Answer:
(24) 3 - 4b = 10c + 10
(25) 4(3c+5) = 8
(26) - 6
(27) 4
Step-by-step explanation:
These questions require that words are translated into equations and then may be solved.
(24) Three minus four times a number is equal to ten times a number plus ten.
let the first number be b.
(a)Three minus four times a number ... can be represented as:
3 - (4 x b) = 3 - 4b
(b) ...ten times a number plus 10
let the other number be c. Therefore we have;
(10 x c) + 10 = 10c + 10
Now, three minus four times a number is equal to ten times a number plus ten means that expressions in (a) and (b) above are equal. i.e
3 - 4b = 10c + 10
(25) Four times the quantity of three times c plus 5 is equal to 8.
(a) four times the quantity of three times c plus 5 can be represented as
4 x (3 x c + 5) = 4(3c + 5)
(b) ... is equal to 8. This means that the expression in (a) is equal to 8.
4(3c + 5) = 8
(26) Six less than two thirds of a number is negative ten. Find the number.
(a) six less than can be represented as:
- 6
(b) two thirds of a number can be represented as
([tex]\frac{2}{3}[/tex])x [where x is the number]
(c) six less than two thirds of a number can thus be written as;
([tex]\frac{2}{3}[/tex])x - 6
(d) ... is negative 10 means that the expression is (c) above is equal to -10. i.e
([tex]\frac{2}{3}[/tex])x - 6 = -10
(e) Find the number.
The number can be found by solving for x in the expression in (d) above.
([tex]\frac{2}{3}[/tex])x - 6 = -10 [multiply through by 3]
2x - 18 = -30 [collect like terms]
2x = -30 + 18
2x = -12 [divide both sides by 2]
x = - 6
Therefore, the number is -6
(27) Twenty-nine is thirteen added to four times a number. What is the number.
(a) ... thirteen added to four times a number can be written as:
13 + 4b [where the number is b]
(b) Twenty-nine is thirteen added to four times a number means that the 29 is equal to the expression in (a) above. i.e
29 = 13 + 4b
(c) Find the number.
The number can be found by solving for b in the expression in (b) above. i.e
29 = 13 + 4b [collect like terms]
4b = 29 - 13
4b = 16 [divide both sides by 4]
b = 4
Therefore, the number is 4.
Find the distance across the lake. Assume the triangles are similar.
85 m
X
у
20 m
60 m
Answer:
B. 255 m
Step-by-step explanation:
use similar triangle
L / 60 = 85 / 20
L = (85 * 60) / 20
L = 255 m
The distance across the lake will be 255 meters. Then the correct option is B.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If the two triangles are similar, the ratio of the corresponding sides will be constant.
In an isosceles triangle, two angles and their opposite sides are equal.
The dimensions of the first triangle are L, 85, and y. And the dimensions of the second triangle are 60, 20, and x.
It is given that the triangles are similar.
Then the ratio of their corresponding sides will be
L / 60 = 85 / 20 = x / y
From first two terms, then the equation will be
L / 60 = 85 / 20
L / 60 = 4.25
L = 4.25 x 60
L = 255 m
The distance across the lake will be 255 meters.
Then the correct option is B.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ5
a rectangle is 12 in wide and 18 in tall.if it is reduce to a height of 3 inches, then how wide will it be?
Answer:
2 in
Step-by-step explanation:
18/3=6 , 6 is the scale factor
12/6=2
Answer:
width= 2
Step-by-step explanation:
18 inches is the original height and we are now reducing that to 3 inches.
In order to do that, we have to divide 18 by 3 which equals 6.
Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which equals 2.
Your final answers should be: width= 2
how many are 5 raised to 3 ???
Answer:
[tex]\boxed{125}[/tex]
Step-by-step explanation:
Hey there!
Well 5 raised to the 3 can be written as,
[tex]5^3[/tex]
This is 5*5*5
= 125
Hope this helps :)
Jami bought 4 cookies that cost $1.45, each. She paid with 6 one-dollar bills. how much change does Jami recive?
Answer:
$0.20
Step-by-step explanation:
4 x 1.45 = $5.80
6.00 - 5.80 = 0.20
Answer: $0.20
Step-by-step explanation:
Do 4 *$1.45 = $5.80
This is how much her total was.
She gave $6 in cash.
Subtract.
6-5.80=$.20
Soda Tak claims that Diet Tak has 40mg of sodium per can. You work for a consumer organization that tests such claims. You take a random sample of 60 cans and find that the mean amount of sodium in the sample is 41.9mg. The population standard deviation in all cans is 5.2mg. You suspect that there is more than 40mg of sodium per can. Find the z-score.
