Answer:
The number is 50.
Step-by-step explanation:
0.6x=30
x=30/0.6
x=50
A triangle has a base that measures 6.4 feet. It’s height measures 5 feet. How many square feet is the area of the triangle?
The area of the triangle is 16 square feet.
Explanation:The formula for finding the area of a triangle is given by:
Area = 1/2 * base * height
Given that the base of the triangle measures 6.4 feet and the height measures 5 feet, we can substitute these values into the formula:
Area = 1/2 * 6.4 * 5 = 16 square feet
Therefore, the area of the triangle is 16 square feet.
What are the angle measurements of 6x + 1° = 3x + 11°
Answer:
[tex]x=3\frac{1}{3}^\°[/tex]
Step-by-step explanation:
Given equation:
[tex]6x+1\°=3x+11\°[/tex]
To find the angle measure of [tex]x[/tex]
Solution:
In order to find the angle measure [tex]x[/tex] , we will isolate [tex]x[/tex] on left side by carrying out math operations on both sides.
We have:
[tex]6x+1\°=3x+11\°[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]6x-3x+1\°=3x-3x+11\°[/tex]
[tex]3x+1\°=11\°[/tex]
Subtracting both sides by 1°.
[tex]3x+1\°-1\°=11\°-1\°[/tex]
[tex]3x=10\°[/tex]
Dividing both sides by 3.
[tex]\frac{3x}{3}=\frac{10\°}{3}[/tex]
[tex]x=\frac{10}3}^\°[/tex]
Converting fraction to mixed number by dividing and writing the quotient as whole number and the remainder as numerator.
∴ [tex]x=3\frac{1}{3}^\°[/tex] (Answer)
5. Running shoes are regularly priced at $80. They were on sale for $46. What was the discount
expressed as a percent of the regular price?
Answer:
Discounted percent = 42.5% and price of the discounted product compared to original is 57.5%
Step-by-step explanation:
$46 = Discount of some decimal of $80
46 = x(80)
46/80 = 0.575
Change it to percent
57.5% discount
The discount expressed as a percent of the regular price is approximately 42.5%.
Here, we have,
To calculate the discount as a percent of the regular price, we can use the following formula:
Discount Percentage = (Discount Amount / Regular Price) × 100%
Given that
the regular price is $80 and the sale price is $46, we can calculate the discount amount by subtracting the sale price from the regular price:
Discount Amount = Regular Price - Sale Price
Discount Amount = $80 - $46
Discount Amount = $34
Now we can calculate the discount percentage:
Discount Percentage = (Discount Amount / Regular Price) × 100%
Discount Percentage = ($34 / $80) × 100%
Discount Percentage ≈ 42.5%
Therefore, the discount expressed as a percent of the regular price is approximately 42.5%.
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consider the functions given below
f(x) + -3x-5
g(x) + f(x)+9
what is the y intercept of g
The y-intercept of the function g(x), defined as g(x) = f(x) + 9 where f(x) = -3x - 5, is 4. This is determined by evaluating g(0), resulting in a y-intercept at the point (0, 4).
Explanation:The question asks about finding the y-intercept of the function g(x), which is defined in terms of another function f(x). Given that f(x) is equal to -3x - 5 and g(x) equals f(x) + 9, to find the y-intercept of g(x), we substitute x with 0 in the function f(x) and then add 9. The y-intercept is the point where the function crosses the y-axis, which is when x = 0.
First, we find the value of f(0):
f(0) = -3(0) - 5 = -5Next, we determine g(0) by adding 9 to the value of f(0):
g(0) = f(0) + 9 = -5 + 9 = 4Therefore, the y-intercept of g(x) is 4, which means the line representing g(x) crosses the y-axis at the point (0, 4).
What value of b will cause the system to have an infinite number of solutions? Y=6x+b -3x+1/2y=-3
Answer:
b = -6
Step-by-step explanation:
Given:
y=6x+b ----- (eq 1)
and
-3x+1/2y=-3 (Rearrange this equation to look likes eq (1) , add -3x to both sides)
(1/2) y = 3x - 3 (multiply both sides by 2)
y = 2(3x -3) (distribute the 2 into parentheses)
y = 6x - 6 -----(eq 2)
Recall that a system of equations will have an infinite number of solutions if both equations are the same line. (i.e they have the same slope and y intercept)
In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)
In Mr. Martinez’s class there are 8 boys and 12 girls. What is the probability of randomly selecting a girl?
