Answer:
2x²+7x-4
Step-by-step explanation:
(x+4)(x-1/2)
First multiply (x-1/2) by 2.
We have (2x-1)
(x+4)(2x-1)
Expanding it, we have
x(2x-1)+4(2x-1)
2x²-x+8x-4
2x²+7x-4
The regular selling price of an item is $169. For a special year-end sale the price is at a markdown of 20%. Find the discount sale price.
Use the relationships between the angles to find the value of x (please answer)
Step-by-step explanation:
[tex]x + 15 \degree = 102 \degree \: \\ (corresponding \: \angle s) \\ \therefore \: x = 102 \degree - 15 \degree \\ \huge \red { \boxed{\therefore \: x = 87 \degree}}[/tex]
The value of x according to the relationship between the angles is; x= 87°
Corresponding angles:By mathematical convention, Corresponding angles (otherwise called F-angles) are equal.
On this note; the angle 102° and x +15° are equal.
Therefore,
102 = x + 15x = 102 -15x = 87°.
Read more on corresponding angles;
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. If you pick one card at random from a standard deck of cards, what is the probability it
will be a Diamond?
Answer:
13/52
Step-by-step explanation:
i think that because in one deck of cards there are 52 cards in total and you divide 52 ÷ 4 it will give you 13 and you divide by four because there are 4 suits in total.
Solve The Expression :
-6x + 5 – 4x < 45
Answer:
x > -4
Step-by-step explanation:
Step 1: To combine like terms means to add the same variable numbers together.
-6x + 5 - 4x < 45
-10x + 5 < 45
Step 2: Subtract 5 from both sides
-10x + 5 - 5 < 45 - 5
-10x < 40
Step 3: Divide both sides by -10
-10x / -10 < 40 / -10
Since you divided by a negative, you need to reverse/flip the sign.
x > -4
Answer: x > -4
Steps to solve:
-6x + 5 – 4x < 45
~Combine Like Terms
(-6x - 4x) + 5 < 45
~Simplify
-10x + 5 < 45
~Subtract 5 to both sides
-10x + 5 - 5 < 45 - 5
~Simplify
-10x < 40
~Divide -10 to both sides and switch the symbol since we're dividing a negative number
-10x/-10 > 40 / -10
~Simplify
x > -4
Best of Luck!
Francisco uses 12 ounces of milk for every 18 ounces of fruit in his smoothie recipe, Nia uses 8 ounces of milk for every 12 ounces of fruit in her smoothie recipe. Who would use more milk if they each use 6 ounces of fruit?
Answer: there both equal
Step-by-step explanation: first we have to find the unit rate of both. Francisco unit rate for his recipe is 12/18=6/9=2/3 so the unit rate is 2/3
Nia uses 8/12=4/6=2/3 so the both will have the same if they use 6 ounces
Final answer:
Both Francisco and Nia use a proportional amount of milk in their smoothies; thus, they would both use 4 ounces of milk for 6 ounces of fruit.
Explanation:
To determine who would use more milk if they each use 6 ounces of fruit, we need to compare Francisco's and Nia's milk-to-fruit ratios. Francisco uses 12 ounces of milk for every 18 ounces of fruit, and Nia uses 8 ounces of milk for every 12 ounces of fruit. To find how much milk they would use for 6 ounces of fruit, we can set up a proportion for each and solve for the amount of milk.
For Francisco:
12 ounces of milk / 18 ounces of fruit = x ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
18x = 12 × 6.
Dividing both sides by 18 gives us:
x = (12 × 6) / 18 = 4 ounces of milk.
For Nia:
8 ounces of milk / 12 ounces of fruit = y ounces of milk / 6 ounces of fruit.
Using cross-multiplication, we get:
12y = 8 × 6.
Dividing both sides by 12 gives us:
y = (8 × 6) / 12 = 4 ounces of milk.
Therefore, both Francisco and Nia would use 4 ounces of milk for 6 ounces of fruit in their smoothie recipes.
Which algebraic expression represents the phrase "seven more than half of a number"?
Answer:
7 + q/2
Step-by-step explanation:
"seven more than half of a number"?
There are two sides to the phrase
1) let the number be "q"
2) Seven (7) more: Adding seven (7 +)
3) Half of a number: dividing the number by '2'
Equation = 7 + q/2
If (6,39) and (-5,-49) are two anchor pint find the equation of the line
Answer:
[tex]y =8x+9[/tex]
Step-by-step explanation:
The points are (6,39) and (-5,-49)
We need to find the equation of this line.
The slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m = \frac{ - 49 - 39}{ - 5 - 6} [/tex]
[tex]m = \frac{ - 88}{ - 11} [/tex]
[tex]m = 8[/tex]
We use the formula:
[tex]y-y_1=m(x-x_1)[/tex]
We substitute the point (6,39) and m=8 to get:
[tex]y - 39 = 8(x - 6)[/tex]
We expand to obtain:
[tex]y - 39=8x-48[/tex]
[tex]y =8x-48 + 39[/tex]
[tex]y =8x + 9[/tex]
To find the equation of the line passing through two points, we can use the point-slope form of a linear equation:
[tex]\[y - y_1 = m(x - x_1)\][/tex]
Where:
- [tex]\( (x_1, y_1) \)[/tex] is one point on the line.
- [tex]\( m \)[/tex] is the slope of the line.
First, let's find the slope (\(m\)) using the two given points:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\( (x_1, y_1) = (6, 39) \)\( (x_2, y_2) = (-5, -49) \)\[ m = \frac{-49 - 39}{-5 - 6} \]\[ m = \frac{-88}{-11} \]\[ m = 8 \][/tex]
Now, we have the slope (\(m\)). We can choose either of the two given points and plug them into the point-slope form. Let's use \( (6, 39) \):
[tex]\[ y - 39 = 8(x - 6) \][/tex]
Now, we can simplify this equation to get it into slope-intercept form (\(y = mx + b\)):
[tex]\[ y - 39 = 8x - 48 \]\[ y = 8x - 48 + 39 \]\[ y = 8x - 9 \][/tex]
So, the equation of the line passing through the points (6, 39) and (-5, -49) is [tex]\( y = 8x - 9 \).[/tex]
30% of number A is 10 more than 20% of number B. 30% of number B is 35 more than 20% of number A. Find the numbers A and B.
PLEASE PLEASE DUE TODAY!!!
Final answer:
To solve for A and B, we translated the word problem into two algebraic equations and then solved the system of equations step-by-step to find that A equals 200 and B equals 250.
Explanation:
We are given two equations based on the relationship between 30% of number A and 20% of number B, and vice versa. Let's translate the words into algebraic expressions where A and B represent the numbers we need to find:
0.30A = 0.20B + 10 (Equation 1)
0.30B = 0.20A + 35 (Equation 2)
Now let's solve this system of equations step-by-step:
Multiply both sides of Equation 1 by 10 to clear out decimals: 3A = 2B + 100.
Multiply both sides of Equation 2 by 10 as well: 3B = 2A + 350.
Rearrange Equation 1 to get A on its own: A = (2B + 100) / 3.
Substitute the expression for A from step 3 into Equation 2: 3B = 2((2B + 100) / 3) + 350.
Multiply through by 3 to clear the fraction: 9B = 4B + 200 + 1050.
Simplify to find B: 5B = 1250, so B = 250.
Substitute B back into the equation from step 3 to find A: A = (2(250) + 100) / 3, so A = 200.
Therefore, the numbers we are looking for are A = 200 and B = 250.
Draw a picture that shows 1/4*3 explain in words your picture with connections to the expression
Answer:
look at pic
Step-by-step explanation:
Solve the expression :
-6x + 5 – 4x < 45
Answer:
x>-4
Step-by-step explanation:
-6x + 5 – 4x < 45
Combine like terms
-10x + 5 < 45
Subtract 5 from each side
-10x + 5 – 5 < 45-5
-10x< 40
Divide each side by -10, remembering to flip the inequality
-10x/-10 >40/-10
x >-4
1. What are the solutions (coordinate points) to the system of equations?
y=x^2+5x+6 and y=3x+6
2. Prove algebraically what type of function this is (even, odd, or neither).
f(x)=x^6-x^4
3. Given the function f(x)=x^2+3x-2
What is the average rate of change for the function from 2 to 6? Show your work.
Question 1
The given system of equations is:
[tex]y = {x}^{2} + 5x + 6 \\ y = 3x + 6[/tex]
Equate the two equations:
[tex] {x}^{2} + 5x + 6 = 3x + 6[/tex]
Rewrite in standard form:
[tex] {x}^{2} + 5x - 3x + 6 - 6 = 0[/tex]
[tex] {x}^{2} + 2x = 0[/tex]
[tex]x(x + 2) = 0[/tex]
[tex]x = 0 \: or \: x = - 2[/tex]
When we put x=0, in y=3x +6, we get:
[tex]y = 3(0) + 6 = 6[/tex]
One solution is (0,6)
When we put x=-2, into y=3x+6, we get:
[tex]y = 3( - 2) + 6 = 0[/tex]
Another solution is (-2,0)
The solutions are; (0,6) and (-2,0)
Question 2:
The function is
[tex]f(x) = {x}^{6} - {x}^{4} [/tex]
Let us put x=-x,
[tex]f( - x) = {( - x)}^{6} - {( - x)}^{4} [/tex]
This gives:
[tex]f( - x) = {x}^{6} - {x}^{4} [/tex]
We can observe that:
[tex]f(x) = f( - x)[/tex]
This is the property of an even function.