Answer:
Z - score = 2.83
Step-by-step explanation:
Given the following :
Number of samples (N) = 60
Sample mean (x) = 41.9mg
Population mean (μ) = 40mg
Population standard deviation (sd) = 5.2
Using the relation :
Z = (x - μ) / (sd / √N)
Z = (41.9 - 40) / (5.2 / √60)
Z = 1.9 / (5.2 / 7.7459666)
Z = 1.9 / 0.6713171
Z = 2.8302570
Therefore, the z-score = 2.83
Compare the functions shown below: f(x) cosine graph with points at 0, negative 1 and pi over 2, 1 and pi, 3 and 3 pi over 2, 1 and 2 pi, negative 1 g(x) x y −6 −11 −5 −6 −4 −3 −3 −2 −2 −3 −1 −6 0 −11 h(x) = 2 cos x + 1 Which function has the greatest maximum y-value?
Answer:
f(x) and h(x) have the same maximum value: 3
Step-by-step explanation:
The maximum value of f(x) is 3 at (π, 3).
The maximum value of g(x) is -2 at (-3, -2).
The maximum value of h(x) is 3 at (0, 3).
Both f(x) and h(x) have the same (greatest) maximum value.
Can someone please explain this to me? I don’t understand it at all
Answer:
Step-by-step explanation:
Angle 1 and angle 4 are Alternative angles:
Alternative angles are pair of angles on the inner side of each of those two lines but on opposite sides.
∠1+∠2 =180 sum of straight angle =180 ( angle 2=118)∠2-∠2=180 ,∠2=180-62=118
∠4+∠2=180 sum of straight angles=180 (∠4=62 degrees)∠4+118=180 ⇒∠4=180-118 ⇒∠4=62 degrees
∠1=∠4 alternative angles
You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item
Answer:
1.5p + 3p + 2.5p
Step-by-step explanation:
This expression, 1.5p + 3p + 2.5p, will represent the amount of money received when p people buy one of each food item.
Since the price of each is the coefficient for p, this will represent how much money will be gained from each food item. All 3 terms will be added together to represent the total amount of money gained from selling all 3 items.
2. The fraction 84 by 98 in simplest form is
Answer: 6/7
Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7
Answer:6/7
Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.
A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand. Law of cosines: A triangle is created between a lifeguard stand and 2 floating docks. The distance from the lifeguard stand to one dock is 750 meters, and the distance to the second dock is 650 meters. The angle between the 2 sides is 60 degrees. Rounded to the nearest meter, what is the distance between the docks? Round to the nearest meter. 589 meters 705 meters 792 meters 861 meters
Answer:
705 meters
Step-by-step explanation:
[tex]cos~60=\frac{650^2+750^2-d^2}{2 \times 650 \times 750} \\2 \times 650 \times 750 \times \frac{1}{2}=50^2(13^2+15^2)-d^2 \\487500=2500(169+225)-d^2\\487500=2500(394)-d^2\\487500=985000-d^2\\487500-985000=-d^2\\d^2=497500\\d=\sqrt{497500}\\or~d\approx705.337 \approx 705~meters[/tex]
Answer:
7 0 5 M E T E R S !!!!!
Step-by-step explanation:
Graph the following inequality and then select the correct graph below. x - y - 2 ≥ 0
Answer:
x - y - 2 ≥ 0
Step-by-step explanation:
Find the next three terms in the geometric sequence.
Answer: D
Step-by-step explanation:
The common difference is -2/3 so using the last term which is -8/27 multiply it by -2/3 to find the next terms.
[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]
[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]
[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]
Find the measure of each angle indicated. Round to the nearest tenth.
A) 65.20
C) 55.1°
B) 51°
D) 55.70
Answer:
51
Step-by-step explanation:
=====================================================
The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.
--------
tan(angle) = opposite/adjacent
tan(theta) = AC/BC
tan(theta) = 12.3/8.4
theta = arctan(12.3/8.4)
theta = 55.6697828044967
theta = 55.7 degrees approximately
--------
arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]
make sure your calculator is in degree mode
Multiply.
(7c+6)(-5c-4)
Simplify your answer.
Х
Answer:
120c
Step-by-step explanation:
7c(-5c)*(-4+6)
7c+5c*4+6
12c*10
120c
Answer:
the answer can be step by step explanation will be found in the answer was Matilda by 776 7 x 6 then the answer you will you - with the answer dancer used you New divide the answer that answer the simple your answer if we multiply you can contact me and say me in which is correct or wrong and I am a teacher
PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A AND B
Answer:
a) [tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b) (i) [tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) [tex]k=2[/tex]
Step-by-step explanation:
It is given that,
[tex]a=\begin{pmatrix}4\\-10\end{pmatrix},b=\begin{pmatrix}-2\\1\end{pmatrix},c=\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
a)
We need to find the value of a+b+c.
