Answer:
x = -7, 7
Step-by-step explanation:
Step 1: Write out equation
-2x² - 9 = -107
Step 2: Add 9 on both sides
-2x² = -98
Step 3: Divide both sides by -2
x² = 49
Step 4: Square root both sides
x = ±7
Step 5: Arrange
-7 < 7
So x = -7, 7
can irrational numbers also be integers/ True or False
Answer:
true
Step-by-step explanation:
Evaluate the following expression where x = 6, y = 24andz = 4 z(-y+x)
Answer:
-96+24= -72 or just -72
Step-by-step explanation:
4(-24+6)
-96+24= - 72
put the values of x,y and z
4(-24+6)
4(-18)
= -72
If all the letters of the English alphabet were written on a piece of paper, over and over again, which letter would be the ten millionth letter to be written?
Answer:
Alphabet J
Step-by-step explanation:
Given
Alphabet: A - Z
Required
Determine which alphabet is at the 10 millionth position
Represent the number of alphabets with n
n = 26
To get the alphabet at the required position, we have to divide 10 million by 26 and note down the remainder
[tex]\frac{10000000}{26} = 384615\ R\ 10[/tex]
The division gives, 384615 remainder 10
This implies that, the alphabet at the 10th position is the same alphabet at the 10 millionth position;
And this alphabet is J
The length of a rectangle is five inches more than four times it’s width if the perimeter of the rectangle is 90 inches , find it’s dimensions
Answer:
length = 37 incheswidth = 8 inchesStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where
l is the length
w is the width
From the question
Perimeter = 90 inches
The statement
The length of a rectangle is five inches more than four times it’s width is written as
l = 5 + 4w
Substitute this expression into the above formula and solve for the width
That's
90 = 2(5 + 4w) + 2w
90 = 10 + 8w + 2w
10w = 90 - 10
10w = 80
Divide both sides by 10
w = 8
Substitute this value into l = 5 + 4w
That's
l = 5 + 4(8)
l = 5 + 32
l = 37
Therefore we have
length = 37 incheswidth = 8 inchesHope this helps you
Simplify the radical /8106.
Answer:
√8106
Step-by-step explanation:
8106 = 2·3·7·193
It has no square factors, so the radical cannot be simplified further.
what type OK f number is -0.5/-0.5
find the slope of the line passing through (-9,-6) and (-4,5)
Answer:
11/5
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (5 - -6)/(-4 - -9)
= (5+6)/( -4+9)
= 11/5
Let's find the slope using the graphing method.
First set up a coordinate system like I have done below.
Now, graph each ordered pair.
Let's call (-9, -6) point A and (-4, 5) point B.
Now remember that the slope or m is equal
to the rise over run from point A to point B.
To get from point A to point B, we rise 11 units and run 5 units.
So our slope is 11/5.
help really quick .
Answer:2y
Step-by-step explanation:
!!!
Answer:
Answer: h(x) = 1/5x
Step-by-step explanation:
6x + y = 4x + 11y
-y -y
6x = 4x + 10y
-4x -4x
2x = 10y
÷10 ÷10
1/5x = y
Since "y" represents h(x), then h(x) =
What is the equation in slope form of line passing through (1,9) and(-1,11)
Answer:
y = -x + 10
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (11 - 9)/(-1 - 1)
m = 2/-2
m = -1
y = -x + b
Step 2: Find y-intercept b
9 = -(1) + b
9 = -1 + b
b = 10
Step 3: Rewrite linear equation
y = -x + 10
Carson needs 3 quarts of water to make fruit punch, but has only a l-cup measuring cup.
She knows there are 2 cups in 1 pint, and 2 pints in 1 quart.
Use the drop-down menus to explain how Carson can find the number of cups of water she
needs to make the punch.
Please help!!!
Answer:
Cups of water she needs to make the punch is 12.
Step-by-step explanation:
Amount of water Carson need to make fruit punch = 3 quarts
2 cups is 1 pint
2 pints is 1 quart
1 pint = 1/2 quarts
2 cups is 1 pint which is 1/2 quarts
So, 1 cup:
1 cup is 1/2 times 2 quarts
1 quart is 1 times 2 times 2 cups equals 4 cups
So, 3 quarts equals 3 times 4 cups which equals 12 cups.
So it is 12 cups.
Cups of water she needs to make the punch is 12.
What is unit conversion?
A unit conversion expresses the same property as a different unit of measurement.
Given that, Carson needs 3 quarts of water to make fruit punch, but has only an l-cup measuring cup.
She knows there are 2 cups in 1 pint, and 2 pints in 1 quart.
