If x = -7, evaluate the following expression:
(x − 2)(x+14)
——————-
x(x + 8)
Answers
Answer:
9
Step-by-step explanation:
[tex]\text{Given that}~ x = -7\\\\\dfrac{(x-2)(x+14)}{x(x+8)}\\\\\\=\dfrac{(-7-2)(-7+14)}{-7(-7+8)}\\\\\\=\dfrac{(-9)(7)}{-7(1)}\\\\\\=\dfrac{-63}{-7}\\\\\\=9[/tex]
Related Questions
Can someone please help me? I put the answer at 47.1 but it says it's wrong.
Answers
Answer:
47.14 cm
Step-by-step explanation:
Circumference :
π x diameterπ x 1515π15 x 22/7330/747.14 cm (approximately)find the solutions(s) to 9x^2-54x+0
Answers
Answer:
x = 6
x = 0
As shown, there are 2 values for x. The question is why, which we will go over in the explanation part.Step-by-step explanation:
identify the coefficients
[tex]9x^2-54x=0\\a=9\\b=-54\\c=0[/tex]
coefficient a = 1
[tex]9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0[/tex]
complete the square
[tex]b=-6\\(\frac{b}{2})^2=(\frac{-6}{2})^2\\(\frac{x}{y})^2=\frac{x^2}{y^2}\\=(\frac{-6}{2})^2=\frac{-6^2}{2^2}\\\frac{-6^2}{2^2}=\frac{36}{4}\\36 \div 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\\frac{b}{2}\\\frac{b}{2}=\frac{-6}{2}\\\frac{b}{2}=\frac{\left(-3\cdot 2\right)}{\left(1\cdot 2\right)}\\\frac{b}{2}=-3\\x^2-6x+9=9\\(x-3)^2=9\\[/tex]
solve for x
[tex](x-3)^2=9\\\sqrt{(x-3)^2}=\sqrt{9}\\x-3=+-\sqrt{9}\\x-3+3=3+-\sqrt{9}\\x=3+-\sqrt{9}\\x=3+-3\\x_1=6\\x_2=0[/tex]
≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.
the table below shows the cost of downloading songs from an online music store.
Answers
Answer:
I believe it's c because Greg downloaded 5 song which is 6.45 total then bought certain song at sale price Wich ended at 9.42
Please!!! Help!!! Brainliest of Right! it goes as 50 point in the end but i used 100 point if you help me i will help you!!
Answers
Answer:
2. 3.913 kg (3 dp)
3. light cream
4. 240 CoffeeStops
5. 7 CoffeeStops per square mile
6. 2,861 cups of coffee each day
Step-by-step explanation:
Given:
Skim milk density at 20 °C = 1.033 kg/lLight cream density at 20 °C = 1.012 kg/l1 liter = 0.264 gallonsQuestion 2
[tex]\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}[/tex]
Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)
---------------------------------------------------------------------------------------------
Question 3
Given:
Volume of liquid = 9 litersMass of liquid = 9.108 kg[tex]\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}[/tex]
Therefore, the container holds light cream.
---------------------------------------------------------------------------------------------
Question 4
Given:
15 CoffeeStops per 100,000 peoplePopulation of Manhattan ≈ 1,602,000 people[tex]\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}[/tex]
Therefore, there are 240 CoffeeStops.
---------------------------------------------------------------------------------------------
Question 5
Given
Manhattan ≈ 34 square miles[tex]\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}[/tex]
Therefore, the density of CoffeeStops is 7 per square mile.
---------------------------------------------------------------------------------------------
Question 6
Given:
Each person buys 3 cups of coffee per week[tex]\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}[/tex]
[tex]\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}[/tex]
Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.
