Answer:
C. x ≥ -4
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-10x ≤ 40
Step 2: Solve for x
[Division Property of Equality] Divide -10 on both sides: x ≥ -4Answer:
C. x ≥ -4
Step-by-step explanation:
To solve this inequality isolate the variable. Do this by using the properties of equality, specifically the division property. So, divide both sides by -10. This equals, x ≤ -4. However, whenever an inequality is divided or multiplied by a negative number the sign must be flipped. Therefore, the final answer is x ≥ -4.
The two triangles below are congruent. Which of the following are congruent by CPCTC?
Answer:
B.
Step-by-step explanation:
If you put the second triangle upright then turn it over (as if you were flipping a pancake). That would make B equal to R.
C would equal S
A would equal T
and
B would equal R
Answer:
b = R, mark me brainiest cause we besties
Step-by-step explanation:
solve for x
5x = 10
Answer:
x = 2
Step-by-step explanation:
To solve for x, isolate it by dividing both sides of the equations by 5.
5x / 5 = 10 / 5
x = 2
Answer:
x = 2
Step-by-step explanation:
5x = 10
Divide both sides by 5.
x = 2
POINTS!!
Draw a diagram of the archway modeled by the equation y = -x2 + 5x + 24. Find and label the y-intercept and the x-intercepts on the sketch. Then find and label the width of the archway at its base and the height of the archway at its highest point, assuming the base of the archway is along the x-axis.
Answer:
1) Please find the attached drawing of the archway created with MS Excel
2) The y-intercept is (0, 24)
The x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base is 11
The height of the archway at its highest point = 30.25
Step-by-step explanation:
The given function representing the archway is y = -x² + 5·x + 24
1) Please find attached the required drawing of the archway created with MS Excel
2) The y-intercept is given by the point where x = 0
Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24
The y-intercept = (0, 24)
The x-intercept is given by the point where y = 0
Therefore, the x-values at the x-intercept are found using the following equation;
0 = -x² + 5·x + 24
x² - 5·x - 24 = 0
By inspection, we have;
x² - 8·x + 3·x - 24 = 0
x·(x - 8) + 3·(x - 8) = 0
∴ (x + 3) × (x - 8) = 0
Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8
Therefore, the x-intercepts are (-3, 0), and (8, 0)
3) The width of the archway at its base = The distance between the x-values at the two x-intercepts
∴ The width of the archway at its base = 8 - (-3) = 11
The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)
∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5
Therefore;
The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point
∴ The height of the archway at its highest point = 30.25.
ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages
Answer:
Their present ages are 12 years and 16 years.
Step-by-step explanation:
Given that,
Ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5.
Let their present age is 3x and 4x.
Ages after four years from now will be:
[tex]\dfrac{3x+4}{4x+4}=\dfrac{4}{5}\\\\5(3x+4)=4(4x+4)\\\\15x+20=16x+16\\\\20-16=16x-15x\\\\x=4[/tex]
So,
Raju's present age is 3(4) = 12 years
Ravi's present age is 4(4) = 16 years
You and your friend are playing a game by tosing two coins land on different sides your friend wins the table shows the possible outcome? Is this a fair game
what single transformation maps triangle ABC onto A’B’C?
Answer:
the answer is rotation hope it helps ahhaha
15% of $9 is $______
Answer:
$1.35
Step-by-step explanation:
multiply 9 by 15% which relates to .15. so 9×0.15 is $1.35
Answer: 9 times .15=1.35
15% of $9 is 1.35
Step-by-step explanation:
the length of each side of a nonagon is 3.25cm the perimeter of the nonagon is?