Amount of water Carson need to make fruit punch = 3 quarts
2 cups is 1 pint
2 pints is 1 quart
1 pint = 1/2 quarts
2 cups is 1 pint which is 1/2 quarts
So, 1 cup:
1 cup is 1/2 times 2 quarts
1 quart is 1 times 2 times 2 cups equals 4 cups
So, 3 quarts equals 3 times 4 cups, which equals 12 cups.
Hence, she need 12 cups.
For more references on unit conversion, click;
https://brainly.com/question/19420601
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A and B have certain number of mangoes. A says to B, " If you give me 10 of your mangoes, I will have twice as many as left with you." B replies, "If you give me 10 of your mangoes, I will have thrice the number of mangoes left with you. Find the original number of mangoes each had.
Answer:
A had 22 mangoes, B had 26 mangoes
Step-by-step explanation:
We can write the following system:
A + 10 = 2(B - 10) -- Equation 1
3(A - 10) = B + 10 -- Equation 2
A + 10 = 2B - 20 → A = 2B - 30 -- Equation 3 (Simplify Equation 1)
3(2B - 30 - 10) = B + 10 -- Equation 4 (Substitute 3 into 2)
3(2B - 40) = B + 10
6B - 120 = B + 10
5B = 130
B = 26 -- (Solve for B in Equation 4)
A = 2 * 26 - 30 = 22 -- (Substitute B = 26 into Equation 3)
Use trig ratios to find the measure of the angle in this triangle. A .cos^-1(4/5) B. tan(4/5) tan^-1(4/5) C. sin(4/5) D. cos(4/5) E. sin^-1(4/5)
Answer:
The answer is A
Step-by-step explanation:
Step 1: Use Cosine to find ∅
Cos∅=[tex]\frac{4}{5}[/tex]
∅=Cos[tex]^{-1}[/tex]([tex]\frac{4}{5}[/tex])
Therefore the answer is A
An underwater canyon begins at 40 feet
below sea level and is 105 feet deep.
What is the elevation of the bottom of
the canyon?
Answer:
145 feet.
Step-by-step explanation:
Given that:
An underwater canyon begins at depth = 40 ft
Depth of canyon = 105 ft
To find:
The elevation of the bottom of the canyon = ?
Solution:
Kindly refer to the image attached for the given dimensions.
A is the sea level.
B is the point at which the canyon starts and
C is the bottom of the canyon.
As per question statement, we are given that:
AB = 40 feet
BC = 105 feet
And we have to find the distance AC = ?
It is clearly observable that:
[tex]AC = AB + BC\\\Rightarrow AC = 40 + 105\\\Rightarrow \bold{AC = 145 ft}[/tex]
So, the elevation of the bottom of the canyon is 145 ft.
X is all the following except
a term
a variable
a constant
an expression
Answer: a constant
Step-by-step explanation:
A constant is a numerical expression like 2, 0,78 etc .
A variable is a alphabetical expression that vary like a,b,c,d,x,y,z.
An expression can consists of both numerical and alphabets and also any arithmetic expression like x, 2abc, 6a+2c etc
A term consist of either numbers and variables multiplied together or only numbers or variable like 2xy, x, 2ab etc.
X is all (a term, a variable , an expression) except a constant because a constant is a numerical expression.
Answer: D, a constant
Step-by-step explanation: A constant is an expression without variables.
Joshua spins a spinner twice. The spinner consists of 3 equally spaced colors, Red, Blue, and Yellow. What is the probability that the spinner will stop on green and then yellow? ASAP
Answer:
[tex]\dfrac{1}{9}[/tex]
Step-by-step explanation:
Given a spinner with 3 equally spaced colors Red, Blue, Yellow.
The colors are equally spaced, therefore probability of each color must be same.
i.e. Probability of occurrence of any one color in one spin is [tex]\frac{1}{3}[/tex].
To find:
Probability that spinner will stop one green in first spin and yellow in the second spin = ?
Solution:
As all the colors are equally likely to occur, so
Probability of green color in the first spin, P(G) = [tex]\frac{1}{3}[/tex]
Probability of yellow color in the second spin, P(Y) = [tex]\frac{1}{3}[/tex]
As we can observe that occurrence of any color in the second round of spin is not dependent on the color occurrence in the first spin, therefore these are the independent events.
P(G and Y) = P(G) [tex]\times[/tex] P(Y)
[tex]\Rightarrow P(G\ and\ Y) = \dfrac{1}{3} \times \dfrac{1}{3}\\\Rightarrow P(G\ and\ Y) = \bold{\dfrac{1}{9}}[/tex]
Therefore, the required probability is
[tex]\dfrac{1}{9}[/tex].