3. Find f(5)+j(-2) if f(x)=12-3x and j(x)=x² + 4x - 1.
HELP ME PLEASEEEE
Answers
The value of the expression f(5) + j(-2) is -8 where f(x)=12-3x and j(x)=x² + 4x - 1
How to solve the equation?The expression is given as:
f(5) + j(-2)
Where f(x)=12-3x and j(x)=x² + 4x - 1
Calculate f(5) and j(-2)
f(5)= 12 - 3(5) = -3
j(-2) = (-2)² + 4(-2) - 1 = -5
So, we have:
f(5) + j(-2) = -3 - 5
Evaluate
f(5) + j(-2) = -8
Hence, the value of the expression f(5) + j(-2) is -8
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Daniel has read 10% of a book. He has 45 more pages to finish. How many pages are there in the book?
Answers
Answer:
He read 10% of the book, so 90% remains to be read. That 90% consists of 45 pages, so
45=0.90n
n= 45/0.90
n=50
There are 50 pages total in the book
Step-by-step explanation:
The 45 pages left is 90 percent of it.
If the 10% is _ pages then whatever that number is times 9 (bc of 90%) should be 45.
If u do the math 5 pages is 10%. 45+5=50 pages in total
A teacher has a large container of blue, red, and green beads. she reports to the students that the proportion of blue beads in the container is 0.30. the students feel the proportion of blue beads is lower than 0.30. a student randomly selects 60 beads and finds that 12 of the beads are blue. the p-value for the test of the hypotheses, h0:p=0.30 and ha:p<0.30, is 0.045. what is the correct interpretation of this value?
Answers
The interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.
What is a null hypothesis?It should be noted that the null hypothesis simply means a statical theory that suggests that there's no relationship between the variables given in the data set.
From the information given, it was stated that the proportion of blue beads in the container is 0.30. Here, the interpretation of this value is that the null hypothesis is that the proportion of blue beads in the container is 0.30 and the alternative hypothesis is 0.045.
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|2x -8| < 2
a. 3
b. -5
c. x>5 or x<3
d. x>-3 or x<-5
Answers
Answer:
[tex]3 < x < 5[/tex]
Step-by-step explanation:
Given inequality:
[tex]|2x - 8| < 2[/tex]
[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]
[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]
[tex]\implies -2 < 2x-8 < 2[/tex]
Therefore:
[tex]\implies -2 < 2x-8[/tex]
[tex]\implies 6 < 2x[/tex]
[tex]\implies 3 < x[/tex]
And:
[tex]\implies 2x-8 < 2[/tex]
[tex]\implies 2x < 10[/tex]
[tex]\implies x < 5[/tex]
Merge the overlapping intervals: [tex]3 < x < 5[/tex]
Proof
Graph: [tex]y=|2x-8|[/tex]
Add a line at [tex]y=2[/tex]
The interval that satisfies [tex]|2x - 8| < 2[/tex] is the area under the points of intersection (shaded area on the attached graph).
The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.
So
Case-1
2x-8<22x<2+82x<10x<5Case-2
2x-8>-22x>6x>3So solution is
3<x<5somebody please help me
Answers
Answer:
66°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles in a triangle is 180°.
__
79° +x +35° = 180°
x = 180° -114° . . . . . . . . subtract 114° from both sides
x = 66° . . . . . simplify
Question 9 of 9
Which of the expressions are equivalent to the one below? Check all that
apply.
(15.3)-20
A. (3.15)-20
B. 20-(3.15)
C. 6 (15-20)
D. (3-20) (15-20)
Answers
Find ∠ if ∠=+49, ∠=+63, and ∠=106∘.
Answers
The vslue of the angle based on the information given will be 142°.
How to calculate the angle?From the information given, it can be deduced that the shape has four sides. The total angles will be:
= (n - 2) × 180
= (4 - 2) × 180°
= 360°
The value of the last angle will be:
= 360° - (49° + 63° + 106°)
= 360° - 218°
= 142°
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How many solutions does the equation below have? 1/(-6-8x) = -3- 1x
Answers
Answer:
This equation has 2 solutions.
1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]
2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]
What is the name of the red dot located on the curve of the parabola below?