Question 3:
The given function is
[tex]f(x) = {x}^{2} + 3x - 2[/tex]
The average rate of change of f(x) from x=a to x=b is given as:
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
This is the slope of the secant line connecting the two points on f(x)
From x=2 to x=6, the average rate of change
[tex] = \frac{f(6) - f(2)}{6 - 2} \\ = \frac{ {6}^{2} + 3 \times 6 - 2 - {2}^{2} - 3 \times 2 + 2 }{4} \\ = \frac{36 + 18 - 4 - 6}{4} \\ = \frac{44}{4} \\ = 11[/tex]
The average rate of change is 11
How many times larger is 6•10^8 than 1•10^5
Answer:
6 * [tex]10^{3}[/tex] larger
Step-by-step explanation:
divide [tex]\frac{6*10^{8}}{1*10^{5} }[/tex]
[tex]\frac{6*10^{8}}{1*10^{5} }[/tex] = 6 * [tex]10^{3}[/tex]
Answer:
6000
Step-by-step explanation:
aka 6*10^3
In the figure, assume that angles that appear to be right angles are right angles.
What is the area of the figure?
Use 3.14 for a
Area of the figure is 71.13
Step-by-step explanation:
Step 1: Area of the figure can be found out by considering the parts individually as a semicircle, rectangle and a right triangle. Then add all the areas.Find the area of the semicircle. Here, radius = 3.
Area = 1/2 πr² = 1/2 × 3.14 × 3² = 14.13
Step 2: Find the area of the rectangle. Here, width = 6 and length = 8Area = length × width = 8 × 6 = 48
Step 3: Find the area of the right triangle. Here the height = width of the rectangle = 6 and base = 11 - 8 = 3Area = 1/2 × base × height = 1/2 × 3 × 6 = 9
Step 4: Find the total area.Area of the figure = 14.13 + 48 + 9 = 71.13
Use the Distributive Property to find 3(13+5) written as an equivalent expression.
Answer:
54 or as an expression (3 * 13) + (3 * 5)
Step-by-step explanation:
Step 1: Distribute
To distribute means to break the parenthesis apart. To make two different combinations.
3(13 + 5)
(3 * 13) + (3 * 5)
Step 2: Multiply it out
(3 * 13) + (3 * 5)
39 + 15
54
Answer: 54 or as an expression (3 * 13) + (3 * 5)
Answer: 39 + 15
Step-by-step explanation: 3(13 + 5) can be simplified by distributing the 3 through both terms that are inside the parentheses.
So we have 3(13) + 3(5) which simplifies to 39 + 15 or 54.
So 3(13) + 3(5) is an equivalent.
A factory makes 48.8 liters of apple juice per minute. How many liters of apple juice will the factory make in 7.2 minutes?
The factory will make 350.56 liters of apple juice in 7.2 minutes.
Explanation:To find out how many liters of apple juice the factory will make in 7.2 minutes, we can set up a proportion. If the factory makes 48.8 liters of apple juice per minute, then the amount of apple juice made in 7.2 minutes would be:
48.8 liters of apple juice / 1 minute = x liters of apple juice / 7.2 minute
Cross multiplying, we get:
x = (48.8 liters of apple juice / 1 minute) * (7.2 minutes)
Simplifying the expression, we find that the factory will make 350.56 liters of apple juice in 7.2 minutes.
Learn more about Proportions here:https://brainly.com/question/32430980
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In which set does −173 belong?
Answer:
Step-by-step explanation:
rational number
What is 0.7(repeating) as a fraction in simplest form? show work
Answer:
0.7=7/10
this is the fraction in the simplest form
Step-by-step explanation:
Calculate the M.A.D 13, 17, 19, 27
Answer:
4
Step-by-step explanation:
Sample size: 4
Mean: 19
MAD: 4
How many digits are in a phone number including the area code
Answer:
11 digits
Step-by-step explanation:
x-xxx-xxx-xxxx
Counting these x's they would be 11. (if living in U.S.A)
The area code has 3 numbers. The first section has 3. Last section has 4. 6+4=10
There are 10 digits in a phone number.
A softball pitcher has a 0.42 probability of throwing a strike for each pitch. If the softball pitcher throws 20 pitches, what is the probability that exactly 7 of them are strikes?
Round your answer to three decimal places.
Answer: 0.15
Step-by-step explanation:
7 (0.42)/ 20
What is the volume of this?
Answer:
Step-by-step explanation: 288
HELP PLZ FILL IN THE BLANK AND EXPLAIN the missing dimension. Use the scale 1:5
Item Model Actual
Bicycle wheel Diameter: __in Diameter: 2 ft
Final answer:
The model diameter of the bicycle wheel is found using the scale factor of 1:5 and the actual diameter of 24 inches (2 feet). By setting up a proportion and solving for the model diameter, we find it to be 4.8 inches.