a,12.25
b,29.25m
c,29.25
d,none
Answer:
,29.25m
Step-by-step explanation:
maybe answer is correct
Answer: B. 29.25 cm
Step-by-step explanation:
Given
The prefix nona- came from Latin meaning "nineth"
Thus, nonagon has 9 sides
Solve
1 side = 3.25 cm
9 sides = 3.25 × 9 = 29.25 cm
Hope this helps!! :)
Please let me know if you have any question
calcula el área lateral de un prisma cuya base es un pentagono de 10cm de arista, 16.88 cm de apotema y 15 cm de altura
Answer:
Lateral surface area of pentagonal prism = 750 cm²
Step-by-step explanation:
Given information:
Height of pentagonal prism = 15 cm
Length of edge = 10 cm
Length of apothem = 16.8 cm
Find:
Lateral surface area of pentagonal prism
Computation:
Lateral surface area of pentagonal prism = 5(a)(h)
Lateral surface area of pentagonal prism = 5(10)(15)
Lateral surface area of pentagonal prism = 750 cm²
help me out please, thank you
Answer:
Answer D is TRUE because on the graph if you were to keep going left even after the picture of the graph ends, the graph will still keep going up infinitely.
Step-by-step explanation:
For his long distance phone service, Justin pays a $3 monthly fee plus 11 cents per minute. Last month, Justin's long distance bill was $12.79. For hov minutes was Justin billed?
Answer:
89 minutes
Step-by-step explanation:
let he talked for x minutes.
$12.79=1279 cents
1279=300+11x
11x=1279-300=979
x=89
On a standard baseball field, consecutive bases are 90 feet apart. How far does the catcher have to throw the ball to get from home plate to 2nd base
Abc similar to def the area of abc is 45cm and the area of triangle def is 20cm one side of triangle abc is 3.6cm the the length of corresponding side of triangle def is
Answer:
2.4cm
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
that means two lengths of the triangle have to be multiplied.
and to have 2 similar triangles means that all lengths inside one triangle are the corresponding lengths inside the other triangle multiplied by the scaling factor f.
multiplying 2 if these lengths with each other means also including the square of the scaling factor (multiplying with the scaling factor twice).
so, if the area of triangle 1 is
"baseline 1" × "height 1" / 2 = 45 cm²
then the area of triangle 2 is
"baseline 2" × "height 2" / 2 =
= "baseline 1"×f × "height 1"×f /2 =
= "baseline 1" × "height 1" × f² / 2 =
= ("baseline 1" × "height 1" / 2) × f² =
= 45 × f² = 20 cm²
f² = 20/45 = 4/9
f = 2/3
so, for a side of ABC being 3.6cm long, that means the corresponding side in DEF is
3.6 × f = 3.6 × 2/3 = 7.2/3 = 2.4cm
What is the following product?
Answer:
[tex]10\sqrt{3}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\sqrt{30}*\sqrt{10}[/tex]
One property of multiplying square roots is that one can multiply the numbers under the radical by each other, and then put the radical on top of the result. The following is an example of this general format of this property:
[tex]\sqrt{a}*\sqrt{b}=\sqrt{ab}[/tex]
Apply this to the real problem:
[tex]\sqrt{30}*\sqrt{10}=\sqrt{30*10}[/tex]
Simplify,
[tex]\sqrt{30*10}=\sqrt{300}[/tex]
Rewrite as (300) as the product of two numbers, such that one number is a perfect square:
[tex]\sqrt{300}=\sqrt{3*10^2}[/tex]
Simplify, take a term out of the radical:
[tex]\sqrt{3*10^2}=10\sqrt{3}[/tex]
5 tons of sand cost $7,200.00. What is the price per pound?
Answer:
$0.72 per pound
Step-by-step explanation:
1 ton = 2000
5 tons = 10000
10000 lb = $7200
7200/10000 = 0.72
0.72 dollars a pound
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Someone please help me with this algebra problem
Answer:
$110
Step-by-step explanation:
We are looking for the decrease in money per desk purchased. Because the x-axis is the number of desks purchased, what we have to find is the (opposite) of the slope. The formula to represent slope can be written as:
[tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
We can substitute the points given, (2, 480) and (5, 150) and simplify:
[tex]\frac{150-480}{5-2} =\frac{-330}{3} = -110[/tex]
We would multiply by -1 because we are asking for the decrease, and negative increase is decrease. -1 * -110, gives us $110
Which of the following are integers?