Answer:
3/5
Step-by-step explanation:
there are 20 people altogether in the class (12 plus 8)
since 12 of them are girls the probability it 12/20
but to simplify it we divide both sides of the fraction by 4 (as that's the largest whole number they will both divide by) and we get 3/5
Betty is canning 104 pears and 126 apples separately.each jar holds 8 pears or 6 apples. How many jars does Betty need?
Final answer:
Betty needs 13 jars to can 104 pears and 21 jars to can 126 apples, making a total of 34 jars.
Explanation:
To determine how many jars Betty needs to can 104 pears and 126 apples, we must consider the capacity of the jars. Each jar holds 8 pears or 6 apples. Therefore, we need to calculate how many jars are required for each fruit separately.
For pears:
Total pears: 104Pears per jar: 8Jars needed for pears: 104 / 8 = 13For apples:
Total apples: 126Apples per jar: 6Jars needed for apples: 126 / 6 = 21The total jars needed equals the sum of the jars needed for pears and the jars needed for apples, which is 13 jars for pears plus 21 jars for apples, totaling to 34 jars.
the sum of two numbers is 108. the difference of the same numbers is 78. what are the numbers
The sum of two numbers:
x + y = 108
The difference of the same two numbers:
x - y = 78
We can use substitution to figure out x and y:
x - y = 78 can be changed to x = 78 + y
We can plug this into the first equation:
78 + y + y = 108
78 + 2y = 108
2y = 30
y = 15
Now solve for x using any of the two equations. I'll use the first equation since it's easier:
x + 15 = 108
x = 93
I need help to solve this equation.
Answer:
WHERE IS IT
Step-by-step explanation:
anna buys groceries for her family hamburger meat is $3.38 per pound , sweet potatoes are $0.79 each,and hamburger rolls are $2.30 a bag . if anna buys 3 pounds of meat , 5 sweet potatoes , and one of hamburger rolls, what will she pay in all for the groceries.?
Answer:
Step-by-step explanation:
3.38times3=10.14
5times.79=3.95
1times2.30=2.30
10.14+3.95+2.30=18.04
Answer:
3.38times3=10.14
5times.79=3.95
1times2.30=2.30
10.14+3.95+2.30=18.04
Step-by-step explanation:
Find the simple interest earned in an account with $300 at 5% annual interest for 7 years.
A. $105.00
B. $420.00
C. $214.29
D. $11.67
Option A
The simple interest earned is $ 105
Solution:
Given that, $300 at 5% annual interest for 7 years
Therefore,
Principal = $ 300
Rate of interest = 5 %
Number of years = 7
The simple interest is given by formula:
[tex]Simple\ Interest = \frac{p \times n \times r }{100}[/tex]
Where,
p is the principal
r is the rate of interest
n is the number of years
Substituting the values in formula,
[tex]Simple\ Interest = \frac{300 \times 7 \times 5 }{100}\\\\Simple\ Interest = 3 \times 7 \times 5\\\\Simple\ Interest = 105[/tex]
Thus simple interest earned is $ 105
How many solutions does this system have? x- y = - 4. 3 x + y = 8.
Answer:
one solution (1,5)
Step-by-step explanation:
if you graph the equations on a graph the line would intersect.
intersect = one solution
overlap = infinite solutions
parallel = no solution
Joanna buys a table and 2 chairs. She receives a 25% discount for being a preferred customer and then pays 6% sales tax on the discounted purchase price. If the table costs $250 and each chair costs $100, what is the total purchase price?
The total purchase price is $ 357.75
Solution:
Joanna buys a table and 2 chairs
Cost of table = $ 250
Cost of 1 chair = $ 100
Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450
Thus, cost price = $ 450
She receives a 25% discount for being a preferred customer
Therefore, discount = 25 % of cost price
[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]
Thus, amount after discount = cost price - discount
amount after discount = 450 - 112.5 = 337.5
Thus, amount after discount is $ 337.5
Then pays 6% sales tax on the discounted purchase price
Sales tax = 6 % of 337.5
[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]
Thus, total purchase price is given as:
total purchase price = Amount after discount + sales tax
total purchase price = 337.5 + 20.25 = 357.75
Thus total purchase price is $ 357.75
Which is the graph of the piecewise function f(x)?
f(x) = StartLayout Enlarged left-brace 1st row 1st column negative x + 1, 2nd column x less-than-or-equal-to 0 2nd row 1st column x + 1, 2nd column x greater-than 0 EndLayout
Answer:
None of the above graph gives the function.