Hi can u please help will mark brainliest
Answer:
$-48
Step-by-step explanation:
(-125 + -86 +54 +-35)/4 = -48
Add all the Profits/losses and divide by the number of weeks.
Write the equation in slope intercept form: passing through the x-axis at x=3 and passing through the y-axis at y= -5
Answer:
[tex]y=\frac{5}{3}x-5[/tex]
Step-by-step explanation:
Slope-intercept:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. We know that the line passes through the y-axis at -5, so this is the y-intercept (where x is equal to 0). Insert this into the equation:
[tex]y=mx-5[/tex]
With the given information, we can form two points:
[tex](3,0)(0,-5)[/tex]
The first one is the x-intercept and the second the y-intercept. Use these to find the slope:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert the appropriate values:
[tex](3_{x1},0_{y1})\\(0_{x2},-5_{y2})\\\\\frac{-5-0}{0-3}[/tex]
Solve:
[tex]\frac{-5-0}{0-3}=\frac{-5}{-3}[/tex]
Note that both the numerator and denominator are negatives. Two negatives make a positive, so:
[tex]\frac{5}{3}[/tex]
The slope is [tex]\frac{5}{3}[/tex]
Insert into the equation:
[tex]y=\frac{5}{3}x-5[/tex]
:Done
Can you help me with this maths q please?
Answer:
See below
Step-by-step explanation:
a) line marked a is tangent
b) line marked b is radius
c) line marked c is diameter
d) line marked d is chord
find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13)
Answer:
y = 2( x-3)^2 +5
Step-by-step explanation:
The vertex form of a parabolic functions is
y = a( x-h)^2 +k
where (h,k) is the vertex
y = a( x-3)^2 +5
Substituting the point into the equation
13 = a( 1-3)^2 +5
13 = a*( -2)^2 +5
13 = 4a +5
Subtract 5
8 = 4a
Divide by 4
8/4 =a
2=a
y = 2( x-3)^2 +5
Select TWO possible values for x in the equation x2=45.
Answer:
[tex]3 \sqrt 5}[/tex] and [tex]-3 \sqrt 5}[/tex]
Step-by-step explanation:
Given
[tex]x^2 = 45[/tex]
Required
Determine the values of x
[tex]x^2 = 45[/tex]
Take square root of both sides
[tex]\sqrt{x^2} = \±\sqrt{45}[/tex]
[tex]x = \±\sqrt{45}[/tex]
Expand 45 as 9 * 5
[tex]x = \±\sqrt{9 * 5}[/tex]
Split the square root
[tex]x = \±(\sqrt{9} *\sqrt 5}[/tex]
[tex]x = \±3 *\sqrt 5}[/tex]
[tex]x = \±3 \sqrt 5}[/tex]
This can be further split to:
[tex]x = 3 \sqrt 5}[/tex] or [tex]x = -3 \sqrt 5}[/tex]
Hence, the possible values of x are
[tex]3 \sqrt 5}[/tex] and [tex]-3 \sqrt 5}[/tex]
A calculator company plans to sell two models of graphing calculators that cost $100 and $150, respectively. The $100 model yields a profit of $40 and the $150 model yields a profit of $50. The company estimates that the total monthly demand will not exceed 250 units. What are the number of units of each model should be stocked in in order to maximize profit, assuming that the merchant does not want to invest more than $30,000 in inventory?
Answer:
The quantity of the first model is 150 and the second model is 100 that maximize the profit.
Step-by-step explanation:
Let the quantity of first model = x
Let the quantity of second model = y
The cost of the first model = $100
The cost of the second model = $150
Total number of models = 250 units
Total amount to spend on units = $30000
Now form the equations.
x + y = 250
100x + 150y = 30000
Now solve for the x and y.
x = 250 – y
Now insert this value in the 100x + 150y = 30000.
100(250 –y) + 150y = 30000
25000 – 100y + 150y = 30000
50y = 30000 – 25000
50y = 5000
Y = 100
Now insert the Y in x + y = 250
x = 250 – y
x = 250 – 100
x = 150
Therefore, the first model is 150 units and the second model is 100 units that maximize the profit.
identify the property illustrated by the equation 8x(5x9)=(8x5)x9
Answer:
assosiative property
please help :) Write the number shown in standard notation. 5.29 x 10 to the 4th power A. 52,900 B. 5,290,000 C. 5,290 D. 529,000
Answer: Hi!
The equation given is 5.29 * 10^4.
First, we need to solve the exponent.
