadrant so cosine will be positive there
knowing the unit circle we should know that if sin(x)=-1/2 then cos(x)=sqrt(3)/2 while in 4th quadrant.
So the answer is sin(2x)=-1*sqrt(3)/2=-sqrt(3)/2
A 16oz bottle of a new soda cost $3.49. What is the unit rate, rounded to the nearest tenth of a cent?
Final answer:
To find the unit rate of a 16oz soda bottle that costs $3.49, divide the price by the ounces, resulting in $0.218125 per ounce, which rounds to $0.22 per ounce.
Explanation:
The question is about calculating the unit rate of a 16oz bottle of soda that costs $3.49. To find the unit rate, we divide the total cost by the number of ounces. Thus, the unit rate is $3.49 ÷ 16 oz, which equals approximately $0.218125 per ounce. Rounding to the nearest tenth of a cent, the unit rate is $0.22 per ounce.
Which circles are congruent?
B and C
B and D
A and D
Answer:
Circles A and D are congruent because they both have a radius of 3
Step-by-step explanation:
Answer:
Circle A and circle D are congruent ⇒ 3rd answer
Step-by-step explanation:
* Lets talk about the circle
- Any circle has diameter
- Any circle has radius which is half the diameter in length
- All the circles are similar because the measure of all circles is 360°
and there is the ratio between the radii
- The two circles are congruent if they have the same radii because
the congruence is special case of similarity when the ratio equal 1
* Lets look to the figure to solve the problem
- There are four circles in the figure
# Circle A with radius 3"
# Circle B with radius 4"
# Circle C with radius 5"
# Circle D with radius 3"
∵ The radius of circle A = 3"
∵ The radius of circle D = 3"
∴ The radii of circle A and circle D are congruent
∴ Circle A and circle D are congruent
find three consecutive positive even integers such that the product of the second and third integers is 20 more than 10 times the first integer.
Answer: 6, 8, 10
Step-by-step explanation:
We can write the three numbers as: x, x+2, and x+4
(x+2)(x+4) = 10x + 20
x² + 6x + 8 = 10x + 20
x² - 4x - 12 = 0
(x-6)(x+2) = 0
x = -2,6
We will focus on x = 6 and ignore -2
To check our answer: (6+2)(6+4) = 10(6) + 20?
8*10 = 60 + 20?
Yes, 80 = 80
Which is the solution to the inequality |x-4|<3
Answer:
[tex]\large\boxed{1<x<7\to x\in(1,\ 7)}[/tex]
Step-by-step explanation:
[tex]|x-4|<3\iff x-4<3\ \wedge\ x-4>-3\qquad\text{add 4 to both sides}\\\\x<7\ \wedge\ x>1\Rightarrow1<x<7[/tex]
you have to make a negative and positive equation for this situation
x-4<3 and x+4<3
for the first equation you have to add 4 to both sides to get x<7
for the second equation you have to subtract 4 from both sides to get x<-1
hope this helps
find the area of a rectangular garden that measures 4 feet by 6/7 feet
Answer:
A=3.43 ft^2
Step-by-step explanation:
A=lw
A=4(6/7)
A=3.43 ft^2
To find the area of a rectangular garden 4 feet by 6/7 feet, multiply the length by the width to get 24/7 square feet.
The area of a rectangular garden measuring 4 feet by 6/7 feet can be calculated as follows:
Area = Length x WidthArea = 4 ft × (6/7) ftArea = 24/7 ft²Therefore, the area of the rectangular garden is 24/7 square feet.
Which polygons are similar?
1,2,3,4
Answer:
1 and 4
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
The corresponding angles of Triangle 1 and Triangle 4 are congruent
therefore
Both triangles are similar
Answer:
similar polygons are 1 and 4
Step-by-step explanation:
From the figure we can see some triangles and angles are given
Similar triangles means that the angles are same and their corresponding sides are in proportion.
