The value of x is 11.
m∠ACD is 65 degrees and m∠BDC is 115 degrees.
To find the value of x, we need to establish a relationship between these two angles.
Given that m∠ACD = (7x - 12) and m∠BDC = (10x + 5), we can analyze the figure to determine how these angles are related. Since there is no additional information about the angles, let's assume that they are supplementary angles, meaning that their sum is equal to 180 degrees. This is a common situation when dealing with adjacent angles that form a straight line.
So, we can write an equation expressing that the sum of m∠ACD and m∠BDC equals 180°:
(7x - 12) + (10x + 5) = 180
Now, we'll solve this equation to find the value of x:
7x - 12 + 10x + 5 = 180
17x - 7 = 180
Next, isolate x by adding 7 to both sides of the equation:
17x = 187
Finally, divide by 17 to obtain the value of x:
x = 187 ÷ 17
x = 11
So, the value of x is 11. With this information, you can now find the measures of m∠ACD and m∠BDC by plugging the value of x back into their respective expressions:
m∠ACD = 7(11) - 12 = 77 - 12 = 65°
m∠BDC = 10(11) + 5 = 110 + 5 = 115°
Therefore, m∠ACD is 65 degrees and m∠BDC is 115 degrees.
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Which value is the solution for this equation
2/3(6h-9)=6
A) -1
B) 1
C) 3
D) 5
Answer:
h = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
2/3(6h - 9) = 6
Step 2: Solve for h
[Division Property of Equality] Divide 2/3 on both sides: 6h - 9 = 9[Addition Property of Equality] Add 9 on both sides: 6h = 18[Division Property of Equality] Divide 6 on both sides: h = 3 Determine which points are a solution to the system of inequalities.
the answer choices are:
a. (0,0)
b. (4,1)
c. (3,-2)
d. (2,0)
e (4,-4)
f (1,3)
Answer:
I think it's e 4 -4
Step-by-step explanation:
hope this helps
Suppose $ 1,250 is placed in a savings account over 2 years. Find the interest earned if the rate is 4.5%
Answer: $112.50
Step-by-step explanation:
The Simple interest will be calculated using:
= Principal × Rate × Time
= 1250 × 4.5% × 2
= 1250 × 0.045 × 2
= $112.50
Therefore, the interest earned will be $112.50
Answer:$112.50
Step-by-step explanation:
Alec is thirsty and wants to know how much milk can fit in his favorite mug. His mug is a cylinder and has a radius
(r) of 2 inches and a height (h) of 8 inches. The formula for the volume of a cylinder is given.
V = trh
How much milk can Alec's mug hold?
Answer:
i think it is v=8 love
Step-by-step explanation:
Answer:
It's 10
Step-by-step explanation:
the sum of the number and 5 is 12
Answer:7
Step-by-step explanation: x+5=12 solve for x = 7
Answer:
"a number" = 7
Step-by-step explanation:
let "a number" = x.
x + 5 = 12
Isolate the variable x. Note the equal sign, what you do to one side, you do to the other. Subtract 5 from both sides.
x + 5 (-5) = 12 (-5)
x = 12 - 5
x = 7
7 is your answer.
~
subtract (2y + 3x-x²) from (5x²-y2-2x)
Answer:
6x² - 5x - y² - 2y
Step-by-step explanation:
We have
5x² - y² - 2x - (2y + 3x - x² ) ← distribute parenthesis by - 1
= 5x² - y² - 2x - 2y - 3x + x² ← collect like terms
= 6x² - 5x - y² - 2y
A certain sum of money gives $ 510 as compound interest 12¹/₂ % per annum for 2 years. Find the simple interest on the same sum of money at the same rate for the same period of time.
Answer:
$127.5
Step-by-step explanation:
Given data
P = $510
r= 12.5%
t= 2 years
The expression for simple interest is
SI= PRT/100
SI= 510*12.5*2/100
SI= 12750/100
SI= 127.5
Hence the Simple interest is $127.5
what is the radius of a circle with the ratio 1:4 when the smaller one is 12cm
Answer:
48
Step-by-step explanation:
1 to 4 = 12 to ?
multiply the small one by 4 to get the bigger one
Step-by-step explanation:
1:4
12:x
1=4
12=x
cross multiply
x=4×12
x=48
please help! how do you do this question?
9514 1404 393
Answer:
(0.75, -1)
Step-by-step explanation:
The center of the circle is at the midpoint of any diameter segment. The midpoint formula can be used.