Step-by-step explanation:
The function is given by
f(x) = - x + 1 for, x ≤ 0 .......... (1) and
f(x) = x + 1 for, x > 0 ............. (2)
Now, from this definition we can write for x = 0, the value of f(x) will be governed by the equation (1) and f(0) = - 0 + 1 = 1
So, (0,1) is a point on the graph and for x < 0 the f(x) will have negative slope and for x > 0, the f(x) will have positive slope.
So, none of the above graphs gives the function. (Answer)
Answer:
the 4 graph
Step-by-step explanation:
The running back for the Bulldogs football team carried the ball 5 times for a total loss of 11 1/4 yards. Find the average change in field position on each run. Enter the average change as a simplified mixed number.
Answer:
[tex]\displaystyle 2\ \frac{1}{4}[/tex]
Step-by-step explanation:
Fractions
They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.
Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.
The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.
The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like
[tex]\displaystyle 11+\frac{1}{4}=\frac{45}{4}[/tex]
This improper fraction will now be divided by 5 to find the average of 5 runs:
[tex]\displaystyle \frac{\frac{45}{4}}{5}=\frac{9}{4}[/tex]
We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus
[tex]\boxed{\displaystyle \frac{9}{4}=2\ \frac{1}{4}}[/tex]
If m^2 + 8 = 39, then m^2-7=?
Answer:
24
Step-by-step explanation:
Subtract 15 from both sides of the equation:
m^2 +8 -15 = 39 -15
m^2 -7 = 24
f(x) = x^2. What is g(x)?
Answer:
g(x) = -x^2 - 4
Step-by-step explanation:
f(x) = x^2
To flip the graph, you need the negative of the right side,
y = -x^2
This is a parabola that opens downward, but the vertex is at (0, 0).
Now you need to translate the graph 4 units down, so subtract 4 from -x^2.
g(x) = -x^2 - 4
What is 36/5 simplified by a whole number
Answer:
36/5 = 7 1/5
Step-by-step explanation: hope this help!
jake ordered 275 large pizzas for a party. when the party was over he had 250 large pizzas remaining. estimate the percent decrease in the number of large pizzas.
Answer:
9% decrease
Step-by-step explanation:
what is 10 digits of pi
Answer:
3.1415926535
I can't explain why but I tried my best, I hope it helped.
kevin has 56 stamps he gives away three sevenths to his friends how much did he give to his friends
Answer:
24
Step-by-step explanation:
[tex]\dfrac{3}{7}\times 56=3\times\dfrac{56}{7}=3\times 8=24[/tex]
Even if you don't know your times tables or how to multiply fractions, you can use a calculator to compute the value.
Kevin gave 24 stamps to his friends.
5 2/3 - 1 1/6
———————-
8. 5/8 - 4. 1/4
Answer:
The solution is 36/35
Step-by-step explanation:
5 2/3 - 1 1/6
———————-
8 5/8 - 4 1/4
17/3 - 7/6
= ———————-
69/8 - 17/4
17/3×2 - 7/6
= ———————-
69/8 - 17/4 × 2
34/6 - 7/6
= ———————-
69/8 - 34/8
9/2
= ———————-
35/8
= 9/2 ÷ 35/8
= 9/2 × 8/35
= 9(8)/2(35)
= 9(4)/35
= 36/35
Give two ways to write the algebraic expression 13 ÷ y in words
Answer:
thirteen divided by y
Step-by-step explanation:
An egg is dropped from a height of 90 ft. If acceleration due to gravity is -16 ft/s2 and initial velocity is Ofts, approximately how
long will it take for the egg to reach the ground?
Final answer:
The egg will take approximately 3.35 seconds to reach the ground.
Explanation:
To solve this problem, we can use the equation [tex]y = yo + vot + 0.5at^2[/tex] position, yo is the initial position, vo is the initial velocity, a is the acceleration, and t is the time.
In this case, yo = 90 ft, vo = 0 ft/s, a = -16 [tex]ft/s^2[/tex]y = 0 ft (since the egg reaches the ground). Plugging these values into the equation, we get 0 = 90 + (0)(t) + 0.5(-16)t^2.