Explanation:
To find the missing diameter of the bicycle wheel model when given the actual diameter and a scale factor, we use a proportion:
The scale is given as 1:5, which means 1 unit on the model represents 5 units in reality. First, we need to convert the actual diameter of 2 feet into inches because the model's diameter will be given in inches. There are 12 inches in 1 foot, so 2 feet is 24 inches.
Write the proportion using the scale: 1/5 = model diameter/actual diameter.Substitute the known values into the proportion: 1/5 = model diameter/24 inches.Solve for the model diameter: model diameter = 1/5 * 24 inches.After calculating, the model diameter is 4.8 inches.
Rational Numbers
Every integer is a
number
A.
rational
B. whole
C. natural
D.
negative
Reset
Submit
Answer:
a. Every integer is a __________ number.
A.
rational < this onee
B.
whole
C.
natural
D.
negative
Step-by-step explanation:
6yd 7yd 3yd Find the volume of this rectangular pyramid.
Answer: The volume is 126 yards
Step-by-step explanation:
Answer:
the answer is 128
Step-by-step explanation:
first, i did 6x7 and got 42
then, i muutiplied 42 and 3 and got 128
thank me
Can u help me with my homework please it is a little bit harder then I thought
The distance around the pool is 43.96 m.
Solution:
The distance across the circle is diameter.
The distance around the circle is circumference.
The value of π = 3.14
Diameter of the circle = 14 m
Circumference of the circle = πd
= 3.14 × 14 m
Circumference of the circle = 43.96 m
The distance around the pool is 43.96 m.
How do you write 11/3 as a whole number?
Answer: 11/3 is a fraction that cannot be written as a whole number
Step-by-step explanation:
11/3 is a fraction that can only be reduced to 3 2/3
The two sets of shipping containers shown have the same total volume.
Complete the equation and expression below about the volume of the containers.
WHATS THE Volume for the red container in set 2
Plz answer ASAP!!!
Answer:
Set 1: 43 ft3 + 21 ft3 = 64ft3
Red prism in set 2: 16ft3
Step-by-step explanation:
When you add the first one together you get 64. So what plus 48 = 64? Your answer is 16.
Solve for X
3. 4x - 4<8 AND 9x + 5 > 23
Answer:
[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]
Step-by-step explanation:
The given inequality is
[tex]4x - 4 \: < \: 8 \: and \: 9x + 5 \: > \: 23[/tex]
Add 4 to both sides of the first inequality and subtract 5 from both sides of the second inequality.
[tex]4x \: < \: 8 + 4 \: and \: 9x\: > \: 23 - 5[/tex]
We simplify to get:
[tex]4x \: < \: 12 \: and \: 9x\: > \: 18[/tex]
Divide through the first inequality by 4 and the second by 9.
[tex]x \: < \: 3\: and \: x\: > \: 2[/tex]
The fraction bar represents which equation?
Answer: The last option
Step-by-step explanation:
3/4÷1/8=6
This is the answer because this is the only equation that gives a true answer all the others give an incorrect answer.
Simplify and leave in radical form.
8√x^2 y^6
Step-by-step explanation:
[tex] \sqrt[8]{ {x}^{2} {y}^{6} } \\ \\ = ( {x}^{2} {y}^{6} )^{ \frac{1}{8} } \\ \\ = {x}^{2 \times \frac{1}{8}} {y}^{6\times \frac{1}{8}} \\ \\ = x^{\frac{1}{4}} {y}^{3\times \frac{1}{4}} \\ \\ = x^{\frac{1}{4}} {y}^{\frac{3}{4}} \\ \\ = \sqrt[4]{x {y}^{3} } \\ [/tex]
Final answer:
[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex] This is the expression in its simplest radical form.
Explanation:
To simplify the given expression [tex]\sqrt[8]{x^2 y^6}[/tex], we must consider the rules for radicals and exponents.
Recall that [tex]\(\sqrt[n]{a^m} = a^{\frac{m}{n}}\)[/tex], assuming [tex]\(a\geq0\)[/tex] when n is even. Breaking down the radicals, we can rewrite the expression as:
[tex]\(\sqrt[8]{x^2} = x^{\frac{2}{8}} = x^{\frac{1}{4}}\)[/tex][tex]\(\sqrt[8]{y^6} = y^{\frac{6}{8}} = y^{\frac{3}{4}}\)[/tex]Since both terms are under the same radical, we can multiply them together:
[tex]\(\sqrt[8]{x^2 y^6} = x^{\frac{1}{4}} y^{\frac{3}{4}}\)[/tex]
This is the expression in its simplest radical form.