C = (A +B)/2
C = ((-1, 1) +(2.5, -3))/2 . . . . fill in A and B
C = (-1+2.5, 1-3)/2 . . . . . . . add the coordinates
C = (1.5, -2)/2 . . . . . . finish the addition; next, divide by 2
C = (0.75, -1) . . . . . . the center of the circle
solve the inequality -3x + 6 > -2
Answer:
x<8/3
Step-by-step explanation:
Your answer is x is less than 8 over 3
Answer:
Answer is d
Step-by-step explanation:
x<8/
Otis is packing two gift boxes in a shipping carton. The rest of the space in the carton will be filled with packing pellets. What is the volume of the space that needs to be filled with packing pellets?
Answer:
[tex]V_3 = 1916in^3[/tex]
Step-by-step explanation:
Given
See attachment for gift items and the shipping carton
Required
Determine the volume of the empty space
First, we calculate the volume of the carton.
[tex]V = LWH[/tex]
From the attachment
L = 16; W =11 and H =13
So:
[tex]V = 16*11*13[/tex]
[tex]V = 2288[/tex]
Next, calculate the volume of the blue wrap
[tex]V = lwh[/tex]
From the attachment
l = 9; w =9 and h =2
So:
[tex]V_1 = 9 * 9 * 2[/tex]
[tex]V_1 = 162[/tex]
Next, calculate the volume of the pink wrap
[tex]V = lwh[/tex]
From the attachment
l = 6; w =5 and h =7
So:
[tex]V_2 = 6*5*7[/tex]
[tex]V_2 = 210[/tex]
The volume of the rest space (V3) is then calculated as:
[tex]V_3 = V - V_1 -V_2[/tex]
[tex]V_3 = 2288 - 162 -210[/tex]
[tex]V_3 = 1916[/tex]
Hence, the rest volume is 1916in^3\
write a quadratic equation with the roots 1/2 and -5
x = 1/2 or x = -5
2x - 1 = 0 or x + 5 = 0
(2x-1)(x+5) = 0
2x² + 10x - x - 5 = 0
2x² + 9x - 5 = 0
Hope it helps!
Answer:
2[tex]x^{2}[/tex] + 9x - 5 = 0
Step-by-step explanation:
// Use the Vijet's theorem,
// note that the kofficient before [tex]x^{2}[/tex] = 1
Sum of the roots is:
1/2 + (-5) = - 4,5
Product of the roots is:
0,5 * (-5) = - 2,5
Formation of quadratic equation:
[tex]x^{2}[/tex] - (sum of the roots) x + product of the roots = 0
[tex]x^{2}[/tex] - (-4,5) * x + (-2,5) = 0
[tex]x^{2}[/tex] + 4,5x -2,5 = 0
// multiply both sides by 2
2[tex]x^{2}[/tex] + 9x - 5 = 0
Make me the brainliest ;)
A line is represented by the equation y = 3x – 7. Which statement about the line is TRUE?
A.
The y-intercept is 7.
B.
The line has a positive slope.
C.
The point (1, 4) lies on the line.
D.
This line is parallel to the line whose equation is y = 2x – 7.
Answer:
B
Step-by-step explanation:
because the slopes is 3.
A meal costs $30 before tax and tip.
There is a 7% sales tax. After the tax, a 20% tip is
added.
What is the total after tax and tip?
Answer:
$38.1
Step-by-step explanation:
Tax: 30*0.07 = 2.1
Tip: 30*0.2 = 6
Total: 30 + 2.1 + 6 = 38.1
A flower vase bought for Rs. 72 and sold for Rs. 63. Find the loss percent.
Answer:
12.5% is loss....
hope it helps.
Answer:
the lost percentage is 14.28%
Step-by-step explanation:
1 - (72÷63) = -0.1428 x 100% = -14.28 %
(Please heart the answer if you find it helpful, it's a motivation for me to help more people)
y = -[tex]\frac{4}{5}[/tex]x - 2
Which equation best describes the graph?
A. y = -[tex]\frac{4}{5}[/tex]x + 2
B. y = [tex]\frac{4}{5}[/tex]x + 2
C. y = [tex]\frac{5}{4}[/tex]x - 2
D. y = -[tex]\frac{5}{4}[/tex]x + 2
Can someone please help me with this I will give brainliest
Answer:
Step-by-step explanation:
2(2x +4) - 2x = x + 18
4x +8 -2x = x +18
2x -x = 18-8
X = 10
Put the value of x in both side
Left side *+*+*+*+*+
2 ( 2*10+4)-2*10
48-20 = 28
Right side +*+*+*+*+*
X + 18
10+ 18 = 28
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The terrace of a house is rectangular in shape with a length of 10m and a width of 5m. Find the volume of
rainfall collected on the terrace if its height is 1m, Express in liter.
Answer:
Step-by-step explanation:
Volume = Area of the base times the height
V = length * width * height
V = 10 * 5 * 1
V = 50 m^3
Now change it to liters
50 * 1000 = 50000 liters^3
4.