100
78
35
5
There can be more than one
line F has a slope of. -6/3 and line G has a slope of -8/4.
what can be determined about distinct lines F and G?
Given:
Slope of line F = [tex]-\dfrac{6}{3}[/tex]
Slope of line G = [tex]-\dfrac{8}{4}[/tex]
To find:
The conclusion about distinct lines F and G.
Solution:
We have,
Slope of line F = [tex]-\dfrac{6}{3}[/tex]
= [tex]-2[/tex]
Slope of line G = [tex]-\dfrac{8}{4}[/tex]
= [tex]-2[/tex]
The slopes of lines F and G are equal and we know that the slopes of two parallel lines are always equal.
Therefore, the line F and line G are parallel to each other.
Area of this figure
A skydiver jumps from an airplane and accelerates toward the ground. His velocity can be modeled by the function
v(t) = 1000t/5t+8, where v (t) is the velocity in feet per second, and t represents time in seconds. Due to air resistance, there is
a limiting velocity the skydiver will not exceed, called the "terminal velocity". At terminal velocity, the velocity does not
continue to increase. What is the terminal velocity? Justify your answer.
Answer:
The terminal velocity is 8.00ft/s
Step-by-step explanation:
Given
[tex]v(t) = 1000t^2 - 5t + 8[/tex]
Required
The terminal velocity
This implies that we calculate the maximum velocity.
First, we calculate the maximum value of t using:
[tex]t_{max} = -\frac{b}{2a}[/tex]
Where:
[tex]v(t) = at^2 + bt + c[/tex]
So, we have:
[tex]t_{max} = -\frac{-5}{2*1000}[/tex]
[tex]t_{max} = \frac{5}{2000}[/tex]
[tex]t_{max} = 0.0025[/tex]
Substitute this value of t in [tex]v(t) = 1000t^2 - 5t + 8[/tex] to get the maximum velocity
[tex]v(t) = 1000t^2 - 5t + 8[/tex]
[tex]v(t) = 1000 * 0.0025^2 - 5 * 0.0025 + 8[/tex]
Using a calculator, we have:
[tex]v(t) = 7.99375[/tex]
Approximate
[tex]v_{max} = 8.00ft/s[/tex]
Velocity is the rate of change of its position with respect to time. The terminal velocity of the skydiver is 200 ft/sec.
What is velocity?Velocity is the rate of change of its position with respect to time.
[tex]V = \dfrac{dy}{dt}[/tex]
Given the velocity of the skydiver by the function v(t)=1000t/(5t+8), after some time, the velocity will become terminal velocity and then it can not be increased further, therefore, the terminal velocity can be written as,
[tex]\lim_{t \to \infty} V(t) = \lim_{t \to \infty} \dfrac{1000t}{5t+8}\\\\[/tex]
[tex]= \lim_{t \to \infty} \dfrac{\frac{1000t}{t}}{\frac{5t}{t}+\frac{8}{t}}\\\\[/tex]
[tex]= \dfrac{1000}{5+\frac{8}{t}}\\\\= \dfrac{1000}{5}\\\\=200[/tex]
Hence, the terminal velocity of the skydiver is 200 ft/sec. It can be confirmed by plotting the function on the graph.
Learn more about the Terminal Velocity:
https://brainly.com/question/18084516
#SPJ5
Which of the following is the equation of the quadratic function below?
Answer:
C y=x^2+2x+1
Step-by-step explanation:
Suppose that the natural rate of unemployment in a particular year is 4 percent and the actual unemployment rate is 13 percent. Instructions: Enter your answers as a whole number. a. Use Okun's law to determine the size of the GDP gap in percentage-point terms. percent b. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment? $ billion
Answer:
a. 18 percent
b. $90 billion
Step-by-step explanation:
a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.