O A. Center
B. Focus
C. Vertex
D. Directrix
Answers
C. Vertex (x,y). The vertex is right in the middle of the quadratic graph.
In an agricultural class, there are 17 freshmen students and 19 sophomore students. What ratio compares the number of freshmen to the number of sophomores (F:S), and what ratio compares the number of sophomores to the number of freshmen (S:F)
Answers
Answer:
Freshmen to sophomores - (17:19)
Sophomores to freshmen - (19:17)
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
Find the area of this rectangle.
11M 9M
Answers
Answer: 99M
Step-by-step explanation:
Rectangle area
A=LW
A = 11 x 9
A = 99
Mark as brainliest please TT. Thank you :D
Answer:
99 m
Step-by-step explanation:
width times length = area
11 ×9= 99m
(72 divided by 8-x2x3+1 plese help
Answers
Answer:
[tex]\frac{72}{-x^{5} +9}[/tex]
Step-by-step explanation:
Let me know if that is not the same equation you wrote and if you have any questions !!
Select the correct answer from each drop-down menu.
veronica wants to cut a sheet of paper into squares with an area of 12 square inches. for the best approximation, the length of each side o
the square pieces of paper must be approximately equal to
inches. if each side were exactly this length, the area of each square
would be _____
square inches
Answers
Answer:3.46
Step-by-step explanation:i dont know the other one
what fraction is at point M?
Answers
Answer:
D
Step-by-step explanation:
because 3/10 is 0.3
Hope this helps!
m=p-2b/2
p=57.4
b=8.7
Answers
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
What is the value of m?Given that;
m = ( p-2b ) / 2p = 57.4b = 8.7Value of m = ?First, we substitute the value of p and b into the equation.
m = ( p-2b ) / 2
m = ( 57.4 - 2(8.7) ) / 2
m = ( 57.4 - 17.4 ) / 2
m = 40 / 2
m = 20
Given the value of p and b in the equation (( p-2b ) / 2 ), the value of m is 20.
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12. Round 2,870 to the nearest hundred.
Answers
Answer:
2900
Step-by-step explanation:
2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representations of the given inequality are
–6x + 15 < 10 – 5x
and
A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options
Solving inequalityFrom the question, we are to solve the inequality
The given inequality is
–3(2x – 5) < 5(2 – x)
First, clear the brackets
–6x + 15 < 10 – 5x
NOTE: This is one of the correct representations of the inequality
Collect like terms
-6x + 5x < 10 - 15
-x < -5
Divide both sides by -1 and flip the sign
x > 5
Representing this on a number line, we get a number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right.
Hence, the correct representations of the given inequality are
–6x + 15 < 10 – 5x
and
A number line with an open circle at 5 and a bold line that starts at 5 and is pointing to the right. The correct options are the third and fourth options
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if f(x)= 3x -2, find f-1(x)
Answers
Answer: 1/3x + 2/3
Step-by-step explanation:
f(x)= 3x - 2 =>
y= 3x - 2 =>
x= 3y - 2 =>
3y - 2= x =>
3y= x + 2 =>
y= 1/3x + 2/3 =>
f-1(x)=1/3x + 2/3
Jared and Zach are practicing their free throws. Jared attempted x shots and made 75% of them. Zach attempted 10 more shots than Jared did and made 80% of them. Together, they made a total of 101 shots. Which equation represents this situation?
A. 0.75x = 0.8(x + 10)
B. 0.75(x + 10) + 0.8x = 101
C. 0.75x + 0.8x + 10 = 101
D. 0.75x + 0.8(x + 10) = 101
Jared attempted ____ shots.
Zach attempted ____ shots.
Answers
.75x + .8(x+10) = 101
.75x + .8x + 8 = 101
1.55x + .8 -.8 = 101-8
1.55x = 93
Divide both sides be 1.55
X = 60. Jared
X + 10 = 70 Zach
Have a great day!