[tex]a+b+c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-2\\1\end{pmatrix}+\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}4+(-2)+(-4)\\-10+1+6\end{pmatrix}[/tex]
[tex]a+b+c=\begin{pmatrix}-2\\-3\end{pmatrix}[/tex]
b)
(i) We need to find the value of a+2c.
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+2\begin{pmatrix}-4\\6\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4\\-10\end{pmatrix}+\begin{pmatrix}-8\\12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}4+(-8)\\-10+12\end{pmatrix}[/tex]
[tex]a+2c=\begin{pmatrix}-4\\2\end{pmatrix}[/tex]
(ii) It is given that a+2c=kb, where k is an integer. We need to find the value of k.
[tex]a+2c=k\begin{pmatrix}-2\\1\end{pmatrix}[/tex]
[tex]\begin{pmatrix}-4\\2\end{pmatrix}=\begin{pmatrix}-2k\\k\end{pmatrix}[/tex]
On comparing both sides, we get
[tex]k=2[/tex]
Jonathan's parents told him that for every 2 hours of homework or reading he completes, he would be able to play 30 minutes of video games. His friend Lucas's
parents told their son that he could play 1.5 hours for 5 hours of homework or reading time he completes. What is the unit rate for each boy? You must label both unit rates.
Answer:
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games)
Step-by-step explanation:
The unit rate is the rate per unit of a quantity, that is the rate at which the denominator has been made a unit or one
The given parameters are;
The number of hours of homework or reading Jonathan needs to do for his parents to allow him to play video games for 30 minutes = 2 hours
The number of hours of homework or reading Lucas needs to do for his parents to allow him to play video games for 30 minutes = 1.5 hours
We note that 30 minutes = 0.5 hours
For Jonathan we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (2 hours)/(0.5 hours) = 4 hours of reading or homework per hour of paying video games
Jonathan's Unit rate = 4 hr (reading/homework)/(1 hour for video games)
For Lucas we have
Unit rate = (Number of hours of reading or homework)/(Number of hours playing video games)
Unit rate = (1.5 hours)/(0.5 hours) = 3 hours of reading or homework per hour of paying video games
Lucas' Unit rate = 3 hr (reading/homework)/(1 hour for video games).
Explain what each of them is.
Answer:
What are natural numbers?the positive integers or whole numbers include 1, 2, 3, and etc. sometimes zero.
What are whole numbers?Whole numbers are 0, 1, 2, 3, 4, 5, 6. Whole numbers include positive integers along with 0.
17, 99, 267, 8107 and 999999999 are examples of whole numbers.
What are rational numbers?A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. For example, one third in decimal form is 0.33333333333333
What are irrational numbers?A real number that can NOT be made by dividing two integers (an integer has no fractional part). "Irrational" means "no ratio", so it isn't a rational number.
Example: π is an irrational number.
What are real numbers?The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2.
Included within the irrationals are the transcendental numbers, such as π
plz help me. how many solutions
Answer:
no solutions
Step-by-step explanation:
2y = 4x+6
y = 2x+6
Divide the first equation by 2
y = 2x+3
These are parallel lines ( same slope) but different y intercepts
They will never intersect, so they have no solutions
Answer:
B No solutions
Step-by-step explanation:
2y = 4x + 6 first equatión
y = 2x + 6 second equation
from the first equation
y = (4x+6)/2
y = 4x/2 + 6/2
y = 2x + 3 third equation
matching second equatión and third equation
2x + 6 = 2x + 3
2x - 2x = 3 - 6
0 ≠ -3
then:
Β No solutions
Please help.. very confused
Answer:
D { -1,0,3,5}
R { -3,-1,1,7}
Step-by-step explanation:
The domain is the input values
3,-1,5,0
We normally put them from smallest to largest
D { -1,0,3,5}
The range is the output values
1,-3,7, -1
We normally put them from smallest to largest
R { -3,-1,1,7}
1. Which of the following is a true statement?
?
a. To square a number, multiply the number
by 2.
b. The inverse of squaring a number is to
divide the number by 2.
c. To square a number, multiply the number
by itself.
d. A perfect square is a number who's
square root is an even number.
Answer:
C
Step-by-step explanation:
Definitely not a! To square a number you multiply it by itself. for example, if you were squaring 3, you would do 3x3.
Not b either! You will have to take the SQUARE ROOT of the number!
C is the right answer, as I said for a.
D is wrong! The perfect square 49 has a sqrt (square root) of 7. That is NOT even, so d cannot be true.
C is the only true statement. Also, if this is right, can I get branliest answer? Thx :)
I need helpp!! match the building block of geometry to the statement that defines it.
1)DIAGRAM
A)a formal statement declaring the meaning of
a word
2)DEFINITION
B)a visual tool representing mathematical
ideas to be interpreted
3)THEOREM
C)a mathematical statement proven using
postulates and definitions
4)POSTULATE
D)a mathematical statement taken as a fact
Answer:
1) [tex]DIAGRAM \mapsto B[/tex]
2) DEFINITION [tex]\mapsto A[/tex]
3) THEOREM [tex]\mapsto C[/tex]
4) POSTULATE [tex]\mapsto D[/tex]
Step-by-step explanation:
1) DIAGRAM B) A visual tool representing mathematical ideas to be interpreted
A diagram is the depiction or representation of information using symbols
2) DEFINITION A) A formal statement declaring the meaning of a word
A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign
3) THEOREM C) A mathematical statement proven using postulates and definitions
A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates
4) POSTULATE D) A mathematical statement taken as a fact
An assumed truth taken as the foundation for further reasoning
PLEASE - Select the correct answer.
Answer:
D
Step-by-step explanation:
-10(x+5) with steps canvas
Answer:
[tex]\Large \boxed{-10x-50}[/tex]
Step-by-step explanation:
[tex]-10(x+5)[/tex]
Distribute -10 to the terms in the brackets.
[tex]-10(x)-10(5)[/tex]
[tex]-10x-50[/tex]
Answer: -10x - 50
Step-by-step explanation:
Distribute -10 to both terms.
-10 * x = -10x
-10 * 5 = -50
The equation now looks like this:
-10x - 50
You have nothing to simplify, so you're finished.
Hope this helps!
Maddy is carrying a 555 liter jug of sports drink that weighs 7.5\text{ kg}7.5 kg7, point, 5, start text, space, k, g, end text. She wants to know how many kilograms a 222 liter jug of sports drink would weigh (w)left parenthesis, w, right parenthesis. She assumes the relationship between volume and weight is proportional. What is the weight of the 2 liter jug?
Answer:
w/2 = 7.5/5
3kg
Step-by-step explanation:
Remaining question below:
Which proportion could Maddy use to model this situation?
a. w/2 = 7.5/5
b. w/7.5 = 5/2
Solve the proportion to determine the weight of a 2 liter jug.
_____kg
5 liters jug of sport drink weighs 7.5kg
2 liters jug of sport drink will weigh x kg
Find w
Ratio of weight to volume
7.5kg : 5liters=7.5/5
wkg : 2 liters=w/2
Equates the ratio
7.5 / 5 = w / 2
Cross product
7.5*2=5*w
15=5w
Divide both sides by 5
3=w
w=3kg
Therefore, weight of the 2liters jug of sport drink is 3kg
Answer:
The answer is 3kg!
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
Help Someone please!! Given the following perfect square trinomial, find the missing term: 4x2 + ___x + 49 7 14 28 36
Answer:
28
Step-by-step explanation:
[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]
Answer:
[tex]\huge \boxed{28}[/tex]
Step-by-step explanation:
The trinomial is a perfect square.
Take the square root of the first term and the last term.
[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]
[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]
[tex](2x+7)^2[/tex]
Expand to find the second term of the trinomial.
[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]
The second term of the trinomial is 28x.
A kitchen helper stacked some identical bowls into 2stacks.The height of the first stack of 6 bowls. is 16.82cm.The height of the second stack of 8 bowls in 21.2cm. A)Find the height of one bowl.
Answer:
about 2.72 cm.
Step-by-step explanation:
Since, all the bowls are identical, I just added the heights of bothe stacks together and I divided that sum by the number of bowls in each stack all added together.
16.82+21.2=38.02 cm in total height of both stacks.
8+6=14 bowls in all from both stacks
38.02 cm/14 bowls=2.71571428, or rounded, about 2.72 cm
meagan worked 24 hours and earned $84 what is her rate pay
Answer: 3.50 Per hour
Step-by-step explanation:
Divide 84 by 24
8 is subtracted from the square of a number
Answer:
n^2-8 is the answer
Step-by-step explanation:
Match the vocab word
Answer:
1). Algebraic expression - a letter or symbol used to represent an unknown.
2). Coefficient - a numerical value.
3). Constant - the constant preceding the variables in a product.
4). Expression - a mathematical expression containing one or more variables.
5). Variable - a mathematical phrase that cannot be determined true or false.
2. A curve has equation y = x2 – 2x - 3. A point moves along the curve in such a way that at P
the y coordinate is increasing at 4 units per second and the x coordinate is increasing at 6
units per second. Find the x coordinate of P.
[3]
Answer:
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:
[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]
According to the statement of the problem, these variables are known:
[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]
Hence, the x coordinate of P is found by direct substitution:
[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]
[tex]4 = 12\cdot x -12[/tex]
[tex]x = \frac{4}{3}[/tex]
The x coordinate of P is [tex]\frac{4}{3}[/tex].