First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment
Difference=13%-4%
Difference= 9%
Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.
Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).
Therefore the the size of the GDP gap in percentage-point terms is 18 percent
b. Calculation to determine how much output is forgone because of cyclical unemployment
Forgone Output :
By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,
Hence,
Output forgone = (18/100) ×$500 billion
Output forgone=0.18×$500 billion
Output forgone=$90 billion
Therefore the Forgone Output is $90 billion
Please help me asap!
Answer:
Its 48
Step-by-step explanation:
subtract 69 and 56 from 173, what you have left is your answer
48
Step-by-step explanation:
total 176 subtract 69 and 58 since they are given.
176 - 69 -56 = 48
Cutting of 11.25 by 15
Answer:
it may be 0.75 i am not sure
Answer:
answer will be 0.75
11.25÷15=0.75The table shows the altitudes of four different cities. What is the correct way to arrange the altitudes in decreasing order?
City Altitude (feet)
Snowvale 13
Highbridge 58
Westsilver -51
Springmoor -35
A.
58, 13, -35, -51
B.
-51, -35, 13, 58
C.
-35, -51, 13, 58
D.
58, 13, -51, -35
Answer:
Step-by-step explanation:
i think A
Hope this helps!
Marcos buys a pumpkin that weighs 1.37 pounds. Gabriel buys a pumpkin that weighs 0.24 pounds more than Marcos' pumpkin. How much does Gabriel's pumpkin weigh, in pounds?
Answer:
1.61 pounds
Step-by-step explanation:
Weight of Marcos pumpkin = 1.37 pounds
Weight of Gabriel's pumpkin = Weight of Marcos pumpkin + 0.24 pounds
= 1.37 pounds + 0.24 pounds
= 1.61 pounds
Weight of Gabriel's pumpkin = 1.61 pounds
help me if tou don't then no brainlist for you
Answer:
Equal to 1,204-299
Step-by-step explanation:
Anything divided by 1 is equal to itself.
if x = 3 and y = 2, then the value of ( x - y )(x² + xy + y²) is
(a) 31 (b) 19 (c) 1 (d) 25
Answer:
19
Step-by-step explanation:
(3-2)(3^2+3x2+2^2)
(1)(9+6+4)
(1)(19)
[tex]\displaystyle\bf \underbrace{ (x-y)(x^2+xy+y^2)}}_{x^3-y^3}=3^3-2^3=19\\\\Answer: b)19[/tex]
If y is proportional to x, find the missing number.
A. 15
B. 12
C. 16
D. 18
HELPPP!!!!
Answer:
C. 16
Step-by-step explanation:
5 is half of 10, so 8 should be half of the next number.
Answer:
C. 16
Step-by-step explanation:
[tex] \frac{y}{x} = \frac{10}{5} = \frac{?}{8} \\ \frac{2}{1} = \frac{?}{8} [/tex]
cross multiplying
[tex]16 = ?[/tex]
so the missing number is 16
Ayudaaa!! Cortamos una cuerda de 60cm en 5 trozos. Hay 3 trozos cortos que miden lo mismo y los otros 2 trozos miden 5cm mas que los cortos. ¿Cuánto miden los trozos?
Answer:
The short pieces are 10 cm each and the long pieces are 15 cm each.
Step-by-step explanation:
We cut a 60cm rope into 5 pieces. There are 3 short pieces that measure the same and the other 2 pieces are 5cm longer than the short ones. How long are the pieces?
let the length of the short pieces is p.
Length of longer pieces = p + 5
So,
60 = 3 p + 2 (p+ 5)
60 = 3 p + 2p + 10
5 p = 50
p = 10 cm
So, the short pieces are 10 cm each and the long pieces are 15 cm each.