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus
with diagonals 16cm and 12cm is
Answer:
48 cm²
Step-by-step explanation:
The diagonals are in a proportion of 4:3, thus sides of a Pythagorean Triple; they cross at a right angle. The figure formed by joining the midpoints of adjacent sides is a rectangle with sides half the lengths of the original diagonals. 8×6=48
This is for today help!!!!
Answer:
Part A 73 Part B 113
Step-by-step explanation:
1/8 = 2/5 times X . What is X
Answer: 5/16
Step-by-step explanation:
Answer:
0.0125
Step-by-step explanation:
1/8=2/5x
Divide by 2/5 on each side of the equation. X=0.0125. 0.0125=1/80. The last option.
A 15 foot ladder leans against a house with the base of the ladder 4 feet from the house. How high, to the nearest foot, up the wall will the ladder reach?
Answer:
height of house to ladder reach is 14 ft
Explanation:
Given data
ladder = 15 ft
base = 4 ft
to find out
height of house
solution
we know this is triangle shape so we apply here
so we consider here x is ladder and y is base and z is height
so
by pythagoras theorem
z² + y² = x²
so here
z² = x² - y²
put value
z² = 15² - 4²
z² = 209
z = 14.45 = 14
so height of house to ladder reach is 14 ft
Step-by-step explanation:
The ladder and the ground form a right triangle. Use the Pythagorean Theorem to find the other leg of the triangle.
a^2 + b^2 = c^2
a^2 + 4^2 = 15^2
a^2 + 16 = 225
a^2 = 209
a = 14.5 feet
Eight minus a number divided by three is greater than or equal to eleven
Answer:
Step-by-step explanation:
8-x/3>=11 is the equation, and the answer is:
x<= -9, so any number less than -9 is correct.
The solution is x ≤ -9
What are Inequality Equations?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number be x
8 - x/3 ≥ 11
Subtracting 8 on both sides , we get
-x/3 ≥ 3
Multiplying by 3 on both sides , we get
-x ≥ 9
Interchanging the sign on both sides , we get
x ≤ -9
Hence , the solution is x ≤ -9
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A dairy facility has a bulk milk tank that is shaped like a right circular cylinder. The
tank has a height of 12 feet and a diameter of 216 inches.
Answer:336
Step-by-step explanation:
12
216 = 336
What is the name for a savings account in which money must stay deposited for a specific amount of time? A. Traditional savings account B. Certificate of deposit C. Money market account D. Retirement account
Answer:
B. Certificate of deposit
Step-by-step explanation:
in traditional savings account you can take the money out anytime (usually up to 5 times a month)
in retirement account (well this could include 401k ,etc..)
Answer: B
Step-by-step explanation:
Plz help with all 3 questions i will give Brainliest
Answer:
Step-by-step explanation:
8) entire cost of meal = m
m = 14.68 + 14.68
= 29.36
Solution $29.36
9) Let Elijah's height = h
h + 6 = 48
h = 48 - 6
Solution 42 inches
10) x - 15 = 20
x = 20 + 15
Solution 35 ounces
five litres of paint costs R575 .Work out the cost of fifteen litres of paint
Answer:
first of all learn how to spell liters
1725
Step-by-step explanation:
15 liters of pain will cost Rs.225
What is multiplication?Multiplication is a process of adding a number repetitively. Mathematically, we can write -
m = a x b
Given is that the 5 liters of paint costs Rs. 75.
5 liters of paint costs Rs. 75.
1 liter of paint will cost Rs. (75/5)
15 liters of pain will cost Rs. (75/5 x 15) = 75 x 3 = Rs. 225
Therefore, 15 liters of pain will cost Rs.225
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Abby got a summer job. The table shows how much money she will earn based on the number of hours she works.
Hours Worked 20 30 40 50
Dollars Earned 150 225 300 375
Based on the table, how much money will she earn if she works 65 hours?
O A $450.00
B. $475.50
C. $487.50
D. $525.00
Answer:
C
Step-by-step explanation:
She earns $487.50
375+75+37.5=487.5
Answer: c
Step-by-step explanation
First find the unit rate
$150 divided by 20 = $7.50
So she's earning $7.50 an hour
$7.50 times 65 hours = $487.50
So the correct answer is C
HELP PLEASE!! I WILL GIVE BRAINLIEST
Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record the
height, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t. (make an equation to illustrate the relationship between the height of the tree
and the number of years since it was planted. How tall will the tree be in 8 years?)
melitón se comió 3 rebanadas de una pizza pequeña de seis rebanadas Cómo se representa una fracción
[tex] \frac{3}{6} [/tex]
Explicación:El numerador es lo que melitón se comió...
Y el denominador son las porciones (rebanadas) en que esta dividida la pizza.