10^4 = 10,000
Next, we multiply 10,000 by 5.29.
10,000 * 5.29 = 52,900
Therefore, your answer is a), 52,900.
Hope this helps!
Answer:
A.
Step-by-step explanation:
It is 5.29 x 10,000
= 52,900.
solve for x in 3( x+ 2)=2(x+2)
Answer:
-2
Step-by-step explanation:
3( x+ 2)=2(x+2)
=>3x+6=2x+4
=>3x-2x=4-6
=>x=-2
-2 is the value of x
Answer:
The answer is
x = - 2Step-by-step explanation:
3( x+ 2)=2(x+2)
First expand the terms in the bracket
That's
3x + 6 = 2x + 4
Group like terms
Send the constants to the right side of the equation and those with variables to the left side
3x - 2x = 4 - 6
Simplify
We have the final answer as
x = - 2Hope this helps you
Erik and Caleb were trying to solve the equation: 0=(3x+2)(x-4) Erik said, "The right-hand side is factored, so I'll use the zero product property." Caleb said, "I'll multiply (3x+2)(x-4) and rewrite the equation as 0=3x^2-10x-8 Then I'll use the quadratic formula with a=3, b=-10, and c=-8. Whose solution strategy would work? A) Erik B) Caleb C) Both D) Neither
Answer:
C) Both
Step-by-step explanation:
The given equation is:
[tex]0=(3x+2)(x-4)[/tex]
To solve the given equation, we can use the Zero Product Property according to which if the product A.B = 0, then either A = 0 OR B = 0.
Using this property:
[tex](3x+2) = 0 \Rightarrow \bold{x = -\frac{2}{3}}\\(x-4) = 0 \Rightarrow \bold{x = 4}[/tex]
So, Erik's solution strategy would work.
Now, let us discuss about Caleb's solution strategy:
Multiply [tex](3x+2)(x-4)[/tex] i.e. [tex]3x^2-12x+2x-8[/tex] = [tex]3x^2-10x-8[/tex]
So, the equation becomes:
[tex]0=3x^2-10x-8[/tex]
Comparing this equation to standard quadratic equation:
[tex]ax^2+bx+c=0[/tex]
a = 3, b = -10, c = -8
So, this can be solved using the quadratic formula.
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-10)\pm\sqrt{(-10)^2-4\times3 \times (-8)}}{2\times 3}\\x=\dfrac{-(-10)\pm\sqrt{196}}{6}\\x=\dfrac{10\pm14}{6} \\\Rightarrow x= 4, -\dfrac{2}{3}[/tex]
The answer is same from both the approaches.
So, the correct answer is:
C) Both
Answer:
Both
Step-by-step explanation:
Determine the slope of a line given points, (-5, 8) and (-8,5).
Answer:
1
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (5-8)/(-8 - -5)
= -3/(-8+5)
= -3/-3
= 1
Simply the following radical expressions completely. Use the radical symbol in the equation editor to enter your response.
2✔️48
Answer:
[tex]\huge \boxed{8\sqrt{3}}[/tex]
Step-by-step explanation:
[tex]2\sqrt{48}[/tex]
Simplify [tex]\sqrt{48}[/tex].
[tex]2\sqrt{16} \sqrt{3}[/tex]
[tex]\sqrt{16}=4[/tex]
[tex]2 \times 4\sqrt{3}[/tex]
Apply rule : [tex]a \times b\sqrt{c} =ab\sqrt{c}[/tex]
[tex]8\sqrt{3}[/tex]
You purchase a 189-day, $1000 U.S. Treasury bill at 4.19% discount. On the date of maturity, you will receive $1000. How much interest does the U.S. Government pay to you on the date of maturity?
Answer:
The government paid an interest of $41.9, which is 4.19%
Step-by-step explanation:
Given the 189-day, $1,000 U.S Treasury bill is purchased at a discount of 4.19%, this means that:
It was purchased at a discount of:
4.19% of $1000
= (4.19/100) × 1000
= $41.9
Purchase price = $1000 - $41.9 = $958.1
Because the treasure is sold for $1000 on maturity day, that means the government paid an interest of $41.9, which is 4.19%
Solve the following inequality for d. Write your answer in simplest form. 3−(9d−1)< −6d+2+7
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
How does the value of the digit 2 in the number 32000 compare with the value of the digit 2 in the number 26000
Answer
the second value is ten times higher then the refference one
Hope it helped u if yes mark me BRAINLIEST!
Tysm!
Answer:
2 in 32000 is in the thousands place
2 in 26000 is in the ten thousands place
Step-by-step explanation: