Answer:
side: 17 inchesaltitude: 6 inchesStep-by-step explanation:
The formula for the area of a triangle gives a relationship between area, height, and base length. The problem statement gives the area, and it gives another relation between height and base length. Using these two relations, you can solve for the dimensions of the triangle.
__
setupThe side to which the altitude is measured is called the "base" in the area formula. The altitude is called the "height." The relation between them given by the area formula is ...
A = 1/2bh
51 = 1/2bh . . . . . . using the given value for area
The other relation given by the problem statement is that the base is 1 less than 3 times the height:
b = 3h -1 . . . . . . . base is 1 less than 3 times altitude
__
solutionUsing this second equation to substitute for 'b' in the first equation, we have ...
51 = 1/2(3h -1)h
102 = 3h² -h . . . . multiply by 2, eliminate parentheses
3h² -h -102 = 0 . . . . . put in standard form
3h² -18h +17h -102 = 0 . . . . . prepare to factor
3h(h -6) +17(h -6) = 0 . . . . . factor pairs of terms
(3h +17)(h -6) = 0 . . . . . . . . finish factoring
Solutions are the values of h that make these factors zero:
3h +17 = 0 ⇒ h = -17/3
h -6 = 0 ⇒ h = 6
We know that dimensions in a geometry problem must be positive, so the solution here is h = 6. Then b = 3h -1 = 3(6) -1 = 17. The dimensions are all in inches.
The length of the side is 17 inches; the altitude to that side is 6 inches.
Soccer is played on a rectangular field that is usually 120 yards long and 75 yards wide. Find the perimeter and the area of the soccer field. Perimeter: .yds. Area: yds\large ^2
Answer:
Perimeter: 120*2 + 75*2 = 240 + 150 = 390 yards
Area: 120*75 = 9000 [tex]yards^{2}[/tex]
What is the probability of landing on an odd number and then landing on a number greater than 7?
Answer:
72%
Step-by-step explanation:
If a marble is randomly chosen from a bag thay contains exactly 8 red marbles, 6 blue marbles, and 6 white marbles, what is the probability that the marble will not be white?
Answer: 7/10
Step-by-step explanation:
The probability of an event can be calculated as:
[tex]P(E)=\frac{n(F)}{n(T)}[/tex]
Where n(F) is favorable outcomes and n(T) is total possible outcomes.
The total number of marbles can be obtained as,
8 + 6 + 6 = 20
The probability of marble being white can be calculated as,
[tex]P(W)=\underline{\frac{6}{20}}[/tex]
Now, the probability of the marble not being white can be evaluated as,
[tex]\begin{aligned}P^{\prime}(W) &=1-\frac{6}{20} \\&=\frac{20-6}{20} \\&=\frac{14}{20} \\&=\frac{7}{10}\end{aligned}[/tex]
Therefore, the probability of the marble not being white is 7/10
one day a store sells 14 pairs of jeans . The 14 jeans represents 20% of total number of items sold that day. How many items did the store sell in one day
Answer:
items sold in 1 day = 140
Step-by-step explanation:
14 pairs of jeans = 28 jeans total
the 14 "pair of jeans" repesents 20% of the total = x
28 = 20x/100
2800/20 = x
x = 140
Ezekiel manages a clothing store. In May, sales were $129,800. In June, sales were $131,975. What was the rate of change?
The rate of change of the sles of the clothing store that Ezekiel manages from May to June is $2,175
What is the rate of change?
Subtraction is the mathematical operation that involves determining the difference between two or more numbers.
Rate of change = sales in June - sales in May
$131,975 - $129,800 = $2,175
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Rewrite as a single logarithm: 3 log b x+4 log b y
Answer:
log_b x^3y^4
Step-by-step explanation:
see image
23) A movie theatre has 900 seats of which 15% are in the balcony. How many seats are NOT in the balcony?
A.
765
B.
90
C.
785
D.
875
Answer:
A.765 seats are not in the balcony
Step-by-step explanation:
if 15% are in the balcony then 85% are not in the balcony so..
900 * 0.85 = 765
Answer:
765
Step-by-step explanation:
900*.15=135
900-135 = 765
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answer:
77 cm²
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
where b is the base length, and h is the altitude perpendicular to the base.
__
Here, you are shown b=22 cm and h=7 cm. The area is ...
A = 1/2(22 cm)(7 cm) = 77 cm²
will pay the first one that answers this question
Answer:
a. I
b. II
c. IV
3) Solve the equation for x.
10(4x + 4) = 400
A) 2
B) 4
C) 9
D) 18
Answer:
C) 9
Step-by-step explanation:
10(4x + 4) = 400
40x + 40 = 400
40x = 360
x = 9
Answer:
First factor out the expression
(10•4x)+(10•4)=400
40x+40=400
Then solve
40x+40=400
-40 = -40
40x=360
------ ------
40 40
x=9
C) 9
☆anvipatel77☆
•Expert•
Brainly Community Contributor
what is the product of mixed number 2 x 2 7/8?
Answer:
[tex]5\frac{3}{4}[/tex]
----------------------------------------------------------------------------------------------------------
Since we have to convert mixed numbers to fractions, [tex]2\frac{7}{8}[/tex] becomes [tex]\frac{23}{8}[/tex]
And for whole number, add a 1 as the denominator.
[tex]\frac{2}{1}[/tex]
Now, the equation becomes...
[tex]\frac{2~*~23}{1~*~8}[/tex]
[tex]2 * 23 = 46[/tex]
[tex]1 * 8 = 8[/tex]
Convert these two numbers to a fraction.
[tex]46~and~8~-- > ~\frac{46}{8}[/tex]
Simplify 46 over 8 and make it a mixed number.
[tex]\frac{46}{8} -- > 5\frac{3}{4}[/tex]
why is the denominator 4? we had to simplify 8 using its GCF along with 46
the GCF is 2, so simplify using 2. to simplify, divide the number by its GCF.
[tex]\frac{46}{2} = 23\\\\\frac{8}{2} = 4[/tex]
now you have [tex]\frac{23}{4}[/tex]
and that, in mixed number, translates to [tex]5\frac{3}{4}[/tex]
________________________________________________________
Questions?Ask in comments.
50PTS Consider this equation .sin(0) = 4 If is an angle in quadrant II, what is the value of ? A. B. C. D.
Answer:
A.
[tex] - \frac{ \sqrt{377} }{29} [/tex]
Susan made $550 baby sitting during the summer. She made $256 helping her grandmother working on the farm She spent $175 on a new dress. Which number sentence could be used to find how much money Susan had left?
1. $550 - $256 + $75
2. $550 - $256 - $75
3. $550 + $256 + $75
4. $550 + $256 + $75
Help me with this math problem please
Answer:
First Option (-4,-3)
Step-by-step explanation:
x+2y=-10
-y=3x+15
-4+2(-3)=-10
-10=-10
-3=3(-4)+15
-3=-3
. If you have a cube measuring 1 unit on
each side, how many of those cubes
would fit into a space 5 units by 5 units
by 5 units?
Answer:
cubes = (5)(5)(5)
number of cubes =125
to fit
PLS HELP ME I NEED AN A I GIVE 50 POINTS
Answer:
The one on the left shows a proportional relationship between x and y.
Step-by-step explanation:
equation your going to use = y ÷ x or y/x (both mean divide)
2÷4 = 0.5
5÷10 = 0.5
6÷12= 0.5
All have the same answers so that makes it a proportional relationship.
In the figure below, AD and EC intersect at point G, mAGB = 35°, and mAGE = 69°
What is mBGC?
A.
111°
B.
145°
C.
76°
D.
104°
Answer:
The correct answer is C.76.
Hope this helps you!!
Please Mark me Brainleast Czn!!!!!!!!
A standard number cube is tossed. Find P( greater than 3 or odd).
Answer:
Step-by-step explanation:
P= probablity
P (>3 or odd)
assuming this std. number cube is 1 to 6, then,
greater than 3 is 50%
so we've accounted for 1, 3, 4, 5, 6 on the dice what's left 2 :D
so P( >3 or odd) = 5/6 or 83.3333333333333%
Answergrater than 3
Step-by-step explanation:
What number to be added to each of the number 6,16,36 and 76 to be in proportion?
Answer:
[tex] \pink{ \pmb{SOLUTION:-}}[/tex]
Here,
Let x must be added.[tex]\displaystyle{ \frac{6 + x}{16 + x} = \frac{36 + x}{76 + x} }[/tex]
[tex](6 + x)(76 + x) = (36 + x)(16 + x)[/tex]
[tex]456 + 6x + 76x + {x}^{2} = 576 + 36x + 16x + {x}^{2} [/tex]
[tex]82x + 456 = 576 + 52x[/tex]
[tex]82x - 52x = 576 - 456[/tex]
[tex]30x = 120[/tex]
[tex]\displaystyle{x = \frac{120}{30} }[/tex]
[tex]{ \rightarrow{ \pmb{x = 4}}}[/tex]
An architect drew the blueprint for a new office building. He used a scale in which 1 inch represents 7.5 feet. The floor of an office in the building will have actual dimensions of 14 feet by 24 feet. What will the dimensions on the blueprint be?
A.
105 inches by 180 inches
B.
21.5 inches by 31.5 inches
C.
6.5 inches by 16.5 inches
D.
1.87 inches by 3.2 inches
Since we know the scale factor of 1 inch represents 7.5 feet, we can plug in the dimensions for the scale on which the architect drew.
For 14 feet, we can multiply 14 by 1 inch/7.5 feet to get a product of 1.87 inches. Then, we can do the exact same thing with the other width of the floor, which is 24. 24 × 1/7.5 = 3.2
The final dimensions of the blueprint will be D, 1.87 inches by 3.2 inches.
A tissue box shaped like a cube, has a volume of about 90 cubic inches. What is the approximate length of one side of the tissue box?
The approximate length of one side of the tissue box which has a volume of about 90 cubic inches is 4.5 inches.
What is of volume of cube?Volume of cube is the amount of quantity, which is obtained by it in the 3 dimensional space.
The volume of the cube can be given as,
[tex]V=a^3[/tex]
Here, (a) is the side of the cube.
A tissue box, shaped like a cube, has a volume of about 90 cubic inches. Put the value of volume in above formula,
[tex]90=a^3\\a^3=90\\a=\sqrt[3]{90}\\a=4.48\\a\approx 4.5\rm\; in[/tex]
Thus, the approximate length of one side of the tissue box which has a volume of about 90 cubic inches is 4.5 inches.
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A person has a bag containing quarters and dimes. There are a total of 61 coins in the bag, and the total value of the coins is $10.45.
Answer:
Q+D = 65, multiply both sides by 2525Q + 25D = 162525Q + 10D = 950 subtract to get 15D = 675 D = 675/15 = 135/3 = 45 dimes Q = 65-45 = 20 quarters25(20) + 10(45) = 500+450 = 950
Every time Liliana bakes a batch of brownies, she uses 3/4 cup of chocolate. If she has 128 cup(s) of chocolate remaining, how many batches of brownies can Liliana make
Answer:
2
Step-by-step explanation:
12/8 is equal to 6/4.
6 divided by 3 is 2.
Sophia invest money in an account paying simple interest. She invest 100$ and no money is added or removed from the investment. After one year, she has 108. What is the simple percent interest per year ?
Answer:
8%
Step-by-step explanation:
She earned 8 dollars on a 100 dollar investment
8/100 = 8%
The answer is 8%
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Principal as $100 and return as $108 and t=1
Thus 8=100×1×r /100
r=8%
Hence, The rate of interest is 8%
Learn more about simple interest here:
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In the equation 4x4=16, 4 is a:
Answer:
4 is a factor
Step-by-step explanation:
thats what a number being multiplied is called
Efficiently solve
A. 30x70+37x70
B. 335x11-135x11
C. 223x87-123x87
D. 3.2x120+16.8x120
E. 555x0.08-545x0.08
F. 3.45x17-1.45x17
G. 0.7x0.7x85
Thanks so Much if you Help me!
Answer:
Step-by-step explanation:
A. 2100+2590= 4,690
B. 3685-1485=2,200
C. 19,401-10,701= 8,700
D. 384+2,016=2,400
E. 44.4-43.6=0.8
F. 58.65-24.65=34
G. 41.65
Line /has a what slope.
1.negative
2.0
3.positive
4.undefined
help me please i need help please
Answer:
Step-by-step explanation:
your dad said he will help you
a
It takes 15 minutes to drain a pool containing
45 gallons of water. If a similar pool takes 35
minutes to drain at the same rate, how many
gallons of water are in the similar pool?
Answer:
there is 92.25
Step-by-step explanation:
15x2=30
then you have to find out 5% out of 45 because you need to get 35 not 30.
rewrite each equation in exponential form. log 100=2
Answer:
10x^{2} = 100Step-by-step explanation:
Use the definition of a logarithm, logb(x)=y ⟹ by=x, to convert from the logarithmic form to the exponential form.
Hopefully this helps you
- Matthew