To find the correct answer
From the figure we get 1 and 2 are similar triangle, because angles of triangle 1 are 10°, 60° and 110°,
and angles of triangle 4 are 10°, 60° and 110°,
Therefore the correct answer is 1 and 4
Please answer this correctly
Answer:
21.66
20.545
20.479
20.15
20.1
Hello There!
From Least To Greatest, The Numbers Would Be
20.1, 20.15, 20.479, 20.545, 21.66
Solve the formula C = ad for a.
[tex]C=ad\\\\a=\dfrac{C}{d}[/tex]
How can 7 go into 424 as a whole number
Answer:
Step-by-step explanation:
It can't.
The answer is 60 with a remainder of 4
What is the solution of Square -4x =100?
For this case we have the following expression:
[tex](-4x) ^ 2 = 100[/tex]
To look for the solution:
We apply root to both sides of the equation to eliminate the exponent:
[tex]-4x = \pm \sqrt {100}\\-4x = \pm10[/tex]
Then we have two solutions:
[tex]-4x = 10[/tex]
Dividing between -4 on both sides of the equation:
[tex]x = \frac {10} {- 4}\\x = - \frac {5} {2}[/tex]
The second solution:
[tex]-4x = -10[/tex]
Dividing between -4 on both sides of the equation:
[tex]x = \frac {-10} {- 4}\\x = \frac {5} {2}[/tex]
Answer:
[tex]x_ {1} = - \frac {5} {2}\\x_ {2} = \frac {5} {2}[/tex]
Type the correct answer in the box. Use numerals instead of words for numbers.
Use the rewritten equation from part A to find the value of x when a equals -2. the answer to part A was x=8a
Answer:
x=-16
Step-by-step explanation:
The given equation is:
x = 8a
which was written to find the value of x.
We have to find the value of x when the value of a is inserted as -2
So, putting the value
x = 8(-2)
x= -16
So the value of x when a = -2 is -16 ..
Answer:
x= -16
Step-by-step explanation:
The rewritten equation for x from part A is x = 8a.
Substitute -2 for a in the equation and solve:
x = 8(-2)
x = -16
Easy ₛₕᵢₜ Yo
what is The best decimal to represent 5 3/7
Step-by-step explanation:
First, change the mixed fraction into an improper fraction:
5 3/7 =
5 x 7 = 35 + 3 = 38/7
Next, divide:
38/7 = 5.42857...
5.43 (rounded) is your answer.
Of course, the more digits behind it the better, so it is up to your discretion and your answer choices.
~
Answer:
5*7+3 = 38/7 ~5.43
we can multiple 5 by 7 and add them by 3
What’s the answer?? Need Help
Answer:
∠2 and ∠3 are complementary
Step-by-step explanation:
Complementary angles add up to 90°. Angles 1 and 3 are complementary, so the formula is ∠1 + ∠3 = 90°. Given that Angle 1 equals to angle 2, we substitute angle 2 for angle one in the equation stated before. Now we have ∠2 + ∠3 = 90°, so angles 2 and 3 are complementary
which of the numbers below are whole numbers A.7934.26 B.0.7735 C.878 D 1 E.638793.7 F.415.167
Answer:
Step-by-step explanation:
C. 878 and D. 1 are the only whole numbers. The rest are either mixed numbers or fractions.
what are the zeros of the function f (x)=x^2+5x+5 written in simplest radical form
Answer:
The zeros are
[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex] and [tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]f(x)=x^{2} +5x+5[/tex]
To find the zeros equate the function to 0
[tex]x^{2} +5x+5=0[/tex]
so
[tex]a=1\\b=5\\c=5[/tex]
substitute in the formula
[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(1)(5)}} {2(1)}[/tex]
[tex]x=\frac{-5(+/-)\sqrt{5}} {2}[/tex]
[tex]x1=\frac{-5+\sqrt{5}} {2}[/tex]
[tex]x2=\frac{-5-\sqrt{5}} {2}[/tex]
real square roots of 144
Answer:
±[tex]12[/tex]
Step-by-step explanation:
We need to find [tex]\sqrt{144}[/tex].
Now, we know that [tex](12)^{2} = 144[/tex] and [tex](-12)^{2} = 144[/tex]
Therefore: [tex]\sqrt{144}=[/tex]±[tex]12[/tex]
Summarizing, the real square roots of 144 are ±[tex]12[/tex]
[tex]\sqrt{144}=\pm12[/tex]
What is the area of a triangle with vertices at (0, −2) , (0, −3) , and (8, -3) ?Enter your answer in the box.___ units²
Answer:
The area of the triangle is [tex]A=4\ units^{2}[/tex]
Step-by-step explanation:
Let
A(0, −2),B (0, −3) and C(8, -3)
Plot the vertices
see the attached figure
Triangle ABC is a righ triangle
The area of the triangle ABC is equal to
[tex]A=\frac{1}{2}(BC)(AB)[/tex]
[tex]BC=8-0=8\ units[/tex]
[tex]AB=-2-(-3)=1\ units[/tex]
substitute
[tex]A=\frac{1}{2}(8)(1)[/tex]
[tex]A=4\ units^{2}[/tex]
Which inequality is equivalent to 4 x − 2 y ≤ 8 ?
Answer:
y≥2-4
Step-by-step explanation:
Simplify your equation.
4x-2y≤8
-4x -4x
-2y≤-4x+8
/-2 /-2
y≥2-4
Which of the following expressions is equivalent to the one shown below?
Answer:
A (7^6)
Step-by-step explanation:
Step 1: Find the property of 7^13/7^7
b^m/b^n=b^m-n
Therefore, when the numerator and denominator are the same number, the powers can be subtracted to simplify the answer.
Step 2: Apply the property to the question
7^13/7^7 = 7^13-7
=7^6
Hence, option A is the correct answer.
!!
Answer:
The equivalent expression is [tex]7^{6}[/tex] ⇒ answer A
Step-by-step explanation:
* Lets revise some rules of the exponents
- In the exponential functions we have some rules
# In multiplication if we have same base then add the power
b^m × b^n = b^(m + n)
- Ex: [tex]5^{11}*5^{4}=5^{11+4}=5^{15}[/tex]
# In division if we have same base we subtract the power
b^m ÷ b^n = b^(m – n)
- Ex: [tex]\frac{3^{10}}{3^{4}}=3^{10-4}=3^{6}[/tex]
* Now lets solve the problem
- There is the expression [tex]\frac{7^{13}}{7^{7}}[/tex]
- We have base 7 up and down
∵ In division if we have same base we subtract the power
∵ The base up is 7 and the base down is 7
- We will subtract the powers
∴ [tex]\frac{7^{13}}{7^{7}}=7^{13-7}=7^{6}[/tex]
∴ The answer is [tex]7^{6}[/tex]
* The equivalent expression is [tex]7^{6}[/tex]
Find the scale factor of the larger figure to the bigger figure.5-8 solve for x. The polygons in each pair are similar.
Answer:
See below in BOLD.
Step-by-step explanation:
What you need to do is identify the corresponding sides in the polygon than divide the larger length by the smaller.
3. The side length 8 corresponds to the 4 in the other polygon.
So the scale factor is 8/4 = 2.
4. Scale Factor = 24/20 = 1.2.
5. 40/32 = 5x / 24
5x = 40*24 / 32
5x = 30
x = 6.
6. 25/30 = 4x + 7 / 42
5/6 = 4x + 7 / 42
6(4x + 7) = 210
24x = 210 - 42 = 168
x = 168/24
x = 7.
7. 40/24 = 3x + 5 / 21
5/3 = (3x + 5) / 21
9x + 15 = 105
9x = 90
x = 10.
8. 24 / 40 = (x + 3) / 15
3/5 = (x + 3) / 15
5x + 15 = 45
5x = 30
x = 6.