Answer: the other person is correct
Simplify the expression |1/12 - 5/6| - (2/5 + 1/10)
Answers
Answer:
x+2
Step-by-step explanation:
x^2+x-7 = x+2
Answer:
The answer is 1/4!!
<3 love
Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54.
what is the first term of the sequence?
to get to the next term, you would_____
this is a _____ sequence
there are 27 weeks left in this school year for monique. if she continues getting coffee at this rate how much money will she have spent on coffee by the end of the year?
Answers
If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n+1)d, ...
Its nth term is
Tₙ = a + (n-1)d
(for all positive integer values of n)
Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,
4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........
Therefore,
The first term of the sequence is 4.54, To get the next term you need to add 4.54. This is an arithmetic sequence.Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,
a₃₆ = 4.54 + (36-1)4.54
a₃₆ = 163.44
Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.
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Bottles of water come in packages of 6. Cheese sticks come in packages of 10.
What is the least number of packages of each a person has to buy to have the same number of bottles of water and cheese sticks?
Drag and drop a number into each box to complete the statement.
That person needs to buy Response area packages of bottles water and Response area packages of cheese sticks.
Answers
Answer:
water: 5 packagescheese sticks: 3 packagesStep-by-step explanation:
The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.
__
The LCM can be found by factoring out the greatest common divisor of each of the numbers:
6 = 2 × 3
10 = 2 × 5
The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.
The number of packages of bottles of water will be 30/6 = 5 packages.
The number of packages of cheese sticks will be 30/10 = 3 packages.
_____
Additional comment
You may notice that the number of packages of each kind is the unique factor in the other number.
Which one of these points lies on the given circle
O (-2.5, -2.5)
O (1, 3)
O (2, - √5)
O (-√3, -√7)
Answers
Step-by-step explanation:
every point on the circle has the same distance from the center : r (radius).
we can see that radius right there on the x-axis : the distance of (3, 0) to (0, 0) is simply 3. that is our radius.
the distance formula is applied Pythagoras
distance² = (difference in x coordinates)² +
+ (difference in y coordinates)²
distance = sqrt( ... )
so,
(-2.5, - 2.5)
(-2.5 - 0)² + (-2.5 - 0)² = 6.25 + 6.25 = 12.5
that is not 3² = 9, so the point is NOT on the circle.
(1, 3)
(1 - 0)² + (3 - 0)² = 1 + 9 = 10
that is not 3² = 9, so the point is NOT on the circle.
(2, -sqrt(5))
(2 - 0)² + (-sqrt(5) - 0)² = 4 + 5 = 9
that IS 3² = 9, so, the point IS on the circle.
(-sqrt(3), -sqrt(7))
(-sqrt(3) - 0)² + (-sqrt(7) - 0)² = 3 + 7 = 10
that is not 3² = 9, so the point is NOT on the circle.
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Answers
Answer:
-2
Step-by-step explanation:
For a straight-line graph, pick two points on the graph.
The gradient of the line = (change in y-coordinate)/(change in x-coordinate)
(x, y)
Point 1: (2, 0)
Point 2: (3, 2)
Gradient = (change in y)/(change in x)
= (2 - 0) / (3 - 2)
= 2 / 1
= 2
Note: gradient is basically slope where slope = rise / run
Answer:
help has arrived its -2
Step-by-step explanation:
How many inches are in 12 feet?
Answers
Answer:
144 inches in 12 feet.
Step-by-step explanation:
There are 12 inches in 1 foot.
Find inches when you have 12 ft.
[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]
Feet cancel out leaving inches.
There are 144 inches in 12 feet.
find the nature of the roots of the roots of the equation (x-705)(x-795)+800(x-750)(x-835)=0.
(A) Imaginary roots.
(B) Real and distinct.
(C) Real and equal.
(D) None.
Answers
Answer:
B
Step-by-step explanation:
If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.
These roots are real and distinct, or choice B.
If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.
I hope that helps!