Simplifying the equation, we have [tex]0 = 90 - 8t^2[/tex], we get[tex]8t^2 = 90[/tex] both sides by 8, we get [tex]t^2 = 11.25[/tex]e square root of both sides, we find that t ≈ 3.35 seconds.
what is the product? [ 4 2 ] x [ -2 5 7 -1 ]
Answer:
[ 4 2 ] x [ -2 5 7 -1 ] = [- 10,836]
Step-by-step explanation:
Here, the given expression is:
[ 4 2 ] x [ -2 5 7 -1 ]
Now solving : [ -2 5 7 -1 ] , we get
[ -2 5 7 -1 ] = [-258]
Now simplifying
[-258] x [ 4 2 ] = - 10,836
⇒ [ 4 2 ] x [ -2 5 7 -1 ] = [- 10,836]
Hence the solution is: [- 10,836]
Answer:
D. [6 18]
Step-by-step explanation:
Edge2020
Have a great day y'all :)
Claire wants to solve the equation -1/4(x-1)=2/3x+2. Which step would not be an appropriate first step for Claire to take to solve for x?
A. Multiply both sides by -4.
B. Use the distributive property to distribute -1/4
C. Add 1 to both sides.
D. Multiply both sides by 3/2.
Answer:
A
Step-by-step explanation:
The answer is A because it says -4 and not -1/4.
Final answer:
Option C, adding 1 to both sides, is not an appropriate first step in solving the equation -1/4(x-1)=2/3x+2. Claire should instead focus on simplifying the equation, such as using distributive property or eliminating fractions.
Explanation:
To solve the equation -1/4(x-1)=2/3x+2, there are several steps that Claire can take. However, answer option C, which suggests adding 1 to both sides, is not an appropriate first step for solving for x. Instead, Claire might consider other steps like using the distributive property or getting rid of the fractions by multiplying both sides of the equation by a common denominator.
When solving linear equations, it is generally more logical to start by simplifying each side of the equation by using distribution or by eliminating fractions. This makes further manipulation of the equation simpler and more straightforward. The inappropriate step of adding 1 would create an extra unnecessary step, not simplifying the equation in a beneficial way.
Kwesi is putting on sunscreen. He uses 3\text{ ml}3 ml3, start text, space, m, l, end text to cover 45 \text{ cm}^245 cm
2
45, start text, space, c, m, end text, squared of his skin. He wants to know how many milliliters of sunscreen (g)(g)left parenthesis, g, right parenthesis he needs to cover 240\text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin. He assumes the relationship between milliliters of sunscreen and area is proportional.
How many milliliters of sunscreen does Kwesi need to cover 240 \text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin?
Answer:
16 mL
Step-by-step explanation:
The ratio of areas is (245 cm²)/(45 cm²) = 16/3, so Kwesi expects the ratio of volumes to be the same:
(needed volume)/(3 mL) = 16/3
needed volume = (16/3)×(3 mL) = 16 mL
Kwesi expects to need 16 mL of sunscreen to cover 240 cm² of skin.
Which expression is equivalent to (2x^2+4-7)(x-3)
Answer:
0
Step-by-step explanation:
Solve the inequalities by graphing. Select the correct graph. y > 2x y < 3
Answer:
The graph is shown below.
Step-by-step explanation:
Given:
The inequalities to solve by graphing are given as:
[tex]y>2x\\\\y<3[/tex]
Now, in order to graph them, we first replace inequality sign by equal to sign.
So, the two equations are given as:
[tex]y=2x\\\\y=3[/tex]
Now, the first equation is a straight line of the form [tex]y=mx[/tex]. This is a line that passes through origin with slope equal to 'm'.
So, the slope of the first line is 2.
In order to plot the line,we take a random value of 'x'. Let [tex]x=1[/tex]
So, [tex]y=2\times 1=2[/tex]
So, the point on the line is (1, 2)
Now, we draw a line passing through the points (0, 0) and (1, 2). This is the line for the first equation.
Now, the second equation is a straight line parallel to the x-axis.
So, the equation [tex]y=3[/tex] is a straight line parallel to x-axis passing through the point (0, 3) as shown below.
Now, since the first inequality has 'y' greater than '2x'. So, the solution region is left of the line excluding the line.
Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.
The common region for both the line inequalities is the solution.
The solution region is shown below.
Answer:
o, the solution region is left of the line excluding the line.
Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.
Step-by-step explanation: